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Title 40 CFR Part 191Subparts B and CCompliance RecertificationApplicationfor theWaste Isolation Pilot Plant
Appendix PA-2009Performance Assessment
United States Department of EnergyWaste Isolation Pilot Plant
Carlsbad Field OfficeCarlsbad, New Mexico
DOCPROPERTY PageMark \* MERGEFORMAT DOCPROPERTY PageMark \* MERGEFORMAT DOCPROPERTY PageMark \* MERGEFORMAT DOCPROPERTY PageMark \* MERGEFORMAT DOCPROPERTY PageMark \* MERGEFORMAT DOCPROPERTY PageMark \* MERGEFORMAT DOCPROPERTY PageMark \* MERGEFORMAT Appendix PA-2009Performance Assessment
DOCPROPERTY PageMark \* MERGEFORMAT DOCPROPERTY PageMark \* MERGEFORMAT DOCPROPERTY PageMark \* MERGEFORMAT DOCPROPERTY PageMark \* MERGEFORMAT DOCPROPERTY PageMark \* MERGEFORMAT DOCPROPERTY PageMark \* MERGEFORMAT DOCPROPERTY PageMark \* MERGEFORMAT Table of Contents
TOC \o "3-3" \z \t "Heading 1,1,Heading 2,2" PA-1.0 Introduction PA- PAGEREF _Toc215821217 \h 1
PA-2.0 Overview and Conceptual Structure of the PA PA- PAGEREF _Toc215821218 \h 4
PA-2.1 Overview of Performance Assessment PA- PAGEREF _Toc215821219 \h 4
PA-2.1.1 Changes in the CRA-2009 PA PA- PAGEREF _Toc215821220 \h 5
PA-2.1.2 Conceptual Basis for PA PA- PAGEREF _Toc215821221 \h 6
PA-2.1.3 Undisturbed Repository Performance PA- PAGEREF _Toc215821222 \h 7
PA-2.1.4 Disturbed Repository Performance PA- PAGEREF _Toc215821223 \h 9
PA-2.1.5 Compliance Demonstration Method PA- PAGEREF _Toc215821224 \h 15
PA-2.1.6 Results of the PA PA- PAGEREF _Toc215821225 \h 16
PA-2.2 Conceptual Structure of the PA PA- PAGEREF _Toc215821226 \h 17
PA-2.2.1 Regulatory Requirements PA- PAGEREF _Toc215821227 \h 18
PA-2.2.2 Probabilistic Characterization of Different Futures PA- PAGEREF _Toc215821228 \h 20
PA-2.2.3 Estimation of Releases PA- PAGEREF _Toc215821229 \h 21
PA-2.2.4 Probabilistic Characterization of Parameter Uncertainty PA- PAGEREF _Toc215821230 \h 24
PA-2.3 PA Methodology PA- PAGEREF _Toc215821231 \h 27
PA-2.3.1 Identification and Screening of FEPs PA- PAGEREF _Toc215821232 \h 27
PA-2.3.2 Scenario Development and Selection PA- PAGEREF _Toc215821233 \h 28
PA-2.3.3 Calculation of Scenario Consequences PA- PAGEREF _Toc215821234 \h 37
PA-3.0 Probabilistic Characterization of Futures PA- PAGEREF _Toc215821235 \h 39
PA-3.1 Probability Space PA- PAGEREF _Toc215821236 \h 40
PA-3.2 AICs and PICs PA- PAGEREF _Toc215821237 \h 40
PA-3.3 Drilling Intrusion PA- PAGEREF _Toc215821238 \h 40
PA-3.4 Penetration of Excavated/Nonexcavated Area PA- PAGEREF _Toc215821239 \h 41
PA-3.5 Drilling Location PA- PAGEREF _Toc215821240 \h 42
PA-3.6 Penetration of Pressurized Brine PA- PAGEREF _Toc215821241 \h 42
PA-3.7 Plugging Pattern PA- PAGEREF _Toc215821242 \h 43
PA-3.8 Activity Level PA- PAGEREF _Toc215821243 \h 43
PA-3.9 Mining Time PA- PAGEREF _Toc215821244 \h 44
PA-3.10 Scenarios and Scenario Probabilities PA- PAGEREF _Toc215821245 \h 45
PA-3.11 CCDF Construction PA- PAGEREF _Toc215821246 \h 47
PA-4.0 Estimation of Releases PA- PAGEREF _Toc215821247 \h 47
PA-4.1 Results for Specific Futures PA- PAGEREF _Toc215821248 \h 47
PA-4.2 Two-Phase Flow: BRAGFLO PA- PAGEREF _Toc215821249 \h 49
PA-4.2.1 Mathematical Description PA- PAGEREF _Toc215821250 \h 49
PA-4.2.2 Initial Conditions PA- PAGEREF _Toc215821251 \h 64
PA-4.2.3 Creep Closure of Repository PA- PAGEREF _Toc215821252 \h 66
PA-4.2.4 Fracturing of MBs and DRZ PA- PAGEREF _Toc215821253 \h 67
PA-4.2.5 Gas Generation PA- PAGEREF _Toc215821254 \h 68
PA-4.2.6 Capillary Action in the Waste PA- PAGEREF _Toc215821255 \h 75
PA-4.2.7 Shaft Treatment PA- PAGEREF _Toc215821256 \h 76
PA-4.2.8 Option D Panel Closures PA- PAGEREF _Toc215821257 \h 77
PA-4.2.9 Borehole Model PA- PAGEREF _Toc215821258 \h 80
DOCPROPERTY PageMark \* MERGEFORMAT DOCPROPERTY PageMark \* MERGEFORMAT DOCPROPERTY PageMark \* MERGEFORMAT DOCPROPERTY PageMark \* MERGEFORMAT DOCPROPERTY PageMark \* MERGEFORMAT DOCPROPERTY PageMark \* MERGEFORMAT DOCPROPERTY PageMark \* MERGEFORMAT PA-4.2.10 Castile Brine Reservoir PA- PAGEREF _Toc215821259 \h 80
PA-4.2.11 Numerical Solution PA- PAGEREF _Toc215821260 \h 82
PA-4.2.12 Gas and Brine Flow across Specified Boundaries PA- PAGEREF _Toc215821261 \h 85
PA-4.2.13 Additional Information PA- PAGEREF _Toc215821262 \h 85
PA-4.3 Radionuclide Transport in the Salado: NUTS PA- PAGEREF _Toc215821263 \h 85
PA-4.3.1 Mathematical Description PA- PAGEREF _Toc215821264 \h 87
PA-4.3.2 Calculation of Maximum Concentration ST(Br, Ox, El) PA- PAGEREF _Toc215821265 \h 90
PA-4.3.3 Radionuclides Transported PA- PAGEREF _Toc215821266 \h 92
PA-4.3.4 NUTS Tracer Calculations PA- PAGEREF _Toc215821267 \h 95
PA-4.3.5 NUTS Transport Calculations PA- PAGEREF _Toc215821268 \h 96
PA-4.3.6 Numerical Solution PA- PAGEREF _Toc215821269 \h 96
PA-4.3.7 Additional Information PA- PAGEREF _Toc215821270 \h 99
PA-4.4 Radionuclide Transport in the Salado: PANEL PA- PAGEREF _Toc215821271 \h 100
PA-4.4.1 Mathematical Description PA- PAGEREF _Toc215821272 \h 100
PA-4.4.2 Numerical Solution PA- PAGEREF _Toc215821273 \h 101
PA-4.4.3 Implementation in PA PA- PAGEREF _Toc215821274 \h 102
PA-4.4.4 Additional Information PA- PAGEREF _Toc215821275 \h 102
PA-4.5 Cuttings and Cavings to Surface: CUTTINGS_S PA- PAGEREF _Toc215821276 \h 102
PA-4.5.1 Cuttings PA- PAGEREF _Toc215821277 \h 103
PA-4.5.2 Cavings PA- PAGEREF _Toc215821278 \h 103
PA-4.5.3 Additional Information PA- PAGEREF _Toc215821279 \h 110
PA-4.6 Spallings to Surface: DRSPALL and CUTTINGS_S PA- PAGEREF _Toc215821280 \h 110
PA-4.6.1 Summary of Assumptions PA- PAGEREF _Toc215821281 \h 110
PA-4.6.2 Conceptual Model PA- PAGEREF _Toc215821282 \h 111
PA-4.6.3 Numerical Model PA- PAGEREF _Toc215821283 \h 123
PA-4.6.4 Implementation PA- PAGEREF _Toc215821284 \h 128
PA-4.6.5 Additional Information PA- PAGEREF _Toc215821285 \h 129
PA-4.7 DBR to Surface: BRAGFLO PA- PAGEREF _Toc215821286 \h 129
PA-4.7.1 Overview of Conceptual Model PA- PAGEREF _Toc215821287 \h 129
PA-4.7.2 Linkage to Two-Phase Flow Calculation PA- PAGEREF _Toc215821288 \h 131
PA-4.7.3 Conceptual Representation for Flow Rate rDBR(t) PA- PAGEREF _Toc215821289 \h 134
PA-4.7.4 Determination of Productivity Index Jp PA- PAGEREF _Toc215821290 \h 134
PA-4.7.5 Determination of Waste Panel Pressure pw(t) and DBR PA- PAGEREF _Toc215821291 \h 136
PA-4.7.6 Boundary Value Pressure pwf PA- PAGEREF _Toc215821292 \h 137
PA-4.7.7 Boundary Value Pressure pwE1 PA- PAGEREF _Toc215821293 \h 144
PA-4.7.8 End of DBR PA- PAGEREF _Toc215821294 \h 149
PA-4.7.9 Numerical Solution PA- PAGEREF _Toc215821295 \h 150
PA-4.7.10 Additional Information PA- PAGEREF _Toc215821296 \h 152
PA-4.8 Groundwater Flow in the Culebra Dolomite PA- PAGEREF _Toc215821297 \h 152
PA-4.8.1 Mathematical Description PA- PAGEREF _Toc215821298 \h 153
PA-4.8.2 Implementation PA- PAGEREF _Toc215821299 \h 154
PA-4.8.3 Computational Grids and Boundary Value Conditions PA- PAGEREF _Toc215821300 \h 157
PA-4.8.4 Numerical Solution PA- PAGEREF _Toc215821301 \h 159
PA-4.8.5 Additional Information PA- PAGEREF _Toc215821302 \h 161
PA-4.9 Radionuclide Transport in the Culebra Dolomite PA- PAGEREF _Toc215821303 \h 161
PA-4.9.1 Mathematical Description PA- PAGEREF _Toc215821304 \h 162
DOCPROPERTY PageMark \* MERGEFORMAT DOCPROPERTY PageMark \* MERGEFORMAT DOCPROPERTY PageMark \* MERGEFORMAT DOCPROPERTY PageMark \* MERGEFORMAT DOCPROPERTY PageMark \* MERGEFORMAT DOCPROPERTY PageMark \* MERGEFORMAT DOCPROPERTY PageMark \* MERGEFORMAT PA-4.9.2 Numerical Solution PA- PAGEREF _Toc215821305 \h 170
PA-4.9.3 Additional Information PA- PAGEREF _Toc215821306 \h 174
PA-5.0 Probabilistic Characterization of Subjective Uncertainty PA- PAGEREF _Toc215821307 \h 175
PA-5.1 Probability Space PA- PAGEREF _Toc215821308 \h 175
PA-5.2 Variables Included for Subjective Uncertainty PA- PAGEREF _Toc215821309 \h 175
PA-5.3 Variable Distributions PA- PAGEREF _Toc215821310 \h 176
PA-5.4 Correlations and Dependencies PA- PAGEREF _Toc215821311 \h 176
PA-5.5 Separation of Aleatory and Epistemic Uncertainty PA- PAGEREF _Toc215821312 \h 179
PA-6.0 Computational Procedures PA- PAGEREF _Toc215821313 \h 180
PA-6.1 Sampling Procedures PA- PAGEREF _Toc215821314 \h 180
PA-6.2 Sample Size for Incorporation of Subjective Uncertainty PA- PAGEREF _Toc215821315 \h 181
PA-6.3 Statistical Confidence on Mean CCDF PA- PAGEREF _Toc215821316 \h 181
PA-6.4 Generation of Latin Hypercube Samples PA- PAGEREF _Toc215821317 \h 182
PA-6.5 Generation of Individual Futures PA- PAGEREF _Toc215821318 \h 184
PA-6.6 Construction of CCDFs PA- PAGEREF _Toc215821319 \h 185
PA-6.7 Mechanistic Calculations PA- PAGEREF _Toc215821320 \h 187
PA-6.7.1 BRAGFLO Calculations PA- PAGEREF _Toc215821321 \h 187
PA-6.7.2 NUTS Calculations PA- PAGEREF _Toc215821322 \h 188
PA-6.7.3 PANEL Calculations PA- PAGEREF _Toc215821323 \h 189
PA-6.7.4 DRSPALL Calculations PA- PAGEREF _Toc215821324 \h 189
PA-6.7.5 CUTTINGS_S Calculations PA- PAGEREF _Toc215821325 \h 190
PA-6.7.6 BRAGFLO Calculations for DBR Volumes PA- PAGEREF _Toc215821326 \h 191
PA-6.7.7 MODFLOW Calculations PA- PAGEREF _Toc215821327 \h 191
PA-6.7.8 SECOTP2D Calculations PA- PAGEREF _Toc215821328 \h 191
PA-6.8 Computation of Releases PA- PAGEREF _Toc215821329 \h 192
PA-6.8.1 Undisturbed Releases PA- PAGEREF _Toc215821330 \h 192
PA-6.8.2 Direct Releases PA- PAGEREF _Toc215821331 \h 193
PA-6.8.3 Radionuclide Transport Through the Culebra PA- PAGEREF _Toc215821332 \h 195
PA-6.8.4 Determining Initial Conditions for Direct and Transport Releases PA- PAGEREF _Toc215821333 \h 196
PA-6.8.5 CCDF Construction PA- PAGEREF _Toc215821334 \h 198
PA-6.9 Sensitivity Analysis PA- PAGEREF _Toc215821335 \h 200
PA-6.9.1 Scatterplots PA- PAGEREF _Toc215821336 \h 200
PA-6.9.2 Regression Analysis PA- PAGEREF _Toc215821337 \h 200
PA-6.9.3 Stepwise Regression Analysis PA- PAGEREF _Toc215821338 \h 202
PA-7.0 Results for the Undisturbed Repository PA- PAGEREF _Toc215821339 \h 203
PA-7.1 Salado Flow PA- PAGEREF _Toc215821340 \h 203
PA-7.1.1 Pressure in the Repository PA- PAGEREF _Toc215821341 \h 203
PA-7.1.2 Brine Saturation in the Waste PA- PAGEREF _Toc215821342 \h 204
PA-7.1.3 Brine Flow Out of the Repository PA- PAGEREF _Toc215821343 \h 207
PA-7.2 Radionuclide Transport PA- PAGEREF _Toc215821344 \h 207
PA-7.2.1 Radionuclide Transport to the Culebra PA- PAGEREF _Toc215821345 \h 209
PA-7.2.2 Radionuclide Transport to the Land Withdrawal Boundary PA- PAGEREF _Toc215821346 \h 209
DOCPROPERTY PageMark \* MERGEFORMAT DOCPROPERTY PageMark \* MERGEFORMAT DOCPROPERTY PageMark \* MERGEFORMAT DOCPROPERTY PageMark \* MERGEFORMAT DOCPROPERTY PageMark \* MERGEFORMAT DOCPROPERTY PageMark \* MERGEFORMAT DOCPROPERTY PageMark \* MERGEFORMAT PA-8.0 Results for a Disturbed Repository PA- PAGEREF _Toc215821347 \h 211
PA-8.1 Drilling Scenarios PA- PAGEREF _Toc215821348 \h 211
PA-8.2 Mining Scenarios PA- PAGEREF _Toc215821349 \h 211
PA-8.3 Salado Flow PA- PAGEREF _Toc215821350 \h 212
PA-8.3.1 Pressure in the Repository PA- PAGEREF _Toc215821351 \h 212
PA-8.3.2 Brine Saturation PA- PAGEREF _Toc215821352 \h 215
PA-8.3.3 Brine Flow out of the Repository PA- PAGEREF _Toc215821353 \h 217
PA-8.4 Radionuclide Transport PA- PAGEREF _Toc215821354 \h 223
PA-8.4.1 Radionuclide Source Term PA- PAGEREF _Toc215821355 \h 223
PA-8.4.2 Transport through MBs and Shaft PA- PAGEREF _Toc215821356 \h 225
PA-8.4.3 Transport to the Culebra PA- PAGEREF _Toc215821357 \h 225
PA-8.4.4 Transport Through the Culebra PA- PAGEREF _Toc215821358 \h 228
PA-8.5 Direct Releases PA- PAGEREF _Toc215821359 \h 230
PA-8.5.1 Cuttings and Cavings PA- PAGEREF _Toc215821360 \h 230
PA-8.5.2 Spallings PA- PAGEREF _Toc215821361 \h 231
PA-8.5.3 DBRs PA- PAGEREF _Toc215821362 \h 234
PA-9.0 Normalized Releases PA- PAGEREF _Toc215821363 \h 236
PA-9.1 Cuttings and Cavings PA- PAGEREF _Toc215821364 \h 236
PA-9.2 Spallings PA- PAGEREF _Toc215821365 \h 236
PA-9.3 Direct Brine PA- PAGEREF _Toc215821366 \h 238
PA-9.4 Groundwater Transport PA- PAGEREF _Toc215821367 \h 239
PA-9.5 Total Normalized Releases PA- PAGEREF _Toc215821368 \h 241
PA-10.0 References PA- PAGEREF _Toc215821369 \h 246
List of Figures
TOC \z \c "Figure PA-" Figure PA-1. Overall Mean CCDFs for Total Normalized Releases: CRA-2009 PA and CRA-2004 PABC PA- PAGEREF _Toc224037330 \h 16
Figure PA-2. Computational Models Used in PA PA- PAGEREF _Toc224037331 \h 23
Figure PA-3. Construction of the CCDF Specified in 40 CFR Part 191 Subpart B PA- PAGEREF _Toc224037332 \h 23
Figure PA-4. Distribution of CCDFs Resulting from Possible Values for the Sampled Parameters PA- PAGEREF _Toc224037333 \h 25
Figure PA-5. Example Mean Probability of Release and the Confidence Limits on the Mean from CRA-2009 PA PA- PAGEREF _Toc224037334 \h 26
Figure PA-6. Example CCDF Distribution From CRA-2009 PA (Replicate 1) PA- PAGEREF _Toc224037335 \h 26
Figure PA-7. Logic Diagram for Scenario Analysis PA- PAGEREF _Toc224037336 \h 29
Figure PA-8. Conceptual Release Pathways for the UP Scenario PA- PAGEREF _Toc224037337 \h 30
Figure PA-9. Conceptual Release Pathways for the Disturbed Repository M Scenario PA- PAGEREF _Toc224037338 \h 32
Figure PA-10. Conceptual Release Pathways for the Disturbed Repository Deep Drilling E2 Scenario PA- PAGEREF _Toc224037339 \h 34
Figure PA-11. Conceptual Release Pathways for the Disturbed Repository Deep Drilling E1 Scenario PA- PAGEREF _Toc224037340 \h 35
Figure PA-12. Conceptual Release Pathways for the Disturbed Repository Deep Drilling E1E2 Scenario PA- PAGEREF _Toc224037341 \h 36
Figure PA-13. CDF for Time Between Drilling Intrusions PA- PAGEREF _Toc224037342 \h 41
Figure PA-14. Discretized Locations for Drilling Intrusions PA- PAGEREF _Toc224037343 \h 42
Figure PA-15. Computational Grid Used in BRAGFLO for PA PA- PAGEREF _Toc224037344 \h 53
Figure PA-16. Definition of Element Depth in BRAGFLO Grid PA- PAGEREF _Toc224037345 \h 54
Figure PA-17. Identification of Individual Cells in BRAGFLO Grid PA- PAGEREF _Toc224037346 \h 55
Figure PA-18. Schematic View of the Simplified Shaft Model (numbers on right indicate dimensions in meters) PA- PAGEREF _Toc224037347 \h 77
Figure PA-19. Schematic Side View of Option D Panel Closure PA- PAGEREF _Toc224037348 \h 78
Figure PA-20. Representation of Option D Panel Closures in the BRAGFLO Grid PA- PAGEREF _Toc224037349 \h 78
Figure PA-21. Selecting Radionuclides for the Release Pathways Conceptualized by PA PA- PAGEREF _Toc224037350 \h 93
Figure PA-22. Detail of Rotary Drill String Adjacent to Drill Bit PA- PAGEREF _Toc224037351 \h 105
Figure PA-23. Schematic Diagram of the Flow Geometry Prior to Repository Penetration PA- PAGEREF _Toc224037352 \h 111
Figure PA-24. Schematic Diagram of the Flow Geometry After Repository Penetration PA- PAGEREF _Toc224037353 \h 112
Figure PA-25. Effective Wellbore Flow Geometry Before Bit Penetration PA- PAGEREF _Toc224037354 \h 112
Figure PA-26. Effective Wellbore Flow Geometry After Bit Penetration PA- PAGEREF _Toc224037355 \h 113
Figure PA-27. Finite-Difference Zoning for Wellbore PA- PAGEREF _Toc224037356 \h 124
Figure PA-28. DBR Grid Used in PA PA- PAGEREF _Toc224037357 \h 130
Figure PA-29. Assignment of Initial Conditions for DBR Calculation PA- PAGEREF _Toc224037358 \h 132
Figure PA-30. Borehole Representation Used for Poettmann-Carpenter Correlation PA- PAGEREF _Toc224037359 \h 139
Figure PA-31. Areas of Potash Mining in the McNutt Potash Zone PA- PAGEREF _Toc224037360 \h 156
Figure PA-32. Modeling Domain for Groundwater Flow (MODFLOW) and Radionuclide Transport (SECOTP2D) in the Culebra PA- PAGEREF _Toc224037361 \h 158
Figure PA-33. Boundary Conditions Used for Simulations of Brine Flow in the Culebra PA- PAGEREF _Toc224037362 \h 159
Figure PA-34. Finite-Difference Grid Showing Cell Index Numbering Convention Used by MODFLOW PA- PAGEREF _Toc224037363 \h 160
Figure PA-35. Parallel-Plate, Dual-Porosity Conceptualization PA- PAGEREF _Toc224037364 \h 162
Figure PA-36. Schematic of Finite-Volume Staggered Mesh Showing Internal and Ghost Cells PA- PAGEREF _Toc224037365 \h 171
Figure PA-37. Illustration of Stretched Grid Used for Matrix Domain Discretization PA- PAGEREF _Toc224037366 \h 173
Figure PA-38. Correlation Between S_HALITE:PRMX_LOG and S_HALITE:COMP_RCK PA- PAGEREF _Toc224037367 \h 178
Figure PA-39. Correlation between CASTILLER:PRMX_LOG and CASTILLER:COMP_RCK PA- PAGEREF _Toc224037368 \h 178
Figure PA-40. Dependency between WAS_AREA:GRATMICI and WAS_AREA:GRATMICH PA- PAGEREF _Toc224037369 \h 179
Figure PA-41. Logic Diagram for Determining the Intrusion Type PA- PAGEREF _Toc224037370 \h 197
Figure PA-42. Processing of Input Data to Produce CCDFs PA- PAGEREF _Toc224037371 \h 199
Figure PA-43. Pressure in the Waste Panel Region, Replicate R1, Scenario S1, CRA-2009 PA PA- PAGEREF _Toc224037372 \h 204
Figure PA-44. Primary Correlations of Pressure in the Waste Panel Region with Uncertain Parameters, Replicate R1, Scenario S1, CRA-2009 PA PA- PAGEREF _Toc224037373 \h 205
Figure PA-45. Brine Saturation in the Waste Panel Region, Replicate R1, Scenario S1, CRA-2009 PA PA- PAGEREF _Toc224037374 \h 206
Figure PA-46. Primary Correlations of Brine Saturation in the Waste Panel Region with Uncertain Parameters, Replicate R1, Scenario S1, CRA-2009 PA PA- PAGEREF _Toc224037375 \h 207
Figure PA-47. Brine Flow Away From the Repository, Replicate R1, Scenario S1, CRA2009 PA PA- PAGEREF _Toc224037376 \h 208
Figure PA-48. Brine Flow via All MBs Across the LWB, Replicate R1, Scenario S1, CRA2009 PA PA- PAGEREF _Toc224037377 \h 209
Figure PA-49. Primary Correlations of Total Cumulative Brine Flow Away from the Repository with Uncertain Parameters, Replicate R1, Scenario S1, CRA2009 PA PA- PAGEREF _Toc224037378 \h 209
Figure PA-50. Pressure in the Waste Panel Region for Replicate R1, Scenario S2, CRA2009 PA PA- PAGEREF _Toc224037379 \h 213
Figure PA-51. Pressure in the Waste Panel Region for Replicate R1, Scenario S4, CRA2009 PA PA- PAGEREF _Toc224037380 \h 213
Figure PA-52. Primary Correlations of Pressure in the Waste Panel Region with Uncertain Parameters, Replicate R1, Scenario S2, CRA-2009 PA PA- PAGEREF _Toc224037381 \h 214
Figure PA-53. Primary Correlations of Pressure in the Waste Panel Region with Uncertain Parameters, Replicate R1, Scenario S4, CRA-2009 PA PA- PAGEREF _Toc224037382 \h 214
Figure PA-54. Brine Saturation in the Waste Panel Region for Replicate R1, Scenario S2, CRA-2009 PA PA- PAGEREF _Toc224037383 \h 216
Figure PA-55. Brine Saturation in the Waste Panel Region for Replicate R1, Scenario S4, CRA-2009 PA PA- PAGEREF _Toc224037384 \h 216
Figure PA-56. Primary Correlations of Brine Saturation in the Waste Panel Region with Uncertain Parameters, Replicate R1, Scenario S2, CRA-2009 PA PA- PAGEREF _Toc224037385 \h 218
Figure PA-57. Primary Correlations of Brine Saturation in the Waste Panel Region with Uncertain Parameters, Replicate R1, Scenario S4, CRA-2009 PA PA- PAGEREF _Toc224037386 \h 218
Figure PA-58. Total Cumulative Brine Outflow in Replicate R1, Scenario S2, CRA-2009 PA PA- PAGEREF _Toc224037387 \h 219
Figure PA-59. Brine Flow via All MBs Across the LWB in Replicate R1, Scenario S2, CRA-2009 PA PA- PAGEREF _Toc224037388 \h 220
Figure PA-60. Total Cumulative Brine Outflow in Replicate R1, Scenario S4, CRA-2009 PA PA- PAGEREF _Toc224037389 \h 220
Figure PA-61. Brine Flow via All MBs Across the LWB in Replicate R1, Scenario S4, CRA-2009 PA PA- PAGEREF _Toc224037390 \h 221
Figure PA-62. Primary Correlations of Cumulative Brine Flow Away from the Repository with Uncertain Parameters, Replicate R1, Scenario S2, CRA-2009 PA PA- PAGEREF _Toc224037391 \h 222
Figure PA-63. Primary Correlations of Cumulative Brine Flow Away from the Repository with Uncertain Parameters, Replicate R1, Scenario S4, CRA-2009 PA PA- PAGEREF _Toc224037392 \h 223
Figure PA-64. Total Mobilized Concentrations in Salado Brine, Replicate R1, CRA2009PA PA- PAGEREF _Toc224037393 \h 224
Figure PA-65. Total Mobilized Concentrations in Castile Brine, Replicate R1, CRA-2009 PA PA- PAGEREF _Toc224037394 \h 225
Figure PA-66. Cumulative Normalized Release to the Culebra, Scenario S2, CRA-2009 PA PA- PAGEREF _Toc224037395 \h 226
Figure PA-67. Cumulative Normalized Release to the Culebra, Scenario S3, CRA-2009 PA PA- PAGEREF _Toc224037396 \h 227
Figure PA-68. Cumulative Normalized Release to the Culebra, Scenario S4, CRA-2009 PA PA- PAGEREF _Toc224037397 \h 227
Figure PA-69. Cumulative Normalized Release to the Culebra, Scenario S5, CRA-2009 PA PA- PAGEREF _Toc224037398 \h 228
Figure PA-70. Cumulative Normalized Release to the Culebra, Replicate R1, Scenario S6, CRA-2009 PA PA- PAGEREF _Toc224037399 \h 228
Figure PA-71. Scatterplot of Waste Particle Diameter Versus Spallings Volume, CRA2009 PA PA- PAGEREF _Toc224037400 \h 232
Figure PA-72. Scatterplot of Waste Permeability Versus Spallings Volume, CRA-2009 PA PA- PAGEREF _Toc224037401 \h 233
Figure PA-73. Sensitivity of DBR Volumes to Pressure and Mobile Brine Saturation, Replicate R1, Scenario S2, Lower Panel, CRA-2009 PA PA- PAGEREF _Toc224037402 \h 236
Figure PA-74. Overall Mean CCDFs for Cuttings and Cavings Releases: CRA-2009 PA and CRA-2004 PABC PA- PAGEREF _Toc224037403 \h 238
Figure PA-75. Overall Mean CCDFs for Spallings Releases: CRA-2009 PA and CRA2004 PABC PA- PAGEREF _Toc224037404 \h 238
Figure PA-76. Overall Mean CCDFs for DBRs: CRA-2009 PA and CRA-2004 PABC PA- PAGEREF _Toc224037405 \h 240
Figure PA-77. Mean CCDFs for Releases from the Culebra for Replicate R2: CRA-2009 PA and CRA-2004 PABC PA- PAGEREF _Toc224037406 \h 241
Figure PA-78. The Preponderance and Distribution of Zeros Can Control the Regression PA- PAGEREF _Toc224037407 \h 241
Figure PA-79. Total Normalized Releases, Replicates R1, R2, and R3, CRA-2009 PA PA- PAGEREF _Toc224037408 \h 243
Figure PA-80. Confidence Interval on Overall Mean CCDF for Total Normalized Releases, CRA-2009 PA PA- PAGEREF _Toc224037409 \h 243
Figure PA-81. Mean CCDFs for Components of Total Normalized Releases, Replicate R1, CRA-2009 PA PA- PAGEREF _Toc224037410 \h 244
Figure PA-82. Mean CCDFs for Components of Total Normalized Releases, Replicate R2, CRA-2009 PA PA- PAGEREF _Toc224037411 \h 244
Figure PA-83. Mean CCDFs for Components of Total Normalized Releases, Replicate R3, CRA-2009 PA PA- PAGEREF _Toc224037412 \h 245
Figure PA-84. Overall Mean CCDFs for Total Normalized Releases: CRA-2009 PA and CRA-2004 PABC PA- PAGEREF _Toc224037413 \h 245
List of Tables
TOC \z \c "Table PA-" Table PA-1. WIPP Project Changes and Cross References PA- PAGEREF _Toc224037187 \h 5
Table PA-2. Release Limits for the Containment Requirements (U.S. Environmental Protection Agency 1985, Appendix A, Table 1) PA- PAGEREF _Toc224037188 \h 19
Table PA3. Parameter Values Used in Representation of Two-Phase Flow PA- PAGEREF _Toc224037189 \h 56
Table PA-4. Models for Relative Permeability and Capillary Pressure in Two-Phase Flow PA- PAGEREF _Toc224037190 \h 62
Table PA-5. Initial Conditions in the Rustler PA- PAGEREF _Toc224037191 \h 65
Table PA-6. Probabilities for Biodegradation of Different Organic Materials (WAS_AREA:PROBDEG) in the CRA-2009 PA and the CRA-2004 PA PA- PAGEREF _Toc224037192 \h 71
Table PA-7. Permeabilities for Drilling Intrusions Through the Repository PA- PAGEREF _Toc224037193 \h 81
Table PA-8. Boundary Value Conditions for Pg and Pb PA- PAGEREF _Toc224037194 \h 83
Table PA-9. Auxiliary Dirichlet Conditions for Sg and Pb PA- PAGEREF _Toc224037195 \h 83
Table PA-10. Calculated Values for Dissolved Solubility (see Appendix SOTERM-2009, Table SOTERM-16) PA- PAGEREF _Toc224037196 \h 91
Table PA-11. Scale Factor SFHum(Br, Ox, El) Used in Definition of SHum(Br, Ox, El) (see Appendix SOTERM-2009, Table SOTERM-21) PA- PAGEREF _Toc224037197 \h 92
Table PA-12. Scale Factor SFMic(Ox, El) and Upper Bound UBMic(Ox, El) (mol/L) Used in Definition of SMic(Br, Ox, El) (see Appendix SOTERM-2009, Table SOTERM-21) PA- PAGEREF _Toc224037198 \h 92
Table PA-13. Combination of Radionuclides for Transport PA- PAGEREF _Toc224037199 \h 95
Table PA-14. Initial and Boundary Conditions for Cbl(x, y, t) and Csl(x, y, t) PA- PAGEREF _Toc224037200 \h 97
Table PA-15. Uncertain Parameters in the DRSPALL Calculations PA- PAGEREF _Toc224037201 \h 128
Table PA-16. Initial Porosity in the DBR Calculation PA- PAGEREF _Toc224037202 \h 133
Table PA-17. Boundary Conditions for pb and Sg in DBR Calculations PA- PAGEREF _Toc224037203 \h 138
Table PA-18. Radionuclide Culebra Transport Diffusion Coefficients PA- PAGEREF _Toc224037204 \h 163
Table PA-19. Variables Representing Epistemic Uncertainty in the CRA-2009 PA PA- PAGEREF _Toc224037205 \h 164
Table PA-20. Sampled Parameters Added Since the CRA-2004 PA PA- PAGEREF _Toc224037206 \h 176
Table PA-21. Sampled Parameters Removed Since the CRA-2004 PA PA- PAGEREF _Toc224037207 \h 176
Table PA-22. Correlation Observed Between Variables S_HALITE:PRMX_LOG and S_HALITE:COMP_RCK in Replicate 1 PA- PAGEREF _Toc224037208 \h 183
Table PA-23. Correlation Observed Between Variables CASTILER:PRMX_LOG and CASTILER:COMP_RCK in Replicate 1 PA- PAGEREF _Toc224037209 \h 183
Table PA-24. Algorithm to Generate a Single Future PA- PAGEREF _Toc224037210 \h 184
Table PA-25. BRAGFLO Scenarios in the CRA2009 PA PA- PAGEREF _Toc224037211 \h 187
Table PA-26. NUTS Release Calculations in the CRA-2009 PA PA- PAGEREF _Toc224037212 \h 188
Table PA-27. CUTTINGS_S Release Calculations in the CRA-2009 PA PA- PAGEREF _Toc224037213 \h 190
Table PA-28. MODFLOW Scenarios in the CRA-2009 PA PA- PAGEREF _Toc224037214 \h 192
Table PA-29. SECOTP2D Scenarios in the CRA-2004 PA PA- PAGEREF _Toc224037215 \h 192
Table PA-30. Number of Realizations with Radionuclide Transport to the LWB Under Partial-Mining Conditionsa,b PA- PAGEREF _Toc224037216 \h 230
Table PA-31. Number of Realizations with Radionuclide Transport to the LWB Under Full-Mining Conditionsa,b PA- PAGEREF _Toc224037217 \h 230
Table PA-32. CRA-2009 PA Cuttings and Cavings Area Statistics PA- PAGEREF _Toc224037218 \h 231
Table PA-33. CRA-2009 PA Spallings Volume Statistics PA- PAGEREF _Toc224037219 \h 233
Table PA-34. CRA-2009 PA DBR Volume Statistics PA- PAGEREF _Toc224037220 \h 235
Table PA-35. CRA-2009 PA and CRA-2004 PABCa Statistics on the Overall Mean for Total Normalized Releases in EPA Units at Probabilities of 0.1 and 0.001 PA- PAGEREF _Toc224037221 \h 246
DOCPROPERTY PageMark \* MERGEFORMAT DOCPROPERTY PageMark \* MERGEFORMAT DOCPROPERTY PageMark \* MERGEFORMAT DOCPROPERTY PageMark \* MERGEFORMAT DOCPROPERTY PageMark \* MERGEFORMAT DOCPROPERTY PageMark \* MERGEFORMAT DOCPROPERTY PageMark \* MERGEFORMAT Acronyms and Abbreviations
% percent
AIC active institutional control
An actinide
BRAGFLO BRine And Gas FLOw computer code
C Celsius
CCA Compliance Certification Application
CCDF complementary cumulative distribution function
CDF cumulative distribution function
CFR Code of Federal Regulations
CH-TRU contact-handled transuranic
Ci curies
CL Confidence Limit
CPR cellulosic, plastic, and rubber
CRA Compliance Recertification Application
DBR direct brine release
DDZ drilling damaged zone
DOE U.S. Department of Energy
DP disturbed repository performance
DRZ disturbed rock zone
E deep drilling scenario
EPA U.S. Environmental Protection Agency
ERDA U.S. Energy Research and Development Administration
FEP feature, event, and process
FMT Fracture-Matrix Transport
FVW fraction of excavated repository volume occupied by waste
gal gallon
GWB Generic Weep Brine
in inch
J Joule
K Kelvin
Kd distribution coefficient
DOCPROPERTY PageMark \* MERGEFORMAT DOCPROPERTY PageMark \* MERGEFORMAT DOCPROPERTY PageMark \* MERGEFORMAT DOCPROPERTY PageMark \* MERGEFORMAT DOCPROPERTY PageMark \* MERGEFORMAT DOCPROPERTY PageMark \* MERGEFORMAT DOCPROPERTY PageMark \* MERGEFORMAT kg kilogram
km kilometer
km2 square kilometers
L liter
LHS Latin hypercube sampling
LWB land withdrawal boundary
M mining scenario
m meter
m2 square meters
m3 cubic meters
MB marker bed
ME mining and drilling scenario
mi miles
mol mole
MPa megapascal
MTHM metric tons of heavy metal
MWd megawatt-days
N Newton
Pa Pascal
PA performance assessment
PABC performance assessment baseline calculation
PAVT Performance Assessment Verification Test
PCC partial correlation coefficient
PCS panel closure system
PDE partial differential equation
PDF probability distribution function
PIC passive institutional control
PRCC partial rank correlation coefficient
RH-TRU remote-handled transuranic
RKS Redlich-Kwong-Soave
RoR Rest of Repository
s second
DOCPROPERTY PageMark \* MERGEFORMAT DOCPROPERTY PageMark \* MERGEFORMAT DOCPROPERTY PageMark \* MERGEFORMAT DOCPROPERTY PageMark \* MERGEFORMAT DOCPROPERTY PageMark \* MERGEFORMAT DOCPROPERTY PageMark \* MERGEFORMAT s2 seconds squared
DOCPROPERTY PageMark \* MERGEFORMAT SCF/d standard cubic feet per day
SMC Salado Mass Concrete
SNL Sandia National Laboratories
SRC standardized regression coefficient
T field transmissivity field
TRU transuranic
TVD Total Variation Diminishing
UP undisturbed repository performance
WIPP Waste Isolation Pilot Plant
yr year
Elements and Chemical Compounds
Al aluminum
Am americium
C carbon
C6H10O5 generic formula for CPR
Ca calcium
CH4 methane
Cm curium
CO2 carbon dioxide
Cr chromium
Cs cesium
Fe iron
H2 hydrogen gas
H2O water
H2S hydrogen sulfide
I iodine
Mg magnesium
Mg(OH)2 brucite
Mg5(CO3)4(OH)2(4H2O hydromagnesite (5424)
DOCPROPERTY PageMark \* MERGEFORMAT MgO magnesium oxide, or periclase
Mn manganese
Ni nickel
NO3( nitrate
Np neptunium
Pb lead
Pm promethium
Pu plutonium
Ra radium
Sn tin
SO4 sulfate
SO42 sulfate ion
Sr strontium
Tc technetium
Th thorium
U uranium
V vanadium
Introduction
This appendix presents the mathematical models used to evaluate performance of the Waste Isolation Pilot Plant (WIPP) disposal system and the results of these models for the 2009 Compliance Recertification Application (CRA-2009) Performance Assessment (PA). The term PA signifies an analysis that (1) identifies the processes and events that might affect the disposal system; (2) examines the effects of these processes and events on the performance of the disposal system; and (3) estimates the cumulative releases of radionuclides, considering the associated uncertainties, caused by all significant processes and events ( HYPERLINK "40CFR191_12" 40 CFR 191.12 [U.S. Environmental Protection Agency 1993]). PA is designed to address three primary questions about the WIPP:
Q1: What processes and events that might affect the disposal system could take place at the WIPP site over the next 10,000 years?
Q2: How likely are the various processes and events that might affect the disposal system to take place at the WIPP site over the next 10,000 years?
Q3: What are the consequences of the various processes and events that might affect the disposal system that could take place at the WIPP site over the next 10,000 years?
In addition, accounting for uncertainty in the parameters of the PA models leads to a further question:
Q4: How much confidence should be placed in answers to the first three questions?
These questions give rise to a methodology for quantifying the probability distribution of possible radionuclide releases from the WIPP repository over the next 10,000 years and characterizing the uncertainty in that distribution due to imperfect knowledge about the parameters contained in the models used to predict releases. The containment requirements of HYPERLINK "40CFR191_13" 40 CFR 191.13 require this probabilistic methodology.
This appendix is organized as follows: HYPERLINK \l "PA-2_0" Section REF _Ref200958397 \r \h \* MERGEFORMAT PA-2.0 gives an overview and describes the overall conceptual structure of the CRA-2009 PA. The WIPP PA is designed to address the requirements of section 191.13, and thus involves three basic entities: (1) a probabilistic characterization of different futures that could occur at the WIPP site over the next 10,000 years, (2) models for both the physical processes that take place at the WIPP site and the estimation of potential radionuclide releases that may be associated with these processes, and (3) a probabilistic characterization of the uncertainty in the models and parameters that underlies the WIPP PA. Section REF _Ref200958447 \r \h \* MERGEFORMAT PA-2.0 is supplemented by HYPERLINK "../Appendix_SCR/Appendix_SCR.htm" Appendix SCR-2009, which documents the results of the screening process for features, events, and processes (FEPs) that are retained in the conceptual models of repository performance.
HYPERLINK \l "PA-3_0" Section REF _Ref200958472 \r \h \* MERGEFORMAT PA-3.0 describes the probabilistic characterization of different futures. This characterization plays an important role in the construction of the complementary cumulative distribution function (CCDF) specified in section 191.13. Regulatory guidance and extensive review of the WIPP site identified exploratory drilling for natural resources and the mining of potash as the only significant disruptions at the WIPP site with the potential to affect radionuclide releases to the accessible environment. Section REF _Ref200958522 \r \h \* MERGEFORMAT PA-3.0 summarizes the stochastic variables that represent future drilling and mining events in the PA. The results of the PA for CRA-2009, as documented in HYPERLINK \l "PA-7_0" Section REF _Ref219704545 \r \h PA-7.0, HYPERLINK \l "PA-8_0"Section REF _Ref219618600 \r \h PA-8.0, and HYPERLINK \l "PA-9_0" Section REF _Ref219257515 \r \h PA-9.0 of this appendix, confirm that direct releases from drilling intrusions are the major contributors to radionuclide releases to the accessible environment.
HYPERLINK \l "PA-4_0" Section REF _Ref200958559 \r \h \* MERGEFORMAT PA-4.0 presents the mathematical models for both the physical processes that take place at the WIPP and the estimation of potential radionuclide releases. The mathematical models implement the conceptual models as prescribed in HYPERLINK "40CFR194_23" 40 CFR 194.23 (2004), and permit the construction of the CCDF specified in HYPERLINK "40CFR191_13" section 191.13. Models presented in Section REF _Ref200958586 \r \h \* MERGEFORMAT PA-4.0 include two-phase (i.e., gas and brine) flow in the vicinity of the repository; radionuclide transport in the Salado Formation (hereafter referred to as the Salado); releases to the surface at the time of a drilling intrusion due to cuttings, cavings, spallings, and direct brine releases (DBRs); brine flow in the Culebra Dolomite Member of the Rustler Formation (hereafter referred to as the Culebra); and radionuclide transport in the Culebra. Section REF _Ref200958609 \r \h \* MERGEFORMAT PA-4.0 is supplemented by HYPERLINK "../Appendix_MASS/Appendix_MASS.htm" Appendices MASS-2009, HYPERLINK "../Appendix_TFIELD/Appendix_TFIELD.htm" TFIELD-2009, and HYPERLINK "../Appendix_PORSURF/Appendix_PORSURF.htm" PORSURF-2009. Appendix MASS-2009 discusses the modeling assumptions used in the WIPP PA. Appendix TFIELD-2009 discusses the generation of the transmissivity fields (T fields) used to model groundwater flow in the Culebra. Appendix PORSURF-2009 presents results from modeling the effects of excavated region closure, waste consolidation, and gas generation in the repository.
HYPERLINK \l "PA-5_0" Section REF _Ref200958641 \r \h \* MERGEFORMAT PA-5.0 discusses the probabilistic characterization of parameter uncertainty, and summarizes the uncertain variables incorporated into the CRA-2009 PA, the distributions assigned to these variables, and the correlations between variables. Section REF _Ref200958663 \r \h \* MERGEFORMAT PA-5.0 is supplemented by Fox ( HYPERLINK "../../references/Others/Fox_2008_Parameter_Report_CRA_2009_ERMS549747.pdf" 2008) and HYPERLINK "../Appendix_SOTERM/Appendix_SOTERM.htm" Appendix SOTERM-2009. Fox (2008) catalogs the full set of parameters used in the CRA-2009 PA, previously referred to as the HYPERLINK "../../references/CCA/Appendix_PAR.pdf" CCA Appendix PAR and the HYPERLINK "../../references/CRA-2004/Appendix_PA_Attachment_PAR.pdf" CRA-2004, Appendix PA, Attachment PAR. Appendix SOTERM-2009 describes the actinide (An) source term for the WIPP performance calculations, including the mobile concentrations of actinides that may be released from the repository in brine.
HYPERLINK \l "PA-6_0" Section REF _Ref200960089 \r \h \* MERGEFORMAT PA-6.0 summarizes the computational procedures used in the CRA-2009 PA, including sampling techniques (i.e., random and Latin hypercube sampling (LHS)); sample size, statistical confidence for mean CCDF, generation of sample, generation of individual futures, construction of CCDFs, calculations performed with the models discussed in HYPERLINK \l "PA-4_0" Section REF _Ref200960106 \r \h \* MERGEFORMAT PA-4.0, construction of releases for each future, and the sensitivity analysis techniques in use.
HYPERLINK \l "PA-7_0" Section REF _Ref200960181 \r \h \* MERGEFORMAT PA-7.0 presents the results of the PA for an undisturbed repository. Releases from the undisturbed repository are determined by radionuclide transport in brine flowing from the repository to the land withdrawal boundary (LWB) through the marker beds (MBs) or shafts. Releases in the undisturbed scenario are used to demonstrate compliance with the individual and groundwater protection requirements in HYPERLINK "40CFR191" 40 CFR Part 191 ( HYPERLINK "40CFR194_51" 40 CFR 194.51 and HYPERLINK "40CFR194_52" 40 CFR 194.52).
HYPERLINK \l "PA-8_0" Section REF _Ref200960223 \r \h \* MERGEFORMAT PA-8.0 presents PA results for a disturbed repository. As will be discussed in HYPERLINK \l "PA-2_3_1" Section REF _Ref203993034 \r \h \* MERGEFORMAT PA-2.3.1, the only future events and processes in the analysis of disturbed repository performance are those associated with mining and deep drilling. Release mechanisms include direct releases at the time of the intrusion via cuttings, cavings, spallings, and DBR, and long-term releases via radionuclide transport up abandoned boreholes to the Culebra and thence to the LWB.
HYPERLINK \l "PA-9_0" Section REF _Ref201626116 \r \h \* MERGEFORMAT PA-9.0 presents the set of CCDFs resulting from the CRA-2009 PA. This material supplements HYPERLINK "40CFR194_34" 40 CFR 194.34, which demonstrates compliance with the containment requirements of HYPERLINK "40CFR191_13" section 191.13. Section REF _Ref201626116 \r \h \* MERGEFORMAT PA-9.0 presents the most significant output variables from the PA models, accompanied by sensitivity analyses to determine which subjectively uncertain parameters are most influential in the uncertainty of PA results.
The overall structure of the CRA-2009 PA does not differ from that presented in the first WIPP Compliance Certification Application (CCA) ( HYPERLINK "../../references/CCA/CCA.htm" U.S. Department of Energy 1996), the CRA-2004 (U.S. Department of Energy 2004) or the CRA-2004 Performance Assessment Baseline Calculation (PABC) ( HYPERLINK "../../references/Others/Leigh_et_al_2004_CRA_PABC_rev0_ERMS541521.pdf" Leigh et al. 2005). This recertification application appendix follows the approach used by Helton etal. ( HYPERLINK "../../references/Others/Helton_et_al_1998_Uncertainty_Sensitivity_Analysis_Results_SAND98_0365.pdf" 1998) to document the mathematical models used in the CCA PA and the results of that analysis. Much of the content of this appendix derives from Helton etal. (1998); these authors contributions are gratefully acknowledged.
Overview and Conceptual Structure of the PA
Because of the amount and complexity of the material presented in Appendix PA-2009, an introductory summary is provided below, followed by detailed discussions of the topics in the remainder of this section, which is organized as follows:
HYPERLINK \l "PA-2_1" Section REF _Ref202585398 \r \h \* MERGEFORMAT PA-2.1 Overview of PA and the results
HYPERLINK \l "PA-2_2" Section REF _Ref203991422 \r \h \* MERGEFORMAT PA-2.2 The conceptual structure of the PA used to evaluate compliance with the containment requirements
HYPERLINK \l "PA-2_3" Section REF _Ref203994331 \r \h \* MERGEFORMAT PA-2.3 The overall methodology used to develop FEPs, the screening methodology applied to the FEPs, the results of the screening process, and the development of the scenarios considered in the system-level consequence analysis
The U.S. Department of Energy (DOE) continues to use the same PA methodology as in the CCA and CRA-2004 because changes that have been made since the U.S. Environmental Protection Agency (EPA) certified WIPP do not impact PA methodology. A corresponding detailed presentation for the CRA-2004 PA methodology is provided in the HYPERLINK "../../references/CRA-2004/Chapter_6.pdf" \l "page=20" CRA-2004, Chapter 6.0, Section 6.1, and a detailed presentation for the CRA-2004 PABC implementation is provided in Leigh et al. ( HYPERLINK "../../references/Others/Leigh_et_al_2004_CRA_PABC_rev0_ERMS541521.pdf" 2005). A corresponding detailed presentation for the CCA PA methodology is provided in Helton et al. ( HYPERLINK "../../references/Others/Helton_et_al_1998_Uncertainty_Sensitivity_Analysis_Results_SAND98_0365.pdf" \l "page=27" 1998, Section 2).
Overview of Performance Assessment
A demonstration of future repository performance was required by the disposal standards in HYPERLINK "40CFR191" Part 191. The EPA required a PA to demonstrate that potential cumulative releases of radionuclides to the accessible environment over a 10,000-year period after disposal are less than specified limits based on the nature of the materials disposed ( HYPERLINK "40CFR191_13" section 191.13). The PA is to determine the effects of all significant processes and events that may affect the disposal system, consider the associated uncertainties of the processes and events, and estimate the probable cumulative releases of radionuclides.
A PA was included in the CCA. This was the first demonstration of compliance by the DOE with the EPAs disposal standards. The EPA required a verification PA based on the CCA PA that included revised parameters and distributions. This PA was termed the CCA Performance Assessment Verification Test (PAVT) ( HYPERLINK "../../references/Others/Trovato_to_Alm_1997_March_19_Letter_ERMS245835.pdf" Trovoto 1997). The EPA based the original certification of the WIPP on the information in the CCA and the results of the CCA PAVT ( HYPERLINK "../../references/Others/EPA_63_FR_27353_408_May_18_1998.pdf" U.S. Environmental Protection Agency 1998a). The CCA PAVT is documented in HYPERLINK "../../references/Others/ERMS420667.pdf" Sandia National Laboratories (SNL) 1997 and HYPERLINK "../../references/Others/DOE_1997_Supplemental_Summary_of_EPA_Mandated_PAVT_All_Replicates_ERMS414879.pdf" U.S. Department of Energy 1997.
The WIPP is required to be recertified every five years after first waste receipt (Public Law 02579). A revised PA was included in the first recertification application in 2004. This PA is termed the CRA-2004 PA, and is documented in the HYPERLINK "../../references/CRA-2004/Chapter_6.pdf" CRA-2004, Chapter 6.0. The EPA again required a verification PA using revised modeling assumptions and parameters ( HYPERLINK "../../references/Others/Cotsworth_to_Triay_March_4_2005_EPA_Letter_on_Conducting_ERMS538858.pdf" Cotsworth 2005). This PA was termed the CRA-2004 PABC and was documented in Leigh et al. ( HYPERLINK "../../references/Others/Leigh_et_al_2004_CRA_PABC_rev0_ERMS541521.pdf" 2005).
As part of the five-year recertification cycle, a PA is included in the CRA-2009. The CRA-2009 PA is a culmination of the previous PAs and is not significantly different from the CRA-2004 PABC, as the methodologies, conceptual models, and assumptions have not changed. Updates to parameters and improvements to computer codes are incorporated in the CRA-2009.
SEQ CHAPTER \h \r 1Changes in the CRA-2009 PA
A list of changes to PA since the CRA-2004 and citations for where they are discussed is shown in HYPERLINK \l "Table_PA-1" REF _Ref201625696 \h \* MERGEFORMAT Table PA-1. In addition to the changes discussed in REF _Ref201625696 \h \* MERGEFORMAT Table PA-1, the terminology used to describe uncertainty has been updated to reflect the usage now prevalent in the risk assessment literature. Previously, uncertainty in model parameters was referred to as subjective uncertainty, and that due to stochastic processes was referred to as stochastic uncertainty. In the years since these terms were first employed, these concepts have matured, and the term epistemic uncertainty is now used to describe uncertainty from lack of knowledge, while the term aleatory uncertainty now describes uncertainty due to natural variability, e.g. uncertainty arising from future events whose occurrence can be defined in terms of probabilities. In this text, the terms epistemic uncertainty and aleatory uncertainty are used in place of the terms subjective uncertainty and stochastic uncertainty, respectively.
Table PA- SEQ Table_PA- \* ARABIC 1 SEQ CHAPTER \h \r 1. WIPP Project Changes and Cross References
SEQ CHAPTER \h \r 1WIPP Project ChangeCross ReferenceCRA-2004 to CRA-2004 PABC ChangesaInventory Information HYPERLINK "../../references/Others/Leigh_Trone_Fox_2005_TRU_Waste_Inventory_for_CRA2004_PABC_ERMS541118.pdf" Leigh, Trone, and Fox 2005An Solubility Values HYPERLINK "../../references/Others/Garner_Leigh_2005_Analysis_Package_for_PANEL_CRA_2004_PABC_ERMS540572.pdf" Garner and Leigh 2005An Solubility Uncertainty RangesGarner and Leigh 2005Microbial Gas Generation Model HYPERLINK "../../references/Others/Nemer_and_Stein_2005_Analysis_Package_for_BRAGFLO_ERMS540527.pdf" Nemer and Stein 2005Culebra T Fields Mining Modification HYPERLINK "../../references/Others/Lowry_Kanney_2005_Analysis_Report_for_CRA_2004_PABC_Culebra_Flow_ERMS541508.pdf" Lowry and Kanney 2005Anhydrite Material ParametersHYPERLINK "../../references/Others/Vugrin_et_al_2005_Analysis_Report_for_Modifying_Parameter_Distributions_ERMS539301.pdf"Vugrin et al. 2005SPALL Model Parameters HYPERLINK "../../references/Others/Vurgin_2005_Analysis_Package_for_DRSPALL_CRA_2004_PABC_ERMS540415.pdf" Vugrin 2005CRA-2004 PABC to CRA-2009 ChangesbDBR Maximum Duration Parameter HYPERLINK "../../references/Others/Kirkes_2007_Evaluation_of_the_Duration_of_Direct_Brine_ERMS545988.pdf" Kirkes 2007Conditional Relationship Between Humid and Inundated Cellulosic, Plastic, or Rubber (CPR) Degradation Rates HYPERLINK "../../references/Others/Kirchner_2008_Generation_of_LHS_Samples_ERMS547971.pdf" Kirchner 2008aBRAGFLO Code Improvements HYPERLINK "../../references/Others/Nemer_Clayton_2008_Analysis_Package_for_Salado_Flow_Modeling_ERMS548607.pdf" Nemer and Clayton 2008Capillary Pressure and Relative Permeability ModelNemer and Clayton 2008Drilling Rate HYPERLINK "../../references/Others/Clayton_2008_AP137_Analysis_Plan_for_the_Performance_Assessment_for_CRA_2009_ERMS547905.pdf" Clayton 2008aParameter Error Corrections
Emplaced CPR
Halite/Disturbed Rock Zone (DRZ) Parameter
Fraction of Repository Occupied by Waste
NUTS and DBR Calculation Input Files HYPERLINK "../../references/Others/Nemer_2007_Effects_of_Not_Including_Emplacement_Materials_ERMS545689.pdf" Nemer 2007a, HYPERLINK "../../references/Others/Ismail_2007_Revised_Porosity_estimates_ERMS545755.pdf" Ismail 2007a, HYPERLINK "../../references/Others/Dunagan_2007_Parameter_Problem_Report_for_REFCONFVW_ERMS545481.pdf" Dunagan 2007, HYPERLINK "../../references/Others/Ismail_to_Vugrin_et_al_2007_June_11_Errors_in_Input_Files_for_NUTS_ERMS546200.pdf" Ismail 2007b, HYPERLINK "../../references/Others/Clayton_to_Vugrin_et_al_2007_June_6_Corrections_to_Input_Files_for_DBR_PABC_ERMS546311.pdf" Clayton 2007a See HYPERLINK "../../references/Others/Leigh_et_al_2004_CRA_PABC_rev0_ERMS541521.pdf" Leigh et al. 2005 for additional discussion of these changes and their implementation in the CRA-2004 PABC.
b See HYPERLINK "../../references/Others/Clayton_et_al_2008_Summary_Report_of_CRA_2009_PA_ERMS548862.pdf" Clayton et al. 2008 for additional discussions of these changes and their implementation in the CRA-2009 PA.
From this assessment, the DOE has demonstrated that the WIPP continues to comply with the containment requirements of HYPERLINK "40CFR191_13" section 191.13. The containment requirements are stringent and state that the DOE must demonstrate a reasonable expectation that the probabilities of cumulative radionuclide releases from the disposal system during the 10,000 years following closure will fall below specified limits. The PA analyses supporting this determination must be quantitative and consider uncertainties caused by all significant processes and events that may affect the disposal system, including future inadvertent human intrusion into the repository. A quantitative PA is conducted using a series of loosely coupled computer models in which epistemic parameter uncertainties are addressed by a stratified Monte Carlo sampling procedure on selected input parameters, and uncertainties related to future intrusion events are addressed using simple random sampling.
As required by regulation, results of the PA are displayed as CCDFs showing the probability that cumulative radionuclide releases from the disposal system will exceed the values calculated for scenarios considered in the analysis. These CCDFs are calculated using reasonable and, in some cases, conservative conceptual models based on the scientific understanding of the disposal systems behavior. Parameters used in these models are derived from experimental data, field observations, and relevant technical literature. Changes to the CCA and CRA-2004 parameters and models since the original certification have been incorporated into the CRA-2009 PA ( HYPERLINK "../../references/Others/Clayton_2008_AP137_Analysis_Plan_for_the_Performance_Assessment_for_CRA_2009_ERMS547905.pdf" Clayton 2008a). The overall mean CCDF continues to lie entirely below the specified limits, and the WIPP therefore continues to be in compliance with the containment requirements of HYPERLINK "40CFR191_Subpart_B" 40 CFR Part 191 Subpart B (see HYPERLINK \l "PA-2_1_6" Section REF _Ref203992508 \r \h \* MERGEFORMAT PA-2.1.6). Sensitivity analysis of results shows that the location of the mean CCDF is dominated by radionuclide releases that could occur on the surface during an inadvertent penetration of the repository by a future drilling operation ( HYPERLINK \l "PA-9_0" Section REF _Ref201626116 \r \h \* MERGEFORMAT PA-9.0). Releases of radionuclides to the accessible environment from transport in groundwater through the shaft seal systems and the subsurface geology are negligible, with or without human intrusion, and do not significantly contribute to the mean CCDF. No releases are predicted to occur at the ground surface in the absence of human intrusion. The natural and engineered barrier systems of the WIPP provide robust and effective containment of transuranic (TRU) waste, even if the repository is penetrated by multiple boreholes.
SEQ CHAPTER \h \r 1Conceptual Basis for PA
The foundations of PA are a thorough understanding of the disposal system and the possible future interactions of the repository, waste, and surrounding geology. The DOEs confidence in the results of PA is based in part on the strength of the original research done during site characterization, experimental results used to develop and confirm parameters and models, and robustness of the facility design.
The progression of compliance applications document these aspects of PA leading up to the CRA-2009 PA (i.e., the CCA, the CCA PAVT [ HYPERLINK "../../references/Others/ERMS420667.pdf" Sandia National Laboratories 1997 and HYPERLINK "../../references/Others/DOE_1997_Supplemental_Summary_of_EPA_Mandated_PAVT_All_Replicates_ERMS414879.pdf" U.S. Department of Energy 1997], the CRA-2004 PA, and the CRA-2004 PABC [ HYPERLINK "../../references/Others/Leigh_et_al_2004_CRA_PABC_rev0_ERMS541521.pdf" Leigh et al. 2005]).
The interactions of the repository and waste with the geologic system, and the response of the disposal system to possible future inadvertent human intrusion, are described in HYPERLINK \l "PA-2_1_4" Section REF _Ref49934479 \r \h \* MERGEFORMAT PA-2.1.4.
Undisturbed Repository Performance
An evaluation of undisturbed repository performance, which is defined to exclude human intrusion and unlikely disruptive natural events, is required by regulation (see HYPERLINK "40CFR191_15" 40 CFR 191.15 and HYPERLINK "40CFR191_24" 40 CFR 191.24). Evaluations of past and present natural geologic processes in the region indicate that none has the potential to breach the repository within 10,000 years (see the HYPERLINK "../../references/CCA/Appendix_SCR.pdf" \l "page=11" CCA, Appendix SCR, Section SCR.1). Disposal system behavior is dominated by the coupled processes of rock deformation surrounding the excavation, fluid flow, and waste degradation. Each of these processes can be described independently, but the extent to which they occur is affected by the others.
Rock deformation immediately around the repository begins as soon as excavation creates a disturbance in the stress field. Stress relief results in some degree of brittle fracturing and the formation of a DRZ, which surrounds excavations in all deep mines including the WIPP repository. For the WIPP, the DRZ is characterized by an increase in permeability and porosity, and it may ultimately extend a few meters (m) from the excavated region. Salt will also deform by creep processes resulting from deviatoric stress, causing the salt to move inward and fill voids. Salt creep will continue until deviatoric stress is dissipated and the system is once again at stress equilibrium (see the HYPERLINK "../../references/CRA-2004/Chapter_6.pdf" \l "page=84" CRA-2004, Chapter 6.0, Section 6.4.3.1).
The ability of salt to creep, thereby healing fractures and filling porosity, is one of its fundamental advantages as a medium for geologic disposal of radioactive waste, and one reason it was recommended by the National Academy of Sciences (see the HYPERLINK "../../references/CCA/Chapter_1.pdf" \l "page=12" CCA, Chapter 1.0, Section 1.3). Salt creep provides the mechanism for crushed salt compaction in the shaft seal system, yielding properties approaching those of intact salt within 200 years (see the HYPERLINK "../../references/CCA/Appendix_SEAL_D.pdf" \l "page=62" CCA, Appendix SEAL, Appendix D, Section D5.2). Salt creep will also cause the DRZ surrounding the shaft to heal rapidly around the concrete components of the seal system. In the absence of elevated gas pressure in the repository, salt creep would also substantially compact the waste and heal the DRZ around the disposal region. Fluid pressures can become large enough through the combined effect of salt creep reducing pore volumes, and gas generation from waste degradation processes, to maintain significant porosity (greater than 20%) within the disposal room throughout the performance period (see also the HYPERLINK "../../references/CRA-2004/Chapter_6.pdf" \l "page=80" CRA-2004, Chapter 6.0, Section 6.4.3).
Characterization of the Salado indicates that fluid flow from the far field does not occur on time scales of interest in the absence of an artificially imposed hydraulic gradient (see the HYPERLINK "../../references/CRA-2004/Chapter_2.pdf" \l "page=30" CRA-2004, Chapter 2.0, Section 2.1.3.4 for a description of Salado investigations). This lack of fluid flow is the second fundamental reason for choosing salt as a medium for geologic disposal of radioactive waste. Lack of fluid flow is a result of the extremely low permeability of evaporite rocks that make up the Salado. Excavating the repository has disturbed the natural hydraulic gradient and rock properties, resulting in fluid flow. Small quantities of interstitial brine present in the Salado move toward regions of low hydraulic potential, and brine seeps are observed in the underground repository. The slow flow of brine from halite into more permeable anhydrite MBs, and then through the DRZ into the repository, is expected to continue as long as the hydraulic potential within the repository is below that of the far field. The repository environment will also include gas, so the fluid flow must be modeled as a two-phase process. Initially, the gaseous phase will consist primarily of air trapped at the time of closure, although other gases may form from waste degradation. In the PA, the gaseous phase pressure will rise due to creep closure, gas generation, and brine inflow, creating the potential for flow from the excavated region (see also the HYPERLINK "../../references/CRA-2004/Chapter_6.pdf" \l "page=86" CRA2004, Chapter 6.0, Section 6.4.3.2).
An understanding of waste degradation processes indicates that the gaseous phase in fluid flow and the repositorys pressure history will be far more important than if the initial air were the only gas present. Waste degradation can generate significant additional gas by two processes (see also the HYPERLINK "../../references/CRA-2004/Chapter_6.pdf" \l "page=87" CRA-2004, Chapter 6.0, Section 6.4.3.3 for historical perspective, and HYPERLINK "../../references/Others/Leigh_et_al_2004_CRA_PABC_rev0_ERMS541521.pdf" \l "page=23"Leigh et al. 2005, Section 2.3 and HYPERLINK "../../references/Others/Leigh_et_al_2004_CRA_PABC_rev0_ERMS541521.pdf" \l "page=24"Section 2.4 for changes):
The generation of hydrogen (H2) gas by anoxic corrosion of steels, other iron (Fe)-based alloys, and aluminum (Al) and Al-based alloys
The generation of carbon dioxide (CO2), hydrogen sulfide (H2S), and methane (CH4) by anaerobic microbial consumption of waste containing CPR materials
Coupling these gas-generation reactions to fluid-flow and salt-creep processes is complex. Gas generation will increase fluid pressure in the repository, thereby decreasing the hydraulic gradient and deviatoric stress between the far field and the excavated region and inhibiting the processes of brine inflow and salt creep. Anoxic corrosion will also consume brine as it breaks down water to oxidize steels and other Fe-based alloys and release H2. Thus, corrosion has the potential to be a self-limiting process, in that as it consumes all water in contact with steels and other Fe-based alloys, it will cease. Microbial reactions also require water, either in brine or the gaseous phase. It is assumed that microbial reactions will result in neither the consumption nor production of water.
The total volume of gas generated by corrosion and microbial consumption may be sufficient to result in repository pressures that approach lithostatic. Sustained pressures above lithostatic are not physically reasonable within the disposal system, because the more brittle anhydrite layers are expected to fracture if sufficient gas is present. The conceptual model implemented in the PA causes anhydrite MB permeability and porosity to increase rapidly as pore pressure approaches and exceeds lithostatic. This conceptual model for pressure-dependent fracturing approximates the hydraulic effect of pressure-induced fracturing and allows gas and brine to move more freely within the MBs at higher pressures (see the HYPERLINK "../../references/CRA-2004/Chapter_6.pdf" \l "page=102" CRA-2004, Chapter 6.0, Section 6.4.5.2).
Overall, the behavior of the undisturbed disposal system will result in extremely effective isolation of the radioactive waste. Concrete, clay, and asphalt components of the shaft seal system will provide an immediate and effective barrier to fluid flow through the shafts, isolating the repository until salt creep has consolidated the compacted crushed salt components and permanently sealed the shafts. Around the shafts, the DRZ in halite layers will heal rapidly because the presence of the solid material within the shafts will provide rigid resistance to creep. The DRZ around the shaft, therefore, will not provide a continuous pathway for fluid flow (see the HYPERLINK "../../references/CRA-2004/Chapter_6.pdf" \l "page=99"CRA-2004, Chapter 6.0, Section 6.4.4). Similarly, the panel closure will rigidly resist creep, leading to a build-up of compressive stress which in turn will cause a rapid elimination of the DRZ locally. In PA, it is conservatively assumed that the DRZ does not heal around either the disposal region or the operations and experimental regions, and pathways for fluid flow may exist indefinitely to the overlying and underlying anhydrite layers (e.g., MB139 and Anhydrites A and B). Some quantity of brine will be present in the repository under most conditions and may contain actinides mobilized as both dissolved and colloidal species. Gas generation by corrosion and microbial degradation is expected to occur, and will result in elevated pressures within the repository. These pressures will not significantly exceed lithostatic because the more brittle anhydrite layers will fracture and provide a pathway for gas to leave the repository. Fracturing due to high gas pressures may enhance gas and brine migration from the repository, but gas transport will not contribute to the release of actinides from the disposal system. Brine flowing out of the waste disposal region through anhydrite layers may transport actinides as dissolved and colloidal species. However, the quantity of actinides that may reach the accessible environment boundary through the interbeds during undisturbed repository performance is insignificant and has no effect on the compliance determination. No migration of radionuclides is expected to occur vertically through the Salado (see HYPERLINK \l "PA-7_0" Section REF _Ref203991167 \r \h \* MERGEFORMAT PA-7.0, and HYPERLINK "../../references/Others/Ismail_Garner_2008_Analysis_Package_for_Salado_Transport_Calculations_CRA_2009_ERMS548845.pdf" Ismail and Garner 2008).
Disturbed Repository Performance
The WIPP PA is required by the performance standards to consider scenarios that include intrusions into the repository by inadvertent and intermittent drilling for resources. The probability of these intrusions is based on a future drilling rate. This rate was calculated using the method outlined in HYPERLINK "../Section_33/Section_33.htm" Section 33, which analyzes the past record of drilling events in the Delaware Basin. Active institutional controls (AICs) are assumed to prevent intrusion during the first 100 years after closure ( HYPERLINK "40CFR194_41" 40 CFR 194.41). Passive institutional controls (PICs) were assumed in the CCA to effectively reduce the drilling rate by two orders of magnitude for the 600-year period following 100 years of active control. However, in certifying the WIPP, the EPA denied credit for the effectiveness of passive controls for 600 years ( HYPERLINK "../../references/Others/EPA_63_FR_27353_408_May_18_1998.pdf" U.S. Environmental Protection Agency 1998a). Although the CRA-2009 PA does not include a reduced drilling intrusion rate to account for PICs, future PAs may do so. Future drilling practices are assumed to be the same as current practice, also consistent with regulatory criteria. These practices include the type and rate of drilling, emplacement of casing in boreholes, and the procedures implemented when boreholes are plugged and abandoned (see HYPERLINK "40CFR194_33" 40 CFR 194.33).
Human intrusion by drilling may cause releases from the disposal system through five mechanisms:
Cuttings, which include material intersected by the rotary drilling bit
Cavings, which include material eroded from the borehole wall during drilling
Spallings, which include solid material carried into the borehole during rapid depressurization of the waste disposal region
DBRs, which include contaminated brine that may flow to the surface during drilling
Long-term brine releases, which include the contaminated brine that may flow through a borehole after it is abandoned
The first four mechanisms immediately follow an intrusion event and are collectively referred to as direct releases. The accessible environment boundary for these releases is the ground surface. The fifth mechanism, An transport by long-term groundwater flow, begins when concrete plugs are assumed to degrade in an abandoned borehole and may continue throughout the regulatory period. The accessible environment boundary for these releases is the lateral subsurface limit of the controlled area ( HYPERLINK "../../references/CRA-2004/Chapter_6.pdf" \l "page=12" CRA-2004, Chapter 6.0, Section 6.0.2.3).
Repository conditions prior to intrusion will be the same as those for undisturbed repository performance, and all processes active in undisturbed repository performance will continue to occur following intrusion. Because an intrusion provides a pathway for radionuclides to reach the ground surface and enter the geological units above the Salado, additional processes will occur that dont in the undisturbed repository performance. These processes include the mobilization of radionuclides as dissolved and colloidal species in repository brine and groundwater flow, and subsequent An transport in the overlying units. Flow and transport in the Culebra are of particular interest because it is the most transmissive unit above the repository. Thus, the Culebra is a potential pathway for lateral migration of contaminated brine in the event of a drilling intrusion accompanied by significant flow up the intrusion borehole (see the HYPERLINK "../../references/CRA-2004/Chapter_6.pdf" \l "page=109" CRA2004, Chapter 6.0, Section 6.4.6.2).
Cuttings and Cavings
In a rotary drilling operation, the volume of material brought to the surface as cuttings is calculated as the cylinder defined by the thickness of the unit and the diameter of the drill bit. The quantity of radionuclides released as cuttings is therefore a function of the activity of the intersected waste and the diameter of the intruding drill bit. The DOE uses a constant value of 0.31115m (12.25inches [in]), consistent with bits currently used at the WIPP depth in the Delaware Basin (see the HYPERLINK "../../references/CRA-2004/Chapter_6.pdf" \l "page=159" CRA-2004, Chapter 6.0, Section 6.4.12.5). The intersected waste activity may vary depending on the type of waste intersected. The DOE considers random penetrations into remote-handled (RH) transuranic (TRU) (RH-TRU) waste and each of the 690 different waste streams (HYPERLINK "../../references/Others/Leigh_Trone_Fox_2005_TRU_Waste_Inventory_for_CRA2004_PABC_ERMS541118.pdf" \l "page=35"Leigh, Trone, and Fox 2005, Section 4.4) identified for contact-handled (CH) transuranic (TRU) (CH-TRU) waste (569 and 693 waste streams were used in the CCA and the CRA-2004, respectively; see the HYPERLINK "../../references/CRA-2004/Chapter_6.pdf" \l "page=14" CRA2004, Chapter 6.0, Section 6.0.2.3.1).
The volume of particulate material eroded from the borehole wall by the drilling fluids and brought to the surface as cavings may be affected by the drill bit diameter, effective shear resistance of the intruded material, speed of the drill bit, viscosity of the drilling fluid and rate at which it is circulated in the borehole, and other properties related to the drilling process. The most important of these parameters, after drill bit diameter, is the effective shear resistance of the intruded material (HYPERLINK "../../references/Others/Leigh_et_al_2004_CRA_PABC_rev0_ERMS541521.pdf" \l "page=136"Leigh et al. 2005, Section 7.2). In the absence of data describing the reasonable and realistic future properties of degraded waste and magnesium oxide (MgO) backfill, the DOE used conservative parameter values based on the properties of fine-grained sediment. Other properties are assigned fixed values consistent with current practice. The quantity of radionuclides released as cavings depends on the volume of eroded material and its activity, which is treated in the same manner as the activity of cuttings (see also HYPERLINK \l "PA-4_5" Section REF _Ref203992003 \r \h \* MERGEFORMAT PA-4.5 and HYPERLINK \l "PA-6_8_2_1" Section REF _Ref203992004 \r \h \* MERGEFORMAT PA-6.8.2.1).
Spallings
Unlike releases from cuttings and cavings, which occur with every modeled borehole intrusion, spalling releases will occur only if pressure in the waste-disposal region exceeds the hydrostatic pressure in the borehole. At lower pressures, below about 8 megapascals (MPa), fluid in the waste-disposal region will not flow toward the borehole. At higher pressures, gas flow toward the borehole may be sufficiently rapid to cause additional solid material to enter the borehole. If spalling occurs, the volume of spalled material will be affected by the physical properties of the waste, such as its tensile strength and particle diameter. The DOE based the parameter values used in the PA on reasonable and conservative assumptions. Since the CCA, a revised conceptual model for the spallings phenomena has been developed (see the HYPERLINK "../../references/CRA-2004/Appendix_PA.pdf" \l "page=96" CRA-2004, Appendix PA, Section PA-4.6 and HYPERLINK "../../references/CRA-2004/Appendix_PA_Attachment_MASS.pdf" \l "page=76" Appendix PA, Attachment MASS, Section MASS-16.1.3). Model development, execution, and sensitivity studies necessitated implementing parameter values pertaining to waste characteristics, drilling practices, and physics of the process. The parameter range for particle size was derived by expert elicitation ( HYPERLINK "../../references/Others/CTAC_1997_Expert_Elicitation_on_WIPP_Waste_Particle_Diameter_Size_ERMS541365.pdf" U.S. Department of Energy 1997).
The quantity of radionuclides released as spalled material depends on the volume of spalled waste and its activity. Because spalling may occur at a greater distance from the borehole than cuttings and cavings, spalled waste is assumed to have the volume-averaged activity of CH-TRU waste, rather than the sampled activities of individual waste streams. The low permeability of the region surrounding the RH-TRU waste means it is isolated from the spallings process and does not contribute to the volume or activity of spalled material (see also HYPERLINK \l "PA-4_6" Section REF _Ref203991327 \r \h \* MERGEFORMAT PA-4.6 and HYPERLINK \l "PA-6_8_2_2" Section REF _Ref203991337 \r \h \* MERGEFORMAT PA-6.8.2.2 for more description of the spallings model).
Direct Brine Flow
Radionuclides may be released to the accessible environment if repository brine enters the borehole during drilling and flows to the ground surface. The quantity of radionuclides released by direct brine flow depends on the volume of brine reaching the ground surface and the concentration of radionuclides contained in the brine. As with spallings, DBRs will not occur if repository pressure is below the hydrostatic pressure in the borehole. At higher repository pressures, mobile brine present in the repository will flow toward the borehole. If the volume of brine flowing from the repository into the borehole is small, it will not affect the drilling operation, and flow may continue until the driller reaches the base of the evaporite section and installs casing in the borehole (see also HYPERLINK \l "PA-4_7" Section REF _Ref203992005 \r \h \* MERGEFORMAT PA-4.7 and HYPERLINK \l "PA-6_8_2_3" Section REF _Ref203992006 \r \h \* MERGEFORMAT PA-6.8.2.3).
Mobilization of Actinides in Repository Brine
Actinides may be mobilized in repository brine in two principal ways:
As dissolved species
As colloidal species
The solubilities of actinides depend on their oxidation states, with the more reduced forms (for example, III and IV oxidation states) being less soluble than the oxidized forms (V and VI). Conditions within the repository will be strongly reducing because of large quantities of metallic Fe in the steel containers and the waste, andin the case of plutonium (Pu)only the lower-solubility oxidation states (Pu(III) and Pu(IV)) will persist. Microbial activity will also help create reducing conditions. Solubilities also vary with pH. The DOE is therefore emplacing MgO in the waste-disposal region to ensure conditions that reduce uncertainty and establish low An solubilities. MgO consumes CO2 and buffers pH, lowering An solubilities in WIPP brines (see HYPERLINK "../Appendix_SOTERM/Appendix_SOTERM.htm" Appendix SOTERM-2009 and HYPERLINK "../Appendix_MgO/Appendix_MgO.htm" Appendix MgO-2009). Solubilities in the PA are based on the chemistry of brines that might be present in the waste-disposal region, reactions of these brines with the MgO engineered barrier, and strongly reducing conditions produced by anoxic corrosion of steels and other Fe-based alloys.
The waste contains organic ligands that could increase An solubilities by forming complexes with dissolved An species. However, these organic ligands also form complexes with other dissolved metals, such as magnesium (Mg), calcium (Ca), Fe, lead (Pb), vanadium (V), chromium (Cr), manganese (Mn), and nickel (Ni), that will be present in repository brines due to corrosion of steels and other Fe-based alloys. The CRA-2009 PA speciation and solubility calculations include the effect of organic ligands but not the beneficial effect of competition with Fe, Pb, V, Cr, Mn, and Ni. ( HYPERLINK "../Appendix_SOTERM/Appendix_SOTERM.htm" \l "SOTERM-2_3_6" Appendix SOTERM-2009, Section SOTERM-2.3.6 and HYPERLINK "../Appendix_SOTERM/Appendix_SOTERM.htm" \l "SOTERM-4_6" Section SOTERM-4.6, and HYPERLINK "../../references/Others/Brush_and_Xiong_2005_Calculation_of_Organic_Ligand_Concentrations_for_WIPP_PABC_ERMS539635.pdf" Brush and Xiong 2005).
Colloidal transport of actinides has been examined, and four types of colloids have been determined to represent the possible behavior at the WIPP. These include microbial colloids, humic substances, An intrinsic colloids, and mineral fragments. Concentrations of An mobilized as these colloidal forms are included in the estimates of total An concentrations used in PA ( HYPERLINK "../Appendix_SOTERM/Appendix_SOTERM.htm" \l "SOTERM-3_8_1" Appendix SOTERM-2009, Section SOTERM-3.8.1 and HYPERLINK "../Appendix_SOTERM/Appendix_SOTERM.htm" \l "SOTERM-4_7" Section SOTERM-4.7, and HYPERLINK "../../references/Others/Garner_Leigh_2005_Analysis_Package_for_PANEL_CRA_2004_PABC_ERMS540572.pdf" Garner and Leigh 2005).
SEQ CHAPTER \h \r 1Long-Term Brine Flow up an Intrusion Borehole
Long-term releases to the ground surface or groundwater in the Rustler Formation (hereafter referred to as the Rustler) or overlying units may occur after the borehole has been plugged and abandoned. In keeping with regulatory criteria, borehole plugs are assumed to have properties consistent with current practice in the basin. Thus, boreholes are assumed to have concrete plugs emplaced at various locations. Initially, concrete plugs effectively limit fluid flow in the borehole. However, under most circumstances, these plugs cannot be expected to remain fully effective indefinitely. For the purposes of PA, discontinuous borehole plugs above the repository are assumed to degrade 200 years after emplacement. From then on, the borehole is assumed to fill with a silty-sand-like material containing degraded concrete, corrosion products from degraded casing, and material that sloughs into the hole from the walls. Of six possible plugged borehole configurations in the Delaware Basin, three are considered either likely or adequately representative of other possible configurations; one configuration (a two-plug configuration) is explicitly modeled in the flow and transport model (see HYPERLINK \l "PA-3_7" Section REF _Ref203992007 \r \h \* MERGEFORMAT PA-3.7 and HYPERLINK "../Appendix_MASS/Appendix_MASS.htm" \l "MASS-16_3" Appendix MASS-2009, Section MASS-16.3).
If sufficient brine is available in the repository, and if pressure in the repository is higher than in the overlying units, brine may flow up the borehole following plug degradation. In principle, this brine could flow into any permeable unit or to the ground surface if repository pressure were high enough. For modeling purposes, brine is allowed to flow only into the higher-permeability units and to the surface. Lower-permeability anhydrite and mudstone layers in the Rustler are treated as if they were impermeable to simplify the analysis while maximizing the amount of flow into units where it could potentially contribute to disposal system releases. Model results indicate that essentially all flow occurs into the Culebra, which has been recognized since the early stages of site characterization as the most transmissive unit above the repository and the most likely pathway for subsurface transport (see also the HYPERLINK "../../references/CRA-2004/Chapter_2.pdf" \l "page=101" CRA-2004, Chapter 2.0, Section 2.2.1.4.1.2).
Groundwater Flow in the Culebra
Site characterization activities in the units above the Salado have focused on the Culebra. These activities have shown that the direction of groundwater flow in the Culebra varies somewhat regionally, but in the area that overlies the repository, flow is southward. These characterization and modeling activities conducted in the units above the Salado confirm that the Culebra is the most transmissive unit above the Salado. The Culebra is the unit into which actinides are likely to be introduced from long-term flow up an abandoned borehole. Regional variation in the Culebras groundwater flow direction is influenced by the transmissivity observed, as well as the lateral (facies) changes in the lithology of the Culebra in the groundwater basin where the WIPP is located. Site characterization activities have provided no evidence of karst groundwater systems in the controlled area, although groundwater flow in the Culebra is affected by the presence of fractures, fracture fillings, and vuggy pore features (see HYPERLINK "../Appendix_HYDRO/Appendix_HYDRO.htm" Appendix HYDRO-2009 and the HYPERLINK "../../references/CRA-2004/Chapter_2.pdf" \l "page=38" CRA-2004, Chapter 2.0, Section 2.1.3.5). Other laboratory and field activities have focused on the behavior of dissolved and colloidal actinides in the Culebra.
Basin-scale regional modeling of three-dimensional groundwater flow in the units above the Salado demonstrates that it is appropriate, for the purposes of estimating radionuclide transport, to conceptualize the Culebra as a two-dimensional confined aquifer (see the HYPERLINK "../../references/CRA-2004/Chapter_2.pdf" \l "page=87" CRA-2004, Chapter 2.0, Section 2.2.1.1). Uncertainty in the flow field is incorporated by using 100 different geostatistically based T fields, each of which is consistent with available head and transmissivity data (Appendix PA-2009, HYPERLINK "../Appendix_TFIELD/Appendix_TFIELD.htm" Appendix TFIELD-2009).
Groundwater flow in the Culebra is modeled as a steady-state process, but two mechanisms considered in the PA could affect flow in the future. Potash mining in the McNutt Potash Zone (hereafter referred to as the McNutt) of the Salado, which occurs now in the Delaware Basin outside the controlled area and may continue in the future, could affect flow in the Culebra if subsidence over mined areas causes fracturing or other changes in rock properties (see the HYPERLINK "../../references/CRA-2004/Chapter_6.pdf" \l "page=74" CRA2004, Chapter 6.0, Section 6.3.2.3). Climatic changes during the next 10,000 years may also affect groundwater flow by altering recharge to the Culebra (see the HYPERLINK "../../references/CRA-2004/Chapter_6.pdf" \l "page=138" CRA-2004, Chapter 6.0, Section 6.4.9 and the HYPERLINK "../../references/CCA/Appendix_CLI.pdf" CCA, Appendix CLI).
Consistent with regulatory criteria of HYPERLINK "40CFR194_32" 40 CFR 194.32, mining outside the controlled area is assumed to occur in the near future, and mining within the controlled area is assumed to occur with a probability of 1 in 100 per century (adjusted for the effectiveness of AICs during the first 100 years after closure). Consistent with regulatory guidance, the effects of mine subsidence are incorporated in PA by increasing the transmissivity of the Culebra over the areas identified as mineable by a factor sampled from a uniform distribution between 1 and 1000 ( HYPERLINK "../../references/Others/EPA_61_FR_5224_5245_February_9_1996.pdf" U.S. Environmental Protection Agency 1996a, p. 5229). T fields used in PA are therefore adjusted and steady-state flow fields calculated accordingly; once for mining that occurs only outside the controlled area, and once for mining that occurs both inside and outside the controlled area ( HYPERLINK "../Appendix_TFIELD/Appendix_TFIELD.htm" \l "TFIELD-9_0" Appendix TFIELD-2009, Section 9.0). Mining outside the controlled area is considered in both undisturbed and disturbed repository performance.
The extent to which the climate will change during the next 10,000 years and how such a change will affect groundwater flow in the Culebra are uncertain. Regional three-dimensional modeling of groundwater flow in the units above the Salado indicates that flow velocities in the Culebra may increase by a factor of 1 to 2.25 for reasonably possible future climates (see the HYPERLINK "../../references/CCA/Appendix_CLI.pdf" CCA, Appendix CLI). This uncertainty is incorporated in PA by scaling the calculated steady-state specific discharge within the Culebra by a sampled parameter within this range.
Actinide Transport in the Culebra
Field tests have shown that the Culebra is best characterized as a double-porosity medium for estimating contaminant transport in groundwater (see the HYPERLINK "../../references/CRA-2004/Chapter_2.pdf" \l "page=101" CRA-2004, Chapter 2.0, Section 2.2.1.4.1.2 and HYPERLINK "../Appendix_HYDRO/Appendix_HYDRO.htm" Appendix HYDRO-2009). Groundwater flow and advective transport of dissolved or colloidal species and particles occurs primarily in a small fraction of the rocks total porosity and corresponds to the porosity of open and interconnected fractures and vugs. Diffusion and slower advective flow occur in the remainder of the porosity, which is associated with the low-permeability dolomite matrix. Transported species, including actinides (if present), will diffuse into this porosity.
Diffusion from the advective porosity into the dolomite matrix will retard An transport through two mechanisms. Physical retardation occurs simply because actinides that diffuse into the matrix are no longer transported with the flowing groundwater. Transport is interrupted until they diffuse back into the advective porosity. In situ tracer tests have demonstrated this phenomenon. Chemical retardation also occurs within the matrix as actinides are sorbed onto dolomite grains. The relationship between sorbed and liquid concentrations is assumed to be linear and reversible. The distribution coefficients (Kds) that characterize the extent to which actinides will sorb on dolomite were based on experimental data (see the HYPERLINK "../../references/CRA-2004/Chapter_6.pdf" \l "page=109" CRA-2004, Chapter 6.0, Section 6.4.6.2).
Intrusion Scenarios
Human intrusion scenarios evaluated in the PA include both single intrusion events and combinations of multiple boreholes. Two different types of boreholes are considered: those that penetrate a pressurized brine reservoir in the underlying Castile Formation (hereafter referred to as the Castile), and those that do not.
The presence of a brine reservoir under the repository is speculative, but on the basis of current information cannot be ruled out. A pressurized brine reservoir was encountered at the WIPP-12 borehole within the controlled area to the north of the disposal region, and other pressurized brine reservoirs associated with regions of deformation in the Castile have been encountered elsewhere in the Delaware Basin (see the HYPERLINK "../../references/CRA-2004/Chapter_2.pdf" \l "page=90" CRA-2004, Chapter 2.0, Section 2.2.1.2.2). Based on a geostatistical analysis of the geophysical data of brine encounters in the region, the DOE estimates that there is a 0.08 probability that a random borehole penetrating waste in the WIPP will also penetrate an underlying brine reservoir (see the HYPERLINK "../../references/CCA/Appendix_MASS_Attachment_18.pdf" \l "page=26" CCA, Appendix MASS, Attachment 18-6). Upon their review of the CCA, the EPA determined that the DOE should treat this probability as uncertain, ranging from 0.01 to 0.60 in the CCA PAVT. The EPA also required the DOE to modify the assumptions concerning Castile properties to increase the brine reservoir volumes (HYPERLINK "../../references/Others/EPA_1998_TSD_194_23_Parameter_Justification_Report.pdf" \l "page=40"U.S. Environmental Protection Agency 1998b; Technical Support Document for 194.23: Parameter Justification Report, Section 5). The EPA determined that changing the rock compressibility and porosity of the Castile effectively modified the sampled brine reservoir volume to include the possibility of larger brine reservoir volumes like those encountered by the WIPP-12 borehole.
The primary consequence of penetrating a pressurized reservoir is to provide an additional source of brine beyond that which might flow into the repository from the Salado. Direct releases at the ground surface resulting from the first repository intrusion would be unaffected by additional Castile brine, even if it flowed to the surface, because brine moving straight up a borehole will not significantly mix with waste. However, the presence of Castile brine could significantly increase radionuclide releases in two ways. First, the volume of contaminated brine that could flow to the surface may be greater for a second or subsequent intrusion into a repository that has already been connected by a previous borehole to a Castile reservoir. Second, the volume of contaminated brine that may flow up an abandoned borehole after plug degradation may be greater for combinations of two or more boreholes that intrude the same panel if one of the boreholes penetrates a pressurized reservoir. Both processes are modeled in PA.
Compliance Demonstration Method
The DOEs approach to demonstrating continued compliance is the PA, which is based on the criteria indicated in HYPERLINK "40CFR194_34" section 194.34. The PA process comprehensively considers the FEPs relevant to disposal system performance (see HYPERLINK "../Appendix_SCR/Appendix_SCR.htm" Appendix SCR-2009). Those FEPs shown by screening analyses to potentially affect performance are included in quantitative calculations using a system of loosely coupled computer models to describe the interaction of the repository with the natural system, both with and without human intrusion. Uncertainty in parameter values is incorporated in the analysis by a Monte Carlo approach, in which multiple simulations (or realizations) are completed using sampled values for the imprecisely known input parameters (see the HYPERLINK "../../references/CRA-2004/Chapter_6.pdf" \l "page=32" CRA-2004, Chapter 6.0, Section 6.1.5). Distribution functions characterize the state of knowledge for these parameters, and each realization of the modeling system uses a different set of sampled input values. A sample size of 300 results in 300 different values of each parameter. Thus, there are 300 different sets (vectors) of input parameter values. These 300 vectors were divided among 3 replicates. Quality assurance activities demonstrate that the parameters, software, and analysis used in PA were the result of a rigorous process conducted under controlled conditions ( HYPERLINK "40CFR194_22" 40 CFR 194.22).
Of the FEPs considered, exploratory drilling for natural resources was identified as the only disruption with sufficient likelihood and consequence of impacting releases from the repository. For each vector of parameters values, 10,000 possible futures (realizations) are simulated, where a single future is defined as a series of intrusion events that occur randomly in space and time ( HYPERLINK \l "PA-2_2" Section REF _Ref203901263 \r \h \* MERGEFORMAT PA-2.2). Each of these futures is assumed to have an equal probability of occurring; hence a probability of 0.0001. Cumulative radionuclide releases from the disposal system are calculated for each future, and CCDFs are constructed by sorting the releases from smallest to largest and then summing the probabilities across the future. Mean CCDFs were then computed for the three replicates of sampled parameters (Section REF _Ref203901284 \r \h \* MERGEFORMAT PA-2.2).
Results of the PA
This section summarizes the results of the CRA-2009 PA and demonstrates that the WIPP continues to comply with the quantitative containment requirements in HYPERLINK "40CFR191_13" 40 CFR 191.13(a). The CRA-2009 PA is different than the original certification PA in the CCA and the PA in the CRA2004 PABC because it includes additional information, changes, and new data required by HYPERLINK "40CFR194_15" 40 CFR 194.15 recertification application requirements. HYPERLINK \l "Table_PA-1" REF _Ref49763357 \h \* MERGEFORMAT Table PA-1 details the changes and new information included in this PA.
The results of the CRA-2009 PA demonstrate that the repository continues to comply with the disposal standards. The key metric for regulatory compliance is the mean CCDF. HYPERLINK \l "Figure_PA-1" REF _Ref201626082 \h \* MERGEFORMAT Figure PA-1, which compares the overall mean CCDF for the CRA-2009 PA to the overall mean CCDF for the CRA-2004 PABC, demonstrates two key points. First, the overall mean CCDF lies entirely below the limits specified in section 191.13(a). Thus, the WIPP is in compliance with the containment requirements of HYPERLINK "40CFR191" Part 191. Second, for any probability, the expected releases in the CRA-2009 PA are only slightly higher than those in the CRA-2004 PABC, primarily because of the increased drilling rate.
Figure PA- SEQ Figure_PA- \* ARABIC 1. Overall Mean CCDFs for Total Normalized Releases: CRA-2009 PA and CRA-2004 PABC
Detailed results of the CRA-2009 PA are contained in HYPERLINK \l "PA-9_0" Section REF _Ref201632921 \r \h \* MERGEFORMAT PA-9.0, which describes sensitivity analyses conducted as the final step in the Monte Carlo analysis. These sensitivity analyses indicate the relative importance of each sampled parameter in terms of its contribution to uncertainty in estimating disposal system performance. Analyses also examine the sensitivity of intermediate performance measures to the sampled parameters. Examples of such intermediate performance measures include the quantity of radionuclides released to the accessible environment by any one mechanism (for example, cuttings or DBRs), and other model results that describe conditions of interest, such as disposal region pressure.
HYPERLINK \l "PA-9_0" Section REF _Ref201627224 \r \h \* MERGEFORMAT PA-9.0 presents CCDF distributions for each replication of the analysis, mean CCDFs, and an overall mean CCDF with the 95% confidence interval estimated from the 3 independent mean distributions. All 300 individual CCDFs, as well as the overall mean CCDF determined from the 3 replicates, lie entirely below and to the left of the limits specified in HYPERLINK "40CFR191_13" section191.13(a) (see HYPERLINK \l "Figure_PA-79" REF _Ref201123853 \h \* MERGEFORMAT Figure PA-79). Thus, the WIPP continues to comply with the containment requirements of HYPERLINK "40CFR191" Part 191. Comparing the results of the 3 replicates indicates that the sample size of 100 in each replicate is sufficient to generate a stable distribution of outcomes (see HYPERLINK \l "Figure_PA-80" REF _Ref201123868 \h \* MERGEFORMAT Figure PA-80). Within the region of regulatory interest (that is, at probabilities greater than 10(3/104 year [yr]), the mean CCDFs from each replicate are essentially indistinguishable from the overall mean.
As discussed in HYPERLINK \l "PA-9_1" Section REF _Ref201627265 \r \h \* MERGEFORMAT PA-9.1, HYPERLINK \l "PA-9_2" Section REF _Ref219618652 \r \h PA-9.2, and HYPERLINK \l "PA-9_3" Section REF _Ref201627267 \r \h \* MERGEFORMAT PA-9.3, examining the normalized releases from cuttings and cavings, spallings, and DBRs provides insight into the relative importance of each release modes contribution to the mean CCDFs location and the compliance determination. Releases from cuttings and cavings dominate the mean CCDF at high probabilities, while DBRs dominate the mean CCDF at low probabilities. Spallings are less important and have very little effect on the location of the mean. Subsurface releases from groundwater transport are less than 10(6 EPA units and make no contribution to the mean CCDFs location.
Uncertainties characterized in the natural system and the interaction of waste with the disposal system environment show little variation between the location of the mean CCDFs of the three replicates, providing additional confidence in the compliance determination. The natural and engineered barrier systems of the WIPP provide robust and effective containment of TRU waste even if the repository is penetrated by multiple borehole intrusions.
Conceptual Structure of the PA
This section outlines the conceptual structure of the WIPP PA. First, a discussion of the regulatory requirements is given. The requirements of HYPERLINK "40CFR191_13" section 191.13 and HYPERLINK "40CFR194_34" section 194.34 (summarized in HYPERLINK \l "PA-2_2_1" Section REF _Ref205275697 \r \h \* MERGEFORMAT PA-2.2.1) lead to the identification of three main PA components:
1. A probabilistic characterization of the likelihood for different futures to occur at the WIPP site over the next 10,000 years
2. A procedure for estimating the radionuclide releases to the accessible environment associated with each possible future that could occur at the WIPP site over the next 10,000 years
3. A probabilistic characterization of the uncertainty in the parameters used to estimate potential releases
The probabilistic methods employed in WIPP PA give rise to the CCDF specified in section 191.13(a) and the distributions specified by 40 CFR 194.34(b).
Regulatory Requirements
The methodology employed in PA derives from the EPAs standard for the geologic disposal of radioactive waste, Environmental Radiation Protection Standards for the Management and Disposal of Spent Nuclear Fuel, High-Level and Transuranic Radioactive Wastes ( HYPERLINK "40CFR191" Part 191) (U.S. Environmental Protection Agency 1993), which is divided into three subparts. HYPERLINK "40CFR191_Subpart_A" 40 CFR Part 191 Subpart A applies to a disposal facility prior to decommissioning and establishes standards for the annual radiation doses to members of the public from waste management and storage operations. HYPERLINK "40CFR191_Subpart_B" Part 191 Subpart B applies after decommissioning and sets probabilistic limits on cumulative releases of radionuclides to the accessible environment for 10,000 years ( HYPERLINK "40CFR191_13" section 191.13) and assurance requirements to provide confidence that section 191.13 will be met ( HYPERLINK "40CFR191_14" 40 CFR 191.14). Part 191 Subpart B also sets limits on radiation doses to members of the public in the accessible environment for 10,000 years of undisturbed repository performance ( HYPERLINK "40CFR191_15" section 191.15). HYPERLINK "40CFR191_Subpart_C" 40 CFR Part 191 Subpart C limits radioactive contamination of groundwater for 10,000 years after disposal ( HYPERLINK "40CFR191_24" section 191.24). In this recertification application, the DOE must demonstrate a reasonable expectation that the WIPP will continue to comply with the requirements of Part 191 Subparts B and C.
The following is the central requirement in Part 191 Subpart B, and the primary determinant of the PA methodology (HYPERLINK "../../references/Others/EPA_50_FR_38066_089_September_19_1985.pdf" \l "page=9"U.S. Environmental Protection Agency 1985, p. 38086).
191.13 Containment Requirements:
(a) Disposal systems for spent nuclear fuel or high-level or transuranic radioactive wastes shall be designed to provide a reasonable expectation, based upon performance assessments, that cumulative releases of radionuclides to the accessible environment for 10,000 years after disposal from all significant processes and events that may affect the disposal system shall:
(1) Have a likelihood of less than one chance in 10 of exceeding the quantities calculated according to Table 1 (Appendix A); and
(2) Have a likelihood of less than one chance in 1,000 of exceeding ten times the quantities calculated according to Table 1 (Appendix A).
(b) Performance assessments need not provide complete assurance that the requirements of 191.13(a) will be met. Because of the long time period involved and the nature of the events and processes of interest, there will inevitably be substantial uncertainties in projecting disposal system performance. Proof of the future performance of a disposal system is not to be had in the ordinary sense of the word in situations that deal with much shorter time frames. Instead, what is required is a reasonable expectation, on the basis of the record before the implementing agency, that compliance with 191.13(a) will be achieved.
HYPERLINK "40CFR191_13" Section 191.13(a) refers to quantities calculated according to Table 1 (Appendix A), which means a normalized radionuclide release to the accessible environment based on the type of waste being disposed, the initial waste inventory, and the size of release that may occur (HYPERLINK "../../references/Others/EPA_50_FR_38066_089_September_19_1985.pdf" \l "page=33"U.S. Environmental Protection Agency 1985, Appendix A). Table 1 of Appendix A specifies allowable releases (i.e., release limits) for individual radionuclides and is reproduced as HYPERLINK \l "Table_PA-2" REF _Ref207593286 \h \* MERGEFORMAT Table PA-2. The WIPP is a repository for TRU waste, which is defined as waste containing more than 100 nanocuries of alpha-emitting TRU isotopes, with half-lives greater than twenty years, per gram of waste ( HYPERLINK "../../references/Others/EPA_50_FR_38066_089_September_19_1985.pdf" \l "page=28" U.S. Environmental Protection Agency 1985, p. 38084). The normalized release R for TRU waste is defined by
(PA. SEQ Eq._PA- \* ARABIC 1)
where Qi is the cumulative release of radionuclide i to the accessible environment during the 10,000-year period following closure of the repository (curies [Ci]), Li is the release limit for radionuclide i given in REF _Ref207593286 \h \* MERGEFORMAT Table PA-2 (Ci), and C is the amount of TRU waste emplaced in the repository (Ci). In the CRA-2009 PA, C = 2.32 ( 106 Ci (HYPERLINK "../../references/Others/Leigh_Trone_2005_Calculation_of_Waste_Unit_Factor_ERMS539613.pdf" \l "page=5"Leigh and Trone 2005, Section 3). Further, accessible environment means (1) the atmosphere, (2) land surfaces, (3) surface waters, (4) oceans, and (5) all of the lithosphere beyond the controlled area. Controlled area means (1) a surface location, to be identified by PICs, that encompasses no more than 100 square kilometers (km2) and extends horizontally no more than 5 kilometers (km) in any direction from the outer boundary of the original radioactive wastes location in a disposal system, and (2) the subsurface underlying such a location ( HYPERLINK "40CFR191_12" section 191.12).
PAs are the basis for addressing the containment requirements. To help clarify the intent of HYPERLINK "40CFR191" Part 191, the EPA promulgated HYPERLINK "40CFR194" 40 CFR Part 194 (2004), Criteria for the Certification and
Table PA- SEQ Table_PA- \* ARABIC 2. Release Limits for the Containment Requirements ( HYPERLINK "../../references/Others/EPA_50_FR_38066_089_September_19_1985.pdf" \l "page=33" U.S. Environmental Protection Agency 1985, Appendix A, Table 1)
RadionuclideRelease Limit Li per 1000 MTHMa or Other Unit of WastebAmericium-241 or -243100Carbon-14100Cesium-135 or -1371,000Iodine-129100Neptunium-237100Pu-238, -239, -240, or -242100Radium-226100Strontium-901,000Technetium-9910,000Thorium (Th) -230 or -23210Tin-1261,000Uranium (U) -233, -234, -235, -236, or -238100Any other alpha-emitting radionuclide with a half-life greater than 20 years100Any other radionuclide with a half-life greater than 20 years that does not emit alpha particles1,000a Metric tons of heavy metal (MTHM) exposed to a burnup between 25,000 megawatt-days (MWd) per metric ton of heavy metal (MWd/MTHM) and 40,000 MWd/MTHM.
b An amount of TRU wastes containing one million Ci of alpha-emitting TRU radionuclides with half-lives greater than 20 years.Recertification of the Waste Isolation Pilot Plants Compliance with the HYPERLINK "40CFR191" Part 191 Disposal Regulations. There, an elaboration on the intent of HYPERLINK "40CFR191_13" section 191.13 is prescribed.
194.34 Results of performance assessments.
(a) The results of performance assessments shall be assembled into complementary, cumulative distributions functions (CCDFs) that represent the probability of exceeding various levels of cumulative release caused by all significant processes and events.
(b) Probability distributions for uncertain disposal system parameter values used in performance assessments shall be developed and documented in any compliance application.
(c) Computational techniques, which draw random samples from across the entire range of the probability distributions developed pursuant to paragraph (b) of this section, shall be used in generating CCDFs and shall be documented in any compliance application.
(d) The number of CCDFs generated shall be large enough such that, at cumulative releases of 1 and 10, the maximum CCDF generated exceeds the 99th percentile of the population of CCDFs with at least a 0.95 probability.
(e) Any compliance application shall display the full range of CCDFs generated.
(f) Any compliance application shall provide information which demonstrates that there is at least a 95% level of statistical confidence that the mean of the population of CCDFs meets the containment requirements of 191.13 of this chapter.
The DOEs methodology for PA uses information about the disposal system and waste to evaluate performance over the 10,000-year regulatory time period. To accomplish this task, the FEPs with potential to affect the future of the WIPP are first defined ( HYPERLINK \l "PA-2_3_1" Section REF _Ref203993034 \r \h \* MERGEFORMAT PA-2.3.1). Next, scenarios that describe potential future conditions in the WIPP are formed from logical groupings of retained FEPs ( HYPERLINK \l "PA-2_3_2" Section REF _Ref203993502 \r \h \* MERGEFORMAT PA-2.3.2). The scenario development process results in a probabilistic characterization for the likelihood of different futures that could occur at the WIPP ( HYPERLINK \l "PA-2_2_2" Section REF _Ref203993083 \r \h \* MERGEFORMAT PA-2.2.2). Using the retained FEPs, models are developed to estimate the radionuclide releases from the repository ( HYPERLINK \l "PA-2_2_3" Section REF _Ref203993091 \r \h \* MERGEFORMAT PA-2.2.3). Finally, uncertainty in model parameters is characterized probabilistically ( HYPERLINK \l "PA-2_2_4" Section REF _Ref203993095 \r \h \* MERGEFORMAT PA-2.2.4).
Probabilistic Characterization of Different Futures
As discussed in HYPERLINK \l "PA-2_3_1" Section REF _Ref203993476 \r \h \* MERGEFORMAT PA-2.3.1, the CCA PA scenario development process for the WIPP identified exploratory drilling for natural resources as the only disruption with sufficient likelihood and consequence of impacting releases from the repository (see the HYPERLINK "../../references/CCA/Appendix_SCR.pdf" CCA, Appendix SCR). In addition, HYPERLINK "40CFR194" Part 194 specifies that the occurrence of mining within the LWB must be included in the PA. This has not changed for the CRA-2009 PA. As a result, the projection of releases over the 10,000 years following closure of the WIPP is driven by the nature and timing of intrusion events.
The collection of all possible futures xst forms the basis for the probability space (Sst, Sst, pst) characterizing aleatory uncertainty, where Sst = {xst : xst is a possible future of the WIPP}, Sst is a suitably restricted collection of sets of futures, called scenarios ( HYPERLINK \l "PA-3_10" Section PA-3.10), and pst is a probability measure for the elements of Sst . A possible future, xst,i, is thus characterized by the collection of intrusion events that occur in that future:
EMBED Equation.DSMT4 (PA. SEQ Eq._PA- \* ARABIC 2)
where
n is the number of drilling intrusions
tj is the time (year) of the jth intrusion
lj designates the location of the jth intrusion
ej designates the penetration of an excavated or nonexcavated area by the jth intrusion
bj designates whether or not the jth intrusion penetrates pressurized brine in the Castile Formation
pj designates the plugging procedure used with the jth intrusion (i.e., continuous plug, two discrete plugs, three discrete plugs)
aj designates the type of waste penetrated by the jth intrusion (i.e., no waste, CH-TRU waste, RH-TRU waste, and, for CH-TRU waste, the waste streams encountered)
tmin is the time at which potash mining occurs within the LWB
The subscript st indicates that aleatory (i.e., stochastic) uncertainty is being considered; the letters st are retained for historical context. The subscript i indicates that the future xst is one of many sample elements from Sst.
The probabilistic characterization of n, tj, lj, and ej is based on the assumption that drilling intrusions will occur randomly in time and space at a constant average rate (i.e., follow a Poisson process); the probabilistic characterization of bj derives from assessed properties of brine pockets; the probabilistic characterization of aj derives from the volumes of waste emplaced in the WIPP in relation to the volume of the repository; and the probabilistic characterization of pj derives from current drilling practices in the sedimentary basin (i.e., the Delaware Basin) in which the WIPP is located. A vector notation is used for aj because it is possible for a given drilling intrusion to miss the waste or to penetrate different waste types (CH-TRU and RH-TRU) as well as to encounter different waste streams in the CH-TRU waste. Further, the probabilistic characterization for tmin follows from the criteria in HYPERLINK "40CFR194" Part 194 that the occurrence of potash mining within the LWB should be assumed to occur randomly in time (i.e., follow a Poisson process with a rate constant of (m = 10(4 yr(1), with all commercially viable potash reserves within the LWB extracted at time tmin. In practice, the probability measure pst is defined by specifying probability distributions for each component of xst, as discussed further in HYPERLINK \l "PA-3_0"Section REF _Ref205874985 \r \h \* MERGEFORMAT PA-3.0.
Estimation of Releases
Based on the retained FEPs ( HYPERLINK \l "PA-2_3_1" Section REF _Ref203993744 \r \h \* MERGEFORMAT PA-2.3.1), release mechanisms include direct transport of material to the surface at the time of a drilling intrusion (i.e., cuttings, spallings, and brine flow) and release subsequent to a drilling intrusion due to brine flow up a borehole with a degraded plug (i.e., groundwater transport). The quantities of releases are determined by the state of the repository through time, which is determined by the type, timing, and sequence of prior intrusion events. For example, pressure in the repository is an important determinant of spallings, and the amount of pressure depends on whether the drilling events that have occurred penetrated brine pockets and how long prior to the current drilling event the repository was inundated.
Computational models for estimating releases were developed using the retained FEPs; these models are summarized in HYPERLINK \l "Figure_PA-2" REF _Ref200960852 \h \* MERGEFORMAT Figure PA-2. These computational models implement the conceptual models representing the repository system as described in HYPERLINK "40CFR194_23" section 194.23 and the mathematical models for physical processes presented in HYPERLINK \l "PA-4_0"Section REF _Ref205874997 \r \h \* MERGEFORMAT PA-4.0. Most of the computational models involve the numerical solution of partial differential equations (PDEs) used to represent processes such as material deformation, fluid flow, and radionuclide transport.
The collection of computation models can be represented abstractly as a function f(xst|vsu), which quantifies the release that could result from the occurrence of a specific future xst and a specific set of values for model parameters vsu. Because the future of the WIPP is unknown, the values of f(xst|vsu) are uncertain. Thus, the probability space (Sst, Sst, pst), together with the function f(xst|vsu), give rise to the CCDF specified in HYPERLINK "40CFR191_13" section 191.13(a), as illustrated in HYPERLINK \l "Figure_PA-3" REF _Ref200960816 \h \* MERGEFORMAT Figure PA-3. The CCDF represents the probability that a release from the repository greater than R will be observed, where R is a point on the abscissa (x-axis) of the graph ( REF _Ref200960816 \h \* MERGEFORMAT Figure PA-3).
Formally, the CCDF depicted in REF _Ref200960816 \h \* MERGEFORMAT Figure PA-3 results from an integration over the probability space (Sst, Sst, pst):
EMBED Equation.DSMT4 (PA. SEQ Eq._PA- \* ARABIC 3)
where (R(f(xst|vsu)) = 1 if f(xst|vsu) > R, (R(f(xst|vsu)) = 0 if f(xst|vsu) ( R, and dst(xst|vsu) is the probability density function associated with the probability space (Sst, Sst, pst). In practice, the integral in Equation ( REF EQ_PA3 \h \* MERGEFORMAT PA.3) is evaluated by a Monte Carlo technique, where a random sample xst,i, i = 1, nR, is generated from Sst consistent with the probability distribution pst. Using this random sample, Equation ( REF EQ_PA3 \h \* MERGEFORMAT PA.3) is numerically evaluated as
EMBED Equation.DSMT4 (PA. SEQ Eq._PA- \* ARABIC 4)
The models in REF _Ref200960852 \h \* MERGEFORMAT Figure PA-2 are too complex to permit a closed-form evaluation of the integral in Equation ( REF EQ_PA4 \h \* MERGEFORMAT PA.4) that defines the CCDF specified in HYPERLINK "40CFR191" Part 191. In WIPP PA, these probability distribution functions (PDFs) are constructed using Monte Carlo simulation to sample the entire possible set of release outcomes. As long as the sampling is conducted properly and a sufficient number of samples is collected, the PDF of the sample should successfully approximate the PDF of the sample universe of all possible releases.
Figure PA- SEQ Figure_PA- \* ARABIC 2. Computational Models Used in PA
Figure PA- SEQ Figure_PA- \* ARABIC 3. Construction of the CCDF Specified in HYPERLINK "40CFR191_Subpart_B" 40 CFR Part 191 Subpart B
In PA, the number of samples nR used to construct a CCDF is 10,000. However, the models in HYPERLINK \l "Figure_PA-2" REF _Ref200960852 \h \* MERGEFORMAT Figure PA-2 are also too computationally intensive to permit their evaluation for each of these 10,000 futures. Due to this constraint, the models in REF _Ref200960852 \h \* MERGEFORMAT Figure PA-2 are evaluated for a relatively small number of specific scenarios, and the results of these evaluations are used to construct CCDFs. The representative scenarios are labeled E0, E1, E2, and E1E2, and are defined in HYPERLINK \l "PA-3_10" Section REF _Ref200960987 \r \h \* MERGEFORMAT PA-3.10; the procedure for constructing a CCDF from these scenarios is described in HYPERLINK \l "PA-6_0" Section REF _Ref203994350 \r \h \* MERGEFORMAT PA-6.0.
Probabilistic Characterization of Parameter Uncertainty
If the parameters used in the process-level models of HYPERLINK \l "Figure_PA-2" REF _Ref200960852 \h \* MERGEFORMAT Figure PA-2 were precisely known and if the models could accurately predict the future behavior of the repository, the evaluation of repository performance alone would be sufficient to answer the first three questions related to repository performance. However, the models do not perfectly represent the dynamics of the system and their parameters are not precisely known. Therefore, it is necessary to estimate the confidence one has in the CCDFs being constructed. The confidence in the CCDFs is established using Monte Carlo methods to evaluate how the uncertainty in the model parameters impacts the CCDFs or releases. The probabilistic characterization of the uncertainty in the model parameters is the outcome of the data development effort for the WIPP (summarized in HYPERLINK "../../references/Others/Fox_2008_Parameter_Report_CRA_2009_ERMS549747.pdf" \l "page=36"Section 8.0 in Fox 2008).
Formally, uncertainty in the parameters that underlie the WIPP PA can be characterized by a second probability space (Ssu, Ssu, psu), where the sample space Ssu is defined by
Ssu = {vsu: vsu is a sampled vector of parameter values} (PA. SEQ Eq._PA- \* ARABIC 5)
The subscript su indicates that epistemic (i.e., subjective) uncertainty is being considered; the letters su are retained for historical context. An element vsu ( Ssu is a vector vsu = vsu,1, vsu,2, & , vsu,N) of length N, where each element vsu,k is an uncertain parameter used in the models to estimate releases. In practice, the probability measure psu is defined by specifying probability distributions for each element of vsu, discussed further in HYPERLINK \l "PA-5_0" Section REF _Ref203994505 \r \h \* MERGEFORMAT PA-5.0.
If the actual value for vsu were known, the CCDF resulting from evaluation of Equation ( REF EQ_PA4 \h \* MERGEFORMAT PA.4) could be determined with certainty and compared with the criteria specified in HYPERLINK "40CFR191" Part 191. However, given the complexity of the WIPP site, the 10,000-year period under consideration, and the state of knowledge about the natural and engineered system, values for vsu are not known with certainty. Rather, the uncertainty in vsu is characterized probabilistically, as described above, leading to a distribution of CCDFs ( HYPERLINK \l "Figure_PA-4" REF _Ref200961257 \h \* MERGEFORMAT Figure PA-4) with each CCDF resulting from one of many vectors of values of vsu. The uncertainty associated with the parameters is termed epistemic uncertainty, and has been referred to in WIPP PA documentation as subjective uncertainty.
WIPP PA uses a Monte Carlo procedure for evaluating the effects of epistemic uncertainty on releases. The procedure involves sampling the distributions assigned to the uncertain parameters and generating a CCDF of releases based on the results of the process-level models generated using those parameters values. By repeating this process many times, a distribution of the
Figure PA- SEQ Figure_PA- \* ARABIC 4. Distribution of CCDFs Resulting from Possible Values for the Sampled Parameters
CCDFs can be constructed. The requirements of HYPERLINK "40CFR191_13" section 191.13 are evaluated, in part, using the mean probability of release. The overall mean probability curve is created by averaging across the CCDFs for releases, i.e., averaging the CCDFs across vertical slices ( HYPERLINK \l "Figure_PA-4" REF _Ref200961257 \h \* MERGEFORMAT Figure PA-4) (a formal definition is provided in HYPERLINK "../../references/Others/Helton_et_al_1998_Uncertainty_Sensitivity_Analysis_Results_SAND98_0365.pdf" Helton et al. 1998). In addition, confidence limits on the mean are computed using standard t-statistics ( HYPERLINK \l "Figure_PA-5" REF _Ref200961270 \h \* MERGEFORMAT Figure PA-5). The proximity of these curves to the boundary line in HYPERLINK \l "Figure_PA-3" REF _Ref200960816 \h \* MERGEFORMAT Figure PA-3 indicates the confidence with which HYPERLINK "40CFR191" Part 191 will be met. Confidence is also established by examining the distribution of the CCDFs in relation to the release limits ( HYPERLINK \l "Figure_PA-6" REF _Ref200961294 \h \* MERGEFORMAT Figure PA-6).
WIPP PA uses a stratified sampling design called LHS ( HYPERLINK "../../references/Others/Mckay_Beckman_Conover_1979.pdf" McKay, Beckman, and Conover 1979) to generate a sample vsu, i = 1, , nLHS, from Ssu consistent with the probability distribution psu. LHS is an efficient scheme for sampling the range of a distribution using a relatively small sample. Based on order statistics, the sample size of nLHS = 300 replicates would provide coverage of 99% of the CCDF distribution with a confidence of 95%.
In HYPERLINK "40CFR194" Part 194, the EPA decided that the statistical portion of the determination of compliance with Part 191 will be based on the sample mean. The LHS sample sizes should be demonstrated operationally to improve (reduce the size of) the confidence interval for the estimated mean. The underlying principle is to show convergence of the mean (HYPERLINK "../../references/Others/EPA_1996_Background_Information_Document_for_40CFR194.pdf" \l "page=261"U.S. Environmental Protection Agency 1996b, p. 8-41).
Figure PA- SEQ Figure_PA- \* ARABIC 5. Example Mean Probability of Release and the Confidence Limits on the Mean from CRA-2009 PA
Figure PA- SEQ Figure_PA- \* ARABIC 6. Example CCDF Distribution From CRA-2009 PA (Replicate 1)
The DOE has chosen to demonstrate repeatability of the mean and to address the associated criteria of HYPERLINK "40CFR194" Part 194 using an operational approach of multiple replication, as proposed by Iman ( HYPERLINK "../../references/Others/NUREG_CP_0022.pdf" 1982). The complete set of PA calculations was repeated three times with all aspects of the analysis identical except for the random seed used to initiate the LHS procedure. Thus, PA results are available for 3 replicates, each based on an independent set of 100 LHS vectors drawn from identical distributions for imprecisely known parameters and propagated through an identical modeling system. This technique of multiple replication allows the adequacy of the sample size chosen in the Monte Carlo analysis to be evaluated and provides a suitable measure of confidence in the mean CCDF estimation used to demonstrate compliance with HYPERLINK "40CFR191_13" section 191.13(a).
PA Methodology SEQ CHAPTER \h \r 1
This section addresses scenarios formed from FEPs that were retained for PA calculations, and introduces the specification of scenarios for consequence analysis.
Identification and Screening of FEPs
The EPA has provided criteria concerning the scope of PAs in HYPERLINK "40CFR194_32" 40 CFR 194.32. In particular, criteria relating to the identification of potential processes and events that may affect disposal system performance are provided in 40 CFR 194.32(e), which states
Any compliance application(s) shall include information which:
(1) Identifies all potential processes, events or sequences and combinations of processes and events that may occur during the regulatory time frame and may affect the disposal system;
(2) Identifies the processes, events or sequences and combinations of processes and events included in performance assessments; and
(3) Documents why any processes, events or sequences and combinations of processes and events identified pursuant to paragraph (e)(1) of this section were not included in performance assessment results provided in any compliance application.
HYPERLINK "../Section_32/Section_32.htm" Section 32 of this application fulfills these criteria by documenting the DOEs identification, screening, and screening results of all potential processes and events consistent with the criteria specified in section194.32(e).
The first two steps in scenario development involve identifying and screening FEPs that are potentially relevant to the performance of the disposal system. The HYPERLINK "../../references/CRA-2004/Chapter_6.pdf" \l "page=35" CRA-2004, Chapter 6.0, Section 6.2 discusses the development of a comprehensive initial FEPs set used in the CCA, the methodology and criteria used for screening, the method used to reassess the CCA FEPs for the CRA-2004, and a summary of the FEPs retained for scenario development. Changes to FEPs since the CRA-2004 are outlined in Section 32 and HYPERLINK "../Appendix_SCR/Appendix_SCR.htm" Appendix SCR-2009 of this application.
The original FEPs generation and screening were documented in the CCA, and the resulting FEPs list became the FEPs compliance baseline. The baseline contained 237 FEPs and was documented the HYPERLINK "../../references/CCA/Appendix_SCR.pdf" CCA, Appendix SCR. The EPA compliance review of FEPs was documented in EPAs Technical Support Document 194.32: Scope of PA ( HYPERLINK "../../references/Others/EPA_1998_TSD_194_32_Scope_of_Performance_Assessments.pdf" U.S. Environmental Protection Agency 1998c). The EPA numbered each FEP with a different scheme than the DOE used for the CCA. The DOE has since adopted the EPAs numbering scheme.
Scenario Development and Selection
Logic diagrams illustrate the formation of scenarios for consequence analysis from combinations of events that remain after FEP screening ( HYPERLINK "../../references/Others/Cranwell_et_al_Risk_Methodology_for_Geologic_Disposal_SAND80_1429.pdf" Cranwell et al. 1990) ( HYPERLINK \l "Figure_PA-7" REF _Ref203992008 \h \* MERGEFORMAT Figure PA-7). Each scenario shown in REF _Ref203992008 \h \* MERGEFORMAT Figure PA-7 is defined by a combination of occurrence and nonoccurrence for all potentially disruptive events. Disruptive events are defined as those that create new pathways or significantly alter existing pathways for fluid flow and, potentially, radionuclide transport within the disposal system. Each of these scenarios also contains a set of features and nondisruptive events and processes that remain after FEP screening. As shown in REF _Ref203992008 \h \* MERGEFORMAT Figure PA-7, undisturbed repository performance (UP) and disturbed repository performance (DP) scenarios are considered in consequence modeling for the WIPP PA. The UP scenario is used for compliance assessments ( HYPERLINK "40CFR194_54" 40 CFR 194.54 and HYPERLINK "40CFR194_55" 40 CFR 194.55). Important aspects of UP and DP scenarios are summarized in this section.
Undisturbed Repository Performance
The UP scenario is defined in HYPERLINK "40CFR191_12" 40 CFR 191.12 to mean the predicted behavior of a disposal system, including consideration of the uncertainties in predicted behavior, if the disposal system is not disrupted by human intrusion or the occurrence of unlikely natural events. For compliance assessments with respect to the Individual and Groundwater Protection Requirements ( HYPERLINK "40CFR191_15" section191.15; HYPERLINK "../Appendix_IGP/Appendix_IGP.htm" Appendix IGP-2009), it is only necessary to consider the UP scenario. The UP scenario is also considered with DP scenario for PA with respect to the containment requirements ( HYPERLINK "40CFR191_13" section191.13).
No potentially disruptive natural events and processes are likely to occur during the regulatory time frame. Therefore, all naturally occurring events and processes retained for scenario construction are nondisruptive and are considered part of the UP scenario. Mining outside the LWB is assumed at the end of AIC for all scenarios. The M scenario involves future mining within the controlled area. The disturbed repository E scenario involves at least one deep drilling event that intersects the waste disposal region. The M scenario and the E scenario may both occur in the future. The DOE calls a future in which both of these events occur the ME scenario. More detailed descriptions are found in HYPERLINK \l "PA-2_3_2_2" Section REF _Ref212453078 \r \h PA-2.3.2.2.
The only natural features and waste- and repository-induced FEPs retained after screening that are excluded in the UP scenario, but included in the DP scenario, are those directly associated with the potential effects of future deep drilling within the controlled area. Among the most significant FEPs that will affect the UP scenario within the disposal system are excavation-induced fracturing, gas generation, salt creep, and MgO in the disposal rooms.
The repository excavation and consequent changes in the rock stress field surrounding the excavated opening will create a DRZ immediately adjacent to excavated openings. The DRZ will exhibit mechanical and hydrological properties different than those of the intact rock.
Figure PA- SEQ Figure_PA- \* ARABIC 7. Logic Diagram for Scenario Analysis
Organic material in the waste may degrade because of microbial activity, and brine will corrode metals in the waste and waste containers, with concomitant generation of gases. Gas generation may result in pressures sufficient to both maintain or develop fractures and change the fluid flow pattern around the waste disposal region.
At the repository depth, salt creep will tend to heal fractures and reduce the permeability of the DRZ and the crushed salt component of the long-term shaft seals to near that of the host rock salt.
The MgO engineered barrier emplaced in the disposal rooms will react with CO2 and maintain mildly alkaline conditions. Metal corrosion in the waste and waste containers will maintain reducing conditions. These effects will maintain low radionuclide solubility.
Radionuclides can become mobile as a result of waste dissolution and colloid generation following brine flow into the disposal rooms. Colloids may be generated from the waste (humics, mineral fragments, and An intrinsic colloids) or from other sources (humics, mineral fragments, and microbes).
Conceptually, there are several pathways for radionuclide transport within the undisturbed disposal system that may result in releases to the accessible environment ( HYPERLINK \l "Figure_PA-8" REF _Ref203994850 \h \* MERGEFORMAT Figure PA-8). Contaminated brine may migrate away from the waste-disposal panels if pressure within the panels is elevated by gas generated from corrosion or microbial consumption. Radionuclide transport may occur laterally, through the anhydrite interbeds toward the subsurface boundary of the accessible environment in the Salado, or through access drifts or anhydrite interbeds to the base of the shafts. In the latter case, if the pressure gradient between the panels and overlying strata is sufficient, contaminated brine may migrate up the shafts. As a result, radionuclides may be transported directly to the ground surface, or laterally away from the shafts through permeable strata such as the Culebra, toward the subsurface boundary of the accessible environment. These conceptual pathways are shown in REF _Ref203994850 \h \* MERGEFORMAT Figure PA-8.
Figure PA- SEQ Figure_PA- \* ARABIC 8. Conceptual Release Pathways for the UP Scenario
The modeling system described in HYPERLINK \l "PA-4_0" Section REF _Ref201628228 \r \h \* MERGEFORMAT PA-4.0 includes potential radionuclide transport along other pathways, such as migration through Salado halite. However, the natural properties of the undisturbed system make radionuclide transport to the accessible environment via these other pathways unlikely.
Disturbed Repository Performance
Assessments for compliance with HYPERLINK "40CFR191_13" section191.13 need to consider the potential effects of future disruptive natural and human-initiated events and processes on the performance of the disposal system. No potentially disruptive natural events and processes are considered sufficiently likely to require inclusion in analyses of either the UP or DP scenario. The only future human-initiated events and processes retained after FEP screening are those associated with mining and deep drilling (but not the subsequent use of a borehole) within the controlled area or LWB when institutional controls cannot be assumed to eliminate the possibility of such activities ( HYPERLINK \l "PA-3_2" Section REF _Ref205875488 \r \h PA-3.2 and the HYPERLINK "../../references/CRA-2004/Chapter_6.pdf" \l "page=151" CRA-2004, Chapter 6.0, Section 6.4.12.1). In total, 21 disturbed repository FEPs associated with future mining and deep drilling have been identified. These FEPs were assigned a screening designator of the DP scenario.
For evaluating the consequences of disturbed repository performance, the DOE has defined the mining scenario (M), the deep drilling scenario (E), and a mining and drilling scenario (ME). These scenarios are described in the following sections.
Disturbed Repository M Scenario
The M scenario involves future mining within the controlled area. Consistent with the criteria stated by the EPA in HYPERLINK "40CFR194_32" 40 CFR 194.32(b) for PA calculations, the effects of potential future mining within the controlled area are limited to changes in hydraulic conductivity of the Culebra that result from subsidence (as described in HYPERLINK \l "PA-3_9"Section REF _Ref201628497 \r \h \* MERGEFORMAT PA-3.9).
Radionuclide transport may be affected in the M scenario if a head gradient between the waste-disposal panels and the Culebra causes brine contaminated with radionuclides to move from the waste-disposal panels to the base of the shafts and up to the Culebra. The changes in the Culebra T field may affect the rate and direction of radionuclide transport within the Culebra. Features of the M scenario are illustrated in HYPERLINK \l "Figure_PA-9" REF _Ref203994934 \h \* MERGEFORMAT Figure PA-9.
The three disturbed repository FEPs labeled M in the HYPERLINK "../../references/CRA-2004/Chapter_6.pdf" \l "page=70" CRA-2004, Chapter 6.0, Table 6-9 are related to the occurrence and effects of future mining. The modeling system used for the M scenario is similar to that developed for the UP scenario, but with a modified Culebra T field in the controlled area to account for the mining effects.
Disturbed Repository E Scenario
The disturbed repository E scenario involves at least one deep drilling event that intersects the waste disposal region. The EPA provides criteria for analyzing the consequences of future drilling events in PA in HYPERLINK "40CFR194_33" 40 CFR 194.33(c).
Performance assessments shall document that in analyzing the consequences of drilling events, the Department assumed that:
(1) Future drilling practices and technology will remain consistent with practices in the Delaware Basin at the time a compliance application is prepared. Such future drilling practices shall include, but shall not be limited to: the types and amounts of drilling fluids; borehole depths, diameters, and seals; and the fraction of such boreholes that are sealed by humans; and
Figure PA- SEQ Figure_PA- \* ARABIC 9. Conceptual Release Pathways for the Disturbed Repository M Scenario
(2) Natural processes will degrade or otherwise affect the capability of boreholes to transmit fluids over the regulatory time frame.
Consistent with these criteria, there are several pathways for radionuclides to reach the accessible environment in the E scenario. Before any deep drilling intersects the waste, potential release pathways are identical to those in the undisturbed repository scenario.
If a borehole intersects the waste in the disposal rooms, releases to the accessible environment may occur as material entrained in the circulating drilling fluid is brought to the surface. Particulate waste brought to the surface may include cuttings, cavings, and spallings. Cuttings are the materials cut by the drill bit as it passes through waste. Cavings are the materials eroded by the drilling fluid in the annulus around the drill bit. Spallings are the materials forced into the circulating drilling fluid if there is sufficient pressure in the waste disposal panels. During drilling, contaminated brine may flow up the borehole and reach the surface, depending on fluid pressure within the waste disposal panels.
When abandoned, the borehole is assumed to be plugged in a manner consistent with current practices in the Delaware Basin as prescribed in HYPERLINK "40CFR194_33" 40 CFR 194.33(c)(1). An abandoned intrusion borehole with degraded casing and/or plugs may provide a pathway for fluid flow and contaminant transport from the intersected waste panel to the ground surface if the fluid pressure within the panel is sufficiently greater than hydrostatic. Additionally, if brine flows through the borehole to overlying units, such as the Culebra, it may carry dissolved and colloidal actinides that can be transported laterally to the accessible environment by natural groundwater flow in the overlying units.
Alternatively, the units intersected by an intrusion borehole may provide sources for brine flow to a waste panel during or after drilling. For example, in the northern Delaware Basin, the Castile, which underlies the Salado, contains isolated volumes of brine at fluid pressures greater than hydrostatic (as discussed in the HYPERLINK "../../references/CRA-2004/Chapter_2.pdf" \l "page=90" CRA-2004, Chapter 2.0, Section 2.2.1.2.2). The WIPP-12 penetration of one of these reservoirs provided data on one brine reservoir within the controlled area. The location and properties of brine reservoirs cannot be reliably predicted; thus, the possibility of a deep borehole penetrating both a waste panel and a brine reservoir is accounted for in consequence analysis of the WIPP, as discussed in the HYPERLINK "../../references/CRA-2004/Chapter_6.pdf" \l "page=136"CRA-2004, Chapter 6.0, Section 6.4.8. Such a borehole could provide a connection for brine flow from the Castile to the waste panel, thus increasing fluid pressure and brine volume in the waste panel.
A borehole that is drilled through a disposal room pillar, but does not intersect waste, could also penetrate the brine reservoir underlying the waste disposal region. Such an event would, to some extent, depressurize the brine reservoir, and thus would affect the consequences of any subsequent reservoir intersections. The PA does not take credit for possible brine reservoir depressurization.
The DOE has distinguished two types of deep drilling events by whether or not the borehole intersects a Castile brine reservoir. A borehole that intersects a waste disposal panel and penetrates a Castile brine reservoir is designated an E1 event. A borehole that intersects a waste panel but does not penetrate a Castile brine reservoir is designated an E2 event. The consequences of deep drilling intrusions depend not only on the type of a drilling event, but on whether the repository was penetrated by an earlier E2 event or flooded due to an earlier E1 event. The PA also does not take credit for depressurization of brine reservoirs from multiple drilling intrusions. These scenarios are described in order of increasing complexity in the following sections.
The E2 Scenario
The E2 scenario is the simplest scenario for inadvertent human intrusion into a waste disposal panel. In this scenario, a panel is penetrated by a drill bit; cuttings, cavings, spallings, and brine flow releases may occur; and brine flow may occur in the borehole after it is plugged and abandoned. Sources for brine that may contribute to long-term flow up the abandoned borehole are the Salado or, under certain conditions, the units above the Salado. An E2 scenario may involve more than one E2 drilling event, although the flow and transport model configuration developed for the E2 scenario evaluates the consequences of futures that have only one E2 event. Features of the E2 scenario are illustrated in HYPERLINK \l "Figure_PA-10" REF _Ref203994960 \h \* MERGEFORMAT Figure PA-10.
Figure PA- SEQ Figure_PA- \* ARABIC 10. Conceptual Release Pathways for the Disturbed Repository Deep Drilling E2 Scenario
The E1 Scenario
Any scenario with exactly one inadvertent penetration of a waste panel that also penetrates a Castile brine reservoir is called E1. Features of this scenario are illustrated in HYPERLINK \l "Figure_PA-11" REF _Ref204048331 \h \* MERGEFORMAT Figure PA-11.
Sources of brine in the E1 scenario are the brine reservoir, the Salado, and, under certain conditions, the units above the Salado. However, the brine reservoir is conceptually the dominant source of brine in this scenario. The flow and transport model configuration developed for the E1 scenario evaluates the consequences of futures that have only one E1 event.
Figure PA- SEQ Figure_PA- \* ARABIC 11. Conceptual Release Pathways for the Disturbed Repository Deep Drilling E1 Scenario
The E1E2 Scenario
The E1E2 scenario is defined as all futures with multiple penetrations of a waste panel of which at least one intrusion is an E1. One example of this scenario, with a single E1 event and a single E2 event penetrating the same panel, is illustrated in HYPERLINK \l "Figure_PA-12" REF _Ref204048347 \h \* MERGEFORMAT Figure PA-12. However, the E1E2 scenario can include many possible combinations of intrusion times, locations, and types of event (E1 or E2). The sources of brine in this scenario are those listed for the E1 scenario, and multiple E1 sources may be present. The E1E2 scenario has a potential flow path not present in the E1 or E2 scenarios: flow from an E1 borehole through the waste to another borehole. This flow path has the potential to (1) bring large quantities of brine in direct contact with waste and (2) provide a
Figure PA- SEQ Figure_PA- \* ARABIC 12. Conceptual Release Pathways for the Disturbed Repository Deep Drilling E1E2 Scenario
less restrictive path for this brine to flow to the units above the Salado (via multiple boreholes) compared to either the individual E1 or E2 scenarios. It is both the presence of brine reservoirs and the potential for flow through the waste to other boreholes that make this scenario different from combinations of E2 boreholes in terms of potential consequences. Estimates from flow and transport modeling are used to determine the extent of flow between boreholes and whether modeled combinations of E1 and E2 boreholes at specific locations in the repository should be treated as E1E2 scenarios or as independent E1 and E2 scenarios in the consequence analysis.
Disturbed Repository ME Scenario
The M scenario and the E scenario may both occur in the future. The DOE calls a future in which both of these events occur the ME scenario. The occurrence of both mining and deep drilling do not create processes beyond those already described separately for the M and E scenarios. For example, the occurrence of mining does not influence any of the interactions between deep boreholes and the repository or brine reservoirs, nor does the occurrence of drilling impact the effects of mining on Culebra hydrogeology.
Scenarios Retained for Consequence Analysis
The scenarios described in HYPERLINK \l "PA-2_3_2_1" Section REF _Ref203972045 \r \h \* MERGEFORMAT PA-2.3.2.1, HYPERLINK \l "PA-2_3_2_2" Section REF _Ref212453078 \r \h PA-2.3.2.2, and HYPERLINK \l "PA-2_3_2_3" Section REF _Ref213677366 \r \h \* MERGEFORMAT PA-2.3.2.3 have been retained for consequence analysis to determine compliance with the containment requirements in HYPERLINK "40CFR191_13" section 191.13. The modeling systems used to evaluate the consequences of these undisturbed and disturbed scenarios are discussed in HYPERLINK \l "PA-2_3_3" Section REF _Ref201629036 \r \h \* MERGEFORMAT PA-2.3.3.
Calculation of Scenario Consequences
Calculating scenario consequences requires quantitative modeling. This section discusses the conceptual and computational models and some parameter values used to estimate the consequence of the scenarios described in HYPERLINK \l "PA-2_3_2" Section REF _Ref203993502 \r \h \* MERGEFORMAT PA-2.3.2. Additional discussion of conceptual models and modeling assumptions is provided in HYPERLINK \l "PA-4_0" Section REF _Ref202317866 \r \h \* MERGEFORMAT PA-4.0. Additional descriptions of sampled parameter values are included in Fox ( HYPERLINK "../../references/Others/Fox_2008_Parameter_Report_CRA_2009_ERMS549747.pdf" 2008).
A single modeling system was used to represent the disposal system and calculate the CCDFs. The modeling system, however, can be conveniently described in terms of various submodels, with each describing a part of the overall system. The models used in the WIPP PA, as in other complex analyses, exist at four different levels.
Conceptual models are a set of qualitative assumptions that describe a system or subsystem for a given purpose. At a minimum, these assumptions concern the geometry and dimensionality of the system, initial and boundary conditions, time dependence, and the nature of the relevant physical and chemical processes. The assumptions should be consistent with one another and with existing information within the context of the given purpose.
Mathematical models represent the processes at the site. The conceptual models provide the context within which these mathematical models must operate, and define the processes they must characterize. The mathematical models are predictive in the sense that, once provided with the known or assumed properties of the system and possible perturbations to the system, they predict the response of the system. The processes represented by these mathematical models include fluid flow, mechanical deformation, radionuclide transport in groundwater, and removal of waste through intruding boreholes.
Numerical models are developed to approximate mathematical model solutions because most mathematical models do not have closed-form solutions.
The complexity of the system requires computer codes to solve the numerical models. The implementation of the numerical model in the computer code with specific initial and boundary conditions and parameter values is generally referred to as the computational model.
Data are descriptors of the physical system being considered, normally obtained by experiment or observation. Parameters are values necessary in mathematical, numerical, or computational models. The distinction between data and parameters can be subtle. Parameters are distinct from data, however, for three reasons: (1) Data may be evaluated, statistically or otherwise, to generate model parameters to account for uncertainty in data. (2) Some parameters have no relation to the physical system, such as the parameters in a numerical model to determine when an iterative solution scheme has converged. (3) Many model parameters are applied at a different scale than one directly observed or measured in the physical system. The distinction between data and parameter values is described further in Fox ( HYPERLINK "../../references/Others/Fox_2008_Parameter_Report_CRA_2009_ERMS549747.pdf" 2008) and Tierney ( HYPERLINK "../../references/Others/Tierney_1990_Constructing_Probability_Distribution_SAND_90_2510.pdf" 1990), where distribution derivations for specific parameters are given. The interpretation and scaling of experimental and field data are discussed in Fox (2008) for individual and sampled parameters, as appropriate.
Probabilistic Characterization of Futures
The PA for the WIPP identifies uncertainty in parameters and uncertainty in future events as distinctly different entities and requires sampling to be conducted in two dimensions. One dimension focuses on characterizing the uncertainty in terms of the probability that various possible futures will occur at the WIPP site over the next 10,000 years. The other dimension characterizes the uncertainty due to lack of knowledge about the precise values of model parameters appropriate for the WIPP repository. Each dimension of the analysis is characterized by a probability space. Monte Carlo methods are used with the WIPP PA modeling system to sample each of the two probability spaces.
Characterizing the probability distribution for the first dimension of the PA depends on identifying the kinds of events that could impact releases from the repository over the next 10,000 years. Screening analyses of possible future events concluded that the only significant events with the potential to affect radionuclide releases to the accessible environment are drilling and mining within the LWB ( HYPERLINK "../Appendix_SCR/Appendix_SCR.htm" \l "SCR-5_0" Appendix SCR-2009, Section SCR-5.0). Consequently, modeling the future states of the repository focuses on representing the occurrences and effects of these two events. CCDFGF uses stochastic processes to simulate intrusion events by drilling and the occurrence of mining for natural resources. CCDFGF assembles the results from the deterministic models and selects the most appropriate scenario data provided by these models to use as the simulation of a 10,000year future progresses. Ten thousand potential futures are simulated and used to create distributions of potential releases, and then compiled into a single CCDF of potential releases.
WIPP PA is required not only to estimate the likelihood of future releases, but to establish confidence in those estimates. Confidence is established using the second dimension of the analysis, which is based on the evaluation of uncertainty in the values of some of the parameters of the deterministic models. This uncertainty is assumed to represent a lack of knowledge about the true values of the parameters, and is labeled epistemic uncertainty. Epistemic uncertainty can be viewed as the representation of potential systematic errors in the results. The impact of epistemic uncertainty on the results is determined by generating 300 sets of parameter values using a stratified random sampling design, LHS, and then running the deterministic models and CCDFGF with each set of sampled parameters. Thus, 300 CCDFs are generated by CCDFGF. One set of parameters is often referred to as a vector. The 300 simulations are organized as 3 replicates of 100 vectors each. Because the uncertainty assigned to the parameters represents a lack of knowledge, this epistemic uncertainty could theoretically be reduced by collecting data to improve knowledge about the parameters. Epistemic uncertainty is represented in the projections of potential releases from the repository by the variability among the 300 CCDFs.
The WIPP PA modeling system consists of a set of loosely coupled deterministic models (BRAGFLO, PANEL, NUTS, SECOTP2D, and CUTTINGS_S) that provide scenario-specific results to the code CCDFGF ( HYPERLINK \l "Figure_PA-2" REF _Ref200960852 \h \* MERGEFORMAT Figure PA-2). CCDFGF is, in contrast, a stochastic simulation model used to simulate potential futures of repository performance where drilling and mining intrusions can impact the state of the repository and produce release events. CCDFGF implements intrusions as stochastic events, thus incorporating the aleatory uncertainty associated with projections of future events. This section describes how aleatory uncertainty is implemented in PA. Epistemic uncertainty is discussed in HYPERLINK \l "PA-6_0" Section REF _Ref200961458 \r \h \* MERGEFORMAT PA-6.0.
Probability Space
As discussed in HYPERLINK \l "PA-2_2_2" Section REF _Ref200961473 \r \h \* MERGEFORMAT PA-2.2.2, aleatory uncertainty is defined by the possible futures xst,i conditional on the set i of parameters used in Equation ( REF EQ_PA2 \h \* MERGEFORMAT PA.2). HYPERLINK \l "PA-3_2" Section REF _Ref200961611 \r \h \* MERGEFORMAT PA-3.2, HYPERLINK \l "PA-3_3" Section REF _Ref210114798 \r \h PA-3.3, HYPERLINK \l "PA-3_4" Section REF _Ref219618865 \r \h PA-3.4, HYPERLINK \l "PA-3_5" Section REF _Ref213680697 \r \h PA-3.5, HYPERLINK \l "PA-3_6"Section REF _Ref219618877 \r \h PA-3.6, HYPERLINK \l "PA-3_7"Section REF _Ref215817203 \r \h PA-3.7, HYPERLINK \l "PA-3_8"Section REF _Ref215817224 \r \h PA-3.8, and HYPERLINK \l "PA-3_9" Section REF _Ref200961624 \r \h \* MERGEFORMAT PA-3.9 describe the individual components tj, ej, lj, bj, pj, aj, and tmin of xst,i and their associated probability distributions. The concept of a scenario as a subset of the sample space of xst,i is discussed in HYPERLINK \l "PA-3_10" Section REF _Ref200961636 \r \h \* MERGEFORMAT PA-3.10. The procedure used to sample the individual elements xst,i is described in HYPERLINK \l "PA_6_5" Section REF _Ref204048601 \r \h \* MERGEFORMAT PA-6.5.
AICs and PICs
AICs and PICs will be implemented at the WIPP site to deter human activity detrimental to repository performance. AICs and PICs are described in detail in the HYPERLINK "../../references/CRA-2004/Chapter_7.pdf" CRA-2004, Chapter 7.0 and in appendices referenced in Chapter 7.0. In this section, the impact of AICs and PICs on PA is described.
AICs will be implemented at the WIPP after final facility closure to control site access and ensure that activities detrimental to disposal system performance do not occur within the controlled area. The AICs will preclude human intrusion in the disposal system. A 100-year limit on the effectiveness of AICs in PA is established in HYPERLINK "40CFR191_14" 40 CFR 191.14(a). Because of the regulatory restrictions and the nature of the AICs that will be implemented, PA assumes there are no inadvertent human intrusions or mining in the controlled area for 100 years following repository closure.
PICs are designed to deter inadvertent human intrusion into the disposal system. Only minimal assumptions were made about the nature of future society when designing the PICs to comply with the assurance requirements. The preamble to HYPERLINK "40CFR194" Part 194 limits any credit for PICs in deterring human intrusion to 700 years after disposal (HYPERLINK "../../references/Others/EPA_61_FR_5224_5245_February_9_1996.pdf" \l "page=9"U.S. Environmental Protection Agency 1996a, p. 5231). Although the DOE originally took credit for PICs in the CCA PA, but has not taken credit since. Not including PICs is a conservative implementation, as no credit is taken for a beneficial process.
Drilling Intrusion
As described in HYPERLINK \l "PA-2_3_2_2" Section REF _Ref212453078 \r \h \* MERGEFORMAT PA-2.3.2.2, drilling intrusions in PA are assumed to occur randomly in time and space following a Poisson process. Specifically, the drilling rate considered within the area marked by a berm as part of the system for PICs (HYPERLINK "../../references/Others/Fox_2008_Parameter_Report_CRA_2009_ERMS549747.pdf" \l "page=241"Fox 2008, Table 46) is 5.85 ( 10-3 intrusions per square kilometer per year (km2/yr). AICs are assumed to prevent any drilling intrusions for the first 100 years after the decommissioning of the WIPP ( HYPERLINK \l "PA-3_2" Section REF _Ref201735510 \r \h \* MERGEFORMAT PA-3.2). In the computational implementation of PA, it is convenient to represent the Poisson process for drilling intrusions by its corresponding rate term (d(t) for intrusions into the area marked by the berm. Specifically,
EMBED Equation.DSMT4 (PA. SEQ Eq._PA- \* ARABIC 6)
where 0.6285 km2 is the area enclosed by the berm (HYPERLINK "../../references/Others/Fox_2008_Parameter_Report_CRA_2009_ERMS549747.pdf" \l "page=237"Fox 2008, Table 45) and t is elapsed time since decommissioning the WIPP.
The function (d(t) defines the parameter of the exponential distribution that gives rise to the times of intrusions, tj of Equation ( REF EQ_PA2 \h \* MERGEFORMAT PA.2). In the computational implementation of the analysis, the exponential distribution is sampled to define the times between successive drilling intrusions ( HYPERLINK \l "Figure_PA-13" REF _Ref200962964 \h \* MERGEFORMAT Figure PA-13, HYPERLINK \l "PA-6_5" Section REF _Ref204048601 \r \h \* MERGEFORMAT PA-6.5). A key assumption of the exponential distribution is that events are independent of each other, so the occurrence of one has no effect on the occurrence of the next event. The process giving rise to such events is sometimes called a Poisson process because the distribution of such events over a fixed interval of time is a Poisson distribution. Due to the 10,000-year regulatory period specified in HYPERLINK "40CFR191_13" section 191.13, tj is assumed to be bounded above by 10,000 years in the definition of xst,i. Further, tj is bounded below by 100 years as defined in Equation ( REF EQ_PA5 \h \* MERGEFORMAT PA.6).
Figure PA- SEQ Figure_PA- \* ARABIC 13. CDF for Time Between Drilling Intrusions
Penetration of Excavated/Nonexcavated Area
The variable ej is a designator for whether or not the jth drilling intrusion penetrates an excavated, waste-filled area of the repository: ej = 0 or 1 implies penetration of nonexcavated or excavated area, respectively. The corresponding probabilities P[ej = 0] and P[ej = 1] for ej = 0 and ej = 1 are
EMBED Equation.DSMT4 (PA. SEQ Eq._PA- \* ARABIC 7)
EMBED Equation.DSMT4 (PA. SEQ Eq._PA- \* ARABIC 8)
where 0.1273 km2 and 0.6285 km2 are the excavated area of the repository and the area of the berm, respectively (HYPERLINK "../../references/Others/Fox_2008_Parameter_Report_CRA_2009_ERMS549747.pdf" \l "page=237"Fox 2008, Table 45).
Drilling Location
Locations of drilling intrusions through the excavated, waste-filled area of the repository are discretized to the 144 locations in HYPERLINK \l "Figure_PA-14" REF _Ref205822409 \h \* MERGEFORMAT Figure PA-14. Assuming that a drilling intrusion occurs within the excavated area, it is assumed to be equally likely to occur at each of these 144 locations. Thus, the probability pLk that drilling intrusion j will occur at location lk, k = 1, 2, (, 144 in REF _Ref205822409 \h \* MERGEFORMAT Figure PA-14 is
(PA. SEQ Eq._PA- \* ARABIC 9)
Figure PA- SEQ Figure_PA- \* ARABIC 14. Discretized Locations for Drilling Intrusions
Penetration of Pressurized Brine
The conceptual models for the Castile include the possibility that pressurized brine reservoirs underlie the repository ( HYPERLINK \l "PA-4_2_10" Section REF _Ref201735728 \r \h \* MERGEFORMAT PA-4.2.10). The variable bj is a designator for whether or not the jth drilling intrusion penetrates pressurized brine, where bj = 0 signifies nonpenetration and bj = 1 signifies penetration of pressurized brine. In PA, the probability pB1 = P[bj= 1] is sampled from a uniform distribution ranging from 0.01 to 0.60 (see GLOBAL:PBRINE in HYPERLINK \l "Table_PA-19" REF _Ref219705647 \h Table PA-19).
Plugging Pattern
Three borehole plugging patterns, pk, are considered in PA: (1) p1, a full concrete plug through the Salado to the Bell Canyon Formation (hereafter referred to as Bell Canyon), (2) p2, a two-plug configuration with concrete plugs at the Rustler/Salado interface and the Castile/Bell Canyon interface, and (3) p3, a three-plug configuration with concrete plugs at the Rustler/ Salado, Salado/Castile, and Castile/Bell Canyon interfaces. The probability that a given drilling intrusion will be sealed with plugging pattern pk, k= 1, 2, 3, is given by pPLk, where pPL1 = P[k = 1] = 0.015, pPL2 = P[k = 2] = 0.696, pPL3 = P[k = 3] = 0.289 (HYPERLINK "../../references/Others/Fox_2008_Parameter_Report_CRA_2009_ERMS549747.pdf" \l "page=241"Fox 2008, Table 46).
Activity Level
The waste intended for disposal at the WIPP is represented by 767 distinct waste streams, with 690 of these waste streams designated as CH-TRU waste and 77 designated as RH-TRU waste (HYPERLINK "../../references/Others/Leigh_Trone_Fox_2005_TRU_Waste_Inventory_for_CRA2004_PABC_ERMS541118.pdf" \l "page=35"Leigh, Trone, and Fox 2005, Section 4.4). For the CRA-2009 PA, the 77 separate RH-TRU waste streams are represented by a single, combined RH-TRU waste stream. The activity levels for the waste streams are given in Fox ( HYPERLINK "../../references/Others/Fox_2008_Parameter_Report_CRA_2009_ERMS549747.pdf" \l "page=242" 2008, Table 48 and HYPERLINK "../../references/Others/Fox_2008_Parameter_Report_CRA_2009_ERMS549747.pdf" \l "page=243" Table 49). Each waste container emplaced in the repository contains waste from a single CH-TRU waste stream. Waste packaged in 55-gallon (gal) drums is stacked 3 drums high within the repository. Although waste in other packages (e.g., standard waste boxes, 10-drum overpacks, etc.) may not be stacked 3 high, PA assumes that each drilling intrusion into CH-TRU waste intersects 3 different waste streams. In contrast, all RH-TRU waste is represented by a single waste stream, and so each drilling intrusion through RH-TRU waste is assumed to intersect this single waste stream. HYPERLINK "../Appendix_MASS/Appendix_MASS.htm" \l "MASS-21_0" Appendix MASS-2009, Section MASS-21.0 examines the sensitivity of PA results to the assumption that three waste streams are intersected by each drilling intrusion into CH-TRU waste.
The vector aj characterizes the type of waste penetrated by the jth drilling intrusion. Specifically,
aj = 0 if ej = 0 (PA. SEQ Eq._PA- \* ARABIC 10)
(i.e., if the ith drilling intrusion does not penetrate an excavated area of the repository);
aj = 1 if ej = 1 and RH-TRU is penetrated (PA. SEQ Eq._PA- \* ARABIC 11)
aj = [iCHj1, iCHj2, iCHj3] if ej = 1 and CH-TRU is penetrated (PA. SEQ Eq._PA- \* ARABIC 12)
where iCHj1, iCHj2, and iCHj3 are integer designators for the CH-TRU waste streams intersected by the jth drilling intrusion (i.e., each of iCHj1, iCHj2, and iCHj3 is an integer between 1 and 690).
Whether the jth intrusion penetrates a nonexcavated or excavated area is determined by the probabilities pE0 and pE1 discussed in HYPERLINK \l "PA-3_4" Section REF _Ref213677565 \r \h \* MERGEFORMAT PA-3.4. The type of waste penetrated is determined by the probabilities pCH and pRH. The excavated area used for disposal of CH-TRU waste (aCH) is 1.115 ( 105 square meters (m2) and the area used for disposal of RH-TRU waste (aRH) is 1.576 ( 104 m2 (HYPERLINK "../../references/Others/Fox_2008_Parameter_Report_CRA_2009_ERMS549747.pdf" \l "page=237"Fox 2008, Table 45), for a total disposal area of aEX = aCH + aRH = 1.273 ( 105 m2. Given that the jth intrusion penetrates an excavated area, the probabilities pCH and pRH of penetrating CH-TRU and RH-TRU waste are given by
(PA. SEQ Eq._PA- \* ARABIC 13)
(PA. SEQ Eq._PA- \* ARABIC 14)
As indicated in this section, the probabilistic characterization of aj depends on a number of individual probabilities. Specifically, pEx0 and pEx1 determine whether a nonexcavated or excavated area is penetrated ( HYPERLINK \l "PA-3_5" Section REF _Ref200963747 \r \h \* MERGEFORMAT PA-3.5); pCH and pRH determine whether CH-TRU or RH-TRU waste is encountered, given penetration of an excavated area; and the individual waste stream probabilities in Fox (2008, HYPERLINK "../../references/Others/Fox_2008_Parameter_Report_CRA_2009_ERMS549747.pdf" \l "page=242"Table 48 and HYPERLINK "../../references/Others/Fox_2008_Parameter_Report_CRA_2009_ERMS549747.pdf" \l "page=243" Table 49), determine the specific waste streams iCHj1, iCHj2, and iCHj3 encountered given a penetration of CH-TRU waste. The probability of encountering a particular CH-TRU waste stream is computed as the ratio of the volume of that waste stream to the volume of CH-TRU waste.
Mining Time
Full mining of known potash reserves within the LWB is assumed to occur at time tmin. The occurrence of mining within the LWB in the absence of institutional controls is specified as following a Poisson process with a rate of (m = 1 ( 10(4 yr(1 (HYPERLINK "../../references/Others/Fox_2008_Parameter_Report_CRA_2009_ERMS549747.pdf" \l "page=241"Fox 2008, Table 46). However, this rate can be reduced by AICs and PICs. Specifically, AICs are assumed to result in no possibility of mining for the first 100 years after decommissioning of the WIPP. In PA, PICs do not affect the mining rate. Thus, the mining rate (m(t) is
EMBED Equation.DSMT4 (PA. SEQ Eq._PA- \* ARABIC 15)
(PA. SEQ Eq._PA- \* ARABIC 16)
where t is the elapsed time since decommissioning of the WIPP.
In the computational implementation of the analysis, (m(t) is used to define the distribution of time to mining. The use of ( m(t) to characterize tmin is analogous to the use of (d to characterize the tj, except that only one mining event is assumed to occur (i.e., xst,i contains only one value for tmin) in order to be consistent with guidance given in HYPERLINK "40CFR194" Part 194 that mining within the LWB should be assumed to remove all economically viable potash reserves. Due to the 10,000-year regulatory period specified in HYPERLINK "40CFR191_13" section 191.13, tmin is assumed to be bounded above by 10,000 years in the definition of xst,i.
Scenarios and Scenario Probabilities
A scenario is a subset of the sample space for aleatory uncertainty. The underlying goal of scenario definition is to define the state of repository conditions prior to and following intrusion events. Scenarios are specific cases of inputs or system states that are selected to cover the range of possible cases. Given the complexity of the futures xst,i (see Equation ( REF EQ_PA2 \h \* MERGEFORMAT PA.2)), many different scenarios can be defined. The computational complexity of the function f(xst|vsu) in HYPERLINK \l "PA-2_2_3" Section REF _Ref200963886 \r \h \* MERGEFORMAT PA-2.2.3 limits evaluation to only a few intrusion scenarios. As presented in HYPERLINK \l "PA-2_3_2" Section REF _Ref203993502 \r \h \* MERGEFORMAT PA-2.3.2, PA considers four fundamental intrusion scenarios:
E0 = no drilling intrusion through an excavated area of the repository
E1 = a drilling intrusion through an excavated area of the repository that penetrates pressurized brine in the Castile
E2 = a drilling intrusion through an excavated area of the repository that does not penetrate pressurized brine in the Castile
E1E2 = two or more previous intrusions, at least one of which is an E1 intrusion
These definitions of intrusion scenarios capture the most important events impacting the state of the repository: whether or not the repository is inundated by the penetration of a brine pocket, and whether or not there exists a possible route of release upward via a borehole. The state of the repository is also designated as E0, E1, E2, or E1E2. Scenarios for some of the process-level models consist of a single intrusion scenario occurring at specific times. CCDFGF is used to simulate multiple intrusions over 10,000 years.
If only the intrusion scenarios controlled the state of the repository, then the state would be defined by the sequence of drilling events alone. However, CCDFGF also considers the impact of plugging pattern on boreholes. A borehole with a full plugging pattern that penetrates the waste area is also assumed to have no impact, and leaves the repository in its previous state, including the undisturbed state (see HYPERLINK \l "PA-6_8_4_1" Section REF _Ref203981211 \r \h \* MERGEFORMAT PA-6.8.4.1 and HYPERLINK \l "Figure_PA-41" REF _Ref201122146 \h \* MERGEFORMAT Figure PA-41 for more details). Thus, an E2 intrusion event into an E0 repository will result in an E0 state if a full plugging pattern is used, or an E2 state otherwise. An E1 intrusion subsequent to an E2 intrusion will leave the repository in an E1E2 state, where it will remain, regardless of subsequent intrusions. It is therefore important to distinguish between the type of intrusion, listed above, and the state of the repository.
The probability that no excavated area will be penetrated during the 10,000-year interval can be computed using a distribution of the number of penetration events and the probability that a drilling event will penetrate the excavated area. For the Poisson distribution of drilling events, the probability of there being n events in the 10,000-year history is
EMBED Equation.DSMT4 (PA. SEQ Eq._PA- \* ARABIC 17)
where ld is the mean drilling rate per year in the period following the period of AICs, 9,900 is the number of years in which drilling can occur after the institutional control period of 100 years, and n is the number of drilling events. The probability of having n events all within the nonexcavated area is pEx0n, or specifically 0.797n. Thus, the probability of having only events in the nonexcavated area over 10,000 years, i.e., having no drilling intrusions into the excavated area, is just the sum across all n of the products of the probability of having exactly n drilling events and the probability that all n events penetrate the unexcavated area:
EMBED Equation.DSMT4 (PA. SEQ Eq._PA- \* ARABIC 18)
The calculated probability becomes
EMBED Equation.DSMT4 (PA. SEQ Eq._PA- \* ARABIC 19)
This probability is the lower bound on the probability of the repository being in an E0 state, given that it does not include the consideration of the plugging pattern.
The probability of a single E1, E2, or E1E2 intrusion over 10,000 years is relatively small. Assuming that pB1 takes on its mean value of 0.305 (see HYPERLINK \l "PA-3_6" Section REF _Ref200964146 \r \* MERGEFORMAT PA-3.6), and ignoring the impact of the plugging pattern, for a constant rate of drilling, (d, these equations are
EMBED Equation.DSMT4 (PA. SEQ Eq._PA- \* ARABIC 20)
and
EMBED Equation.DSMT4 (PA. SEQ Eq._PA- \* ARABIC 21)
respectively, where (pEx1 (d) represents the annual rate of drilling into the excavated region of the repository which is multiplied by 9900 to give the rate per 9,900 years. The probability of an intrusion into the excavated area is subsequently multiplied by the probability of hitting or missing a brine pocket. In this form, it can be seen that the term for the probability for intrusion is equivalent to the PDF of the Poisson distribution for n = 1:
(PA. SEQ Eq._PA- \* ARABIC 22)
The expressions defining the probability of being in the E0 state after 10,000 years and of having a single E1 or E2 intrusion event after 10,000 years are relatively simple because the scenarios E0, E1, and E2 are relatively simple. The scenario E1E2 is more complex and, as a result, computing its probability is also more complex. Closed-form formulas for the probabilities of quite complex scenarios can be derived, but they are very complicated and involve large numbers of iterated integrals ( HYPERLINK "../../references/Others/Helton_1993.pdf" Helton 1993). These probabilities of single E1 and E2 intrusions are relevant to the scenarios used by the process-level models.
CCDF Construction
CCDFGF simulates histories that can have many intrusion events ( HYPERLINK "../../references/Others/WIPP_PA_2003_Design_Document_Users_Manual_for_CCDFGF_Version_500_ERMS530471.pdf" WIPP Performance Assessment 2003a). The process-level models evaluate the releases at a small number of specific times for each of the four intrusion scenarios. Releases from the repository are calculated using results from these fundamental scenarios ( HYPERLINK \l "PA-6_7" Section REF _Ref201036297 \r \* MERGEFORMAT PA-6.7 and HYPERLINK \l "PA-6_8" Section REF _Ref201036312 \r \* MERGEFORMAT PA-6.8). Releases for an arbitrary future are estimated from the results of these fundamental scenarios (Section REF _Ref201036312 \r \* MERGEFORMAT PA-6.8); these releases are used to construct CCDFs by Equation ( REF EQ_PA4 \h \* MERGEFORMAT PA.4).
Previous WIPP PAs have used the Monte Carlo approach to construct the CCDF indicated in Equation ( REF EQ_PA4 \h \* MERGEFORMAT PA.4). The Monte Carlo approach generates releases for 10,000 possible futures. CCDFs are constructed by treating the 10,000 releases values as order statistics; each release is assigned a probability of 1 ( 10-4, and the CCDF can be constructed by plotting the complement of the sum of the probabilities ordered by the release value. The CRA-2009 PA uses the same approach as the CRA-2004 PA.
Estimation of Releases
This section describes how releases to the accessible environment are estimated for a particular future in PA.
Results for Specific Futures
The function f(xst,i) estimates the radionuclide releases to the accessible environment associated with each of the possible futures (xst,i) that could occur at the WIPP site over the next 10,000 years. In practice, f(xst,i) is quite complex and is constructed by the models implemented in computer programs used to simulate important processes and releases at the WIPP. In the context of these models, f(xst,i) has the form
EMBED Equation.DSMT4 (PA. SEQ Eq._PA- \* ARABIC 23)
where
xst,i ~ particular future under consideration
EMBED Equation.DSMT4 ~ future involving no drilling intrusions but a mining event at the same time tmin as in xst
fC(xst,i) ~ cuttings and cavings release to accessible environment for xst,i calculated with CUTTINGS_S
fB(xst,i) ~ two-phase flow in and around the repository calculated for xst,i with BRAGFLO; in practice, fB(xst,i) is a vector containing a large amount of information, including pressure and brine saturation in various geologic members
EMBED Equation.DSMT4 ~ spallings release to accessible environment for xst,i calculated with the spallings model contained in DRSPALL and CUTTINGS_S; this calculation requires repository conditions calculated by fB(xst,i) as input
EMBED Equation.DSMT4 ~ DBR to accessible environment for xst,i also calculated with BRAGFLO; this calculation requires repository conditions calculated by fB(xst,i) as input
EMBED Equation.DSMT4 ~ release through anhydrite MBs to accessible environment for xst,i calculated with NUTS; this calculation requires flows in and around the repository calculated by fB(xst,i) as input
EMBED Equation.DSMT4 ~ release through Dewey Lake to accessible environment for xst,i calculated with NUTS; this calculation requires flows in and around the repository calculated by fB(xst,i) as input
EMBED Equation.DSMT4 ~ release to land surface due to brine flow up a plugged borehole for xst,i calculated with NUTS; this calculation requires flows in and around the repository calculated by fB(xst,i) as input
EMBED Equation.DSMT4 ~ flow field in the Culebra calculated for xst,0 with MODFLOW; xst,0 is used as an argument to fMF because drilling intrusions are assumed to cause no perturbations to the flow field in the Culebra
EMBED Equation.DSMT4 ~ release to Culebra for xst,i calculated with NUTS or PANEL as appropriate; this calculation requires flows in and around the repository calculated by fB(xst,i) as input
EMBED Equation.DSMT4 ~ groundwater transport release through Culebra to accessible environment calculated with SECOTP2D. This calculation requires MODFLOW results (i.e., fMF(xst,i)) and NUTS or PANEL results (i.e., EMBED Equation.DSMT4 ) as input
The remainder of this section describes the mathematical structure of the mechanistic models that underlie the component functions of f(xst,i) in Equation ( REF EQ_PA25 \h \* MERGEFORMAT PA.23).
The Monte Carlo CCDF construction procedure, implemented in the code CCDFGF ( HYPERLINK "../../references/Others/WIPP_PA_2003_Design_Document_Users_Manual_for_CCDFGF_Version_500_ERMS530471.pdf" WIPP Performance Assessment 2003a), uses a sample of size nS = 10,000 in PA. The individual programs that estimate releases do not run fast enough to allow this many evaluations of f. As a result, a two-step procedure is being used to evaluate f in calculating the summation in Equation ( REF EQ_PA25 \h \* MERGEFORMAT PA.23). First, f and its component functions are evaluated with the procedures (i.e., models) described in this section for a group of preselected futures. Second, values of f(xst) for the randomly selected futures xst,i used in the numerical evaluation of the summation in Equation ( REF EQ_PA25 \h \* MERGEFORMAT PA.23) are then constructed from results obtained in the first step. These constructions are described in HYPERLINK \l "PA-6_7" Section REF _Ref201036297 \r \* MERGEFORMAT PA-6.7 and HYPERLINK \l "PA-6_8"Section REF _Ref201036312 \r \* MERGEFORMAT PA-6.8, and produce the evaluations of f(xst) that are actually used in Equation ( REF EQ_PA25 \h \* MERGEFORMAT PA.23).
For notational simplicity, the functions on the right-hand side of Equation ( REF EQ_PA25 \h \* MERGEFORMAT PA.23) will typically be written with only xst as an argument (e.g., fSP(xst) will be used instead of fSP[xst, fB(xst)]). However, the underlying dependency on the other arguments will still be present.
The major topics considered in this chapter are two-phase flow in the vicinity of the repository as modeled by BRAGFLO (i.e., fB) ( HYPERLINK \l "PA-4_2" Section REF _Ref201036708 \r \* MERGEFORMAT PA-4.2), radionuclide transport in the vicinity of the repository as modeled by NUTS (i.e., fMB, fDL, fS, fNP) ( HYPERLINK \l "PA-4_3" Section REF _Ref201036724 \r \* MERGEFORMAT PA-4.3), radionuclide transport in the vicinity of the repository as modeled by PANEL (i.e., fNP) ( HYPERLINK \l "PA-4_4" Section REF _Ref201036739 \r \* MERGEFORMAT PA-4.4), cuttings and cavings releases to the surface as modeled by CUTTINGS_S (i.e., fC) (HYPERLINK \l "PA-4_5"Section REF _Ref201036753 \r \* MERGEFORMAT PA-4.5), spallings releases to the surface as modeled by DRSPALL and CUTTINGS_S (i.e., fSP) ( HYPERLINK \l "PA-4_6" Section REF _Ref201036770 \r \* MERGEFORMAT PA-4.6), DBRs to the surface as modeled by BRAGFLO (i.e., fDBR) ( HYPERLINK \l "PA-4_7" Section REF _Ref201036787 \r \* MERGEFORMAT PA-4.7), brine flow in the Culebra as modeled by MODFLOW (i.e., fMF) (HYPERLINK \l "PA-4_8"Section REF _Ref201036804 \r \* MERGEFORMAT PA-4.8), and radionuclide transport in the Culebra as modeled by SECOTP2D (i.e., fST) ( HYPERLINK \l "PA-4_9" Section REF _Ref210114056 \r \h \* MERGEFORMAT PA-4.9).
Two-Phase Flow: BRAGFLO
Quantifying the effects of gas and brine flow on radionuclide transport from the repository requires a two-phase (brine and gas) flow code. The two-phase flow code BRAGFLO is used to simulate gas and brine flow in and around the repository ( HYPERLINK "../../references/Others/ERMS545015.pdf" Nemer 2007b and HYPERLINK "../../references/Others/Nemer_2007_Users_Manual_for_BRAGFLO_Version_6_ERMS545016.pdf" 2007c) ADDIN EN.CITE Nemer200651451427Nemer, Martin B.Design Document for BRAGFLO Version 6.002006Carlsbad, NMSandia National LaboratoriesERMS 545015Nemer200651351327Nemer, Martin B.Users Manual for BRAGFLO Version 6.002006Carlsbad, NMSandia National LaboratoriesERMS 545016. Additionally, the BRAGFLO code incorporates the effects of disposal room consolidation and closure, gas generation, and rock fracturing in response to gas pressure. This section describes the mathematical models on which BRAGFLO is based, the representation of the repository in the model, and the numerical techniques employed in the solution.
Mathematical Description
Two-phase flow in the vicinity of the repository is represented by the following system of two conservation equations, two constraint equations, and three equations of state:
Gas Conservation
(( (PA. SEQ Eq._PA- \* ARABIC 24)
Brine Conservation
(( (PA. SEQ Eq._PA- \* ARABIC 25)
Saturation Constraint
(PA. SEQ Eq._PA- \* ARABIC 26)
Capillary Pressure Constraint
(PA. SEQ Eq._PA- \* ARABIC 27)
Gas Density
(g (determined by Redlich-Kwong-Soave (RKS) equation of state; see Equation ( REF EQ_PA53 \h \* MERGEFORMAT PA.51)) (PA. SEQ Eq._PA- \* ARABIC 28)
Brine Density
(PA. SEQ Eq._PA- \* ARABIC 29)
Formation Porosity
(PA. SEQ Eq._PA- \* ARABIC 30)
where
g = acceleration due to gravity (meters per second squared [m])
h = vertical distance from a reference location (m)
krl = relative permeability (dimensionless) to fluid l, l = b (brine), g (gas)
Pc = capillary pressure in Pascals (Pa)
Pl = pressure of fluid l (Pa)
qrl = rate of production (or consumption, if negative) of fluid l due to chemical reaction (kilograms per cubic meter per seconds [kg/m3/s])
ql = rate of injection (or removal, if negative) of fluid l (kg/m3/s)
Sl = saturation of fluid l (dimensionless)
t = time (s)
( = geometry factor (m)
rl = density of fluid l (kg/m3)
ml = viscosity of fluid l (Pa s)
f = porosity (dimensionless)
f0 = reference (i.e., initial) porosity (dimensionless)
Pb0 = reference (i.e., initial) brine pressure (Pa), constant in Equation ( REF EQ_PA31 \h \* MERGEFORMAT PA.29) and spatially variable in Equation ( REF EQ_PA32 \h \* MERGEFORMAT PA.30)
(0 = reference (i.e., initial) brine density (kg/m3)
c( = pore compressibility (Pa-1)
cb = brine compressibility (Pa-1)
K = permeability of the material (m2), isotropic for PA ( HYPERLINK "../../references/Others/Howarth_Christian_Frear_1997_Porosity_Single_Phase_Permeability_SAND94_0472.pdf" Howarth and Christian-Frear 1997)
For the brine transport Equation ( REF EQ_PA27 \h \* MERGEFORMAT PA.25), the intrinsic permeability of the material is used. For the gas transport Equation ( REF EQ_PA26 \h \* MERGEFORMAT PA.24), the permeability K is modified to account for the Klinkenberg effect (HYPERLINK "../../references/Others/Klinkenberg_1941_The_Permeability_of_Porous_Media_ERMS208556.pdf"Klinkenberg 1941). Specifically,
EMBED Equation.DSMT4 (PA. SEQ Eq._PA- \* ARABIC 31)
where a and b are gas and formation-dependent constants. Values of a= (0.3410 and b= 0.2710 were determined from data obtained for MB 139 (HYPERLINK "../../references/Others/Christian_Frear_Salado_Halite_Permeability_ERMS230721.PDF"Christian-Frear 1996), with these values used for all regions in HYPERLINK \l "Figure_PA-15" REF _Ref201037169 \h \* MERGEFORMAT Figure PA-15.
The conservation equations are valid in one (i.e., ( = [(/(x]), two (i.e., ( = [(/(x, (/(y]), and three (i.e., ( = [(/(x, (/(y, (/(z]) dimensions. In PA, the preceding system of equations is used to model two-phase fluid flow within the two-dimensional region shown in REF _Ref201037169 \* MERGEFORMAT Figure PA-15. The details of this system are now discussed.
The ( term in Equation ( REF EQ_PA26 \h \* MERGEFORMAT PA.24) and Equation ( REF EQ_PA27 \h \* MERGEFORMAT PA.25) is a dimension-dependent geometry factor and is specified by
( = area normal to flow direction in one-dimensional flow (i.e., (y(z; units = m2)
= thickness normal to flow plane in two-dimensional flow (i.e., (z; units = m)
= 1 in three-dimensional flow (dimensionless) (PA. SEQ Eq._PA- \* ARABIC 32)
PA uses a two-dimensional geometry to compute two-phase flow in the vicinity of the repository, and as a result, ( is the thickness of the modeled region (i.e., (z) normal to the flow plane ( REF _Ref201037169 \* MERGEFORMAT Figure PA-15). Due to the use of the two-dimensional grid in REF _Ref201037169 \* MERGEFORMAT Figure PA-15, ( is spatially dependent, with the values used for ( defined in the column labeled (z. Specifically, ( increases with distance away from the repository edge in both directions to incorporate the increasing pore volume through which fluid flow occurs. The method used in PA, called rectangular flaring, is illustrated in HYPERLINK \l "Figure_PA-16" REF _Ref201037264 \* MERGEFORMAT Figure PA-16 and ensures that the total volume surrounding the repository is conserved in the numerical grid. The equations and method used to determine ( for the grid shown in REF _Ref201037169 \* MERGEFORMAT Figure PA-15 are described in detail by Stein (HYPERLINK "../../references/Others/Stein_to_Knowles_2002_May_13_Methodology_Behind_the_TBM_BRAGFLO_Grid_ERMS522373.PDF"2002).
The h term in Equation ( REF EQ_PA26 \h \* MERGEFORMAT PA.24) and Equation ( REF EQ_PA27 \h \* MERGEFORMAT PA.25) defines vertical distance from a reference point. In PA, this reference point is taken to be the center of MB 139 at the location of the shaft (i.e., (xref, yref) = (23664.9 m, 378.685 m), which is the center of cell 1266 in HYPERLINK \l "Figure_PA-17" REF _Ref201037354 \* MERGEFORMAT Figure PA-17). Specifically, h is defined by
(PA. SEQ Eq._PA- \* ARABIC 33)
where ( is the inclination of the formation in which the point (x, y) is located. In PA, the Salado is modeled as having an inclination of 1 degree from north to south, and all other formations are modeled as being horizontal. Thus, ( = 1 degree for points within the Salado, and ( = 0 degrees otherwise. Treating the Salado as an inclined formation and treating the Castile, Castile brine reservoir, Rustler, and overlying units as horizontal creates discontinuities in the grid at the lower and upper boundaries of the Salado. However, this treatment does not create a computational problem, since the Salado is isolated from vertical flow; its upper boundary adjoins the impermeable Los Medaos Member (formerly referred to as the Unnamed Member) at the base of the Rustler, and its lower boundary adjoins the impermeable Castile.
In the solution of Equations ( REF EQ_PA26 \h \* MERGEFORMAT PA.24) through ( REF EQ_PA32 \h \* MERGEFORMAT PA.30), Sb and Sg are functions of location and time. Thus, Pc, krb, and krg are functions of the form Pc(x, y, t), krb(x, y, t), and krg(x, y, t). In the computational implementation of the solution of the preceding equations, flow of phase l out of a computational cell ( HYPERLINK \l "Figure_PA-17" REF _Ref201037354 \* MERGEFORMAT Figure PA-17) cannot occur when Sl(x, y, t) ( Slr(x, y, t), where Slr denotes the residual saturation for phase l. The values used for Slr, l = b, g are summarized in HYPERLINK \l "Table_PA-3" REF _Ref201037522 \* MERGEFORMAT Table PA3.
Values for (0 and c( (Equation ( REF EQ_PA32 \h \* MERGEFORMAT PA.30)) are also given in REF _Ref201037522 \* MERGEFORMAT Table PA3. Initial porosity (0 for the DRZ is a function of the uncertain parameter for initial halite porosity (0H (HALPOR; see HYPERLINK \l "Table_PA-19" REF TablePA_19 \h Table PA-19) and is given by HYPERLINK "../../references/Others/Martell_to_Lattier_1996_November_14_Additional_Information_for_DRZ_Porosity_ERMS242257.pdf" Martell (1996a) and HYPERLINK "../../references/Others/Bean_et_al_1996_Analysis_Package_for_Salado_Flow_Calculations_Task_1_ERMS420238.pdf" Bean et al. (1996), Section 4):
(0 = (0H + 0.0029 (PA. SEQ Eq._PA- \* ARABIC 34)
Initial porosity (0 of the Castile brine reservoir is calculated from the uncertain sampled parameter for the bulk Castile rock compressibility (BPCOMP; see REF TablePA_19 \h Table PA-19), according to the following relationship:
EMBED Equation.DSMT4 (PA. SEQ Eq._PA- \* ARABIC 35)
where 1.0860 ( 10-10 is a scaling constant that ensures that the productivity ratio, PR, remains constant at 2.0 ( 10-3 m3/Pa. The productivity ratio PR is computed by
(PA. SEQ Eq._PA- \* ARABIC 36)
where V is the volume of the grid block representing the Castile brine reservoir in HYPERLINK \l "Figure_PA-15" REF _Ref201037169 \* MERGEFORMAT Figure PA-15. Because of this relationship, the initial porosity of the brine reservoir ranges from 0.1842 to 0.9208. This range of porosity is not meant to represent an actual reservoir, but rather allows a reservoir to supply a volume of brine to the repository in the event of an E1 intrusion consistent with observed brine flows in the Delaware Basin.
The compressibility c( in Equation ( REF EQ_PA32 \h \* MERGEFORMAT PA.30) and HYPERLINK \l "Table_PA-3" REF _Ref201037522 \* MERGEFORMAT Table PA3 is pore compressibility. Compressibility is treated as uncertain for Salado anhydrite, Salado halite, and regions of pressurized brine in the Castile. However, the sampled value for each of these variables corresponds to bulk compressibility rather than to the pore compressibility actually used in the calculation. Assuming all of the change in volume during compression occurs in the pore volume, the conversion from bulk compressibility cr to pore compressibility c( is approximated by
EMBED Equation.DSMT4 (PA. SEQ Eq._PA- \* ARABIC 37)
where (0 is the initial porosity in the region under consideration.
The primary model used in PA for capillary pressure Pc and relative permeability krl is a modification of the Brooks-Corey model ( HYPERLINK "../../references/Others/Brooks_Corey_1964_Hydraulic_Properties_ERMS241117.pdf" Brooks and Corey 1964). In this model, Pc, krb, and krg are defined by
EMBED Equation.DSMT4 (PA. SEQ Eq._PA- \* ARABIC 38)
Figure PA- SEQ Figure_PA- \* ARABIC 15. Computational Grid Used in BRAGFLO for PA
Figure PA- SEQ Figure_PA- \* ARABIC 16. Definition of Element Depth in BRAGFLO Grid
Figure PA- SEQ Figure_PA- \* ARABIC 17. Identification of Individual Cells in BRAGFLO Grid
Table PA SEQ Table_PA- \* ARABIC 3. Parameter Values Used in Representation of Two-Phase FlowRegionMaterialMaterial DescriptionBrooks-Corey Pore Distribution (PORE_DIS)a(Threshold Pressure Linear Parameter (PCT_A)aaThreshold Pressure Exponential Parameter(PCT_EXP)a(Residual Brine Saturation(SAT_RBRN)aSbrResidual Gas Saturation(SAT_RGAS)aSgrPorosity(POROSITY)a(0Pore Compressibilityac( , Pa-1Intrinsic Permeability(PRMX_LOG)ak, m2SaladoS_HALITEUndisturbed halite0.70.56(0.3460.30.2HALPORbf(HALCOMP)b,d10x, x = HALPRMbDRZDRZ_0DRZ, (5 to 0 years0.70.00.00.00.0f(HALPOR)b,cf(HALCOMP)b,d1.0 ( 10-17DRZ_1DRZ, 0 to 10,000 years0.70.00.00.00.0f(HALPOR)b,cf(HALCOMP)b,d10x, x = DRZPRMbMB 138S_MB138Anhydrite MB in Salado ANHBCEXPb0.26(0.348ANRBSATbANRGSSATb0.011f(ANHCOMP)b,d10x, x = ANHPRMbAnhydrite ABS_ANH_ABAnhydrite layers A and B in Salado ANHBCEXPb0.26(0.348ANRBSATbANRGSSATb0.011f(ANHCOMP)b,d10x, x = ANHPRMbMB 139S_MB139Anhydrite MB in Salado ANHBCEXPb0.26(0.348ANRBSATbANRGSSATb0.011f(ANHCOMP)b,d10x, x = ANHPRMbWaste PanelCAVITY_1Single waste panel, (5 to 0 yearsNAeNAeNAe0.00.01.00.01.0 ( 10(10WAS_AREASingle waste panel, 0 to 10,000 years2.890.00.0WRBRNSATbWRGSSATb0.848f0.02.4 ( 10(13Rest of Repository (RoR)CAVITY_2RoR, (5 to 0 yearsNAeNAeNAe0.00.01.00.01.0 ( 10(10REPOSITRoR, 0 to 10,000 years2.890.00.0WRBRNSATbWRGSSATb0.848f0.02.4 ( 10(13Ops and ExpCAVITY_3Operations area, (5 to 0 yearsNAeNAeNAe0.00.01.00.01.0 ( 10(10OPS_AREAOperations area, 0 to 10,000 yearsNAeNAeNAe0.00.00.180.01.0 ( 10(11ExpCAVITY_3Experimental area, (5 to 0 yearsNAeNAeNAe0.00.01.00.01.0 ( 10(10a Parenthetical parameter names are property names for the corresponding material, as indicated in HYPERLINK \l "Table_PA-19" REF TablePA_19 \h \* MERGEFORMAT Table PA-19.
b Uncertain variable; see REF TablePA_19 \h \* MERGEFORMAT Table PA-19.
c See Equation ( REF EQ_PA36 \h \* MERGEFORMAT PA.34).
d See Equation ( REF EQ_PA39 \h \* MERGEFORMAT PA.37); (0 can also be defined by an uncertain variable.
e These materials are using relative permeability model = 11; see HYPERLINK \l "Table_PA-4" REF _Ref201038785 \h \* MERGEFORMAT Table PA-4.
f Initial value of porosity (0; porosity changes dynamically to account for creep closure (see HYPERLINK \l "PA-4_2_3"Section REF _Ref201038067 \r \* MERGEFORMAT PA-4.2.3).
g See Equation ( REF EQ_PA37 \h \* MERGEFORMAT PA.35).
Table PA-3. Parameter Values Used in Representation of Two-Phase Flow (Continued)RegionMaterialMaterial DescriptionBrooks-Corey Pore Distribution (PORE_DIS)a(Threshold Pressure Linear Parameter (PCT_A)aaThreshold Pressure Exponential Parameter(PCT_EXP)a(Residual Brine Saturation(SAT_RBRN)aSbrResidual Gas Saturation(SAT_RGAS)aSgrPorosity(POROSITY)a(0Pore Compressibilityac( , Pa-1Intrinsic Permeability(PRMX_LOG)ak, m2EXP_AREAExperimental area, 0 to 10,000 yearsNAeNAeNAe0.00.00.180.01.0 ( 10(11CastileIMPERM_ZCastile 0.70.00.00.00.00.0050.01.0 ( 10(35Castile Brine ReservoirCASTILERBrine Reservoir in Castile 0.70.56(0.3460.20.2f(BPCOMP)b,gf(BPCOMP)b,d10x, x = BPPRMbCulebraCULEBRACulebra Member of Rustler 0.64360.26(0.3480.083630.077110.1516.622517 ( 10(107.72681 ( 10(14MagentaMAGENTAMagenta Member of Rustler 0.64360.26(0.3480.083630.077110.1381.915942 ( 10(96.309576 ( 10(16Dewey LakeDEWYLAKEDewey Lake Redbeds0.64360.00.00.083630.077110.1436.993007 ( 10(85.011881 ( 10(17Santa RosaSANTAROSSanta Rosa Formation0.64360.00.00.083630.077110.1755.714286 ( 10(81.0 ( 10(10Los MedaosUNNAMEDLos Medaos Member of Rustler 0.70.00.00.20.20.1810.01.0 ( 10(35TamariskTAMARISKTamarisk Member of Rustler 0.70.00.00.20.20.0640.01.0 ( 10(35Forty-ninerFORTYNINForty-niner Member of Rustler 0.70.00.00.20.20.0820.01.0 ( 10(35DRZ_PCSDRZ_0DRZ, -5 to 0 years0.70.00.00.00.0f(HALPOR)b,cf(HALCOMP)b,d1.0 ( 10(17DRZ_PCSDRZ_PCSDRZ above the panel closures, 0 to 10,000 years0.70.00.00.00.0f(HALPOR)b,cf(HALCOMP)b,d10x, x = DRZPCPRMba Parenthetical parameter names are property names for the corresponding material, as indicated in HYPERLINK \l "Table_PA-19" REF TablePA_19 \h \* MERGEFORMAT Table PA-19.
b Uncertain variable; see REF TablePA_19 \h Table PA-19.
c See Equation ( REF EQ_PA36 \h \* MERGEFORMAT PA.34).
d See Equation ( REF EQ_PA39 \h \* MERGEFORMAT PA.37); (0 can also be defined by an uncertain variable.
e These materials are using relative permeability model = 11; see HYPERLINK \l "Table_PA-4" REF _Ref201038785 \h \* MERGEFORMAT Table PA-4.
f Initial value of porosity (0; porosity changes dynamically to account for creep closure (see HYPERLINK \l "PA-4_2_3" Section REF _Ref201038067 \r \* MERGEFORMAT PA-4.2.3).
g See Equation ( REF EQ_PA37 \h \* MERGEFORMAT PA.35).CONC_PCSCAVITY_4Concrete portion of panel closures, (5 to 0 yearsNAeNAeNAe0.00.01.00.01.0 ( 10(10CONC_PCSConcrete portion of panel closures, 0 to 10,000 yearsCONBCEXPb0.00.0CONBRSATbCONGSSATb0.051.2 ( 10(910x, x = CONPRMbDRF_PCSCAVITY_4Drift adjacent to panel closures, (5 to 0 yearsNAeNAeNAe0.00.01.00.01.0 ( 10(10DRF_PCSDrift adjacent to panel closures, 0 to 10,000 years2.890.00.0WRBRNSATbWRGSSATb0.848f0.02.4 ( 10(13CONC_MONCAVITY_4Concrete monolith portion of shaft seals, (5 to 0 yearsNAeNAeNAe0.00.01.00.01.0 ( 10(10CONC_MONConcrete monolith portion of shaft seals, 0 to 10,000 years0.940.00.0SHURBRNbSHURGASb0.051.2 ( 10(91.0 ( 10(14Upper ShaftCAVITY_4Upper portion of shaft seals, (5 to 0 yearsNAeNAeNAe0.00.01.00.01.0 ( 10(10SHFTUUpper portion of shaft seals, 0 to 10,000 yearsCONBCEXPb0.00.0SHURBRNbSHURGASb0.0052.05 ( 10(810x, x = SHUPRMba Parenthetical parameter names are property names for the corresponding material, as indicated in HYPERLINK \l "Table_PA-19" REF TablePA_19 \h \* MERGEFORMAT Table PA-19.
b Uncertain variable; see REF TablePA_19 \h Table PA-19.
c See Equation ( REF EQ_PA36 \h \* MERGEFORMAT PA.34).
d See Equation ( REF EQ_PA39 \h \* MERGEFORMAT PA.37); (0 can also be defined by an uncertain variable.
e These materials are using relative permeability model = 11; see HYPERLINK \l "Table_PA-4" REF _Ref201038785 \h \* MERGEFORMAT Table PA-4.
f Initial value of porosity (0; porosity changes dynamically to account for creep closure (see HYPERLINK \l "PA-4_2_3" Section REF _Ref201038067 \r \* MERGEFORMAT PA-4.2.3).
g See Equation ( REF EQ_PA37 \h \* MERGEFORMAT PA.35).Lower ShaftCAVITY_4Lower portion of shaft seals, (5 to 0 yearsNAeNAeNAe0.00.01.00.01.0 ( 10(10SHFTL_T1Lower portion of shaft seals, 0 to 200 yearsCONBCEXPb0.00.0SHURBRNbSHURGASb0.0054.28 ( 10(910x, x = SHLPRM1bSHFTL_T2Lower portion of shaft seals, 200 to 10,000 yearsCONBCEXPb0.00.0SHURBRNbSHURGASb0.0054.28 ( 10(910x, x = SHLPRM2bBorehole plugsCONC_PLGConcrete borehole plug, before plug degradation0.940.00.00.00.00.321.1875 ( 10-910x, x = PLGPRMbBH_SANDBorehole after plug degradation, 200 years after intrusion0.940.00.00.00.00.320.010x, x = BHPRMbUpper BoreholeBH_OPENBorehole above repository before plug degradation0.70.00.00.00.00.320.01.0 ( 10(9BH_SANDBorehole after plug degradation, 200 years after intrusion0.940.00.00.00.00.320.010x, x = BHPRMbLower BoreholeBH_OPENBorehole below repository before creep closure0.70.00.00.00.00.320.01.0 ( 10(9BH_CREEPBorehole below repository after creep closure, 1,000 years after intrusion0.940.00.00.00.00.320.010x/10, x = BHPRMaa Parenthetical parameter names are property names for the corresponding material, as indicated in HYPERLINK \l "Table_PA-19" REF TablePA_19 \h \* MERGEFORMAT Table PA-19.
b Uncertain variable; see REF TablePA_19 \h Table PA-19.
c See Equation ( REF EQ_PA36 \h \* MERGEFORMAT PA.34).
d See Equation ( REF EQ_PA39 \h \* MERGEFORMAT PA.37); (0 can also be defined by an uncertain variable.
e These materials are using relative permeability model = 11; see HYPERLINK \l "Table_PA-4" REF _Ref201038785 \h \* MERGEFORMAT Table PA-4.
f Initial value of porosity (0; porosity changes dynamically to account for creep closure (see HYPERLINK \l "PA-4_2_3" Section REF _Ref201038067 \r \* MERGEFORMAT PA-4.2.3).
g See Equation ( REF EQ_PA37 \h \* MERGEFORMAT PA.35). EMBED Equation.DSMT4 (PA. SEQ Eq._PA- \* ARABIC 39)
(PA. SEQ Eq._PA- \* ARABIC 40)
where
( = pore distribution parameter (dimensionless)
Pt(k) = capillary threshold pressure (Pa) as a function of intrinsic permeability k (HYPERLINK "../../references/Others/Webb_1992_Appendix_A_Uncertainty_Estimates_for_Two_Phase.pdf"Webb 1992)
= (PA. SEQ Eq._PA- \* ARABIC 41)
= effective brine saturation (dimensionless) without correction for residual gas saturation
= (PA. SEQ Eq._PA- \* ARABIC 42)
= effective brine saturation (dimensionless) with correction for residual gas saturation
= (PA. SEQ Eq._PA- \* ARABIC 43)
The values used for (, a, (, Sbr, Sgr, and k are summarized in HYPERLINK \l "Table_PA-3" REF _Ref201037522 \* MERGEFORMAT Table PA3. The statement that the Brooks-Corey model is in use means that Pc, krb, and krg are defined by Equation ( REF EQ_PA40 \h \* MERGEFORMAT PA.38) through Equation ( REF EQ_PA42 \h \* MERGEFORMAT PA.40).
In the anhydrite MBs, either the Brooks-Corey model or the van Genuchten-Parker model is used as determined by the subjectively uncertain parameter ANHBCVGP (see HYPERLINK \l "Table_PA-19" REF TablePA_19 \h Table PA-19). A linear model is used to represent two-phase flow in an open borehole (i.e., for the first 200 years after a drilling intrusion for boreholes with two-plug or three-plug configurations, in the open cavities [CAVITY_1, . . , CAVITY_4], and for the experimental and operations areas). This is discussed further below.
In the van Genuchten-Parker model, Pc, krb, and krg are defined by ( HYPERLINK "../../references/Others/van_Genuchten_1978_Calculating_Unsaturated_Hydraulic_Conductivity_Report_78_WR_08.pdf" van Genuchten 1978)
EMBED Equation.DSMT4 (PA. SEQ Eq._PA- \* ARABIC 44)
(PA. SEQ Eq._PA- \* ARABIC 45)
(PA. SEQ Eq._PA- \* ARABIC 46)
where m = (/(1 + () and the capillary pressure parameter PVGP is determined by requiring that the capillary pressures defined in Equation ( REF EQ_PA40 \h \* MERGEFORMAT PA.38) and Equation ( REF EQ_PA46 \h \* MERGEFORMAT PA.44) are equal at an effective brine saturation of Se2 = 0.5 (HYPERLINK "../../references/Others/Webb_1992_Appendix_A_Uncertainty_Estimates_for_Two_Phase.pdf"Webb 1992). The van Genuchten-Parker model is only used for the anhydrite MBs in the Salado and uses the same values for (, Sbr, and Sgr as the Brooks-Corey model ( HYPERLINK \l "Table_PA-3" REF _Ref201037522 \* MERGEFORMAT Table PA3).
In the linear model used for the open borehole (RELP_MOD = 5), Pc, krb, and krg are defined by
Pc = 0, krb = Se1, krg = 1 Se1 (PA. SEQ Eq._PA- \* ARABIC 47)
Another linear model (RELP_MOD = 11) is used for the open cavities (CAVITY_1, . . . , CAVITY_4) for the "5 to 0 year portion of the simulation (see HYPERLINK \l "PA-4_2_2" Section REF _Ref201038752 \r \* MERGEFORMAT PA-4.2.2) and the experimental and operations areas (t = 0 to 10,000 years) which, in PA, are modeled without a time-dependent creep closure:
(PA. SEQ Eq._PA- \* ARABIC 48)
(PA. SEQ Eq._PA- \* ARABIC 49)
(PA. SEQ Eq._PA- \* ARABIC 50)
where l = gas or brine and tol is a tolerance (slope) over which the relative permeability changes linearly from 0 to 1. In PA, tol = 1 ( 10-2 (dimensionless). Thus, the relative permeabilities are ~ 1 for saturations away from residual saturation.
Capillary pressure Pc for both the van Genuchten-Parker and Brooks-Corey models becomes unbounded as brine saturation Sb approaches the residual brine saturation, Sbr. To avoid unbounded values, Pc is capped at 1 ( 108 Pa in selected regions ( HYPERLINK \l "Table_PA-4" REF _Ref201038785 \* MERGEFORMAT Table PA-4).
Gas density is computed using the RKS equation of state, with the gas assumed to be pure H2. For a pure gas, the RKS equation of state has the form ( HYPERLINK "../../references/Others/Walas_1985.pdf" Walas 1985, pp. 43"54)
(PA. SEQ Eq._PA- \* ARABIC 51)
where
R = gas constant = 8.31451 Joules (J) mole (mol)(1 K(1
T = temperature (K) = 300.15 K (= 30 (C; 81 (F)
V = molar volume (m3 mol(1)
a = 0.42747/Pcrit
b = 0.08664 RTcrit /Pcrit
Table PA- SEQ Table_PA- \* ARABIC 4. Models for Relative Permeability and Capillary Pressure in Two-Phase Flow
MaterialRelative Permeabilitya(RELP_MOD)Capillary Pressureb(CAP_MOD)MaterialRelative Permeabilitya(RELP_MOD)Capillary Pressureb(CAP_MOD)S_HALITE42WAS_AREA 121DRZ_041DRZ_141S_MB139ANHBCVGPc2DRZ_PCSSampled1S_ANH_ABANHBCVGPc2CONC_PCS42S_MB138ANHBCVGPc2UNNAMED 41CAVITY_1111TAMARISK41CAVITY_2111FORTYNIN41CAVITY_3111DRF_PCS121CAVITY_4111REPOSIT 121IMPERM_Z 41CONC_MON42CASTILER42SHFTU41OPS_AREA111SHFTL_T141EXP_AREA111SHFTL_T241CULEBRA42CONC_PLG41MAGENTA42BH_OPEN51DEWYLAKE42BH_SAND41SANTAROS41BH_CREEP41a Relative permeability model, where 4 = Brooks-Corey model given by Equation ( REF EQ_PA40 \h \* MERGEFORMAT PA.38) through Equation ( REF EQ_PA42 \h \* MERGEFORMAT PA.40), 5 = linear model given by Equation ( REF EQ_PA49 \h \* MERGEFORMAT PA.47), 11 = linear model given by Equation ( REF EQ_PA50 \h \* MERGEFORMAT PA.48) through Equation ( REF EQ_PA52 \h \* MERGEFORMAT PA.50), 12 = modified Brooks-Corey model to account for cutoff saturation ( HYPERLINK "../../references/Others/Nemer_2007_Users_Manual_for_BRAGFLO_Version_6_ERMS545016.pdf" Nemer 2007c), and ANHBCVGP ~ use of Brooks-Corey or van Genuchten-Parker model treated as a subjective uncertainty.
b Capillary pressure model, where 1 = capillary pressure is unbounded, 2 = Pc bounded above by 1 ( 108 Pa as Sb approaches Sbr.
c See ANHBCVGP in HYPERLINK \l "Table_PA-19" REF TablePA_19 \h Table PA-19.
( =
( for H2 ( HYPERLINK "../../references/Others/Graboski_Daubert_1979.pdf" Graboski and Daubert 1979)
Tcrit = critical temperature (K)
Pcrit = critical pressure (Pa)
Tr = T / Tcrit = reduced temperature
( = acentric factor
= 0 for H2 (Graboski and Daubert 1979)
In order to account for quantum effects in H2, effective critical temperature and pressure values of Tcrit = 43.6 K and Pcrit = 2.047 ( 106 Pa are used instead of the true values for these properties ( HYPERLINK "../../references/Others/Prausnitz_1969.pdf" Prausnitz 1969). Equation ( REF EQ_PA53 \h \* MERGEFORMAT PA.51) is solved for molar volume V. The gas density (g then is given by
(PA. SEQ Eq._PA- \* ARABIC 52)
where Mw,H2 is the molecular weight of H2 (i.e., 2.01588 ( 10(3 kg/mol; see HYPERLINK "../../references/Others/Weast_1969.pdf" Weast 1969, p. B26).
Brine density (b is defined by Equation ( REF EQ_PA31 \h \* MERGEFORMAT PA.29), with (b0 = 1230.0 kg/m3 at a pressure of Pb0 = 1.0132 ( 105 Pa and cb = 2.5 ( 10(10 Pa(1 (HYPERLINK "../../references/Others/Roberts_1996_Salado_Brine_Compressibility_ERMS412842.pdf"Roberts 1996). Porosity, (, is used as defined by Equation ( REF EQ_PA32 \h \* MERGEFORMAT PA.30) with two exceptions: in the repository (see HYPERLINK \l "PA-4_2_3" Section REF _Ref201039028 \r \* MERGEFORMAT PA-4.2.3) and in the DRZ and MBs subsequent to fracturing (see HYPERLINK \l "PA-4_2_4" Section REF _Ref201039039 \r \* MERGEFORMAT PA-4.2.4). The values of (0 and c( used in conjunction with Equation ( REF EQ_PA32 \h \* MERGEFORMAT PA.30) are listed in HYPERLINK \l "Table_PA-3" REF _Ref201037522 \* MERGEFORMAT Table PA3. The reference pressure Pb0 in Equation ( REF EQ_PA32 \h \* MERGEFORMAT PA.30) is spatially variable and corresponds to the initial pressures Pb(x, y, "5) (here, "5 means at time equal to "5 years; see HYPERLINK \l "PA-4_2_2" Section REF _Ref201039137 \r \* MERGEFORMAT PA-4.2.2). The gas and brine viscosities (l, l=g, b in Equation ( REF EQ_PA26 \h \* MERGEFORMAT PA.24) and Equation ( REF EQ_PA27 \h \* MERGEFORMAT PA.25) were assumed to have values of (g = 8.93(10(6 Pas (H2:VISCO; see HYPERLINK "../../references/Others/Vargaftik_1975.pdf" Vargaftik 1975) and (b = 2.1 ( 10(3 Pa s (BRINESAL:VISCO; see HYPERLINK "../../references/Others/McTigue_1993_Permeability_and_Hydraulic_Diffusivity_of_WIPP_SAND92_1911.pdf" McTigue 1993).
The terms qg, qrg, qb, and qrb in Equation ( REF EQ_PA26 \h \* MERGEFORMAT PA.24) and Equation ( REF EQ_PA27 \h \* MERGEFORMAT PA.25) relate to well injection or removal (i.e., qg, qb) and reaction, production, or consumption (i.e., qrg, qrb) of gas and brine, with positive signs corresponding to injection or production and negative signs corresponding to removal or consumption. In the long-term Salado flow calculations, no injection or removal of gas or brine is calculated using qg and qb. Thus, qg and qb are equal to zero. That is, after an intrusion, the borehole is treated as a porous media, rather than a point source or sink of brine and gas. Furthermore, the mass and pressure lost to a DBR during the intrusion is conservatively ignored in the BRAGFLO calculations. In the DBR calculations discussed in HYPERLINK \l "PA-4_7" Section REF _Ref201111316 \r \h \* MERGEFORMAT PA-4.7, qg and qb are used to describe injection and production wells in the DBR grid.
In PA, no gas consumption occurs through the term qrg (see below), and gas production has the potential to occur (due to corrosion of steel or microbial degradation of CPR materials) only in the waste disposal regions of the repository (i.e., Waste Panel, South RoR, and North RoR in HYPERLINK \l "Figure_PA-15" REF _Ref201037169 \* MERGEFORMAT Figure PA-15). Thus,
qrg ( 0 in waste disposal regions of REF _Ref201037169 \* MERGEFORMAT Figure PA-15
= 0 elsewhere (PA. SEQ Eq._PA- \* ARABIC 53)
Gas consumption occurs due to the reaction of CO2 with MgO in the waste panels, and potentially from the sulfidation of steel. This gas consumption is not modeled using qrg, but is accounted for by reducing the gas generation rate qrg, as discussed in HYPERLINK \l "PA-4_2_5" Section REF _Ref201039315 \r \* MERGEFORMAT PA-4.2.5. Finally, no brine production occurs, and brine consumption has the potential to occur (due to the consumption of brine during steel corrosion) only in the waste disposal regions of the repository. Thus,
qrb ( 0 in waste disposal regions of REF _Ref201037169 \* MERGEFORMAT Figure PA-15
= 0 elsewhere (PA. SEQ Eq._PA- \* ARABIC 54)
More detail on the definition of qrg and qrb is provided in Section REF _Ref201039345 \r \* MERGEFORMAT PA-4.2.5.
Initial Conditions
In each two-phase flow simulation, a short period of time representing disposal operations is simulated. This period of time is called the start-up period, and covers 5 years from t = (5 years to 0 years, corresponding to the amount of time a typical panel is expected to be open during disposal operations. All grid locations require initial brine pressure and gas saturation at the beginning of the simulation (t = (5 years).
The Rustler and overlying units (except in the shaft) are modeled as horizontal with spatially constant initial pressure in each layer (see HYPERLINK \l "Figure_PA-15" REF _Ref201037169 \* MERGEFORMAT Figure PA-15). HYPERLINK \l "Table_PA-5" REF _Ref201039380 \* MERGEFORMAT Table PA-5 lists the initial brine pressure, Pb, and gas saturation, Sg, for the Rustler.
The Salado (Mesh Rows 324 in REF _Ref201037169 \* MERGEFORMAT Figure PA-15) is assumed to dip uniformly ( = 1 degree downward from north to south (right to left in REF _Ref201037169 \* MERGEFORMAT Figure PA-15). Except in the repository excavations and the shaft, brine is initially assumed (i.e., at (5 years) to be in hydrostatic equilibrium relative to an uncertain initial pressure Pb,ref (SALPRES; see HYPERLINK \l "Table_PA-19" REF TablePA_19 \h Table PA-19) at a reference point located at shaft center at the elevation of the midpoint of MB 139, which is the center of Cell 1266 in HYPERLINK \l "Figure_PA-17" REF _Ref201037354 \* MERGEFORMAT Figure PA-17. This gives rise to the condition
(PA. SEQ Eq._PA- \* ARABIC 55)
(PA. SEQ Eq._PA- \* ARABIC 56)
(PA. SEQ Eq._PA- \* ARABIC 57)
(PA. SEQ Eq._PA- \* ARABIC 58)
(PA. SEQ Eq._PA- \* ARABIC 59)
Table PA- SEQ Table_PA- \* ARABIC 5. Initial Conditions in the Rustler
NameMesh Row( HYPERLINK \l "Figure_PA-15" REF _Ref201037169 \h \* MERGEFORMAT Figure PA-15)Pb(x, y, -5), PaSg(x, y, -5)Santa Rosa c331.013250 ( 1051 ( Sb = 0.916(Sb = SANTAROS:SAT_IBRN)aSanta Rosa c321.013250 ( 1051 ( Sb = 0.916(Sb = SANTAROS:SAT_IBRN)aDewey Lakec311.013250 ( 1051 ( Sb = 0.916(Sb = SANTAROS:SAT_USAT)aDewey Lakec307.355092 ( 1051 ( Sb = 0.916(Sb = SANTAROS:SAT_USAT)aForty-ninerc291.47328 ( 1060bMagenta289.465 ( 105(MAGENTA:PRESSURE)0bTamariskc271.82709 ( 1060bCulebra269.141 ( 105
(CULEBRA:PRESSURE)0bLos Medaos c252.28346 ( 1060ba The names in parenthesis are parameters in the WIPP PA Parameter Database.
b The Rustler is assumed to be fully saturated. This initial condition is set in the program ICSET. See Nemer and Clayton ( HYPERLINK "../../references/Others/Nemer_Clayton_2008_Analysis_Package_for_Salado_Flow_Modeling_ERMS548607.pdf" \l "page=19" 2008, Section 3.2).
c These pressures are calculated in the ALGEBRA1 step analogously to Equation ( REF EQ_PA57 \h \* MERGEFORMAT PA.55) below, using the brine density of 1220 kg/m3. See subsequent discussion taking = 0 and the reference point (xref, yref) at the top of the Dewey Lake. See the ALGEBRA input file ALG1_BF_CRA09.INP in library LIBCRA09_BF, class CRA09-1 on the WIPP PA cluster for details. See Nemer and Clayton ( HYPERLINK "../../references/Others/Nemer_Clayton_2008_Analysis_Package_for_Salado_Flow_Modeling_ERMS548607.pdf" \l "page=29" 2008, Section 4.1.7) for details on the ALGEBRA1 step.
where
h(x, y) is defined in Equation ( REF EQ_PA35 \h \* MERGEFORMAT PA.33)
(b0 = 1220 kg/m3 (BRINESAL:DNSFLUID)
cb = 3.1 ( 10(10 Pa(1 (BRINESAL:COMPRES)
g = 9.80665 m/s2
Pb,ref = 1.01325 ( 105 Pa (BRINESAL:REF_PRES)
Pb0 = sampled far-field pressure in the undisturbed halite (S_HALITE:PRESSURE)
In the Salado, initial gas saturation Sg(x, y, (5) = 0 (see HYPERLINK "../../references/Others/Nemer_Clayton_2008_Analysis_Package_for_Salado_Flow_Modeling_ERMS548607.pdf" \l "page=23"Nemer and Clayton 2008, Section 4.1.6).
The Castile (Mesh Rows 1 and 2) is modeled as horizontal, and initial brine pressure is spatially constant within each layer (no dip), except that the brine reservoir is treated as a different material from rest of Castile and has a different initial pressure which is a sampled parameter. Specifically, outside the brine reservoir, pressure is calculated using Equation ( REF EQ_PA57 \h \* MERGEFORMAT PA.55) above with no dip (( = 0) in the ALGEBRA1 step. Within the reservoir, Pb(x, y, (5) = BPINTPRS, the uncertain initial pressure in the reservoir (see HYPERLINK \l "Table_PA-19" REF TablePA_19 \h Table PA-19). Initial gas saturation Sg(x, y, (5) = 0.
Within the shaft (areas Upper Shaft, Lower Shaft, and CONC_MON) and panel closures (areas CONC_PCS and DRF_PCS), Pb(x, y, (5) = 1.01325 ( 105 Pa and Sg(x, y, (5) = 0. Within the excavated areas (Waste Panel, South RoR, and North RoR, Ops and Exp), Pb(x, y, (5) = 1.01325 ( 105 Pa and Sg(x, y, (5) = 0.
At the end of the initial five-year start-up period and the beginning of the regulatory period (t = 0 years), brine pressure and gas saturation are reset in the shaft, panel closures, and excavated areas. In the shaft (areas Upper Shaft, Lower Shaft, and CONC_MON) and panel closures (areas CONC_PCS and DRF_PCS), Pb(x, y, 0) = 1.01325 ( 105 Pa and Sg(x, y, 0) = 1 ( 10(7 (see CONC_MON:SAT_IBRN). In the waste disposal regions (areas Waste Panel, South RoR, and North RoR), Pb(x, y, 0) = 1.01325 ( 105 Pa and Sg(x, y, 05) = 0.985 (see WAS_AREA:SAT_IBRN). In the other excavated areas, Pb(x, y, 0) = 1.01325 ( 105 Pa and Sg(x,y, 0) = 1.0.
Creep Closure of Repository
Salt creep occurs naturally in the Salado halite in response to deviatoric stress. Inward creep of rock is generally referred to as creep closure. Creep closure of excavated regions begins immediately from excavation-induced deviatoric stress. If the rooms were empty, closure would proceed to the point where the void volume created by the excavation would be eliminated as the surrounding formation returned to a uniform stress state. In the waste disposal region, inward creep of salt causes consolidation of the waste, and this waste consolidation continues until loading in the surrounding rock is uniform, at which point salt creep and waste consolidation ceases. The amount of waste consolidation that occurs and the time it takes to consolidate are governed by the waste properties (e.g., waste strength, modulus, etc.), the surrounding rock properties, the dimensions and location of the room, and relative quantities of brine and gas present.
The porosity of the waste disposal regions and neighboring access drifts (i.e., Waste Panel, South RoR, North RoR, and DRF_PCS in HYPERLINK \l "Figure_PA-15" REF _Ref201037169 \* MERGEFORMAT Figure PA-15) is assumed to change through time due to creep closure of the halite surrounding the excavations. The equations on which BRAGFLO is based do not incorporate this type of deformation. Therefore, the changes in repository porosity due to halite deformation are modeled in a separate analysis with the geomechanical program SANTOS, which implements a quasi-static, large-deformation, finite-element procedure ( HYPERLINK "../../references/Others/Stone_1997_SANTOS_A_Two_Dimensional_Finite_Element_Program_SAND90_0543.pdf" Stone 1997). Interpolation procedures are then used with the SANTOS results to define porosity (() within the repository as a function of time, pressure, and gas generation rate.
For more information on the generation of the porosity surface for BRAGFLO in PA, see HYPERLINK "../Appendix_PORSURF/Appendix_PORSURF.htm" Appendix PORSURF-2009.
Fracturing of MBs and DRZ
Fracturing within the anhydrite MBs (i.e., regions MB 138, Anhydrite AB, and MB 139 in HYPERLINK \l "Figure_PA-15" REF _Ref201037169 \* MERGEFORMAT Figure PA-15) and in the DRZ (region DRZ in REF _Ref201037169 \* MERGEFORMAT Figure PA-15) is assumed to occur at pressures slightly above lithostatic pressure, and is implemented through a pressure-dependent compressibility cr(Pb) ( HYPERLINK "../../references/Others/Mendenhall_Gerstle_to_Distribution_1993_December_6_WIPP_Anhydrite_Fracture_Modeling_WPO39830.pdf" Mendenhall and Gerstle 1995). Specifically, MB fracturing begins at a brine pressure of
(PA. SEQ Eq._PA- \* ARABIC 60)
where Pbi and Pb0 are spatially dependent (i.e., Pb0 = P(x, y, 0) as in HYPERLINK \l "PA-4_2_2" Section REF _Ref201039863 \r \* MERGEFORMAT PA-4.2.2) and (Pi = 2 ( 105 Pa (see HYPERLINK "../../references/Others/Fox_2008_Parameter_Report_CRA_2009_ERMS549747.pdf" \l "page=209" S_MB138:PI_DELTA in Fox 2008, Table 30)
Fracturing ceases at a pressure of
(PA. SEQ Eq._PA- \* ARABIC 61)
and a fully fractured porosity of
(PA. SEQ Eq._PA- \* ARABIC 62)
where (Pa = 3.8 ( 106 Pa (see HYPERLINK "../../references/Others/Fox_2008_Parameter_Report_CRA_2009_ERMS549747.pdf" \l "page=209"S_MB138:PF_DELTA in Fox 2008, Table 30), (0 is spatially dependent ( HYPERLINK \l "Table_PA-3" REF _Ref201037522 \* MERGEFORMAT Table PA3), and ((a = 0.04, 0.24, and 0.04 for anhydrite materials S_MB138, S_ANH_AB, and S_MB139, respectively (see HYPERLINK "../../references/Others/Fox_2008_Parameter_Report_CRA_2009_ERMS549747.pdf" \l "page=209"S_MB138:DPHIMAX in Fox 2008, Table 30).
Once fractured, compressibility cr becomes a linear function
(PA. SEQ Eq._PA- \* ARABIC 63)
of brine pressure for Pbi ( Pb ( Pba, with cra defined so that the solution ( of
(PA. SEQ Eq._PA- \* ARABIC 64)
satisfies ((Pba) = (a; specifically, cra is given by
(PA. SEQ Eq._PA- \* ARABIC 65)
The permeability kf(Pb) of fractured material at brine pressure Pb is related to the permeability of unfractured material at brine pressure Pbi by
(PA. SEQ Eq._PA- \* ARABIC 66)
where k is the permeability of unfractured material (i.e., at Pbi) and n is defined so that kf(Pba) = 1( 10(9 m2 (i.e., n is a function of k, which is an uncertain input to the analysis; see ANHPRM in HYPERLINK \l "Table_PA-19" REF TablePA_19 \h Table PA-19). When fracturing occurs, kf(Pb) is used instead of k in the definition of the permeability for the fractured areas of the anhydrite MBs.
Fracturing is also modeled in the DRZ region in HYPERLINK \l "Figure_PA-15" REF _Ref201037169 \* MERGEFORMAT Figure PA-15. The fracture model implementation is the same as for the anhydrite materials. In this case, fracturing would be in halite rather than anhydrite, but because of the limited extent of the DRZ and the proximity of the nearby interbeds, this representation was deemed acceptable by the Salado Flow Peer Review panel ( HYPERLINK "../../references/Others/Caporuscio_et_al_2003_Salado_Flow_Conceptual_Models_ERMS526879.pdf" Caporuscio, Gibbons, and Oswald 2003).
Gas Generation
Gas production is assumed to result from anoxic corrosion of steel and the microbial degradation of CPR materials. Thus, the gas generation rate qrg in Equation ( REF EQ_PA26 \h \* MERGEFORMAT PA.24) is of the form
(PA. SEQ Eq._PA- \* ARABIC 67)
where qrgc is the rate of gas production per unit volume of waste (kg/m3/s) due to anoxic corrosion of Fe-base metals, and qrgm is the rate of gas production per unit volume of waste (kg/m3/s) due to microbial degradation of CPR materials. Furthermore, qrb in Equation ( REF EQ_PA27 \h \* MERGEFORMAT PA.25) is used to describe the consumption of brine during the corrosion process.
Gas generation takes place only within the waste disposal regions (i.e., Waste Panel, South RoR, and North RoR in HYPERLINK \l "Figure_PA-15" REF _Ref201037169 \* MERGEFORMAT Figure PA-15) and all the generated gas is assumed to have the same properties as H2 (see discussion in HYPERLINK "../Appendix_MASS/Appendix_MASS.htm" \l "MASS-3_2" Appendix MASS-2009, Section MASS-3.2). In PA, the consumable materials are assumed to be homogeneously distributed throughout the waste disposal regions (i.e., the concentration of Fe-base metals and CPR materials in the waste is not spatially dependent). A separate analysis examined the potential effects on PA results of spatially varying Fe-base metal and CPR material concentrations, and concluded that PA results are not affected by representing these materials with spatially varying concentrations (see HYPERLINK "../Appendix_MASS/Appendix_MASS.htm" \l "MASS-21_0" Appendix MASS-2009, Section MASS-21.0).
The rates qrgc, qrb, and qrgm (kg/m3/s) are defined by
gas generation by corrosion
(PA. SEQ Eq._PA- \* ARABIC 68)
brine consumption by corrosion
(PA. SEQ Eq._PA- \* ARABIC 69)
and microbial gas generation
(PA. SEQ Eq._PA- \* ARABIC 70)
where
Ds = surface area concentration of steel in the repository (m2 surface area steel/ m3 disposal volume)
Dc = mass concentration of cellulosics in the repository (kg biodegradable material/m3 disposal volume)
= molecular weight of H2 (kg H2/mol H2)
= molecular weight of water (H2O) (kg H2O/mol H2O)
Rci = corrosion rate under inundated conditions (m/s)
Rch = corrosion rate under humid conditions (m/s)
Rmi = rate of cellulose biodegradation under inundated conditions (mol C6H10O5/kg C6H10O5/s)
Rmh = rate of cellulose biodegradation under humid conditions (mol C6H10O5/kg C6H10O5/s)
Sb,eff = effective brine saturation due to capillary action in the waste materials (see Equation ( REF EQ_PA91 \h \* MERGEFORMAT PA.90) in HYPERLINK \l "PA-4_2_6" Section REF _Ref201040586 \r \* MERGEFORMAT PA-4.2.6)
= EMBED Equation.DSMT4
= stoichiometric coefficient for gas generation due to corrosion of steel, i.e., moles of H2 produced by the corrosion of 1 mole of Fe (mol H2/mol Fe)
= stoichiometric coefficient for brine consumption due to corrosion of steel, i.e., moles of H2O consumed per mole of H2 generated by corrosion (mol H2O/mol H2)
= average stoichiometric factor for microbial degradation of cellulose, i.e., the moles of H2 generated per mole of carbon consumed by microbial action (mol H2/mol C)
(Fe = molar density of steel (mol/m3)
Bfc = parameter (WAS_AREA:BIOGENFC; discussed in detail later in this section) uniformly sampled from 0 to 1, used to account for the uncertainty in whether microbial gas generation could be realized in the WIPP at experimentally measured rates.
The products Rci Ds (Fe Xc , Rch Ds (Fe Xc, Rmi Dc y, and Rmh in Equation ( REF EQ_PA70 \h \* MERGEFORMAT PA.68) and Equation ( REF EQ_PA72 \h \* MERGEFORMAT PA.70) define constant rates of gas generation (mol/m3/s) that continue until the associated substrate (i.e., steel or cellulose) is exhausted (i.e., zero order kinetics are assumed). The terms Sb,eff and EMBED Equation.DSMT4 in Equation ( REF EQ_PA70 \h \* MERGEFORMAT PA.68) and Equation ( REF EQ_PA72 \h \* MERGEFORMAT PA.70), which are functions of location and time, correct for the amount of substrate exposed to inundated and humid conditions, respectively. All the corrosion and microbial action is assumed to cease when no brine is present, which is the reason that 0 replaces Sg = 1 in the definition of EMBED Equation.DSMT4 . In PA, Rch = 0 and Rci, Rmh, and Rmi are defined by uncertain variables (see WGRCOR, WGRMICH, WGRMICI in HYPERLINK \l "Table_PA-19" REF TablePA_19 \h Table PA-19). However, Rmh is now sampled based on the sampled value of Rmi: see Nemer and Clayton ( HYPERLINK "../../references/Others/Nemer_Clayton_2008_Analysis_Package_for_Salado_Flow_Modeling_ERMS548607.pdf" \l "page=36" 2008, Section 5.1.3). Further, MH2 = 2.02 ( 10(3 kg/mol ( HYPERLINK "../../references/Others/Lide_1991.pdf" Lide 1991, pp. 1-7, 1-8), MH2O = 1.80 ( 10(2 kg/mol (Lide 1991, pp. 1-7, 1-8), (Fe = 1.41 ( 105 mol/m3 ( HYPERLINK "../../references/Others/Telander_Westerman_1993_Hydrogen_Generation_by_Metal_Corrosion_SAND92_7347.pdf" Telander and Westerman 1993), and Ds, Dc, Xc(H2O|H2), Xc(H2|Fe), and y(H2|C) are discussed below.
The concentration Ds in Equation ( REF EQ_PA70 \h \* MERGEFORMAT PA.68) is defined by
(PA. SEQ Eq._PA- \* ARABIC 71)
where
Ad = surface area of steel associated with a waste disposal drum (m2/drum)
VR = initial volume of a single room in the repository (m3)
nd = ideal number of waste drums that can be close-packed into a single room
In PA, Ad = 6 m2/drum (REFCON:ASDRUM), VR = 3,644 m3 (REFCON:VROOM), and nd = 6804 drums (REFCON:DRROOM).
The biodegradable materials to be disposed at the WIPP consist of cellulosic materials, plastics, and rubbers. Cellulosics have been demonstrated experimentally to be the most biodegradable of these materials ( HYPERLINK "../../references/Others/Francis_Gillow_Giles_1997_Microbial_Gas_Generation_SAND96_2582.pdf" Francis, Gillow, and Giles 1997). The occurrence of significant microbial gas generation in the repository will depend on whether (1) microbes capable of consuming the emplaced organic materials will be present and active, (2) sufficient electron acceptors will be present and available, and (3) enough nutrients will be present and available.
During the CRA-2004 PABC, the EPA ( HYPERLINK "../../references/Others/Cotsworth_to_Triay_March_4_2005_EPA_Letter_on_Conducting_ERMS538858.pdf" Cotsworth 2005) indicated that the probability that microbial gas generation could occur (WMICDFLG) should be set equal to 1 in PA calculations. In the CRA-2004, the probability that microbial gas generation could occur was assigned a value of 0.5. To comply with the EPAs letter, in the CRA-2004 PABC and the CRA-2009 PA the parameter WMICDFLG was changed so that the probability that microbial gas generation could occur was set to 1 while preserving the previous probability distribution on whether CPR could be degraded. This is summarized in HYPERLINK \l "Table_PA-6" REF _Ref201040936 \* MERGEFORMAT Table PA-6, and is discussed further in Nemer and Stein
Table PA- SEQ Table_PA- \* ARABIC 6. Probabilities for Biodegradation of Different Organic Materials (WAS_AREA:PROBDEG) in the CRA-2009 PA and the CRA-2004 PA
WAS_AREA:PROBDEGMeaningProbability CRA-2004Probability CRA-20090No microbial degradation can occur0.50.01Biodegradation of only cellulose can occur0.250.752Biodegradation of CPR materials can occur0.250.25
( HYPERLINK "../../references/Others/Nemer_and_Stein_2005_Analysis_Package_for_BRAGFLO_ERMS540527.pdf" \l "page=35" 2005, Section 5.4). Because there are significant uncertainties in whether the experimentally observed gas-generation rates could be realized in the WIPP repository, during the CRA-2004 PABC the EPA agreed to allow the DOE to multiply the sampled microbial rates by a parameter (WAS_AREA:BIOGENFC) uniformly sampled from 0 to 1. This is discussed further in Nemer, Stein, and Zelinski ( HYPERLINK "../../references/Others/Nemer_Stein_Zelinski_2005_Analysis_Report_of_BRAGFLO_ERMS539437.pdf" \l "page=19" 2005, Section 4.2.2).
In cases where biodegradation of rubbers and plastics occur, rubbers and plastics are converted to an equivalent quantity of cellulosics based on their carbon equivalence ( HYPERLINK "../../references/Others/Wang_and_Brush_to_Tierney_1996_January_26_Estimates_of_Gas_Generation_Parameters_ERMS231943.pdf" Wang and Brush 1996a). This produces the density calculation
for biodegradation of cellulosics only(PA. SEQ Eq._PA- \* ARABIC 72)for biodegradation of CPR materials
where mcel is the mass of cellulosics (kg), mr is the mass of rubbers (kg), and mp is the mass of plastics (kg).
In the CRA-2009 PA, the emplacement materials (cellulose and plastic) have been added to mcel and mp. This is discussed further in Nemer and Clayton ( HYPERLINK "../../references/Others/Nemer_Clayton_2008_Analysis_Package_for_Salado_Flow_Modeling_ERMS548607.pdf" \l "page=33" 2008, Section 5.1.1). Density values for CPR materials can be found in Fox ( HYPERLINK "../../references/Others/Fox_2008_Parameter_Report_CRA_2009_ERMS549747.pdf" \l "page=217" 2008, Table 34).
The most plausible corrosion reactions after closure of the WIPP are believed to be ( HYPERLINK "../../references/Others/Wang_and_Brush_to_Tierney_1996_January_26_Estimates_of_Gas_Generation_Parameters_ERMS231943.pdf" Wang and Brush 1996a)
Fe + 2H2O = Fe(OH)2 + H2 (PA. SEQ Eq._PA- \* ARABIC 73)
and
3Fe + 4H2O = Fe3O4 + 4H2 (PA. SEQ Eq._PA- \* ARABIC 74)
When normalized to 1 mole of Fe and linearly weighted by the factors x and , the two preceding reactions become
(PA. SEQ Eq._PA- \* ARABIC 75)
where x and are the fractions of Fe consumed in the reactions in Equation ( REF EQ_PA75 \h \* MERGEFORMAT PA.73) and Equation ( REF EQ_PA76 \h \* MERGEFORMAT PA.74), respectively. Although magnetite (Fe3O4) has been observed to form on Fe as a corrosion product in low-Mg anoxic brines at elevated temperatures ( HYPERLINK "../../references/Others/Telander_Westerman_1997_Hydrogen_Generation_by_Metal_Corrosion_SAND96_2538.pdf" Telander and Westerman 1997) and in oxic brine ( HYPERLINK "../../references/Others/Haberman_Frydrych_1988.pdf" Haberman and Frydrych 1988), there is no evidence that it will form at WIPP repository temperatures. If Fe3O4 were to form, H2 would be produced (on a molar basis) in excess of the amount of Fe consumed. However, anoxic corrosion experiments ( HYPERLINK "../../references/Others/Telander_Westerman_1993_Hydrogen_Generation_by_Metal_Corrosion_SAND92_7347.pdf" Telander and Westerman 1993) did not indicate the production of H2 in excess of the amount of Fe consumed. Therefore, the stoichiometric factor x in Reaction ( REF EQ_PA77 \h \* MERGEFORMAT PA.75) is set to 1.0 (i.e., x = 1), which implies that Reaction ( REF EQ_PA75 \h \* MERGEFORMAT PA.73) represents corrosion. Thus, the stoichiometric factor for corrosion is
(PA. SEQ Eq._PA- \* ARABIC 76)
which implies that one mole of H2 is produced for each mole of Fe consumed, and the stoichiometric factor for brine consumption is
(PA. SEQ Eq._PA- \* ARABIC 77)
which implies that two moles of H2O are consumed for each mole of H2 produced.
The most plausible biodegradation reactions after closure of the WIPP are believed to be (Wang and Brush 1996a)
denitrification C6H1OO5 + 4.8H+ + 4.8NO3( = 7.4H2O + 6CO2 + 2.4N2 (PA. SEQ Eq._PA- \* ARABIC 78)
sulfate reduction C6H1OO5 + 6H+ + 3SO42( = 5H2O + 6CO2 + 3H2S (PA. SEQ Eq._PA- \* ARABIC 79)
methanogenesis C6H1OO5 + H2O = 3CH4 + 3CO2 (PA. SEQ Eq._PA- \* ARABIC 80)
Accumulation of CO2 produced by the above reactions could decrease pH and add carbonate to increase An solubility in the repository ( HYPERLINK "../../references/Others/Wang_Brush_to_Tierney_1996_February_23_Modify_the_Stoichiometric_Factory_in_BRAGFLO.pdf" Wang and Brush 1996b).
However, in the CRA-2004 PABC, the EPA ( HYPERLINK "../../references/Others/Cotsworth_to_Triay_March_4_2005_EPA_Letter_on_Conducting_ERMS538858.pdf" Cotsworth 2005) directed the DOE to remove methanogenesis (Equation ( REF EQ_PA82 \h \* MERGEFORMAT PA.80)) from PA. The EPA cited the presence of calcium sulfate as gypsum and anhydrite in the bedded salt surrounding the repository as possible sources of sulfate. These sources of sulfate would, if accessible, promote sulfate reduction (Equation ( REF EQ_PA83 \h \* MERGEFORMAT PA.82)), which is energetically and kinetically favored over methanogenesis. In response, the DOE removed methanogenesis from PA. Additionally, the DOE removed Fe sulfidation from PA as a gas-consuming reaction because sulfidation of steel produces one mole of H2 for every mole of H2S consumed,
Fe + H2S = FeS + H2 (PA. SEQ Eq._PA- \* ARABIC 81)
This and the removal of methanogenesis are discussed fully in Nemer and Zelinski (HYPERLINK "../../references/Others/Nemer_Zelinski_2005_Analysis_Report_for_BRAGFLO_Modeling_Results_ERMS538748.PDF"2005).
To provide added assurance of WIPP performance, a sufficient amount of MgO is added to the repository to remove CO2 ( HYPERLINK "../../references/Others/Bynum_et_al_Implementation_of_Chemical_Controls_SAND96_2656C.pdf" Bynum et al. 1997). MgO in polypropylene supersacks is emplaced on top of the three-layer waste stacks to create conditions that reduce An solubilities in the repository (see HYPERLINK "../Appendix_MgO/Appendix_MgO.htm" Appendix MgO-2009 and HYPERLINK "../Appendix_SOTERM/Appendix_SOTERM.htm" \l "SOTERM-2_3" Appendix SOTERM-2009, Section SOTERM-2.3). If brine flows into the repository, MgO will react with water in brine and in the gaseous phase to produce brucite (Mg[OH]2). MgO will react with essentially all of the CO2 that could be produced by complete microbial consumption of the CPR materials in the waste, and will create hydromagnesite with the composition Mg5(CO3)4(OH)24H2O (Appendix MgO-2009; HYPERLINK "../Appendix_SOTERM/Appendix_SOTERM.htm" \l "SOTERM-2_0" Appendix SOTERM-2009, Section SOTERM-2.0). The most important MgO hydration and carbonation reactions that will occur in the WIPP are
MgO + H2O(aq and/or g) ! Mg(OH)2 (PA. SEQ Eq._PA- \* ARABIC 82)
5Mg(OH)2 + 4CO2(aq and/or g) ! Mg5(CO3)4(OH)2(4H2O (PA. SEQ Eq._PA- \* ARABIC 83)
In these equations, aq and/or g indicates that the H2O or CO2 that reacts with MgO and/or brucite could be present in the aqueous phase (brine) and/or the gaseous phase. The removal of CO2 by MgO is not explicitly modeled as a separate reaction in PA. Rather, the effect of CO2 consumption is accounted for by modifying the stoichiometry of Reaction ( REF EQ_PA80 \h \* MERGEFORMAT PA.78), Reaction ( REF EQ_PA81 \h PA.79), and Reaction ( REF EQ_PA82 \h \* MERGEFORMAT PA.80) to remove the CO2 from the mass of gas produced by microbial action.
The average stoichiometry of Reaction ( REF EQ_PA80 \h \* MERGEFORMAT PA.78) , Reaction ( REF EQ_PA81 \h PA.79), and Reaction ( REF EQ_PA82 \h \* MERGEFORMAT PA.80), is
(PA. SEQ Eq._PA- \* ARABIC 84)
where the average stoichiometric factor y in Reaction ( REF EQ_PA85 \h \* MERGEFORMAT PA.84) represents the number of moles of gas produced and retained in the repository from each mole of carbon consumed. This factor y depends on the extent of the individual biodegradation pathways in Reaction ( REF EQ_PA85 \h \* MERGEFORMAT PA.84), and the consumption of CO2 by MgO. A range of values for y is estimated by considering the maximum mass of gas that can be produced from consumption of cellulosics (Mcel) and Fe-base metals (MFe), and is derived as follows ( HYPERLINK "../../references/Others/Wang_Brush_to_Tierney_1996_February_23_Modify_the_Stoichiometric_Factory_in_BRAGFLO.pdf" Wang and Brush 1996b). Estimates of the maximum quantities Mcel and MFe (mol) of cellulosics (i.e., C6H10O5) and steels that can be potentially consumed in 10,000 years are given by
(PA. SEQ Eq._PA- \* ARABIC 85)
(PA. SEQ Eq._PA- \* ARABIC 86)
where mcel and mFe are the masses (kg) of cellulosics (see Equation ( REF EQ_PA74 \h \* MERGEFORMAT PA.72) for definition) and steels initially present in the repository. The mass of cellulosics that can be consumed is determined by the uncertain parameter WMICDFLG (see HYPERLINK \l "Table_PA-19" REF TablePA_19 \h Table PA-19). The mass of steels mFe = 5.16 ( 107 kg; this value is calculated as
(PA. SEQ Eq._PA- \* ARABIC 87)
where VCH and VRH are the volumes of CH-TRU and RH-TRU waste, (WCH and (WRH are the Fe densities in CH-TRU and RH-TRU waste, and (CCH and (CRH are the Fe densities of the containers of CH-TRU and RH-TRU waste (see HYPERLINK "../../references/Others/Fox_2008_Parameter_Report_CRA_2009_ERMS549747.pdf" \l "page=217"Fox 2008, Table 34). The terms 6000mcel/162 and 1000 mFe/56 in Equation ( REF EQ_PA86 \h \* MERGEFORMAT PA.85) and Equation ( REF EQ_PA87 \h \* MERGEFORMAT PA.86) equal the inventories in moles of cellulosics and steel, respectively. The terms 3.2 ( 1011 Rmmcel and 4.4(1016RciAdnd equal the maximum amounts of cellulosics and steel that could be consumed over 10,000 years. In Equation ( REF EQ_PA86 \h \* MERGEFORMAT PA.85), Rm = max{Rmh, Rmi}, where Rmh and Rmi are defined by uncertain variables (see WGRMICH and WGRMICI in REF TablePA_19 \h Table PA-19, respectively), and 3.2 ( 1011 = (3.15569 ( 107 s/yr) (104 yr). In Equation ( REF EQ_PA87 \h \* MERGEFORMAT PA.86), Adnd is the total surface area of all drums (m2) and the factor 4.4 ( 1016 = (3.15569 ( 107 s/yr) (104 yr) (1.41(105mol/ m3), where (Fe = 1.41 ( 105 mol/m3 (see Equation ( REF EQ_PA74 \h \* MERGEFORMAT PA.72)) ( HYPERLINK "../../references/Others/Telander_Westerman_1993_Hydrogen_Generation_by_Metal_Corrosion_SAND92_7347.pdf" Telander and Westerman 1993), converts the corrosion rate from m/s to mol/m2/s.
A range of possible values for the average stoichiometric factor y in Reaction ( REF EQ_PA85 \h \* MERGEFORMAT PA.84) can be obtained by considering individual biodegradation pathways involving Mcel and accounting for the removal of CO2 by the MgO.
In the absence of methanogenesis and steel sulfidation, y from Equation ( REF EQ_PA85 \h \* MERGEFORMAT PA.84) becomes
(PA. SEQ Eq._PA- \* ARABIC 88)
EMBED Equation.3 (PA. SEQ Eq._PA- \* ARABIC 89)
where EMBED Equation.DSMT4 is the quantity of NO3( (mols) initially present in the repository. Specifically, EMBED Equation.DSMT4 = 4.31 ( 107 mol (HYPERLINK "../../references/Others/Fox_2008_Parameter_Report_CRA_2009_ERMS549747.pdf" \l "page=230"Fox 2008, Table 39).
Capillary Action in the Waste
Capillary action (wicking) is the ability of a material to carry a fluid by capillary forces above the level it would normally seek in response to gravity. In the current analysis, this phenomena is accounted for by defining an effective saturation given by
EMBED Equation.DSMT4 (PA. SEQ Eq._PA- \* ARABIC 90)
where
Sb,eff = effective brine saturation
Sb = brine saturation
Swick = wicking saturation
Smin = minimum brine saturation at which code can run in the waste-filled areas
= smoothing parameter = (1000
The effective saturation given by Equation ( REF EQ_PA91 \h \* MERGEFORMAT PA.90) differs from that in the CRA-2004 PA in that Sb,eff now approaches zero as Sb approaches a small value Smin. In simulations where Fe corrosion dried out the repository, the time required to complete the simulation could be quite long. In order to speed up the code and increase robustness, the parameter Smin was added. For PA, Smin = 0.015, which was small enough to not affect the results, while greatly reducing run time. This is explained fully in Nemer and Clayton ( HYPERLINK "../../references/Others/Nemer_Clayton_2008_Analysis_Package_for_Salado_Flow_Modeling_ERMS548607.pdf" \l "page=41" 2008, Section 5.2.2).
The effective saturation is used on a grid block basis within all waste regions (Waste Panel, South RoR, and North RoR in HYPERLINK \l "Figure_PA-15" REF _Ref201037169 \* MERGEFORMAT Figure PA-15). The wicking saturation, Swick, is treated as an uncertain variable (see WASTWICK in HYPERLINK \l "Table_PA-19" REF TablePA_19 \h Table PA-19). The effective brine saturation Sb,eff is currently used only to calculate the corrosion of steel (Equation ( REF EQ_PA70 \h \* MERGEFORMAT PA.68)) and the microbial degradation of cellulose (Equation ( REF EQ_PA72 \h \* MERGEFORMAT PA.70)), and does not directly affect the two-phase flow calculations indicated.
Shaft Treatment
The WIPP excavation includes four shafts that connect the repository region to the surface: the air intake shaft, salt handling shaft, waste handling shaft, and exhaust shaft. In PA, these four shafts are modeled as a single shaft. The rationale for this modeling treatment is set forth in SNL (HYPERLINK "../../references/Others/SNL_1992_Preliminary_PA_for_WIPP_SAND92_0700_1_5.pdf" \l "page=1577"Sandia National Laboratories 1992, Volume 5, Section 2.3).
The shaft seal model included in the PA grid (Column 43 in HYPERLINK \l "Figure_PA-15" REF _Ref201037169 \* MERGEFORMAT Figure PA-15) is the simplified shaft model used in the CRA-2004 PA and the CRA-2004 PABC. The simplified shaft seal model used in PA is described by Stein and Zelinski ( HYPERLINK "../../references/Others/Stein_Zelinski_2003_Analysis_Report_for_Testing_Proposed_BRAGFLO_Grid_ERMS526868.pdf" 2003) and is briefly discussed below; this model was approved by the Salado Flow Peer Review Panel ( HYPERLINK "../../references/Others/Caporuscio_et_al_2003_Salado_Flow_Conceptual_Models_ERMS526879.pdf" Caporuscio, Gibbons, and Oswald 2003).
The planned design of the shaft seals involves numerous materials, including earth, crushed salt, clay, asphalt, and Salado Mass Concrete (SMC) (see the HYPERLINK "../../references/CCA/Appendix_SEAL.pdf" CCA, Appendix SEAL). The design is intended to control both short-term and long-term fluid flow through the Salado portion of the shafts. For the CCA PA, each material in the shaft seal was represented in the BRAGFLO grid. Analysis of the flow results from the CCA PA and the subsequent CCA PAVT ( HYPERLINK "../../references/Others/ERMS420667.pdf" Sandia National Laboratories 1997 and HYPERLINK "../../references/Others/DOE_1997_Supplemental_Summary_of_EPA_Mandated_PAVT_All_Replicates_ERMS414879.pdf" U.S. Department of Energy 1997) indicated that no significant flows of brine or gas occurred in the shaft during the 10,000-year regulatory period. As a result of these analyses, a simplified shaft seal model was developed for the CRA-2004 PA.
A conceptual representation of the simplified shaft seal system used in PA is shown in HYPERLINK \l "Figure_PA-18" REF _Ref201042231 \* MERGEFORMAT Figure PA-18. The simplified model divides the shaft into three sections: an upper section (shaft seal above the Salado), a lower section (within the Salado), and a concrete monolith section within the repository horizon. A detailed discussion of how the material properties were assigned for the simplified shaft seal model is included in James and Stein ( HYPERLINK "../../references/Others/James_Stein_2003_Analysis_Report_for_Development_ERMS525203.pdf" 2003). The permeability value used to represent the upper and lower sections is defined as the harmonic mean of the component materials permeability in the detailed shaft seal model (including permeability adjustments made for the DRZ assumed to surround the lower shaft seal section within the Salado). Porosity is defined as the thickness-weighted mean porosity of the component materials. Other material properties are described in James and Stein (2003).
The lower section of the shaft experiences a change in material properties at 200 years. This change simulates the consolidation of seal materials within the Salado and significantly decreases permeability. This time was chosen as a conservative overestimate of the amount of time expected for this section of the shaft to become consolidated. The concrete monolith section of the shaft is unchanged from the CCA PA and is represented as being highly permeable for 10,000 years to ensure that fluids can access the north end (operations and experimental areas) in the model. In three thin regions at the stratigraphic position of the anhydrite MBs, the shaft seal is modeled as MB material ( HYPERLINK \l "Figure_PA-18" REF _Ref201042231 \* MERGEFORMAT Figure PA-18). This model feature is included so that fluids flowing in the DRZ and MB fractures can access the interbeds to the north of the repository around the shaft seals. Because these layers are so thin, they have virtually no effect on the effective permeability of the shaft seal itself.
The simplified shaft model was tested in the AP-106 analysis ( HYPERLINK "../../references/Others/Stein_Zelinski_2003_Analysis_Report_for_Testing_Proposed_BRAGFLO_Grid_ERMS526868.pdf" Stein and Zelinski 2003), which supports the Salado Flow Peer Review ( HYPERLINK "../../references/Others/Caporuscio_et_al_2003_Salado_Flow_Conceptual_Models_ERMS526879.pdf" Caporuscio, Gibbons, and Oswald 2003). The results of the AP-106 analysis demonstrate that vertical brine flow through the simplified shaft model is comparable to brine flows seen through the detailed shaft model used in the CCA PA and subsequent CCA PAVT calculations.
Option D Panel Closures
PA includes panel closures models that represent the Option D panel closure design (see the HYPERLINK "../../references/CRA-2004/Chapter_6.pdf" \l "page=80" CRA-2004, Chapter 6.0, Section 6.4.3), which are unchanged from the CRA-2004. Option D closures ( HYPERLINK \l "Figure_PA-19" REF _Ref201042335 \* MERGEFORMAT Figure PA-19) are designed to allow minimal fluid flow between panels. PA explicitly represents selected Option D panel closures in the computational grid using a model approved by the Salado Flow Peer Review Panel ( HYPERLINK "../../references/Others/Caporuscio_et_al_2003_Salado_Flow_Conceptual_Models_ERMS526879.pdf" Caporuscio, Gibbons, and Oswald 2003). The Option D panel closure design has several components: an SMC monolith, which extends into the DRZ in all directions; an empty drift section; and a block and mortar explosion wall ( REF _Ref201042335 \h \* MERGEFORMAT Figure PA-19). Each set of panel closures are represented in the BRAGFLO grid by 4 materials in 13 grid cells ( HYPERLINK \l "Figure_PA-20" REF _Ref201042351 \* MERGEFORMAT Figure PA-20):
Figure PA- SEQ Figure_PA- \* ARABIC 18. Schematic View of the Simplified Shaft Model (numbers on right indicate dimensions in meters)
Figure PA- SEQ Figure_PA- \* ARABIC 19. Schematic Side View of Option D Panel Closure
Six cells of panel closure concrete (area CONC_PCS, material CONC_PCS)
One cell above and one cell below the concrete material consisting of MB anhydrite (areas MB 139 and Anhydrite AB, materials S_MB139 and S_ANH_AB, respectively)
Two cells of healed DRZ above Anhydrite AB and the panel closure system (PCS) (area DRZ_PCS, material DRZ_PCS)
Three cells of empty drift and explosion wall (area DRF_PCS, material DRF_PCS)
Figure PA- SEQ Figure_PA- \* ARABIC 20. Representation of Option D Panel Closures in the BRAGFLO Grid
Properties for the materials making up the panel closure system are listed in HYPERLINK \l "Table_PA-3" REF _Ref201037522 \* MERGEFORMAT Table PA3.
Panel Closure Concrete
The Option D panel closure design requires the use of a salt-saturated concrete, identified as SMC, as specified for the shaft seal system. The design of the shaft seal system and the properties of SMC are described in the HYPERLINK "../../references/CCA/Appendix_SEAL.pdf" CCA, Appendix SEAL. The BRAGFLO grid incorporates the material CONC_PCS, which is assigned the material properties of undegraded SMC and is used to represent the concrete portion of the Option D panel closure system ( HYPERLINK \l "Figure_PA-15" REF _Ref201037169 \* MERGEFORMAT Figure PA-15). A double-thickness concrete segment represents the northernmost set of panel closures (between the north RoR and the operations area). This feature represents the two sets of panel closures in series that will be emplaced between the waste-filled repository and the shaft.
Panel Closure Abutment with MBs
In the BRAGFLO grid, regions where the Option D panel closures intersect the MBs are represented as blocks of MB material ( HYPERLINK \l "Figure_PA-15" REF _Ref201037169 \* MERGEFORMAT Figure PA-15). This representation is warranted for two reasons:
1. The MB material has a very similar permeability distribution (10(21 to 10(17.1 m2) to the concrete portion of the Option D panel closures (10(20.699 to 10(17 m2), and thus, assigning this material as anhydrite MB in the model has essentially the same effect as calling it concrete, as long as pressures are below the fracture initiation pressure.
2. In the case of high pressures, it is expected that fracturing may occur in the anhydrite MBs and flow could go around the panel closures and out of the two-dimensional plane considered in the model grid. In this case, the flow would be through the MB material, which incorporates a fracture model, as described above.
DRZ Above the Panel Closure
After constructing the concrete portion of the panel closure, the salt surrounding the monolith will be subjected to compressive stresses, which will facilitate the rapid healing of disturbed halite. The rounded configuration of the monolith creates a situation very favorable for concrete durability: high compressive stresses and low stress differences. In turn, the compressive stresses developed within the salt will quickly heal any damage caused by construction excavation, thereby eliminating the DRZ along this portion of the panel closure. The permeability of the salt immediately above and below the rigid concrete monolith component of Option D will approach the intrinsic permeability of the undisturbed Salado halite.
To represent the DRZ above the monoliths, PA uses the material DRZ_PCS in the BRAGFLO grid ( HYPERLINK \l "Figure_PA-15" REF _Ref201037169 \* MERGEFORMAT Figure PA-15). The values assigned to DRZ_PCS are the same as those used for the DRZ above the excavated areas (material DRZ_1, see HYPERLINK \l "Table_PA-3" REF _Ref201037522 \* MERGEFORMAT Table PA3), except for the properties PRMX_LOG, PRMY_LOG, and PRMZ_LOG, the logarithms of permeability in the x, y, and z directions, respectively. These permeability values are assigned the same distributions used for the material CONC_PCS. In this instance, the values are based on the nature of the model setup, not directly on experimental data (although the general range of the distribution agrees with experimental observations of healed salt). The use of these permeabilities ensures that any fluid flow is equally probable through or around the Option D panel closures, and represents the range of uncertainty that exists in the performance of the panel closure system.
Empty Drift and Explosion Wall Materials
The DRF_PCS is the material representing the empty drift and explosion wall. For simplicity, this material is assumed to have hydrologic properties equivalent to the material representing the waste panel and is used for the three sets of panel closures represented in the grid ( HYPERLINK \l "Figure_PA-15" REF _Ref201037169 \* MERGEFORMAT Figure PA-15). The creep closure model is applied to this material to be consistent with the neighboring materials. The assignment of a high permeability to this region for the PA calculations, which contains the explosion wall, is justified because the explosion wall is not designed to withstand the stresses imposed by creep closure beyond the operational period and will be highly permeable following rapid room closure.
Borehole Model
The major disruptive event in PA is the penetration of the repository by a drilling intrusion. In the undisturbed scenario (see HYPERLINK \l "PA-6_7_1" Section REF _Ref201042504 \r \* MERGEFORMAT PA-6.7.1), these blocks have the material properties of the neighboring stratigraphic or excavated modeling unit, and there is no designation in the borehole grid except for the reduced lateral dimensions of this particular column of grid blocks.
In the scenarios simulating drilling disturbance, these cells start out with the same material properties as in the undisturbed scenario, but at the time of intrusion, the borehole grid blocks are reassigned to borehole material properties. The drilling intrusion is modeled by modifying the permeability of the grid blocks in Column 26 of HYPERLINK \l "Figure_PA-15" REF _Ref201037169 \* MERGEFORMAT Figure PA-15 (values listed in HYPERLINK \l "Table_PA-7" REF _Ref201126320 \h \* MERGEFORMAT Table PA-7). Furthermore, the drilling intrusion is assumed to produce a borehole with a diameter of 12.25 in. (0.31m) ( HYPERLINK "../../references/Others/Vaughn_to_Tierney_1996_February_13_WAS_AREA_and_REPOSIT_SAT_RBRN_ERMS234902.pdf" Vaughn 1996, HYPERLINK "../../references/Others/Howard_to_SNL_1996_February_23_PA_Parameter_Input_ERMS247595.pdf" Howard 1996), borehole fill is assumed to be incompressible, capillary effects are ignored, residual gas and brine saturations are set to zero, and porosity is set to 0.32 (see materials CONC_PLG, BH_OPEN, BH_SAND, and BH_CREEP in HYPERLINK \l "Table_PA-3" REF _Ref201037522 \* MERGEFORMAT Table PA3). When a borehole that penetrates pressurized brine in the Castile is simulated (i.e., an E1 intrusion), the permeability modifications indicated in REF _Ref201126320 \h \* MERGEFORMAT Table PA-7 extend from the ground surface (i.e., Grid Cell 2155 in HYPERLINK \l "Figure_PA-17" REF _Ref201037354 \* MERGEFORMAT Figure PA-17) to the base of the pressurized brine (i.e., Grid Cell 2225 in REF _Ref201037354 \* MERGEFORMAT Figure PA-17). When a borehole that does not penetrate pressurized brine in the Castile is under consideration (i.e., an E2 intrusion), the permeability modifications indicated in REF _Ref201126320 \h \* MERGEFORMAT Table PA-7 stop at the bottom of the lower DRZ (i.e., Grid Cell 1111 in REF _Ref201037354 \* MERGEFORMAT Figure PA-17).
Castile Brine Reservoir
High-pressure Castile brine was encountered in several WIPP-area boreholes, including the WIPP-12 borehole within the controlled area and the ERDA-6 borehole northeast of the site. Consequently, the conceptual model for the Castile includes the possibility that brine reservoirs underlie the repository. The E1 and E1E2 scenarios include borehole penetration of both the repository and a brine reservoir in the Castile.
Unless a borehole penetrates both the repository and a brine reservoir in the Castile, the Castile is conceptually unimportant to PA because of its expected low permeability. Two regions are specified in the disposal system geometry of the Castile horizon: the Castile (Rows 1 and 2 in
Table PA- SEQ Table_PA- \* ARABIC 7. Permeabilities for Drilling Intrusions Through the Repository
Time After IntrusionAssigned Permeabilities0200 yearsConcrete plugs are assumed to be emplaced at the Santa Rosa (i.e., a surface plug with a length of 15.76 m; corresponds to Grid Cells 2113, 2155 in HYPERLINK \l "Figure_PA-17" REF _Ref201037354 \* MERGEFORMAT Figure PA-17) and the Los Medaos Member of the Rustler (i.e., a plug at the top of the Salado with a length of 36 m; corresponds to Grid Cell 1644 in REF _Ref201037354 \* MERGEFORMAT Figure PA-17). Concrete plugs are assumed to have a permeability log-uniformly sampled between 10-19 m2 to 10-17m2 (see material CONC_PLG in HYPERLINK \l "Table_PA-4" REF _Ref201038785 \* MERGEFORMAT Table PA-4). The open portions of the borehole are assumed to have a permeability of 1 ( 10(9 m2.2001200 yearsConcrete plugs are assumed to fail after 200 years ( HYPERLINK "../../references/Others/DOE_1995_WIPP_Sealing_System_Design_Report_95_3117.pdf" U.S. Department of Energy 1995). An entire borehole is assigned a permeability typical of silty sand log-uniformly sampled between 10-16.3 m2 and 10-11 m2 (see parameter BHPRM in HYPERLINK \l "Table_PA-19" REF TablePA_19 \h Table PA-19 and material BH_SAND in REF _Ref201038785 \* MERGEFORMAT Table PA-4).> 1200 yearsPermeability of borehole reduced by one order of magnitude in the Salado beneath the repository due to creep closure of borehole ( HYPERLINK "../../references/Others/Thompson_et_al_1996_Inadvertent_Intrusion_Borehole_Permeability.pdf" Thompson et al. 1996) (i.e., k = 10x/10, x = BHPRM, in Grid Cells 2225, 1576, 26, 94, 162, 230 of REF _Ref201037354 \* MERGEFORMAT Figure PA-17). No changes are made within and above the lower DRZ (see material BH_CREEP in REF _Ref201038785 \* MERGEFORMAT Table PA-4).
HYPERLINK \l "Figure_PA-15" REF _Ref201037169 \h \* MERGEFORMAT Figure PA-15) and a reservoir (Row 1, Columns 23 to 45 in REF _Ref201037169 \h \* MERGEFORMAT Figure PA-15). The Castile region has an extremely low permeability, which prevents it from participating in fluid flow processes.
It is unknown whether a brine reservoir exists below the repository. As a result, the conceptual model for the brine reservoirs is somewhat different from those for known major properties of the natural barrier system, such as stratigraphy. The principal difference is that a reasonable treatment of the uncertainty of the existence of a brine reservoir requires assumptions about the spatial distribution of such reservoir and the probability of intersection (see HYPERLINK "../Appendix_MASS/Appendix_MASS.htm" \l "MASS-18_1" Attachment MASS-2009, Section MASS.18.1). A range of probabilities for a borehole hitting a brine reservoir is used (see HYPERLINK \l "PA-3_6" Section REF _Ref201732833 \r \h \* MERGEFORMAT PA-3.6).
In addition to the stochastic uncertainty in the location and hence in the probability of intersecting reservoirs, there is also uncertainty in the properties of reservoirs. The manner in which brine reservoirs would behave if penetrated is captured by parameter ranges and is incorporated in the BRAGFLO calculations of disposal system performance. The conceptual model for the behavior of such a brine reservoir is discussed below. The properties specified for brine reservoirs are pressure, permeability, compressibility, and porosity, and are sampled from parameter ranges (see HYPERLINK \l "Table_PA-19" REF TablePA_19 \h Table PA-19).
Where they exist, Castile brine reservoirs in the northern Delaware Basin are believed to be fractured systems, with high-angle fractures spaced widely enough that a borehole can penetrate through a volume of rock containing a brine reservoir without intersecting any fractures, and therefore not producing brine. Castile brine reservoirs occur in the upper portion of the Castile ( HYPERLINK "../../references/Others/Popielak_et_al_1983_Brine_Reservoirs_in_the_Castile_Formation_TME3153.pdf" Popielak et al. 1983). Appreciable volumes of brine have been produced from several reservoirs in the Delaware Basin, but there is little direct information on the areal extent of the reservoirs or the existence of the interconnection between them. Data from WIPP-12 and ERDA-6 indicate that fractures have a variety of apertures and permeabilities, and they deplete at different rates. Brine occurrences in the Castile behave as reservoirs; that is, they are bounded systems.
Numerical Solution
Determining gas and brine flow in the vicinity of the repository requires solving the two nonlinear PDEs in Equation ( REF EQ_PA26 \h \* MERGEFORMAT PA.24) through Equation ( REF EQ_PA32 \h \* MERGEFORMAT PA.30) on the computational domain in HYPERLINK \l "Figure_PA-15" REF _Ref201037169 \* MERGEFORMAT Figure PA-15, along with evaluating appropriate auxiliary conditions. The actual unknown functions in this solution are Pb and Sg, although the constraint conditions also give rise to values for Pg and Sb. As two dimensions in space and one dimension in time are in use, Pb, Pg, Sb, and Sg are functions of the form Pb(x, y, t), Pg(x, y, t), Sb(x, y, t), and Sg(x, y, t).
Solving Equation ( REF EQ_PA26 \h \* MERGEFORMAT PA.24) through Equation ( REF EQ_PA32 \h \* MERGEFORMAT PA.30) requires both initial value and boundary value conditions for Pb and Sg. The initial value conditions for Pb and Sg are given in HYPERLINK \l "PA-4_2_2" Section REF _Ref201043110 \r \* MERGEFORMAT PA-4.2.2. As indicated there, the calculation starts at time t = "5 years, with a possible resetting of values at t = 0 years, which corresponds to final waste emplacement and sealing of the repository. The boundary conditions are such that no brine or gas moves across the exterior grid boundary ( HYPERLINK \l "Table_PA-8" REF _Ref210625172 \h \* MERGEFORMAT Table PA-8). This Neumann-type boundary condition is maintained for all time. Further, BRAGFLO allows the user to maintain a specified pressure and/or saturation at any grid
Table PA- SEQ Table_PA- \* ARABIC 8. Boundary Value Conditions for Pg and Pb
Boundaries below (Row 1, y = 0 m) and above (Row 33, y = 1039 m) system for 0 ( x ( 46630 m (Columns 1-68) and -5 yr ( t. Below, j refers to the unit normal vector in the positive y direction.(j = 0 Pa / mNo gas flow condition(j = 0 Pa / mNo brine flow conditionBoundaries at left (Column 1, x = 0 m) and right (Column 68, x = 46630 m) of system for 0 ( y ( 1039 m (Rows 1-33) and -5 yr ( t. Below, i refers to the unit normal vector in the positive x direction. (i = 0 Pa / mNo gas flow condition(i = 0 Pa / mNo brine flow condition
block. This is not a boundary condition and is not required to close the problem. This feature is used to specify Dirichlet-type conditions at the surface grid blocks (Columns 1-68, Row 33, HYPERLINK \l "Figure_PA-15" REF _Ref201037169 \* MERGEFORMAT Figure PA-15) and at the far-field locations in the Culebra and Magenta (Columns 1 and 68, Row 26, and Columns 1 and 68, Row 28, REF _Ref201037169 \* MERGEFORMAT Figure PA-15). These auxiliary conditions are summarized in HYPERLINK \l "Table_PA-9" REF _Ref211931830 \h \* MERGEFORMAT Table PA-9.
A fully implicit finite-difference procedure is used to solve Equation ( REF EQ_PA26 \h \* MERGEFORMAT PA.24) through Equation ( REF EQ_PA32 \h \* MERGEFORMAT PA.30). The associated discretization of the gas mass balance equation is given by
Table PA- SEQ Table_PA- \* ARABIC 9. Auxiliary Dirichlet Conditions for Sg and Pb
Surface Grid Blocks = 0.08363Columns 142, 4468, Row 33, -5 yr ( t
Saturation is not forced at the shaft cell on the surface because its saturation is reset to 1.0 at t = 0 yr. = 1.01 ( 105 PaColumns 168, row 33, 5 yr ( tCulebra and Magenta Far Field = 9.14 ( 105 Pai = 1 and 68, j = 26, 5 yr ( t (Culebra) = 9.47 ( 105 Pai = 1 and 68, j = 28, 5 yr ( t (Magenta)
(PA. SEQ Eq._PA- \* ARABIC 91)
where ( represents the phase potentials given by
and
the subscripts are defined by
i = x-direction grid index
j = y-direction grid index
= x-direction grid block interface
= y-direction grid block interface
xi = grid block center in the x-coordinate direction (m)
yj = grid block center in the y-coordinate direction (m)
= grid block length in the x-coordinate direction (m)
= grid block length in the y-coordinate direction (m)
the superscripts are defined by
n = index in the time discretization, known solution time level
n+1 = index in the time discretization, unknown solution time level
and the interblock densities are defined by
The interface values of krg in Equation ( REF EQ_PA92 \h \* MERGEFORMAT PA.91) are evaluated using upstream weighted values (i.e., the relative permeabilities at each grid block interface are defined to be the relative permeabilities at the center of the adjacent grid block with the highest potential). Further, interface values for ((gkx/(g and ((gky/(g are obtained by harmonic averaging of adjacent grid block values for these expressions. Currently all materials are isotropic, i.e. kx = ky = kz.
The discretization of the brine mass balance equation is obtained by replacing the subscript for gas, g, by the subscript for brine, b. As a reminder, Pg and Sb are replaced in the numerical implementation with the substitutions indicated by Equation ( REF EQ_PA29 \h \* MERGEFORMAT PA.27) and Equation ( REF EQ_PA28 \h \* MERGEFORMAT PA.26), respectively. Wells are not used in the conceptual model for long-term Salado flow calculations, but they are used for DBR calculations. Thus, for long-term Salado flow calculations, the terms qg and qb are zero. For long-term Salado flow calculations, the wellbore is not treated by a well model, but rather is explicitly modeled within the grid as a distinct material region (i.e., Upper Borehole and Lower Borehole in HYPERLINK \l "Figure_PA-15" REF _Ref201037169 \* MERGEFORMAT Figure PA-15).
The resultant coupled system of nonlinear brine and gas mass balance equations is integrated in time using the Newton-Raphson method with upstream weighting of the relative permeabilities, as previously indicated. The primary unknowns at each computational cell center are brine pressure and gas saturation.
Gas and Brine Flow across Specified Boundaries
The Darcy velocity vectors vg(x, y, t) and vb(x, y, t) for gas and brine flow (m3/m2/s = m/s) are defined by the expressions
(PA. SEQ Eq._PA- \* ARABIC 92)
and
(PA. SEQ Eq._PA- \* ARABIC 93)
Values for vg and vb are obtained and saved as the numerical solution of Equation ( REF EQ_PA26 \h \* MERGEFORMAT PA.24) through Equation ( REF EQ_PA32 \h \* MERGEFORMAT PA.30) is carried out. Cumulative flows of gas, Cg(t, B), and brine, Cb(t, B), from time 0 to time t across an arbitrary boundary B in the domain of ( HYPERLINK \l "Figure_PA-15" REF _Ref201037169 \* MERGEFORMAT Figure PA-15) is then given by
EMBED Equation.DSMT4 (PA. SEQ Eq._PA- \* ARABIC 94)
for l = g, b, where ((x, y) is the geometry factor defined in Equation ( REF EQ_PA34 \h \* MERGEFORMAT PA.32), n(x, y) is an outward-pointing unit normal vector, and denotes a line integral. As an example, B could correspond to the boundary of the waste disposal regions in REF _Ref201037169 \* MERGEFORMAT Figure PA-15. The integrals defining Cg(t, B) and Cb(t, B) are evaluated using the Darcy velocities defined by Equation ( REF EQ_PA93 \h \* MERGEFORMAT PA.92) and Equation ( REF EQ_PA94 \h \* MERGEFORMAT PA.93). Due to the dependence of gas volume on pressure, Cg(t, B) is typically calculated in moles or cubic meters at standard temperature and pressure, which requires an appropriate change of units for vg in Equation ( REF EQ_PA96 \h \* MERGEFORMAT PA.95).
Additional Information
Additional information on BRAGFLO and its use in the CRA-2009 PA can be found in the BRAGFLO users manual ( HYPERLINK "../../references/Others/Nemer_2007_Users_Manual_for_BRAGFLO_Version_6_ERMS545016.pdf" Nemer 2007c), the BRAGFLO design document ( HYPERLINK "../../references/Others/ERMS545015.pdf" Nemer 2007b) and the analysis package for the Salado flow calculations in the CRA-2009 PA ( HYPERLINK "../../references/Others/Nemer_Clayton_2008_Analysis_Package_for_Salado_Flow_Modeling_ERMS548607.pdf" Nemer and Clayton 2008).
Radionuclide Transport in the Salado: NUTS
The NUTS code is used to model radionuclide transport in the Salado. NUTS models radionuclide transport within all regions for which BRAGFLO computes brine and gas flow, and for each realization uses as input the corresponding BRAGFLO velocity field, pressures, porosities, saturations, and other model parameters, including, for example, the geometrical grid, residual saturation, material map, and compressibility. Of the radionuclides that are transported vertically due to an intrusion or up shaft, it is assumed that the lateral radionuclide transport is in the most transmissive unit, the Culebra. Therefore, the radionuclide transport through the Dewey Lake to the accessible environment (fDL in Equation [ REF EQ_PA35 \h \* MERGEFORMAT PA.33]) and to the land surface due to long-term flow (fS in Equation [ REF EQ_PA35 \h \* MERGEFORMAT PA.33]) are set to zero for consistency.
The PA uses NUTS in two different modes. First, the code is used in a computationally fast screening mode to identify those BRAGFLO realizations for which it is unnecessary to do full transport calculations because the amount of contaminated brine that reaches the Culebra or the LWB within the Salado is insufficient to significantly contribute to the total integrated release of radionuclides from the disposal system. For the remaining realizations, which have the possibility of consequential release, a more computationally intensive calculation of each radionuclides full transport is performed (see HYPERLINK \l "PA-6_7_2" Section REF _Ref201048300 \r \* MERGEFORMAT PA-6.7.2).
This section describes the model used to compute radionuclide transport in the Salado for E0, E1, and E2 scenarios (defined in HYPERLINK \l "PA-2_3_2" Section REF _Ref203993502 \r \h \* MERGEFORMAT PA-2.3.2). The model for transport in the E1E2 scenario, which is computed using the PANEL code, is described in HYPERLINK \l "PA-4_4" Section REF _Ref201048328 \r \* MERGEFORMAT PA-4.4.
NUTS models radionuclide transport by advection (see HYPERLINK "../Appendix_MASS/Appendix_MASS.htm" \l "MASS-13_5" Attachment MASS-2009, Section MASS-13.5). NUTS disregards sorptive and other retarding effects throughout the entire flow region. Physically, some degree of retardation must occur at locations within the repository and the geologic media; it is therefore conservative to ignore retardation processes. NUTS also ignores reaction-rate aspects of dissolution and colloid formation processes, and mobilization is assumed to occur instantaneously. Neither molecular nor mechanical dispersion is modeled in NUTS. These processes are assumed to be insignificant compared to advection, as discussed further in Attachment MASS-2009, Section MASS-13.5.
Colloidal actinides are subject to retardation by chemical interaction between colloids and solid surfaces and by clogging of small pore throats (i.e., by sieving). There will be some interaction of colloids with solid surfaces in the anhydrite interbeds. Given the low permeability of intact interbeds, it is likely that pore apertures will be small and some sieving will occur. However, colloidal particles, if not retarded, are transported slightly more rapidly than the average velocity of the bulk liquid flow. Because the effects on transport of slightly increased average pore velocity and retarded interactions with solid surfaces and sieving offset one another, the DOE assumes residual effects of these opposing processes will be either small or beneficial, and does not incorporate them when modeling An transport in the Salado interbeds.
If brine in the repository moves into interbeds, it is likely that mineral precipitation reactions will occur. Precipitated minerals may contain actinides as trace constituents. Furthermore, colloidal-sized precipitates will behave like mineral-fragment colloids, which are destabilized by brines, quickly agglomerating and settling by gravity. The beneficial effects of precipitation and coprecipitation are neglected in PA.
Fractures, channeling, and viscous fingering may also impact transport in Salado interbeds, which contain natural fractures. Because of the low permeability of unfractured anhydrite, most fluid flow in interbeds will occur in fractures. Even though some properties of naturally fractured interbeds are characterized by in situ tests, other uncertainty exists in the characteristics of the fracture network that may be created with high gas pressure in the repository. The PA modeling system accounts for the possible effects on porosity and permeability of fracturing by using a fracturing model (see HYPERLINK \l "PA-4_2_4" Section REF _Ref201735905 \r \h \* MERGEFORMAT PA-4.2.4). The processes and effects associated with fracture dilation or fracture propagation not already captured by the PA fracture model are negligible (see the HYPERLINK "../../references/CCA/Appendix_MASS.pdf" \l "page=73" CCA, Appendix MASS, Section MASS.13.3 and HYPERLINK "../../references/CCA/Appendix_MASS_Attachment_13.pdf" \l "page=10" Appendix MASS Attachment 13.2). Of those processes not already incorporated, channeling has the greatest potential effect.
Channeling is the movement of fluid through the larger-aperture sections of a fracture network with locally high permeabilities. It could locally enhance An transport. However, it is assumed that the effects of channeled flow in existing or altered fractures will be negligible for the length and time scales associated with the disposal system. The DOE believes this assumption is reasonable because processes are likely to occur that limit the effectiveness of channels or the dispersion of actinides in them. First, if gas is present in the fracture network, it will be present as a nonwetting phase and will occupy the portions of the fracture network with relatively large apertures, where the highest local permeabilities will exist. The presence of gas thus removes the most rapid transport pathways from the contaminated brine and decreases the impact of channeling. Second, brine penetrating the Salado from the repository is likely to be completely miscible with in situ brine. Because of miscibility, diffusion or other local mixing processes will probably broaden fingers (reduce concentration gradients) until the propagating fingers are indistinguishable from the advancing front.
Gas will likely penetrate the liquid-saturated interbeds as a fingered front, rather than a uniform front. Fingers form when there is a difference in viscosity between the invading fluid (gas) and the resident fluid (liquid brine), and because of channeling effects. This process does not affect An transport, however, because actinides of interest are transported only in the liquid phase, which will not displace gas in the relatively high-permeability regions due to capillary effects.
Mathematical Description
The following system of PDEs is used to model radionuclide transport in the Salado:
((( (PA. SEQ Eq._PA- \* ARABIC 95)
(PA. SEQ Eq._PA- \* ARABIC 96)
for l = 1, 2, , nR, where
= Darcy velocity vector (m3/m2/s = m/s) for brine (supplied by BRAGFLO from solution of Equation ( REF EQ_PA94 \h \* MERGEFORMAT PA.93))
Cbl = concentration (kg/m3) of radionuclide l in brine
Csl = concentration (kg/m3) of radionuclide l in solid phase (i.e., not in brine), with concentration defined with respect to total (i.e., bulk) formation volume (only used in repository; see HYPERLINK \l "Figure_PA-15" REF _Ref201037169 \* MERGEFORMAT Figure PA-15)
Sl = linkage term (kg/m3/s) due to dissolution/precipitation between radionuclide l in brine and in solid phase (see Equation ( REF EQ_PA98 \h \* MERGEFORMAT PA.97))
( = porosity (supplied by BRAGFLO from solution of Equation ( REF EQ_PA26 \h \* MERGEFORMAT PA.24) through Equation ( REF EQ_PA32 \h \* MERGEFORMAT PA.30))
Sb = brine saturation (supplied by BRAGFLO from solution of Equation ( REF EQ_PA26 \h \* MERGEFORMAT PA.24) through Equation ( REF EQ_PA32 \h \* MERGEFORMAT PA.30))
(l = decay constant (s(1) for radionuclide l
P(l) = {p: radionuclide p is a parent of radionuclide l}
nR = number of radionuclides,
and ( is the dimension-dependent geometry factor in Equation ( REF EQ_PA34 \h \* MERGEFORMAT PA.32). PA uses a two-dimensional representation for fluid flow and radionuclide transport in the vicinity of the repository, with ( defined by the element depths in REF _Ref201037169 \* MERGEFORMAT Figure PA-15. Although omitted for brevity, the terms (, vb, Cbl, Csl, Sl, Sb, and ( are functions ((x, y), vb(x, y, t), Cbl(x, y, t), Csl(x, y, t), Sl(x, y, t), Sb(x, y, t), and ((x, y, t) of time t and the spatial variables x and y. Equation ( REF EQ_PA96 \h \* MERGEFORMAT PA.95) and Equation ( REF EQ_PA97 \h \* MERGEFORMAT PA.96) are defined and solved on the same computational grid ( REF _Ref201037169 \* MERGEFORMAT Figure PA-15) used by BRAGFLO for the solution of Equation ( REF EQ_PA26 \h \* MERGEFORMAT PA.24) through Equation ( REF EQ_PA32 \h \* MERGEFORMAT PA.30).
Radionuclides are assumed to be present in both brine (Equation ( REF EQ_PA96 \h \* MERGEFORMAT PA.95)) and in an immobile solid phase (Equation ( REF EQ_PA97 \h \* MERGEFORMAT PA.96)), although radionuclide transport takes place only by brine flow (Equation ( REF EQ_PA96 \h \* MERGEFORMAT PA.95)). The maximum radionuclide concentration is assumed to equilibrate instantly for each element ( HYPERLINK \l "PA-4_3_2" Section REF _Ref201051214 \r \* MERGEFORMAT PA-4.3.2). Then each individual radionuclide equilibrates between the brine and solid phases based on the maximum concentration of its associated element and the mole fractions of other isotopes included in the calculation. The linkage between the brine and solid phases in Equation ( REF EQ_PA96 \h \* MERGEFORMAT PA.95) and Equation ( REF EQ_PA97 \h \* MERGEFORMAT PA.96) is accomplished by the term Sl, where
(PA. SEQ Eq._PA- \* ARABIC 97)
where
= maximum concentration (kg/m3) of element El(l) in oxidation state Ox(l) in brine type Br(t), where El(l) denotes the element of which radionuclide l is an isotope, Ox(l) denotes the oxidation state in which element El(l) is present, and Br(t) denotes the type of brine present in the repository at time t (see Section REF _Ref201051214 \r \* MERGEFORMAT PA-4.3.2 for definition of ).
= concentration (kg/m3) of element El(l) in brine (p = b) or solid (p = s), which is equal to the sum of concentrations of radionuclides that are isotopes of same element as radionuclide l, where k ( El(l) only if k is an isotope of element El(l):
(PA. SEQ Eq._PA- \* ARABIC 98)
= difference (kg/m3) between maximum concentration of element El(l) in brine and existing concentration of element El(l) in brine
(PA. SEQ Eq._PA- \* ARABIC 99)
MFpl = mole fraction of radionuclide l in phase p, where p = b (brine) or p = s (solid)
(PA. SEQ Eq._PA- \* ARABIC 100)
CMl = conversion factor (mol/kg) from kilograms to moles for radionuclide l
= Dirac delta function (s(1) (((( ( t) = 0 if ( ( t and )
In the CCA and the CRA-2004, the function ST had an additional parameter, Mi, representing the presence or absence of microbial activity. However, during preparations for the CRA-2004 PABC, the EPA directed the DOE to change the probability of microbial activity to 1.0 ( HYPERLINK "../../references/Others/Cotsworth_to_Triay_March_4_2005_EPA_Letter_on_Conducting_ERMS538858.pdf" Cotsworth 2005). The DOE therefore revised the probability distribution so that all vectors would have the possibility for microbial degradation of cellulose, while retaining the percentage of vectors showing microbial degradation of rubbers and plastic at 0.25 (HYPERLINK "../../references/Others/Nemer_2005_Updated_Value_of_WAS_AREAPROBDEG_ERMS539441.pdf"Nemer 2005). This, in effect, sets Mi equal to Yes for all vectors. Mi is therefore suppressed as an argument of ST in the remainder of this section.
The terms Sl, Sb, Cp,El(l), MFpl , and ( are functions of time t and the spatial variables x and y, although the dependencies are omitted for brevity. The Dirac delta function, ((( t), appears in Equation ( REF EQ_PA98 \h \* MERGEFORMAT PA.97) to indicate that the adjustments to concentration are implemented instantaneously within the numerical solution of Equation ( REF EQ_PA96 \h \* MERGEFORMAT PA.95) and Equation ( REF EQ_PA97 \h \* MERGEFORMAT PA.96) whenever a concentration imbalance is observed.
The velocity vector vb in Equation ( REF EQ_PA96 \h \* MERGEFORMAT PA.95) and Equation ( REF EQ_PA97 \h \* MERGEFORMAT PA.96) is defined in Equation ( REF EQ_PA94 \h \* MERGEFORMAT PA.93) and is obtained from the numerical solution of Equation ( REF EQ_PA26 \h \* MERGEFORMAT PA.24) through Equation ( REF EQ_PA32 \h \* MERGEFORMAT PA.30). If B denotes an arbitrary boundary (e.g., the LWB) in the domain of Equation ( REF EQ_PA96 \h \* MERGEFORMAT PA.95) and Equation ( REF EQ_PA97 \h \* MERGEFORMAT PA.96) (as shown in HYPERLINK \l "Figure_PA-15" REF _Ref201037169 \* MERGEFORMAT Figure PA-15), the cumulative transport of Cl(t, B) of radionuclide l from time 0 to time t across B is given by
EMBED Equation.DSMT4 (PA. SEQ Eq._PA- \* ARABIC 101)
where n(x, y) is an outward-pointing unit normal vector and denotes a line integral over B.
Equation ( REF EQ_PA96 \h \* MERGEFORMAT PA.95) and Equation ( REF EQ_PA97 \h \* MERGEFORMAT PA.96) models advective radionuclide transport due to the velocity vector vb. Although the effects of solubility limits are considered, no chemical or physical retardation is included in the model. Molecular diffusion is not included in the model, because the radionuclides under consideration have molecular diffusion coefficients on the order of 10(10 m2/s, and thus can be expected to move only approximately 10 m over 10,000 years due to molecular diffusion. Mechanical dispersion is also omitted in NUTS, as the uniform initial radionuclide concentrations assumed within the repository and the use of time-integrated releases in assessing compliance with HYPERLINK "40CFR191_13" section 191.13 mean that mechanical dispersion will have negligible impact on overall performance.
Calculation of Maximum Concentration ST(Br, Ox, El)
A maximum concentration ST(Br, Ox, El) (mol/liter [L]) is calculated for each brine type (Br ( {Salado, Castile}), oxidation state (Ox ( {III, IV, V, VI}), and element (El ( {Am, Pu, U, Th}). The maximum concentration is given by
(PA. SEQ Eq._PA- \* ARABIC 102)
where SD(Br, Ox) is the dissolved solubility (mol/L) and SC(Br, Ox, El) is the concentration (mol/L) of the element sorbed to colloids.
The dissolved solubility SD(Br, Ox) is given by
(PA. SEQ Eq._PA- \* ARABIC 103)
where
SFMT(Br, Ox) = dissolved solubility (mol/L) calculated by Fracture-Matrix Transport (FMT) model (HYPERLINK "../../references/Others/WIPP_PA_1998_Users_Manual_for_FMT_Version_240_ERMS243037.pdf"WIPP Performance Assessment 1998a) for brine type Br and oxidation state Ox
= logarithm (base 10) of uncertainty factor for solubilities calculated by FMT expressed as a function of oxidation state Ox
HYPERLINK \l "Table_PA-10" REF _Ref201052340 \h \* MERGEFORMAT Table PA-10 lists the calculated values of SFMT(Br, Ox); details of the calculation are provided in HYPERLINK "../Appendix_SOTERM/Appendix_SOTERM.htm" Appendix SOTERM-2009 and Brush ( HYPERLINK "../../references/Others/Brush_2005_Results_of_Calculations_of_Actinide_Solubilities_ERMS539800.pdf" 2005). The uncertainty factors UF(Ox) are determined by the uncertain parameters WSOLVAR3 for the III oxidation state and WSOLVAR4 for the IV oxidation state; definitions of these parameters are provided in HYPERLINK \l "Table_PA-19" REF TablePA_19 \h Table PA-19, and further details regarding the calculation of the solubilities is given in HYPERLINK "../Appendix_SOTERM/Appendix_SOTERM.htm" \l "SOTERM-5_1_3" Appendix SOTERM-2009, Section SOTERM-5.1.3.
Table PA- SEQ Table_PA- \* ARABIC 10. Calculated Values for Dissolved Solubility (see HYPERLINK \l "Table_SOTERM-16" Appendix SOTERM-2009, Table SOTERM-16)
BrineOxidation StateIIIIVVVIaSalado3.87 ( 10(75.64 ( 10(83.55 ( 10(61.0 ( 10(3Castile2.88 ( 10(76.79 ( 10(88.24 ( 10(71.0 ( 10(3a Values for the VI solubilities were mandated by the EPA (HYPERLINK "../../references/Others/EPA_2005_March_2_Teleconference.pdf"U.S. Environmental Protection Agency 2005).
The concentration (mol/L) of the element sorbed to colloids SC (Br, Ox, El) is given by
(PA. SEQ Eq._PA- \* ARABIC 104)
where
= solubility (concentration expressed in mol/L) in brine type Br of element El in oxidation state Ox resulting from humic colloid formation
=
= scale factor used as a multiplier on SD(Br, Ox) in definition of SHum(Br, Ox, El) (see HYPERLINK \l "Table_PA-11" REF _Ref201052404 \h \* MERGEFORMAT Table PA-11)
UBHum = upper bound on solubility (concentration expressed in mol/L) of individual An elements resulting from humic colloid formation
= 1.1 ( 10(5 mol/L
= solubility (concentration expressed in mol/L) in brine type Br of element El in oxidation state Ox resulting from microbial colloid formation
=
= scale factor used as multiplier on SD(Br, Ox) in definition of SMic(Br, Ox, El) (see HYPERLINK \l "Table_PA-12" REF _Ref211685259 \h \* MERGEFORMAT Table PA-12)
= upper bound on solubility (concentration expressed in mol/L) of element El in oxidation state Ox resulting from microbial colloid formation (see REF _Ref211685259 \h \* MERGEFORMAT Table PA-12)
Table PA- SEQ Table_PA- \* ARABIC 11. Scale Factor SFHum(Br, Ox, El) Used in Definition of SHum(Br, Ox, El) (see HYPERLINK "../Appendix_SOTERM/Appendix_SOTERM.htm" \l "Table_SOTERM-21" Appendix SOTERM-2009, Table SOTERM-21)
BrineElement (Oxidation State)Am(III)Pu(III)Pu(IV)U(IV)Th(IV)Np(IV)Np(V)U(VI)Salado0.190.196.36.36.36.39.1 ( 10-40.12CastileWPHUMOX3aWPHUMOX3a6.36.36.36.37.4 ( 10-30.51a See HYPERLINK \l "Table_PA-19" REF TablePA_19 \h Table PA-19.
Table PA- SEQ Table_PA- \* ARABIC 12. Scale Factor SFMic(Ox, El) and Upper Bound UBMic(Ox, El) (mol/L) Used in Definition of SMic(Br, Ox, El) (see HYPERLINK "../Appendix_SOTERM/Appendix_SOTERM.htm" \l "Table_SOTERM-21" Appendix SOTERM-2009, Table SOTERM-21)
ParameterElement (Oxidation State)Am(III)Pu(III)Pu(IV)U(IV)Th(IV)Np(IV)Np(V)U(VI)SFMic(Ox, El)3.60.30.30.00213.112.012.00.0021UBMic(Ox, El)16.8 ( 10(56.8 ( 10(50.00210.00190.00270.00270.0021
= solubility (concentration in mol/L) of element El resulting from An intrinsic colloid formation
= EMBED Equation.DSMT4
SMn = solubility (concentration in mol/L) of individual An element resulting from mineral fragment colloid formation
= 2.6 ( 10(8 mol/L
Radionuclides Transported
Since the solution of Equation ( REF EQ_PA96 \h \* MERGEFORMAT PA.95) and Equation ( REF EQ_PA97 \h \* MERGEFORMAT PA.96) for this many radionuclides and decay chains would be very time-consuming, the number of radionuclides for direct inclusion in the analysis was reduced using the algorithm shown in HYPERLINK \l "Figure_PA-21" REF _Ref201119766 \h \* MERGEFORMAT Figure PA-21. The CRA-2009 PA uses the same reduction algorithm as the CCA PA (see the HYPERLINK "../../references/CCA/Appendix_WCA.pdf" CCA, Appendix WCA); the algorithm was found to be acceptable in the CCA review ( HYPERLINK "../../references/Others/EPA_63_FR_27353_408_May_18_1998.pdf" U.S. Environmental Protection Agency 1998a, Section 4.6.1.1).
Figure PA- SEQ Figure_PA- \* ARABIC 21. Selecting Radionuclides for the Release Pathways Conceptualized by PA
Using HYPERLINK \l "Figure_PA-21" REF _Ref201119766 \h \* MERGEFORMAT Figure PA-21, the number of radionuclides considered was reduced from 135 to a total of 29 included in the decay calculations carried out by the PANEL code ( HYPERLINK "../../references/Others/Garner_Leigh_2005_Analysis_Package_for_PANEL_CRA_2004_PABC_ERMS540572.pdf" Garner and Leigh 2005). These radionuclides belong to the following decay chains:
EMBED Equation.DSMT4 (PA. SEQ Eq._PA- \* ARABIC 105)
EMBED Equation.DSMT4 (PA. SEQ Eq._PA- \* ARABIC 106)
EMBED Equation.DSMT4 (PA. SEQ Eq._PA- \* ARABIC 107)
EMBED Equation.DSMT4 (PA. SEQ Eq._PA- \* ARABIC 108)
Radionuclides considered in the decay calculations that do not belong to one of the decay chains listed above are 147Pm, 137Cs, and 90Sr. In addition, some intermediates with extremely short half-lives, such as 240U, were omitted from the decay chains.
Further simplification of the decay chains is possible based on the total inventories. Releases of radionuclides whose inventories total less than one EPA unit are essentially insignificant, as any release that transports essentially all of a given species outside the LWB will be dominated by the releases of other species with much larger inventories. In addition, 137Cs and 90Sr can be omitted because their concentrations drop to below 1 EPA unit within 150 years, which makes it improbable that a significant release of these radionuclides will occur. Isotopes such as 241Pu, whose decay could affect the inventory of measurable isotopes, were reinstated.
After the reduction of radionuclides outlined in HYPERLINK \l "Figure_PA-21" REF _Ref201119766 \h \* MERGEFORMAT Figure PA-21 and the above paragraph, the following 10 radionuclides remained from the decay chains shown above:
(PA. SEQ Eq._PA- \* ARABIC 109)
(PA. SEQ Eq._PA- \* ARABIC 110)
(PA. SEQ Eq._PA- \* ARABIC 111)
(PA. SEQ Eq._PA- \* ARABIC 112)
238Pu does not significantly affect transport calculations because of its short half-life (87.8 years). The remaining nine radionuclides were then further reduced by combining those with similar decay and transport properties. In particular, 234U, 230Th, and 239Pu were used as surrogates for the groups {234U, 233U}, {230Th, 229Th}, and {242Pu, 240Pu, 239Pu}, with the initial inventories of 234U, 230Th, and 239Pu being increased to account for the additional radionuclide(s) in each group.
In increasing the initial inventories, the individual radionuclides were combined on either a mole or curie basis (i.e., moles added and then converted back to curies, or curies added directly). In each case, the method that maximized the combined inventory was used; thus, 233U was added to 234U, 240Pu to 239Pu, and 229Th to 230Th by curies, while 242Pu was added to 239Pu by moles. In addition, 241Pu was added to 241Am by moles because 241Pu has a half-life of 14 years and will quickly decay to 241Am, and neglect of this ingrowth would underestimate the 241Am inventory by about 4% ( HYPERLINK \l "Table_PA-13" REF _Ref201126601 \h \* MERGEFORMAT Table PA-13). The outcome of this process was the following set of five radionuclides in three simplified decay chains:
(PA. SEQ Eq._PA- \* ARABIC 113)
which were then used with Equation ( REF EQ_PA96 \h \* MERGEFORMAT PA.95) and Equation ( REF EQ_PA97 \h \* MERGEFORMAT PA.96) for transport in the vicinity of the repository. As 238Pu does not significantly affect transport calculations, only the remaining four radionuclides are used in the Culebra transport calculations ( HYPERLINK \l "PA-4_9" Section REF _Ref207777095 \r \h \* MERGEFORMAT PA-4.9). These radionuclides account for 99% of the EPA units in the waste after 2,000 years ( HYPERLINK "../../references/Others/Garner_Leigh_2005_Analysis_Package_for_PANEL_CRA_2004_PABC_ERMS540572.pdf" Garner and Leigh 2005), and hence will dominate any releases by transport.
Table PA- SEQ Table_PA- \* ARABIC 13. Combination of Radionuclides for Transport
CombinationIsotope Initial ValuesCombination ProcedureCombined Inventory233U ( 234U1.23 ( 103 Ci 233U3.44 ( 102 Ci 234U1.23 ( 103 Ci 233U ( 1.23 ( 103 Ci 234U1.57 ( 103 Ci 234U242Pu ( 239Pu
240Pu ( 239Pu1.27 ( 101 Ci 242Pu9.55 ( 104 Ci 240Pu5.82 ( 105 Ci 239Pu1.27 ( 101 Ci 242Pu = 1.32 ( 101 moles 242Pu ( 1.32 ( 101 moles 239Pu = 1.98 ( 102 Ci 239Pu9.55 ( 104 Ci 240Pu ( 9.55 ( 104 Ci 239Pu6.78 ( 105 Ci 239Pu229Th ( 230Th5.21 ( 100 Ci 229Th1.80 ( 10(1 Ci 230Th5.21 ( 100 Ci 229Th ( 5.21 ( 100 Ci 230Th5.39 ( 100 Ci 230Th241Pu ( 241Am4.48 ( 105 Ci 241Pu5.18 ( 105 Ci 241Am5.38 ( 105 Ci 241Pu = 1.79 ( 101 moles 241Pu ( 1.79 ( 101 moles 241Am = 1.50 ( 104 Ci 241Am5.33 ( 105 Ci 241Am
NUTS Tracer Calculations
All BRAGFLO realizations are first evaluated using NUTS in a screening mode to identify those realizations for which a significant release of radionuclides to the LWB cannot occur. The screening simulations consider an infinitely soluble, nondecaying, nondispersive, and nonsorbing species as a tracer element. The tracer is given a unit concentration in all waste disposal areas of 1 kg/m3. If the amount of tracer that reaches the selected boundaries (the top of the Salado and the LWB within the Salado) does not exceed a cumulative mass of 107 kg within 10,000 years, it is assumed there is no consequential release to these boundaries. If the cumulative mass outside the boundaries within 10,000 years exceeds 107 kg, a complete transport analysis is conducted. The value of 10(7 kg is selected because, regardless of the isotopic composition of the release, it corresponds to a normalized release less than 106 EPA units, the smallest release displayed in CCDF construction (HYPERLINK "../../references/Others/Stockman_Shinta_Garner_1996_Analysis_Package_for_the_Salado_Transport_Calculations_Task_2_ERMS422314.pdf"Stockman 1996). The largest normalized release would be 9.98 107 EPA units, corresponding to 10(7 kg of 241Am if the release was entirely 241Am.
NUTS Transport Calculations
For BRAGFLO realizations with greater than 10(7 kg reaching the boundaries in the tracer calculations, NUTS models the transport of five different radionuclide species (241Am, 239Pu, 238Pu, 234U, and 230Th). These radionuclides represent a larger number of radionuclides: as discussed in HYPERLINK \l "PA-4_3_3" Section REF _Ref202328801 \r \h \* MERGEFORMAT PA-4.3.3, radionuclides were grouped together based on similarities, such as isotopes of the same element and those with similar half-lives, to simplify the calculations. For transport purposes, solubilities are lumped to represent both dissolved and colloidal forms. These groupings simplify and expedite calculations.
Numerical Solution
Equation ( REF EQ_PA96 \h \* MERGEFORMAT PA.95) and Equation ( REF EQ_PA97 \h \* MERGEFORMAT PA.96) are numerically solved by the NUTS program ( HYPERLINK "../../references/Others/WIPP_PA_1997_Users_Manual_for_NUTS_Version_205_ERMS246002.pdf" WIPP Performance Assessment 1997a) on the same computational grid ( HYPERLINK \l "Figure_PA-15" REF _Ref201037169 \h \* MERGEFORMAT Figure PA-15) used by BRAGFLO for the solution of Equation ( REF EQ_PA26 \h \* MERGEFORMAT PA.24), Equation ( REF EQ_PA27 \h PA.25), Equation ( REF EQ_PA28 \h PA.26), Equation ( REF EQ_PA29 \h PA.27), Equation ( REF EQ_PA30 \h PA.28), Equation ( REF EQ_PA31 \h PA.29), and Equation ( REF EQ_PA32 \h \* MERGEFORMAT PA.30). In the solution procedure, Equation ( REF EQ_PA96 \h \* MERGEFORMAT PA.95) and Equation ( REF EQ_PA97 \h \* MERGEFORMAT PA.96) are numerically solved with Sl = 0 for each time step, with the instantaneous updating of concentrations indicated in Equation ( REF EQ_PA98 \h \* MERGEFORMAT PA.97) and the appropriate modification to Csl in Equation ( REF EQ_PA97 \h \* MERGEFORMAT PA.96) taking place after the time step. The solution is carried out for the five radionuclides indicated in Equation ( REF EQ_PA114 \h \* MERGEFORMAT PA.113).
The initial value and boundary value conditions used with Equation ( REF EQ_PA96 \h \* MERGEFORMAT PA.95) and Equation ( REF EQ_PA97 \h \* MERGEFORMAT PA.96) are given in HYPERLINK \l "Table_PA-14" REF _Ref201126627 \h \* MERGEFORMAT Table PA-14. At time t = 0 (corresponding to the year 2033), the total inventory of each radionuclide is assumed to be in brine; the solubility constraints associated with Equation ( REF EQ_PA98 \h \* MERGEFORMAT PA.97) then immediately adjust the values for Cbl(x, y, t) and Csl(x, y, t) for consistency with the constraints imposed by ST(Br, Ox, El) and available radionuclide inventory.
The nR PDEs in Equation ( REF EQ_PA96 \h \* MERGEFORMAT PA.95) and Equation ( REF EQ_PA97 \h \* MERGEFORMAT PA.96) are discretized in two dimensions and then developed into a linear system of algebraic equations for numerical implementation. The following conventions are used in the representation of each discretized equation:
The subscript b is dropped from Cbl, so that the unknown function is represented by Cl.
A superscript n denotes time tn, with the assumption that the solution Cl is known at time tn and is to be propagated to time tn+1.
The grid indices are i in the x-direction and j in the y-direction, and are the same as the BRAGFLO grid indices.
Table PA- SEQ Table_PA- \* ARABIC 14. Initial and Boundary Conditions for Cbl(x, y, t) and Csl(x, y, t)
Initial Conditions for Cbl(x, y, t) and Csl(x, y, t) = if (x, y) is a point in the repository (i.e., areas Waste Panel, South RoR and North RoR, in HYPERLINK \l "Figure_PA-15" REF _Ref201037169 \h \* MERGEFORMAT Figure PA-15), where Al(0) is the amount (kg) of radionuclide l present at time t = 0 ( HYPERLINK \l "Table_PA-13" REF _Ref201126601 \h \* MERGEFORMAT Table PA-13) and Vb(0) is the amount (m3) of brine in repository at time t = 0 (from solution of Equation ( REF EQ_PA26 \h \* MERGEFORMAT PA.24) through Equation ( REF EQ_PA32 \h \* MERGEFORMAT PA.30) with BRAGFLO) for all (x, y).
= 0 otherwise.
= 0 if (x, y) is a point in the repository.Boundary Conditions for Cbl(x, y, t) = EMBED Equation.DSMT4 , where B is any subset of the outer boundary of the computational grid in REF _Ref201037169 \h \* MERGEFORMAT Figure PA-15, is the flux (kg/s) at time t of radionuclide l across B, vb(x, y, t) is the Darcy velocity (m3/m2/s) of brine at (x, y) on B and is obtained from the solution of Equation ( REF EQ_PA26 \h \* MERGEFORMAT PA.24) through Equation ( REF EQ_PA32 \h \* MERGEFORMAT PA.30) by BRAGFLO, n(x, y) denotes an outward-pointing unit normal vector, and denotes a line integral along B.
Fractional indices refer to quantities evaluated at grid block interfaces.
Each time step by NUTS is equal to 20 BRAGFLO time steps because BRAGFLO stores results (here, vb, (, and Sb) every 20 time steps.
The following finite-difference discretization is used for the lth equation in each grid block (i, j):
(PA. SEQ Eq._PA- \* ARABIC 114)
where qb is the grid block interfacial brine flow rate (m3/s) and VR is the grid block volume (m3). The quantity qb is based on and ( in Equation ( REF EQ_PA96 \h \* MERGEFORMAT PA.95) and Equation ( REF EQ_PA97 \h \* MERGEFORMAT PA.96), and the quantity VR is based on grid block dimensions ( HYPERLINK \l "Figure_PA-15" REF _Ref201037169 \h \* MERGEFORMAT Figure PA-15) and (.
The interfacial values of concentration in Equation ( REF EQ_PA115 \h \* MERGEFORMAT PA.114) are discretized using the one-point upstream weighting method ( HYPERLINK "../../references/Others/Aziz_Settari_1979.pdf" Aziz and Settari 1979), which results in
(PA. SEQ Eq._PA- \* ARABIC 115)
where ( derives from the upstream weighting for flow between adjacent grid blocks and is defined by
By collecting similar terms, Equation ( REF EQ_PA116 \h \* MERGEFORMAT PA.115) can be represented by the linear equation
(PA. SEQ Eq._PA- \* ARABIC 116)
where
Given the form of Equation ( REF EQ_PA117 \h \* MERGEFORMAT PA.116), the solution of Equation ( REF EQ_PA96 \h \* MERGEFORMAT PA.95) and Equation ( REF EQ_PA97 \h \* MERGEFORMAT PA.96) has now been reduced to the solution of nR ( nG linear algebraic equations in nR ( nG unknowns, where nR is the number of equations for each grid block (i.e., the number of radionuclides) and nG is the number of grid blocks into which the spatial domain is discretized ( HYPERLINK \l "Figure_PA-15" REF _Ref201037169 \h \* MERGEFORMAT Figure PA-15).
The system of PDEs in Equation ( REF EQ_PA96 \h \* MERGEFORMAT PA.95) and Equation ( REF EQ_PA97 \h \* MERGEFORMAT PA.96) is strongly coupled because of the contribution from parental decay to the equation governing the immediate daughter. Consequently, a sequential method is used to solve for the radionuclide concentrations by starting at the top of a decay chain and working down from parent to daughter. This implies that when solving Equation ( REF EQ_PA117 \h \* MERGEFORMAT PA.116) for the lth isotope concentration, all parent concentrations occurring in the right-hand-side term R are known. The system of equations is then linear in the concentrations of the lth isotope. As a result, solving Equation ( REF EQ_PA96 \h \* MERGEFORMAT PA.95) and Equation ( REF EQ_PA97 \h \* MERGEFORMAT PA.96) is reduced from the solution of one algebraic equation at each time step with nR ( nG unknowns to the solution of nR algebraic equations each with nG unknowns at each time step, which can result in a significant computational savings.
The matrix resulting from one-point upstream weighting has the following structural form for a 3(3 system of grid blocks, and a similar structure for a larger number of grid blocks:
1234567891XX0X2XXX0X30XX00X4X00XX0X5X0XXX0X6X0XX00X7X00XX08X0XXX9X0XX
where X designates possible nonzero matrix entries, and 0 designates zero entries within the banded structure. All entries outside of the banded structure are zero. Because of this structure, a banded direct elimination solver ( HYPERLINK "../../references/Others/Aziz_Settari_1979.pdf" Aziz and Settari 1979, Section 8.2.1) is used to solve the linear system for each radionuclide. The bandwidth is minimized by first indexing equations in the coordinate direction with the minimum number of grid blocks. The coefficient matrix is stored in this banded structure, and all infill coefficients calculated during the elimination procedure are contained within the band structure. Therefore, for the matrix system in two dimensions, a pentadiagonal matrix of dimension IBW ( nG is inverted instead of a full nG ( nG matrix, where IBW is the bandwidth.
The numerical implementation of Equation ( REF EQ_PA97 \h \* MERGEFORMAT PA.96) enters the solution process through updates to the radionuclide concentrations in Equation ( REF EQ_PA116 \h \* MERGEFORMAT PA.115) between each time step, as indicated in Equation ( REF EQ_PA98 \h \* MERGEFORMAT PA.97). The numerical solution of Equation ( REF EQ_PA96 \h \* MERGEFORMAT PA.95) and Equation ( REF EQ_PA97 \h \* MERGEFORMAT PA.96) also generates the concentrations required to integrate numerically evaluating the integral that defines Cl(t, B) in Equation ( REF EQ_PA102 \h \* MERGEFORMAT PA.101).
Additional Information
Additional information on NUTS and its use in WIPP PA can be found in the NUTS users manual ( HYPERLINK "../../references/Others/WIPP_PA_1997_Users_Manual_for_NUTS_Version_205_ERMS246002.pdf" WIPP Performance Assessment 1997a) and in the analysis package of Salado transport calculations for the CRA-2009 PA ( HYPERLINK "../../references/Others/Ismail_Garner_2008_Analysis_Package_for_Salado_Transport_Calculations_CRA_2009_ERMS548845.pdf" Ismail and Garner 2008). Furthermore, additional information on dissolved and colloidal actinides is given in HYPERLINK "../Appendix_SOTERM/Appendix_SOTERM.htm" Appendix SOTERM-2009.
Radionuclide Transport in the Salado: PANEL
This section describes the model used to compute radionuclide transport in the Salado for the E1E2 scenario. The model for transport in E0, E1, and E2 scenarios is described in HYPERLINK \l "PA-4_3" Section REF _Ref201111862 \r \h \* MERGEFORMAT PA-4.3.
Mathematical Description
A relatively simple mixed-cell model is used for radionuclide transport in the vicinity of the repository after an E1E2 intrusion, when connecting flow between two drilling intrusions into the same waste panel is assumed to take place. With this model, the amount of radionuclide l contained in a waste panel is represented by
(PA. SEQ Eq._PA- \* ARABIC 117)
where
= amount (mol) of radionuclide l in waste panel at time t
= concentration (mol/m3) of radionuclide l in brine in waste panel at time t (Equation ( REF EQ_PA119 \h \* MERGEFORMAT PA.118) and Equation ( REF EQ_PA120 \h \* MERGEFORMAT PA.119))
= rate (m3/s) at which brine flows out of the repository at time t (supplied by BRAGFLO from solution of Equation ( REF EQ_PA94 \h \* MERGEFORMAT PA.93))
and (l and P(l) are defined in conjunction with Equation ( REF EQ_PA96 \h \* MERGEFORMAT PA.95) and Equation ( REF EQ_PA97 \h \* MERGEFORMAT PA.96).
The brine concentration Cbl in Equation ( REF EQ_PA118 \h \* MERGEFORMAT PA.117) is defined by
(PA. SEQ Eq._PA- \* ARABIC 118)
(PA. SEQ Eq._PA- \* ARABIC 119)
where
= mole fraction of radionuclide l in waste panel at time t
= (PA. SEQ Eq._PA- \* ARABIC 120)
= volume (m3) of brine in waste panel at time t (supplied by BRAGFLO from solution of Equation ( REF EQ_PA26 \h \* MERGEFORMAT PA.24), Equation ( REF EQ_PA27 \h PA.25), Equation ( REF EQ_PA28 \h PA.26), Equation ( REF EQ_PA29 \h PA.27), Equation ( REF EQ_PA30 \h PA.28), Equation ( REF EQ_PA31 \h PA.29), and Equation ( REF EQ_PA32 \h \* MERGEFORMAT PA.30))
and ST[Br, Ox, El] is supplied by Equation ( REF EQ_PA103 \h \* MERGEFORMAT PA.102).
For Equation ( REF EQ_PA119 \h \* MERGEFORMAT PA.118) and Equation ( REF EQ_PA120 \h \* MERGEFORMAT PA.119), ST[Br, Ox, El] must be expressed in units of mol/L. In other words, Cbl(t) is defined to be the maximum concentration (ST in Equation ( REF EQ_PA103 \h \* MERGEFORMAT PA.102)) if there is sufficient radionuclide inventory in the waste panel to generate this concentration (Equation ( REF EQ_PA119 \h \* MERGEFORMAT PA.118)); otherwise, Cbl(t) is defined by the concentration that results when all the relevant element in the waste panel is placed in solution (Equation ( REF EQ_PA120 \h \* MERGEFORMAT PA.119)). The dissolved and colloidal An equilibrate instantly for each element.
Given rb and Cbl, evaluation of the integral
(PA. SEQ Eq._PA- \* ARABIC 121)
provides the cumulative release Rl(t) of radionuclide l from the waste panel through time t.
Numerical Solution
Equation ( REF EQ_PA118 \h \* MERGEFORMAT PA.117) is numerically evaluated by the PANEL model ( HYPERLINK "../../references/Others/WIPP_PA_1998_Design_Document_for_PANEL_Version_400_ERMS52169.pdf" WIPP Performance Assessment 1998b) using a discretization based on time steps of 50 years or less. Specifically, Equation ( REF EQ_PA118 \h \* MERGEFORMAT PA.117) is evaluated with the approximation
(PA. SEQ Eq._PA- \* ARABIC 122)
where
= gain in radionuclide l due to the decay of precursor radionuclides between tn
and tn+1 (see Equation ( REF EQ_PA124 \h \* MERGEFORMAT PA.123)), = .
As the solution progresses, values for Cbl(tn) are updated in consistency with Equation ( REF EQ_PA119 \h \* MERGEFORMAT PA.118) and Equation ( REF EQ_PA120 \h \* MERGEFORMAT PA.119), and the products rb(tn)Cbl(tn) are accumulated to provide an approximation to Rl in Equation ( REF EQ_PA122 \h \* MERGEFORMAT PA.121).
The term Gl(tn, tn+1) in Equation ( REF EQ_PA123 \h \* MERGEFORMAT PA.122) is evaluated with the Bateman equations ( HYPERLINK "../../references/Others/Bateman_1910.pdf" Bateman 1910), with PANEL programmed to handle decay chains of up to five (four decay daughters for a given radionuclide). As a single example, if radionuclide l is the third radionuclide in a decay chain (i.e., l = 3) and the two preceding radionuclides in the decay chain are designated by l = 1 and l = 2, then
EMBED Equation.DSMT4 (PA. SEQ Eq._PA- \* ARABIC 123)
in Equation ( REF EQ_PA123 \h \* MERGEFORMAT PA.122).
Implementation in PA
The preceding model is used in two ways in PA. First, Equation ( REF EQ_PA122 \h \* MERGEFORMAT PA.121) estimates releases to the Culebra associated with E1E2 intrusion scenarios (see HYPERLINK \l "PA-6_7_3" Section REF _Ref213680046 \r \h \* MERGEFORMAT PA-6.7.3). Second, the radionuclide concentrations are computed using the minimum brine volume for a significant release to estimate DBRs (see HYPERLINK \l "PA-6_8_2_3" Section REF _Ref201111903 \r \h \* MERGEFORMAT PA-6.8.2.3). The calculation of the minimum brine volume used in the CRA-2009 PA is found in Stein ( HYPERLINK "../../references/Others/Stein_to_Brush_2005_April_13_Estimate_of_Volume_of_Brine_ERMS539372.pdf" 2005). The calculated concentrations are the Sl term indicated in Equation ( REF EQ_PA98 \h \* MERGEFORMAT PA.97) which are used in the NUTS calculations discussed in HYPERLINK \l "PA-4_3" Section REF _Ref204065533 \r \h \* MERGEFORMAT PA-4.3.
For E1E2 intrusions, the initial amount Al of radionuclide l is the inventory of the decayed isotope at the time of the E1 intrusion. PANEL calculates the inventory of each of the 29 radioisotopes throughout the regulatory period. The initial concentration Cbl of radionuclide l is computed by Equation ( REF EQ_PA118 \h \* MERGEFORMAT PA.117), Equation ( REF EQ_PA119 \h \* MERGEFORMAT PA.118), and Equation ( REF EQ_PA120 \h \* MERGEFORMAT PA.119). For the DBR calculations, the initial amount Al of radionuclide l is the inventory of the isotope at the time of repository closure.
Additional Information
Additional information on PANEL and its use in the CRA-2009 PA calculations can be found in the PANEL users manual ( HYPERLINK "../../references/Others/WIPP_PA_2003_Users_Manual_for_PANEL_Version_402_ERMS526652.pdf" WIPP Performance Assessment 2003b), the analysis package for PANEL calculations ( HYPERLINK "../../references/Others/Garner_Leigh_2005_Analysis_Package_for_PANEL_CRA_2004_PABC_ERMS540572.pdf" Garner and Leigh 2005), and the analysis package for Salado transport calculations in the CRA-2009 PA ( HYPERLINK "../../references/Others/Ismail_Garner_2008_Analysis_Package_for_Salado_Transport_Calculations_CRA_2009_ERMS548845.pdf" Ismail and Garner 2008).
Cuttings and Cavings to Surface: CUTTINGS_S
Cuttings are waste solids contained in the cylindrical volume created by the cutting action of the drill bit passing through the waste, while cavings are additional waste solids eroded from the borehole by the upward-flowing drilling fluid within the borehole. The releases associated with these processes are computed within the CUTTINGS_S code ( HYPERLINK "../../references/Others/WIPP_PA_2003_Users_Manual_for_CUTTINGS_S_Version_510_ERMS532340.pdf" WIPP Performance Assessment 2003c). The mathematical representations used for cuttings and cavings are described in this section.
Cuttings
The uncompacted volume of cuttings removed and transported to the surface in the drilling fluid, Vcut, is given by
(PA. SEQ Eq._PA- \* ARABIC 124)
where A is the drill bit area (m2), Hi is the initial (or uncompacted) repository height (3.96 m), and D is the drill-bit diameter (0.31115 m) (HYPERLINK "../../references/Others/Fox_2008_Parameter_Report_CRA_2009_ERMS549747.pdf" \l "page=188"Fox 2008, Table 13). For drilling intrusions through RH-TRU waste, Hi = 0.509 m is used (HYPERLINK "../../references/Others/Fox_2008_Parameter_Report_CRA_2009_ERMS549747.pdf" \l "page=237"Fox 2008, Table 45).
Cavings
The cavings component of the direct surface release is caused by the shearing action of the drilling fluid on the waste as it flows up the borehole annulus. Like the cuttings release, the cavings release is assumed to be independent of the conditions that exist in the repository during a drilling intrusion.
The final diameter of the borehole depends on the diameter of the drillbit and on the extent to which the actual borehole diameter exceeds the drill-bit diameter. Although a number of factors affect erosion within a borehole ( HYPERLINK "../../references/Others/Chambre_1982.pdf" Chambre Syndicale de la Recherche et de la Production du Petrole et du Gaz Naturel 1982), the most important is the fluid shear stress on the borehole wall (i.e., the shearing force per unit area, N/m2) resulting from circulating drilling fluids ( HYPERLINK "../../references/Others/Darley_1969.pdf" Darley 1969, HYPERLINK "../../references/Others/Walker_Holman_1971.pdf" Walker and Holman 1971). As a result, PA estimates cavings removal with a model based on the effect of shear stress on the borehole diameter. In particular, the borehole diameter is assumed to grow until the shear stress on the borehole wall is equal to the shear strength of the waste, which is the limit below which waste erosion ceases.
The final eroded diameter Df (m) of the borehole through the waste determines the total volume V(m3) of uncompacted waste removed to the surface by circulating drilling fluid. Specifically,
(PA. SEQ Eq._PA- \* ARABIC 125)
where Vcav is the volume (m3) of waste removed as cavings.
Most borehole erosion is believed to occur in the vicinity of the drill collar ( HYPERLINK \l "Figure_PA-22" REF _Ref201119915 \h \* MERGEFORMAT Figure PA-22) because of decreased flow area and consequent increased mud velocity (HYPERLINK "../../references/Others/SAND89_2408.pdf" \l "271"Rechard, Iuzzolino, and Sandha 1990, Letters 1a and HYPERLINK "../../references/Others/Rechard_Iuzzolino_Sandha_1990_Data_Used_in_Preliminary_PA_SAND89_2408.pdf" \l "page=278"1b, HYPERLINK "../../references/Others/Rechard_Iuzzolino_Sandha_1990_Data_Used_in_Preliminary_PA_SAND89_2408.pdf" \l "page=139"App. A). An important determinant of the extent of this erosion is whether the flow of the drilling fluid in the vicinity of the collar is laminar or turbulent. PA uses Reynolds numbers to distinguish between the occurrence of laminar flow and turbulent flow. The Reynolds number is the ratio between inertial and viscous (or shear) forces in a fluid, and can be expressed as ( HYPERLINK "../../references/Others/Fox_McDonald_1985.pdf" Fox and McDonald 1985)
EMBED Equation.DSMT4 (PA. SEQ Eq._PA- \* ARABIC 126)
where Re is the Reynolds number (dimensionless), (f is the fluid density (kg/m3), De is the equivalent diameter (m), is the fluid speed (m s(1), and ( is the fluid viscosity (kg m(1 s(1).
Typically, (f, v, and ( are averages over a control volume with an equivalent diameter of De, where (f = 1.21 ( 103 kg/m3 (HYPERLINK "../../references/Others/Fox_2008_Parameter_Report_CRA_2009_ERMS549747.pdf" \l "page=188"Fox 2008, Table 13), v = 0.7089 m s(1 (based on 40 gal/min/in of drill diameter) (HYPERLINK "../../references/Others/Berglund_JW_1992_Mechanisms_Governing_the_Direct_Removal_SAND92_7295.pdf"Berglund 1992), and De = 2 (R ( Ri), as shown in HYPERLINK \l "Figure_PA-22" REF _Ref201119915 \h \* MERGEFORMAT Figure PA-22. The diameter of the drill collar (i.e., 2Ri in REF _Ref201119915 \h \* MERGEFORMAT Figure PA-22) is 8.0 in = 0.2032 m ( HYPERLINK "../../references/Others/Ismail_2008_Analysis_Package_for_CUTTINGS_S_Rev1_ERMS548618.pdf" Ismail 2008). The determination of ( is discussed below. PA assumes that Reynolds numbers less than 2100 are associated with laminar flow, while Reynolds numbers greater than 2100 are associated with turbulent flow ( HYPERLINK "../../references/Others/Walker_1976.pdf" Walker 1976).
Drilling fluids are modeled as non-Newtonian, which means that the viscosity ( is a function of the shear rate within the fluid (i.e., the rate at which the fluid velocity changes normal to the flow direction, m/s/m). PA uses a model proposed by Oldroyd ( HYPERLINK "../../references/Others/ERMS243211.pdf" 1958) to estimate the viscosity of drilling fluids. As discussed in the Drilling Mud and Cement Slurry Rheology Manual ( HYPERLINK "../../references/Others/Chambre_1982.pdf" Chambre Syndicale de la Recherche et de la Production du Petrole et du Gaz Naturel 1982), the Oldroyd model leads to the following expression for the Reynolds number associated with the helical flow of a drilling fluid within an annulus:
(PA. SEQ Eq._PA- \* ARABIC 127)
where (f, De, and v are defined as in Equation ( REF EQ_PA127 \h \* MERGEFORMAT PA.126), and (( is the asymptotic value for the derivative of the shear stress (( , kg m(1 s(2) with respect to the shear rate ((, s(1) obtained as the shear rate increases (i.e., as ). PA uses Equation ( REF EQ_PA128 \h \* MERGEFORMAT PA.127) to determine whether drilling fluids in the area of the drill collar are undergoing laminar or turbulent flow.
The Oldroyd model assumes that the shear stress ( is related to the shear rate ( through the relationship
(PA. SEQ Eq._PA- \* ARABIC 128)
where (0 is the asymptotic value of the viscosity (kg m(1 s(1) that results as the shear rate ( approaches zero, and (1 and (2 are constants (s2). The expression leads to
(PA. SEQ Eq._PA- \* ARABIC 129)
PA uses values of (0 = 1.834 ( 10(2 kg m(1 s(1, (1 = 1.082 ( 10(6 s2, and (2 = 5.410 ( 10(7 s2 ( HYPERLINK "../../references/Others/Berglund_1996_Analysis_Package_for_the_Cuttings_and_Spallings_Calculations_ERMS417876.pdf" Berglund 1996), from which viscosity in the limit of infinite shear rate is found to be (( =
Figure PA- SEQ Figure_PA- \* ARABIC 22. Detail of Rotary Drill String Adjacent to Drill Bit
9.17(10(3 kg m(1 s(1. The quantity (( is comparable to the plastic viscosity of the fluid ( HYPERLINK "../../references/Others/Chambre_1982.pdf" Chambre Syndicale de la Recherche et de la Production du Petrole et du Gaz Naturel 1982).
As previously indicated, different models are used to determine the eroded diameter Df of a borehole depending on whether flow in the vicinity of the drill collar is laminar or turbulent. The model for borehole erosion in the presence of laminar flow is described next, and then the model for borehole erosion in the presence of turbulent flow is described.
Laminar Flow Model
As shown by Savins and Wallick ( HYPERLINK "../../references/Others/Savins_Wallick_1966.pdf" 1966), the shear stresses associated with the laminar helical flow of a non-Newtonian fluid, as a function of the normalized radius, r, can be expressed as
(PA. SEQ Eq._PA- \* ARABIC 130)
for Ri/R ( r ( 1, where Ri and R are the inner and outer radii within which the flow occurs, as indicated in HYPERLINK \l "Figure_PA-22" REF _Ref201119915 \h \* MERGEFORMAT Figure PA-22; ((R,() is the shear stress (kg m(1 s(2) at a radial distance (R beyond the inner boundary (i.e., at r = (Ri + (R)/R); and the variables C, J, and ( depend on R and satisfy conditions Equation ( REF EQ_PA133 \h \* MERGEFORMAT PA.132) through Equation ( REF EQ_PA135 \h \* MERGEFORMAT PA.134) indicated below. The shear stress at the outer radius R is given by
(PA. SEQ Eq._PA- \* ARABIC 131)
As previously indicated, the borehole radius R is assumed to increase as a result of erosional processes until a value of R is reached at which ( (R, 1) is equal to the shear strength of the waste. In PA, the shear strength of the waste is treated as an uncertain parameter (see WTAUFAIL in HYPERLINK \l "Table_PA-19" REF TablePA_19 \h Table PA-19). Computationally, determining the eroded borehole diameter R associated with a particular value of the waste shear strength requires repeated evaluation of ((R, 1), as indicated in Equation ( REF EQ_PA132 \h \* MERGEFORMAT PA.131), until a value of R is determined for which ( (R, 1) equals the shear strength.
The quantities C, J, and ( must satisfy the following three conditions (Savins and Wallick 1966) for Equation ( REF EQ_PA132 \h \* MERGEFORMAT PA.131) to be valid:
(PA. SEQ Eq._PA- \* ARABIC 132)
(PA. SEQ Eq._PA- \* ARABIC 133)
(PA. SEQ Eq._PA- \* ARABIC 134)
where (, the drilling fluid viscosity (kg m(1 s(1), is a function of R and (; (( is the drill string angular velocity (rad s(1); and Q is the drilling fluid flow rate (m3 s(1).
The viscosity ( in Equation ( REF EQ_PA133 \h \* MERGEFORMAT PA.132) through Equation ( REF EQ_PA135 \h \* MERGEFORMAT PA.134) is introduced into the analysis by assuming that the drilling fluid follows the Oldroyd model for shear stress in Equation ( REF EQ_PA129 \h \* MERGEFORMAT PA.128). By definition of the viscosity (,
( = (( (PA. SEQ Eq._PA- \* ARABIC 135)
and from Equation ( REF EQ_PA129 \h \* MERGEFORMAT PA.128)
(PA. SEQ Eq._PA- \* ARABIC 136)
thus the expression in Equation ( REF EQ_PA131 \h \* MERGEFORMAT PA.130) can be reformulated as
(PA. SEQ Eq._PA- \* ARABIC 137)
As discussed by Savins and Wallick ( HYPERLINK "../../references/Others/Savins_Wallick_1966.pdf" 1966) and Berglund (HYPERLINK "../../references/Others/Berglund_JW_1992_Mechanisms_Governing_the_Direct_Removal_SAND92_7295.pdf"1992), the expressions in Equation ( REF EQ_PA133 \h \* MERGEFORMAT PA.132) through Equation ( REF EQ_PA135 \h \* MERGEFORMAT PA.134) and Equation ( REF EQ_PA137 \h \* MERGEFORMAT PA.136) can be numerically evaluated to obtain C, J, and ( for use in Equation ( REF EQ_PA131 \h \* MERGEFORMAT PA.130) and Equation ( REF EQ_PA132 \h \* MERGEFORMAT PA.131). In PA, the drill string angular velocity (( is treated as an uncertain parameter (see DOMEGA in HYPERLINK \l "Table_PA-19" REF TablePA_19 \h Table PA-19), and
(PA. SEQ Eq._PA- \* ARABIC 138)
where v = 0.7089 m s(1 as used in Equation ( REF EQ_PA127 \h \* MERGEFORMAT PA.126), and (0, (1, and (2 are defined as in Equation ( REF EQ_PA129 \h \* MERGEFORMAT PA.128) and Equation ( REF EQ_PA130 \h \* MERGEFORMAT PA.129).
Turbulent Flow Model
The model for borehole erosion in the presence of turbulent flow is now described. Unlike the theoretically derived relationship for erosion in the presence of laminar flow, the model for borehole erosion in the presence of turbulent flow is empirical. In particular, pressure loss for axial flow in an annulus under turbulent flow conditions can be approximated by ( HYPERLINK "../../references/Others/Chambre_1982.pdf" Chambre Syndicale de la Recherche et de la Production du Petrole et du Gaz Naturel 1982)
(PA. SEQ Eq._PA- \* ARABIC 139)
where (P is the pressure change (Pa), f is the Fanning friction factor (dimensionless), L is the distance (m) over which pressure change (P occurs, and (f , v, and De are defined in Equation ( REF EQ_PA127 \h \* MERGEFORMAT PA.126).
For turbulent pipe flow, f is empirically related to the Reynolds number Re defined in Equation ( REF EQ_PA127 \h \* MERGEFORMAT PA.126) by ( HYPERLINK "../../references/Others/Wittaker_1985.pdf" Whittaker 1985)
(PA. SEQ Eq._PA- \* ARABIC 140)
where D is the inside diameter (m) of the pipe and ( is a roughness term equal to the average depth (m) of pipe wall irregularities. In the absence of a similar equation for flow in an annulus, Equation ( REF EQ_PA141 \h \* MERGEFORMAT PA.140) is used in PA to define f for use in Equation ( REF EQ_PA140 \h \* MERGEFORMAT PA.139), with D replaced by the effective diameter De = 2(R Ri) and ( equal to the average depth of irregularities in the waste-borehole interface. In the present analysis, ( = 0.025 m (HYPERLINK "../../references/Others/Fox_2008_Parameter_Report_CRA_2009_ERMS549747.pdf" \l "page=217"Fox 2008, Table 34), which exceeds the value often selected in calculations involving very rough concrete or riveted steel piping ( HYPERLINK "../../references/Others/Streeter_1958.pdf" Streeter 1958).
The pressure change (P in Equation ( REF EQ_PA140 \h \* MERGEFORMAT PA.139) and the corresponding shear stress ( at the walls of the annulus are approximately related by
(PA. SEQ Eq._PA- \* ARABIC 141)
where is the cross-sectional area of the annulus (see HYPERLINK \l "Figure_PA-22" REF _Ref201119915 \h \* MERGEFORMAT Figure PA-22) and 2(L(R + Ri) is the total surface area of the annulus. Rearranging Equation ( REF EQ_PA140 \h \* MERGEFORMAT PA.139) and using the relationship in Equation ( REF EQ_PA136 \h \* MERGEFORMAT PA.135) yields
(PA. SEQ Eq._PA- \* ARABIC 142)
which was used in the 1991 and 1992 WIPP PAs to define the shear stress at the surface of a borehole of radius R. The radius R enters into Equation ( REF EQ_PA133 \h \* MERGEFORMAT PA.132) through Equation ( REF EQ_PA135 \h \* MERGEFORMAT PA.134) through the use of D = 2(R Ri) in the definition of f in Equation ( REF EQ_PA141 \h \* MERGEFORMAT PA.140). As with laminar flow, the borehole radius R is assumed to increase until a value of ((R) is reached that equals the sample value for the shear strength of the waste (i.e., the uncertain parameter WTAUFAIL in HYPERLINK \l "Table_PA-19" REF TablePA_19 \h Table PA-19). Computationally, the eroded borehole diameter is determined by solving Equation ( REF EQ_PA143 \h \* MERGEFORMAT PA.142) for R under the assumption that ((R) equals the assumed shear strength of the waste.
For the CRA-2004 PA, a slight modification to the definition of ( in Equation ( REF EQ_PA143 \h \* MERGEFORMAT PA.142) was made to account for drill string rotation when fluid flow in the vicinity of the drill collars is turbulent ( HYPERLINK "../../references/Others/Abdul_Khader_Rao_1974.pdf" Abdul Khader and Rao 1974; HYPERLINK "../../references/Others/Bilgen_Boulos_Akgungor_1973.pdf" Bilgen, Boulos, and Akgungor 1973). Specifically, an axial flow velocity correction factor (i.e., a rotation factor), Fr, was introduced into the definition of (. The correction factor Fr is defined by
Fr = v2100 / v (PA. SEQ Eq._PA- \* ARABIC 143)
where v2100 is the norm of the flow velocity required for the eroded diameters to be the same for turbulent and laminar flow at a Reynolds number of Re = 2100, and is obtained by solving
(PA. SEQ Eq._PA- \* ARABIC 144)
for v2100 with D in the definition of f in Equation ( REF EQ_PA141 \h \* MERGEFORMAT PA.140) assigned the final diameter value that results for laminar flow at a Reynolds number of Re = 2100 (that is, the D in De = 2(R Ri) = D 2Ri obtained from Equation ( REF EQ_PA128 \h \* MERGEFORMAT PA.127) with Re = 2100). The modified definition of ( is
(PA. SEQ Eq._PA- \* ARABIC 145)
and results in turbulent and laminar flow with the same eroded diameter at a Reynolds number of 2100, where PA assumes that the transition between turbulent and laminar flow takes place.
Calculation of Rf
The following algorithm was used to determine the final eroded radius Rf of a borehole and incorporates a possible transition from turbulent to laminar fluid flow within a borehole:
Step 1. Use Equation ( REF EQ_PA128 \h \* MERGEFORMAT PA.127) to determine an initial Reynolds number Re, with R initially set to the drill-bit radius, R0 = 0.31115 m (HYPERLINK "../../references/Others/Fox_2008_Parameter_Report_CRA_2009_ERMS549747.pdf" \l "page=188"Fox 2008, Table 13).
Step 2. If Re < 2100, the flow is laminar and the procedure in HYPERLINK \l "PA-4_5_2_1" Section REF _Ref201112006 \r \h \* MERGEFORMAT PA-4.5.2.1 is used to determine Rf. Because any increase in the borehole diameter will cause the Reynolds number to decrease, the flow will remain laminar and there is no need to consider the possibility of turbulent flow as the borehole diameter increases, with the result that Rf determined in this step is the final eroded radius of the borehole.
Step 3. If Re ( 2100, then the flow is turbulent, and the procedure discussed in HYPERLINK \l "PA-4_5_2_2" Section REF _Ref201112024 \r \h \* MERGEFORMAT PA-4.5.2.2 is used to determine Rf . Once Rf is determined, the associated Reynolds number Re is recalculated using Equation ( REF EQ_PA128 \h \* MERGEFORMAT PA.127) and R = Rf . If the recalculated Re > 2100, a transition from turbulent to laminar flow cannot take place, and the final eroded radius is Rf determined in this step. If not, go to Step 4.
Step 4. If the Reynolds number Re with the new Rf in Step 3 satisfies the inequality Re ( 2100, a transition from turbulent to laminar flow is assumed to have taken place. In this case, Rf is recalculated assuming laminar flow, with the outer borehole radius R initially defined to be the radius associated with Re = 2100. In particular, the initial value for R is given by the radius at which the transition from laminar to turbulent flow takes place:
(PA. SEQ Eq._PA- \* ARABIC 146)
which is obtained from Equation ( REF EQ_PA128 \h \* MERGEFORMAT PA.127) by solving for R with Re = 2100. A new value for Rf is then calculated with the procedure discussed in HYPERLINK \l "PA-4_5_2_1" Section REF _Ref201112006 \r \h \* MERGEFORMAT PA-4.5.2.1 for laminar flow, with this value of Rf replacing the value from Step 3 as the final eroded diameter of the borehole.
Step 5. Once Rf is known, the amount of waste removed to the surface is determined using Equation ( REF EQ_PA126 \h \* MERGEFORMAT PA.125) with Df = 2Rf .
Additional Information
Additional information on CUTTINGS_S and its use in the CRA-2004 PA to determine cuttings and cavings releases can be found in the CUTTINGS_S users manual ( HYPERLINK "../../references/Others/WIPP_PA_2003_Users_Manual_for_CUTTINGS_S_Version_510_ERMS532340.pdf" WIPP Performance Assessment 2003c) and in the analysis package for cuttings and cavings releases ( HYPERLINK "../../references/Others/Ismail_2008_Analysis_Package_for_CUTTINGS_S_Rev1_ERMS548618.pdf" Ismail 2008).
Spallings to Surface: DRSPALL and CUTTINGS_S
Spallings are waste solids introduced into a borehole by the movement of waste-generated gas towards the lower-pressure borehole. In engineering literature, the term spalling describes the dynamic fracture of a solid material, such as rock or metal ( HYPERLINK "../../references/Others/Antoun_et_al_2003.pdf" Antoun et al. 2003). In WIPP PA, the spallings model describes a series of processes, including tensile failure of solid waste, fluidization of failed material, entrainment into the wellbore flow, and transport up the wellbore to the land surface. Spallings releases could occur when pressure differences between the repository and the wellbore cause solid stresses in the waste exceeding the waste material strength and gas velocities sufficient to mobilize failed waste material.
The spallings model is described in the following sections. Presented first are the primary modeling assumptions used to build the conceptual model. Next, the mathematical model and its numerical implementation in the computer code DRSPALL are described. Finally, implementation of the spallings model in WIPP PA by means of the code CUTTINGS_S is discussed.
Summary of Assumptions
Assumptions underlying the spallings model include the future state of the waste, specifications of drilling equipment, and the drillers actions at the time of intrusion. Consistent with the other PA models, the spallings model assumes massive degradation of the emplaced waste through mechanical compaction, corrosion, and biodegradation. Waste is modeled as a homogeneous, isotropic, weakly consolidated material with uniform particle size and shape. The rationale for selecting the spallings model material properties is addressed in detail by Hansen et al. ( HYPERLINK "../../references/Others/Hansen_et_al_1997_Description_&_Evaluation_of_Mechanistically_Based_Conceptual_Model_SAND97_1369.pdf" 1997) and Hansen, Pfeifle, and Lord ( HYPERLINK "../../references/Others/Hansen_PLfeifle_Lord_2003_Parameter_Justification_Report_ERMS531057.pdf" 2003).
Drilling equipment specifications, such as bit diameter and drilling mud density, are based on surveys of drillers in the Delaware Basin (Hansen, Pfeifle, and Lord 2003). Assumptions about the drillers actions during the intrusion are conservative. Typically, the drilling mud density is controlled to maintain a slightly overbalanced condition so that the mud pressure is always slightly higher than the fluid pressures in the formation. If the borehole suddenly passes through a high-pressure zone, the well can quickly become underbalanced, with a resulting fluid pressure gradient driving formation fluids into the wellbore. This situation is known as a kick and is of great concern to drillers because a violent kick can lead to a blowout of mud, gas, and oil from the wellbore, leading to equipment damage and worker injury. Standard drilling practice is to watch diligently for kicks. The first indicator of a kick is typically an increase in mud return rate, leading to an increase in mud pit volume ( HYPERLINK "../../references/Others/SPE_paper_37953.pdf" Frigaard and Humphries 1997). Downhole monitors detect whether the kick is air, H2S, or brine. If the kick fluid is air, the standard procedure is to stop drilling and continue pumping mud in order to circulate the air pocket out. If the mud return rate continues to grow after drilling has stopped and the driller believes that the kick is sufficiently large to cause damage, the well may be shut in by closing the blowout preventer. Once shut in, the well pressure may be bled off slowly and mud weight eventually increased and circulated to offset the higher formation pressure before drilling continues. The spallings model simulates an underbalanced system in which a gas kick is assured, and the kick proceeds with no intervention from the drill operation. Therefore, drilling and pumping continue during the entire blowout event.
Conceptual Model
The spallings model calculates transient repository and wellbore fluid flow before, during, and after a drilling intrusion. To simplify the calculations, both the wellbore and the repository are modeled by one-dimensional geometries. The wellbore assumes a compressible Newtonian fluid consisting of a mixture of mud, gas, salt, and waste solids; viscosity of the mixture varies with the fraction of waste solids in the flow. In the repository, flow is viscous, isothermal, compressible single-phase (gas) flow in a porous medium.
The wellbore and repository flows are coupled by a cylinder of porous media before penetration, and by a cavity representing the bottom of the borehole after penetration. Schematic diagrams of the flow geometry prior to and after penetration are shown in HYPERLINK \l "Figure_PA-23" REF _Ref201119954 \h \* MERGEFORMAT Figure PA-23 and HYPERLINK \l "Figure_PA-24" REF _Ref201119955 \h \* MERGEFORMAT Figure PA-24, respectively. The drill bit moves downward as a function of time, removing salt or waste material. After penetration, waste solids freed by drilling, tensile failure, and associated fluidization may enter the wellbore flow stream at the cavity forming the repository-wellbore boundary.
Figure PA- SEQ Figure_PA- \* ARABIC 23. Schematic Diagram of the Flow Geometry Prior to Repository Penetration
Figure PA- SEQ Figure_PA- \* ARABIC 24. Schematic Diagram of the Flow Geometry After Repository Penetration
Wellbore Flow Model
Flow in the well is modeled as a one-dimensional pipe flow with cross-sectional areas corresponding to the appropriate flow area at a given position in the well, as shown in HYPERLINK \l "Figure_PA-25" REF _Ref201119980 \h \* MERGEFORMAT Figure PA-25 and HYPERLINK \l "Figure_PA-26" REF _Ref201119988 \h \* MERGEFORMAT Figure PA-26. This model is conceptually similar to that proposed by Podio and Yang ( HYPERLINK "../../references/Others/IADC_SPE_14737.pdf" 1986) for use in the oil and gas industry. Drilling mud is added at the wellbore entrance by the pump. Flow through the drill bit is treated as a choke with cross-sectional area appropriate for the bit nozzle area. At the annulus output to the surface, the mixture is ejected at a constant atmospheric pressure. The gravitational body force acts in its appropriate direction based on position before or after the bit.
Figure PA- SEQ Figure_PA- \* ARABIC 25. Effective Wellbore Flow Geometry Before Bit Penetration
Figure PA- SEQ Figure_PA- \* ARABIC 26. Effective Wellbore Flow Geometry After Bit Penetration
Prior to drill bit penetration into the repository, gas from the repository can flow through drilling-damaged salt into the well. After penetration, the cavity at the bottom of the wellbore couples the wellbore flow and the repository flow models; gas and waste material can exit the repository domain into the cavity. The cavity radius increases as waste materials are moved into the wellbore.
The system of equations representing flow in the wellbore consists of four equations for mass conservation, one for each phase (salt, waste, mud, and gas); one equation for conservation of total momentum; two equations relating gas and mud density to pressure; the definition of density for the fluid mixture; and one constraint imposed by the fixed volume of the wellbore. The conservation of mass and momentum is described by
(PA. SEQ Eq._PA- \* ARABIC 147)
(PA. SEQ Eq._PA- \* ARABIC 148)
where
q = phase (w for waste, s for salt, m for mud, and g for gas)
Vq = volume (m3) of phase q
V = total volume (m3)
(q = density (kg/m3) of phase q, constant for salt and waste (2,180 and 2,650 kg/m3, respectively) and pressure-dependent for gas and mud (see Equation ( REF EQ_PA150 \h \* MERGEFORMAT PA.149) and Equation ( REF EQ_PA151 \h \* MERGEFORMAT PA.150))
( = density of fluid mixture (kg/m3) determined by Equation ( REF EQ_PA152 \h \* MERGEFORMAT PA.151)
u = velocity (m/s) of fluid mixture in wellbore
t = time (s)
z = distance (m) from inlet at top of well
Sq = rate of mass (kg/s) in phase q entering and exiting wellbore domain at position z (Equation ( REF EQ_PA163 \h \* MERGEFORMAT PA.162))
Smom = rate of momentum (kg m/s2) entering and exiting wellbore domain at position z (Equation ( REF EQ_PA166 \h \* MERGEFORMAT PA.165))
P = pressure (Pa) at position z
g = standard gravity (9.8067 kg/m/s2)
F = friction loss using pipe flow model (kg/m2/s2) determined by Equation ( REF EQ_PA154 \h \* MERGEFORMAT PA.153)
Gas is treated as isothermal and ideal, so the pressure and density are related by Boyles law:
(PA. SEQ Eq._PA- \* ARABIC 149)
where (g,0 is the density of H2 gas at atmospheric pressure and 298 K (8.24182 ( 10-2 kg/m3).
The mud is assumed to be a compressible fluid, so
(PA. SEQ Eq._PA- \* ARABIC 150)
where (m,0 is the density of the mud at atmospheric pressure (1,210 kg/m3) and cm is the compressibility of the mud (3.1 ( 10-10 Pa-1).
The density of the fluid mixture is determined from the densities and volumes occupied by the phases:
(PA. SEQ Eq._PA- \* ARABIC 151)
The volume of each phase is constrained by the fixed total volume of the wellbore:
(PA. SEQ Eq._PA- \* ARABIC 152)
The friction loss is a standard formulation for pipe flow ( HYPERLINK "../../references/Others/Fox_McDonald_1985.pdf" Fox and McDonald 1985), where the head loss per unit length is given as
(PA. SEQ Eq._PA- \* ARABIC 153)
where the hydraulic diameter dh is given by
(PA. SEQ Eq._PA- \* ARABIC 154)
In PA, Do = 0.31115 m throughout the domain. From the bit to the top of the collar, Di = 0.2032m; above the collar, Di = 0.1143 m. The area A is calculated as the area of the annulus between the outer and inner radii:
(PA. SEQ Eq._PA- \* ARABIC 155)
Thus, dh = 0.108 m from the bit to the top of the collar, and dh = 0.197 m above the collar.
The Darcy friction factor f in Equation ( REF EQ_PA154 \h \* MERGEFORMAT PA.153) is determined by the method of Colebrook ( HYPERLINK "../../references/Others/Fox_McDonald_1985.pdf" Fox and MacDonald 1985). In the laminar regime, which is assumed to be characterized by Reynolds numbers below 2100 ( HYPERLINK "../../references/Others/Walker_1976.pdf" Walker 1976),
(PA. SEQ Eq._PA- \* ARABIC 156)
and in the turbulent regime (Re > 2100)
(PA. SEQ Eq._PA- \* ARABIC 157)
where is the Reynolds number of the mixture, and ( is the viscosity calculated in Equation ( REF EQ_PA159 \h \* MERGEFORMAT PA.158), below. As the wellbore mixture becomes particle-laden, the viscosity of the mixture is determined from an empirical relationship developed for proppant slurry flows in channels for the oil and gas industry ( HYPERLINK "../../references/Others/Barree_Conway_1995.pdf" Barree and Conway 1995). Viscosity is computed by an approximate slurry formula based on the volume fraction of waste solids:
(PA. SEQ Eq._PA- \* ARABIC 158)
where (0 is a base mixture viscosity (9.17 ( 10(3 Pa s), w = Vw/V is the current volume fraction of waste solids, wmax is an empirically determined maximal volume fraction above which flow is choked (0.615), and s is an empirically determined constant ((1.5) ( HYPERLINK "../../references/Others/Hansen_PLfeifle_Lord_2003_Parameter_Justification_Report_ERMS531057.pdf" Hansen, Pfeifle, and Lord 2003).
Wellbore Initial Conditions
Initial conditions in the wellbore approximate mixture flow conditions just prior to waste penetration. The wellbore is assumed to contain only mud and salt. Initial conditions for the pressure, fluid density, volume fractions of mud and salt, and the mixture velocity are set by the following algorithm:
Step 1. Set pressure in the wellbore to hydrostatic: P(z) = Patm (m,0gz.
Step 2. Set mud density using Equation ( REF EQ_PA151 \h \* MERGEFORMAT PA.150).
Step 3. Set mixture velocity: u(z) = Rm/A(z), where Rm is the volume flow rate of the pump (0.0202 m3/s), and A(z) is the cross-sectional area of the wellbore.
Step 4. Set volume of salt in each cell: Vs,i= RdrillAbit(zi/ui, where Rdrill is the rate of drilling (0.004445 m/s), is the area of the bottom of the wellbore, and dbit is the diameter of the bit (0.31115 m).
Step 5. Set volume fraction of mud in each cell: Vm,i = Vi Vs,i.
Step 6. Recalculate mixture density using Equation ( REF EQ_PA152 \h \* MERGEFORMAT PA.151), assuming no waste or gas in the wellbore.
The initial conditions set by this algorithm approximate a solution to the wellbore flow (Equation ( REF EQ_PA148 \h \* MERGEFORMAT PA.147) and Equation ( REF EQ_PA149 \h \* MERGEFORMAT PA.148)) for constant flow of mud and salt in the well. The approximation rapidly converges to a solution for wellbore flow if steady-state conditions are maintained ( HYPERLINK "../../references/Others/WIPP_PA_2003_Verification_and_Validation_Plan_and_Validation_Document_for_DRSPALL_ERMS524782.pdf" WIPP Performance Assessment 2003d).
Wellbore Boundary Conditions
For simplicity, DRSPALL does not model flow of mud down the pipe to the bit. Mass can enter the wellbore below the drill bit and exit at the wellbore outlet. Below the bit, mud, salt, gas, and waste can enter the wellbore. PA assumes a constant volume of mud flow down the drilling pipe; therefore, the source term for mud, Sm,in, is set by the volumetric flow rate of the pump Rm (0.0202 m3/s) and the density of the mud at the bottom of the wellbore:
(PA. SEQ Eq._PA- \* ARABIC 159)
Until the drill bit penetrates the repository, salt enters the wellbore at a constant rate:
(PA. SEQ Eq._PA- \* ARABIC 160)
Additional mass enters the wellbore by gas flow from the repository (Sgas,in) and spalling of waste material (Sw,in); these mass sources are discussed in HYPERLINK \l "PA-4_6_2_3" Section REF _Ref201112068 \r \h \* MERGEFORMAT PA-4.6.2.3. The outlet of the wellbore is set to atmospheric pressure. Mass exiting the wellbore is determined from the mixture velocity, the area of the outlet Aout (0.066 m2), and the density and volume fraction of each phase at the outlet of the wellbore:
(PA. SEQ Eq._PA- \* ARABIC 161)
Finally, the net change in mass and momentum for phase q is
(PA. SEQ Eq._PA- \* ARABIC 162)
(PA. SEQ Eq._PA- \* ARABIC 163)
The outlet of the wellbore is set to atmospheric pressure. Momentum exiting the wellbore is determined from the fluid velocity and the area of the outlet Aout (0.066 m2):
(PA. SEQ Eq._PA- \* ARABIC 164)
No momentum is added by mass flow into the wellbore from the repository; thus
(PA. SEQ Eq._PA- \* ARABIC 165)
Repository Flow Model
The repository is modeled as a radially symmetric domain. A spherical coordinate system is used for this presentation and for most DRSPALL calculations. In a few circumstances, cylindrical coordinates are used in PA calculations, where spall volumes are large enough that spherical coordinates are not representative of the physical process ( HYPERLINK "../../references/Others/Lord_et_al_2003_Analysis_Package_for_DRSPALL_CRA_ERMS532766_533157.pdf" Lord, Rudeen, and Hansen 2003). Cylindrical coordinates are also available; the design document for DRSPALL ( HYPERLINK "../../references/Others/WIPP_PA_2003_Design_Document_for_DRSPALL_ERMS529878.pdf" WIPP Performance Assessment 2003e) provides details on implementing the repository flow model in cylindrical coordinates.
Flow in the repository is transient, compressible, viscous, and single-phase (gas) flow in a porous medium. Gas is treated as isothermal and ideal. The equations governing flow in the repository are the equation of state for ideal gases (written in the form of Boyles law for an ideal gas at constant temperature), conservation of mass, and Darcys law with the Forchheimer correction ( HYPERLINK "../../references/Others/Aronson_1986.pdf" Aronson 1986, HYPERLINK "../../references/Others/Whitaker_1996.pdf" Whitaker 1996):
(PA. SEQ Eq._PA- \* ARABIC 166)
(PA. SEQ Eq._PA- \* ARABIC 167)
(PA. SEQ Eq._PA- \* ARABIC 168)
where
P = pressure in pore space (Pa)
(g = density of gas (kg/m3)
u = velocity of gas in pore space (m/s)
( = porosity of the solid (unitless)
(g = gas viscosity (8.934 ( 10-6 Pa s)
k = permeability of waste solid (m2)
F = Forchheimer correction (unitless)
The Forchheimer correction is included in Equation ( REF EQ_PA169 \h \* MERGEFORMAT PA.168) to account for inertia in the flowing gas, which becomes important at high gas velocities ( HYPERLINK "../../references/Others/Ruth_Ma_1992.pdf" Ruth and Ma 1992). When the Forchheimer coefficient is zero, Equation ( REF EQ_PA169 \h \* MERGEFORMAT PA.168) reduces to Darcys law. A derivation of Equation ( REF EQ_PA169 \h \* MERGEFORMAT PA.168) from the Navier-Stokes equations is given by Whitaker ( HYPERLINK "../../references/Others/Whitaker_1996.pdf" 1996); the derivation suggests that F is a linear function of gas velocity for a wide range of Reynolds numbers.
In PA, the Forchheimer correction takes the form
F = (nd(u (PA. SEQ Eq._PA- \* ARABIC 169)
where (nd is the non-Darcy coefficient, which depends on material properties such as the tortuosity and area of internal flow channels, and is empirically determined ( HYPERLINK "../../references/Others/SPE_81499.pdf" Belhaj et al. 2003). DRSPALL uses a value from Li et al. ( HYPERLINK "../../references/Others/SPE_68822.pdf" 2001) that measured high-velocity nitrogen flow through porous sandstone wafers, giving the result
(PA. SEQ Eq._PA- \* ARABIC 170)
Equation ( REF EQ_PA167 \h \* MERGEFORMAT PA.166) through Equation ( REF EQ_PA169 \h \* MERGEFORMAT PA.168) combines into a single equation for pressure in the porous solid:
(PA. SEQ Eq._PA- \* ARABIC 171)
where
(PA. SEQ Eq._PA- \* ARABIC 172)
and the Laplacian operator in a radially symmetric coordinate system is given by
(PA. SEQ Eq._PA- \* ARABIC 173)
where n = 2 and n = 3 for polar and spherical coordinates, respectively.
In DRSPALL, the permeability of the waste solid is a subjectively uncertain parameter that is constant for waste material that has not failed and fluidized. In a region of waste that has failed, the permeability increases as the waste fluidizes by a factor of 1 + Ff, where Ff is the fraction of failed material that has fluidized and is based on the fluidization relaxation time. This approximately accounts for the material bulking as it fluidizes.
Initial pressure in the repository is set to a constant value Pff. A no-flow boundary condition is imposed at the outer boundary (r = R):
(P(R) = 0 (PA. SEQ Eq._PA- \* ARABIC 174)
At the inner boundary (r = rcav), the pressure is specified as P(rcav,t) = Pcav(t), where Pcav(t) is defined in the next section. The cavity radius rcav increases as drilling progresses and waste material fails and moves into the wellbore; calculation of rcav is described in HYPERLINK \l "PA-4_6_2_3" Section REF _Ref201112092 \r \h \* MERGEFORMAT PA-4.6.2.3.3.
Wellbore to Repository Coupling
Prior to penetration, a cylinder of altered-permeability salt material with diameter equal to the drill bit is assumed to connect the bottom of the wellbore to the repository. At the junction of the repository and this cylinder of salt, a small, artificial cavity is used to determine the boundary pressure for repository flow. After penetration, the cavity merges with the bottom of the wellbore to connect the wellbore to the repository.
Flow Prior to Penetration
The cylinder of salt connecting the wellbore to the repository is referred to as the DDZ in HYPERLINK \l "Figure_PA-23" REF _Ref201119954 \h \* MERGEFORMAT Figure PA-23. The permeability of the DDZ, kDDZ, is 1 ( 10-14 m2. The spallings model starts with the bit 0.15 m above the repository; the bit advances at a rate of Rdrill = 0.004445 m/s.
To couple the repository to the DDZ, the model uses an artificial pseudo-cavity in the small hemispherical region of the repository below the wellbore with the same surface area as the bottom of the wellbore ( HYPERLINK \l "Figure_PA-26" REF _Ref201119988 \h \* MERGEFORMAT Figure PA-26). The pseudo-cavity is a numerical device that smoothes the discontinuities in pressure and flow that would otherwise occur upon bit penetration of the repository. The pseudo-cavity contains only gas, and is initially at repository pressure. The mass of gas in the cavity mcav is given by
(PA. SEQ Eq._PA- \* ARABIC 175)
where
Srep = gas flow from repository into pseudo-cavity (kg/s); see Equation ( REF EQ_PA177 \h \* MERGEFORMAT PA.176)
Sg, in = gas flow from pseudo-cavity through DDZ into wellbore (kg/s); see Equation ( REF EQ_PA178 \h \* MERGEFORMAT PA.177)
Flow from the repository into the pseudo-cavity is given by
(PA. SEQ Eq._PA- \* ARABIC 176)
where
(g,rep = gas density in repository at cavity surface (kg/m3) =
urep = gas velocity (m/s) in repository at cavity surface =
( = porosity of waste (unitless)
Acav = surface area of hemispherical part of the cavity (m2)
= , where dbit is the diameter of the bit (m)
Flow out of the pseudo-cavity through the DDZ and into the wellbore is modeled as steady-state using Darcys Law:
(PA. SEQ Eq._PA- \* ARABIC 177)
where
(g = viscosity of H2 gas (8.934 ( 10(6 Pa s)
Mw = molecular weight of H2 gas (0.00202 kg / mol)
R = ideal gas constant (8.314 J/mol K)
T = repository temperature (constant at 300 K (27 C; 80 F))
L = length (m) of DDZ (from bottom of borehole to top of repository)
Pcav = pressure in pseudo-cavity (Pa)
PBH = pressure at bottom of wellbore (Pa)
A justification for using this steady-state equation is provided in the design document for DRSPALL ( HYPERLINK "../../references/Others/WIPP_PA_2003_Design_Document_for_DRSPALL_ERMS529878.pdf" WIPP Performance Assessment 2003e). The pseudo-cavity is initially filled with gas at a pressure of Pff. The boundary pressure on the well side (PBH) is the pressure immediately below the bit, determined by Equation ( REF EQ_PA148 \h \* MERGEFORMAT PA.147) and Equation ( REF EQ_PA149 \h \* MERGEFORMAT PA.148). The pressure in the pseudo-cavity (Pcav) is determined by the ideal gas law:
(PA. SEQ Eq._PA- \* ARABIC 178)
where mcav is the number of moles of gas in the cavity and the cavity volume Vcav is given by
(PA. SEQ Eq._PA- \* ARABIC 179)
In PA, the drilling rate into the ground is assumed constant at 0.004445 m/s; thus L = Li 0.004445t until L = 0, at which time the bit penetrates the waste. The term Li is the distance from the bit to the waste at the start of calculation (0.15 m).
Flow After Penetration
After waste penetration, the bottom of the wellbore is modeled as a hemispherical cavity in the repository, the radius of which grows as drilling progresses and as material fails and moves into the cavity. Gas, drilling mud, and waste are assumed to thoroughly mix in this cavity; the resulting mixture flows around the drill collars and then up the annulus between the wellbore and the drill string. Gas flow from the repository into the cavity is given by Equation ( REF EQ_PA177 \h \* MERGEFORMAT PA.176); however, Acav is now dependent on the increasing radius of the cavity (see HYPERLINK \l "PA-4_6_2_3" Section REF _Ref201112092 \r \h \* MERGEFORMAT PA-4.6.2.3.3). Mudflow into the cavity from the wellbore is given by Equation ( REF EQ_PA160 \h \* MERGEFORMAT PA.159). Waste flow into the cavity is possible if the waste fails and fluidizes; these mechanisms are discussed in HYPERLINK \l "PA-4_6_2_3_4" Section REF _Ref201112128 \r \h \* MERGEFORMAT PA-4.6.2.3.4 and HYPERLINK \l "PA-4_6_2_3_5" Section REF _Ref201112129 \r \h \* MERGEFORMAT PA-4.6.2.3.5. Pressure in the cavity is equal to that at the bottom of the wellbore, and is computed by Equation ( REF EQ_PA179 \h \* MERGEFORMAT PA.178).
Cavity Volume After Penetration
The cylindrical cavity of increasing depth created by drilling is mapped to a hemispherical volume at the bottom of the wellbore to form the cavity. This mapping maintains equal surface areas in order to preserve the gas flux from the repository to the wellbore. The cavity radius from drilling is thus
(PA. SEQ Eq._PA- \* ARABIC 180)
where (H is the depth of the drilled cylinder. In PA, the drilling rate into the ground is assumed constant at 0.004445 m/s; thus (H = 0.004445t until (H = H, the height of compacted waste (m). Since the initial height of the repository is 3.96 m, H is computed from the porosity ( by , where (0 is the initial porosity of a waste-filled room.
The cavity radius rcav is increased by the radius of failed and fluidized material rfluid, which is the depth to which fluidization has occurred beyond the drilled radius. That is,
(PA. SEQ Eq._PA- \* ARABIC 181)
Waste Failure
Gas flow from the waste creates a pressure gradient within the waste, which induces elastic stresses in addition to the far-field confining stress. These stresses may lead to tensile failure of the waste material, an assumed prerequisite to spallings releases. While the fluid calculations using Equation ( REF EQ_PA167 \h \* MERGEFORMAT PA.166), Equation ( REF EQ_PA168 \h PA.167), and Equation ( REF EQ_PA169 \h \* MERGEFORMAT PA.168) are fully transient, the elastic stress calculations are assumed to be quasi-static (i.e., sound-speed phenomena in the solid are ignored). Elastic effective stresses are ( HYPERLINK "../../references/Others/Timoshenko_Goodier_1970.pdf" Timoshenko and Goodier 1970)
(PA. SEQ Eq._PA- \* ARABIC 182)
(PA. SEQ Eq._PA- \* ARABIC 183)
where ( is Biots constant (assumed here to be 1.0) and (ff is the confining far-field stress (assumed constant at 14.8MPa).
The flow-related radial and tangential stresses ((sr and (s( , respectively) are computed by equations analogous to differential thermal expansion ( HYPERLINK "../../references/Others/Timoshenko_Goodier_1970.pdf" Timoshenko and Goodier 1970):
(PA. SEQ Eq._PA- \* ARABIC 184)
(PA. SEQ Eq._PA- \* ARABIC 185)
where Pff is the initial repository pressure and ( is Poissons ratio (0.38).
Since stresses are calculated as quasi-static, an initial stress reduction caused by an instantaneous pressure drop at the cavity face propagates instantaneously through the waste. The result of calculating Equation ( REF EQ_PA183 \h \* MERGEFORMAT PA.182) can be an instantaneous early-time tensile failure of the entire repository if the boundary pressure is allowed to change suddenly. This is nonphysical and merely a result of the quasi-static stress assumption, combined with the true transient pore pressure and flow-related stress equations. To prevent this nonphysical behavior, tensile failure propagation is limited by a tensile failure velocity (1000 m/s; see HYPERLINK "../../references/Others/Hansen_et_al_1997_Description_&_Evaluation_of_Mechanistically_Based_Conceptual_Model_SAND97_1369.pdf" Hansen et al. 1997). This limit has no quantitative effect on results, other than to prevent nonphysical tensile failure.
At the cavity face, Equation ( REF EQ_PA183 \h \* MERGEFORMAT PA.182) and Equation ( REF EQ_PA185 \h \* MERGEFORMAT PA.184) evaluate to zero, consistent with the quasistatic stress assumption. This implies that the waste immediately at the cavity face cannot experience tensile failure; however, tensile failure may occur at some distance into the waste material. Consequently, the radial effective stress (r is averaged from the cavity boundary into the waste over a characteristic length Lt (0.02 m). If this average radial stress is tensile and its magnitude exceeds the material tensile strength (|| > TENSLSTR), the waste is no longer capable of supporting radial stress and fails, permitting fluidization. The waste tensile strength is an uncertain parameter in the analysis (see TENSLSTR in HYPERLINK \l "Table_PA-15" REF _Ref201126771 \h \* MERGEFORMAT Table PA-15).
Equation ( REF EQ_PA184 \h \* MERGEFORMAT PA.183) and Equation ( REF EQ_PA186 \h \* MERGEFORMAT PA.185) evaluate shear stresses in the waste. DRSPALL does not use the waste shear stresses to calculate waste failure for spall releases. These stresses are included in this discussion for completeness.
Waste Fluidization
Failed waste material is assumed to be disaggregated, but not in motion; it remains as a porous, bedded material lining the cavity face, and is treated as a continuous part of the repository from the perspective of the porous flow calculations. The bedded material may be mobilized and enter the wellbore if the gas velocity in the failed material (see Equation ( REF EQ_PA169 \h \* MERGEFORMAT PA.168)) exceeds a minimum fluidization velocity, Uf. The minimum fluidization velocity is determined by solving the following quadratic equation ( HYPERLINK "../../references/Others/Cherimisinoff_Cherimisinoff_1984.pdf" Cherimisinoff and Cherimisinoff 1984, HYPERLINK "../../references/Others/Ergun_1952.pdf" Ergun 1952)
(PA. SEQ Eq._PA- \* ARABIC 186)
where
a = particle shape factor (unitless)
dp = particle diameter (m)
Fluidization occurs in the failed material to the depth at which gas velocity does not exceed the fluidization velocity; this depth is denoted by rfluid and is used to determine cavity radius ( HYPERLINK \l "PA-4_6_2_3_3" Section REF _Ref201112092 \r \h \* MERGEFORMAT PA-4.6.2.3.3). If fluidization occurs, the gas and waste particles mix into the cavity at the bottom of the wellbore. Because this mixing cannot be instantaneous, which would be nonphysical (much as allowing instantaneous tensile failure propagation would be nonphysical), a small artificial relaxation time, equal to the cavity radius rcav divided by the superficial gas velocity u(rcav), is imposed upon the mixing phenomenon. The fluidized material is released into the cavity uniformly over the relaxation time.
Numerical Model
The numerical model implements the conceptual and mathematical models described above ( HYPERLINK \l "PA-4_6_2" Section REF _Ref212435988 \r \h \* MERGEFORMAT PA-4.6.2). Both the wellbore and the repository domain calculations use time-marching finite differences. These are part of a single computational loop and therefore use the same time step. The differencing schemes for the wellbore and repository calculations are similar, but not identical.
Numerical MethodWellbore
The wellbore is zoned for finite differencing, as illustrated in HYPERLINK \l "Figure_PA-27" REF _Ref201120063 \h \* MERGEFORMAT Figure PA-27, which shows zones, zone indices, grid boundaries, volumes, and interface areas. The method is Eulerian: zone boundaries are fixed, and fluid flows across the interfaces by advection. Quantities are zone-centered and integration is explicit in time.
To reduce computation time, an iterative scheme is employed to update the wellbore flow solution. The finite-difference scheme first solves Equation ( REF EQ_PA148 \h \* MERGEFORMAT PA.147) and Equation ( REF EQ_PA149 \h \* MERGEFORMAT PA.148) for the mass of each phase in each grid cell and the momentum in each grid cell.
The updated solution to Equation ( REF EQ_PA148 \h \* MERGEFORMAT PA.147) and Equation ( REF EQ_PA149 \h \* MERGEFORMAT PA.148) is then used to compute the volume of each phase, the pressure, and the mixture velocity in each grid cell.
All of the materials (mud, salt, gas, and waste) are assumed to move together as a mixture. Because fluid moves through the cell boundaries, the calculation requires a value for the flow through each cell boundary during a time step. These values are obtained by averaging the fluid velocities at the zone centers, given by
SHAPE \* MERGEFORMAT
Figure PA- SEQ Figure_PA- \* ARABIC 27. Finite-Difference Zoning for Wellbore
(PA. SEQ Eq._PA- \* ARABIC 187)
The mass transport equation, prior to any volume change, becomes
(PA. SEQ Eq._PA- \* ARABIC 188)
Here, the source terms Sm,i correspond to material entering or exiting at the pump, cavity, and surface. The upwind zone-centered densities are used for the interfaces values, and .
Finally, any changed volumes are incorporated and numerical mass diffusion is added for stability:
(PA. SEQ Eq._PA- \* ARABIC 189)
where
and (q is the diffusion coefficient for phase q. The density (fq for phase q being diffused is calculated from the mixture density, (, and the mass fraction, fq, of phase q in the referenced cell (fq = (Vq,i/(Vi). The numerical diffusion coefficient (q is chosen empirically for stability. Separate diffusion coefficients could be used for the different materials (mud, gas, etc.); however, sufficient stability is obtained by diffusing only mud and salt using the same coefficient ((m = (s = 0.0001 and (w = (g = 0).
Momentum is differenced as
(PA. SEQ Eq._PA- \* ARABIC 190)
where the dissipation term is obtained from Equation ( REF EQ_PA154 \h \* MERGEFORMAT PA.153) and is constrained by
(PA. SEQ Eq._PA- \* ARABIC 191)
and the sign of is chosen to oppose flow. Finally, numerical momentum diffusion is added without distinguishing between phases in the mixture (( is the mixture density):
(PA. SEQ Eq._PA- \* ARABIC 192)
In PA, (p = 0.01.
Equation ( REF EQ_PA151 \h \* MERGEFORMAT PA.150), Equation ( REF EQ_PA152 \h \* MERGEFORMAT PA.151), and Equation ( REF EQ_PA153 \h \* MERGEFORMAT PA.152) comprise a simultaneous system of equations for the volumes of gas and mud and the pressure in the wellbore. The volumes of salt and waste are known, since they are considered incompressible. Equation ( REF EQ_PA151 \h \* MERGEFORMAT PA.150) and Equation ( REF EQ_PA152 \h \* MERGEFORMAT PA.151) combine into a quadratic equation for gas volume:
(PA. SEQ Eq._PA- \* ARABIC 193)
where
The volume of the mud phase follows from Equation ( REF EQ_PA151 \h \* MERGEFORMAT PA.150) and the pressure from Equation ( REF EQ_PA150 \h \* MERGEFORMAT PA.149). Once the mixture density in each cell ((i) is updated by Equation ( REF EQ_PA152 \h \* MERGEFORMAT PA.151), the mixture velocity in each cell (ui) is computed by
(PA. SEQ Eq._PA- \* ARABIC 194)
where the quantity (u is determined by Equation ( REF EQ_PA193 \h \* MERGEFORMAT PA.192).
Numerical MethodRepository
The time integration method for the repository flow is implicit, with spatial derivatives determined after the time increment. This method requires the inversion of a matrix for the entire repository, which is usually straightforward. The implicit scheme is unconditionally stable. However, it is still necessary to use small time steps to ensure gradient accuracy.
The numerical method follows Press et al. ( HYPERLINK "../../references/Others/Press_et_al_1989.pdf" 1989). For simplicity, the equations are presented for constant zone size, although DRSPALL implements difference equations that allow for a variable zone size. Near the cavity, a small, constant zone size is used, and then zones are allowed to grow geometrically as the outer boundary is approached. This procedure greatly increases computational efficiency without sacrificing accuracy in the region of interest.
For an isothermal ideal gas, the pseudopressure ( is defined as
(PA. SEQ Eq._PA- \* ARABIC 195)
Using Equation ( REF EQ_PA196 \h \* MERGEFORMAT PA.195), Equation ( REF EQ_PA172 \h \* MERGEFORMAT PA.171) is expanded to
(PA. SEQ Eq._PA- \* ARABIC 196)
where ; Equation ( REF EQ_PA197 \h \* MERGEFORMAT PA.196) is then converted to a difference equation by treating D(() as constant over a zone, using its zone-centered value at the current time :
(PA. SEQ Eq._PA- \* ARABIC 197)
Collecting similar terms in ( leads to a tridiagonal system:
, j = 1,2. (PA. SEQ Eq._PA- \* ARABIC 198)
where
Equation ( REF EQ_PA199 \h \* MERGEFORMAT PA.198) may be solved by simplified LU decomposition, as presented in Press et al. ( HYPERLINK "../../references/Others/Press_et_al_1989.pdf" 1989).
The boundary condition at the inner radius is implemented by noting that for i = 1 (the first intact or nonfluidized cell), is the cavity pseudopressure, which is known, and therefore can be moved to the right-hand side of Equation ( REF EQ_PA199 \h \* MERGEFORMAT PA.198):
(PA. SEQ Eq._PA- \* ARABIC 199)
The far-field boundary condition is a zero gradient, which is implemented by setting in Equation ( REF EQ_PA200 \h \* MERGEFORMAT PA.199), recognizing that and rearranging, which gives
(PA. SEQ Eq._PA- \* ARABIC 200)
where j is the index of the last computational cell.
Numerical MethodWellbore to Repository Coupling
The term urep, appearing in Equation ( REF EQ_PA177 \h \* MERGEFORMAT PA.176), is the gas velocity in the repository at the waste-cavity interface and is determined from the pressure gradient inside the waste. DRSPALL uses the pressure (P1) at the center of the first numerical zone in the waste to determine urep:
(PA. SEQ Eq._PA- \* ARABIC 201)
Implementation
During development of the spallings model, a total of five parameters were determined to be both uncertain and potentially significant to model results ( HYPERLINK "../../references/Others/Hansen_PLfeifle_Lord_2003_Parameter_Justification_Report_ERMS531057.pdf" Hansen, Pfeifle, and Lord 2003; HYPERLINK "../../references/Others/Lord_Rudeen_2003_Sensitivity_Analysis_Report_Parts_1_2_DRSPALL_Version_100_ERMS524400.pdf" Lord and Rudeen 2003). All five parameters relate to the repository conditions or the state of the waste at the time of intrusion. HYPERLINK \l "Table_PA-15" REF _Ref201126771 \h \* MERGEFORMAT Table PA-15 lists the uncertain parameters in the DRSPALL calculations; these parameters are also listed in HYPERLINK \l "Table_PA-19" REF TablePA_19 \h Table PA-19.
Table PA- SEQ Table_PA- \* ARABIC 15. Uncertain Parameters in the DRSPALL Calculations
ParameterVariableImplementationRepository PressureREPIPRESInitial repository pressure (Pa); spall calculated for values of 10, 12, 14, and 14.8 MPa. Defines initial repository pressure in Equation ( REF EQ_PA172 \h \* MERGEFORMAT PA.171) (see HYPERLINK \l "PA-4_6_2_2" Section REF _Ref201113286 \r \h \* MERGEFORMAT PA-4.6.2.2) and Pff in Equation ( REF EQ_PA185 \h \* MERGEFORMAT PA.184).Repository Permeability REPIPERMPermeability (m2) of waste, implemented by parameter SPALLMOD/REPIPERM. Log-uniform distribution from 2.4 ( 10 to 2.4 ( 10(12. Defines k in Equation ( REF EQ_PA169 \h \* MERGEFORMAT PA.168).Repository PorosityREPIPORPorosity (dimensionless) of waste, implemented by parameter SPALLMOD/REPIPOR. Uniform distribution from 0.35 to 0.66. Defines ( in Equation ( REF EQ_PA168 \h \* MERGEFORMAT PA.167).Particle DiameterPARTDIAMParticle diameter of waste (m) after tensile failure, implemented by parameter SPALLMOD/PARTDIAM. Log-uniform distribution from 0.001 to 0.1 (m). Defines dp in Equation ( REF EQ_PA187 \h \* MERGEFORMAT PA.186).Tensile StrengthTENSLSTRTensile strength of waste (Pa), implemented by parameter SPALLMOD/TENSLSTR. Uniform distribution from 0.12 MPa to 0.17MPa. Defines maximum for HYPERLINK \l "PA-4_6_2_3_4" Section REF _Ref204068663 \r \h \* MERGEFORMAT PA-4.6.2.3.4.
The computational requirements of DRSPALL prohibit calculation of spall volumes for all possible combinations of initial conditions and parameter values. Since repository pressure is a time-dependent value computed by the BRAGFLO model (see HYPERLINK \l "PA-4_2" Section REF _Ref201112173 \r \h \* MERGEFORMAT PA-4.2), DRSPALL calculations were performed for a small number of pressures. Sensitivity studies showed that spall does not occur at pressures below 10 MPa; this value was used as the lower bound on pressure. In DRSPALL, the repository pressure cannot exceed the far-field confining stress (14.8MPa); consequently, 14.8 MPa was used as the upper bound on pressure. Computations were also performed for intermediate pressures of 12 and 14 MPa. The remaining four parameters listed in REF _Ref201126771 \h \* MERGEFORMAT Table PA-15 are treated as subjectively uncertain. The uncertainty represented by these parameters pertains to the future state of the waste, which is modeled in PA as a homogeneous material with uncertain properties (see HYPERLINK \l "PA-5_0" Section REF _Ref205279373 \r \h \* MERGEFORMAT PA-5.0).
Spall volumes are computed for each combination of initial pressure and sample element, for a total of 4 ( 300 = 1,200 model runs. Although repository porosity could be treated as an initial condition (using the time-dependent value computed by BRAGFLO), to reduce the number of computational cases and ensure that extreme porosity values were represented, repository porosity was included as a sampled parameter.
The spallings submodel of the code CUTTINGS_S uses the DRSPALL results to compute the spall volume for a given initial pressure P. If P < 10 MPa or P > 14.8 MPa, the spall volume is the value computed for REPIPRESS = 10 MPa or REPIPRESS = 14.8 MPa, respectively. If P falls between 10 and 14.8 MPa, the spall volume is constructed by linear interpolation between the DRSPALL results for pressures that bracket P.
Additional Information
Additional information on DRSPALL and its use in PA to determine spallings releases can be found in the DRSPALL users manual ( HYPERLINK "../../references/Others/WIPP_PA_2003_Users_Manual_for_DRSPALL_Version_100_ERMS524780.pdf" WIPP Performance Assessment 2003f) and in the analysis package for spallings releases ( HYPERLINK "../../references/Others/Ismail_2008_Analysis_Package_for_CUTTINGS_S_Rev1_ERMS548618.pdf" Ismail 2008). Additional information on the construction of spall volumes by the code CUTTINGS_S can be found in the CUTTINGS_S design document ( HYPERLINK "../../references/Others/WIPP_PA_2003_Design_Document_for_CUTTINGS_Version_510.pdf" WIPP Performance Assessment 2003g).
DBR to Surface: BRAGFLO
This section describes the model for DBR volumes, which are volumes of brine released to the surface at the time of a drilling intrusion. DBR volumes are calculated by the code BRAGFLO, the same code used to compute two-phase flow in and around the repository (see HYPERLINK \l "PA-4_2" Section REF _Ref201113354 \r \h \* MERGEFORMAT PA-4.2).
Overview of Conceptual Model
DBRs could occur if the pressure in the repository at the time of a drilling intrusion exceeds 8MPa, which is the pressure exerted by a column of brine-saturated drilling fluid at the depth of the repository ( HYPERLINK "../../references/Others/Stoelzel_Brien_Analysis_Package_for_the_BRAGFLO_Direct_Release_Calculations_Task_4_ERMS417870.pdf" Stoelzel and OBrien 1996). For repository pressures less than 8 MPa, no DBRs are assumed to occur. However, even if the repository pressure exceeds 8 MPa at the time of a drilling intrusion, a DBR is not assured, as there might not be sufficient mobile brine in the repository to result in movement towards the borehole.
DBRs are estimated for the following cases: (1) an initial intrusion into the repository into either a lower (down-dip), middle, or upper (up-dip) panel; (2) an intrusion into a waste panel preceded by an E1 intrusion into either the same waste panel, an adjacent panel, or a nonadjacent panel; and (3) an intrusion into a waste panel preceded by an E2 intrusion into either the same waste panel, an adjacent panel, or a nonadjacent panel (see HYPERLINK \l "PA-6_7" Section REF _Ref201036297 \r \h \* MERGEFORMAT PA-6.7). To determine releases for the above cases, the DBR calculations use a computational grid that explicitly includes all 10 waste panels ( HYPERLINK \l "Figure_PA-28" REF _Ref201120074 \h \* MERGEFORMAT Figure PA-28).
For perspective, the following list provides a comparison of the BRAGFLO mesh for the Salado flow calculations ( HYPERLINK \l "Figure_PA-15" REF _Ref201037169 \h \* MERGEFORMAT Figure PA-15) and the DBR mesh used for the DBR calculations ( REF _Ref201120074 \h \* MERGEFORMAT Figure PA-28):
The DBR mesh is defined in the areal plane with the z dimension (height) one element thick; the BRAGFLO mesh is defined as a cross section, with multiple layers in height and the thickness (y dimension) one element thick.
Figure PA- SEQ Figure_PA- \* ARABIC 28. DBR Grid Used in PA
The DBR mesh uses constant thickness, while the BRAGFLO mesh uses rectangular flaring to account for three-dimensional volumes in a two-dimensional grid ( HYPERLINK \l "Figure_PA-16" REF _Ref201037264 \h \* MERGEFORMAT Figure PA-16).
The DBR mesh represents flow only in the waste area. The BRAGFLO model includes the surrounding geology as well as the entire WIPP excavation (including operations, experimental, and shaft regions).
Local scale heterogeneities are included in the DBR mesh, including the salt pillars, rooms, panel closures, and passageways that contain waste. These are not fully represented in the BRAGFLO mesh.
The DRZ is included in both models, but exists above and below the excavated regions in the BRAGFLO model, whereas the DRZ surrounds the waste rooms on the sides of the DBR mesh.
Both models include a one-degree formation dip through the excavated regions (Equation ( REF EQ_PA35 \h \* MERGEFORMAT PA.33)).
The DBRs are assumed to take place over a relatively short period of time (i.e., 3 to 4.5 days; see HYPERLINK \l "PA-4_7_8" Section REF _Ref210114755 \r \h \* MERGEFORMAT PA-4.7.8) following the drilling intrusion. The initial value conditions for determining DBR volumes are obtained by mapping solutions of Equation ( REF EQ_PA26 \h \* MERGEFORMAT PA.24), Equation ( REF EQ_PA27 \h PA.25), Equation ( REF EQ_PA28 \h PA.26), Equation ( REF EQ_PA29 \h PA.27), Equation ( REF EQ_PA30 \h PA.28), Equation ( REF EQ_PA31 \h PA.29), and Equation ( REF EQ_PA32 \h \* MERGEFORMAT PA.30) obtained from BRAGFLO with the computational grid in HYPERLINK \l "Figure_PA-15" REF _Ref201037169 \h \* MERGEFORMAT Figure PA-15 onto the grid in HYPERLINK \l "Figure_PA-28" REF _Ref201120074 \h \* MERGEFORMAT Figure PA-28.
In concept, the DBR for a drilling intrusion has the form
(PA. SEQ Eq._PA- \* ARABIC 202)
where
DBR = DBR volume (m3) for drilling intrusion
= rate (m3) at time t at which brine flows up intruding borehole
t = elapsed time (s) since drilling intrusion
te = time (s) at which DBR ends
The definition of rDBR(t) is discussed in the following sections. It is based on the two-phase flow relationships in Equation ( REF EQ_PA26 \h \* MERGEFORMAT PA.24) , Equation ( REF EQ_PA27 \h PA.25), Equation ( REF EQ_PA28 \h PA.26), Equation ( REF EQ_PA29 \h PA.27), Equation ( REF EQ_PA30 \h PA.28), Equation ( REF EQ_PA31 \h PA.29), and Equation ( REF EQ_PA32 \h \* MERGEFORMAT PA.30) and use of the Poettmann-Carpenter correlation ( HYPERLINK "../../references/Others/Poettmann_Carpenter_1952.pdf" Poettmann and Carpenter 1952) to determine a boundary pressure at the connection between the intruding borehole and the repository. The time te is based on current drilling practices in the Delaware Basin ( HYPERLINK \l "PA-4_7_8" Section REF _Ref201113394 \r \h \* MERGEFORMAT PA-4.7.8).
Linkage to Two-Phase Flow Calculation
The mesh in HYPERLINK \l "Figure_PA-28" REF _Ref201120074 \h \* MERGEFORMAT Figure PA-28 was linked to the mesh in HYPERLINK \l "Figure_PA-15" REF _Ref201037169 \h \* MERGEFORMAT Figure PA-15 by subdividing the waste disposal area in the mesh in REF _Ref201037169 \h \* MERGEFORMAT Figure PA-15 into three regions ( HYPERLINK \l "Figure_PA-29" REF _Ref201120129 \h \* MERGEFORMAT Figure PA-29). The upper region represents the northern rest of repository (North RoR) area in REF _Ref201037169 \h \* MERGEFORMAT Figure PA-15. The middle region represents the southern rest of repository (South RoR) area in REF _Ref201037169 \h \* MERGEFORMAT Figure PA-15. The lower region represents the farthest down-dip repository area (Waste Panel) in REF _Ref201037169 \h \* MERGEFORMAT Figure PA-15 that contained waste and thus corresponds to the single down-dip waste panel. The linkage between the solutions to Equation ( REF EQ_PA26 \h \* MERGEFORMAT PA.24) , Equation ( REF EQ_PA27 \h PA.25), Equation ( REF EQ_PA28 \h PA.26), Equation ( REF EQ_PA29 \h PA.27), Equation ( REF EQ_PA30 \h PA.28), Equation ( REF EQ_PA31 \h PA.29), and Equation ( REF EQ_PA32 \h \* MERGEFORMAT PA.30) and the DBR calculations was made by assigning quantities calculated by BRAGFLO for each region in REF _Ref201037169 \h \* MERGEFORMAT Figure PA-15 to the corresponding waste region in REF _Ref201120074 \h \* MERGEFORMAT Figure PA-28.
The height of the grid in REF _Ref201120074 \h \* MERGEFORMAT Figure PA-28 was assigned a value that corresponded to the crushed height, h (m), of the waste as predicted by the solution of Equation ( REF EQ_PA26 \h \* MERGEFORMAT PA.24) through Equation ( REF EQ_PA32 \h \* MERGEFORMAT PA.30). Specifically,
(PA. SEQ Eq._PA- \* ARABIC 203)
where hi and (i are the initial height (m) and porosity of the waste and ( is the volume-averaged porosity of the waste at the particular time under consideration ( HYPERLINK \l "PA-4_2_3" Section REF _Ref201113417 \r \h \* MERGEFORMAT PA-4.2.3). The areas designated equivalent panel closures, DRZ, and impure halite in REF _Ref201120074 \h \* MERGEFORMAT Figure PA-28 were assigned the
Figure PA- SEQ Figure_PA- \* ARABIC 29. Assignment of Initial Conditions for DBR Calculation
same pressures and saturations as the corresponding grid blocks in the 10,000-year BRAGFLO calculations. The area designated equivalent DRZ/concrete ( REF _Ref201120074 \h \* MERGEFORMAT Figure PA-28) was assigned the same pressures and saturations as the DRZ. These areas were assigned porosities that resulted in a conservation of the initial pore volumes used in the solution of Equation ( REF EQ_PA26 \h \* MERGEFORMAT PA.24) , Equation ( REF EQ_PA27 \h PA.25), Equation ( REF EQ_PA28 \h PA.26), Equation ( REF EQ_PA29 \h PA.27), Equation ( REF EQ_PA30 \h PA.28), Equation ( REF EQ_PA31 \h PA.29), and Equation ( REF EQ_PA32 \h \* MERGEFORMAT PA.30) on the grid in HYPERLINK \l "Figure_PA-15" REF _Ref201037169 \h \* MERGEFORMAT Figure PA-15. Specifically, the pore volumes associated with the panel closures, DRZ, and impure halite do not change with time the constant values being given by the definitions of ((x, y, 0) in HYPERLINK \l "Table_PA-16" REF _Ref210718469 \h \* MERGEFORMAT Table PA-16.
The initial brine pressure pb(x, y, 0) and gas saturation Sg(x, y, 0) in the grid in HYPERLINK \l "Figure_PA-28" REF _Ref201120074 \h \* MERGEFORMAT Figure PA-28 are assigned by
(PA. SEQ Eq._PA- \* ARABIC 204)
(PA. SEQ Eq._PA- \* ARABIC 205)
where designates a point in the grid in REF _Ref201120074 \h \* MERGEFORMAT Figure PA-28, and denote solutions to Equation ( REF EQ_PA26 \h \* MERGEFORMAT PA.24), Equation ( REF EQ_PA27 \h PA.25), Equation ( REF EQ_PA28 \h PA.26), Equation ( REF EQ_PA29 \h PA.27), Equation ( REF EQ_PA30 \h PA.28), Equation ( REF EQ_PA31 \h PA.29), and Equation ( REF EQ_PA32 \h \* MERGEFORMAT PA.30), and denote the variables of integration, tint is the time at which the drilling intrusion occurs, and R corresponds to the region in the BRAGFLO computational grid ( REF _Ref201037169 \h \* MERGEFORMAT Figure PA-15) that is mapped into the region in the DBR computational grid ( REF _Ref201120074 \h \* MERGEFORMAT Figure PA-28) that contains the point (x, y) ( HYPERLINK \l "Figure_PA-29" REF _Ref201120129 \h \* MERGEFORMAT Figure PA-29). Note that tint defines a time in the solution of Equation ( REF EQ_PA26 \h \* MERGEFORMAT PA.24), Equation ( REF EQ_PA27 \h PA.25), Equation ( REF EQ_PA28 \h PA.26), Equation ( REF EQ_PA29 \h PA.27), Equation ( REF EQ_PA30 \h PA.28), Equation ( REF EQ_PA31 \h PA.29), and Equation ( REF EQ_PA32 \h \* MERGEFORMAT PA.30); t = 0 defines the start time for the DBR calculation and corresponds to tint in the solution of Equation ( REF EQ_PA26 \h \* MERGEFORMAT PA.24), Equation ( REF EQ_PA27 \h PA.25), Equation ( REF EQ_PA28 \h PA.26), Equation ( REF EQ_PA29 \h PA.27), Equation ( REF EQ_PA30 \h PA.28), Equation ( REF EQ_PA31 \h PA.29), and Equation ( REF EQ_PA32 \h \* MERGEFORMAT PA.30).
The initial porosity ((x, y, 0) in the grid in HYPERLINK \l "Figure_PA-28" REF _Ref201120074 \h \* MERGEFORMAT Figure PA-28 is set by the equations listed in HYPERLINK \l "Table_PA-15" REF _Ref201126771 \h \* MERGEFORMAT Table PA-15. In HYPERLINK \l "Table_PA-16" REF _Ref210718469 \h \* MERGEFORMAT Table PA-16, hi is the initial height of the waste panels (3.96 m), (WP,i is the initial porosity of the waste panels (0.848), h(tint) is the height of the repository at the time of intrusion (typically 1 to 1.5 m; corresponds to h in Equation ( REF EQ_PA26 \h \* MERGEFORMAT PA.24), Equation ( REF EQ_PA27 \h PA.25), Equation ( REF EQ_PA28 \h PA.26), Equation ( REF EQ_PA29 \h PA.27), Equation ( REF EQ_PA30 \h PA.28), Equation ( REF EQ_PA31 \h PA.29), and Equation ( REF EQ_PA32 \h \* MERGEFORMAT PA.30)), hDRZ,i is the initial DRZ height (43.60 m) that results in the DRZ in REF _Ref201120074 \h \* MERGEFORMAT Figure PA-28 having the same pore volume as the initial pore volume of the DRZ in HYPERLINK \l "Figure_PA-15" REF _Ref201037169 \h \* MERGEFORMAT Figure PA-15, ADRZ is the area associated with DRZ in REF _Ref201120074 \h \* MERGEFORMAT Figure PA-28, and (DRZ,i is the initial porosity of DRZ (see HYPERLINK \l "Table_PA-3" REF _Ref201037522 \h \* MERGEFORMAT Table PA3). The quantity hDRZ,i ( ADRZ ( (DRZ,i is equal to the pore volume of DRZ above and below the waste filled regions in REF _Ref201037169 \h \* MERGEFORMAT Figure PA-15. In REF _Ref210718469 \h \* MERGEFORMAT Table PA-16, the term (C is the porosity of the panel closure concrete material (CONC_PCS; see REF _Ref201037522 \h \* MERGEFORMAT Table PA3), d1 is the length of the drift/explosion wall portion of the panel closure (32.1 m; see HYPERLINK \l "Figure_PA-20" REF _Ref201042351 \h \* MERGEFORMAT Figure PA-20), and d2 is the length of the concrete portion of the panel closure (7.9 m; see REF _Ref201042351 \h \* MERGEFORMAT Figure PA-20). The porosity of the panel closure and the equivalent DRZ/concrete materials are defined as the volume-weighted mean porosity of the component materials; this definition results in the same brine volume within the pore space in each set of panel closures in REF _Ref201037169 \h \* MERGEFORMAT Figure PA-15 and REF _Ref201120074 \h \* MERGEFORMAT Figure PA-28. In REF _Ref210718469 \h \* MERGEFORMAT Table PA-16, hH,i is the initial height of undisturbed halite in REF _Ref201120074 \h \* MERGEFORMAT Figure PA-28, which is arbitrarily taken to be 8.98 m. However, this value is unimportant because of the extremely low permeability of the undisturbed halite (~3.16 ( 10(23 m2); any brine in the halite could not flow into the waste over the short time period of the DBR calculation, so no effort was made to preserve halite pore volume when mapping from the computational grid in REF _Ref201037169 \h \* MERGEFORMAT Figure PA-15 to the computational grid in HYPERLINK \l "Figure_PA-28" REF _Ref201120074 \h \* MERGEFORMAT Figure PA-28. The quantity (H,i is the initial porosity of halite (HALPOR, see HYPERLINK \l "Table_PA-19" REF TablePA_19 \h Table PA-19).
Conceptual Representation for Flow Rate rDBR(t)
The driving force that would give rise to the DBR is a difference between waste panel pressure, pw (Pa), and the flowing bottomhole pressure in the borehole, pwf (Pa), at the time of the intrusion. The flowing bottomhole pressure pwf, defined as the dynamic pressure at the inlet of the intruding borehole to the waste panel, is less than the static pressure pw due to friction and acceleration effects. The rate at which brine and gas are transported up the intruding borehole is determined by the difference pw ( pwf and a productivity index Jp for the intruded waste panel (HYPERLINK "../../references/Others/Mattax_Dalton_1990.pdf"Mattax and Dalton 1990, p. 79):
(PA. SEQ Eq._PA- \* ARABIC 206)
where
Table PA- SEQ Table_PA- \* ARABIC 16. Initial Porosity in the DBR Calculation
Grid RegionInitial Porosity Waste ((W)Panel ClosuresDRZImpure HaliteEquivalent DRZ/Concrete
EMBED Equation.DSMT4 = flow rate (m3/s) at time t for phase p (p = b ~ brine, p = g ~ gas)
= productivity index (m3/Pas) for phase p
and pw and pwf are defined above. As indicated by the inclusion/exclusion of a dependence on t, the terms Jp and pwf are constant during the determination of qp(t) for a particular drilling intrusion in the present analysis, and pw(t) changes as a function of time. In concept, the DBR is given by
(PA. SEQ Eq._PA- \* ARABIC 207)
once Jb (brine), pw, and pwf are determined. HYPERLINK \l "PA-4_7_4" Section REF _Ref201113437 \r \h \* MERGEFORMAT PA-4.7.4 discusses the determination of Jp (for both gas and brine), HYPERLINK \l "PA-4_7_5" Section REF _Ref201113438 \r \h \* MERGEFORMAT PA-4.7.5 presents the numerical determination of pw and DBR, and the determination of pwf is discussed in HYPERLINK \l "PA-4_7_6" Section REF _Ref212011572 \r \h \* MERGEFORMAT PA-4.7.6. The associated gas release is given by the corresponding integral with Jg (gas) rather than Jb (brine). In the computational implementation of the analysis, DBR is determined as part of the numerical solution of the system of PDEs that defines pw (Section REF _Ref201113438 \r \h \* MERGEFORMAT PA-4.7.5).
Determination of Productivity Index Jp
In a radial drainage area with uniform saturation, which is assumed to be valid throughout the DBR, the following representation for Jp can be determined from Darcys law ( HYPERLINK "../../references/Others/Mattax_Dalton_1990.pdf" Mattax and Dalton 1990, p. 79; HYPERLINK "../../references/Others/Williamson_Chappelear_1981.pdf" Williamson and Chappelear 1981; HYPERLINK "../../references/Others/Chappelear_Williamson_1981.pdf" Chappelear and Williamson 1981):
(PA. SEQ Eq._PA- \* ARABIC 208)
where
k = absolute permeability (assumed to be constant through time at 2.4 ( 10(13 m2)
krp = relative permeability to phase p (calculated with modified Brooks-Corey model in Equation ( REF EQ_PA140 \h \* MERGEFORMAT PA.139), Equation ( REF EQ_PA141 \h PA.140), and Equation ( REF EQ_PA142 \h \* MERGEFORMAT PA.141) and brine and gas saturations, Sb and Sg, obtained by mapping solutions of Equation ( REF EQ_PA26 \h \* MERGEFORMAT PA.24), Equation ( REF EQ_PA27 \h PA.25), Equation ( REF EQ_PA28 \h PA.26), Equation ( REF EQ_PA29 \h PA.27), Equation ( REF EQ_PA30 \h PA.28), Equation ( REF EQ_PA31 \h PA.29), and Equation ( REF EQ_PA32 \h \* MERGEFORMAT PA.30) obtained with the grid in HYPERLINK \l "Figure_PA-15" REF _Ref201037169 \h \* MERGEFORMAT Figure PA-15 onto the grid in HYPERLINK \l "Figure_PA-28" REF _Ref201120074 \h \* MERGEFORMAT Figure PA-28)
h = crushed panel height (Equation ( REF EQ_PA204 \h \* MERGEFORMAT PA.203))
(p = viscosity of fluid phase (assumed to be constant through time with (b = 1.8 ( 10(3 Pas, and (g = 8.92 ( 10(6 Pas [ HYPERLINK "../../references/Others/Kaufmann_1960.pdf" Kaufmann 1960])
re = external drainage radius (for use with the rectangular grid blocks in REF _Ref201120074 \h \* MERGEFORMAT Figure PA-28, re is taken to be the equivalent areal radius; see Equation ( REF EQ_PA210 \h \* MERGEFORMAT PA.209))
rw = wellbore radius (assumed to be constant through time at 0.1556 m ( HYPERLINK "../../references/Others/Gatlin_1960.pdf" Gatlin 1960, Table 14.7)
c = (0.50 for pseudo-steady-state flow
s = skin factor, which is used to incorporate flow stimulation caused by cavings and spallings release (see Equation ( REF EQ_PA211 \h \* MERGEFORMAT PA.210))
In the present analysis,
(PA. SEQ Eq._PA- \* ARABIC 209)
where Dx is the x dimension (m) and Dy is the y dimension (m) of the grid block containing the down-dip well in REF _Ref201120074 \h \* MERGEFORMAT Figure PA-28 (Dx = 10 m and Dy = 32.7 m).
The skin factor s is derived from the cavings and spallings release. Due to the uncertainty in the cavings and spallings parameters, the calculated solid release volume can vary for each realization. The skin factor is calculated for each realization, based on the calculated solid release volume, through the following petroleum engineering well testing relationship ( HYPERLINK "../../references/Others/Lee_1982.pdf" Lee 1982, pp. 57):
(PA. SEQ Eq._PA- \* ARABIC 210)
where
ks = permeability (m2) of an open channel as a result of spallings releases (assumed to be infinite)
rs = effective radius (m) of the wellbore with the cuttings, cavings, and spallings volume removed
The effective radius rs is obtained by converting the cuttings, cavings, and spallings volume removed into a cylinder of equal volume with the initial height of the waste (hi), and then computing the radius of the cylinder:
(PA. SEQ Eq._PA- \* ARABIC 211)
and substitution of rs into Equation ( REF EQ_PA211 \h \* MERGEFORMAT PA.210) with ks = ( yields
(PA. SEQ Eq._PA- \* ARABIC 212)
Determination of Waste Panel Pressure pw(t) and DBR
The repository pressure pw(t) in Equation ( REF EQ_PA208 \h \* MERGEFORMAT PA.207) after a drilling intrusion is determined with the same system of nonlinear PDEs discussed in HYPERLINK \l "PA-4_2" Section REF _Ref201113488 \r \h \* MERGEFORMAT PA-4.2. These equations are solved numerically by the code BRAGFLO used with the computational grid in HYPERLINK \l "Figure_PA-28" REF _Ref201120074 \h \* MERGEFORMAT Figure PA-28 and assumptions (i.e., parameter values, initial value conditions, and boundary value conditions) appropriate for representing brine flow to an intruding borehole over a relatively short time period immediately after the intrusion (e.g., 3 to 4.5 days). Due to the short time periods under consideration, the model for DBR does not include gas generation due to either corrosion or microbial action or changes in repository height due to creep closure. Furthermore, to stabilize the calculation and thus allow longer time steps in the numerical solution, the capillary pressure was assigned a value of 0 Pa in all modeled regions ( REF _Ref201120074 \h \* MERGEFORMAT Figure PA-28); in the analysis of the full system in Section REF _Ref201113488 \r \h \* MERGEFORMAT PA-4.2, capillary pressure had a value of 0 Pa in the waste regions and the DRZ, but a nonzero value in the panel closures ( HYPERLINK \l "Table_PA-4" REF _Ref201038785 \h \* MERGEFORMAT Table PA-4). Use of a capillary pressure of 0 Pa results in the brine pressure pb(x, y, t) and the gas pressure pg(x, y, t) being equal, with the pressure pw(t) in Equation ( REF EQ_PA208 \h \* MERGEFORMAT PA.207) given by
(PA. SEQ Eq._PA- \* ARABIC 213)
Although the determination of DBR can be conceptually represented by the integral in Equation ( REF EQ_PA203 \h \* MERGEFORMAT PA.202), in the numerical implementation of the analysis, DBR is determined within the numerical solution of the system of PDEs that defines pb(x, y, t).
With the specific assumptions for DBR, Equation ( REF EQ_PA26 \h \* MERGEFORMAT PA.24), Equation ( REF EQ_PA27 \h PA.25), Equation ( REF EQ_PA28 \h PA.26), Equation ( REF EQ_PA29 \h PA.27), Equation ( REF EQ_PA30 \h PA.28), Equation ( REF EQ_PA31 \h PA.29), and Equation ( REF EQ_PA32 \h \* MERGEFORMAT PA.30) become
Gas Conservation (( (PA. SEQ Eq._PA- \* ARABIC 214)
Brine Conservation (( (PA. SEQ Eq._PA- \* ARABIC 215)
Saturation Constraint (PA. SEQ Eq._PA- \* ARABIC 216)
Capillary Pressure Constraint (PA. SEQ Eq._PA- \* ARABIC 217)
Gas Density (g determined by RKS equation of state (Equation ( REF EQ_PA56 \h \* MERGEFORMAT PA.54)) (PA. SEQ Eq._PA- \* ARABIC 218)
Brine Density (PA. SEQ Eq._PA- \* ARABIC 219)
Formation Porosity (PA. SEQ Eq._PA- \* ARABIC 220)
with all symbols having the same definitions as in Equation ( REF EQ_PA26 \h \* MERGEFORMAT PA.24), Equation ( REF EQ_PA27 \h PA.25), Equation ( REF EQ_PA28 \h PA.26), Equation ( REF EQ_PA29 \h PA.27), Equation ( REF EQ_PA30 \h PA.28), Equation ( REF EQ_PA31 \h PA.29), and Equation ( REF EQ_PA32 \h \* MERGEFORMAT PA.30).
The primary differences between the BRAGFLO calculations described in HYPERLINK \l "PA-4_2" Section REF _Ref201113488 \r \h \* MERGEFORMAT PA-4.2 and the BRAGFLO calculations described in this section are in the computational meshes ( HYPERLINK \l "Figure_PA-28" REF _Ref201120074 \h \* MERGEFORMAT Figure PA-28 and HYPERLINK \l "Figure_PA-15" REF _Ref201037169 \h \* MERGEFORMAT Figure PA-15), initial values ( HYPERLINK \l "Table_PA-3" REF _Ref201037522 \h \* MERGEFORMAT Table PA3 and HYPERLINK \l "PA-4_7_2" Section REF _Ref201113534 \r \h \* MERGEFORMAT PA-4.7.2), and boundary conditions ( HYPERLINK \l "Table_PA-17" REF _Ref201037594 \h \* MERGEFORMAT Table PA-17). In particular, brine and gas flow associated with intruding boreholes in the DBR calculations are incorporated by the assignment of appropriate boundary conditions. Specifically, brine flow up an intruding borehole is incorporated into Equation ( REF EQ_PA215 \h \* MERGEFORMAT PA.214), Equation ( REF EQ_PA216 \h PA.215), Equation ( REF EQ_PA217 \h PA.216), Equation ( REF EQ_PA218 \h PA.217), Equation ( REF EQ_PA219 \h PA.218), Equation ( REF EQ_PA220 \h PA.219) and Equation ( REF EQ_PA221 \h \* MERGEFORMAT PA.220) by using the Poettmann-Carpenter wellbore model to determine the pressure at the outflow point in a waste panel ( REF _Ref201120074 \h \* MERGEFORMAT Figure PA-28), with this pressure entering the calculation as a boundary value condition ( REF _Ref201037594 \h \* MERGEFORMAT Table PA-17). The details of this determination are discussed in HYPERLINK \l "PA-4_7_6" Section REF _Ref212011616 \r \h \* MERGEFORMAT PA-4.7.6. Furthermore, for calculations that assume a prior E1 intrusion, the effects of this intrusion are also incorporated into the analysis by specifying a pressure as a boundary condition ( REF _Ref201037594 \h \* MERGEFORMAT Table PA-17). The determination of this pressure is discussed in Section REF _Ref212011635 \r \h \* MERGEFORMAT PA-4.7.6.
Boundary Value Pressure pwf
The boundary value pressure pwf at the inlet of the intruding borehole is defined by a system of equations of the following form:
Table PA- SEQ Table_PA- \* ARABIC 17. Boundary Conditions for pb and Sg in DBR Calculations
on Upper (Northern) or Lower (Southern) Boundary in HYPERLINK \l "Figure_PA-28" REF _Ref201120074 \h \* MERGEFORMAT Figure PA-28, 0 ( t (j = 0 Pa/mNo gas flow condition (j = 0 Pa/mNo brine flow condition on Right (Eastern) or Left (Western) Boundary in REF _Ref201120074 \h \* MERGEFORMAT Figure PA-28, 0 ( t (i = 0 Pa/mNo gas flow condition (i = 0 Pa/mNo brine flow condition at Location of Drilling Intrusion under Consideration (see indicated points in REF _Ref201120074 \h \* MERGEFORMAT Figure PA-28), 0 ( t (see HYPERLINK \l "PA-4_7_6" Section REF _Ref201113540 \r \h \* MERGEFORMAT PA-4.7.6)Constant pressure condition at Location of Prior Drilling Intrusion into Pressurized Brine (see indicated point in REF _Ref201120074 \h \* MERGEFORMAT Figure PA-28), 0 ( t (see HYPERLINK \l "PA-4_7_7" Section REF _Ref201113614 \r \h \* MERGEFORMAT PA-4.7.7)Constant pressure condition
(PA. SEQ Eq._PA- \* ARABIC 221)
(PA. SEQ Eq._PA- \* ARABIC 222)
(PA. SEQ Eq._PA- \* ARABIC 223)
(PA. SEQ Eq._PA- \* ARABIC 224)
where p(h) is pressure (Pa) at elevation h in the borehole, with h = 0 m corresponding to the entry point of the borehole into the waste panel and h = 655 m corresponding to the land surface ( HYPERLINK \l "Figure_PA-30" REF _Ref201120508 \h \* MERGEFORMAT Figure PA-30); G is a function (Pa/m) characterizing the change of pressure with elevation in the borehole; p(655) is an initial value condition requiring that pressure at the land surface (i.e., the outlet point of the borehole) be equal to atmospheric pressure; qb[p(0)] and qg[p(0)] define brine and gas flow rates (m3/s) into the borehole; Jb and Jg are productivity indexes (m3/Pa s) (see Equation ( REF EQ_PA209 \h \* MERGEFORMAT PA.208); and pw is the pressure (Pa) in the repository at the time of the drilling intrusion.
The boundary value pressure pwf is defined by
(PA. SEQ Eq._PA- \* ARABIC 225)
Figure PA- SEQ Figure_PA- \* ARABIC 30. Borehole Representation Used for Poettmann-Carpenter Correlation
Thus, pwf is determined by the numerical solution of Equation ( REF EQ_PA222 \h \* MERGEFORMAT PA.221) for p(0) subject to the constraints in Equation ( REF EQ_PA223 \h \* MERGEFORMAT PA.222), Equation ( REF EQ_PA224 \h \* MERGEFORMAT PA.223), and Equation ( REF EQ_PA225 \h \* MERGEFORMAT PA.224).
The pressure pw corresponds to the pressure pw(0) in Equation ( REF EQ_PA214 \h \* MERGEFORMAT PA.213) and is obtained from the solution of Equation ( REF EQ_PA26 \h \* MERGEFORMAT PA.24), Equation ( REF EQ_PA27 \h PA.25), Equation ( REF EQ_PA28 \h PA.26), Equation ( REF EQ_PA29 \h PA.27), Equation ( REF EQ_PA30 \h PA.28), Equation ( REF EQ_PA31 \h PA.29), and Equation ( REF EQ_PA32 \h \* MERGEFORMAT PA.30) with the computational grid in HYPERLINK \l "Figure_PA-15" REF _Ref201037169 \h \* MERGEFORMAT Figure PA-15 (see HYPERLINK \l "PA-4_7_2" Section REF _Ref201113639 \r \h \* MERGEFORMAT PA-4.7.2). The production indexes Jb and Jg are defined in Equation ( REF EQ_PA209 \h \* MERGEFORMAT PA.208). Thus, the only quantity remaining to be specified in Equation ( REF EQ_PA222 \h \* MERGEFORMAT PA.221), Equation ( REF EQ_PA223 \h PA.222), Equation ( REF EQ_PA224 \h PA.223), and Equation ( REF EQ_PA225 \h \* MERGEFORMAT PA.224) is the function G.
Brine and gas flow up a borehole is governed by complex physics dependent on frictional effects and two-phase fluid properties. This phenomenon has been widely studied in the petroleum industry and many modeling procedures have been developed to predict flow rates and pressures in vertical two-phase pipe flow (i.e., to define G in Equation ( REF EQ_PA222 \h \* MERGEFORMAT PA.221)) ( HYPERLINK "../../references/Others/Brill_Beggs_1986.pdf" Brill and Beggs 1986). For this analysis, the Poettmann-Carpenter model ( HYPERLINK "../../references/Others/Poettmann_Carpenter_1952.pdf" Poettmann and Carpenter 1952; HYPERLINK "../../references/Others/Welchon_Bertuzzi_Poettmann_1962.pdf" Welchon, Bertuzzi, and Poettmann 1962) was used to define G because it accounts for multiphase frictional effects based on empirical (i.e., field) data from flowing wells, is one of the few modeling approaches that included annular flow data in its development, and is relatively easy to implement. Specifically, the Poettmann-Carpenter model defines G by
(PA. SEQ Eq._PA- \* ARABIC 226)
where
g = acceleration due to gravity (9.8 m/s2)
m(h) = density (kg/m3) of fluids (i.e., gas and brine) in wellbore at elevation h (Note: m(h) is a function of qb[p(0)] and qg[p(0)]; see Equation ( REF EQ_PA228 \h \* MERGEFORMAT PA.227) below)
= empirically defined scale factor (m/s2) (Note: f( is the scale factor in the Poettmann-Carpenter model for fluid flow in a wellbore [HYPERLINK "../../references/Others/Poettmann_Carpenter_1952.pdf"Poettmann and Carpenter 1952]; see discussion below)
= flow rate (m3/s) of fluids (i.e., gas and brine) in wellbore at elevation h (Note: F(h) is a function of qb[p(0)] and qg[p(0)]; see Equation ( REF EQ_PA229 \h \* MERGEFORMAT PA.228))
= effective diameter (m) of wellbore (see Equation ( REF EQ_PA232 \h \* MERGEFORMAT PA.231))
The first term, gm(h), in Equation ( REF EQ_PA227 \h \* MERGEFORMAT PA.226) results from the contribution of elevation to pressure; the second term results from frictional effects (Poettmann and Carpenter 1952). The fluid density m(h) at elevation h is given by
(PA. SEQ Eq._PA- \* ARABIC 227)
where
(PA. SEQ Eq._PA- \* ARABIC 228)
and
= density (kg/m3) of brine at pressure p(0) and temperature 300.1 K, which is fixed at 1230 kg/m3
= density (kg/m3) of H2 at pressure p(0) and temperature 300.1 K (see Equation ( REF EQ_PA230 \h \* MERGEFORMAT PA.229), below)
= z-factor for compressibility of H2 at elevation h (Note: z(h) is a function of p(h); see Equation ( REF EQ_PA231 \h \* MERGEFORMAT PA.230), below), and qb[p(0)] and qg[p(0)] are defined in Equation ( REF EQ_PA222 \h \* MERGEFORMAT PA.221), Equation ( REF EQ_PA223 \h PA.222), Equation ( REF EQ_PA224 \h PA.223), and Equation ( REF EQ_PA225 \h \* MERGEFORMAT PA.224)
The gas density in Equation ( REF EQ_PA228 \h \* MERGEFORMAT PA.227) is obtained from the universal gas law, , by
(PA. SEQ Eq._PA- \* ARABIC 229)
where n is the amount of gas (mol) in a volume V, Cm,kg is the conversion factor from moles to kilograms for H2 (i.e., 2.02 ( 10(3 kg/mol), P = p(0), R = 8.3145 J/mol K, and T = 300.1K. The z-factor is given by
(PA. SEQ Eq._PA- \* ARABIC 230)
and was obtained from calculations performed with the SUPERTRAPP program ( HYPERLINK "../../references/Others/ERMS242589.pdf" Ely and Huber 1992) for pure H2 and a temperature of 300.1 K ( HYPERLINK "../../references/Others/Stoelzel_Brien_Analysis_Package_for_the_BRAGFLO_Direct_Release_Calculations_Task_4_ERMS417870.pdf" Stoelzel and OBrien 1996, Figure 4.7.4). The preceding approximation to z(h) was obtained by fitting a straight line between the results for pressures of 0 psi and 3000 psi and a H2 mole fraction of 1 in Stoelzel and OBrien (1996, Figure 4.7.4); the actual calculations used the more complex, but numerically similar, regression model given in Stoelzel and OBrien (1996, Figure 4.7.4). The numerator and denominator in Equation ( REF EQ_PA228 \h \* MERGEFORMAT PA.227) involve rates, with the time units canceling to give m(h) in units of kg/m3.
The effective diameter D(h) in Equation ( REF EQ_PA227 \h \* MERGEFORMAT PA.226) is defined with the hydraulic radius concept. Specifically,
(PA. SEQ Eq._PA- \* ARABIC 231)
where Di(h) and Do(h) are the inner and outer diameters (m) of the wellbore at elevation h(m) (see HYPERLINK \l "Figure_PA-30" REF _Ref201120508 \h \* MERGEFORMAT Figure PA-30). The factor in Equation ( REF EQ_PA227 \h \* MERGEFORMAT PA.226) is a function of m(h), D(h), and qb[p(0)].
Subsequent to submittal of the CCA PA, it was discovered that the factor of was omitted from Equation ( REF EQ_PA209 \h \* MERGEFORMAT PA.208). This error was determined to be of no consequence to the CCA PA conclusions ( HYPERLINK "../../references/Others/Hadgu_et_al_to_Marietta_1999_November_2_Modifications_CCA_direct_brine_release_calculations_ERMS511276.pdf" Hadgu et al. 1999) and was corrected in the CRA-2004 PA. As a consequence of the error correction, the regression models used to determine the boundary pressure pwf were recalculated (Hadgu et al. 1999). The corrected regression models are reported in this appendix.
The following iterative procedure based on the bisection method was used to approximate solutions to Equation ( REF EQ_PA222 \h \* MERGEFORMAT PA.221), Equation ( REF EQ_PA223 \h PA.222), Equation ( REF EQ_PA224 \h PA.223), and Equation ( REF EQ_PA225 \h \* MERGEFORMAT PA.224).
Step 1. Estimate p(0) using a bisection algorithm:
The initial guess for p(0) is the midpoint EMBED Equation.DSMT4 of interval [0, pw], where pw is the pressure in the repository at the time of the drilling intrusion used in Equation ( REF EQ_PA222 \h \* MERGEFORMAT PA.221), Equation ( REF EQ_PA223 \h PA.222), Equation ( REF EQ_PA224 \h PA.223), and Equation ( REF EQ_PA225 \h \* MERGEFORMAT PA.224).
The next guess for p(0) is at the midpoint of either or , depending on whether the resultant approximation to p(655) is above or below atmospheric pressure.
Subsequent guesses for p(0) are made in a similar manner.
Step 2. Use p(0), known values for Jb, Jg, and pw, and Equation ( REF EQ_PA222 \h \* MERGEFORMAT PA.221), Equation ( REF EQ_PA223 \h PA.222), Equation ( REF EQ_PA224 \h PA.223), and Equation ( REF EQ_PA225 \h \* MERGEFORMAT PA.224) to determine qb[p(0)] and qg[p(0)].
Step 3. Use the bisection method with (h = 25 ft = 7.62 m and appropriate changes in annular diameter ( HYPERLINK \l "Figure_PA-30" REF _Ref201120508 \h \* MERGEFORMAT Figure PA-30) to determine p(655) (i.e., p(h + (h) = p(h) + G(qb[p(0)], qg[p(0)], p(h), h), (h)).
Step 4. Stop if p(655) is within 0.07% of atmospheric pressure (i.e., if |1.013105 Pa(p(655)| ( 70 Pa)). Otherwise, return to Step 1 and repeat process.
The preceding procedure is continued until the specified error tolerance (i.e., 0.07%) has been met. The computational design of the PA has the potential to require more than 23,000 separate DBR calculations (3 replicates ( 5 scenarios ( 3 drilling locations ( 100 vectors ( 5 to 6 intrusion times per scenario). In concept, each of these cases requires the solution of Equation ( REF EQ_PA222 \h \* MERGEFORMAT PA.221), Equation ( REF EQ_PA223 \h PA.222), Equation ( REF EQ_PA224 \h PA.223), and Equation ( REF EQ_PA225 \h \* MERGEFORMAT PA.224) with the iterative procedure just presented to obtain the boundary value condition pwf = p(0) ( HYPERLINK \l "Table_PA-17" REF _Ref201037594 \h \* MERGEFORMAT Table PA-17). To help hold computational costs down, p(0) was calculated for approximately 2,000 randomly generated vectors of the form
(PA. SEQ Eq._PA- \* ARABIC 232)
where pw is the repository pressure (used in definition of qb[p(0)] and qg[p(0)] in Equation ( REF EQ_PA222 \h \* MERGEFORMAT PA.221), Equation ( REF EQ_PA223 \h PA.222), Equation ( REF EQ_PA224 \h PA.223), and Equation ( REF EQ_PA225 \h \* MERGEFORMAT PA.224)), h is the crushed height of the repository (used in definition of Jp in Equation ( REF EQ_PA209 \h \* MERGEFORMAT PA.208)), Sbr and Sgr are the residual saturations for gas and brine in the repository (used in definition of krp in Equation ( REF EQ_PA209 \h \* MERGEFORMAT PA.208)), Sb is the saturation of brine in the repository (used in definition of krp in Equation ( REF EQ_PA209 \h \* MERGEFORMAT PA.208)), and Ai is the equivalent area of material removed by cuttings, cavings, and spallings (used in definition of skin factor s in Equation ( REF Eq_PA213 \h \* MERGEFORMAT PA.212)). The outcomes of these calculations were divided into three cases:
Mobile brine only (i.e., krg = 0 in Equation ( REF EQ_PA215 \h \* MERGEFORMAT PA.214))
Brine-dominated flow (i.e., krb > krg)
Gas-dominated flow (i.e., krg > krb)
Regression procedures were then used to fit algebraic models that can be used to estimate p(0). These regression models were then used to determine p(0), and hence, pwf. The resulting three regression models (or curve fit equations) for flowing bottomhole pressure (pwf) are as follows:
1. For a system with only mobile brine (krg = 0)
(PA. SEQ Eq._PA- \* ARABIC 233)
where x = log(jb) and y = pw (= repository pressure), the coefficients in Equation ( REF EQ_PA234 \h \* MERGEFORMAT PA.233) were determined to be
a = 3.2279346 ( 1011
b = 9.4816648 ( 1010
c = (6.2002715 ( 103
d = 9.2450601 ( 109
e = 4.1464475 ( 10(6
f = (1.2886068 ( 103
g = 2.9905582 ( 108
h = 1.0857041 ( 10(14
i = 4.7119798 ( 10(7
j = (6.690712 ( 10(1
with a resulting coefficient of determination R2 = 0.974.
2. For brine-dominated flow (krb > krg)
(PA. SEQ Eq._PA- \* ARABIC 234)
where and y = pw (= repository pressure), the coefficients in Equation ( REF EQ_PA235 \h \* MERGEFORMAT PA.234) were determined to be
a = 1.6065077 ( 106
b = 2.6243397 ( 106
c = 2.4768899 ( 106
d = (5.3635476 ( 10(2
e = 7.0815693 ( 10(1
f = 3.8012696 ( 10(1
g = 4.1916956 ( 10(3
h = (2.4887085 ( 10(8
with a resulting coefficient of determination R2 = 0.997.
3. For gas-dominated flow (krg > krb)
(PA. SEQ Eq._PA- \* ARABIC 235)
where x = log(jg) and y = pw (= repository pressure), the coefficients in Equation ( REF EQ_PA236 \h \* MERGEFORMAT PA.235) were determined to be
a = (1.0098405 ( 109
b = (2.3044622 ( 1010
c = 9.8039146
d = (1.7426466 ( 1011
e = 1.8309137 ( 10(7
f = 1.7497064 ( 102
g = (4.3698224 ( 1011
h = (1.4891198 ( 10(16
i = 1.3006196 ( 10(6
j = 7.5744833 ( 102
with a resulting coefficient of determination R2 = 0.949.
Boundary Value Pressure pwE1
Some of the DBR calculations are for a drilling intrusion that has been preceded by an E1 intrusion in either the same waste panel, an adjacent waste panel, or a nonadjacent waste panel ( HYPERLINK \l "PA-6_7_6" Section REF _Ref201113660 \r \h \* MERGEFORMAT PA-6.7.6). The effects of these prior E1 intrusions are incorporated into the solution of Equation ( REF EQ_PA215 \h \* MERGEFORMAT PA.214), Equation ( REF EQ_PA216 \h PA.215), Equation ( REF EQ_PA217 \h PA.216), Equation ( REF EQ_PA218 \h PA.217), Equation ( REF EQ_PA219 \h PA.218), Equation ( REF EQ_PA220 \h PA.219), and Equation ( REF EQ_PA221 \h \* MERGEFORMAT PA.220), and hence into the DBR, by specifying a boundary pressure pwE1 at the location of the E1 intrusion into the repository ( HYPERLINK \l "Table_PA-17" REF _Ref201037594 \h \* MERGEFORMAT Table PA-17).
Two cases are considered for the definition of pwE1: (1) an open borehole between the brine pocket and the repository and (2) a borehole filled with silty-sand-like material between the brine pocket and the repository. The first case corresponds to the situation in which the drilling intrusion occurs within 200 years of a prior drilling intrusion that penetrated the pressurized brine pocket, and the second case corresponds to the situation in which the drilling intrusion occurs more than 200 years after a prior drilling intrusion that penetrated the pressurized brine pocket.
Solution for Open Borehole
In this case, pwE1 is set equal to the flowing well pressure pwfBP of an open borehole between the brine pocket and the repository, and is given by
(PA. SEQ Eq._PA- \* ARABIC 236)
(PA. SEQ Eq._PA- \* ARABIC 237)
(PA. SEQ Eq._PA- \* ARABIC 238)
where
= pressure (Pa) in brine pocket
= flowing well pressure (Pa) at outlet from brine pocket
= flowing well pressure (Pa) at inlet to repository from brine pocket
= flowing well pressure (Pa) at outlet from repository due to intruding borehole (Note: The boreholes associated with pwfBI and pwfBO arise from different drilling intrusions and hence are at different locations; see HYPERLINK \l "Figure_PA-28" REF _Ref201120074 \h \* MERGEFORMAT Figure PA-28)
Q = brine flow rate (m3/s) from brine pocket to repository, through repository, and then to surface
and f1, f2, and f3 are linear functions of their arguments. In the development, pBP and pwfBO are assumed to be known, with the result that Equation ( REF EQ_PA237 \h \* MERGEFORMAT PA.236), Equation ( REF EQ_PA238 \h PA.237), and Equation ( REF EQ_PA239 \h \* MERGEFORMAT PA.238) constitutes a system of three linear equations in three unknowns (i.e., pwfBP, pwbFI and Q) that can be solved to obtain pwfBI. In the determination of pwfBI for use in a particular solution of Equation ( REF EQ_PA215 \h \* MERGEFORMAT PA.214), Equation ( REF EQ_PA216 \h PA.215), Equation ( REF EQ_PA217 \h PA.216), Equation ( REF EQ_PA218 \h PA.217), Equation ( REF EQ_PA219 \h PA.218), Equation ( REF EQ_PA220 \h PA.219), and Equation ( REF EQ_PA221 \h \* MERGEFORMAT PA.220), pBP is the pressure in the brine pocket at the time of the intrusion obtained from the solution of Equation ( REF EQ_PA26 \h \* MERGEFORMAT PA.24), Equation ( REF EQ_PA27 \h PA.25), Equation ( REF EQ_PA28 \h PA.26), Equation ( REF EQ_PA29 \h PA.27), Equation ( REF EQ_PA30 \h PA.28), Equation ( REF EQ_PA31 \h PA.29), and Equation ( REF EQ_PA32 \h \* MERGEFORMAT PA.30) with BRAGFLO, and pwfBO is the flowing well pressure obtained from conditions at the time of the intrusion (from the solution of Equation ( REF EQ_PA26 \h \* MERGEFORMAT PA.24), Equation ( REF EQ_PA27 \h PA.25), Equation ( REF EQ_PA28 \h PA.26), Equation ( REF EQ_PA29 \h PA.27), Equation ( REF EQ_PA30 \h PA.28), Equation ( REF EQ_PA31 \h PA.29), and Equation ( REF EQ_PA32 \h \* MERGEFORMAT PA.30)) and the solutions of the Poettmann-Carpenter model embodied in Equation ( REF EQ_PA234 \h \* MERGEFORMAT PA.233), Equation ( REF EQ_PA235 \h PA.234), and Equation ( REF EQ_PA236 \h \* MERGEFORMAT PA.235) (i.e., given pressure, krg and krb at the time of the intrusion, and Jp, pwfBO is determined from the regression models indicated in Equation ( REF EQ_PA234 \h \* MERGEFORMAT PA.233), Equation ( REF EQ_PA235 \h PA.234), and Equation ( REF EQ_PA236 \h \* MERGEFORMAT PA.235)).
The definition of Equation ( REF EQ_PA237 \h \* MERGEFORMAT PA.236), Equation ( REF EQ_PA238 \h PA.237), and Equation ( REF EQ_PA239 \h \* MERGEFORMAT PA.238) is now discussed. Equation ( REF EQ_PA237 \h \* MERGEFORMAT PA.236) characterizes flow out of the brine pocket into an open borehole and has the form ( HYPERLINK "../../references/Others/Williamson_Chappelear_1981.pdf" Williamson and Chappelear 1981, HYPERLINK "../../references/Others/Chappelear_Williamson_1981.pdf" Chappelear and Williamson 1981)
(PA. SEQ Eq._PA- \* ARABIC 239)
where
= brine pocket permeability (m2)
= effective brine pocket height (m)
= effective brine pocket radius (m)
= wellbore radius (m)
( = brine viscosity (Pa s)
In the present analysis, kBP is an uncertain analysis input (see BHPRM in HYPERLINK \l "Table_PA-19" REF TablePA_19 \h Table PA-19); hBP = 125.83 m; reBP = 114 m ( HYPERLINK "../../references/Others/Stoelzel_Brien_Analysis_Package_for_the_BRAGFLO_Direct_Release_Calculations_Task_4_ERMS417870.pdf" Stoelzel and OBrien 1996), which corresponds to the size of the largest brine pocket that could fit under one waste panel; rw = (8.921 in.)/2 = 0.1133 m, which is the inside radius of a 9 5/8 in. outside diameter casing ( HYPERLINK "../../references/Others/Gatlin_1960.pdf" Gatlin 1960, Table 14.7); ( = 1.8 ( 10(3 Pa s; and pBP is determined from the solution of Equation ( REF EQ_PA26 \h \* MERGEFORMAT PA.24), Equation ( REF EQ_PA27 \h PA.25), Equation ( REF EQ_PA28 \h PA.26), Equation ( REF EQ_PA29 \h PA.27), Equation ( REF EQ_PA30 \h PA.28), Equation ( REF EQ_PA31 \h PA.29), and Equation ( REF EQ_PA32 \h \* MERGEFORMAT PA.30), as previously indicated.
Equation ( REF EQ_PA238 \h \* MERGEFORMAT PA.237) characterizes flow up an open borehole from the brine pocket to the repository and is based on Poiseuilles Law ( HYPERLINK "../../references/Others/Prasuhn_1980.pdf" Prasuhn 1980, Eqs. 7-21, 7-22). Specifically, Equation ( REF EQ_PA238 \h \* MERGEFORMAT PA.237) has the form
(PA. SEQ Eq._PA- \* ARABIC 240)
where
D = wellbore diameter (m)
= elevation of repository (m) measured from surface
= elevation of brine pocket (m) measured from surface
g = acceleration due to gravity (9.8 m/s2)
( = density of brine (kg/m3)
and the remaining symbols have already been defined.
In the present analysis, D = 2rw = 0.2266 m, ( = 1230 kg/m3, and yBP ( yrep = 247 m. With the preceding values,
(PA. SEQ Eq._PA- \* ARABIC 241)
(PA. SEQ Eq._PA- \* ARABIC 242)
Thus,
(PA. SEQ Eq._PA- \* ARABIC 243)
when Q is small (( 0.1 m3/s). When appropriate, this approximation can be used to simplify the construction of solutions to Equation ( REF EQ_PA237 \h \* MERGEFORMAT PA.236), Equation ( REF EQ_PA238 \h PA.237), and Equation ( REF EQ_PA239 \h \* MERGEFORMAT PA.238).
Equation ( REF EQ_PA239 \h \* MERGEFORMAT PA.238) characterizes flow through the repository from the lower borehole to the bottom of the borehole associated with the drilling intrusion under consideration and has the same form as Equation ( REF EQ_PA240 \h \* MERGEFORMAT PA.239). Specifically,
(PA. SEQ Eq._PA- \* ARABIC 244)
where
= repository permeability (m2)
= repository height (m)
= effective repository radius (m)
and the remaining symbols have already been defined. In the present analysis, krep = 2.4 ( 10(13 m2; hrep at the time of the drilling intrusion under consideration is obtained from the solution of Equation ( REF EQ_PA26 \h \* MERGEFORMAT PA.24), Equation ( REF EQ_PA27 \h PA.25), Equation ( REF EQ_PA28 \h PA.26), Equation ( REF EQ_PA29 \h PA.27), Equation ( REF EQ_PA30 \h PA.28), Equation ( REF EQ_PA31 \h PA.29), and Equation ( REF EQ_PA32 \h \* MERGEFORMAT PA.30) (see Equation ( REF EQ_PA204 \h \* MERGEFORMAT PA.203)); and re,rep is the same as the radius re defined in Equation ( REF EQ_PA210 \h \* MERGEFORMAT PA.209). As previously indicated, pwfBO is obtained from the solutions to the Poettmann-Carpenter model summarized in Equation ( REF EQ_PA234 \h \* MERGEFORMAT PA.233), Equation ( REF EQ_PA235 \h PA.234), and Equation ( REF EQ_PA236 \h \* MERGEFORMAT PA.235).
Three equations (i.e., Equation ( REF EQ_PA240 \h \* MERGEFORMAT PA.239), Equation ( REF EQ_PA241 \h \* MERGEFORMAT PA.240), and Equation ( REF EQ_PA245 \h \* MERGEFORMAT PA.244)) with three unknowns (i.e., pwfBP, pwfBI and Q) have now been developed. The solution for pwfBI defines the initial value pwE1 in HYPERLINK \l "Table_PA-17" REF _Ref201037594 \h \* MERGEFORMAT Table PA-17. When the simplification in Equation ( REF EQ_PA244 \h \* MERGEFORMAT PA.243) is used, the resultant solution for pwfBI is
(PA. SEQ Eq._PA- \* ARABIC 245)
where
(PA. SEQ Eq._PA- \* ARABIC 246)
and (2.98 ( 106 comes from Equation ( REF EQ_PA243 \h \* MERGEFORMAT PA.242). The expression in Equation ( REF EQ_PA247 \h \* MERGEFORMAT PA.246) was used to define pwE1 in the CCA for the determination of DBRs resulting from a drilling intrusion that occurred within 200 years of a preceding E1 intrusion (see HYPERLINK \l "Table_PA-7" REF _Ref201126320 \h \* MERGEFORMAT Table PA-7). The same approach was used for the CRA-2004 and the CRA-2009.
Solution for Sand-Filled Borehole
The determination of the pressure pwfBI, with the assumption that a borehole filled with silty-sand-like material connects the brine pocket and the repository, is now considered. The approach is similar to that used for the open borehole, except that Equation ( REF EQ_PA237 \h \* MERGEFORMAT PA.236) and Equation ( REF EQ_PA238 \h \* MERGEFORMAT PA.237) are replaced by a single equation based on Darcys Law. Specifically, flow from the brine pocket to the repository is represented by
(PA. SEQ Eq._PA- \* ARABIC 247)
where
= borehole permeability (m2)
= borehole cross-sectional area (m2)
and the remaining symbols have been previously defined. In the present analysis, kBH is an uncertain input (see BHPRM in HYPERLINK \l "Table_PA-19" REF TablePA_19 \h Table PA-19) and ABH is defined by the assumption that the borehole diameter is the same as the drill bit diameter (i.e., 12.25 in. = 0.31115 m).
The representation for flow from the brine pocket inlet point through the repository to the outlet point associated with the drilling intrusion under consideration remains as defined in Equation ( REF EQ_PA245 \h \* MERGEFORMAT PA.244). Thus, two equations (i.e., Equation ( REF EQ_PA245 \h \* MERGEFORMAT PA.244) and Equation ( REF EQ_PA248 \h \* MERGEFORMAT PA.247)) and two unknowns (i.e., pwfBI and Q) are under consideration. Solution for pwfBI yields
(PA. SEQ Eq._PA- \* ARABIC 248)
where
(PA. SEQ Eq._PA- \* ARABIC 249)
and (2.98 ( 106 comes from Equation ( REF EQ_PA243 \h \* MERGEFORMAT PA.242). The expression in Equation ( REF EQ_PA250 \h \* MERGEFORMAT PA.249) was used to define pwE1 in the determination of DBRs for a drilling intrusion that occurred more than 200 years after a preceding E1 intrusion (see HYPERLINK \l "Table_PA-7" REF _Ref201126320 \h \* MERGEFORMAT Table PA-7).
End of DBR
The CRA-2009 PA has 23,400 cases that potentially require solution of Equation ( REF EQ_PA215 \h \* MERGEFORMAT PA.214) through Equation ( REF EQ_PA221 \h \* MERGEFORMAT PA.220) to obtain the DBR volume (See HYPERLINK \l "PA-6_7_6" Section REF _Ref201113677 \r \h \* MERGEFORMAT PA-6.7.6). However, the DBR was set to zero without solution of Equation ( REF EQ_PA215 \h \* MERGEFORMAT PA.214), Equation ( REF EQ_PA216 \h PA.215), Equation ( REF EQ_PA217 \h PA.216), Equation ( REF EQ_PA218 \h PA.217), Equation ( REF EQ_PA219 \h PA.218), Equation ( REF EQ_PA220 \h PA.219),and Equation ( REF EQ_PA221 \h \* MERGEFORMAT PA.220) when there was no possibility of a release (i.e., at the time of the intrusion, the intruded waste panel had either a pressure less than 8 MPa or a brine saturation below the residual brine saturation Sbr).
For the remaining cases, Equation ( REF EQ_PA215 \h \* MERGEFORMAT PA.214), Equation ( REF EQ_PA216 \h PA.215), Equation ( REF EQ_PA217 \h PA.216), Equation ( REF EQ_PA218 \h PA.217), Equation ( REF EQ_PA219 \h PA.218), Equation ( REF EQ_PA220 \h PA.219), and Equation ( REF EQ_PA221 \h \* MERGEFORMAT PA.220) were solved for a time period of 50 days, although the value used for te was always less than 50 days. The minimum value used for te was three days, which is an estimate of the time required to drill from the repository through the Castile Formation and then cement the intermediate casing. If there is little or no gas flow associated with brine inflow into the borehole during drilling in the Salado Formation, the current industry practice is to allow the brine to seep into the drilling mud and be discharged to the mud pits until the salt section is cased.
If there is a significant amount of gas flow, it is possible that the driller will lose control of the well. In such cases, DBRs will take place until the gas flow is brought under control. Two possibilities exist: (1) the driller will regain control of the well when the gas flow drops to a manageable level, and (2) aggressive measures will be taken to shut off the gas flow before it drops to a manageable level. In the CCA PA, the driller was assumed to regain control of the well when the gas flow dropped to a cut-off rate of 1 ( 105 standard cubic feet per day (SCF/d in commonly used oil field units). Experience at the South Culebra Bluff Unit #1, which blew out in January 1978, suggests that approximately 11 days may be needed to bring a well under control before the gas flow drops to a manageable level (i.e., 1 ( 105 SCF/d) (the HYPERLINK "../../references/CCA/Appendix_MASS_Attachment_16_2.pdf" CCA, Appendix MASS, Attachment MASS 16-2). In particular, it took 11 days to assemble the equipment and personnel needed to bring that well under control.
A reevaluation of the current drilling practices, including a review of the historic information and interviews with current drilling personnel in the WIPP area, was conducted ( HYPERLINK "../../references/Others/Kirkes_2007_Evaluation_of_the_Duration_of_Direct_Brine_ERMS545988.pdf" Kirkes 2007). This analysis found
The South Culebra Bluff #1 is not a suitable analogue for a hypothetical WIPP blowout.
Basing the WIPP maximum DBR parameter on the single most catastrophic blowout event in the regions history does not reasonably represent current drilling practice as directed by regulations.
Well-known drilling procedures are sufficient to stop or kill a WIPP blowout under the most extreme anticipated pressures in hours, not days.
Using 4.5 days for a maximum DBR duration is still quite conservative, in that it assumes flow into the wellbore continues throughout the kill procedure and casing/cementing procedures, even though this assumption is not consistent with current practice.
Therefore, for the CRA-2009 PA, a value of 4.5 days was used for the maximum value used for te.
Given the preceding, te is defined by
(PA. SEQ Eq._PA- \* ARABIC 250)
in PA, where tf is the time at which the gas flow out of the well drops below 1(105 SCF/d. As a reminder, gas flow out of the repository in the intruding borehole, and hence te, is determined as part of the solution to Equation ( REF EQ_PA215 \h \* MERGEFORMAT PA.214), Equation ( REF EQ_PA216 \h PA.215), Equation ( REF EQ_PA217 \h PA.216), Equation ( REF EQ_PA218 \h PA.217), Equation ( REF EQ_PA219 \h PA.218), Equation ( REF EQ_PA220 \h PA.219), and Equation ( REF EQ_PA221 \h \* MERGEFORMAT PA.220).
Numerical Solution
As previously indicated, the BRAGFLO program is used to solve Equation ( REF EQ_PA215 \h \* MERGEFORMAT PA.214), Equation ( REF EQ_PA216 \h PA.215), Equation ( REF EQ_PA217 \h PA.216), Equation ( REF EQ_PA218 \h PA.217), Equation ( REF EQ_PA219 \h PA.218), Equation ( REF EQ_PA220 \h PA.219), and Equation ( REF EQ_PA221 \h \* MERGEFORMAT PA.220) with the computational grid in HYPERLINK \l "Figure_PA-28" REF _Ref201120074 \h \* MERGEFORMAT Figure PA-28, the initial value conditions in HYPERLINK \l "PA-4_7_2" Section REF _Ref201113695 \r \h \* MERGEFORMAT PA-4.7.2, the boundary value conditions in HYPERLINK \l "Table_PA-17" REF _Ref201037594 \h \* MERGEFORMAT Table PA-17, and parameter values appropriate for modeling DBRs. Thus, the numerical procedures in use for Equation ( REF EQ_PA215 \h \* MERGEFORMAT PA.214), Equation ( REF EQ_PA216 \h PA.215), Equation ( REF EQ_PA217 \h PA.216), Equation ( REF EQ_PA218 \h PA.217), Equation ( REF EQ_PA219 \h PA.218), Equation ( REF EQ_PA220 \h PA.219), and Equation ( REF EQ_PA221 \h \* MERGEFORMAT PA.220) are the same as those described in HYPERLINK \l "PA-4_2_11" Section REF _Ref202338870 \r \h \* MERGEFORMAT PA-4.2.11 for the solution of Equation ( REF EQ_PA26 \h \* MERGEFORMAT PA.24), Equation ( REF EQ_PA27 \h PA.25), Equation ( REF EQ_PA28 \h PA.26), Equation ( REF EQ_PA29 \h PA.27), Equation ( REF EQ_PA30 \h PA.28), Equation ( REF EQ_PA31 \h PA.29), and Equation ( REF EQ_PA32 \h \* MERGEFORMAT PA.30).
In this solution, the boundary value conditions associated with drilling intrusions (i.e., pwf and pwE1 in REF _Ref201037594 \h \* MERGEFORMAT Table PA-17) are implemented through the specification of fluid withdrawal terms (i.e., qg and qb in Equation ( REF EQ_PA26 \h \* MERGEFORMAT PA.24), Equation ( REF EQ_PA27 \h PA.25), Equation ( REF EQ_PA28 \h PA.26), Equation ( REF EQ_PA29 \h PA.27), Equation ( REF EQ_PA30 \h PA.28), Equation ( REF EQ_PA31 \h PA.29), and Equation ( REF EQ_PA32 \h \* MERGEFORMAT PA.30)), rather than as predetermined boundary value conditions. With this implementation, the representations in Equation ( REF EQ_PA215 \h \* MERGEFORMAT PA.214) and Equation ( REF EQ_PA216 \h \* MERGEFORMAT PA.215) for gas and brine conservation become
(( (PA. SEQ Eq._PA- \* ARABIC 251)
(( (PA. SEQ Eq._PA- \* ARABIC 252)
and the constraints in Equation ( REF EQ_PA215 \h \* MERGEFORMAT PA.214), Equation ( REF EQ_PA216 \h PA.215), Equation ( REF EQ_PA217 \h PA.216), Equation ( REF EQ_PA218 \h PA.217), Equation ( REF EQ_PA219 \h PA.218), Equation ( REF EQ_PA220 \h PA.219), and Equation ( REF EQ_PA221 \h \* MERGEFORMAT PA.220) remain unchanged. As used in Equation ( REF EQ_PA252 \h \* MERGEFORMAT PA.251) and Equation ( REF EQ_PA253 \h \* MERGEFORMAT PA.252), qg and qb are independent of the computational grid in use ( HYPERLINK \l "Figure_PA-28" REF _Ref201120074 \h \* MERGEFORMAT Figure PA-28). In practice, qg and qb are defined with a productivity index (see Equation ( REF EQ_PA209 \h \* MERGEFORMAT PA.208)) that is a function of the specific computational grid in use, with the result that these definitions are only meaningful in the context of the computational grid that they are intended to be used with. This specificity results because qg and qb as used in Equation ( REF EQ_PA252 \h \* MERGEFORMAT PA.251) and Equation ( REF EQ_PA253 \h \* MERGEFORMAT PA.252) are defined on a much smaller scale than can typically be implemented with a reasonably sized computational grid. As a result, the values used for qg and qb in the numerical solution of Equation ( REF EQ_PA252 \h \* MERGEFORMAT PA.251) and Equation ( REF EQ_PA253 \h \* MERGEFORMAT PA.252) must incorporate the actual size of the grid in use.
In the solution of Equation ( REF EQ_PA252 \h \* MERGEFORMAT PA.251) and Equation ( REF EQ_PA253 \h \* MERGEFORMAT PA.252) with the computational grid in REF _Ref201120074 \h \* MERGEFORMAT Figure PA-28, qg is used to incorporate gas flow out of the repository, and qb is used to incorporate both brine inflow to the repository from a pressurized brine pocket and brine flow out of the repository. For gas flow out of the repository,
(PA. SEQ Eq._PA- \* ARABIC 253)
if (x, y) is at the center of the grid cell containing the drilling intrusion ( REF _Ref201120074 \h \* MERGEFORMAT Figure PA-28), and qg(x, y, t) = 0 (kg/m3)/s otherwise, where k, krg, (g, re, rw, s, and c are defined in conjunction with Equation ( REF EQ_PA209 \h \* MERGEFORMAT PA.208), pg is gas pressure, and pwf is the flowing well pressure at the outlet borehole (i.e., the boundary value condition in HYPERLINK \l "Table_PA-17" REF _Ref201037594 \h \* MERGEFORMAT Table PA-17). The factor h in Equation ( REF EQ_PA209 \h \* MERGEFORMAT PA.208) is the crushed height of the repository as indicated in Equation ( REF EQ_PA209 \h \* MERGEFORMAT PA.208) and defines the factor ( in Equation ( REF EQ_PA252 \h \* MERGEFORMAT PA.251) and Equation ( REF EQ_PA253 \h \* MERGEFORMAT PA.252). In the numerical solution, qg(x, y, t) defines in Equation ( REF EQ_PA92 \h \* MERGEFORMAT PA.91), with having a nonzero value only when i, j correspond to the grid cell containing the borehole through which gas outflow is taking place (i.e., the grid cells containing the down-dip, middle, and up-dip wells in REF _Ref201120074 \h \* MERGEFORMAT Figure PA-28).
For brine flow,
(PA. SEQ Eq._PA- \* ARABIC 254)
if (x, y) is at the center of the grid cell containing the drilling intrusion through which brine outflow from the repository is taking place ( HYPERLINK \l "Figure_PA-28" REF _Ref201120074 \h \* MERGEFORMAT Figure PA-28);
(PA. SEQ Eq._PA- \* ARABIC 255)
if (x, y) is at the center of the grid cell containing a prior drilling intrusion into a pressurized brine pocket ( REF _Ref201120074 \h \* MERGEFORMAT Figure PA-28), where is the boundary value condition defined in HYPERLINK \l "Table_PA-17" REF _Ref201037594 \h \* MERGEFORMAT Table PA-17; and qb(x, y, t) = 0 otherwise. In the numerical solution of Equation ( REF EQ_PA252 \h \* MERGEFORMAT PA.251), qg(x, y, t) defines in a discretization for Equation ( REF EQ_PA253 \h \* MERGEFORMAT PA.252) that is equivalent to the discretization for Equation ( REF EQ_PA252 \h \* MERGEFORMAT PA.251) shown in Equation ( REF EQ_PA92 \h \* MERGEFORMAT PA.91), with having a nonzero value only when i, j correspond to the grid cell containing the borehole through which brine outflow is taking place (i.e., the grid cells containing the down-dip, middle, and up-dip wells in HYPERLINK \l "Figure_PA-28" REF _Ref201120074 \h \* MERGEFORMAT Figure PA-28), in which case, Equation ( REF EQ_PA255 \h \* MERGEFORMAT PA.254) defines , or when i, j corresponds to the grid cell containing the borehole through which brine inflow to the repository from a pressurized brine pocket is taking place (i.e., the grid cell containing the E1 intrusion in REF _Ref201120074 \h \* MERGEFORMAT Figure PA-28), in which case Equation ( REF EQ_PA256 \h \* MERGEFORMAT PA.255) defines .
Additional Information
Additional information on BRAGFLO and its use in the CRA-2009 PA to determine DBRs can be found in the analysis package for DBR ( HYPERLINK "../../references/Others/Clayton_2008_Analysis_Package_for_Direct_Brine_Releases_ERMS548571.pdf" Clayton 2008b) and in the BRAGFLO users manual ( HYPERLINK "../../references/Others/Nemer_2007_Users_Manual_for_BRAGFLO_Version_6_ERMS545016.pdf" Nemer 2007c).
Groundwater Flow in the Culebra Dolomite
Extensive site characterization and modeling activities conducted in the WIPP vicinity have confirmed that the Culebra Dolomite Member of the Rustler Formation is the most transmissive geologic unit above the Salado. Thus, the Culebra is the unit into which actinides are most likely to be introduced from long-term flow up a hypothetical abandoned borehole.
The Culebras regional variation in groundwater flow direction is influenced by the distribution of rock types in the groundwater basin where the WIPP is located. Site characterization activities have shown that the direction of groundwater flow in the Culebra varies somewhat regionally, but in the area that overlies the site, flow is generally southward. Site characterization activities have also demonstrated that there is no evidence of karst groundwater systems in the controlled area, although groundwater flow in the Culebra is affected by the presence of fractures, fracture fillings, and vuggy pore features.
Basin-scale regional modeling of three-dimensional groundwater flow in the units above the Salado demonstrates that it is appropriate, for the purposes of estimating radionuclide transport, to conceptualize the Culebra as a two-dimensional confined aquifer. Groundwater flow in the Culebra is modeled as a steady-state process, but uncertainty in the flow field is incorporated in the analysis by using 100 different geostatistically based T fields. The T fields are initially constructed to be consistent with available head, transmissivity, and well testing data. Each T field is subsequently modified to incorporate impacts of uncertain future processes (potash mining and climate change), as described below.
Potash mining in the McNutt Potash Zone (hereafter referred to as the McNutt) of the Salado, which occurs now in the Delaware Basin outside the controlled area and may continue in the future, could affect flow in the Culebra if subsidence over mined areas causes fracturing or other changes in rock properties. Consistent with regulatory criteria, mining outside the controlled area is assumed to occur in the near future, and mining within the controlled area is assumed to occur with a probability of 1 in 100 per century (adjusted for the effectiveness of AICs during the first 100 years following closure). Consistent with regulatory guidance, the effects of mine subsidence are incorporated in the PA by increasing the transmissivity of the Culebra over the areas identified as mineable by a factor sampled from a uniform distribution between 1 and 1000. T fields used in the PA are therefore adjusted to account for this and steady-state flow fields calculated accordingly, once for mining that occurs only outside the controlled area, and once for mining that occurs both inside and outside the controlled area. Mining outside the controlled area is considered in both undisturbed and disturbed performance.
Climatic changes during the next 10,000 years may also affect groundwater flow by altering recharge to the Culebra. The extent to which the climate will change during the next 10,000 years and how such a change will affect groundwater flow in the Culebra are uncertain. However, regional three-dimensional modeling of groundwater flow in the units above the Salado indicates that flow velocities in the Culebra may increase by a factor of 1 to 2.25 for reasonably possible future climates ( HYPERLINK "../../references/Others/Corbet_Swift_to_Tierney_1996_April_12_Distribution_for_Non_Salado_Parameter_ERMS237465.pdf" Corbet and Swift 1996a and HYPERLINK "../../references/Others/Corbet_Swift_Parameters_Required_for_SECOFL2D_Climate_Index_ERMS236425.PDF"1996b). This uncertainty is incorporated in the PA by scaling the calculated steady-state specific discharge within the Culebra by a sampled parameter within this range.
Mathematical Description
Groundwater flow in the Culebra is represented by the PDE
EMBED Equation.DSMT4 (PA. SEQ Eq._PA- \* ARABIC 256)
where
S = medium storativity (dimensionless),
h = hydraulic head (m),
t = time (s),
b = aquifer thickness (m),
K = hydraulic conductivity tensor (m/s),
Q = source/sink term expressed as the volumetric flux per unit area ((m3/m2)/s = m/s).
Further, the Culebra is assumed to be two-dimensional with isotropic hydraulic conductivity. As a result, K is defined by
(PA. SEQ Eq._PA- \* ARABIC 257)
where k(x, y) is the hydraulic conductivity (m/s) at the point (x, y). The following simplifying assumptions are also made: fluid flow in the Culebra is at steady state (i.e., ), and source and sink effects arising from borehole intrusions and infiltration are negligible (i.e., Q = 0). Given these assumptions, Equation ( REF EQ_PA257 \h \* MERGEFORMAT PA.256) simplifies to
EMBED Equation.DSMT4 (PA. SEQ Eq._PA- \* ARABIC 258)
which is the equation actually solved to obtain fluid flow in the Culebra. In PA, b = 7.75 m, and k(x, y) in Equation ( REF EQ_PA258 \h \* MERGEFORMAT PA.257) is a function of an imprecisely known T field, as discussed in HYPERLINK \l "PA-4_8_2" Section REF _Ref201113733 \r \h \* MERGEFORMAT PA-4.8.2.
Implementation
This section describes the salient features of the Culebra flow field calculation implementation. One should note, however, that this implementation has not been changed for the CRA-2009 PA. Instead, the flow fields generated for the CRA-2004 PABC have been reused for the CRA-2009 PA ( HYPERLINK "../../references/Others/Lowry_Kanney_2005_Analysis_Report_for_CRA_2004_PABC_Culebra_Flow_ERMS541508.pdf" Lowry and Kanney 2005).
The first step in the analysis of fluid flow in the Culebra is to generate T fields T(x,y) (m2/s) for the Culebra and to characterize the uncertainty in these fields. This was accomplished by generating a large number of plausible T fields. A description of the method used to construct these T fields is included in HYPERLINK "../Appendix_TFIELD/Appendix_TFIELD.htm" Appendix TFIELD-2009. A brief outline of the method is presented below.
The T fields used for PA are based on several types of information, including a regression model developed on WIPP-site geologic data, measured head levels in the Culebra for the year 2000, and well drawdown test results. The process that led to the final T fields used in the PA is discussed below.
Geologic data, including (1) depth to the top of the Culebra, (2) reduction in thickness of the upper Salado by dissolution, and (3) the spatial distribution of halite in the Rustler below and above the Culebra, were used to define a geologic regression model that relates transmissivity at any location to a set of geologically defined parameters.
Base T fields are defined for a modeling domain measuring 22.4 km (19 miles) east-west by 30.7km north-south using a method of stochastic simulation. The base T fields were constructed from information on the depth to the Culebra, indicator functions defining the location of Salado dissolution, halite occurrence, and high transmissivity zones.
Seed T fields are defined by conditioning base T fields to measured values of transmissivity. This conditioning is performed with a Gaussian geostatistical simulation algorithm.
The seed T fields are calibrated to transient water-level data from the year 2000 in 37 wells across the region using the parameter estimation program PEST ( HYPERLINK "../../references/Others/Doherty_2002_Design_Document_for_PEST_Version_55_ERMS523970.pdf" Doherty 2002). The PEST program iteratively changes the seed T field values to minimize an objective function, using MODFLOW 2000 ( HYPERLINK "../../references/Others/Harbaugh_Banta_Hill_and_McDonald_2000_MODFLOW_2000_Open_File_Report_00_92.pdf" Harbaugh et al. 2000) to compute the flow solution for each iteration. The objective function minimized by PEST is a combination of the weighted sum of the squared residuals between the measured and modeled heads and a second weighted sum of the squared differences in the estimated transmissivity between pairs of pilot points. The second weighted sum is designed to keep the T field as homogeneous as possible and provide numerical stability when estimating more parameters than there are data.
The calibrated T fields produced by PEST and MODFLOW are screened according to specific acceptance criteria ( HYPERLINK "../../references/Others/Beauheim_2003_Analysis_Report_AP100_Task_1_Development_and_Application_of_Acceptance_Criteria_ERMS531136.pdf" Beauheim 2003). Calibrated T fields that meet the acceptance criteria are modified for the partial and full mining scenarios. This modification increases transmissivity by a random factor between 1 and 1000 in areas identified as containing potash reserves, as described below. Steady-state flow simulations are then run using the mining-modified T fields.
Because radionuclide transport calculations are performed using a grid with uniform cells of 50(50m, the final step in the flow simulation is to run MODFLOW with a 50 ( 50 m grid to calculate the flow fields required for the transport code. The hydraulic conductivities for the finer grid are obtained by dividing each 100 ( 100 m cell used in the T field calculations into four 50 ( 50 m cells. The conductivity assigned to each of the four cells is equal to the conductivity of the larger cell ( HYPERLINK "../../references/Others/Leigh_Beauheim_Kanney_2003_AP_for_Calculations_of_Culebra_Flow_and_Transport_ERMS530172.pdf" Leigh, Beauheim, and Kanney 2003).
The hydraulic conductivity k(x, y) in Equation ( REF EQ_PA258 \h \* MERGEFORMAT PA.257) is defined in terms of the T fields T(x, y) by
(PA. SEQ Eq._PA- \* ARABIC 259)
Fluid flow is determined (using MODFLOW to solve Equation ( REF EQ_PA259 \h \* MERGEFORMAT PA.258)) for two different cases: (1) a partial mining case (mining of potash deposits outside the LWB), and (2) a full mining case (mining of potash deposits inside and outside the LWB) ( HYPERLINK \l "Figure_PA-31" REF _Ref201120650 \h \* MERGEFORMAT Figure PA-31; see HYPERLINK "../../references/Others/Lowry_Kanney_2005_Analysis_Report_for_CRA_2004_PABC_Culebra_Flow_ERMS541508.pdf" \l "page=29"Lowry and Kanney 2005, Section 3.2.5 for more details). As specified by guidance in HYPERLINK "40CFR194" 40 CFR Part 194, potash mining increases the Culebras hydraulic conductivity in the vicinity of such mining by an uncertain factor with a value between 1 and 1000. As specified in HYPERLINK "40CFR194_32" section 194.32 and described in HYPERLINK \l "PA-3_9" Section REF _Ref201113769 \r \h \* MERGEFORMAT PA-3.9, economic potash reserves outside the LWB are assumed to have been fully mined by the end of the 100-year period of AICs, after which the occurrence of potash mining within the LWB follows a Poisson process with a rate constant of (m = 1 ( 10(4 yr(1.
In the partial mining case, the hydraulic conductivity kPM(x, y) is defined by Equation ( REF EQ_PA260 \h \* MERGEFORMAT PA.259) inside the WIPP boundary and by kPM(x, y) = k(x, y) ( MF outside the WIPP boundary, where MF is determined by the uncertain parameter CTRANSFM (see HYPERLINK \l "Table_PA-19" REF TablePA_19 \h Table PA-19). In the full mining case, the hydraulic conductivity is defined by kFM(x, y) = k(x, y) ( MF in all areas of the modeling domain.
In turn, kPM(x, y) and kFM(x, y) result in the following definition for the hydraulic conductivity tensor K:
Figure PA- SEQ Figure_PA- \* ARABIC 31. Areas of Potash Mining in the McNutt Potash Zone
(PA. SEQ Eq._PA- \* ARABIC 260)
In the analysis, Equation ( REF EQ_PA259 \h \* MERGEFORMAT PA.258) is solved with each of the preceding definitions of Ki to obtain characterizations of fluid flow in the Culebra for partially-mined conditions and fully mined conditions.
The determination of fluid flow in the Culebra through the solution of Equation ( REF EQ_PA259 \h \* MERGEFORMAT PA.258) does not incorporate the potential effects of climate change on fluid flow. Such effects are incorporated into the analysis by an uncertain scale factor to introduce the potential effects of climate change into the analysis ( HYPERLINK "../../references/Others/Corbet_Swift_to_Tierney_1996_April_12_Distribution_for_Non_Salado_Parameter_ERMS237465.pdf" Corbet and Swift 1996a and HYPERLINK "../../references/Others/Corbet_Swift_Parameters_Required_for_SECOFL2D_Climate_Index_ERMS236425.PDF"1996b). Specifically, the Darcy fluid velocity vi(x,y) actually used in the radionuclide transport calculations is given by
(PA. SEQ Eq._PA- \* ARABIC 261)
where ui(x,y) and vi(x,y) represent Darcy fluid velocities (m/s) at the point (x,y) in the x and y directions, respectively; (hi(x, y) is obtained from Equation ( REF EQ_PA259 \h \* MERGEFORMAT PA.258) with K = Ki; and SFC is a scale factor used to incorporate the uncertainty that results from possible climate changes. The scale factor SFC is determined by the uncertain parameter CCLIMSF (see HYPERLINK \l "Table_PA-19" REF TablePA_19 \h Table PA-19).
Computational Grids and Boundary Value Conditions
The representation for fluid flow in the Culebra in Equation ( REF EQ_PA259 \h \* MERGEFORMAT PA.258) is evaluated on a numerical grid 22.4 km (13 miles) east-west by 30.7 km (19 miles) north-south, aligned with the compass directions ( HYPERLINK \l "Figure_PA-32" REF _Ref201120661 \h \* MERGEFORMAT Figure PA-32). The modeling domain is discretized into 68,768 uniform 100 ( 100 m cells. The northern model boundary is slightly north of the northern end of Nash Draw, 12 km (7.4 mi) north of the northern WIPP site boundary, and about 1 km (0.62 miles) north of Mississippi Potash Incorporateds east tailings pile. The eastern boundary lies in a low-transmissivity region that contributes little flow to the modeling domain. The southern boundary
Figure PA- SEQ Figure_PA- \* ARABIC 32. Modeling Domain for Groundwater Flow (MODFLOW) and Radionuclide Transport (SECOTP2D) in the Culebra
lies 12.2 km (7.5miles) south of the southern WIPP site boundary, far enough from the WIPP site to have little effect on transport rates on the site. The western model boundary passes through the Mosaic (formerly International Minerals and Chemicals) tailings pond (Laguna Uno; see HYPERLINK "../../references/Others/Hunter_1985_A_Regional_Water_Balance_for_WIPP_SAND84_2233.pdf" Hunter [1985]) due west of the WIPP site in Nash Draw.
Two types of boundary conditions are specified: constant-head and no-flow ( HYPERLINK \l "Figure_PA-33" REF _Ref201120673 \h \* MERGEFORMAT Figure PA-33). Constant-head conditions are assigned along the eastern boundary of the model domain, and along the central and eastern portions of the northern and southern boundaries. Values of these heads are obtained from a kriged initial head field. SEQ CHAPTER \h \r 1The western model boundary passes through the Mosaic tailings pond (Laguna Uno) due west of the WIPP site in Nash Draw. A no-flow boundary (a flow line) is specified in the model from this tailings pond up the axis of Nash Draw to the northeast, reflecting the concept that groundwater flows down the axis of Nash Draw, forming a groundwater divide. Similarly, another no-flow boundary is specified from the tailings pond down the axis of the southeastern arm of Nash Draw to the southern model boundary, coinciding with a flow line in the regional modeling of Corbet and Knupp ( HYPERLINK "../../references/Others/Corbet_Knupp_1996_The_Role_of_Regional_Groundwater_Flow_SAND96_2133.pdf" 1996).
Figure PA- SEQ Figure_PA- \* ARABIC 33. Boundary Conditions Used for Simulations of Brine Flow in the Culebra
Thus, the northwestern and southwestern corners of the modeling domain are specified as inactive cells in MODFLOW.
Numerical Solution
The flow model in Equation ( REF EQ_PA259 \h \* MERGEFORMAT PA.258) is evaluated on the computational grid described in HYPERLINK \l "PA-4_8_3" Section REF _Ref201113785 \r \h \* MERGEFORMAT PA-4.8.3 using MODFLOW 2000 (Harbaaugh et al. 2000). MODLFOW discretizes the flow equation with a second-order difference procedure ( HYPERLINK "../../references/Others/McDonald_Harbaugh_1988.pdf" McDonald and Harbaugh 1988, p. 126). Specifically, the discretized form of Equation ( REF EQ_PA259 \h \* MERGEFORMAT PA.258) is
(PA. SEQ Eq._PA- \* ARABIC 262)
where CR and CC are the row and column hydraulic conductances at the cell interface between node i, j and a neighboring node (m2/s). Since the grid is uniform, the hydraulic conductance is simply the harmonic mean of the hydraulic conductivity in the two neighboring cells multiplied by the aquifer thickness. For example, the hydraulic conductance between cells (i, j) and (i, j ( 1) is given by CRi,j(1/2, and the hydraulic conductance between cells (i, j) and (i + 1, j) is given by CCi+1/2, j:
and
where ki, j is the hydraulic conductivity in cell i, j (m/s) and b is the aquifer thickness (m).
HYPERLINK \l "Figure_PA-34" REF _Ref201120684 \h \* MERGEFORMAT Figure PA-34 illustrates the cell numbering convention used in the finite-difference grid for MODFLOW. The determination of h is then completed by the solution of the linear system of equations in Equation ( REF EQ_PA263 \h \* MERGEFORMAT PA.262) for the unknown heads hi,j. Fluxes at cell interfaces are calculated from the values for hi,j internally in MODFLOW.
Additional Information
Additional information on MODFLOW and its use in WIPP PA to determine fluid flow in the Culebra can be found in the MODFLOW-2000 users manual ( HYPERLINK "../../references/Others/Harbaugh_Banta_Hill_and_McDonald_2000_MODFLOW_2000_Open_File_Report_00_92.pdf" Harbaugh et al. 2000) and in McKenna and Hart ( HYPERLINK "../../references/Others/McKenna_Hart_2003_Analysis_Report_Task_4_AP088_ERMS531124.pdf" 2003), Lowry ( HYPERLINK "../../references/Others/Lowry_2003_Analysis_Package_for_Salado_Transport_Calculations_CRA_2004_ERMS530164.pdf" 2003), and Lowry and Kanney ( HYPERLINK "../../references/Others/Lowry_Kanney_2005_Analysis_Report_for_CRA_2004_PABC_Culebra_Flow_ERMS541508.pdf" 2005). Calculation of the flow fields used in the CRA-2009 PA is presented in Lowry and Kanney (2005).
Radionuclide Transport in the Culebra Dolomite
Extensive laboratory and field investigations have focused on the physical mechanisms influencing transport in the Culebra, as well as the behavior of dissolved and colloidal actinides in the Culebra. Field tests have shown that the Culebra is best characterized as a double-porosity
Figure PA- SEQ Figure_PA- \* ARABIC 34. Finite-Difference Grid Showing Cell Index Numbering Convention Used by MODFLOW
medium when estimating radionuclide transport in groundwater. Groundwater flow and advective transport of dissolved or colloidal species and particles occur primarily in a small fraction of the rocks total porosity corresponding to the porosity of open and interconnected fractures and vugs. Diffusion and (much slower) advective flow occur in the remainder of the porosity, which is associated with the low-permeability dolomite matrix. Transported species, including actinides, if present, will diffuse into this porosity.
Diffusion from the advective porosity into the dolomite matrix will retard An transport by two mechanisms. Physical retardation occurs simply because actinides that diffuse into the matrix are no longer transported with the flowing groundwater, so transport is interrupted until they diffuse back into the advective porosity. In situ tracer tests have been conducted to demonstrate this phenomenon ( HYPERLINK "../../references/Others/Meigs_Beauheim_Jones_2000_Interpretations_of_Tracer_Tests_SAND97_3109.pdf" Meigs, Beauheim, and Jones 2000). Chemical retardation also occurs within the matrix as actinides are sorbed onto dolomite grains. The relationship between sorbed and liquid concentrations is assumed to be linear and reversible. The distribution coefficients (Kds) that characterize the extent to which actinides will sorb on dolomite are based on experimental data. After their review of the CCA, the EPA required the DOE to use the same ranges, but to change the distribution from uniform to loguniform. The DOE continues to use the EPAs distributions in the CRA-2009 PA.
Modeling, supported by field tests and laboratory experiments, indicates that physical and chemical retardation will be extremely effective in reducing the transport of dissolved actinides in the Culebra. Experimental work has demonstrated that transport of colloidal actinides is not a significant mechanism in the Culebra. As a result, An transport through the Culebra to the subsurface boundary of the controlled area is not a significant pathway for releases from the WIPP. As discussed in HYPERLINK \l "PA-9_0" Section REF _Ref201658645 \r \h \* MERGEFORMAT PA-9.0, the location of the mean CCDF that demonstrates compliance with the containment requirements of HYPERLINK "40CFR191_13" section191.13 is determined almost entirely by direct releases at the ground surface during drilling (cuttings, cavings, and spallings).
Radionuclide transport in the Culebra is computed using the SECOTP2D computer code ( HYPERLINK "../../references/Others/WIPP_PA_1997_Users_Manual_for_SECOTP2D_Version_141_ERMS245734.pdf" WIPP Performance Assessment 1997b). The mathematical equations solved by SECOTP2D and the numerical methods used in the code are described in the following sections.
Mathematical Description
Radionuclide transport in the Culebra is described by a parallel-plate, dual-porosity model ( HYPERLINK "../../references/Others/Meigs_McCord_1996_Physical_Transport_in_Culebra_Dolmite_WPO37450.pdf" Meigs and McCord 1996). The parallel-plate, dual-porosity conceptualization assumes that the numerous fractures within the formation are aligned in a parallel fashion and treats the fractured porous media as two overlapping continua: one representing the fractures and the other representing the surrounding porous rock matrix (see HYPERLINK \l "Figure_PA-35" REF _Ref201120699 \h \* MERGEFORMAT Figure PA-35). In this model, one system of PDEs is used to represent advective transport in fractures within the Culebra and another PDE system is used to represent diffusive transport and sorption in the matrix that surrounds the fractures.
Figure PA- SEQ Figure_PA- \* ARABIC 35. Parallel-Plate, Dual-Porosity Conceptualization
Advective Transport in Fractures
The PDE system used to represent advective transport in fractures is given by ( HYPERLINK "../../references/Others/WIPP_PA_1997_Users_Manual_for_SECOTP2D_Version_141_ERMS245734.pdf" WIPP Performance Assessment 1997b)
(( (PA. SEQ Eq._PA- \* ARABIC 263)
for k = 1, 2, (, nR, where
nR = number of radionuclides under consideration
Ck = concentration of radionuclide k in brine (kg/m3)
Dk = hydrodynamic dispersion tensor (m2/s)
= Darcy velocity (i.e., specific discharge) of brine (m/s = (m3/m2)/s)
( = advective (i.e., fracture) porosity (dimensionless)
Rk = advective retardation coefficient (dimensionless)
(k = decay constant for radionuclide k (s(1)
Qk = injection rate of radionuclide k per unit bulk volume of formation ((kg/s)/m3) (Note: Qk > 0 corresponds to injection into the fractures)
= mass transfer rate of radionuclide k per unit bulk volume of formation due to diffusion between fractures and surrounding matrix ((kg/s)/m3) (Note: > 0 corresponds to diffusion into fractures)
The Darcy velocity is obtained from the solution of Equation ( REF EQ_PA259 \h \* MERGEFORMAT PA.258); specifically, v is defined by the relationship in Equation ( REF EQ_PA262 \h \* MERGEFORMAT PA.261). The advective porosity (, defined as the ratio of the interconnected fracture pore volume to the total volume, is determined by an uncertain parameter (see CFRCPOR in HYPERLINK \l "Table_PA-19" REF TablePA_19 \h Table PA-19).
The hydrodynamic dispersion tensor is defined by ( HYPERLINK "../../references/Others/WIPP_PA_1997_Users_Manual_for_SECOTP2D_Version_141_ERMS245734.pdf" WIPP Performance Assessment 1997b; HYPERLINK "../../references/Others/Bear_1972.pdf" Bear 1972)
(PA. SEQ Eq._PA- \* ARABIC 264)
where (L and (T are the longitudinal and transverse dispersivities (m); u and v are the x and y components of (i.e., v = [u, v]); is the free water molecular diffusion coefficient (m2s(1) for radionuclide k; and ( is the advective tortuosity, defined as the ratio of the true length of the flow path of a fluid particle to the straight-line distance between the starting and finishing points of the particles motion. As in the CCA PA ( HYPERLINK "../../references/Others/Helton_et_al_1998_Uncertainty_Sensitivity_Analysis_Results_SAND98_0365.pdf" Helton et al. 1998), the CRA-2009 PA uses (L = (T = 0 m and ( = 1. Thus, the definition of Dk used in PA reduces to
(PA. SEQ Eq._PA- \* ARABIC 265)
The diffusion coefficients, D*k, for the oxidation states of the radionuclides under consideration are shown in HYPERLINK \l "Table_PA-18" REF _Ref211493868 \h \* MERGEFORMAT Table PA-18 (see HYPERLINK "../../references/Others/Fox_2008_Parameter_Report_CRA_2009_ERMS549747.pdf" \l "page=219"Fox 2008, Table 35). The existence of Pu in the (III) or (IV) oxidation state (i.e., as Pu(III) or Pu(IV)) and the existence of U in the (IV) or (VI) oxidation state (i.e., as U(IV) or U(VI)) is determined by an uncertain parameter (see WOXSTAT in REF TablePA_19 \h Table PA-19).
Table PA- SEQ Table_PA- \* ARABIC 18. Radionuclide Culebra Transport Diffusion Coefficients
Oxidation StateIIIIVVIDiffusion Coefficient (m2/s)3.00 ( 10(101.53 ( 10(104.26 ( 10(10
Table PA- SEQ Table_PA- \* ARABIC 19. Variables Representing Epistemic Uncertainty in the CRA-2009 PAMaterialPropertyNameDescriptionAM+3MKD_AMCMKDAM3Matrix distribution coefficient (m3/kg) for Am in the III oxidation state. Defines Kdk in Equation ( REF EQ_PA272 \h \* MERGEFORMAT PA.271). BH_SANDPRMX_LOGBHPERMLogarithm of intrinsic permeability (m2) of the silty-sand-filled borehole ( HYPERLINK \l "Table_PA-7" REF _Ref201126320 \h \* MERGEFORMAT Table PA-7). Used in regions Upper Borehole and Lower Borehole in HYPERLINK \l "Figure_PA-15" REF _Ref201037169 \h \* MERGEFORMAT Figure PA-15.BOREHOLEDOMEGADOMEGADrill string angular velocity (rad/s). Defines in Equation ( REF EQ_PA134 \h \* MERGEFORMAT PA.133).BOREHOLETAUFAILWTAUFAILShear strength of waste (Pa). Defines ((R, 1) in Equation ( REF EQ_PA132 \h \* MERGEFORMAT PA.131). CASTILERCOMP_RCKBPCOMPBulk compressibility (Pa1) of Castile brine reservoir. Defines cfB in Equation ( REF EQ_PA37 \h \* MERGEFORMAT PA.35) for region CASTILER of REF _Ref201037169 \h \* MERGEFORMAT Figure PA-15.CASTILERPRESSUREBPINTPRSInitial brine pore pressure in the Castile brine reservoir (region CASTILER in REF _Ref201037169 \h \* MERGEFORMAT Figure PA-15).CASTILERPRMX_LOGBPPRMLogarithm of intrinsic permeability (m2) of the Castile brine reservoir. Used in region CASTILER in REF _Ref201037169 \h \* MERGEFORMAT Figure PA-15.CELLULSFBETAFBETAFactor beta for microbial reaction rates.CONC_PCSPORE_DISCONBCEXPBrooks-Corey pore distribution parameter (dimensionless) for panel closure concrete ( HYPERLINK \l "PA-4_2_8_1" Section REF _Ref201114072 \r \h \* MERGEFORMAT PA-4.2.8.1). Defines in Equation ( REF EQ_PA40 \h \* MERGEFORMAT PA.38), Equation ( REF EQ_PA41 \h PA.39), and Equation ( REF EQ_PA42 \h \* MERGEFORMAT PA.40) for region CONC_PCS of REF _Ref201037169 \h \* MERGEFORMAT Figure PA-15 for use with Brooks-Corey model; defines ( in m = (/(1 + () in Equation ( REF EQ_PA46 \h \* MERGEFORMAT PA.44), Equation ( REF EQ_PA47 \h PA.45), and Equation ( REF EQ_PA48 \h \* MERGEFORMAT PA.46) for use with van Genuchten-Parker model in region CONC_PCS.CONC_PCSPRMX_LOGCONPRMLogarithm of intrinsic permeability (m2) for the concrete portion of the panel closure (Section REF _Ref201114072 \r \h \* MERGEFORMAT PA-4.2.8.1). Used in region CONC_PCS in REF _Ref201037169 \h \* MERGEFORMAT Figure PA-15.CONC_PCSSAT_RBRNCONBRSATResidual brine saturation (dimensionless) in panel closure concrete (Section REF _Ref201114072 \r \h \* MERGEFORMAT PA-4.2.8.1). Defines Sbr in Equation ( REF EQ_PA45 \h \* MERGEFORMAT PA.43) for use in region CONC_PCS in REF _Ref201037169 \h \* MERGEFORMAT Figure PA-15.CONC_PCSSAT_RGASCONGSSATResidual gas saturation (dimensionless) in panel closure concrete (Section REF _Ref201114072 \r \h \* MERGEFORMAT PA-4.2.8.1). Defines Sgr in Equation ( REF EQ_PA45 \h \* MERGEFORMAT PA.43) for area CONC_PCS in REF _Ref201037169 \h \* MERGEFORMAT Figure PA-15.CONC_PLGPRMX_LOGPLGPRMLogarithm of intrinsic permeability (m2) of the concrete borehole plugs ( REF _Ref201126320 \h \* MERGEFORMAT Table PA-7). Used in region Borehole Plugs in REF _Ref201037169 \h \* MERGEFORMAT Figure PA-15.CULEBRAAPOROSCFRACPORCulebra fracture (i.e., advective) porosity (dimensionless). Defines ( in Equation ( REF EQ_PA264 \h \* MERGEFORMAT PA.263).CULEBRADPOROSCMTRXPORCulebra matrix (i.e., diffusive) porosity (dimensionless). Defines ( in Equation ( REF EQ_PA271 \h \* MERGEFORMAT PA.270).
Table PA-19. Variables Representing Epistemic Uncertainty in the CRA-2009 PA (Continued)MaterialPropertyNameDescriptionCULEBRAHMBLKLTCFRACSPCulebra fracture spacing (m). Equal to half the distance between fractures (i.e., the Culebra half-matrix-block length). Defines B in Equation ( REF EQ_PA277 \h \* MERGEFORMAT PA.276) and HYPERLINK \l "Figure_PA-34" REF _Ref201120684 \h \* MERGEFORMAT Figure PA-34.CULEBRAMINP_FACCTRANSFMMultiplier (dimensionless) applied to transmissivity of the Culebra within the LWB after mining of potash reserves. Defines MF in Equation ( REF EQ_PA257 \h \* MERGEFORMAT PA.256) (see HYPERLINK \l "PA-4_8_2" Section REF _Ref201114174 \r \h \* MERGEFORMAT PA-4.8.2).DRZ_1PRMX_LOGDRZPRMLogarithm of intrinsic permeability (m2) of the DRZ. Used in regions Upper DRZ and Lower DRZ in HYPERLINK \l "Figure_PA-15" REF _Ref201037169 \h \* MERGEFORMAT Figure PA-15.DRZ_PCSPRMX_LOGDRZPCPRMLogarithm of intrinsic permeability (m2) of the DRZ immediately above the panel closure concrete ( HYPERLINK \l "PA-4_2_8_3" Section REF _Ref201114191 \r \h \* MERGEFORMAT PA-4.2.8.3). Used in region DRZ_PCS in REF _Ref201037169 \h \* MERGEFORMAT Figure PA-15.GLOBALCLIMTIDXCCLIMSFClimate scale factor (dimensionless) for Culebra flow field. Defines SFC in Equation ( REF EQ_PA262 \h \* MERGEFORMAT PA.261).GLOBALOXSTATWOXSTATIndicator variable for elemental oxidation states (dimensionless). WOXSTAT <= 0.5 indicates radionuclides in lower oxidation states. WOXSTAT >0.5 indicates radionuclides in higher oxidation states.GLOBALPBRINEBPPROBProbability that a drilling intrusion penetrates pressurized brine in the Castile. Defines pB1; see HYPERLINK \l "PA-3_6" Section REF _Ref201114208 \r \h \* MERGEFORMAT PA-3.6.GLOBALTRANSIDXCTRANIndicator variable for selecting T field. See Section REF _Ref201114223 \r \h \* MERGEFORMAT PA-4.8.2.PHUMOX3PHUMCIMWPHUMOX3Ratio (dimensionless) of concentration of actinides attached to humic colloids to dissolved concentration of actinides for oxidation state III in Castile brine. Defines SFHum(Castile, +3, Am) and SFHum(Castile, +3, Pu) for Equation ( REF EQ_PA104 \h \* MERGEFORMAT PA.103).PU(III)MKD_PUCMKDPU3Matrix distribution coefficient (m3/kg) for Pu in III oxidation state. Defines Kdk in Equation ( REF EQ_PA272 \h \* MERGEFORMAT PA.271).PU(IV)MKD_PUCMKDPU4Matrix distribution coefficient (m3/kg) for Pu in IV oxidation state. Defines Kdk in Equation ( REF EQ_PA272 \h \* MERGEFORMAT PA.271).S_HALITECOMP_RCKHALCOMPBulk compressibility of halite (Pa1). Defines cr in Equation ( REF EQ_PA39 \h \* MERGEFORMAT PA.37) for Salado region of REF _Ref201037169 \h \* MERGEFORMAT Figure PA-15.S_HALITEPOROSITYHALPORHalite porosity (dimensionless). Defines (0 in Equation ( REF EQ_PA32 \h \* MERGEFORMAT PA.30) for Salado region in REF _Ref201037169 \h \* MERGEFORMAT Figure PA-15.S_HALITEPRESSURESALPRESInitial brine pore pressure (Pa) in the Salado halite, applied at an elevation consistent with the intersection of MB 139. Defines pb,ref for Equation ( REF EQ_PA57 \h \* MERGEFORMAT PA.55) for Salado region in REF _Ref201037169 \h \* MERGEFORMAT Figure PA-15.S_HALITEPRMX_LOGHALPRMLogarithm of intrinsic halite permeability (m2). Used in region Salado in REF _Ref201037169 \h \* MERGEFORMAT Figure PA-15.S_MB139PORE_DISANHBCEXPBrooks-Corey pore distribution parameter for anhydrite (dimensionless). Defines ( in Equation ( REF EQ_PA40 \h \* MERGEFORMAT PA.38), Equation ( REF EQ_PA41 \h PA.39), and Equation ( REF EQ_PA42 \h \* MERGEFORMAT PA.40) for regions MB 138, Anhydrite AB, and MB 139 of HYPERLINK \l "Figure_PA-15" REF _Ref201037169 \h \* MERGEFORMAT Figure PA-15 for use with Brooks-Corey model; defines ( in m = (/(1 + () in Equation ( REF EQ_PA46 \h \* MERGEFORMAT PA.44), Equation ( REF EQ_PA47 \h PA.45), and Equation ( REF EQ_PA48 \h \* MERGEFORMAT PA.46) for use with van Genuchten-Parker model in the same regions.S_MB139PRMX_LOGANHPRMLogarithm of intrinsic anhydrite permeability (m2). Used in regions MB 138, Anhydrite AB, and MB 139 in REF _Ref201037169 \h \* MERGEFORMAT Figure PA-15.S_MB139RELP_MODANHBCVGPIndicator for relative permeability model (dimensionless) for regions MB 138, Anhydrite AB, and MB 139 in REF _Ref201037169 \h \* MERGEFORMAT Figure PA-15. See HYPERLINK \l "Table_PA-4" REF _Ref201038785 \h \* MERGEFORMAT Table PA-4.S_MB139SAT_RBRNANRBRSATResidual brine saturation in anhydrite (dimensionless). Defines Sbr in Equation ( REF EQ_PA45 \h \* MERGEFORMAT PA.43) for regions MB 138, Anhydrite AB, and MB 139 in REF _Ref201037169 \h \* MERGEFORMAT Figure PA-15.SHFTL_T1PRMX_LOGSHLPRM2Logarithm of intrinsic permeability (m2) of lower shaft-seal materials for the first 200 years after closure. Used in Lower Shaft region in REF _Ref201037169 \h \* MERGEFORMAT Figure PA-15.SHFTL_T2PRMX_LOGSHLPRM3Logarithm of intrinsic permeability (m2) of lower shaft-seal materials from 200 years to 10,000 years after closure. Used in Lower Shaft region in REF _Ref201037169 \h \* MERGEFORMAT Figure PA-15.SHFTUPRMX_LOGSHUPRMLogarithm of intrinsic permeability (m2) of upper shaft-seal materials. Used in Upper Shaft region in REF _Ref201037169 \h \* MERGEFORMAT Figure PA-15.SHFTUSAT_RBRNSHURBRNResidual brine saturation in upper shaft-seal materials (dimensionless). Defines Sbr in Equation ( REF EQ_PA45 \h \* MERGEFORMAT PA.43) for Upper Shaft region in REF _Ref201037169 \h \* MERGEFORMAT Figure PA-15.SHFTUSAT_RGASSHURGASResidual gas saturation in upper shaft-seal materials (dimensionless). Defines Sgr in Equation ( REF EQ_PA44 \h \* MERGEFORMAT PA.42) for Upper Shaft region in REF _Ref201037169 \h \* MERGEFORMAT Figure PA-15.SOLMOD3SOLVARWSOLVAR3Solubility multiplier (dimensionless) for III oxidation states. Used by ALGEBRA prior to PANEL ( HYPERLINK \l "PA-4_4" Section REF _Ref201114241 \r \h \* MERGEFORMAT PA-4.4, HYPERLINK "../../references/Others/Garner_Leigh_2005_Analysis_Package_for_PANEL_CRA_2004_PABC_ERMS540572.pdf" Garner and Leigh 2005).SOLMOD4SOLVARWSOLVAR4Solubility multiplier (dimensionless) for IV oxidation states. Used by ALGEBRA prior to PANEL (Section REF _Ref201114241 \r \h \* MERGEFORMAT PA-4.4, Garner and Leigh 2005).SPALLMODPARTDIAMSPLPTDIAParticle diameter of waste (m) after tensile failure, implemented by parameter SPALLMOD/PARTDIAM. Loguniform distribution from 0.001 to 0.1 (m). Defines dp in Equation ( REF EQ_PA187 \h \* MERGEFORMAT PA.186).SPALLMODREPIPERMREPIPERMWaste permeability of gas (m2) local to intrusion borehole. Defines k in Equation ( REF EQ_PA169 \h \* MERGEFORMAT PA.168).SPALLMODREPIPORSPLRPORWaste porosity (dimensionless) at time of drilling intrusion. Defines ( in Equation ( REF EQ_PA168 \h \* MERGEFORMAT PA.167).SPALLMODTENSLSTRTENSLSTRTensile strength (Pa) of waste. Defines in HYPERLINK \l "PA-4_6_2_3_4" Section REF _Ref201114276 \r \h \* MERGEFORMAT PA-4.6.2.3.4.STEELCORRMCO2WGRCORRate of anoxic steel corrosion (m/s) under brine-inundated conditions with no CO2 present. Defines Rci in Equation ( REF EQ_PA70 \h \* MERGEFORMAT PA.68) for areas Waste Panel, South RoR, and North RoR in HYPERLINK \l "Figure_PA-15" REF _Ref201037169 \h \* MERGEFORMAT Figure PA-15.TH(IV)MKD_THCMKDTH4Matrix distribution coefficient (m3/kg) for Th in IV oxidation state. Defines Kdk in Equation ( REF EQ_PA272 \h \* MERGEFORMAT PA.271).U(IV)MKD_UCMKDU4Matrix distribution coefficient (m3/kg) for U in IV oxidation state. Defines Kdk in Equation ( REF EQ_PA272 \h \* MERGEFORMAT PA.271).U(VI)MKD_UCMKDU6Matrix distribution coefficient (m3/kg) for U in VI oxidation state. Defines Kdk in Equation ( REF EQ_PA272 \h \* MERGEFORMAT PA.271).WAS_AREABIOGENFCWBIOGENFProbability of obtaining sampled microbial gas generation rates.WAS_AREAGRATMICHWGRMICHRate of CPR biodegradation (mol C6H10O5 / kg C6H10O5 /s) under anaerobic, humid conditions. Defines Rmh in Equation ( REF EQ_PA72 \h \* MERGEFORMAT PA.70) for areas Waste Panel, South RoR, and North RoR in REF _Ref201037169 \h \* MERGEFORMAT Figure PA-15.WAS_AREAGRATMICIWGRMICIRate of CPR biodegradation (mol C6H10O5 / kg C6H10O5 /s) under anaerobic, brine-inundated conditions. Defines Rmi in Equation ( REF EQ_PA72 \h \* MERGEFORMAT PA.70) for areas Waste Panel, South RoR, and North RoR in REF _Ref201037169 \h \* MERGEFORMAT Figure PA-15.WAS_AREAPROBDEGWMICDFLGIndex for model of CPR material microbial degradation (dimensionless). Used in Waste Panel, South RoR, and North RoR areas in REF _Ref201037169 \h \* MERGEFORMAT Figure PA-15.WAS_AREASAT_RBRNWRBRNSATResidual brine saturation in waste (dimensionless). Defines Sbr in Equation ( REF EQ_PA44 \h \* MERGEFORMAT PA.42) for Waste Panel, South RoR, and North RoR areas in REF _Ref201037169 \h \* MERGEFORMAT Figure PA-15; also used in waste material in HYPERLINK \l "Figure_PA-28" REF _Ref201120074 \h \* MERGEFORMAT Figure PA-28 for DBR calculation; see HYPERLINK \l "PA-4_7" Section REF _Ref201114303 \r \h \* MERGEFORMAT PA-4.7.WAS_AREASAT_RGASWRGSSATResidual gas saturation in waste (dimensionless). Defines Sgr in Equation ( REF EQ_PA45 \h \* MERGEFORMAT PA.43) for Waste Panel, South RoR, and North RoR areas in REF _Ref201037169 \h \* MERGEFORMAT Figure PA-15; also used in waste material in REF _Ref201120074 \h \* MERGEFORMAT Figure PA-28 for DBR calculation; see Section REF _Ref201114303 \r \h \* MERGEFORMAT PA-4.7. WAS_AREASAT_WICKWASTWICKIncrease in brine saturation of waste due to capillary forces (dimensionless). Defines Swick in Equation ( REF EQ_PA91 \h \* MERGEFORMAT PA.90) for Waste Panel, South RoR, and North RoR areas in REF _Ref201037169 \h \* MERGEFORMAT Figure PA-15.
The advective retardation coefficient Rk is defined by
(PA. SEQ Eq._PA- \* ARABIC 266)
where
(A = surface area density of fractures in Culebra (m2/m3 = 1/m) (i.e., surface area of fractures (m2) divided by volume of fractures (m3))
KAk = surface area distribution coefficient ((kg/m2)/(kg/m3) = m) (i.e., concentration of radionuclide k sorbed on fracture surfaces (kg/m2) divided by concentration of radionuclide k dissolved in brine within fractures (kg/m3))
Following the logic used in the CCA ( HYPERLINK "../../references/Others/Helton_et_al_1998_Uncertainty_Sensitivity_Analysis_Results_SAND98_0365.pdf" Helton et al. 1998), KAk = 0 and thus Rk = 1 are used in the PA.
In concept, the term Qk in Equation ( REF EQ_PA264 \h \* MERGEFORMAT PA.263) provides the link between the releases to the Culebra calculated with NUTS and PANEL ( HYPERLINK \l "PA-6_7" Section REF _Ref201036297 \r \h \* MERGEFORMAT PA-6.7) and transport within the Culebra. In the computational implementation of PA, radionuclide transport calculations in the Culebra were performed for unit radionuclide releases to the Culebra, and the outcomes of these calculations were used to construct the release to the accessible environment associated with time-dependent releases into the Culebra derived from NUTS and PANEL calculations ( HYPERLINK \l "PA-6_8_3" Section REF _Ref201113842 \r \h \* MERGEFORMAT PA-6.8.3). The definition of Qk is discussed in more detail in HYPERLINK \l "PA-4_9_1_4" Section REF _Ref201113850 \r \h \* MERGEFORMAT PA-4.9.1.4.
The initial condition for Equation ( REF EQ_PA264 \h \* MERGEFORMAT PA.263) is
kg/m3 (PA. SEQ Eq._PA- \* ARABIC 267)
Furthermore, the boundary value conditions for Equation ( REF EQ_PA264 \h \* MERGEFORMAT PA.263) are defined at individual points on the boundary of the grid in HYPERLINK \l "Figure_PA-32" REF _Ref201120661 \h \* MERGEFORMAT Figure PA-32 on the basis of whether the flow vector v = [u, v] defines a flow entering the grid or leaving the grid. The following Neumann boundary value condition is imposed at points (x, y) where flow leaves the grid:
EMBED Equation.DSMT4 (PA. SEQ Eq._PA- \* ARABIC 268)
where n(x, y) is an outward-pointing unit normal vector defined at (x, y). The following Dirichlet boundary value condition is imposed at points (x, y) where flow enters the grid:
kg/m3 (PA. SEQ Eq._PA- \* ARABIC 269)
Diffusive Transport in the Matrix
The system of PDEs used to represent diffusive transport in the matrix surrounding the fractures is given by ( HYPERLINK "../../references/Others/WIPP_PA_1997_Users_Manual_for_SECOTP2D_Version_141_ERMS245734.pdf" WIPP Performance Assessment 1997b)
(PA. SEQ Eq._PA- \* ARABIC 270)
where is the spatial coordinate in HYPERLINK \l "Figure_PA-35" REF _Ref201120699 \h \* MERGEFORMAT Figure PA-35, is the matrix diffusion coefficient (m2/s) for radionuclide k defined by , and is the matrix tortuosity. The remaining terms have the same meaning as those in Equation ( REF EQ_PA264 \h \* MERGEFORMAT PA.263), except that the prime denotes properties of the matrix surrounding the fractures. A constant value () for the matrix (i.e., diffusive) tortuosity is used in PA ( HYPERLINK "../../references/Others/Meigs_to_Ramsey_1996_May_16_Non_Salado_Diffusive_Tortuosity_for_Culebra_Dolomite_ERMS238940.pdf" Meigs 1996). The matrix (i.e., diffusive) porosity is an uncertain input to the analysis (see CMTRXPOR in HYPERLINK \l "Table_PA-19" REF _Ref219705647 \h Table PA-19). The matrix retardation is defined by
(PA. SEQ Eq._PA- \* ARABIC 271)
where (s is the particle density (kg/m3) of the matrix and Kdk is the distribution coefficient ((Ci/kg)/(Ci/m3) = m3/kg) for radionuclide k in the matrix. The density (s is assigned a value of 2.82 ( 103 kg/m3 ( HYPERLINK "../../references/Others/Martell_to_Lattier_1996_December_10_Additional_Information_for_Culebra_ERMS232689.pdf" Martell 1996b). The distribution coefficients Kdk are uncertain inputs to the analysis and dependent on the uncertain oxidation state of the relevant element (see CMKDAM3, CMKDPU3, CMKDPU4, CMKDTH4, CMKDU4, CMKDU6, and WOXSTAT in REF _Ref219705647 \h Table PA-19).
The initial and boundary value conditions used in the formulation of Equation ( REF EQ_PA271 \h \* MERGEFORMAT PA.270) are
(PA. SEQ Eq._PA- \* ARABIC 272)
(PA. SEQ Eq._PA- \* ARABIC 273)
(PA. SEQ Eq._PA- \* ARABIC 274)
where (x, y) corresponds to a point in the domain on which Equation ( REF EQ_PA264 \h \* MERGEFORMAT PA.263) is solved and B is the matrix half-block length (m) in HYPERLINK \l "Figure_PA-35" REF _Ref201120699 \h \* MERGEFORMAT Figure PA-35 (i.e., 2B is the thickness of the matrix between two fractures). The initial condition in Equation ( REF EQ_PA273 \h \* MERGEFORMAT PA.272) means that no radionuclide is present in the matrix at the beginning of the calculation. The boundary value condition in Equation ( REF EQ_PA274 \h \* MERGEFORMAT PA.273) implies that no radionuclide movement can take place across the centerline of a matrix block separating two fractures. The boundary value condition in Equation ( REF EQ_PA275 \h \* MERGEFORMAT PA.274) ensures that the dissolved radionuclide concentration in the matrix at the boundary with the fracture is the same as the dissolved radionuclide concentration within the fracture. The matrix half-block length B is an uncertain input to the analysis (see CFRACSP in REF _Ref219705647 \h Table PA-19).
Coupling Between Fracture and Matrix Equations
The linkage between Equation ( REF EQ_PA264 \h \* MERGEFORMAT PA.263) and Equation ( REF EQ_PA271 \h \* MERGEFORMAT PA.270) is accomplished through the term (k, defining the rate at which radionuclide k diffuses across the boundary between a fracture and the adjacent matrix (see HYPERLINK \l "Figure_PA-35" REF _Ref201120699 \h \* MERGEFORMAT Figure PA-35). Specifically,
(PA. SEQ Eq._PA- \* ARABIC 275)
where b is the fracture aperture (m) defined by
(PA. SEQ Eq._PA- \* ARABIC 276)
Source Term
As already indicated, Equation ( REF EQ_PA264 \h \* MERGEFORMAT PA.263) and Equation ( REF EQ_PA271 \h \* MERGEFORMAT PA.270) are solved for unit radionuclide releases to the Culebra. Specifically, a release of 1 kg of each of the four lumped radionuclides (241Am, 234U, 230Th, and 239Pu) under consideration was assumed to take place over a time interval from 0 to 50 years, with this release taking place into the computational cell WPAC, located at the center of the Waste Panel Area in HYPERLINK \l "Figure_PA-32" REF _Ref201120661 \h \* MERGEFORMAT Figure PA-32, that has dimensions of 50 m ( 50m. The volume of this cell is given by
(PA. SEQ Eq._PA- \* ARABIC 277)
where 4 m is the assumed thickness of the Culebra Dolomite ( HYPERLINK "../../references/Others/Meigs_McCord_1996_Physical_Transport_in_Culebra_Dolmite_WPO37450.pdf" Meigs and McCord 1996). As a result, Qk(x, y, t) has the form
(PA. SEQ Eq._PA- \* ARABIC 278)
for 0 ( t ( 50 yr and (x, y) in cell WPAC, and Qk(x, y, t) = 0 (kg/m3/s) otherwise.
Cumulative Releases
If denotes an arbitrary boundary (e.g., the LWB) in the domain of Equation ( REF EQ_PA264 \h \* MERGEFORMAT PA.263) (i.e., HYPERLINK \l "Figure_PA-32" REF _Ref201120661 \h \* MERGEFORMAT Figure PA-32), then the cumulative transport of Ck(t, B) of radionuclide k from time 0 to time t across is given by
EMBED Equation.DSMT4 (PA. SEQ Eq._PA- \* ARABIC 279)
where h is the thickness of the Culebra (4 m), ( is the advective porosity in Equation ( REF EQ_PA264 \h \* MERGEFORMAT PA.263), n(x, y) is an outward pointing unit normal vector, and denotes a line integral over B.
Numerical Solution
The numerical solution to the coupled PDE system represented by Equation ( REF EQ_PA264 \h \* MERGEFORMAT PA.263) and Equation ( REF EQ_PA271 \h \* MERGEFORMAT PA.270) is computed using SECOTP2D, an implicit finite-volume code for the simulation of multispecies reactive transport. A high-level description of the numerical procedures implemented in SECOTP2D follows, with more detail available in WIPP Performance Assessment ( HYPERLINK "../../references/Others/WIPP_PA_1997_Users_Manual_for_SECOTP2D_Version_141_ERMS245734.pdf" 1997b).
Discretization of Fracture Domain
The fracture domain is discretized in space using the block-centered finite-difference method indicated in HYPERLINK \l "Figure_PA-36" REF _Ref201121376 \h \* MERGEFORMAT Figure PA-36. In this formulation, cell concentrations are defined at grid block centers while the velocity components [u, v] are defined on grid cell faces. A uniform mesh with 50 m ( 50 m cells is used for the spatial discretization. Ghost cells are placed outside the problem domain for the purpose of implementing boundary conditions. The temporal discretization is accomplished using variable time step sizes.
Figure PA- SEQ Figure_PA- \* ARABIC 36. Schematic of Finite-Volume Staggered Mesh Showing Internal and Ghost Cells
The dispersive term,((((Dk(Ck), in Equation ( REF EQ_PA264 \h \* MERGEFORMAT PA.263) is approximated using a second-order central difference formula ( HYPERLINK "../../references/Others/Fletcher_1988.pdf" Fletcher 1988).
The advective term, ((vCk, is approximated using the Total Variation Diminishing (TVD) method ( HYPERLINK "../../references/Others/Sweby_1984.pdf" Sweby 1984). The TVD method provides a way of accurately resolving advection-dominated transport problems without the occurrence of nonphysical oscillations commonly present in second-order solutions. This method invokes a weighted upstream differencing scheme that locally adjusts the weighting to prevent oscillatory behavior and maximize solution accuracy. The weighting parameters are known as the TVD flux limiters ((x, y, r), where r is a function of the concentration gradient and direction of flow. PA uses the van Leer TVD limiter ( HYPERLINK "../../references/Others/Sweby_1984.pdf" Sweby 1984, p. 1005), which is defined as
(PA. SEQ Eq._PA- \* ARABIC 280)
At locations where u (i.e., the Darcy velocity in the x direction) is positive, r is defined at the j(1/2, k interface by
(PA. SEQ Eq._PA- \* ARABIC 281)
and at locations where u is negative, r is defined by
(PA. SEQ Eq._PA- \* ARABIC 282)
Similar definitions are made for r at the j, k(1/2 interface in the y-direction with (i.e., the Darcy velocity in the y direction) used instead of u.
Because (k is a function of Ck, the discretized set of equations is nonlinear. This nonlinearity is addressed by treating the flux limiters explicitly (i.e., time lagged). Explicit treatment of the limiter functions, however, can lead to oscillatory and sometimes unstable solutions when the Courant number exceeds unity (Cr > 1), where Cr is defined by
(PA. SEQ Eq._PA- \* ARABIC 283)
To avoid this behavior, the application of the TVD method is restricted to regions in which the Courant numbers are less than one. In regions where Cr > 1, a first-order full upwinding scheme is invoked, which is unconditionally stable and nonoscillatory.
The discretized form of Equation ( REF EQ_PA264 \h \* MERGEFORMAT PA.263) can be expressed in a delta formulation as
(PA. SEQ Eq._PA- \* ARABIC 284)
where is the identity matrix, Lxx and Lyy are finite-difference operators in the x and y directions, is an implicit source term that accounts for decay and mass transfer between the matrix and the fracture, RHS consists of the right-hand-side known values at time level n, and (Cn+1 = Cn+1 ( Cn. Direct inversion of Equation ( REF EQ_PA285 \h \* MERGEFORMAT PA.284) for a typical Culebra transport problem is very computationally intensive, requiring large amounts of memory and time. To reduce these requirements, the operator in Equation ( REF EQ_PA285 \h \* MERGEFORMAT PA.284) is factored as follows:
(PA. SEQ Eq._PA- \* ARABIC 285)
where (x and (y are constants that must sum to one (i.e., (x + (y = 1). The left-hand sides in Equation ( REF EQ_PA285 \h \* MERGEFORMAT PA.284) and Equation ( REF EQ_PA286 \h \* MERGEFORMAT PA.285) are not equivalent, with the result that the factorization of Equation ( REF EQ_PA285 \h \* MERGEFORMAT PA.284) and Equation ( REF EQ_PA286 \h \* MERGEFORMAT PA.285) is referred to as an approximate factorization ( HYPERLINK "../../references/Others/Fletcher_1988.pdf" Fletcher 1988). The advantage of approximately factoring Equation ( REF EQ_PA285 \h \* MERGEFORMAT PA.284) is that the resulting equation consists of the product of two finite-difference operators that are easily inverted independently using a tridiagonal solver. Hence, the solution to the original problem is obtained by solving a sequence of problems in the following order:
(PA. SEQ Eq._PA- \* ARABIC 286)
(PA. SEQ Eq._PA- \* ARABIC 287)
(PA. SEQ Eq._PA- \* ARABIC 288)
Discretization of Matrix Equation
The nonuniform mesh used to discretize the matrix equation is shown in HYPERLINK \l "Figure_PA-37" REF _Ref201121593 \h \* MERGEFORMAT Figure PA-37. Straightforward application of standard finite-difference or finite-volume discretizations on nonuniform meshes results in truncation error terms that are proportional to the mesh spacing variation ( HYPERLINK "../../references/Others/Hirsch_1988.pdf" Hirsch 1988). For nonuniform meshes, the discretization can be performed after a transformation from the Cartesian physical space () to a stretched Cartesian computational space (). The transformation is chosen so that the nonuniform grid spacing in physical space is transformed to a uniform spacing of unit length in computational space (the computational space is thus a one-dimensional domain with a uniform mesh). The transformed equations contain metric coefficients that must be discretized, introducing the mesh size influence into the difference formulas. Standard unweighted differencing schemes can then be applied to the governing equations in the computational space.
Figure PA- SEQ Figure_PA- \* ARABIC 37. Illustration of Stretched Grid Used for Matrix Domain Discretization
The SECOTP2D code applies such a coordinate transformation to the nonuniform diffusion domain mesh, solving the transformed system of equations in the uniform computational space. The transformed matrix equation is written as
(PA. SEQ Eq._PA- \* ARABIC 289)
where
(PA. SEQ Eq._PA- \* ARABIC 290)
(PA. SEQ Eq._PA- \* ARABIC 291)
In the uniform computational space, a first-order backwards difference formula is used to approximate the temporal derivative, while a second-order accurate central difference is used to approximate spatial derivatives.
Fracture-Matrix Coupling
The equations for the fracture and the matrix are coupled through the mass transfer term, (k. In the numerical solution, these equations are coupled in a fully implicit manner and solved simultaneously. A procedure outlined in Huyakorn, Lester, and Mercer ( HYPERLINK "../../references/Others/Huyakorn_Lester_Mercer_1983.pdf" 1983) was adapted and redeveloped for an approximate factorization algorithm with the delta formulation and a finite-volume grid. The coupling procedure consists of three steps:
Step 1. Write the mass transfer term (k in a delta () form.
Step 2. Evaluate terms that are added to the implicit part of the fracture equation. This is accomplished using the inversion process (LU factorization) in the solution of the matrix equation. After the construction of the lower tridiagonal matrix L and the intermediate solution, there is enough information to evaluate the ( terms. This new information is fed into the fracture equation that is subsequently solved for concentrations in the fracture at the new time level (n+1).
Step 3. Construct the boundary condition for the matrix equation at the fracture-matrix interface using fracture concentrations at the (n+1) time level. Matrix concentrations are then obtained using the upper tridiagonal matrix U by back substitution. A detailed description of this technique and its implementation is given in the SECOTP2D users manual ( HYPERLINK "../../references/Others/WIPP_PA_1997_Users_Manual_for_SECOTP2D_Version_141_ERMS245734.pdf" WIPP Performance Assessment 1997b).
Cumulative Releases
The cumulative transport Ck(t, B) of individual radionuclides across specified boundaries indicated in Equation ( REF EQ_PA280 \h \* MERGEFORMAT PA.279) is also accumulated during the numerical solution of Equation ( REF EQ_PA264 \h \* MERGEFORMAT PA.263) and Equation ( REF EQ_PA271 \h \* MERGEFORMAT PA.270).
Additional Information
Because neither the Culebra flow fields nor the random seed used in LHS sampling have been changed from the CRA-2004 PABC, the radionuclide transport calculations from the CRA-2004 PABC were used in the CRA-2009 PA. Additional information on SECOTP2D and its use to determine radionuclide transport in the Culebra can be found in the SECOTP2D users manual ( HYPERLINK "../../references/Others/WIPP_PA_1997_Users_Manual_for_SECOTP2D_Version_141_ERMS245734.pdf" WIPP Performance Assessment 1997b) and in the CRA-2004 PABC analysis package for radionuclide transport in the Culebra Dolomite ( HYPERLINK "../../references/Others/Lowry_Kanney_2005_Analysis_Report_for_CRA_2004_PABC_Culebra_Flow_ERMS541508.pdf" Lowry and Kanney 2005).
Probabilistic Characterization of Subjective Uncertainty
This section summarizes the treatment of uncertainty in the CRA-2009 PA parameters. This uncertainty gives rise to the epistemic uncertainty in the CCDFs defined in HYPERLINK \l "PA-2_2_4" Section REF _Ref201113869 \r \h \* MERGEFORMAT PA-2.2.4.
Probability Space
As discussed in HYPERLINK \l "PA-2_2_4" Section REF _Ref201113869 \r \h \* MERGEFORMAT PA-2.2.4, the statement of confidence in the CCDFs of releases from the CRA-2009 PA is based on a probabilistic characterization of the uncertainty in important input parameters to the analysis. The probability distribution for each parameter is based on all available knowledge about the parameter, including measurements, and describes a degree of belief as to the appropriate range of the parameter value. This degree of belief depends on the numerical, spatial, and temporal resolution of the models selected for use in PA ( HYPERLINK \l "PA-4_0" Section REF _Ref201113895 \r \h \* MERGEFORMAT PA-4.0). Correlations and other dependencies between imprecisely known variables are also possible. These relationships represent observed or logical dependencies between the possible parameter values.
The probability space that characterizes epistemic uncertainty can be represented as (Ssu, Ssu, psu). The subscript su indicates that epistemic (i.e., subjective) uncertainty is being considered; the letters su are retained for historical context. The individual elements of Ssu are vectors vsu of the form
EMBED Equation.DSMT4 (PA. SEQ Eq._PA- \* ARABIC 292)
where each vj is an imprecisely known input to the analysis, and nv is the number of such inputs.
The uncertainty in the vj, and hence in vsu, is characterized by developing a distribution
(PA. SEQ Eq._PA- \* ARABIC 293)
for each vj. Each distribution is based on available knowledge about the corresponding variable and describes a degree of belief as to the appropriate range of this variable. This degree of belief depends on the numerical, spatial, and temporal resolution of the models selected for use in PA (Section REF _Ref205874997 \r \h \* MERGEFORMAT PA-4.0). When appropriate, correlations between imprecisely known variables are also possible, indicating a dependency in the knowledge about the correlated variables. It is the distributions in Equation ( REF EQ_PA293 \h \* MERGEFORMAT PA.292) and any associated correlations between the vj that define (Ssu, Ssu, psu).
The uncertain parameters incorporated into the CRA-2009 PA are discussed in HYPERLINK \l "PA-5_2" Section REF _Ref201113920 \r \h \* MERGEFORMAT PA-5.2, and the distributions and correlations assigned to these variables are described in HYPERLINK \l "PA-5_3" Section REF _Ref201113922 \r \h \* MERGEFORMAT PA-5.3 and HYPERLINK \l "PA-5_4" Section REF _Ref201113923 \r \h \* MERGEFORMAT PA-5.4. Finally, a discussion of the concept of a scenario is given in HYPERLINK \l "PA-5_5" Section REF _Ref201113924 \r \h \* MERGEFORMAT PA-5.5.
Variables Included for Subjective Uncertainty
The CRA-2009 PA identified 56 imprecisely known variables for inclusion in the analysis ( HYPERLINK \l "Table_PA-19" REF _Ref219705647 \h Table PA-19). Most of the variables listed in REF _Ref219705647 \h Table PA-19 were also treated as uncertain in the CRA 2004. HYPERLINK \l "Table_PA-20" REF _Ref201127495 \h \* MERGEFORMAT Table PA-20 and HYPERLINK \l "Table_PA-21" REF _Ref205267579 \h \* MERGEFORMAT Table PA-21 list the additions and removals between the sets of uncertain parameters in the CRA-2004 PA and the CRA-2009 PA, that resulted from changes made for the CRA-2004 PABC. All subjectively uncertain variables incorporated into the CRA2009 PA are used as input to the models discussed in HYPERLINK \l "PA-2_2_3" Section REF _Ref201113989 \r \h \* MERGEFORMAT PA-2.2.3 and HYPERLINK \l "PA-4_0" Section REF _Ref201113895 \r \h \* MERGEFORMAT PA-4.0.
Table PA- SEQ Table_PA- \* ARABIC 20. Sampled Parameters Added Since the CRA-2004 PA
MaterialPropertySOLMOD3SOLVARSOLMOD4SOLVARWAS_AREABIOGENFC
Table PA- SEQ Table_PA- \* ARABIC 21. Sampled Parameters Removed Since the CRA-2004 PA
MaterialPropertySOLU4SOLCIMSOLTH4SOLCIMS_MB139COMP_RCKS_MB139SAT_RGASSOLAM3SOLSIMSOLAM3SOLCIMSOLPU3SOLSIMSOLPU3SOLCIMSOLPU4SOLSIMSOLPU4SOLCIMSOLU4SOLSIMSOLU6SOLSIMSOLU6SOLCIMSOLTH4SOLSIMSPALLMODRNDSPALL
Variable Distributions
Each uncertain variable is assigned a distribution that characterizes the subjective uncertainty in that variable. Distributions for each parameter are described in Fox ( HYPERLINK "../../references/Others/Fox_2008_Parameter_Report_CRA_2009_ERMS549747.pdf" 2008), which also contains documentation for each of the 56 parameters sampled by the LHS code during the PA.
Correlations and Dependencies
Most of the variables in HYPERLINK \l "Table_PA-19" REF _Ref219705647 \h Table PA-19 are assumed to be uncorrelated. However, the pairs (S_HALITE:PRMX_LOG, S_HALITE:COMP_RCK), and (CASTILER:PRMX_LOG, CASTILER:COMP_RCK) are assumed to have rank correlations of 0.99 and 0.75, respectively ( HYPERLINK \l "Figure_PA-38" REF _Ref201121621 \h \* MERGEFORMAT Figure PA-38 and HYPERLINK \l "Figure_PA-39" REF _Ref201121623 \h \* MERGEFORMAT Figure PA-39). These correlations result from a belief that the underlying physics imply that a large value for one variable in a pair should be associated with a small value for the other variable in the pair. The scatterplots in REF _Ref201121621 \h \* MERGEFORMAT Figure PA-38 and REF _Ref201121623 \h \* MERGEFORMAT Figure PA-39 result from the Replicate 1 samples generated by the LHS code and described in HYPERLINK \l "PA-6_4" Section REF _Ref201114010 \r \h \* MERGEFORMAT PA-6.4, with the rank correlations within the pairs induced with the Iman and Conover ( HYPERLINK "../../references/Others/Iman_Conover_1982.pdf" 1982) restricted pairing technique.
A conditional relationship had previously been enforced between WAS_AREA:GRATMICH and WAS_AREA:GRATMICI using ALGEBRA prior to running the BRAGFLO code ( HYPERLINK "../../references/Others/Nemer_and_Stein_2005_Analysis_Package_for_BRAGFLO_ERMS540527.pdf" Nemer and Stein 2005). This relationship was implemented by setting WAS_AREA:GRATMICH to the value of WAS_AREA:GRATMICI if WAS_AREA:GRATMICH exceeded WAS_AREA:GRATMICI in any particular sample of parameter values (vector). Changing these values in this way introduced a small error into the sensitivity analysis for WAS_AREA:GRATMICH because the regression analysis was based on the sampled values rather than the conditional values used in the code. For the CRA-2009 PA, it was assumed that WAS_AREA:GRATMICH was uniformly distributed between 0 and the minimum of either 1.02717E-9 (the upper bound of the uniform distribution specified in the parameter database for the variable) or the value selected for WAS_AREA:GRATMICI. The sampled value of WAS_AREA:GRATMICH was rescaled from the range 0 to 1.02717E-9 to the new range using the equation
(PA. SEQ Eq._PA- \* ARABIC 294)
where is the conditioned value of WAS_AREA:GRATMICH, vi is the sampled value of WAS_AREA:GRATMICH, xi is the sampled value of WAS_AREA:GRATMICI, and UV,lower and UV,upper are the bounds of the uniform distribution assigned to WAS_AREA:GRATMICH ( HYPERLINK \l "Figure_PA-40" REF _Ref201121654 \h \* MERGEFORMAT Figure PA-40). This method preserves the quantile associated with the value of WAS_AREA:GRATMICH. The nature of the correlation is fundamentally different than that which LHS could induce between the variables: if, instead of limiting the value of WAS_AREA:GRATMICH, a correlation had been specified between the variables in the input file to LHS, then LHS would have generated values for WAS_AREA:GRATMICH that exceeded the corresponding value for WAS_AREA:GRATMICI.
The distributions and associated dependencies indicated in HYPERLINK \l "Table_PA-19" REF _Ref219705647 \h Table PA-19 and HYPERLINK \l "Figure_PA-38" REF _Ref201121621 \h \* MERGEFORMAT Figure PA-38, HYPERLINK \l "Figure_PA-39" REF _Ref201121623 \h \* MERGEFORMAT Figure PA-39, and HYPERLINK \l "Figure_PA-40" REF _Ref201121654 \h \* MERGEFORMAT Figure PA-40 define the epistemic uncertainty described in HYPERLINK \l "PA-2_2_4" Section REF _Ref201114020 \r \h \* MERGEFORMAT PA-2.2.4. The set of sampled parameters constitutes a vector, vsu, of the form
EMBED Equation.DSMT4 (PA. SEQ Eq._PA- \* ARABIC 295)
where the individual elements of vsu are the subjectively uncertain variables described in REF _Ref219705647 \h Table PA-19.
Figure PA- SEQ Figure_PA- \* ARABIC 38. Correlation Between S_HALITE:PRMX_LOG and S_HALITE:COMP_RCK
Figure PA- SEQ Figure_PA- \* ARABIC 39. Correlation between CASTILLER:PRMX_LOG and CASTILLER:COMP_RCK
Figure PA- SEQ Figure_PA- \* ARABIC 40. Dependency between WAS_AREA:GRATMICI and WAS_AREA:GRATMICH
Separation of Aleatory and Epistemic Uncertainty
PA uses the term scenario to refer to specific types of events within the sample space for aleatory uncertainty (E0, E1, E2, or E1E2; see HYPERLINK \l "PA-3_10" Section REF _Ref201114041 \r \h \* MERGEFORMAT PA-3.10). This definition is consistent with the concept that a scenario is something that could happen in the future. To maintain the important distinction between the two sample spaces, subsets of the sample space for subjective uncertainty are not referred to as scenarios. A future contains events of the form defined in Equation ( REF EQ_PA2 \h \* MERGEFORMAT PA.2) and is associated with a probability, one that characterizes the likelihood that a possible future will match the occurrences that will take place at the WIPP over the next 10,000 years. In contrast, the probability associated with a specific vector vsu, i.e., a specific set of parameter values, characterizes a degree of belief that the vector contains the appropriate values for the 56 uncertain variables in HYPERLINK \l "Table_PA-19" REF _Ref219705647 \h Table PA-19. This probability represents the impact that epistemic uncertainty in the parameters has on the distribution of possible futures and is used to establish confidence in the results.
Computational Procedures
This section outlines the computational procedures used to execute the CRA-2009 PA. First, the sampling procedures applied to evaluate performance accounting for epistemic and aleatory uncertainty are outlined. The mechanistic calculations used to evaluate the function f(xst) in Equation ( REF EQ_PA25 \h \* MERGEFORMAT PA.23) are tabulated, followed by a description of the algorithms used to compute releases. This section concludes with a discussion of sensitivity analysis techniques used to identify which uncertain parameters are primary contributors to the uncertainty in the PA results.
Sampling Procedures
Extensive use is made of sampling procedures in PA. In particular, simple random sampling is used to generate individual CCDFs ( HYPERLINK \l "PA-2_2_3" Section REF _Ref201114323 \r \h \* MERGEFORMAT PA-2.2.3) and LHS is used to assess the effects of imprecisely known model parameters ( HYPERLINK \l "PA-2_2_4" Section REF _Ref201114329 \r \h \* MERGEFORMAT PA-2.2.4).
Using simple random sampling, a possible future, xst,i,k, is thus characterized by the collection of intrusion events occurring in that future (Equation ( REF EQ_PA2 \h \* MERGEFORMAT PA.2)). The subscript st denotes that intrusion is modeled as a stochastic process, the subscript i indicates that the future is one of many possible futures, and the subscript k indicates that the variable set is one of many possible variable sets. The nR sets of values (possible futures) are selected according to the joint probability distribution for the elements of Sst as defined by (Sst, Sst, pst). In practice, the joint probability distribution is defined by specifying a distribution Dj for each element xj of Sst. Points from different regions of the sample space occur in direct relationship to the probability of occurrence of these regions. Furthermore, each sample element is selected independently of all other sample elements. The values selected using simple random sampling provide unbiased estimates for means, variances, and distributions of the variables. The collection of nR samples can be denoted as a vector xst,k:
EMBED Equation.DSMT4 (PA. SEQ Eq._PA- \* ARABIC 296)
The WIPP PA code CCDFGF is used to simulate possible futures based on the values of the variables sampled. These variables control the stochastic processes defined within CCDFGF, such as the time when a drilling intrusion can take place, where that drilling intrusion is located, and whether the drilling intrusion encounters an excavated area. The code CCDFGF is capable of generating and evaluating thousands of possible futures; PA uses a sample size (nR) of 10,000 to generate a distribution of possible repository releases. This sample size is sufficient to estimate the 0.999 quantile for the distribution of releases to the accessible environment.
LHS is used to sample the parameters for which distributions of epistemic uncertainty were defined to integrate over the probability space for subjective uncertainty (Ssu, Ssu, psu). This technique was first introduced by McKay, Beckman, and Conover ( HYPERLINK "../../references/Others/Mckay_Beckman_Conover_1979.pdf" 1979). In LHS, the range of each uncertain parameter vj is divided into nLHS intervals of equal probability and one value is selected at random from each interval. The nLHS values thus obtained for v1 are paired at random without replacement with the nLHS values obtained for v2. These nLHS pairs are combined in a random manner without replacement with the nLHS values of v3 to form nLHS triples. This process is continued until a set of nLHS nV-tuples is formed. These nV-tuples are of the form
EMBED Equation.DSMT4 , k = 1, ..., nLHS (PA. SEQ Eq._PA- \* ARABIC 297)
and constitute the Latin hypercube sample. The individual vjs must be independent of each other for the preceding construction procedure to work; a method for generating Latin hypercube and random samples from correlated variables was developed by Iman and Conover ( HYPERLINK "../../references/Others/Iman_Conover_1982.pdf" 1982) and is used in WIPP PA. For more information about LHS and a comparison with other sampling techniques, see Helton and Davis ( HYPERLINK "../../references/Others/Helton_Davis_2003.pdf" 2003).
LHS stratifies the sampling to ensure that the sampled values cover the full range of each vj in the nLHS samples. LHS provides unbiased estimates for means and distribution functions of each sampled variable ( HYPERLINK "../../references/Others/Mckay_Beckman_Conover_1979.pdf" McKay, Beckman, and Conover 1979). In particular, uncertainty and sensitivity analysis results obtained with LHS are robust even when relatively small samples (i.e., nLHS = 50 to 200) are used ( HYPERLINK "../../references/Others/Iman_Helton_1988.pdf" Iman and Helton 1988 and HYPERLINK "../../references/Others/Iman_Helton_1991.pdf" 1991; HYPERLINK "../../references/Others/Helton_et_al_1995.pdf" Helton et al. 1995).
When sampling for both aleatory uncertainty and epistemic uncertainty are considered, the joint sample space, x, consists of a vector of nLHS vectors of possible futures:
EMBED Equation.DSMT4 (PA. SEQ Eq._PA- \* ARABIC 298)
The differences between the nLHS futures are due to the uncertainty in the vj, i.e. the epistemic uncertainty in model parameters.
Sample Size for Incorporation of Subjective Uncertainty
HYPERLINK "40CFR194_34" 40 CFR 194.34(d) states that
The number of CCDFs generated shall be large enough such that, at cumulative releases of 1 and 10, the maximum CCDF generated exceeds the 99th percentile of the population of CCDFs with at least a 0.95 probability.
For an LHS of size nLHS, the preceding guidance is equivalent to the inequality
(PA. SEQ Eq._PA- \* ARABIC 299)
which results in a minimum value of 298 for nLHS. PA uses a total sample size of 300 to represent the epistemic uncertainty. As discussed in the next section, the 300 samples are divided among 3 replicates of size 100 each to demonstrate convergence of the mean for the population of CCDFs.
Statistical Confidence on Mean CCDF
HYPERLINK "40CFR194_34" 40 CFR 194.34(f) states,
Any compliance assessment shall provide information which demonstrates that there is at least a 95% level of statistical confidence that the mean of the population of CCDFs meets the containment requirements of 191.13 of this chapter.
Given that LHS is used, the confidence intervals required by section 194.34(f) are obtained with a replicated sampling technique proposed by Iman ( HYPERLINK "../../references/Others/NUREG_CP_0022.pdf" 1982). In this technique, the sampling in Equation ( REF QA_PA300 \h \* MERGEFORMAT PA.300) is repeated nS times with different random seeds. These samples lead to a sequence EMBED Equation.DSMT4 r = 1, 2, , nS of estimated mean exceedance probabilities, where defines the mean CCDF obtained for sample r (i.e., is the mean probability that a normalized release of size R will be exceeded; see HYPERLINK \l "PA-2_2_4"Section REF _Ref201114366 \r \h \* MERGEFORMAT PA-2.2.4) and nS is the number of independent samples generated with different random seeds. The seed of the random number generator determines the sequence of the numbers it generates. Then,
EMBED Equation.DSMT4 (PA. SEQ Eq._PA- \* ARABIC 300)
and
EMBED Equation.DSMT4 (PA. SEQ Eq._PA- \* ARABIC 301)
provide an additional estimate of the mean CCDF and an estimate of the standard error (SE(R)) associated with the mean exceedance probabilities. The t-distribution with nS(1 degrees of freedom can be used to place confidence intervals around the mean exceedance probabilities for individual R values (i.e., around ). Specifically, the 1(( confidence interval is given by , where is the quantile of the t-distribution with nS(1 degrees of freedom (e.g., for ( = 0.05 and nS = 3). The same procedure can also be used to place pointwise confidence intervals around percentile curves. The mean and its standard error could equally well be computed from one replicate of size 300. However, the use of three replicates, each with its own random seed, minimizes the impact of any one seed used in random number generation. The three replicates have also been useful in evaluating the presence of spurious correlations among parameters and releases in the sensitivity analyses.
Generation of Latin Hypercube Samples
The LHS program ( HYPERLINK "../../references/Others/WIPP_PA_1996_Users_Manual_for_LHS_Version_241_ERMS230732.pdf" WIPP Performance Assessment 1996) is used to produce three independently generated Latin hypercube samples of size nLHS = 100 each, for a total of 300 sample elements. Each individual replicate is a Latin hypercube sample of the form
EMBED Equation.DSMT4 , k = 1, 2, (, nLHS = 100 (PA. SEQ Eq._PA- \* ARABIC 302)
In the context of the replicated sampling procedure described in HYPERLINK \l "PA-6_2" Section REF _Ref205282338 \r \h \* MERGEFORMAT PA-6.2, nS = 3 replicates of 100 are used. For notational convenience, the replicates are designated by R1, R2, and R3.
The restricted pairing technique described in HYPERLINK \l "PA-6_1" Section REF _Ref210114781 \r \h \* MERGEFORMAT PA-6.1 is used to induce requested correlations and also to assure that uncorrelated variables have correlations close to zero. The variable pairs (S_HALITE:PRMX_LOG, S_HALITE:COMP_RCK) and (CASTILER:PRMX_LOG, CASTILER:COMP_RCK) are assigned rank correlations of (0.99 and (0.75, respectively ( HYPERLINK \l "PA-5_4" Section REF _Ref201113923 \r \h \* MERGEFORMAT PA-5.4). All other variable pairs are assigned rank correlations of zero. The restricted pairing technique successfully produces these correlations ( HYPERLINK \l "Table_PA-22" REF _Ref201127589 \h \* MERGEFORMAT Table PA-22 and HYPERLINK \l "Table_PA-23" REF _Ref211862972 \h \* MERGEFORMAT Table PA-23). Specifically, the correlated variables have correlations that are close to their specified values and uncorrelated variables have correlations that are close to zero.
Table PA- SEQ Table_PA- \* ARABIC 22. Correlation Observed Between Variables S_HALITE:PRMX_LOG and S_HALITE:COMP_RCK in Replicate 1. A Value of -0.99 was Specified.
CONC_PCS: SAT_RGASCONC_PCS: SAT_RBRNCONC_PCS: PORE_DISS_HALITE:POROSITYS_HALITE:PRMX_LOG CONC_PCS: SAT_RGAS1.0000CONC_PCS: SAT_RBRN-0.01561.0000CONC_PCS: PORE_DIS0.0547-0.09431.0000S_HALITE:POROSITY-0.0177-0.0160-0.07431.0000S_HALITE:PRMX_LOG-0.00220.0287-0.0094-0.04091.0000S_HALITE:COMP_RCK0.0119-0.0249-0.00660.0248-0.9863
Table PA- SEQ Table_PA- \* ARABIC 23. Correlation Observed Between Variables CASTILER:PRMX_LOG and CASTILER:COMP_RCK in Replicate 1. A Value of -0.75 was Specified.
CASTILER:PRMX_LOGCASTILER:COMP_RCKBH_SAND:PRMX_LOGDRZ_1:PRMX_LOGCASTILER: PRMX_LOG1.0000CASTILER: COMP_RCK-0.73621.0000BH_SAND: PRMX_LOG0.0365-0.04141.0000DRZ_1: PRMX_LOG-0.02920.06300.00811.0000
The code LHS_EDIT ( HYPERLINK "../../references/Others/Kirchner_2008_Generation_of_LHS_Samples_ERMS547971.pdf" Kirchner 2008a) was used to enforce a conditional relationship between WAS_AREA:GRATMICH and WAS_AREA:GRATMICI in the LHS transfer file, thus making the conditioned values available for use in the sensitivity analysis ( HYPERLINK \l "PA-5_4" Section REF _Ref201113923 \r \h \* MERGEFORMAT PA-5.4). This code rescaled the sampled value of WAS_AREA:GRATMICH from the range 0 to 1.02717E-9 to the new range using the equation
(PA. SEQ Eq._PA- \* ARABIC 303)
where is the conditioned value of WAS_AREA:GRATMICH, vi is the sampled value of WAS_AREA:GRATMICH, xi is the sampled value of WAS_AREA:GRATMICI, and UV,lower and UV,upper are the bounds of the uniform distribution assigned to WAS_AREA:GRATMICH. This method preserves the cumulative probability associated with the original sampled value of WAS_AREA:GRATMICH.
Generation of Individual Futures
Simple random sampling ( HYPERLINK \l "PA-6_1" Section REF _Ref201114429 \r \h \* MERGEFORMAT PA-6.1) is used to generate 10,000 possible futures that are then used to construct CCDFs of potential releases. HYPERLINK \l "Table_PA-24" REF _Ref201127629 \h \* MERGEFORMAT Table PA-24 outlines the algorithm used to generate a single future in PA.
Table PA- SEQ Table_PA- \* ARABIC 24. Algorithm to Generate a Single Future
1. Sample ti,1 with a time dependent (d given by
where tA = 100 yr (i.e., time at which administrative control ends) and (d = 3.68 ( 10(3 yr(1 (see HYPERLINK \l "PA-3_3" Section REF _Ref210114798 \r \h \* MERGEFORMAT PA-3.3). The index i is the number of the future and 1 represents the first intrusion event.2. Sample ei,1 with a probability of p[E0] = 0.797 that the intrusion will be in an unexcavated area and a probability of p[E1] = 0.203 that the intrusion will be in an excavated area (see HYPERLINK \l "PA-3_4" Section REF _Ref215817182 \r \h PA-3.4).3. Sample li,1 with a probability of p[Lj] = 6.94 ( 10(3 for each of the j = 1, 2, (, 144 nodes in HYPERLINK \l "Figure_PA-14" REF _Ref205822409 \h Figure PA-14 (see HYPERLINK \l "PA-3_5" Section REF _Ref213680697 \r \h \* MERGEFORMAT PA-3.5).4. Sample bi,1 with a probability of p[B1] that the intrusion will penetrate pressurized brine (see HYPERLINK \l "PA-3_6" Section REF _Ref215996975 \r \h PA-3.6). p[B1] is sampled from a uniform distribution ranging from 0.01 to 0.60.5. Sample pi,1 with probabilities of p[PL1] = 0.015, p[PL2] = 0.696, and p[PL3] = 0.289 that plugging pattern 1, 2, or 3, respectively, will be used (see HYPERLINK \l "PA-3_7" Section REF _Ref215817203 \r \h PA-3.7).6. Sample ai,1 (see HYPERLINK \l "PA-3_8" Section REF _Ref215817224 \r \h PA-3.8).6.1 Penetration of nonexcavated area (i.e., ei,1 = 0): ai,1= ai,1 = 0.6.2 Penetration of excavated area (i.e., ei,1 = 1): Sample to determine if intrusion penetrates RH-TRU or CH-TRU waste with probabilities of p[RH] = 0.124 and p[CH] = 0.876 of penetrating RH-TRU and CH-TRU waste, respectively.6.3 Penetration of RH-TRU waste: ai,1 = ai,1 = 1.6.4 Penetration of CH-TRU waste: Use probabilities p[CHj] of intersecting waste stream j, j = 1, 2, (, 690, (see HYPERLINK "../../references/Others/Fox_2005_Analysis_Package_for_EPA_Unit_Loading_Calculations_PABC_ERMS540378.pdf"Fox 2005) to independently sample three intersected waste streams iCH11, iCH12, iCH13 (i.e., each of iCH11, iCH12, iCH13 is an integer between 1 and 690). Then, ai,1= [2, iCH11, iCH12, iCH13].7. Repeat Steps 1 6 to determine properties (i.e., ti,j, ei,j, li,j, bi,j, pi,j, ai,j) of the jth drilling intrusion.8. Continue until tn+1 > 10,000 yr; the n intrusions thusly generated define the drilling intrusions associated with xst,i.9. Sample tmin with a time dependent (m given by
where tA = 100 yr and (m = 1 ( 10(4 yr(1 (see HYPERLINK \l "PA-3_9" Section REF _Ref215817240 \r \h PA-3.9).
For each vector of the LHS sample, a total of nS = 10,000 individual futures of the form
EMBED Equation.DSMT4 (PA. SEQ Eq._PA- \* ARABIC 304)
are generated in the construction of all CCDFs for that LHS vector. As 300 LHS vectors are used in the analysis and 10,000 futures are sampled for each LHS vector, the total number of futures used in the analysis for CCDF construction is 3 ( 106.
The drilling rate (d is used to generate the times at which drilling intrusions occur. For a Poisson process with a constant (d (i.e., a stationary process), the cumulative distribution function (CDF) for the time (t between the successive events is given by ( HYPERLINK "../../references/Others/Ross_1987.pdf" Ross 1987, p. 113)
(PA. SEQ Eq._PA- \* ARABIC 305)
A uniformly distributed random number r1 is selected from [0, 1]. Then, solution of
(PA. SEQ Eq._PA- \* ARABIC 306)
for t1 gives the time of the first drilling intrusion. An initial period of 100 years of administrative control is assumed; thus 100 years is added to the t1 obtained in Equation ( REF EQ_PA306 \h \* MERGEFORMAT PA.306) to obtain the time of the first drilling intrusion. Selecting a second random number r2 and solving
(PA. SEQ Eq._PA- \* ARABIC 307)
for (t1 gives the time interval between the first and second drilling intrusions, with the outcome that . This process continues until tn+1 exceeds 10,000 years. The times t1, t2, (, tn then constitute the drilling times in that possible future..
The mining time tmin is sampled in a manner similar to the drilling times. Additional uniformly distributed random numbers from [0,1] are used to generate the elements ej, lj, bj, pj, aj of xst,i from their assigned distributions (see HYPERLINK \l "PA-2_2_2" Section REF _Ref201114538 \r \h \* MERGEFORMAT PA-2.2.2).
Construction of CCDFs
In PA, the sampling of individual futures ( HYPERLINK \l "PA-6_5" Section REF _Ref201115280 \r \h \* MERGEFORMAT PA-6.5) and associated CCDF construction is carried out by the CCDFGF program ( HYPERLINK "../../references/Others/WIPP_PA_2003_Users_Manual_for_PANEL_Version_402_ERMS526652.pdf" WIPP Performance Assessment 2003b). The sampled futures xst,i in Equation ( REF QA_PA304 \h \* MERGEFORMAT PA.304) are used to construct CCDFs for many different quantities (e.g., cuttings and cavings releases, spallings releases, DBRs, etc.). The construction process is the same for each quantity. For notational convenience, assume that the particular quantity under consideration can be represented by a function f(xst,i), with the result that 10,000 values
, i = 1, 2, (, 10,000 (PA. SEQ Eq._PA- \* ARABIC 308)
are available for use in CCDF construction. Formally, the resultant CCDF is defined by the expression in Equation ( REF EQ_PA3 \h \* MERGEFORMAT PA.3). In practice, the desired CCDF is obtained after ordering f(xst,i) from smallest to largest or largest to smallest, as described below.
PA uses a binning procedure in CCDF construction to simplify sorting the individual f(xst,i) and to reduce the number of plot points. Specifically, the range of f(xst,i) is divided into intervals (i.e., bins) by the specified points
(PA. SEQ Eq._PA- \* ARABIC 309)
where fmin is the minimum value of f(xst,i) to be plotted (typically 10(6 or 10(5 for an EPA-normalized release), fmax is the maximum value of f to be plotted (typically 100 for an EPA-normalized release), n is the number of bins in use, and the bi are typically loguniformly distributed with 20 values per order of magnitude. A counter nBj is used for each interval [bj1,bj]. All counters are initially set to zero. Then, as individual values f(xst,i) are generated, the counter nBj is incremented by 1 when the inequality
EMBED Equation.DSMT4 (PA. SEQ Eq._PA- \* ARABIC 310)
is satisfied. When necessary, fmax is increased in value so that the inequality f(xst,i) < fmax will always be satisfied. Once the 10,000 values for f(xst,i) have been generated, a value of nBj exists for each interval [bj(1, bj]. The quotient
(PA. SEQ Eq._PA- \* ARABIC 311)
provides an approximation to the probability that f(xst,i) will have a value that falls in the interval [bj(1, bj]. The resultant CCDF is then defined by the points
(PA. SEQ Eq._PA- \* ARABIC 312)
for j = 0, 1, 2, (, n(1, where prob(value > bj) is the probability that a value greater than bj will occur.
The binning technique produces histograms that are difficult to read when multiple CCDFs appear in a single plot. As the number of futures is increased and the bins are refined, the histogram CCDF should converge to a continuous CCDF as additional points are used in its construction. The continuous CCDF is approximated by drawing diagonal lines from the left end of one bin to the left end of the next bin.
When multiple CCDFs appear in a single plot, the bottom of the plot becomes very congested as the individual CCDFs drop to zero on the abscissa. For this reason, each CCDF stops at the largest observed consequence value among the 10,000 values calculated for that CCDF. Stopping at the largest consequence value, rather than the left bin boundary of the bin that contains this value, permits the CCDF to explicitly show the largest observed consequence. Because a sample size of 10,000 is used in the generation of CCDFs for comparison with the EPA release limits, the probability corresponding to the largest observed consequence is typically 10(4; HYPERLINK \l "Figure_PA-6" REF _Ref200961294 \h \* MERGEFORMAT Figure PA-6 shows an example of CCDFs from the CRA-2009 PA.
Mechanistic Calculations
In the CRA-2009 PA, calculations were performed with the models described in HYPERLINK \l "PA-4_0" Section REF _Ref201118238 \r \h \* MERGEFORMAT PA-4.0 for selected elements of Sst (see HYPERLINK \l "PA-3_10" Section REF _Ref201115293 \r \h \* MERGEFORMAT PA-3.10), and the results were used to determine the releases to the accessible environment for the large number (i.e., 10,000) of randomly sampled futures used to estimate individual CCDFs. The same set of mechanistic calculations was performed for each LHS element. This section summarizes the calculations performed with each of the models described in HYPERLINK \l "PA-4_0" Section REF _Ref201115316 \r \h \* MERGEFORMAT PA-4.0; HYPERLINK \l "PA-6_8" Section REF _Ref201036312 \r \h \* MERGEFORMAT PA-6.8 outlines the algorithms used to construct releases for the randomly sampled elements xst,i of Sst from the results of the mechanistic calculations. Long (HYPERLINK "../../references/Others/Long_2008_SNL_CPG_WIPP_Execution_of_PA_Codes_ERMS548350.pdf"2008) documents execution of the calculations and archiving of calculation results.
BRAGFLO Calculations
The BRAGFLO code ( HYPERLINK \l "PA-4_2" Section REF _Ref201115337 \r \h \* MERGEFORMAT PA-4.2) computes two-phase (brine and gas) flow in and around the repository. BRAGFLO results are used as initial conditions in the models for Salado transport (implemented in NUTS and PANEL), spallings (implemented in CUTTINGS_S), and DBR (also calculated by BRAGFLO). Thus, the BRAGFLO scenarios are used to define scenarios for other codes.
The four fundamental scenarios for the CRA-2009 PA ( HYPERLINK \l "PA-3_10" Section REF _Ref201115293 \r \h \* MERGEFORMAT PA-3.10) define four categories of calculations to be performed with BRAGFLO (i.e., E0, E1, E2, and E1E2). These four fundamental scenarios were expanded into six general scenarios by specifying the time of drilling intrusions. HYPERLINK \l "Table_PA-25" REF _Ref201127646 \h \* MERGEFORMAT Table PA-25 summarizes the specific scenarios used in the CRA-2009 PA. A total of 6 scenarios ( nR ( nLHS = 6 ( 3 ( 100 = 1,800 BRAGFLO calculations were conducted for the CRA-2009 PA.
Table PA- SEQ Table_PA- \* ARABIC 25. BRAGFLO Scenarios in the CRA2009 PA
Fundamental Scenario( HYPERLINK \l "PA-3_10" Section REF _Ref201115293 \r \h \* MERGEFORMAT PA-3.10)Specific ScenarioTime of Drilling Intrusion(s)E0: no drilling intrusions.S1N/AE1: single intrusion into excavated area (e1 = 1), pressurized brine is penetrated (b1 = 1), and Plugging Pattern 2 is used (p1= 2).S2350 yearsS31,000 yearsE2: single intrusion into excavated area (e1 = 1), pressurized brine is penetrated (b1 = 1) and Plugging Pattern 3 is used (p1= 3), or pressurized brine is not penetrated (b1 = 0).S4350 yearsS51,000 yearsE1E2: two intrusions into the same waste panel (e1 = e2 = 1), the first being an E2 intrusion and the second being an E1 intrusion.S61,000 years for E2 intrusion
2,000 years for E1 intrusion
Values for the activity level a1 and mining time tmin are not needed for the mechanistic calculations; these values are used in the construction of the releases from the results of the mechanistic calculations ( HYPERLINK \l "PA-6_8" Section REF _Ref201036312 \r \h \* MERGEFORMAT PA-6.8). Although a value for drilling location l1 is not specified, a drilling location is required for the BRAGFLO calculations. If equivalent grids were used in the definition of xst,i ( HYPERLINK \l "Figure_PA-14" REF _Ref205822409 \h \* MERGEFORMAT Figure PA-14) and in the numerical solution of the PDEs on which BRAGFLO is based ( HYPERLINK \l "Figure_PA-15" REF _Ref201037169 \h \* MERGEFORMAT Figure PA-15), the location of the drilling intrusion used in the BRAGFLO calculations could be specified as a specific value for l1, which in turn would correspond to one of the 144 locations in REF _Ref205822409 \h \* MERGEFORMAT Figure PA-14 designated by l in the definition of xst,i. However, as these grids are not the same, a unique pairing between a value for l1 and the location of the drilling intrusion used in the computational grid employed with BRAGFLO is not possible. The BRAGFLO computational grid divides the repository into a lower waste panel (Waste Panel area), a middle group of four waste panels (South RoR area), and an upper group of five waste panels (North RoR area), with the drilling intrusion taking place through the center of the lower panel ( REF _Ref201037169 \h \* MERGEFORMAT Figure PA-15). Thus, in the context of the locations in REF _Ref205822409 \h \* MERGEFORMAT Figure PA-14 potentially indexed by l1, the drilling intrusions in Scenarios S2-S5 occur at a location in Panel 5, which is the southernmost panel. In Scenario S6, both intrusions occur at a location in Panel 5, with the effects of flow between the two boreholes implemented through assumptions involving the time-dependent behavior of borehole permeability ( HYPERLINK \l "Table_PA-7" REF _Ref201126320 \h \* MERGEFORMAT Table PA-7).
NUTS Calculations
For Scenarios S1S5, radionuclide transport through the Salado is computed by the code NUTS ( HYPERLINK \l "PA-4_3" Section REF _Ref201115401 \r \h \* MERGEFORMAT PA-4.3) using the flow fields computed by BRAGFLO. Two types of calculations are performed with NUTS. First, a set of screening calculations identifies elements of the sample from Ssu for which radionuclide transport through the Salado to the LWB or Culebra is possible. The screening calculations identify a subset of the sample from Ssu for which transport is possible and for which release calculations are performed. Screening calculations are performed for BRAGFLO Scenarios S1-S5, for a total of 1,500 screening calculations with NUTS ( HYPERLINK \l "Table_PA-25" REF _Ref201127646 \h \* MERGEFORMAT Table PA-25).
HYPERLINK \l "Table_PA-26" REF _Ref210719005 \h \* MERGEFORMAT Table PA-26 summarizes the NUTS release calculations for the CRA-2009 PA. Based on the screening calculations, a total of 1,600 release calculations are performed for the CRA-2009 PA. For each vector that is retained (based on the screening calculations), release calculations are performed for a set of intrusion times.
REF _Ref210719005 \h \* MERGEFORMAT Table PA-26 lists five scenarios for release calculations corresponding to the five BRAGFLO scenarios. Each NUTS scenario uses the flow field computed for the corresponding BRAGFLO scenario. The intrusion times for the NUTS scenarios are accommodated by shifting the BRAGFLO flow fields in time so that the NUTS and BRAGFLO intrusions coincide. For example, the NUTS S3 scenario with an intrusion at 3,000 years requires a flow field for the time interval between (3,000 years and 10,000 years); this scenario uses the BRAGFLO S3 scenario flow field for the time interval between (1,000 years and 8,000 years).
Table PA- SEQ Table_PA- \* ARABIC 26. NUTS Release Calculations in the CRA-2009 PA
NUTS ScenarioNumber of Vectors with ReleasesFlow fieldIntrusion Time ( t1)R1R2R3TotalS11001BRAGFLO S1 scenario N/AS2707677223BRAGFLO S2 scenarioE1 intrusion at 100 and 350 yearsS3555860173BRAGFLO S3 scenarioE1 intrusion at 1,000, 3,000, 5,000, 7,000, or 9,000 yearsS415141544BRAGFLO S4 scenarioE2 intrusion at 100 and 350 yearsS514131340BRAGFLO S5 scenarioE2 intrusion at 1,000, 3,000, 5,000, 7,000, or 9,000 years
Values for the variables indicating intrusion into an excavated area (e1), penetration of pressurized brine (b1), plugging pattern (p1), and drilling location (l1) are the same as in the corresponding BRAGFLO scenario. Values for the activity level a1 and mining time tmin are not specified for the NUTS scenarios.
PANEL Calculations
As outlined in HYPERLINK \l "PA-4_4" Section REF _Ref201115411 \r \h \* MERGEFORMAT PA-4.4, the code PANEL is used to estimate releases to the Culebra associated with E1E2 scenarios and to estimate radionuclide concentrations in brine for use in estimating DBRs. An E1E2 scenario assumes two drilling intrusions into the same waste panel: the first an E2 intrusion ( HYPERLINK \l "Table_PA-25" REF _Ref201127646 \h \* MERGEFORMAT Table PA-25) occurring at time t1 and the second an E1 intrusion ( REF _Ref201127646 \h \* MERGEFORMAT Table PA-25) occurring at time t2. PANEL calculations are performed for t2 = 100, 350, 1,000, 2,000, 4,000, 6,000, and 9,000 years using the flow field produced by the single BRAGFLO calculation for Scenario S6, for a total of 7 ( nR ( nLHS = 7 ( 3 ( 100 = 2,100 PANEL calculations. The BRAGFLO flow field is shifted forward or backward in time as appropriate so that the time of the second intrusion (t2) coincides with the flow field. The shifting of the BRAGFLO flow field results in values for the time (t1) of the first intrusion (E2) for the PANEL calculations given by
(PA. SEQ Eq._PA- \* ARABIC 313)
where the restriction that t1 cannot be less than 100 years results from the definition of xst,i, which does not allow negative intrusion times, and from the assumption of 100 years of administrative control during which there is no drilling (i.e., (d(t) = 0 yr(1 for 0 ( t ( 100 yr; see Equation ( REF EQ_PA5 \h \* MERGEFORMAT PA.6)). Under this convention, the definition of Scenario S6 for the BRAGFLO calculations differs from what is actually done computationally because t1 does not always precede t2 by 1,000 years in the PANEL calculation. Values for the other variables defining the element xst,i of Sst for the PANEL E1E2 scenarios are the same as in the BRAGFLO S6 scenario.
Calculating radionuclide concentrations is not specific to any BRAGFLO scenario. The concentration calculations compute the mobilized activity in two different brines (Castile and Salado) and are performed at 100; 125; 175; 350; 1,000; 3,000; 5,000; 7,500; and 10,000 years for a total of 2 ( 9 ( nR = 54 calculations.
DRSPALL Calculations
The code DRSPALL calculates the spallings volume produced by gas buildup within the repository. Because of the computational expense associated with running the code, rather than evaluating all possible pressures for each vector, a set of four pressures is evaluated for each vector in each replicate. These values are then passed to CUTTINGS_S to act as a lookup table used by the latter code to linearly interpolate the spallings volume as a function of the repository pressure. DRSPALL does not compute releases to the environment, which is computed by the CUTTINGS_S code. A total of 4 pressures ( nR ( nLHS = 4 ( 3 ( 100 = 1,200 DRSPALL calculations were performed. As none of the changes implemented for the CRA-2009 PA affected the DRSPALL calculations, the results from the CRA-2004 PABC DRSPALL calculations were used in the CRA-2009 PA.
CUTTINGS_S Calculations
The code CUTTINGS_S computes the volumes of solids removed from the repository by cuttings and cavings (see HYPERLINK \l "PA-4_5" Section REF _Ref201115425 \r \h \* MERGEFORMAT PA-4.5) and spallings (see HYPERLINK \l "PA-4_6" Section REF _Ref201115427 \r \h \* MERGEFORMAT PA-4.6). HYPERLINK \l "Table_PA-27" REF _Ref201127992 \h \* MERGEFORMAT Table PA-27 lists the CUTTINGS_S calculations performed for the CRA-2009 PA, totaling 78 ( nR ( nLHS = 78 ( 3 ( 100 = 23,400 CUTTINGS_S calculations.
Table PA- SEQ Table_PA- \* ARABIC 27. CUTTINGS_S Release Calculations in the CRA-2009 PA
ScenarioDescriptionS1Intrusion into lower, middle, or upper waste panel in undisturbed (i.e., E0 conditions) repository at 100; 350; 1,000; 3,000; 5,000; or 10,000 years: 18 combinations.S2Initial E1 intrusion at 350 years followed by a second intrusion into the same, adjacent, or nonadjacent waste panel at 550; 750; 2,000; 4,000; or 10,000 years: 15 combinations.S3Initial E1 intrusion at 1,000 years followed by a second intrusion into the same, adjacent, or nonadjacent waste panel at 1,200; 1,400; 3,000; 5,000; or 10,000 years: 15 combinations.S4Initial E2 intrusion at 350 years followed by a second intrusion into the same, adjacent, or nonadjacent waste panel at 550; 750; 2,000; 4,000; or 10,000 years: 15 combinations.S5Initial E2 intrusion at 1,000 years followed by a second intrusion into the same, adjacent, or nonadjacent waste panel at 1,200; 1,400; 3,000; 5,000; or 10,000 years: 15 combinations.
The CUTTINGS_S S1 scenario computes volumes of solid material released from the initial intrusion in the repository. Initial conditions for the CUTTINGS_S S1 scenario are taken from the results of the BRAGFLO S1 scenario during the intrusion of Waste Panel, South RoR, and North RoR areas in HYPERLINK \l "Figure_PA-15" REF _Ref201037169 \h \* MERGEFORMAT Figure PA-15, corresponding to the lower, middle, and upper waste panels. In this scenario, the excavated area is penetrated (e1 = 1) and the drilling location (l1) is defined as one of the nodes (HYPERLINK \l "Figure_PA-14" REF _Ref205822409 \h \* MERGEFORMAT Figure PA-14) in the appropriate panel of HYPERLINK \l "Figure_PA-28" REF _Ref201120074 \h \* MERGEFORMAT Figure PA-28. The actual locations where the intrusions are assumed to occur correspond to the points in REF _Ref201120074 \h \* MERGEFORMAT Figure PA-28 designated Down-dip well, Middle well, and Up-dip well for the lower, middle, and upper waste panel, respectively. Values for the variables indicating penetration of pressurized brine (b1), plugging pattern (p1), activity level (a1), and mining time (tmin) are not specified for the CUTTINGS_S S1 scenario.
The other CUTTINGS_S scenarios (Scenarios S2-S5) compute volumes of solids released by a second or subsequent intrusion. Initial conditions are taken from the results of the corresponding BRAGFLO scenario at the time of the second intrusion. As in the BRAGFLO scenarios, the first intrusion occurs in the lower waste panel (Waste Panel area in REF _Ref201037169 \h \* MERGEFORMAT Figure PA-15), so the drilling location (l1) is defined as one of the nodes in Panel 5 ( REF _Ref205822409 \h \* MERGEFORMAT Figure PA-14). The second intrusion occurs in the same waste panel as the first intrusion (area Waste Panel in REF _Ref201037169 \h \* MERGEFORMAT Figure PA-15), an adjacent waste panel (South RoR area in REF _Ref201037169 \h \* MERGEFORMAT Figure PA-15), or a nonadjacent waste panel (North RoR area in REF _Ref201037169 \h \* MERGEFORMAT Figure PA-15); hence the drilling location (l2) is defined as one of the nodes ( REF _Ref205822409 \h \* MERGEFORMAT Figure PA-14) in the appropriate panel of REF _Ref201120074 \h \* MERGEFORMAT Figure PA-28.
The activity level for the first intrusion a1 takes a value that indicates CH-TRU waste penetration (i.e., a1 = [2, CH11, CH12, CH13]), but the specific waste streams penetrated (i.e. CH11, CH12, CH13) are not specified. For the second intrusion, the excavated area is penetrated (e2 = 1) and the drilling location (l2) is defined as one of the nodes in the appropriate panel ( REF _Ref205822409 \h \* MERGEFORMAT Figure PA-14), as described above. As for the first intrusion, the activity level a2 only indicates CH-TRU waste penetration. Values for the other variables defining the first intrusion (e1, b1, and p1) are the same as in the corresponding BRAGFLO scenario. Values for the other variables defining the second intrusion (b2 and p2) and the mining time tmin are not specified for the CUTTINGS_S scenarios.
BRAGFLO Calculations for DBR Volumes
Volumes of brine released to the surface during an intrusion are calculated using BRAGFLO, as described in HYPERLINK \l "PA-4_7" Section REF _Ref201115445 \r \h \* MERGEFORMAT PA-4.7. Calculations of DBR volumes were conducted for the same scenarios as CUTTINGS_S ( HYPERLINK \l "Table_PA-27" REF _Ref201127992 \h \* MERGEFORMAT Table PA-27). Thus, the elements of Sst described in HYPERLINK \l "PA-6_7_5" Section REF _Ref210114930 \r \h \* MERGEFORMAT PA-6.7.5 also characterize the elements for which DBR volumes are computed. A total of 23,400 BRAGFLO calculations were performed.
MODFLOW Calculations
As described in HYPERLINK \l "PA-4_8" Section REF _Ref201036804 \r \h \* MERGEFORMAT PA-4.8, the MODFLOW calculations produce flow fields in the Culebra for two categories of conditions: partially mined conditions in the vicinity of the repository and fully mined conditions in the vicinity of the repository ( HYPERLINK \l "Figure_PA-31" REF _Ref201120650 \h \* MERGEFORMAT Figure PA-31). As specified in HYPERLINK "40CFR194_32" 40 CFR 194.32(b), partially mined conditions are assumed to exist by the end of the administrative control period (i.e., at 100 years after closure). After the time that mining occurs within the LWB (tmin; see HYPERLINK \l "PA-3_9" Section REF _Ref201115487 \r \h \* MERGEFORMAT PA-3.9), fully mined conditions are assumed for the remainder of the 10,000-year regulatory period. The flow fields for partially mined conditions are calculated by MODFLOW using the T fields for partially mined conditions (see HYPERLINK \l "PA-4_8_2" Section REF _Ref201115506 \r \h \* MERGEFORMAT PA-4.8.2). Additional MODFLOW calculations determine the flow fields for fully mined conditions and are performed using the T fields for fully mined conditions. Thus, a total of 2(nR ( nLHS = 2 ( 3 ( 100 = 600 MODFLOW calculations were performed (HYPERLINK \l "Table_PA-28" REF _Ref201128154 \h \* MERGEFORMAT Table PA-28). As none of the changes implemented for the CRA-2009 PA affected the Culebra flow and transport calculations, the results from the CRA-2004 PABC Culebra flow and transport calculations were used in the CRA-2009 PA.
SECOTP2D Calculations
The SECOTP2D calculations are performed for the same elements xst,0 and xst,m of Sst defined in HYPERLINK \l "PA-6_7_7" Section REF _Ref201115524 \r \h \* MERGEFORMAT PA-6.7.7 for the MODFLOW calculations, giving a total of 2 ( nR ( nLHS = 2 ( 3 ( 100 = 600 SECOTP2D calculations ( HYPERLINK \l "Table_PA-29" REF _Ref201128156 \h \* MERGEFORMAT Table PA-29). As none of the changes implemented for the CRA-2009 PA affected the Culebra flow and transport calculations, the results from the CRA2004 PABC Culebra flow and transport calculations were used in the CRA-2009 PA.
Table PA- SEQ Table_PA- \* ARABIC 28. MODFLOW Scenarios in the CRA-2009 PA
MODFLOW: 600 Flow-Field CalculationsPM: Partially mined conditions in vicinity of repositoryFM: Fully mined conditions in vicinity of repositoryTotal calculations = 2 ( nR ( nLHS = 2 ( 3 ( 100 = 600Note: Only 100 unique T fields were constructed with PEST and MODFLOW for use in the analysis. The T fields are an input to the calculation of flow fields. In each replicate, the T field used for a particular flow field was assigned using an index value (CTRAN; see HYPERLINK \l "Table_PA-19" REF _Ref219705647 \h Table PA-19) included in the LHS.
Table PA- SEQ Table_PA- \* ARABIC 29. SECOTP2D Scenarios in the CRA-2004 PA
SECOTP2D: 600 CalculationsPM: Partially mined conditions in vicinity of repositoryFM: Fully mined conditions in vicinity of repositoryTotal calculations = 2 ( nR ( nLHS = 2 ( 3 ( 100 = 600Note: Each calculation includes a unit release for each of four radionuclides: 241Am, 239Pu, 230Th, and 234U.
Computation of Releases
The mechanistic computations outlined in HYPERLINK \l "PA-6_7" Section REF _Ref201036297 \r \h \* MERGEFORMAT PA-6.7 are used to compute releases for each sampled element xst,i of Sst. Releases from the repository can be partitioned into three categories: undisturbed releases, which may occur in futures without drilling intrusions; direct releases, which occur at the time of a drilling event; and long-term releases, which occur as a consequence of a history of drilling intrusions. For a given future (xst,i of Sst in Equation ( REF QA_PA304 \h \* MERGEFORMAT PA.304)) other than undisturbed conditions (xst,0), the direct and long-term releases are computed by the code CCDFGF ( HYPERLINK "../../references/Others/WIPP_PA_2003_Design_Document_Users_Manual_for_CCDFGF_Version_500_ERMS530471.pdf" WIPP Performance Assessment 2003a) from the results of the mechanistic calculations summarized in Section REF _Ref201036297 \r \h \* MERGEFORMAT PA-6.7, performed with the models presented in HYPERLINK \l "PA-4_0" Section REF _Ref201115572 \r \h \* MERGEFORMAT PA-4.0. Releases from an undisturbed repository are computed from the results of the NUTS S1 scenario ( HYPERLINK \l "PA-6_7_2" Section REF _Ref201115590 \r \h \* MERGEFORMAT PA-6.7.2).
Undisturbed Releases
Repository releases for the futures (xst,0) in which no drilling intrusions occur are computed by the NUTS release calculations for E0 conditions ( HYPERLINK \l "Table_PA-26" REF _Ref210719005 \h \* MERGEFORMAT Table PA-26). The NUTS model computes the activity of each radionuclide that reaches the accessible environment during the regulatory period via transport through the MBs, the Dewey Lake Red Beds and land surface due to brine flow up a plugged borehole. These releases are represented as fMB[xst,0, fB(xst,0)], fDL[xst,0, fB(xst,0)] and fS[xst,0, fB(xst,0)] in Equation ( REF EQ_PA25 \h \* MERGEFORMAT PA.23). The undisturbed releases for the CRA-2009 PA are summarized in HYPERLINK \l "PA-7_2" Section REF _Ref113245025 \r \h \* MERGEFORMAT PA-7.2.
Direct Releases
Direct releases include cuttings, cavings, spallings, and DBRs. The model for each direct release component computes a volume (solids or liquid) released directly to the surface for each drilling intrusion. These volumes are combined with an appropriate concentration of activity in the released waste. Summary information for the CRA-2009 PA direct releases are given in HYPERLINK \l "PA-8_5" Section PA-8.5.
Construction of Cuttings and Cavings Releases
Each drilling intrusion encountering waste is assumed to release a volume of solid material as cuttings, as described in HYPERLINK \l "PA-4_5_1" Section REF _Ref201115621 \r \h \* MERGEFORMAT PA-4.5.1. The uncompacted volume of waste removed by cuttings (Vcut) is computed by Equation ( REF EQ_PA125 \h \* MERGEFORMAT PA.124). In addition, drilling intrusions that encounter CH-TRU waste may release additional solid material as cavings, as described in HYPERLINK \l "PA-4_5_2" Section REF _Ref201115624 \r \h \* MERGEFORMAT PA-4.5.2. The uncompacted volume of material removed by cuttings and cavings combined (V = Vcut + Vcav) is computed by Equation ( REF EQ_PA126 \h \* MERGEFORMAT PA.125). For a drilling intrusion that encounters RH-TRU waste, the final eroded diameter Df in Equation ( REF EQ_PA126 \h \* MERGEFORMAT PA.125) is equal to the bit diameter in Equation ( REF EQ_PA125 \h \* MERGEFORMAT PA.124). In PA, all drilling intrusions assume a drill bit diameter of 0.31115 m (HYPERLINK "../../references/Others/Fox_2008_Parameter_Report_CRA_2009_ERMS549747.pdf" \l "page=188"Fox 2008, Table 13).
The uncompacted volume of material removed is not composed entirely of waste material; rather, the uncompacted volume includes MgO and any void space initially present around the waste containers. The volume of waste removed (Vw) is determined by multiplying the uncompacted volume by the fraction of excavated repository volume (FVW) occupied by waste, thus
(PA. SEQ Eq._PA- \* ARABIC 314)
where FVW = 0.385 for CH-TRU waste and FVW = 1.0 for RH-TRU waste (HYPERLINK "../../references/Others/Fox_2008_Parameter_Report_CRA_2009_ERMS549747.pdf" \l "page=237"Fox 2008, Table 45). The activity in the material released by cuttings and cavings is determined by stochastically selecting a subset of all waste streams. The vector (aj) described in HYPERLINK \l "PA-3_8"Section REF _Ref201115649 \r \h \* MERGEFORMAT PA-3.8 determines which type of waste (CH-TRU or RH-TRU) and which waste streams are selected. The activity per cubic meter of waste stream volume is computed for each waste stream at a discrete set of times accounting for radioactive decay and ingrowth by the code EPAUNI (HYPERLINK "../../references/Others/Fox_2005_Analysis_Package_for_EPA_Unit_Loading_Calculations_PABC_ERMS540378.pdf"Fox 2005); the results of the EPAUNI calculations are presented in Fox (2005). Activities at other times are determined by linear interpolation. The cuttings and cavings release fC(xst,i) is the product of the average activity per cubic meter (Cr, computed as the average activity over the waste streams comprising the selected subset with the assumption that each waste stream contributes an equal volume to the release) and the volume of waste released (Equation ( REF EQ_PA315 \h \* MERGEFORMAT PA.315)):
(PA. SEQ Eq._PA- \* ARABIC 315)
Construction of Spallings Releases
Spallings releases are calculated for all intrusions that encounter CH-TRU waste. The construction of the spallings release fSP(xst,i) is nearly identical to that described in HYPERLINK \l "PA-6_8_2_3"Section REF _Ref201115871 \r \h \* MERGEFORMAT PA-6.8.2.3 for the calculation of DBRs, except that volumes of solid material released will be used rather than volumes of brine. These solid releases are calculated with the spallings submodel of the CUTTINGS_S program for the combinations of repository condition, distance from previous intrusions, and time between intrusions listed in HYPERLINK \l "Table_PA-27" REF _Ref201127992 \h \* MERGEFORMAT Table PA-27. Linear interpolation determines the releases for other combinations of repository condition, distance, and time between intrusions ( HYPERLINK "../../references/Others/WIPP_PA_2003_Design_Document_Users_Manual_for_CCDFGF_Version_500_ERMS530471.pdf" WIPP Performance Assessment 2003a).
The concentration of radionuclides in the spallings release volume is computed as the average activity per cubic meter in the CH-TRU waste at the time of intrusion. Activities in each waste stream are computed at a discrete set of times by the code EPAUNI (HYPERLINK "../../references/Others/Fox_2005_Analysis_Package_for_EPA_Unit_Loading_Calculations_PABC_ERMS540378.pdf"Fox 2005); activities at other times are determined by linear interpolation.
Construction of DBRs
DBRs (also termed blowout releases) are calculated for all intrusions that encounter CH-TRU waste. DBRs fDBR(xst,i) are constructed from the volume of brine released (VDBR) to the surface (Equation ( REF EQ_PA203 \h \* MERGEFORMAT PA.202)) and radionuclide concentrations in brine (Cbl, see Equation ( REF EQ_PA97 \h \* MERGEFORMAT PA.96)). Brine volume released to the surface is computed by BRAGFLO ( HYPERLINK \l "PA-4_7_3" Section REF _Ref201115802 \r \h \* MERGEFORMAT PA-4.7.3) for the times listed in HYPERLINK \l "Table_PA-27" REF _Ref201127992 \h \* MERGEFORMAT Table PA-27; brine volumes released for intrusions at other times are computed by linear interpolation ( HYPERLINK "../../references/Others/WIPP_PA_2003_Users_Manual_for_PANEL_Version_402_ERMS526652.pdf" WIPP Performance Assessment 2003b).
Calculating DBR volumes distinguishes between the first intrusion and subsequent intrusions. The release volumes for the initial intrusion (E0 repository conditions) are further distinguished by the panel group (upper, middle, and lower). As shown in REF _Ref201127992 \h \* MERGEFORMAT Table PA-27, BRAGFLO computes release volumes for the initial intrusion at a series of intrusion times; the release volume for the initial intrusion at other times is computed by linear interpolation ( HYPERLINK "../../references/Others/WIPP_PA_2003_Design_Document_Users_Manual_for_CCDFGF_Version_500_ERMS530471.pdf" WIPP Performance Assessment 2003a). Release volumes for subsequent intrusions are distinguished by the current state of the repository (E1 or E2) and the relative distance between the panel intruded by the current borehole and the panel of the initial intrusion (same, adjacent, nonadjacent). The algorithms for determining repository conditions and distance between intrusions are described in HYPERLINK \l "PA-6_7_5" Section REF _Ref210114955 \r \h \* MERGEFORMAT PA-6.7.5.
As indicated in REF _Ref201127992 \h \* MERGEFORMAT Table PA-27, DBR volumes for a second intrusion are computed by BRAGFLO for combinations of repository condition, distance between intrusions, and time between intrusions. Brine release volumes for other combinations of condition, distance, and time are computed by linear interpolation (WIPP Performance Assessment 2003a). Brine releases from the third and subsequent intrusions are computed as if the current intrusion was the second intrusion into the repository.
Radionuclide concentrations in brine (Cbl) are calculated by PANEL ( HYPERLINK \l "PA-6_7_3" Section REF _Ref201115834 \r \h \* MERGEFORMAT PA-6.7.3) for the times listed in HYPERLINK \l "Table_PA-26" REF _Ref210719005 \h \* MERGEFORMAT Table PA-26; concentrations at other times are computed by linear interpolation (WIPP Performance Assessment 2003a). The type of intrusion (E1 or E2) determines the brine (Salado or Castile brine) selected for the concentration calculation; Castile brine is used for E1 intrusions, and Salado brine is used for E2 intrusions.
The DBR is computed as the product of the release concentration and the volume, VDBR:
(PA. SEQ Eq._PA- \* ARABIC 316)
Radionuclide Transport Through the Culebra
One potential path for radionuclides to leave the repository is through the boreholes to the Culebra, then through the Culebra to the LWB ( HYPERLINK "../../references/Others/Ismail_Garner_2008_Analysis_Package_for_Salado_Transport_Calculations_CRA_2009_ERMS548845.pdf" Ismail and Garner 2008). As indicated in HYPERLINK \l "Table_PA-26" REF _Ref210719005 \h \* MERGEFORMAT Table PA-26, the NUTS and PANEL models are used to estimate radionuclide transport through boreholes to the Culebra fNP(xst,i) for a fixed set of intrusion times; releases to the Culebra for intrusions at other times are determined by linear interpolation ( HYPERLINK "../../references/Others/WIPP_PA_2003_Design_Document_Users_Manual_for_CCDFGF_Version_500_ERMS530471.pdf" WIPP Performance Assessment 2003a). NUTS computes the release to the Culebra over time for E1 and E2 boreholes; PANEL computes the release to the Culebra for an E1E2 borehole.
Each borehole may create a pathway for releases to the Culebra. The first E1 or E2 borehole in each panel creates a release path, with the radionuclide release taken from the appropriate NUTS data. Subsequent E2 boreholes into a panel with only E2 boreholes do not cause additional releases; WIPP PA assumes that a subsequent E2 borehole into a panel having only earlier E2 intrusions does not provide a significant source of additional brine, and thus does not release additional radionuclides to the Culebra.
An E1E2 borehole results from the combination of two or more intrusions into the same panel, at least one of which is an E1 intrusion. A subsequent E1 borehole changes the panels condition to E1E2, as does an E2 borehole into a panel that has an earlier E1 intrusion. Once E1E2 conditions exist in a panel, they persist throughout the regulatory period. However, releases from a panel with E1E2 conditions are restarted for each subsequent E1 intrusion into that panel, since additional E1 intrusions may introduce new volumes of brine to the panel.
Releases to the Culebra are summed across all release pathways to the Culebra to obtain total releases to the Culebra rk(t) for the kth radionuclide at each time t. Releases to the Culebra include both dissolved radionuclides and radionuclides sorbed to colloids. The WIPP PA assumes that radionuclides sorbed to humic colloids disassociate and transport, as do dissolved radionuclides; other colloid species do not transport in the Culebra (see HYPERLINK "../Appendix_SOTERM/Appendix_SOTERM.htm" \l "SOTERM-4_7" Appendix SOTERM-2009, Section SOTERM-4.7). The release to the Culebra is partitioned into dissolved and colloid species by multiplying rk(t) by radionuclide-specific factors for the fraction dissolved and the fraction on colloids. Dissolved radionuclides are always transported through the Culebra.
Radionuclide transport through the Culebra is computed by the code SECOTP2D ( HYPERLINK \l "PA-4_9" Section REF _Ref207777095 \r \h PA-4.9) for partially mined and fully mined conditions, as indicated in HYPERLINK \l "Table_PA-29" REF _Ref201128156 \h \* MERGEFORMAT Table PA-29. These computations assume a 1 kg source of each radionuclide placed in the Culebra between 0 and 50 years and result in the fraction of each source fm,k(t), where m is the mining condition and k is the index for the radionuclide, reaching the LWB at each subsequent time t. For convenience, the time-ordering of the data from SECOTP2D is reversed so that the fraction fm,k(t) associated with year t = 200, for example, represents the release at the boundary at year 10,000 for a release occurring between 150 and 200 years.
The total release through the Culebra RCul,k is calculated for the kth radionuclide by
EMBED Equation.DSMT4 (PA. SEQ Eq._PA- \* ARABIC 317)
where rk(ti) is the release of the kth radionuclide to the Culebra in kg at time ti, and fPM,k(ti) and fFM,k(ti) are the fractions of a unit source placed in the Culebra in the interval (ti(1, ti) that reaches the LWB by the end of the 10,000-year regulatory period for partially mined and fully mined conditions within the LWB, respectively. The function fm,k(t) (m = PM, FM) changes when mining is assumed to occur within the LWB; hence the sum in the equation above is evaluated in two parts, where tmin is the time that mining occurs. The total releases through the Culebra fST(xst,i) is computed by converting the release of each radionuclide RCul,k from kg to EPA units, then summing over all radionuclides.
Determining Initial Conditions for Direct and Transport Releases
A sequence of intrusions into the repository can change the conditions in and around the repository and, hence, affect releases from subsequent intrusions. This section describes how panel and repository conditions are determined for a given intrusion.
Determining Repository and Panel Conditions
Direct releases by DBR and spallings, and subsequent releases by radionuclide transport, require determining the conditions in the intruded panel and the repository at the time of the intrusion. One of three conditions is assigned to the repository:
E0 the repository is undisturbed by drilling,
E1 the repository has at least one E1 intrusion, or
E2 the repository has one or more E2 intrusions, but no E1 intrusions.
In addition, each panel is assigned one of four conditions:
E0 the excavated regions of the panel have not been intruded by drilling,
E1 the panel has one previous E1 intrusions (intersecting a brine reservoir in the Castile),
E2 the panel has one or more previous E2 intrusions (none intersect brine reservoirs), or
E1E2 the panel has at least two previous intrusions, at least one of which is an E1 intrusion.
Repository conditions are used to determine direct releases for each intrusion by DBRs and spallings. Panel conditions are used to determine releases by transport through the Culebra.
When an intrusion into CH-TRU waste occurs, the stochastic variables in HYPERLINK \l "Table_PA-24" REF _Ref201127629 \h \* MERGEFORMAT Table PA-24 are used in the algorithm shown in HYPERLINK \l "Figure_PA-41" REF _Ref201122146 \h \* MERGEFORMAT Figure PA-41 to determine the type of the intrusion (E1 or E2). The type of the intrusion is used to update the conditions for the intruded panel and the repository before stepping forward in time to the next intrusion.
Determining Distance from Previous Intrusions
Direct releases by DBR and spallings require determining the distance between the panel hit by the current intrusion and the panels hit by previous intrusions. In PA, the 10 panels are divided into three groups: lower, consisting of only Panel 5; middle, including Panels 3, 4, 6, and 9; and upper, including Panels 1, 2, 7, 8, and 10, as shown in HYPERLINK \l "Figure_PA-29" REF _Ref201120129 \h \* MERGEFORMAT Figure PA-29. These divisions are consistent with the repository representation in the BRAGFLO model for Salado flow ( HYPERLINK \l "PA-4_2" Section REF _Ref201115663 \r \h \* MERGEFORMAT PA-4.2) and for DBRs ( HYPERLINK \l "PA-4_7" Section REF _Ref201115668 \r \h \* MERGEFORMAT PA-4.7).
The initial intrusion can occur in any of the 10 actual waste panels, so the direct releases for the initial intrusion are modeled as if the initial intrusion occurred in a lower, middle, or upper waste panel based on the division discussed above. Initial conditions for direct releases from subsequent intrusions are modeled by one of three cases: lower, middle, and upper, corresponding to the three panel groups shown in REF _Ref201120129 \h \* MERGEFORMAT Figure PA-29 and listed in HYPERLINK \l "Table_PA-27" REF _Ref201127992 \h \* MERGEFORMAT Table PA-27. The lower case represents a second intrusion into a previously intruded panel. The middle case represents an intrusion into an undisturbed panel that is adjacent to a previously disturbed panel. The upper case represents an intrusion into an undisturbed panel that is not adjacent to a previously disturbed panel. Adjacent panels share one side in common, and nonadjacent panels share no sides in common.
The time and location of the previous intrusion is used to determine distance from the current intrusion and depends on the repository condition, which is determined by the intrusion of greatest consequence across all panels prior to the current intrusion. E1 intrusions are assumed to be of greater consequence than E2 intrusions. The previous intrusion is selected by finding the closest panel (same, adjacent, nonadjacent) whose intrusion condition, excluding the current intrusion, is equal to the repository condition. The time of the previous intrusion is the time of the most recent intrusion with the greatest consequence and closest distance. Likewise, the condition of each panel is equal to the intrusion of greatest consequence into the panel prior to the current intrusion.
Figure PA- SEQ Figure_PA- \* ARABIC 41. Logic Diagram for Determining the Intrusion Type
CCDF Construction
For each vector vsu,k in the space of subjective uncertainty, the code CCDFGF samples a sequence xst,i, i = 1, 2, (, nR of futures. In PA, nR = 10,000; this number of futures is sufficient to adequately estimate the mean CCDF of total releases for comparison with the boundary line specified in HYPERLINK "40CFR191_13" section 191.13, as demonstrated in HYPERLINK \l "PA-9_0" Section REF _Ref202345024 \r \h \* MERGEFORMAT PA-9.0. A release f(xst,i) for each future is then constructed as described in HYPERLINK \l "PA-6_8_1" Section REF _Ref201116040 \r \h \* MERGEFORMAT PA-6.8.1, Section REF _Ref223421023 \r \h PA-6.8.2, and HYPERLINK \l "PA-6_8_3" Section REF _Ref201116043 \r \h \* MERGEFORMAT PA-6.8.3. Once the f(xst,i) are evaluated, the CCDF can be approximated as indicated in Equation ( REF EQ_PA318 \h \* MERGEFORMAT PA.318).
EMBED Equation.DSMT4 (PA. SEQ Eq._PA- \* ARABIC 318)
A binning technique is used to construct the desired CCDF: the consequence axis is divided into a sequence of bins, and the number of values for f(xst,i) falling in each bin is accumulated. In addition, all values for f(xst,i) are saved and subsequently ordered to provide an alternative method for constructing the CCDFs. In addition to the total CCDF for all releases, it will be possible to obtain CCDFs for individual release modes (e.g., cuttings, spallings, DBRs, to Culebra, through MBs, through Culebra). The logic diagram for CCDF production is shown in HYPERLINK \l "Figure_PA-42" REF _Ref201122442 \h \* MERGEFORMAT Figure PA-42.
The CCDF construction indicated in this section is for a single sample element vsu,k of the form indicated in conjunction with Equation ( REF EQ_PA302 \h \* MERGEFORMAT PA.302). Repeated generation of CCDFs for individual sample elements vsu,k, i.e. for the vectors representing epistemic uncertainty in the model results, will lead to the distribution of complete CCDFs.
Sensitivity Analysis
Evaluating one or more of the models discussed in HYPERLINK \l "PA-4_0" Section REF _Ref201116398 \r \h \* MERGEFORMAT PA-4.0 with the LHS in Equation ( REF EQ_PA302 \h \* MERGEFORMAT PA.302) creates a mapping
EMBED Equation.DSMT4 , k = 1, 2, (, nLHS (PA. SEQ Eq._PA- \* ARABIC 319)
from analysis inputs (i.e., vsu,k) to analysis results (i.e., y(vsu,k)), where ysu,k denotes the results obtained with the model or models under consideration. In other words, for each vector of parameters samples, there is a corresponding CCDF of releases, y(vsu,k). A vector notation is used for y because, in general, a large number of predicted results are produced by each of the models used in PA. Sensitivity analysis explores the mapping in Equation ( REF EQ_PA319 \h \* MERGEFORMAT PA.319) to determine how the uncertainty in individual elements of vsu,k affects the uncertainty in individual elements of y(vsu,k). Understanding how uncertainty in analysis inputs affects analysis results aids in understanding PA and improving the models for future PAs.
The presentation of results from each major model in the WIPP PA is accompanied by sensitivity analyses of the most important output of the model. In some cases, sensitivity analysis results are based on pooling the results obtained for the three replicated LHSs (i.e., R1, R2, R3) discussed in HYPERLINK \l "PA-6_4" Section REF _Ref201116418 \r \h \* MERGEFORMAT PA-6.4. In other cases, the sensitivity analysis is based on the results for each replicate, and statistics are compared across the three replicates. Note that pooling LHS replicates that include correlated variables can introduce a small bias into the statistics, although there are methods that allow for correlated variables when pooling replicates (HYPERLINK "../../references/Others/Sallaberry_Helton_Hora_2006_Extension_of_Latin_Hypercube_Samples_SAND2006_6135.pdf"Sallaberry, Helton, and Hora 2006).
Three principal techniques are used in the sensitivity analysis: scatterplots, regression analyses to determine standardized regression coefficients and partial correlation coefficients, and stepwise regression analyses. Each technique is briefly discussed.
Figure PA- SEQ Figure_PA- \* ARABIC 42. Processing of Input Data to Produce CCDFs
Scatterplots
Scatterplots, the simplest sensitivity analysis technique, are performed by plotting the points
, k = 1, 2, (, nLHS (PA. SEQ Eq._PA- \* ARABIC 320)
for each element vj of Ssu. The resulting plots can reveal relationships between y and the elements of Ssu. Scatterplots can be effective at revealing nonlinear relationships or threshold values. Examining such plots when LHS is used can be particularly revealing because of the full stratification over the range of each input variable. Iman and Helton ( HYPERLINK "../../references/Others/Iman_Helton_1988.pdf" 1988) provide an example where the scatterplots revealed a rather complex pattern of variable interactions.
Regression Analysis
A more formal investigation of the mapping in Equation ( REF EQ_PA319 \h \* MERGEFORMAT PA.319) can be based on regression analysis. In this approach, a model of the form
(PA. SEQ Eq._PA- \* ARABIC 321)
is developed from the mapping between analysis inputs and analysis results shown in Equation ( REF EQ_PA319 \h \* MERGEFORMAT PA.319), where the xj are the input variables under consideration and the bj are coefficients that must be determined. The coefficients bj and other aspects of the regression models construction in Equation ( REF EQ_PA321 \h \* MERGEFORMAT PA.321) can indicate the importance of the individual variables xj with respect to the uncertainty in y. The PA employs the method of least squares to determine the coefficients bj ( HYPERLINK "../../references/Others/Myers_1986.pdf" Myers 1986).
Often the regression in Equation ( REF EQ_PA321 \h \* MERGEFORMAT PA.321) is performed after the input and output variables are normalized to mean zero and standard deviation one. The resulting coefficients bj are called standardized regression coefficients (SRCs). When the xj are independent, the absolute value of the SRCs can provide a measure of variable importance. Specifically, the coefficients provide a measure of importance based on the effect of moving each variable away from its expected value by a fixed fraction of its standard deviation while retaining all other variables at their expected values.
Partial correlation coefficients (PCCs) can also measure the linear relationships between the output variable y and the individual input variables. The PCC between y and an individual variable xp is obtained through a sequence of regression models. First, the following two regression models are constructed:
(PA. SEQ Eq._PA- \* ARABIC 322)
The results of the two preceding regressions are then used to define the new variables and . By definition, the PCC between y and xp is the correlation coefficient between and . Thus, the PCC provides a measure of the linear relationship between y and xp with the linear effects of the other variables removed.
Regression and correlation analyses often perform poorly when the relationships between the input and output variables are nonlinear. This is not surprising, as such analyses assume linear relationships between variables. The problems associated with poor linear fits to nonlinear data can be avoided by use of the rank transformation ( HYPERLINK "../../references/Others/Iman_Conover_1979.pdf" Iman and Conover 1979). The rank transformation is a simple concept: data are replaced with their corresponding ranks, and then the usual regression and correlation procedures are performed on these ranks. Specifically, the smallest value of each variable is assigned Rank 1, the next largest value is assigned Rank 2, and so on up to the largest value, which is assigned the rank m, where m denotes the number of observations. The analysis is then performed with these ranks used as the values for the input and output variables. A formal development of PCCs and the relationships between PCCs and SRCs is provided by Iman, Shortencarier, and Johnson ( HYPERLINK "../../references/Others/Iman_Shortencarier_Johnson_1985_A_FORTRAN_77_Program_SAND85_0044.pdf" 1985).
Stepwise Regression Analysis
Stepwise regression analysis provides an alternative to constructing a regression model containing all the input variables. With this approach, a sequence of regression models is constructed. The first regression model contains the single input variable with the largest impact on the uncertainty in the output variable (i.e., the input variable that has the largest correlation with the output variable y). The second regression model contains the two input variables with the largest impact on the output variable: the input variable from the first step, plus whichever of the remaining variables has the largest impact on uncertainty not accounted for by the first variable (i.e., the input variable that has the largest correlation with the uncertainty in y that cannot be accounted for by the first variable). Additional models in the sequence are defined in the same manner, until further models are unable to meaningfully increase the amount of uncertainty that can be accounted for in the output variable.
Stepwise regression analysis can provide insights into the importance of the individual variables. First, the order in which the variables are selected in the stepwise procedure indicates their importance, with the most important variable being selected first, the next most important variable being selected second, and so on. Second, the R2 values at successive steps of the analysis also measure variable importance by indicating how much of the uncertainty in the dependent variable can be accounted for by all variables selected at each step. When the input variables are uncorrelated, the differences in the R2 values for the regression models constructed at successive steps equals the fraction of the total uncertainty in the output variable accounted for by the individual input variable added at each step. Third, the absolute values of the SRCs in the individual regression models indicate variable importance. Further, the sign of an SRC indicates whether the input and output variable tend to increase and decrease together (a positive coefficient) or tend to move in opposite directions (a negative coefficient).
Results for the Undisturbed Repository
The PA tabulates releases from the repository for undisturbed conditions. Releases from the undisturbed repository to the accessible environment fall under two sets of protection requirements. The first, as set forth in HYPERLINK "40CFR191_15" section 191.15, protects individuals from radiological exposure; the second, in HYPERLINK "40CFR191_Subpart_C" Part 191 Subpart C, protects groundwater resources from contamination. This section shows how WIPP complies with these two requirements by presenting brine and gas flow (BRAGFLO) and radionuclide transport (NUTS) results from modeling the undisturbed repository. The results discussed in HYPERLINK \l "PA-7_2" Section REF _Ref113245025 \r \h \* MERGEFORMAT PA-7.2 show that there are no releases to the accessible environment from the undisturbed repository. HYPERLINK \l "PA-7_0" Section REF _Ref201473682 \r \h \* MERGEFORMAT PA-7.0 is taken from Clayton et al. ( HYPERLINK "../../references/Others/Clayton_et_al_2008_Summary_Report_of_CRA_2009_PA_ERMS548862.pdf" \l "page=26" 2008, Section 4.0).
Salado Flow
This section summarizes the Salado flow calculation results for the undisturbed (S1) scenario. Pressure in the repository, brine saturation in the waste, and brine flow out of the repository are presented, along with sensitivity analyses that identify the uncertain parameters to which these results are most sensitive. The Salado flow model represents the repository as five regions in the numerical grid: three waste-filled regions (the Waste Panel, South RoR, and North RoR in HYPERLINK \l "Figure_PA-15" REF _Ref201037169 \h \* MERGEFORMAT Figure PA-15) and two excavated regions with no waste (the operations area and experimental area in REF _Ref201037169 \h \* MERGEFORMAT Figure PA-15). The analysis package for Salado flow contains a detailed presentation on the BRAGFLO model, calculation results, and further sensitivity analyses ( HYPERLINK "../../references/Others/Nemer_Clayton_2008_Analysis_Package_for_Salado_Flow_Modeling_ERMS548607.pdf" Nemer and Clayton 2008).
Pressure in the Repository
In undisturbed conditions, pressure strongly influences the extent to which contaminated brine might migrate from the repository to the accessible environment. In addition, pressure developed under undisturbed conditions is an initial condition for the spallings and DBR models ( HYPERLINK \l "PA-8_5_2" Section REF _Ref215923207 \r \h PA-8.5.2 and HYPERLINK \l "PA-8_5_3" Section REF _Ref112129955 \r \h \* MERGEFORMAT PA-8.5.3, respectively).
HYPERLINK \l "Figure_PA-43" REF _Ref201122509 \h \* MERGEFORMAT Figure PA-43 shows the pressure in the Waste Panel region for 100 vectors in replicate R1 for the CRA-2009 PA. During the first 1,000 years, repository pressure may rapidly increase due to several factors: rapid initial creep closure of rooms, initial inflow of brine causing gas generation due to corrosion, and availability of CPR material to produce gas by microbial degradation. Pressure generally approaches a steady-state value after 2,000 years as room closure ceases, brine inflow slows (thereby reducing gas generation by corrosion), and CPR materials are consumed.
In general, pressure increased for the CRA-2009 PA compared to the CRA-2004 PABC (HYPERLINK "../../references/Others/Nemer_Clayton_2008_Analysis_Package_for_Salado_Flow_Modeling_ERMS548607.pdf" \l "page=58"Nemer and Clayton 2008, Table 6-10). The increase was mainly caused by the correction of halite porosity. The upper bound of the halite porosity distribution was increased, while the lower bound and the mean remained the same. The halite porosity is positively correlated with pressure, so the increase in porosity resulted in an increase in pressure ( HYPERLINK "../../references/Others/Nemer_Clayton_2008_Analysis_Package_for_Salado_Flow_Modeling_ERMS548607.pdf" Nemer and Clayton 2008).
Figure PA- SEQ Figure_PA- \* ARABIC 43. Pressure in the Waste Panel Region, Replicate R1, Scenario S1, CRA-2009 PA
Sensitivity analyses have determined the importance of parameter uncertainty to the uncertainty in model results. HYPERLINK \l "Figure_PA-44" REF _Ref201122626 \h \* MERGEFORMAT Figure PA-44 shows partial rank correlation coefficients (PRCCs) generated by the code PCCSRC (HYPERLINK "../../references/Others/Gilkey_1995_PCCSRC_Version_221_Software_Installation_ERMS227771.pdf"Gilkey 1995) from regression data between the pressure in the waste panel (WAS_PRES) and the uncertain variables in the LHS ( HYPERLINK \l "PA-5_2" Section REF _Ref201117198 \r \h \* MERGEFORMAT PA-5.2) for the CRA-2009 PA. The figure shows that uncertain pressure in the waste panel is primarily determined by the sampled halite porosity (HALPOR) ( HYPERLINK "../../references/Others/Nemer_Clayton_2008_Analysis_Package_for_Salado_Flow_Modeling_ERMS548607.pdf" Nemer and Clayton 2008).
The positive correlation indicates that higher pressures result from higher values of halite porosity (HALPOR). Increases in halite porosity linearly increases the DRZ porosity. This increases the volume of brine available in the material overlying the waste, which, as the brine flows, can then increase the amount of brine in the repository (Nemer and Clayton 2008). Microbial gas generation rates are a function of the brine in the repository and increase as more brine is available. Increased gas generation results in increased repository pressures. Increases in the DRZ permeability (DRZPRM) accelerate brine flow into the waste, which then also increases the gas generation rates, as seen by the positive correlation in REF _Ref201122626 \h \* MERGEFORMAT Figure PA-44. The other PRCCs in REF _Ref201122626 \h \* MERGEFORMAT Figure PA-44 indicate that the uncertainty factor for microbial gas generation (WBIOGENF), the corrosion rate for steel (WGRCOR), and the waste wicking parameter (WASTWICK) determine the remaining variability in waste panel pressure, as they affect the gas generation rate as well.
Brine Saturation in the Waste
Brine saturation is an important result of the model for Salado flow because gas generation processes, which tend to increase pressure, require brine. Brine saturation is also an initial condition in the model for DBR ( HYPERLINK \l "PA-8_5_3" Section REF _Ref112129955 \r \h \* MERGEFORMAT PA-8.5.3).
Figure PA- SEQ Figure_PA- \* ARABIC 44. Primary Correlations of Pressure in the Waste Panel Region with Uncertain Parameters, Replicate R1, Scenario S1, CRA-2009 PA
HYPERLINK \l "Figure_PA-45" REF _Ref201122659 \h \* MERGEFORMAT Figure PA-45 shows brine saturation in the Waste Panel region of the repository for the 100 vectors of Replicate R1, Scenario S1 for the CRA-2009 PA. Brine saturation in the waste-filled areas is set initially to 0.015. Saturation increases very rapidly in the first 100 years in all excavated areas as brine flows toward the excavations, primarily from the DRZ above the excavation. Initially there is a large pressure differential between the DRZ and the excavated regions, and the relatively high permeability of the DRZ, compared to undisturbed halite, permits the rapid influx of brine. Brine inflow slows as the pressures equalize and as brine saturation in the DRZ decreases. Brine saturation in the waste areas decreases over time as brine is consumed by corrosion. Brine may also be driven out of the repository by high pressure.
The brine saturation patterns are similar, but are higher on average in the CRA-2009 PA than the CRA-2004 PABC (HYPERLINK "../../references/Others/Nemer_Clayton_2008_Analysis_Package_for_Salado_Flow_Modeling_ERMS548607.pdf" \l "page=54"Nemer and Clayton 2008, Table 6-6 and HYPERLINK "../../references/Others/Nemer_Clayton_2008_Analysis_Package_for_Salado_Flow_Modeling_ERMS548607.pdf" \l "page=67"Figure 6-8): there are more vectors with saturation greater than 60%. The increase in brine saturation is the result of the increased halite porosity (Nemer and Clayton 2008).
Computing PRCCs between the brine saturation in the waste panel (WAS_SATB) and the uncertain parameters in the LHS identifies a number of parameters that contribute to the uncertainty in brine saturation. The relative importance of these parameters varies over the 10,000-year modeling period, and none of the parameters are clearly dominant. HYPERLINK \l "Figure_PA-46" REF _Ref201122673 \h \* MERGEFORMAT Figure PA-46 shows positive correlations with anhydrite permeability (ANHPRM), DRZ permeability (DRZPRM), and halite porosity (HALPOR). Increases in halite porosity increase the volume of brine available in the material overlying the waste; increases in DRZ and anhydrite permeability accelerate brine flow into the waste. Negative correlations are found between brine saturation
Figure PA- SEQ Figure_PA- \* ARABIC 45. Brine Saturation in the Waste Panel Region, Replicate R1, Scenario S1, CRA-2009 PA
Figure PA- SEQ Figure_PA- \* ARABIC 46. Primary Correlations of Brine Saturation in the Waste Panel Region with Uncertain Parameters, Replicate R1, Scenario S1, CRA-2009 PA
and the corrosion rate (WGRCOR) and the wicking factor (WASTWICK) because increases in these two variables increase the rate at which brine is consumed by corrosion, thus decreasing saturation.
Brine Flow Out of the Repository
The anhydrite MBs and the shafts provide possible pathways for brine flow away from the repository in the undisturbed (S1) scenario. The Salado flow model only tabulates the volume of brine crossing boundaries within the model grid; it does not identify whether the brine contains radionuclides from the waste. Radionuclide transport is calculated separately from the flow and is discussed in HYPERLINK \l "PA-7_2" Section REF _Ref113245025 \r \h \* MERGEFORMAT PA-7.2.
HYPERLINK \l "Figure_PA-47" REF _Ref201122703 \h \* MERGEFORMAT Figure PA-47 shows cumulative brine outflow from the waste-filled regions of the repository (BRNREPOC), while HYPERLINK \l "Figure_PA-48" REF _Ref201122705 \h \* MERGEFORMAT Figure PA-48 shows the volumes of brine that cross the LWB through the MBs (BRAALLWC). The largest outflow across the LWB is ~1,600 m3. Brine crossing the LWB or moving up the shaft does not necessarily indicate releases from the repository, since the brine may not have been in contact with the waste; the brine may have been present in the MBs at the start of the regulatory period. Section REF _Ref113245025 \r \h \* MERGEFORMAT PA-7.2 presents the results of the radionuclide transport calculations that determine the amount of radionuclides that may be released through brine transport.
Compared with the CRA-2004 PABC, an increase in the average and maximum cumulative brine flow away from the repository was observed for the CRA-2009 PA (see HYPERLINK "../../references/Others/Nemer_Clayton_2008_Analysis_Package_for_Salado_Flow_Modeling_ERMS548607.pdf" \l "page=59"Nemer and Clayton [2008, Table 6-11]). The cumulative brine flow to the LWB through the MBs also increased for
Figure PA- SEQ Figure_PA- \* ARABIC 47. Brine Flow Away From the Repository, Replicate R1, Scenario S1, CRA2009 PA
Figure PA- SEQ Figure_PA- \* ARABIC 48. Brine Flow via All MBs Across the LWB, Replicate R1, Scenario S1, CRA2009 PA
the CRA-2009 PA compared to the CRA-2004 PABC. These changes are the result of increased repository pressure (see HYPERLINK \l "PA-7_1_1" Section REF _Ref201117281 \r \h \* MERGEFORMAT PA-7.1.1).
Regression analyses between total cumulative brine flow out of the waste-filled regions (BRNREPOC) and the uncertain parameters are shown in HYPERLINK \l "Figure_PA-49" REF _Ref201122727 \h \* MERGEFORMAT Figure PA-49. The permeability of the DRZ (DRZPRM) has the largest positive correlation, followed by the permeability of the concrete panel seal (CONPRM) and the porosity of undisturbed halite (HALPOR). Increases in the permeability of the DRZ and the concrete panel seal allow more brine to flow out of the repository, as well as into the repository, which increases the gas generation and therefore the pressure. The increase in the halite porosity also increases the pressure, which in turn increases the amount of brine flow out of the repository. The largest negative correlation is with the waste residual brine saturation (WRBRNSAT), which determines the immobile portion of the brine in the waste-filled regions, and limits the amount of brine that can flow out.
Radionuclide Transport
This section summarizes the radionuclide transport results for the undisturbed repository, both up the shaft to the Culebra and through the Salado to the LWB. Ismail and Garner ( HYPERLINK "../../references/Others/Ismail_Garner_2008_Analysis_Package_for_Salado_Transport_Calculations_CRA_2009_ERMS548845.pdf" 2008) present a detailed analysis of the NUTS results for the CRA-2009 PA.
Radionuclide transport in the undisturbed (S1) scenario is calculated by the code NUTS. Screening runs using a conservative tracer determine which vectors have the potential to transport radionuclides to the accessible environment. Full transport simulations are then performed for all screened-in vectors (with the potential to transport radionuclides to the accessible environment). Based upon results of the screening exercise, full radionuclide
Figure PA- SEQ Figure_PA- \* ARABIC 49. Primary Correlations of Total Cumulative Brine Flow Away from the Repository with Uncertain Parameters, Replicate R1, Scenario S1, CRA2009 PA
transport simulations were performed for only one vector in the undisturbed case: Replicate R1, Vector 53. Radionuclide transport simulations were performed for other vectors in the undisturbed case to postprocess fluid-flow conditions for use in the disturbed scenario calculations.
Radionuclide Transport to the Culebra
For the undisturbed repository, no vectors showed radionuclide transport through the shafts to the Culebra. Consequently, no radionuclides could be transported through the Culebra to the accessible environment under undisturbed conditions ( HYPERLINK "../../references/Others/Ismail_Garner_2008_Analysis_Package_for_Salado_Transport_Calculations_CRA_2009_ERMS548845.pdf" Ismail and Garner 2008).
Radionuclide Transport to the Land Withdrawal Boundary
Radionuclides can also be transported through the Salado MBs to the LWB. For the undisturbed case, only one vector was screened in. The maximum total integrated activity across the LWB at the Salado MBs for Replicate R1, Scenario S1, Vector 53 was 2.6נ10(10 EPA units (Ismail and Garner 2008), which is the same vector with the largest outflow of brine across the LWB of ~1,600 m3. This is comparable to the CRA-2004 PABC results for replicate R1, Scenario S1, Vector 53 (the only screened-in vector), which had 1.3נ10-12 EPA units at the boundary ( HYPERLINK "../../references/Others/Lowry_2005_Analysis_Package_for_Salado_Transport_Calculations_CRA_2004_PABC_ERMS541084.pdf" Lowry 2005). Note that these magnitudes are smaller than the effective numerical precision of the transport calculations. As explained in Lowry (2005), this value is most likely due to numerical dispersion as a result of NUTSs finite-difference solution method. The magnitude of the nonzero release is indicative of numerical dispersion resulting from the coarse grid spacing between the repository and the LWB, rather than from actual transport of radionuclides.
Regardless of the significance attached to the numerical values reported above, the releases from the undisturbed scenario are insignificant compared to releases from drilling intrusions (see HYPERLINK \l "PA-8_4" Section PA-8.4). Consequently, releases in the undisturbed (S1) scenario are omitted from the calculation of total releases from the repository.
Results for a Disturbed Repository
The WIPP repository might be disturbed by exploratory drilling for natural resources during the 10,000-year regulatory period. Drilling could create additional pathways for radionuclide transport, especially in the Culebra, and could release material directly to the surface. In addition, mining for potash within the LWB might alter flow in the overlying geologic units and locally accelerate transport through the Culebra. The disturbed scenarios used in PA modeling capture the range of possible releases resulting from drilling and mining.
Total releases are computed by the code CCDFGF. Total releases comprise transport releases and direct releases. Transport releases generally involve movement of radionuclides up an abandoned borehole into the Culebra, then through the Culebra to the LWB. Transport of radionuclides to the Culebra is computed using the codes NUTS and PANEL (see HYPERLINK \l "PA-6_7_2" Section REF _Ref201117417 \r \h \* MERGEFORMAT PA-6.7.2 and HYPERLINK \l "PA-6_7_3" Section REF _Ref201117419 \r \h \* MERGEFORMAT PA-6.7.3) using the brine flows computed by BRAGFLO (see HYPERLINK \l "PA-6_7_1" Section REF _Ref201117425 \r \h \* MERGEFORMAT PA-6.7.1). Radionuclide transport through the Culebra is computed by the code SECOTP2D (see HYPERLINK \l "PA-6_7_8" Section REF _Ref201117430 \r \h \* MERGEFORMAT PA-6.7.8) using flow fields calculated by MODFLOW (see HYPERLINK \l "PA-6_7_7" Section REF _Ref201117431 \r \h \* MERGEFORMAT PA-6.7.7).
Direct releases occur at the time of a drilling intrusion and include releases of solids (cuttings, cavings, and spallings) computed using the code CUTTINGS_S (see HYPERLINK \l "PA-6_7_4" Section REF _Ref201117439 \r \h \* MERGEFORMAT PA-6.7.4) and DBRs computed using BRAGFLO (see HYPERLINK \l "PA-6_7_6" Section REF _Ref201117444 \r \h \* MERGEFORMAT PA-6.7.6). Pressure and brine saturation within the waste areas are used as initial conditions for the direct release models. Results from the undisturbed repository (see HYPERLINK \l "PA-7_0" Section REF _Ref201117517 \r \h \* MERGEFORMAT PA-7.0) are used as the initial conditions for the first intrusion. To calculate initial conditions for subsequent intrusions, and to compute the source of radionuclides for transport in the Culebra, BRAGFLO uses a set of drilling scenarios to calculate conditions within the repository after an intrusion (see Section REF _Ref201117444 \r \h \* MERGEFORMAT PA-6.7.6).
This section first summarizes the scenarios used to represent drilling intrusions and the resulting repository conditions calculated by BRAGFLO. Transport releases are presented next, followed by cuttings, cavings, spallings, and DBRs. HYPERLINK \l "PA-8_0" Section REF _Ref201473740 \r \h \* MERGEFORMAT PA-8.0 is taken from Clayton etal. ( HYPERLINK "../../references/Others/Clayton_et_al_2008_Summary_Report_of_CRA_2009_PA_ERMS548862.pdf" \l "page=35" 2008, Section 5.0).
Drilling Scenarios
As shown in HYPERLINK \l "Table_PA-25" REF _Ref201127646 \h \* MERGEFORMAT Table PA-25, the PA considers two types of drilling intrusions: E1 and E2. The E1 intrusion scenario represents the possibility that a borehole creates a pathway between the repository and a pressurized brine reservoir located within the underlying Castile formation. The E2 intrusion scenario represents a borehole that intrudes into the repository, but does not connect the repository with an underlying brine reservoir. Repository conditions are calculated for the E1 intrusion scenario at 350 and 1,000 years, and are referred to as the BRAGFLO S2 and S3 scenarios, respectively. The BRAGFLO Scenarios S4 and S5 represent E2 intrusions that occur at 350 and 1,000 years, respectively. An additional BRAGFLO scenario, S6, simulates the effects of an E2 intrusion at 1,000 years followed by an E1 intrusion 1,000 years later into the same panel.
Mining Scenarios
Long-term releases within the Culebra could be influenced by future mining activities that remove all the known potash reserves within the LWB and cause the transmissivity within the overlying Culebra to change (see HYPERLINK \l "PA-4_8" Section REF _Ref201036804 \r \h \* MERGEFORMAT PA-4.8). The full mining of known potash reserves within the LWB in the absence of AICs and PICs is modeled as a Poisson process, with a rate of 10(4 yr(1 (see HYPERLINK \l "PA-3_9" Section REF _Ref204073417 \r \h \* MERGEFORMAT PA-3.9). For any particular future, this rate is used to determine a time at which full mining has occurred. Flow fields are calculated for the Culebra for two conditions: partial mining, which assumes all potash has been mined from reserves outside the LWB; and full mining, which assumes all reserves have been mined both inside and outside the LWB. Radionuclide transport through the Culebra uses the partial-mining flow fields prior to the time at which full mining has occurred and the full-mining flow fields after that time.
Salado Flow
This section summarizes the results of the Salado flow calculations for the disturbed scenarios. Nemer and Clayton ( HYPERLINK "../../references/Others/Nemer_Clayton_2008_Analysis_Package_for_Salado_Flow_Modeling_ERMS548607.pdf" 2008) provide a detailed presentation on the BRAGFLO model, calculation results, and further sensitivity analyses.
Pressure in the Repository
HYPERLINK \l "Figure_PA-50" REF _Ref201122767 \h \* MERGEFORMAT Figure PA-50 and HYPERLINK \l "Figure_PA-51" REF _Ref201122768 \h \* MERGEFORMAT Figure PA-51 show pressure in the waste panel (WAS_PRES for Waste Panel area in HYPERLINK \l "Figure_PA-15" REF _Ref201037169 \h \* MERGEFORMAT Figure PA-15) for the 100 vectors of replicate R1 for BRAGFLO Scenarios S2 and S4, respectively. The pressure exhibits varying patterns depending on the type of intrusion.
Scenario S2 represents an E1 intrusion at 350 years. At the time of the intrusion, brine flow from the Castile brine reservoir leads to an increase in pressure ( REF _Ref201122767 \h \* MERGEFORMAT Figure PA-50). However, pressure drops sharply 200 years after the intrusion, when the borehole plugs above the repository are assumed to fail and the permeability of the borehole generally increases. In vectors with low borehole permeability, pressure does not change noticeably as a result of the borehole plug failure ( HYPERLINK "../../references/Others/Nemer_Clayton_2008_Analysis_Package_for_Salado_Flow_Modeling_ERMS548607.pdf" Nemer and Clayton 2008).
Scenario S4 represents an E2 intrusion at 350 years. The borehole plugs effectively prevent any change in repository pressure from the time of the intrusion until the borehole plugs fail ( REF _Ref201122768 \h \* MERGEFORMAT Figure PA-51). As in the scenarios for E1 intrusions, pressure generally drops sharply when the plugs fail, except for vectors with low borehole permeability after plug failure. The pressure is generally lower in the E2 intrusion scenarios compared to the undisturbed and E1 intrusion scenarios (Nemer and Clayton 2008).
The pressure trends in the disturbed scenarios for the CRA-2009 PA are similar to the results obtained for the CRA-2004 PABC. The average and maximum pressures are comparable between the two analyses, as well (see HYPERLINK "../../references/Others/Nemer_Clayton_2008_Analysis_Package_for_Salado_Flow_Modeling_ERMS548607.pdf" \l "page=101"Table 6-16 in Nemer and Clayton [2008]). As the intrusion creates a pathway for brine and gas to flow into and away from the repository, the effect of the increased halite porosity is minimized (Nemer and Clayton 2008).
Figure PA- SEQ Figure_PA- \* ARABIC 50. Pressure in the Waste Panel Region for Replicate R1, Scenario S2, CRA2009 PA
Figure PA- SEQ Figure_PA- \* ARABIC 51. Pressure in the Waste Panel Region for Replicate R1, Scenario S4, CRA2009 PA
Computing PRCCs between the pressure in the waste panel (WAS_PRES) and the uncertain parameters in the LHS identifies a number of parameters that contribute to the uncertainty in pressure for the disturbed scenarios. The relative importance of these parameters varies over the 10,000-year modeling period. HYPERLINK \l "Figure_PA-52" REF _Ref201122819 \h \* MERGEFORMAT Figure PA-52 and HYPERLINK \l "Figure_PA-53" REF _Ref201122821 \h \* MERGEFORMAT Figure PA-53 show the regression analysis results for pressure in the Waste Panel with uncertain parameters versus time for Scenarios S2 and S4, Replicate R1 from the CRA-2009 PA, respectively.
For both scenarios, the borehole permeability (BHPERM) has the largest negative correlation with pressure after the intrusion, as this is the primary means by which pressure may escape the repository in the disturbed scenarios. For Scenario S2 ( REF _Ref201122819 \h \* MERGEFORMAT Figure PA-52), the initial Castile brine pocket pressure (BPINTPRS) has the largest positive correlation after the intrusion, while for Scenario S4 ( REF _Ref201122821 \h \* MERGEFORMAT Figure PA-53), the largest positive correlation for the majority of the time after the intrusion, results from the halite porosity (HALPOR). The negative correlation of the borehole permeability is stronger than the positive correlation of the initial Castile brine pocket pressure and halite porosity for either scenario.
The higher initial Castile brine pocket pressure causes more brine at a higher pressure to flow into the repository, while increasing the halite porosity increases the volume of brine available in the material overlying the waste, which, as the brine flows into the waste panel, can then increase the amount of brine in the repository. Microbial gas generation rates are a function of the brine in the repository and increase as more brine is available. Increased gas generation results in increased repository pressures.
The pressure in the waste panel is also controlled by the corrosion rate for steel (WGRCOR), the waste wicking parameter (WASTWICK), and the index for the model of microbial degradation (WMICDFLG), which all affect the gas generation rates and therefore the pressure. For Scenario S2, increasing the brine pocket compressibility (BPCOMP) increases the brine inflow from the brine pocket to the repository, and thus the pressure in the repository.
Brine Saturation
Brine saturation tends to increase after a drilling intrusion. HYPERLINK \l "Figure_PA-54" REF _Ref201122897 \h \* MERGEFORMAT Figure PA-54 and HYPERLINK \l "Figure_PA-55" REF _Ref201122899 \h \* MERGEFORMAT Figure PA-55 show brine saturation in the waste panel (WAS_SATB for area Waste Panel in HYPERLINK \l "Figure_PA-15" REF _Ref201037169 \h \* MERGEFORMAT Figure PA-15) for Replicate R1 for BRAGFLO Scenarios S2 and S4, respectively.
Scenario S2 represents an E1 intrusion at 350 years. At the time of the intrusion, brine flow from the Castile brine reservoir increases saturation ( REF _Ref201122897 \h \* MERGEFORMAT Figure PA-54). However, saturation can drop sharply 200 years after the intrusion when the borehole plugs above the repository are assumed to fail and the permeability of the borehole generally increases. In vectors with low borehole permeability, saturation does not change noticeably as a result of the borehole plug failure. Twelve hundred years after the drilling intrusion, the permeability of the borehole connecting the repository to the Castile is assumed to be reduced by an order of magnitude because of creep closure. This material change reduces saturation in some vectors, but does not appear to have a significant effect on the saturation in most vectors.
Figure PA- SEQ Figure_PA- \* ARABIC 52. Primary Correlations of Pressure in the Waste Panel Region with Uncertain Parameters, Replicate R1, Scenario S2, CRA-2009 PA
Figure PA- SEQ Figure_PA- \* ARABIC 53. Primary Correlations of Pressure in the Waste Panel Region with Uncertain Parameters, Replicate R1, Scenario S4, CRA-2009 PA
Figure PA- SEQ Figure_PA- \* ARABIC 54. Brine Saturation in the Waste Panel Region for Replicate R1, Scenario S2, CRA-2009 PA
Scenario S4 represents an E2 intrusion at 350 years. The borehole plugs effectively prevent any change in repository saturation from the time of the intrusion until the borehole plugs fail ( HYPERLINK \l "Figure_PA-55" REF _Ref201122899 \h \* MERGEFORMAT Figure PA-55). Unlike the E1 intrusions scenarios, saturation generally increases sharply when the plugs fail, except for vectors with low borehole permeability after plug failure. The saturation is generally lower in the E2 intrusion scenarios compared to the E1 intrusion scenarios.
The brine saturation trends in the disturbed scenarios for the CRA-2009 PA are similar to the results obtained for the CRA-2004 PABC. The average and maximum brine saturations are comparable between the two analyses, as well (see HYPERLINK "../../references/Others/Nemer_Clayton_2008_Analysis_Package_for_Salado_Flow_Modeling_ERMS548607.pdf" \l "page=100"Nemer and Clayton [2008, Table 6-15]).
As the intrusion creates a pathway for brine and gas to flow into and away from the repository, the effect of the increased porosity is minimized ( HYPERLINK "../../references/Others/Nemer_Clayton_2008_Analysis_Package_for_Salado_Flow_Modeling_ERMS548607.pdf" Nemer and Clayton 2008).
Computing PRCCs between the saturation in the waste panel (WAS_SATB) and the uncertain parameters in the LHS identifies a number of parameters that contribute to the uncertainty in pressure for the disturbed scenarios. The relative importance of these parameters varies over the 10,000-year modeling period. HYPERLINK \l "Figure_PA-56" REF _Ref201122970 \h \* MERGEFORMAT Figure PA-56 and HYPERLINK \l "Figure_PA-57" REF _Ref201122972 \h \* MERGEFORMAT Figure PA-57 show the regression analysis results for saturation in the Waste Panel with uncertain parameters versus time for Scenarios S2 and S4, and Replicate R1 from the CRA-2009 PA, respectively.
For Scenario S2 ( REF _Ref201122970 \h \* MERGEFORMAT Figure PA-56), the DRZ permeability (DRZPRM) and the borehole permeability (BHPERM) have positive correlations. Increases in DRZ and borehole permeability accelerate brine flow into the waste. The corrosion rate for steel (WGRCOR) and
Figure PA- SEQ Figure_PA- \* ARABIC 55. Brine Saturation in the Waste Panel Region for Replicate R1, Scenario S4, CRA-2009 PA
Figure PA- SEQ Figure_PA- \* ARABIC 56. Primary Correlations of Brine Saturation in the Waste Panel Region with Uncertain Parameters, Replicate R1, Scenario S2, CRA-2009 PA
the waste wicking parameter (WASTWICK) are negatively correlated with the saturation, as these control the brine-consuming reactions. The halite porosity (HALPOR) has a high positive correlation before the intrusion, which then decreases.
For Scenario S4 ( HYPERLINK \l "Figure_PA-57" REF _Ref201122972 \h \* MERGEFORMAT Figure PA-57), the largest positive correlation results from borehole permeability (BHPERM), with the DRZ permeability (DRZPRM), anhydrite permeability (ANHPRM), and the halite porosity (HALPOR) also showing high positive correlations. Increases in DRZ, borehole, and anhydrite permeability accelerate brine flow into the waste, while increases in halite porosity increase the volume of brine available in the material overlying the waste, all of which control the amount of brine flow into and out of the repository. The corrosion rate for steel (WGRCOR) is negatively correlated with the saturation, as this is a brine-consuming reaction.
Figure PA- SEQ Figure_PA- \* ARABIC 57. Primary Correlations of Brine Saturation in the Waste Panel Region with Uncertain Parameters, Replicate R1, Scenario S4, CRA-2009 PA
Brine Flow out of the Repository
This section describes the flow of brine up a borehole to the Culebra. Brine flow to the Culebra is important in calculating long-term releases to the Culebra. Direct brine flow up the borehole to the surface at the time of drilling is modeled separately in the DBR calculations, presented in HYPERLINK \l "PA-8_5_3" Section REF _Ref112129955 \r \h \* MERGEFORMAT PA-8.5.3.
HYPERLINK \l "Figure_PA-58" REF _Ref201123027 \h \* MERGEFORMAT Figure PA-58 shows cumulative brine flow out of the repository (BRNREPOC) for Scenario S2. Scenario S2 represents an E1 intrusion at 350 years. At the time of the intrusion, brine flow from the Castile brine reservoir fills the repository. At 200 years after the intrusion, when the
Figure PA- SEQ Figure_PA- \* ARABIC 58. Total Cumulative Brine Outflow in Replicate R1, Scenario S2,CRA-2009 PA
borehole plugs above the repository are assumed to fail and the permeability of the borehole generally increases, most of the brine leaving the repository flows up the borehole to the Culebra. In vectors with low borehole permeability, the brine flow out of the repository does not noticeably change as a result of the borehole plug failure. Twelve hundred years after the drilling intrusion, the permeability of the borehole between the repository and the Castile is reduced by an order of magnitude because of creep closure, reducing brine flow into the repository and causing a corresponding decrease in brine flow out of the repository. This material change reduces brine flow out of the repository in some vectors, but does not appear to have a significant effect on the brine flow out of the repository in most vectors.
HYPERLINK \l "Figure_PA-59" REF _Ref201123037 \h \* MERGEFORMAT Figure PA-59 shows the volumes of brine that cross the LWB through the MBs for Scenario S2. The largest outflow across the LWB is ~127 m3, which is significantly less than the undisturbed scenario results (see HYPERLINK \l "PA-7_1_3" Section REF _Ref201117589 \r \h \* MERGEFORMAT PA-7.1.3). As the intrusion creates a pathway to the Culebra, flow to the LWB is reduced. Brine crossing the LWB or moving up the shaft does not necessarily indicate releases from the repository because the brine may not have been in contact with the waste; the brine may have been present in the MBs at the start of the regulatory period. HYPERLINK \l "PA-8_4" Section PA-8.4 presents the results of the radionuclide transport calculations that determine the amount of radionuclides that may be released by transport in brine for the disturbed scenarios.
The total cumulative brine flow away from the repository and the brine flow across the LWB in the disturbed scenarios for the CRA-2009 PA are similar to the results obtained for the CRA-2004 PABC. The average and maximum brine flows are comparable between the two analyses as well (see HYPERLINK "../../references/Others/Nemer_Clayton_2008_Analysis_Package_for_Salado_Flow_Modeling_ERMS548607.pdf" \l "page=103"Nemer and Clayton [2008, Table 6-18]). As the intrusion creates a pathway for brine and gas to flow into and away from the repository, the effect of the increased porosity is minimized ( HYPERLINK "../../references/Others/Nemer_Clayton_2008_Analysis_Package_for_Salado_Flow_Modeling_ERMS548607.pdf" Nemer and Clayton 2008).
Figure PA- SEQ Figure_PA- \* ARABIC 59. Brine Flow via All MBs Across the LWB in Replicate R1, Scenario S2, CRA-2009 PA
HYPERLINK \l "Figure_PA-60" REF _Ref201123067 \h \* MERGEFORMAT Figure PA-60 shows cumulative brine flow out of the repository (BRNREPOC) for the BRAGFLO Scenario S4, which represents an E2 intrusion at 350 years. The results for the S4 scenario are very similar to the results for the Undisturbed Scenario S1 (see HYPERLINK \l "PA-7_1_3" Section REF _Ref201117589 \r \h \* MERGEFORMAT PA-7.1.3).
Figure PA- SEQ Figure_PA- \* ARABIC 60. Total Cumulative Brine Outflow in Replicate R1, Scenario S4,CRA-2009 PA
HYPERLINK \l "Figure_PA-61" REF _Ref201123070 \h \* MERGEFORMAT Figure PA-61 shows the volumes of brine that cross the LWB through the MBs for the BRAGFLO Scenario S4. The largest outflow across the LWB is ~1,200 m3, which is smaller than the undisturbed scenario results (see HYPERLINK \l "PA-7_1_3" Section REF _Ref201117589 \r \h \* MERGEFORMAT PA-7.1.3). As the intrusion creates a pathway to the Culebra, flow to the LWB is reduced. Brine crossing the LWB or moving up the shaft does not necessarily indicate releases from the repository, since the brine may not have been in contact with the waste; the brine may have been present in the MBs at the start of the regulatory period. HYPERLINK \l "PA-8_4" Section PA-8.4 presents the results of the radionuclide transport calculations that determine the amount of radionuclides that may be released by transport in brine for the disturbed scenarios.
Figure PA- SEQ Figure_PA- \* ARABIC 61. Brine Flow via All MBs Across the LWB in Replicate R1, Scenario S4, CRA-2009 PA
Regression between total cumulative brine flow out of the waste-filled regions (BRNREPOC) and the uncertain parameters are shown in HYPERLINK \l "Figure_PA-62" REF _Ref201123091 \h \* MERGEFORMAT Figure PA-62 and HYPERLINK \l "Figure_PA-63" REF _Ref201123092 \h \* MERGEFORMAT Figure PA-63 for the BRAGFLO Scenarios S2 and S4, respectively. For the S2 and S4 scenarios, the permeability of the DRZ (DRZPRM), the borehole permeability (BHPERM), and the porosity of undisturbed halite (HALPOR) have positive correlations. Increases in the DRZ and borehole permeability allow more brine to flow out of the repository. The increase in the halite porosity is correlated with the increase in pressure, and an increase in pressure increases the amount of brine flow out of the repository.
A negative correlation with the waste residual brine saturation (WRBRNSAT) is shown for both the S2 and S4 scenarios, which determines the immobile portion of the waste brine saturation, limiting the amount of brine that can flow out of the waste-filled regions. The permeability of the concrete panel seal (CONPRM) is negatively correlated for the S2 scenario and positively
Figure PA- SEQ Figure_PA- \* ARABIC 62. Primary Correlations of Cumulative Brine Flow Away from the Repository with Uncertain Parameters, Replicate R1, Scenario S2, CRA-2009 PA
Figure PA- SEQ Figure_PA- \* ARABIC 63. Primary Correlations of Cumulative Brine Flow Away from the Repository with Uncertain Parameters, Replicate R1, Scenario S4, CRA-2009 PA
correlated for the S4 scenario. The increased permeability of the concrete panel seal allows more brine to flow from the intruded panel to the remainder of the repository (flow into another panel is not considered out of the repository), reducing the higher-pressure conditions in the intruded panel in the S2 scenario, and therefore the flow out of the repository through the borehole. In contrast, in the S4 scenario, the increased permeability allows the brine from the remainder of the repository to flow into the depressurized intruded panel, increasing the pressure and flow out of the repository up the borehole.
Radionuclide Transport
In the disturbed scenarios, radionuclide transport in the Salado is calculated by the code NUTS (see HYPERLINK \l "PA-6_7_2" Section REF _Ref201117694 \r \h \* MERGEFORMAT PA-6.7.2). Radionuclide transport from the Salado to the Culebra is calculated by NUTS and PANEL (see Section REF _Ref201117694 \r \h \* MERGEFORMAT PA-6.7.2 and HYPERLINK \l "PA-6_7_3"Section REF _Ref201117698 \r \h \* MERGEFORMAT PA-6.7.3). Radionuclide transport within the Culebra is calculated by SECOTP2D (see HYPERLINK \l "PA-6_7_8" Section REF _Ref201117430 \r \h \* MERGEFORMAT PA-6.7.8). For all radionuclide transport calculations, mobilized concentrations of radionuclides in Salado and Castile brines are computed by the code PANEL (see Section REF _Ref201117698 \r \h \* MERGEFORMAT PA-6.7.3).
This section summarizes the radionuclide transport results for the disturbed scenarios. Nemer and Clayton ( HYPERLINK "../../references/Others/Nemer_Clayton_2008_Analysis_Package_for_Salado_Flow_Modeling_ERMS548607.pdf" 2008) describe the brine and gas flow in the Salado. Detailed analysis of the radionuclide transport in the Salado is presented in Ismail and Garner ( HYPERLINK "../../references/Others/Ismail_Garner_2008_Analysis_Package_for_Salado_Transport_Calculations_CRA_2009_ERMS548845.pdf" 2008). Garner and Leigh ( HYPERLINK "../../references/Others/Garner_Leigh_2005_Analysis_Package_for_PANEL_CRA_2004_PABC_ERMS540572.pdf" 2005) provide an analysis of the mobilized concentrations of radionuclides in Salado and Castile brines. Lowry and Kanney ( HYPERLINK "../../references/Others/Lowry_Kanney_2005_Analysis_Report_for_CRA_2004_PABC_Culebra_Flow_ERMS541508.pdf" 2005) present an analysis of the flow and radionuclide transport within the Culebra.
Radionuclide Source Term
The code PANEL calculates the time-varying concentration of radionuclides mobilized in brine, either as dissolved isotopes or as isotopes sorbed to mobile colloids (see Equation ( REF EQ_PA119 \h \* MERGEFORMAT PA.118) and Equation ( REF EQ_PA120 \h \* MERGEFORMAT PA.119)). Two different brines are considered: Generic Weep Brine (GWB), a magnesium-rich interstitial brine present in the Salado Formation; and ERDA-6, a sodium-rich brine in the Castile. Radionuclide solubility in the two brines can be considerably different. Before an E1 intrusion, PA assumes that the brine in the repository is GWB; after an E1 intrusion, brine in the repository is assumed to be ERDA-6.
HYPERLINK \l "Figure_PA-64" REF _Ref201123142 \h \* MERGEFORMAT Figure PA-64 and HYPERLINK \l "Figure_PA-65" REF _Ref201123143 \h \* MERGEFORMAT Figure PA-65 show the concentration of radioactivity mobilized in Salado and Castile brines, respectively, as a function of time for all vectors in Replicate R1 for the CRA2009 PA. Because the inventory is unchanged from the CRA-2004 PABC, the results are identical to the CRA-2004 PABC results. Concentrations are expressed as EPA units/m3 to combine the radioactivity in different isotopes and reduce the computational time required for the transport calculations.
Short-lived radionuclides, such as 238Pu, decay rapidly in the first few years. After this initial decay, the mobilized concentration is dominated by Am ( HYPERLINK "../../references/Others/Garner_Leigh_2005_Analysis_Package_for_PANEL_CRA_2004_PABC_ERMS540572.pdf" Garner and Leigh 2005); the concentration of Am is limited by its solubility until all the inventory of Am is in solution. After all Am is in solution, the total radionuclide concentration generally decreases as the Am decays, until the mobilized concentration becomes dominated by Pu (Garner and Leigh 2005). The
Figure PA- SEQ Figure_PA- \* ARABIC 64. Total Mobilized Concentrations in Salado Brine, Replicate R1, CRA2009PA
Figure PA- SEQ Figure_PA- \* ARABIC 65. Total Mobilized Concentrations in Castile Brine, Replicate R1,CRA-2009 PA
horizontal lines in the figures indicate periods of time when the total radionuclide concentration is limited by the solubility of Am (before about 3,000 years) or Pu (after about 6,000 years). Thus, the uncertainty in total radionuclide concentration is determined by the uncertainty factors used to calculate solubilities for Am and Pu.
Transport through MBs and Shaft
In the disturbed scenarios, of the 300 realizations, only Vectors 53 and 59 in Replicate R1 resulted in transport of radionuclides through the MBs and across the LWB, with a maximum total integrated activity of 3.6נ10(10 EPA units ( HYPERLINK "../../references/Others/Ismail_Garner_2008_Analysis_Package_for_Salado_Transport_Calculations_CRA_2009_ERMS548845.pdf" Ismail and Garner 2008). This is comparable to the CRA-2004 PABC results for maximum integrated activity, which had 2.4נ10(12 EPA units at the boundary ( HYPERLINK "../../references/Others/Lowry_2005_Analysis_Package_for_Salado_Transport_Calculations_CRA_2004_PABC_ERMS541084.pdf" Lowry 2005). The releases through the MBs and across the LWB are insignificant compared to releases from drilling intrusions. In addition, no realization showed transport of radionuclides through the shaft to the Culebra.
Transport to the Culebra
Radionuclide transport to the Culebra via a single intrusion borehole (Disturbed Scenarios S2, S3, S4, and S5) is modeled with the code NUTS ( HYPERLINK \l "PA-4_3" Section REF _Ref204073775 \r \h \* MERGEFORMAT PA-4.3). Transport to the Culebra in the multiple intrusion scenario (S6) is modeled with the code PANEL ( HYPERLINK \l "PA-4_4" Section REF _Ref204073791 \r \h \* MERGEFORMAT PA-4.4). Detailed discussion of the radionuclide transport to the Culebra calculations can be found in Ismail and Garner ( HYPERLINK "../../references/Others/Ismail_Garner_2008_Analysis_Package_for_Salado_Transport_Calculations_CRA_2009_ERMS548845.pdf" 2008).
Single Intrusion Scenarios
HYPERLINK \l "Figure_PA-66" REF _Ref201123244 \h \* MERGEFORMAT Figure PA-66 through HYPERLINK \l "Figure_PA-69" REF _Ref201123256 \h \* MERGEFORMAT Figure PA-69 show cumulative radioactivity transported up the borehole to the Culebra in the single intrusion scenarios. Transport to the Culebra is larger and occurs for more vectors in the S2 and S3 scenarios (E1 intrusions) than in the S4 or S5 scenarios (E2 intrusions). For most vectors that show significant transport, most of the transport occurs over a relatively short period of time immediately after the borehole plugs fail.
When compared to the results of the CRA-2004 PABC, the CRA-2009 PA showed minor differences (see HYPERLINK "../../references/Others/Ismail_Garner_2008_Analysis_Package_for_Salado_Transport_Calculations_CRA_2009_ERMS548845.pdf" \l "page=35"Ismail and Garner [2008, Section 4.2.4]). The primary changes from the CRA-2004 PABC to the CRA-2009 PA that affected the calculations of transport to the Culebra are the correction of the input files ( HYPERLINK "../../references/Others/Ismail_to_Vugrin_et_al_2007_June_11_Errors_in_Input_Files_for_NUTS_ERMS546200.pdf" Ismail 2007b) and the correction of the halite porosity ( HYPERLINK "../../references/Others/Ismail_2007_Revised_Porosity_estimates_ERMS545755.pdf" Ismail 2007a). Neither change significantly affected the results ( HYPERLINK "../../references/Others/Ismail_Garner_2008_Analysis_Package_for_Salado_Transport_Calculations_CRA_2009_ERMS548845.pdf" Ismail and Garner 2008).
Multiple Intrusion Scenario
HYPERLINK "70" REF _Ref201123614 \h \* MERGEFORMAT Figure PA-70 shows total EPA units transported to the Culebra via the borehole in the S6 scenario. Only two vectors show radionuclide transport after the E2 intrusion at 1,000 years; most radionuclide transport occurs immediately following the E1 intrusion at 2,000 years. The results from the CRA-2009 PA are almost identical to the results from the CRA-2004 PABC (see HYPERLINK "../../references/Others/Ismail_Garner_2008_Analysis_Package_for_Salado_Transport_Calculations_CRA_2009_ERMS548845.pdf" \l "page=35"Ismail and Garner [2008, Section 4.3.2]). As the disturbed results from BRAGFLO are similar and the source term for the two calculations are the same, it follows that the radionuclide transport to the Culebra results would be the same ( HYPERLINK "../../references/Others/Ismail_Garner_2008_Analysis_Package_for_Salado_Transport_Calculations_CRA_2009_ERMS548845.pdf" Ismail and Garner 2008).
Figure PA- SEQ Figure_PA- \* ARABIC 66. Cumulative Normalized Release to the Culebra, Scenario S2, CRA-2009 PA
Figure PA- SEQ Figure_PA- \* ARABIC 67. Cumulative Normalized Release to the Culebra, Scenario S3, CRA-2009 PA
Figure PA- SEQ Figure_PA- \* ARABIC 68. Cumulative Normalized Release to the Culebra, Scenario S4, CRA-2009 PA
Figure PA- SEQ Figure_PA- \* ARABIC 69. Cumulative Normalized Release to the Culebra, Scenario S5, CRA-2009 PA
Figure PA- SEQ Figure_PA- \* ARABIC 70. Cumulative Normalized Release to the Culebra, Replicate R1, Scenario S6, CRA-2009 PA
Transport Through the Culebra
Radionuclide transport through the Culebra for a given set of uncertain parameters is calculated with the code SECOTP2D (see HYPERLINK \l "PA-6_7_8" Section REF _Ref201117430 \r \h \* MERGEFORMAT PA-6.7.8). Note that the total release of radionuclides across the LWB at the Culebra for given futures is calculated with the code CCDFGF by convolving the SECOTP2D results with the radionuclide transport to the Culebra calculated by NUTS and PANEL. This section discusses the SECOTP2D results; total releases through the Culebra are presented in HYPERLINK \l "PA-9_4" Section REF _Ref201117852 \r \h \* MERGEFORMAT PA-9.4. As none of the changes implemented for the CRA2009 PA affected the Culebra flow and transport calculations, the results from the CRA2004 PABC Culebra flow and transport calculations were used in the CRA-2009 PA.
Culebra radionuclide transport calculations were performed for three replicates of 100 vectors each for both partial-mining and full-mining scenarios (600 total simulations). Each of the 600 radionuclide transport simulations used a unique flow field computed separately with the code MODFLOW (see HYPERLINK \l "PA-6_7_7" Section REF _Ref201117865 \r \h \* MERGEFORMAT PA-6.7.7 and HYPERLINK "../../references/Others/Lowry_Kanney_2005_Analysis_Report_for_CRA_2004_PABC_Culebra_Flow_ERMS541508.pdf" Lowry and Kanney [2005]). The partial-mining scenario assumes the extraction of all potash reserves outside the LWB, while the full-mining scenario assumes that all potash reserves both inside and outside the LWB are exploited.
In each radionuclide transport simulation, 1 kg of each of four radionuclides (241Am, 234U, 230Th, and 239Pu) are released in the Culebra above the center of the waste panel area. Radionuclide transport of the 230Th daughter product of 234U decay is calculated and tracked as a separate species. In the following discussion, 230Th will refer to the 234U daughter product and 230ThA will refer to that released at the waste panel area.
All SECOTP2D results, regardless of magnitude, are included in the calculation of releases through the Culebra. In practice, most nonzero releases computed by SECOTP2D are vanishingly small and result from numerical dispersion ( HYPERLINK "../../references/Others/Lowry_Kanney_2005_Analysis_Report_for_CRA_2004_PABC_Culebra_Flow_ERMS541508.pdf" Lowry and Kanney 2005). Consequently, the analysis of SECOTP2D results focused on realizations in which at least one billionth (10(9) of the 1-kg source was transported to the LWB.
More detailed information on the results of the Culebra radionuclide transport calculations can be found in the Analysis Package for the Culebra Flow and Transport Calculations: Compliance Recertification Application Performance Assessment Baseline Calculations (Lowry and Kanney 2005).
Partial Mining Results
Under partial-mining conditions, only the 234U species and its 230Th decay product were transported to the LWB in any significant amount during the course of the 10,000-year simulation ( HYPERLINK "../../references/Others/Lowry_Kanney_2005_Analysis_Report_for_CRA_2004_PABC_Culebra_Flow_ERMS541508.pdf" Lowry and Kanney 2005). HYPERLINK \l "Table_PA-30" REF _Ref201128598 \h \* MERGEFORMAT Table PA-30 shows that no releases greater than one billionth of the 1-kg source were calculated for Replicates R1 and R3. For Replicate R2, 3 vectors produced 234U releases greater than 10-9 kg. One of the 3 vectors also resulted in a 230Th release greater than 10-9 kg. These results are identical to the CRA-2004 PABC results.
Table PA- SEQ Table_PA- \* ARABIC 30. Number of Realizations with Radionuclide Transport to the LWB Under Partial-Mining Conditionsa,b
Replicate241Am239Pu234U230Th230ThAR100000R200310R300000a Number of vectors that have releases (transport to LWB) greater than one billionth of the 1-kg source released at center of waste panel.
b 230ThA refers to Th released at the waste panel area. 230Th refers to thorium resulting from 234U decay.
Sensitivity analysis indicates that releases of 234U in the partial-mining condition is associated with the VI oxidation state (Lowry and Kanney 2005; HYPERLINK "../../references/Others/Kanney_2003_Analysis_Report_for_AP_100_Tasks_4_6_ERMS532320.PDF"Kanney 2003). This result is reasonable because the matrix distribution coefficients for U in the IV state are much lower than for the VI state.
Full Mining Results
Under full-mining conditions, only the 234U species and its 230Th decay product were transported to the LWB in any significant amount during the course of the 10,000-year simulation. More vectors resulted in releases greater than 10(9 kg for the full-mining scenario than were seen under partial-mining conditions. In addition, releases greater than 10(9 kg were calculated for all three replicates. HYPERLINK \l "Table_PA-31" REF _Ref201128601 \h \* MERGEFORMAT Table PA-31 shows that 3 vectors in Replicate R1, 6 vectors in Replicate R2, and 3 vectors in Replicate R3 had 234U releases greater than 10(9 kg. None of the 3 vectors in Replicate R1, 3 of the 6 in Replicate R2, and 1 of the 3 in Replicate R3 showed a
Table PA- SEQ Table_PA- \* ARABIC 31. Number of Realizations with Radionuclide Transport to the LWB Under Full-Mining Conditionsa,b
Replicate241Am239Pu234U230Th230ThAR100300R200630R300310a Number of vectors that have releases (transport to LWB) greater than one billionth of the 1-kg source released at center of waste panel.
b 230ThA refers to Th released at the waste panel area. 230Th refers to Th resulting from 234U decay.
release of the 230Th daughter product greater than 10-9 kg. These results are identical to the CRA-2004 PABC results.
Sensitivity analysis indicates that releases of 234U in the full-mining condition is associated with the VI oxidation state ( HYPERLINK "../../references/Others/Lowry_Kanney_2005_Analysis_Report_for_CRA_2004_PABC_Culebra_Flow_ERMS541508.pdf" Lowry and Kanney 2005, HYPERLINK "../../references/Others/Kanney_2003_Analysis_Report_for_AP_100_Tasks_4_6_ERMS532320.PDF"Kanney 2003). This result is reasonable because the matrix distribution coefficients for U in the IV state are much lower than for the VI state.
Direct Releases
Direct releases occur at the time of a drilling intrusion, and include cuttings and cavings, spallings, and DBRs. This section presents an analysis of the volume released by each mechanism.
Ismail ( HYPERLINK "../../references/Others/Ismail_2008_Analysis_Package_for_CUTTINGS_S_Rev1_ERMS548618.pdf" 2008) provides additional information about the cuttings, cavings, and spallings releases calculated for the CRA-2009 PA. Clayton ( HYPERLINK "../../references/Others/Clayton_2008_Analysis_Package_for_Direct_Brine_Releases_ERMS548571.pdf" 2008b) provides a detailed analysis of DBRs in the CRA-2009 PA.
Cuttings and Cavings
Cuttings and cavings are the solid waste material removed from the repository and carried to the surface by the drilling fluid during borehole drilling. Cuttings are the materials removed directly by the drill bit, and cavings are the material eroded from the walls of the borehole by shear stresses from the circulating drill fluid. The volume of cuttings and cavings material removed from a single drilling intrusion into the repository is assumed to be in the shape of a cylinder. The code CUTTINGS_S calculates the area of the base of this cylinder, and cuttings and cavings results in this section are reported in terms of these areas. The volumes of cuttings and cavings removed can be calculated by multiplying these areas with the initial repository height 3.96 m (BLOWOUT:HREPO).
Cuttings and cavings areas calculated for the CRA-2009 PA range between 0.076 m2 and 0.86m2, with a mean area of 0.25 m2 ( HYPERLINK \l "Table_PA-32" REF _Ref201128620 \h \* MERGEFORMAT Table PA-32). None of the changes implemented in the CRA-2009 PA affect the cuttings and cavings calculations, so the results are identical to the CRA-2004 PABC results ( HYPERLINK "../../references/Others/Ismail_2008_Analysis_Package_for_CUTTINGS_S_Rev1_ERMS548618.pdf" Ismail 2008).
Two uncertain sampled parameters affect the cavings calculations. The uncertainty in cavings areas arises primarily from the uncertainty in the shear strength of the waste ( HYPERLINK "../../references/Others/Ismail_2008_Analysis_Package_for_CUTTINGS_S_Rev1_ERMS548618.pdf" Ismail 2008). Lower shear strengths tend to result in larger cavings (HYPERLINK "../../references/Others/Ismail_2008_Analysis_Package_for_CUTTINGS_S_Rev1_ERMS548618.pdf" \l "page=11"Ismail 2008, Figure 1). The uncertainty in the drill string angular velocity has a smaller impact on the cavings results, but the combination of a low angular velocity and high shear strength can prohibit cavings from occurring ( HYPERLINK \l "Figure_PA-71" REF _Ref201123706 \h \* MERGEFORMAT Figure PA-71). In fact, cavings did not occur in 10% of all vectors ( HYPERLINK \l "Table_PA-32" REF _Ref201128620 \h \* MERGEFORMAT Table PA-32).
Figure PA- SEQ Figure_PA- \* ARABIC 71. Scatterplot of Waste Particle Diameter Versus Spallings Volume, CRA2009 PA
Table PA- SEQ Table_PA- \* ARABIC 32. CRA-2009 PA Cuttings and Cavings Area Statistics
ReplicateMinimum (m2)Maximum (m2)Mean (m2)Vectors Without CavingsR10.0760.820.259R20.0760.860.2510R30.0760.830.2511
Spallings
Calculating the volume of solid waste material released to the surface due to spallings from a single drilling intrusion into the repository is a two-part procedure. The code DRSPALL calculates the spallings volumes from a single drilling intrusion at four values of repository pressure (10, 12, 14, and 14.8 MPa). Following this, spallings volumes from a single intrusion are calculated using the code CUTTINGS_S; this code linearly interpolates the spallings volumes calculated using DRSPALL, based on the pressure calculated by BRAGFLO. Results from both of these calculations are documented in this section.
DRSPALL Results
None of the changes implemented in the CRA-2009 PA affect the DRSPALL calculations, so the results from the CRA-2004 PABC were used in the CRA-2009 PA. In the CRA-2004 PABC, the code DRSPALL was run for each of 100 vectors in 3 replicates and for 4 values of repository pressure (10, 12, 14, and 14.8 MPa, see HYPERLINK \l "PA-4_6_4" Section REF _Ref204074072 \r \h \* MERGEFORMAT PA-4.6.4). No spallings occurred at 10 MPa for any vector.
The uncertainty in the spallings volumes arises from four uncertain variables in the DRSPALL calculations: waste permeability, waste porosity, waste tensile strength, and waste particle diameter after tensile failure ( HYPERLINK \l "Table_PA-15" REF _Ref201126771 \h \* MERGEFORMAT Table PA-15). HYPERLINK \l "Figure_PA-72" REF _Ref201123705 \h \* MERGEFORMAT Figure PA-72 indicates that the largest spallings volumes occur when waste permeability is less than 1.0 10(13 m2, but larger permeability values result in a higher frequency of nonzero spallings volumes. This observation can be explained as follows: the higher permeability values sampled result in smaller tensile stresses and less tensile failure, but promote fluidization. Lower permeability leads to greater tensile stresses and tensile failure, but failed material may not be able to fluidize at this low permeability.
Figure PA- SEQ Figure_PA- \* ARABIC 72. Scatterplot of Waste Permeability Versus Spallings Volume, CRA-2009 PA
Smaller particle diameter values (see HYPERLINK \l "Figure_PA-71" REF _Ref201123706 \h \* MERGEFORMAT Figure PA-71) tend to result in larger spallings volumes and a higher frequency of nonzero spallings volumes. The uncertainty in the spallings volumes from a single intrusion is largely determined by the uncertainty in these two parameters. Obvious correlations between spallings volumes and the other two parameters could not be established.
CUTTINGS_S Results
Two factors directly affect the CUTTINGS_S calculation of spallings volumes for the drilling scenarios: the volumes calculated by DRSPALL and the repository pressures calculated by BRAGFLO.
HYPERLINK \l "Table_PA-33" REF _Ref201128647 \h \* MERGEFORMAT Table PA-33 summarizes the statistics for the CRA-2009 PA spallings volumes. Of the 7,800 (26 intrusion time-scenario combinations 3 drilling locations 100 vectors) spallings volumes calculated per replicate, more than 92% of each replicates calculations resulted in no spallings. Only about a third of the vectors in each replicate had spallings occur in at least one of the scenarios; therefore, spallings will not contribute to the total releases calculated for the other vectors.
Table PA- SEQ Table_PA- \* ARABIC 33. CRA-2009 PA Spallings Volume Statistics
Scenario# of CalculationsMaximum Volume(m3)Average Volume(m)Number of Nonzero VolumesR1R2R3R1R2R3R1R2R3S11,8002.522.525.330.100.100.17158177183S21,5008.312.876.320.140.120.12120135122S31,5007.992.133.150.120.100.09129138133S41,5001.672.401.990.040.070.04696456S51,5001.672.203.000.070.090.06919391All7,8008.312.876.320.090.100.10564607585
Scenarios S2 and S3 resulted in the largest maximum spallings volume, while Scenarios S1, S2, and S3 resulted in the largest average spallings volume. For the CRA-2009 PA, Scenarios S2 and S3 have the highest maximum pressures because in these scenarios, the drill bit intrudes into a pressurized brine pocket ( HYPERLINK "../../references/Others/Nemer_Clayton_2008_Analysis_Package_for_Salado_Flow_Modeling_ERMS548607.pdf" Nemer and Clayton 2008). These higher pressures lead to larger spallings volumes. Scenarios S4 and S5 resulted in the lowest maximum and average volumes as, in general, these scenarios have the lowest pressure (see HYPERLINK \l "PA-8_3_1" Section REF _Ref201117964 \r \h \* MERGEFORMAT PA-8.3.1). Scenario S1 resulted in the largest number of nonzero spallings volumes per time intrusion. Without a prior intrusion creating a pathway for brine and gas flow to decrease the pressure, there are more vectors that result in pressures above 10 MPa and, hence, a nonzero spallings volume.
The frequency of nonzero spallings volumes increased for the CRA-2009 PA compared to the CRA-2004 PABC (see HYPERLINK "../../references/Others/Ismail_2008_Analysis_Package_for_CUTTINGS_S_Rev1_ERMS548618.pdf" \l "page=13"Ismail [2008, Table 8]). The maximum spallings volumes are similar between the two analyses, while the CRA-2009 PA average spallings volume increased compared with the CRA-2004 PABC results (see Ismail [2008, Table 8]). As the spallings volumes are calculated from BRAGFLO pressure and an increase in pressure was observed (see HYPERLINK \l "PA-7_1_1" Section REF _Ref201117985 \r \h \* MERGEFORMAT PA-7.1.1 and HYPERLINK \l "PA-8_3_1"Section REF _Ref201117964 \r \h \* MERGEFORMAT PA-8.3.1), an increase in the spallings releases is expected.
DBRs
DBRs to the surface can occur during or shortly after a drilling intrusion. For each element of the Latin hypercube sample, the code BRAGFLO calculates volumes of brine released for a total of 78 combinations of intrusion time, intrusion location, and initial conditions (see HYPERLINK \l "PA-6_7_6" Section REF _Ref204074997 \r \h \* MERGEFORMAT PA-6.7.6). Initial conditions for the DBR calculations are obtained from the BRAGFLO Salado flow model results from Scenarios S1 through S5. Salado flow model results from the S1 scenario ( HYPERLINK \l "PA-7_1" Section REF _Ref112134856 \r \h \* MERGEFORMAT PA-7.1) are used as initial conditions for DBR when modeling a first intrusion into the repository that may have a DBR. Salado flow model results from the S2 through S5 scenarios ( HYPERLINK \l "PA-8_3" Section REF _Ref112152190 \r \h \* MERGEFORMAT PA-8.3) are used as initial conditions for DBR when modeling second or subsequent drilling intrusions that may have a DBR.
Summary statistics of the calculated DBR volumes for Replicate R1 of the CRA-2009 PA are shown in HYPERLINK \l "Table_PA-34" REF _Ref209531102 \h \* MERGEFORMAT Table PA-34. As seen in REF _Ref209531102 \h \* MERGEFORMAT Table PA-34, 1,001 of the 7,800 DBR calculations (100 vectors ( 78 combinations) resulted in a nonzero DBR volume to the surface, the majority of which resulted from Scenarios S2 and S3. The maximum DBR volume is approximately 59 m3, with an average volume of 0.9 m3. Only intrusions into a lower panel (see HYPERLINK "../../references/Others/Clayton_2008_Analysis_Package_for_Direct_Brine_Releases_ERMS548571.pdf" \l "page=22"Clayton [2008b, Section 6.2]) resulted in significant DBR volumes. In the S1 scenario, the lower panel represents an undisturbed panel at the south end of the repository. In the S2 and S3 scenarios, the lower panel represents any panel that has had a previous E1 intrusion; in the S4 and S5 scenarios, the lower panel represents any panel that has had a previous E2 intrusion. DBR volumes are larger and occur more frequently in the S2 and S3 scenarios, because the lower panel has a much higher saturation after an E1 intrusion.
Table PA- SEQ Table_PA- \* ARABIC 34. CRA-2009 PA DBR Volume Statistics
ScenarioMaximum Volume (m3)Average Volume (m3)Number of Nonzero VolumesS1190.1122S2592.9385S3441.5317S4190.170S5210.1107All590.91,001
The frequency of nonzero DBR volumes increased for the CRA-2009 PA compared to the CRA2004 PABC (see HYPERLINK "../../references/Others/Clayton_2008_Analysis_Package_for_Direct_Brine_Releases_ERMS548571.pdf" \l "page=22"Clayton [2008b, Table 6-1]). The maximum DBR volume is lower for the CRA-2009 PA (see Clayton [2008b, Table 6-1]). The CRA-2009 PA average DBR volume increased compared to the CRA-2004 PABC results (see Clayton [ HYPERLINK "../../references/Others/Clayton_2008_Analysis_Package_for_Direct_Brine_Releases_ERMS548571.pdf" \l "page=23" 2008b, Table 6-2, HYPERLINK "../../references/Others/Clayton_2008_Analysis_Package_for_Direct_Brine_Releases_ERMS548571.pdf" \l "page=24" Table 6-3, HYPERLINK "../../references/Others/Clayton_2008_Analysis_Package_for_Direct_Brine_Releases_ERMS548571.pdf" \l "page=25" Table 6-4, and HYPERLINK "../../references/Others/Clayton_2008_Analysis_Package_for_Direct_Brine_Releases_ERMS548571.pdf" \l "page=26" Table 6-5]). The increase in the frequency of nonzero and average DBR volume is due to the porosity correction, while the decrease in the maximum DBR volume is from the reduction in the maximum DBR duration parameter ( HYPERLINK "../../references/Others/Clayton_2008_Analysis_Package_for_Direct_Brine_Releases_ERMS548571.pdf" Clayton 2008b).
Previous sensitivity analyses have determined that a DBR volume from a single intrusion is most sensitive to the initial pressure and brine saturation in the intruded panel. This analysis is repeated below for Scenario S2 in the CRA-2009 PA. The initial pressure and brine saturation in the DBR calculations are transferred from the Salado flow calculations, as described above. Thus, the uncertain parameters that are most influential to the uncertainty in pressure and brine saturation in the Salado flow calculations (see HYPERLINK \l "PA-7_1" Section REF _Ref112134856 \r \h \* MERGEFORMAT PA-7.1 and HYPERLINK \l "PA-8_3" Section REF _Ref112152190 \r \h \* MERGEFORMAT PA-8.3) are also most influential to the uncertainty in DBR volumes.
The combination of relatively high pressure and brine saturation in the intruded panel is required for DBR to the surface. HYPERLINK \l "Figure_PA-73" REF _Ref201123746 \h \* MERGEFORMAT Figure PA-73 shows a scatterplot of pressure in the waste panel versus DBR volumes for scenario S2, lower intrusion, with symbols indicating the value of the mobile brine saturation (defined as brine saturation minus residual brine saturation in the waste). The figure clearly shows that there are no releases until pressures exceed about 8 MPa, as indicated by the vertical line. Above 8 MPa, a significant number of vectors have zero releases, but these vectors have mobile brine saturations less than zero, and thus no brine is available to be released. When mobile brine saturation approaches one, relative permeability of the gas becomes small enough that no gas flows into the well, and in these circumstances, DBR releases end after three days. Thus, in vectors with high mobile brine saturations, DBR releases increase proportionally with increases in pressure, as evidenced by the linear relationship between DBR volume and pressure for mobile brine saturation between 0.8 and 1.0. For vectors with mobile saturations between 0.2 and 0.8, both gas and brine can flow in the well, and the rate of gas flow can be high enough that the ending time of DBR releases may be as long as 4.5 days. Although brine may be flowing at slower rates in these vectors than in vectors with high mobile saturations, brine flow may continue longer and thus result in larger DBR volumes.
Figure PA- SEQ Figure_PA- \* ARABIC 73. Sensitivity of DBR Volumes to Pressure and Mobile Brine Saturation, Replicate R1, Scenario S2, Lower Panel, CRA-2009 PA. (Symbols Indicate the Range of Mobile Brine Saturation Given in the Legend.)
Normalized Releases
The radioactive waste disposal regulations of HYPERLINK "40CFR191_Subpart_B" Part 191, Subparts B and HYPERLINK "40CFR191_Subpart_C" C include containment requirements for radionuclides. The containment requirements of HYPERLINK "40CFR191_13" section 191.13 specify that releases from a disposal system to the accessible environment must not exceed the release limits set forth in HYPERLINK "40CFR191" 40 CFR Part 191, Appendix A, Table 1. As set forth in HYPERLINK "40CFR194_34" section 194.34, the results of PA are required to be expressed as CCDFs of total releases.
This section discusses each of the four categories of releases that constitute the total release: cuttings and cavings, spallings, DBRs, and transport releases, followed by the total normalized releases for the CRA-2009 PA. A comparison between the CRA-2009 PA and the CRA-2004 PABC results is also presented. In summary, despite the changes and corrections made between the CRA-2004 PABC and the CRA-2009 PA, there were no major changes in the overall pattern of releases. Cuttings, cavings, and DBRs remain the most significant pathways for release of radioactive material to the land surface. Release by subsurface transport in the Salado or Culebra continue to make essentially no contribution to total releases. Finally, the resulting CCDFs of total normalized releases for the CRA-2009 PA are within the regulatory limits defined in section 191.13. HYPERLINK \l "PA-9_0" Section REF _Ref201473790 \r \h \* MERGEFORMAT PA-9.0 is taken from Clayton et al. ( HYPERLINK "../../references/Others/Clayton_et_al_2008_Summary_Report_of_CRA_2009_PA_ERMS548862.pdf" \l "page=61" 2008, Section 6.0).
Rank regression analysis was used to evaluate the sensitivity of the normalized releases to the sampled parameters. Scatterplots of the dependent versus independent rank-transformed variables resulting from the sensitivity analysis were examined to determine if there were any obvious nonmonotonic relationships. Obvious nonmonotonic relationships were not found, although there are cases where inputs are categorized as discrete variables (e.g., OXSTAT) and cases where large proportions of the vectors show no release (e.g., CULREL). Application of linear regression to such cases is somewhat problematic with respect to the assumptions of normally distributed residuals and homogeneous variance among the residuals. However, with respect to ranking the relative importance of the parameters, these issues are probably not significant. Details of the analysis can be found in Kirchner ( HYPERLINK "../../references/Others/Kirchner_2008_Sensitivity_of_CRA_2009_PA_Calculation_ERMS548788.pdf" 2008b).
Cuttings and Cavings
The overall mean CCDFs for cuttings and cavings releases from the CRA-2009 PA and the CRA-2004 PABC are shown in HYPERLINK \l "Figure_PA-74" REF _Ref201123767 \h \* MERGEFORMAT Figure PA-74. These resulting overall mean CCDFs are very similar, with only a slight increase in the CRA-2009 PA mean due to the increase in the drilling rate.
The rank regression analysis showed that the uncertainty in waste shear strength (WTAUFAIL in HYPERLINK \l "Table_PA-19" REF _Ref219705647 \h Table PA-19) contributes about 98% of the variability in mean cuttings and cavings releases in both the CRA-2009 PA and CRA-2004 PABC ( HYPERLINK "../../references/Others/Kirchner_2008_Sensitivity_of_CRA_2009_PA_Calculation_ERMS548788.pdf" Kirchner 2008b). Cuttings and caving releases are primarily controlled by the volume of cuttings and cavings produced, which in turn is a highly nonlinear function of the waste shear strength ( HYPERLINK "../../references/Others/Ismail_2008_Analysis_Package_for_CUTTINGS_S_Rev1_ERMS548618.pdf" Ismail 2008).
Figure PA- SEQ Figure_PA- \* ARABIC 74. Overall Mean CCDFs for Cuttings and Cavings Releases: CRA-2009 PA and CRA-2004 PABC
Spallings
HYPERLINK \l "Figure_PA-75" REF _Ref201123782 \h \* MERGEFORMAT Figure PA-75 shows the overall mean spallings release CCDFs from the CRA-2009 PA and the CRA-2004 PABC. This increase in overall mean spallings release values can be directly attributed to an increase in overall mean spallings volumes, with a small increase due to the increase in the drilling rate. The frequency of nonzero spallings volumes calculated by CUTTINGS_S increased. CUTTINGS_S calculates the spallings volume released from a single intrusion for the WIPP PA intrusion scenarios by interpolating the volumes calculated by DRSPALL using the repository pressures calculated by BRAGFLO. These increases are largely attributable to the increase in repository pressure resulting from the larger amounts of brine available ( HYPERLINK "../../references/Others/Ismail_2008_Analysis_Package_for_CUTTINGS_S_Rev1_ERMS548618.pdf" Ismail 2008).
The rank regression analysis indicates that the intact halite porosity (HALPOR in HYPERLINK \l "Table_PA-19" REF _Ref219705647 \h Table PA-19) is the dominant uncertain parameter with regard to the uncertainty in spallings releases in the CRA-2009 PA ( HYPERLINK "../../references/Others/Kirchner_2008_Sensitivity_of_CRA_2009_PA_Calculation_ERMS548788.pdf" Kirchner 2008b). Its higher ranking in the CRA-2009 PA analysis compared to the CRA-2004 PABC analysis is due to the increase in the maximum value of its distribution (Kirchner 2008b). Increases in halite porosity lead to increases in repository pressure (see HYPERLINK \l "PA-7_1_1" Section REF _Ref201118112 \r \h \* MERGEFORMAT PA-7.1.1 and HYPERLINK \l "PA-8_3_1" Section REF _Ref201118116 \r \h \* MERGEFORMAT PA-8.3.1) and thus to increases in spallings releases.
Direct Brine
The overall mean CCDFs for DBRs from the CRA-2009 PA and the CRA-2004 PABC are shown in HYPERLINK \l "Figure_PA-76" REF _Ref201123796 \h \* MERGEFORMAT Figure PA-76. At all probabilities, the CRA-2009 PA mean DBRs increased from the
Figure PA- SEQ Figure_PA- \* ARABIC 75. Overall Mean CCDFs for Spallings Releases: CRA-2009 PA and CRA2004 PABC
Figure PA- SEQ Figure_PA- \* ARABIC 76. Overall Mean CCDFs for DBRs: CRA-2009 PA and CRA-2004 PABC
CRA-2004 PABC values, particularly at higher probabilities. In the CRA-2009 PA, at any level of release, the mean probability that DBRs exceed the release level is increased from the CRA2004 PABC. This increase in the CCDFs for DBRs can be directly attributed to an increase in DBR volumes (HYPERLINK \l "PA-8_5_3"Section REF _Ref204075637 \r \h \* MERGEFORMAT PA-8.5.3), with a small increase due to the increase in the drilling rate ( HYPERLINK "../../references/Others/Clayton_2008_AP137_Analysis_Plan_for_the_Performance_Assessment_for_CRA_2009_ERMS547905.pdf" Clayton 2008a). The frequency of nonzero DBR volumes also increased (Section REF _Ref204075637 \r \h \* MERGEFORMAT PA-8.5.3). The frequency and volume of the DBR are strongly correlated to the repository pressure. These increases are largely attributable to the increase in repository pressure resulting from of the larger amounts of brine available. The increase of the brine in the repository is due to higher intact halite porosities for higher probabilities and drilling rate at lower probabilities ( HYPERLINK "../../references/Others/Clayton_2008_Analysis_Package_for_Direct_Brine_Releases_ERMS548571.pdf" Clayton 2008b).
The rank regression analysis shows that four variables, the solubility multiplier representing solubility uncertainty for all actinides in the III oxidation state (WSOLVAR3 in HYPERLINK \l "Table_PA-19" REF _Ref219705647 \h Table PA-19), the initial brine pore pressure in the Castile (BPINTPRS in REF _Ref219705647 \h Table PA-19), the inundated corrosion rate for steel (WGRCOR in REF _Ref219705647 \h Table PA-19), and the frequency with which Castile brine intrudes the repository as a result of a drilling event (BPPROB in REF _Ref219705647 \h Table PA-19), account for more than 50% of the uncertainty in DBRs for the CRA-2009 PA ( HYPERLINK "../../references/Others/Kirchner_2008_Sensitivity_of_CRA_2009_PA_Calculation_ERMS548788.pdf" Kirchner 2008b). These variables are also important in the CRA-2004 PABC analysis, although the third- and fourth-ranked variables are in reverse order relative to the CRA-2009 PA (Kirchner 2008b).
The solubility of actinides defines the concentration in DBRs. The corrosion of Fe is expected to produce gas, but at the same time it consumes water. When the repository is flooded with brine from the intrusion of a brine pocket, the influence on DBR would likely be positive, because the production of H2 would outweigh the minimal impact of the consumption of water. However, a negative correlation is observed between the ranked variables, suggesting that the corrosion of steel has its strongest influence when the repository is not saturated and DBRs are expected to be small. The frequency with which Castile brine intrudes the repository as a result of a drilling event and the initial pressure of that brine affect the pressure in the repository. As DBR volumes are a strong function of pressure, a positive correlation is expected and shown (Kirchner 2008b).
Groundwater Transport
HYPERLINK \l "Figure_PA-77" REF _Ref201123814 \h \* MERGEFORMAT Figure PA-77 shows the mean CCDFs for normalized releases due to transport through the Culebra for Replicate R2 of the CRA-2009 PA and the CRA-2004 PABC. No transport releases larger than 10-6 EPA units occurred in Replicates R1 and R3. Normalized transport releases for the CRA-2009 PA are qualitatively similar to the CRA-2004 PABC results, in that only one replicate (R2) exhibits releases that are significantly larger than the numerical error inherent in the transport calculations. Overall, the mean releases for Replicate R2 of the two analyses are quite similar and the numbers of vectors that had releases are identical, with only a slight increase in the CRA-2009 PA due to the increase in the drilling rate ( HYPERLINK "../../references/Others/Dunagan_2008_Analysis_Package_for_CCDFGF_CRA_2009_ERMS548776.pdf" Dunagan 2008).
A Culebra release represents the potential release of radioactivity from the Culebra at the LWB over 10,000 years. Analyzing sensitivity of Culebra releases to the input parameters using linear regression is problematic ( HYPERLINK "../../references/Others/Kirchner_2008_Sensitivity_of_CRA_2009_PA_Calculation_ERMS548788.pdf" Kirchner 2008b). In the CRA-2009 PA and the CRA-2004 PABC, ~83% of the vectors had Culebra releases of zero ( HYPERLINK "../../references/Others/Ismail_Garner_2008_Analysis_Package_for_Salado_Transport_Calculations_CRA_2009_ERMS548845.pdf" Ismail and Garner 2008). Releases of zero are found across the entire range of every parameter. This is undoubtedly due, for the most part, to
Figure PA- SEQ Figure_PA- \* ARABIC 77. Mean CCDFs for Releases from the Culebra for Replicate R2: CRA-2009 PA and CRA-2004 PABC
transport rates frequently being too small to enable contaminants to reach the boundary within the 10,000-year simulation period. Thus, the release data are strongly skewed. The times of the intrusions giving rise to flows to the Culebra are also likely to influence whether or not such releases occur. These times are not represented in the sampled input parameters, and thus cannot be associated with the releases. In addition, the preponderance of zero values tends to negate the assumption of linear regression that errors (residuals) are normally distributed. In many cases, it appears that it is the distribution of zeros along the independent axis that determines whether a positive or negative correlation is observed. For example, HYPERLINK \l "Figure_PA-78" REF _Ref201123826 \h \* MERGEFORMAT Figure PA-78 shows the ranks of releases from the Culebra versus the ranks of the parameter CFRACPOR(CULEBRA:APOROS) for Replicate 1. The average rank of the zero values was 42 and was assigned to all cases where no release was observed. Because releases of zero were associated with high values of CFRACPOR, as well as low values, and because there were no nonzero releases for the futures having the highest values of CFRACPOR, the arrangement of the data would lead to a negative correlation. Because of these issues, the linear ranked regression analysis is unlikely to yield a definitive identification of the sensitivity of Culebra releases to the sampled parameters, and most of the variability in Culebra releases remains unexplained by the regression model ( HYPERLINK "../../references/Others/Kirchner_2008_Sensitivity_of_CRA_2009_PA_Calculation_ERMS548788.pdf" Kirchner 2008b).
Total Normalized Releases
Total releases are calculated by totaling the releases from each release pathway: cuttings and cavings releases, spallings releases, DBRs, and transport releases (there were no undisturbed releases to contribute to total release). HYPERLINK \l "Figure_PA-79" REF _Ref201123853 \h \* MERGEFORMAT Figure PA-79 shows the 300 CCDFs for total releases in
Figure PA- SEQ Figure_PA- \* ARABIC 78. The Preponderance and Distribution of Zeros Can Control the Regression
Figure PA- SEQ Figure_PA- \* ARABIC 79. Total Normalized Releases, Replicates R1, R2, and R3, CRA-2009 PA
Replicates R1, R2, and R3 of the CRA-2009 PA. As seen in REF _Ref201123853 \h \* MERGEFORMAT Figure PA-79, all of the CCDFs lie below and to the left of the limits specified in HYPERLINK "40CFR191_13" section 191.13(a).
The overall mean CCDF is computed as the arithmetic mean of the mean CCDFs from each replicate. To quantitatively determine the sufficiency of the sample size, a confidence interval is computed about the overall mean CCDF using the Students t-distribution and the mean CCDFs from each replicate. HYPERLINK \l "Figure_PA-80" REF _Ref201123868 \h \* MERGEFORMAT Figure PA-80 shows 95% confidence intervals about the overall mean. The CCDF and confidences intervals lie below and to the left of the limits specified in 40 CFR 191.13(a). Thus, the WIPP continues to comply with the containment requirements of HYPERLINK "40CFR191" Part 191.
Figure PA- SEQ Figure_PA- \* ARABIC 80. Confidence Interval on Overall Mean CCDF for Total Normalized Releases, CRA-2009 PA
HYPERLINK \l "Figure_PA-81" REF _Ref201123880 \h \* MERGEFORMAT Figure PA-81, HYPERLINK \l "Figure_PA-82" REF _Ref201123881 \h \* MERGEFORMAT Figure PA-82, and HYPERLINK \l "Figure_PA-83" REF _Ref201123883 \h \* MERGEFORMAT Figure PA-83 show the mean CCDFs for each component of total releases for Replicates R1, R2, and R3 of the CRA-2009 PA, respectively. The contributions to total releases for each release pathway in the CRA-2009 PA are the same as those observed in the CRA-2004 PABC ( HYPERLINK "../../references/Others/Dunagan_2008_Analysis_Package_for_CCDFGF_CRA_2009_ERMS548776.pdf" Dunagan 2008).
HYPERLINK \l "Figure_PA-84" REF _Ref201123915 \h \* MERGEFORMAT Figure PA-84 provides a comparison between the CRA-2009 PA and the CRA-2004 PABC. At any level of release, the overall mean probability that total releases exceed the release level is similar between the two analyses. A small increase in the probability is mainly due to the change in the drilling rate parameter (Dunagan 2008).
HYPERLINK \l "Table_PA-35" REF _Ref201128687 \h \* MERGEFORMAT Table PA-35 shows the level of release at the probability of 0.1 and 0.001 from the overall mean CCDF. The CCDF value of the upper and lower 95% confidence levels on the mean CCDF at
Figure PA- SEQ Figure_PA- \* ARABIC 81. Mean CCDFs for Components of Total Normalized Releases, Replicate R1, CRA-2009 PA
Figure PA- SEQ Figure_PA- \* ARABIC 82. Mean CCDFs for Components of Total Normalized Releases, Replicate R2, CRA-2009 PA
Figure PA- SEQ Figure_PA- \* ARABIC 83. Mean CCDFs for Components of Total Normalized Releases, Replicate R3, CRA-2009 PA
Figure PA- SEQ Figure_PA- \* ARABIC 84. Overall Mean CCDFs for Total Normalized Releases: CRA-2009 PA and CRA-2004 PABC
Table PA- SEQ Table_PA- \* ARABIC 35. CRA-2009 PA and CRA-2004 PABCa Statistics on the Overall Mean for Total Normalized Releases in EPA Units at Probabilities of 0.1 and 0.001
ProbabilityAnalysisMean TotalReleaseLower 95% CLUpper 95% CLRelease Limit0.1CRA-2004 PABC0.090.080.091CRA-2009 PA0.100.100.1110.001CRA-2004 PABC0.600.520.6810CRA-2009 PA0.720.480.9210a CRA-2004 PABC data was initially reported in Vugrin and Dunagan (HYPERLINK "../../references/Others/Vugrin_Dunagan_2005_Analysis_Package_for_CCDFGF_CRA2004_PABC_ERMS540771.pdf"2005).
the 0.1 and 0.001 probability, along with the release limit, are also included. The overall mean total release CCDFs differ by ~0.01 EPA units at a probability of 0.1 and by ~0.1 EPA units at a probability of 0.001 ( REF _Ref201128687 \h \* MERGEFORMAT Table PA-35). These increases in the total releases primarily result from the increase in the drilling rate parameter.
There are some definite similarities between the CCDFs for the two analyses. First, for most probabilities, cuttings and cavings are the most significant pathways for release of radioactive material to the land surface. Second, release by spallings and subsurface transport in the Salado or Culebra make essentially no contribution to total releases. Finally, the resulting CCDFs of both analyses are within regulatory limits.
As in the CRA-2004 PABC, cuttings, cavings, and DBRs account for the majority of the total releases estimated in the CRA-2009 PA. As indicated in the rank regression analysis, in both the CRA-2009 PA and the CRA-2004 PABC, the uncertainty in waste shear strength (WTAUFAIL in HYPERLINK \l "Table_PA-19" REF _Ref219705647 \h Table PA-19) contributes to a large portion of the uncertainty in total normalized releases ( HYPERLINK "../../references/Others/Kirchner_2008_Sensitivity_of_CRA_2009_PA_Calculation_ERMS548788.pdf" Kirchner 2008b). The volumes of cuttings and cavings are primarily controlled by shear strength (Kirchner 2008b). The solubility multiplier, which represents uncertainty in solubilities for all actinides in the III oxidation state (WSOLVAR3 in REF _Ref219705647 \h Table PA-19), remained the second-most dominant parameter contributing to variability in total releases in all replicates (Kirchner 2008b). Solubility of actinides defines the concentration in DBRs. The variability in total releases explained by the waste shear strength in the CRA-2009 PA dropped from previous levels. The waste shear strength only accounts for about 81% of the total variability in total releases in the CRA-2009 PA, whereas in the CRA-2004 PABC it accounted for 88% of the variability (Kirchner 2008b). This decrease is due to the relative increase in the DBR contribution to total releases.
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