Title 40 CFR Part 191
Subparts B and C
Compliance Recertification Application 2014 for the
Waste Isolation Pilot Plant
Appendix PA2014
Performance Assessment
United States Department of Energy
Waste Isolation Pilot Plant
Carlsbad Field Office
Carlsbad, New Mexico
Compliance Recertification Application 2014
Appendix PA
PA1.1 Changes since the CRA2009 PA
PA1.1.1 Replacement of Option D with the ROMPCS
PA1.1.2 Additional Mined Volume in the Repository North End
PA1.1.3 Refinement to the Probability of Encountering Pressurized Brine
PA1.1.4 Refinement to the Corrosion Rate of Steel
PA1.1.5 Refinement to the Effective Shear Strength of WIPP Waste
PA1.1.6 Waste Inventory Update
PA1.1.7 Updated Drilling Rate and Plugging Pattern Parameters
PA1.1.8 Refinement to Repository Water Balance
PA1.1.9 Variable Brine Volume
PA1.1.10 Updated Radionuclide Solubilities and Uncertainty
PA1.1.11 Updated Colloid Parameters
PA2.0 Overview and Conceptual Structure of the PA
PA2.1 Overview of Performance Assessment
PA2.1.1 Undisturbed Repository Mechanics
PA2.1.2 Disturbed Repository Mechanics
PA2.1.2.1 Cuttings and Cavings
PA2.1.2.4 Mobilization of Actinides in Repository Brine
PA2.1.2.5 LongTerm Brine Flow up an Intrusion Borehole
PA2.1.2.6 Groundwater Flow in the Culebra
PA2.1.2.7 Actinide Transport in the Culebra
PA2.1.2.8 Intrusion Scenarios
PA2.1.3 Compliance Demonstration Method
PA2.2 Conceptual Structure of the PA
PA2.2.1 Regulatory Requirements
PA2.2.2 Probabilistic Characterization of Different Futures
PA2.2.3 Estimation of Releases
PA2.2.4 Probabilistic Characterization of Parameter Uncertainty
PA2.3.1 Identification and Screening of FEPs
PA2.3.2 Scenario Development and Selection
PA2.3.2.1 Undisturbed Repository Performance
PA2.3.2.2 Disturbed Repository Performance
PA2.3.2.2.1 Disturbed Repository M Scenario
PA2.3.2.2.2 Disturbed Repository E Scenario
PA2.3.2.2.5 The E1E2 Scenario
PA2.3.2.3 Disturbed Repository ME Scenario
PA2.3.2.4 Scenarios Retained for Consequence Analysis
PA2.3.3 Calculation of Scenario Consequences
PA3.0 Probabilistic Characterization of Futures
PA3.4 Penetration of Excavated/Nonexcavated Area
PA3.6 Penetration of Pressurized Brine
PA3.10 Scenarios and Scenario Probabilities
PA4.1 Results for Specific Futures
PA4.2 TwoPhase Flow: BRAGFLO
PA4.2.1 Mathematical Description
PA4.2.3 Creep Closure of Repository
PA4.2.4 Fracturing of MBs and DRZ
PA4.2.5 Gas Generation and Brine Production
PA4.2.6 Capillary Action in the Waste
PA4.2.10 Castile Brine Reservoir
PA4.2.12 Gas and Brine Flow across Specified Boundaries
PA4.2.13 Additional Information
PA4.3 Radionuclide Transport in the Salado: NUTS
PA4.3.1 Mathematical Description
PA4.3.2 Radionuclides Transported
PA4.3.3 NUTS Tracer Calculations
PA4.3.4 NUTS Transport Calculations
PA4.3.6 Additional Information
PA4.4 Radionuclide Transport in the Salado: PANEL
PA4.4.1 Mathematical Description
PA4.4.4 Additional Information
PA4.5 Cuttings and Cavings to Surface: CUTTINGS_S
PA4.5.2.2 Turbulent Flow Model
PA4.5.3 Additional Information
PA4.6 Spallings to Surface: DRSPALL and CUTTINGS_S
PA4.6.1 Summary of Assumptions
PA4.6.2.1 Wellbore Flow Model
PA4.6.2.1.1 Wellbore Initial Conditions
PA4.6.2.1.2 Wellbore Boundary Conditions
PA4.6.2.2 Repository Flow Model
PA4.6.2.3 Wellbore to Repository Coupling
PA4.6.2.3.1 Flow Prior to Penetration
PA4.6.2.3.2 Flow After Penetration
PA4.6.2.3.3 Cavity Volume After Penetration
PA4.6.2.3.5 Waste Fluidization
PA4.6.3.1 Numerical MethodWellbore
PA4.6.3.2 Numerical MethodRepository
PA4.6.3.3 Numerical MethodWellbore to Repository Coupling
PA4.6.4 Implementation in the PA
PA4.6.5 Additional Information
PA4.7 DBR to Surface: BRAGFLO
PA4.7.1 Overview of Conceptual Model
PA4.7.2 Linkage to TwoPhase Flow Calculation
PA4.7.3 Conceptual Representation for Flow Rate rDBR(t)
PA4.7.4 Determination of Productivity Index Jp
PA4.7.5 Determination of Waste Panel Pressure pw(t) and DBR
PA4.7.6 Boundary Value Pressure pwf
PA4.7.7 Boundary Value Pressure pwE1
PA4.7.7.1 Solution for Open Borehole
PA4.7.7.2 Solution for SandFilled Borehole
PA4.7.10 Additional Information
PA4.8 Groundwater Flow in the Culebra Dolomite
PA4.8.1 Mathematical Description
PA4.8.2 Implementation in the PA
PA4.8.3 Computational Grids and Boundary Value Conditions
PA4.8.5 Additional Information
PA4.9 Radionuclide Transport in the Culebra Dolomite
PA4.9.1 Mathematical Description
PA4.9.1.1 Advective Transport in Fractures
PA4.9.1.2 Diffusive Transport in the Matrix
PA4.9.1.3 Coupling Between Fracture and Matrix Equations
PA4.9.1.5 Cumulative Releases
PA4.9.2.1 Discretization of Fracture Domain
PA4.9.2.2 Discretization of Matrix Equation
PA4.9.2.3 FractureMatrix Coupling
PA4.9.2.4 Cumulative Releases
PA4.9.3 Additional Information
PA5.0 Probabilistic Characterization of Subjective Uncertainty
PA5.2 Variables Included for Subjective Uncertainty
PA5.3 Separation of Aleatory and Epistemic Uncertainty
PA6.0 Computational Procedures
PA6.2 Sample Size for Incorporation of Subjective Uncertainty
PA6.3 Statistical Confidence on Mean CCDF
PA6.4 Generation of Latin Hypercube Samples
PA6.5 Generation of Individual Futures
PA6.7 Mechanistic Calculations
PA6.7.5 CUTTINGS_S Calculations
PA6.7.6 BRAGFLO Calculations for DBR Volumes
PA6.7.8 SECOTP2D Calculations
PA6.8 Computation of Releases
PA6.8.2.1 Construction of Cuttings and Cavings Releases
PA6.8.2.2 Construction of Spallings Releases
PA6.8.2.3 Construction of DBRs
PA6.8.3 Radionuclide Transport Through the Culebra
PA6.8.4 Determining Initial Conditions for Direct and Transport Releases
PA6.8.4.1 Determining Repository and Panel Conditions
PA6.8.4.2 Determining Distance from Previous Intrusions
PA6.9.3 Stepwise Regression Analysis
PA7.0 Results for the Undisturbed Repository
PA8.0 Results for a Disturbed Repository
PA8.3.1 Salado Flow Results for E1 Intrusion Scenarios
PA8.3.2 Salado Flow Results for E2 Intrusion Scenarios
PA8.3.3 Salado Flow Results for the Multiple Intrusion Scenario
PA8.4.1 Radionuclide Mobilized Concentrations
PA8.4.2 Transport through MBs and Shaft
PA8.4.3 Transport to the Culebra
PA8.4.4 Transport through the Culebra
Figure PA 1. Computational Models Used in PA
Figure PA 2. Construction of the CCDF Specified in 40 CFR Part 191 Subpart B
Figure PA 3. Distribution of CCDFs Resulting from Possible Values for the Sampled Parameters
Figure PA 4. Logic Diagram for Scenario Analysis
Figure PA 5. Conceptual Release Pathways for the UP Scenario
Figure PA 6. Conceptual Release Pathways for the Disturbed Repository M Scenario
Figure PA 7. Conceptual Release Pathways for the Disturbed Repository Deep Drilling E2 Scenario
Figure PA 8. Conceptual Release Pathways for the Disturbed Repository Deep Drilling E1 Scenario
Figure PA 9. Conceptual Release Pathways for the Disturbed Repository Deep Drilling E1E2 Scenario
Figure PA 10. CDF for Time Between Drilling Intrusions
Figure PA 11. Discretized Locations for Drilling Intrusions
Figure PA 12. Computational Grid Used in BRAGFLO for PA
Figure PA 13. Definition of Element Depth in BRAGFLO Grid
Figure PA 14. BRAGFLO Grid Cell Indices
Figure PA 16. Schematic Diagram of the ROMPCS
Figure PA 17. Selecting Radionuclides for the Release Pathways Conceptualized by PA
Figure PA 18. Detail of Rotary Drill String Adjacent to Drill Bit
Figure PA 19. Schematic Diagram of the Flow Geometry Prior to Repository Penetration
Figure PA 20. Schematic Diagram of the Flow Geometry After Repository Penetration
Figure PA 21. Effective Wellbore Flow Geometry Before Bit Penetration
Figure PA 22. Effective Wellbore Flow Geometry After Bit Penetration
Figure PA 23. FiniteDifference Zoning for Wellbore
Figure PA 24. DBR Grid Used in PA
Figure PA 25. Assignment of Initial Conditions for DBR Calculation
Figure PA 26. Borehole Representation Used for PoettmannCarpenter Correlation
Figure PA 27. Areas of Potash Mining in the McNutt Potash Zone
Figure PA 29. FiniteDifference Grid Showing Cell Index Numbering Convention Used by MODFLOW
Figure PA 30. ParallelPlate, DualPorosity Conceptualization
Figure PA 31. Schematic of FiniteVolume Staggered Mesh Showing Internal and Ghost Cells
Figure PA 32. Illustration of Stretched Grid Used for Matrix Domain Discretization
Figure PA 33. Logic Diagram for Determining the Intrusion Type
Figure PA 34. Processing of Input Data to Produce CCDFs
Figure PA 35. Horsetail Plot of Waste Panel Pressure, Scenario S1BF, CRA2014 PA
Figure PA 36. Overall Means of Waste Panel Pressure, Scenario S1BF
Figure PA 37. Horsetail Plot of SRoR Pressure, Scenario S1BF, CRA2014 PA
Figure PA 38. Overall Means of SRoR Pressure, Scenario S1BF
Figure PA 39. Horsetail Plot of NRoR Pressure, Scenario S1BF, CRA2014 PA
Figure PA 40. Overall Means of NRoR Pressure, Scenario S1BF
Figure PA 41. Horsetail Plot of Waste Panel Brine Saturation, Scenario S1BF, CRA2014 PA
Figure PA 42. Overall Means of Waste Panel Brine Saturation, Scenario S1BF
Figure PA 43. Horsetail Plot of SRoR Brine Saturation, Scenario S1BF, CRA2014 PA
Figure PA 44. Overall Means of SRoR Brine Saturation, Scenario S1BF
Figure PA 45. Horsetail Plot of NRoR Brine Saturation, Scenario S1BF, CRA2014 PA
Figure PA 46. Overall Means of NRoR Brine Saturation, Scenario S1BF
Figure PA 47. Horsetail Plot of Brine Flow up the Shaft, Scenario S1BF, CRA2014 PA
Figure PA 48. Overall Means of Brine Flow up the Shaft, Scenario S1BF
Figure PA 50. Horsetail Plot of Waste Panel Pressure in the CRA2014 PA, Scenario S2BF
Figure PA 51. Overall Means of Waste Panel Pressure, Scenario S2BF
Figure PA 52. Horsetail Plot of Waste Panel Brine Saturation in the CRA2014 PA, Scenario S2BF
Figure PA 53. Overall Means of Waste Panel Brine Saturation, Scenario S2BF
Figure PA 55. Overall Means of Brine Flow up the Borehole, Scenario S2BF
Figure PA 56. Horsetail Plot of Waste Panel Pressure in the CRA2014 PA, Scenario S4BF
Figure PA 57. Overall Means of Waste Panel Pressure, Scenario S4BF
Figure PA 58. Horsetail Plot of Waste Panel Brine Saturation in the CRA2014 PA, Scenario S4BF
Figure PA 59. Overall Means of Waste Panel Brine Saturation, Scenario S4BF
Figure PA 61. Overall Means of Brine Flow up the Borehole, Scenario S4BF
Figure PA 63. Overall Means of Brine Flow up the Borehole, Scenario S6BF
Figure PA 64. CRA2014 PA Total Mobilized Concentrations in Salado Brine, Replicate 1, BV1
Figure PA 65. CRA2014 PA Total Mobilized Concentrations in Salado Brine, Replicate 1, BV5
Figure PA 66. CRA2014 PA Total Mobilized Concentrations in Castile Brine, Replicate 1, BV1
Figure PA 67. CRA2014 PA Total Mobilized Concentrations in Castile Brine, Replicate 1, BV5
Figure PA 68. CRA2014 PA Cumulative Transport Release to the Culebra, Scenario S2BF
Figure PA 69. CRA2014 PA Cumulative Transport Release to the Culebra, Scenario S3BF
Figure PA 70. CRA2014 PA Cumulative Transport Release to the Culebra, Scenario S4BF
Figure PA 71. CRA2014 PA Cumulative Transport Release to the Culebra, Scenario S5BF
Figure PA 72. CRA2014 PA Cumulative Transport Release to the Culebra, Scenario S6BF
Figure PA 73. Scatterplot of Waste Permeability Versus Spallings Volume, CRA2014 PA
Figure PA 74. Scatterplot of Waste Particle Diameter Versus Spallings Volume, CRA2014 PA
Figure PA 76. Overall Mean CCDFs for Cuttings and Cavings Releases: CRA2014 PA and CRA2009 PABC
Figure PA 77. Overall Mean CCDFs for Spallings Releases: CRA2014 PA and CRA 2009 PABC
Figure PA 78. Overall Mean CCDFs for DBRs: CRA2014 PA and CRA2009 PABC
Figure PA 79. Mean CCDFs for Releases from the Culebra: CRA2014 PA and CRA2009 PABC
Figure PA 80. Total Normalized Releases, Replicates R1, R2, and R3, CRA2014 PA
Figure PA 81. Confidence Interval on Overall Mean CCDF for Total Normalized Releases, CRA2014 PA
Figure PA 82. Comparison of Overall Means for Release Componenets of the CRA2014 PA
Figure PA 83. CRA2014 PA and CRA2009 PABC Overall Mean CCDFs for Total Normalized Releases
Table PA 1. Changes since the CRA2009 PA Incorporated in the CRA2014 PA
Table PA 2. Release Limits for the Containment Requirements (U.S. EPA 1985, Appendix A, Table 1)
Table PA 3. Parameter Values Used in Representation of TwoPhase Flow
Table PA3. Parameter Values Used in Representation of TwoPhase Flow (Continued)
Table PA3. Parameter Values Used in Representation of TwoPhase Flow (Continued)
Table PA3. Parameter Values Used in Representation of TwoPhase Flow (Continued)
Table PA 4. Models for Relative Permeability and Capillary Pressure in TwoPhase Flow
Table PA 5. Initial Conditions in the Rustler
Table PA 7. Permeabilities for Drilling Intrusions Through the Repository
Table PA 8. Boundary Value Conditions for P g and P b
Table PA 9. Auxiliary Dirichlet Conditions for S g and P b
Table PA 10. Initial and Boundary Conditions for C bl(x, y, t) and C sl(x, y, t)
Table PA 11. Uncertain Parameters in the DRSPALL Calculations
Table PA 12. Initial DRZ Porosity in the DBR Calculation
Table PA 13. Boundary Conditions for p b and S g in DBR Calculations
Table PA 14. Radionuclide Culebra Transport Diffusion Coefficients
Table PA 15. Sampled Parameters Added Since the CRA2009 PA
Table PA 16. Sampled Parameters Removed Since the CRA2009 PA
Table PA 17. Variables Representing Epistemic Uncertainty in the CRA2014 PA
Table PA17. Variables Representing Epistemic Uncertainty in the CRA2014 PA (Continued)
Table PA 19. Algorithm to Generate a Single Future
Table PA 20. BRAGFLO Scenarios in the CRA2014 PA
Table PA 21. NUTS Release Calculations in the CRA2014 PA
Table PA 22. CUTTINGS_S Release Calculations in the CRA2014 PA
Table PA 23. MODFLOW Scenarios in the CRA2014 PA
Table PA 24. SECOTP2D Scenarios in the CRA2014 PA
Table PA 25. Number of Realizations with Radionuclide Transport to the LWB
Table PA 26. CRA2014 PA Cavings Area Statistics
Table PA 27. CRA2014 PA Spallings Volume Statistics
% percent
AIC active institutional control
C Celsius
CCA Compliance Certification Application
CCDF complementary cumulative distribution function
CDF cumulative distribution function
CFR Code of Federal Regulations
CHTRU contacthandled 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 FractureMatrix Transport
FVW fraction of excavated repository volume occupied by waste
gal gallon
GWB Generic Weep Brine
in inch
J Joule
K Kelvin
K_{d} distribution coefficient
kg kilogram
km kilometer
km^{2} square kilometers
L liter
LHS Latin hypercube sampling
LWB Land Withdrawal Boundary
M mining scenario
m meter
m^{2} square meters
m^{3} cubic meters
MB marker bed
ME mining and drilling scenario
mol mole
MPa megapascal
MTHM metric tons of heavy metal
MWd megawattdays
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
RHTRU remotehandled transuranic
RKS RedlichKwongSoave
RoR Rest of Repository
ROM runofmine
s second
s^{2} seconds squared
SCF/d standard cubic feet per day
SMC Salado Mass Concrete
SNL Sandia National Laboratories
SRC standardized regression coefficient
Tfield transmissivity field
TRU transuranic
TVD Total Variation Diminishing
UP undisturbed repository performance
WIPP Waste Isolation Pilot Plant
yr year
Al aluminum
Am americium
C carbon
C_{6}H_{10}O_{5} generic formula for CPR
Ca calcium
CH_{4} methane
Cm curium
CO_{2} carbon dioxide
Cr chromium
Cs cesium
Fe iron
H_{2} hydrogen gas
H_{2}O water
H_{2}S hydrogen sulfide
I iodine
Mg magnesium
Mg(OH)_{2} brucite
Mg_{5}(CO_{3})_{4}(OH)_{2} ×4H_{2}O hydromagnesite (5424)
MgO magnesium oxide, or periclase
Mn manganese
Ni nickel
NO_{3} ^{} nitrate
Np neptunium
Pb lead
Pm promethium
Pu plutonium
Ra radium
Sn tin
SO_{4} sulfate
SO_{4} ^{2} sulfate ion
Sr strontium
Tc technetium
Th thorium
U uranium
V vanadium
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 2014 Compliance Recertification Application (CRA2014) 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 (section 191.12 [U.S. EPA 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 section 191.13 require this probabilistic methodology.
This appendix is organized as follows: Section PA1.1 summarizes changes made to the WIPP PA since the CRA2009 PA (Clayton et al. 2008). Section PA2.0 gives an overview and describes the overall conceptual structure of the CRA2014 PA. The WIPP PA is designed to address the requirements of section 191.13, and thus involves three basic entities: (1) 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, (2) a probabilistic characterization of the uncertainty in the models and parameters that underlay the WIPP PA (to account for epistemic uncertainty), and (3) a probabilistic characterization of different futures that could occur at the WIPP site over the next 10,000 years (to account for aleatory uncertainty). Section PA1.1 is supplemented by Appendix SCR2014, which documents the results of the screening process for features, events, and processes (FEPs) that are retained in the conceptual models of repository performance, including those FEPs which have been modified since CRA2009.
Section PA3.0 describes the probabilistic characterization of different futures and summarizes the stochastic variables that represent future drilling and mining events in the PA. 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 PA4.0 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 section 194.23, and permit the construction of the CCDF specified in section 191.13. Models presented in Section PA4.0 include twophase (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 PA4.0 is supplemented by Appendices MASS2014, TFIELD2014, and PORSURF2014. Appendix MASS2014 discusses the modeling assumptions used in the WIPP PA. Appendix TFIELD2014 discusses the generation of the transmissivity fields (Tfields) used to model groundwater flow in the Culebra. Appendix PORSURF2014 presents results from modeling the effects of excavated region closure, waste consolidation, and gas generation in the repository.
Section PA5.0 discusses the probabilistic characterization of parameter uncertainty, and summarizes the uncertain variables incorporated into the CRA2014 PA, the distributions assigned to these variables, and the correlations between variables. Section PA5.0 is supplemented by Kicker and Herrick (Kicker and Herrick 2013) and Appendix SOTERM2014. Kicker and Herrick (Kicker and Herrick 2013) catalogs the full set of parameters used in the CRA2014 PA. Appendix SOTERM2014 describes the actinide source term for the WIPP performance calculations, including the mobile concentrations of actinides that may be released from the repository in brine.
Section PA6.0 summarizes the computational procedures used in the CRA2014 PA, including sampling techniques, sample size, statistical confidence for mean CCDF, generation of sample, generation of individual futures, construction of CCDFs, calculations performed with the models discussed in Section PA4.0, construction of releases for each future, and the sensitivity analysis techniques in use.
Section PA7.0 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 40 CFR Part 191 (section 194.51 and section 194.52).
Section PA8.0 presents PA results for a disturbed repository. As discussed in Section PA2.3.1, 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 longterm releases via radionuclide transport up abandoned boreholes to the Culebra and thence to the LWB.
Section PA9.0 presents the set of CCDFs resulting from the CRA2014 PA. This material supports Section 194.34 of CRA2014, which demonstrates compliance with the containment requirements of section 191.13. Section PA9.0 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 results of the PA for CRA2014, as documented in Section PA7.0, Section PA8.0, and Section PA9.0, confirm that direct releases from drilling intrusions are the major contributors to radionuclide releases to the accessible environment. In addition, the CRA2014 PA results demonstrate that the WIPP continues to comply with the quantitative containment requirements in section 191.13(a).
The overall structure of Appendix PA2014 is identical with that of the Appendix PA2009 (U.S. DOE 2009). This appendix follows the approach used by Helton et al. (1998) to document the mathematical models used in the Compliance Certification Application (CCA) PA and the results of that analysis. Much of the content of this appendix derives from Helton et al. (1998); these authors' contributions are gratefully acknowledged.
As part of its review of the CRA2009 (U.S. DOE 2009), the U.S. Environmental Protection Agency (EPA) requested changes to the CRA2009 PA (Cotsworth 2009) including updates to the repository waste inventory, actinide solubilities, Culebra transmissivity fields, drilling parameters, and matrix partition coefficients. These changes were incorporated into the CRA2009 Performance Assessment Baseline Calculation (CRA2009 PABC) (Clayton et al. 2010). Repository performance with these requested changes was subsequently assessed by the EPA, and the WIPP was recertified in 2010 (U.S. EPA 2010a). The CRA2009 PABC is the current regulatory baseline for the WIPP. The U.S. Department of Energy (DOE) continues to use the same PA methodology as in the CCA and the CRA2009 PABC because changes that have been made since the EPA first certified the WIPP in 1998 do not impact PA methodology. A detailed presentation for the CCA PA methodology is provided in (Helton et al. (1998), Section 2).
In addition to including applicable changes from CRA2009 incorporated in the CRA2009 PABC, the CRA2014 PA is updated based on new information since the CRA2009 PABC. Information on the implementation of these updates is contained in Camphouse et al. (Camphouse et al.2013). Changes included in the CRA2014 PA relative to the CRA2009 PA are summarized in Table PA1. Culebra transmissivity fields and matrix partition coefficients were updated as part of the CRA2009 PABC; these updates are carried forward to the CRA2014 PA. Updates to Culebra transmissivity fields (Tfields) and matrix partition coefficients are included in Table PA1 for the sake of completeness as they are changes made since the CRA2009 PA. Other changes between the CRA2009 PA and the CRA2009 PABC have been superseded by new information since the CRA2009 PABC. The random seeds used in the CRA2009 PABC are also used in the CRA2014 PA. Use of the CRA2009 PABC random seeds (and parameter ordering as applicable) results in identical sampled values for sampled parameters that are common to the CRA2009 PABC and the CRA2014 PA.
This section ends with motivations for and brief descriptions of each of the updates developed for and included in the CRA2014 PA.
Table PA 1. Changes since the CRA2009 PA Incorporated in the CRA2014 PA
WIPP Project Change 
Summary of Change and CrossReference 
Culebra Transmissivity Fields (Carried over from CRA2009 PABC) 
Culebra transmissivity fields are updated based on revised hydrogeologic factors for the Culebra (Appendix HYDRO2014, Attachment TFIELD2014). 
Updated Culebra Matrix Partition Coefficients (Carried over from CRA2009 PABC) 
Updated to account for higher organic ligand concentrations in the WIPP waste inventory (Clayton 2009). 
Panel Closure Design 
The Option D panel closure system (PCS) design is replaced with the runofmine panel closure system (ROMPCS) design (see Sections PA1.1.1 and PA4.2.8). 
Added Volume in the Repository Experimental Region 
A volume of 60,335 cubic meters (m^{3}) is added to the volume of the WIPP experimental region for Salt Disposal Investigation experiments (see Section PA1.1.2). 
Probability of Encountering Pressurized Brine during a Drilling Intrusion 
A revised distribution is used for WIPP PA parameter GLOBAL:PBRINE (see Section PA1.1.3). 
Refinement to Steel Corrosion Rate 
A revised distribution is used for WIPP PA parameter STEEL:CORRMCO2 (see Section PA1.1.4). 
Updated Waste Shear Strength 
A revised distribution is used for WIPP PA parameter BOREHOLE:TAUFAIL (see Section PA1.1.5). 
Updated Waste Inventory Information 
Inventory parameters in the CRA2014 PA are updated to reflect information collected through December 31, 2011 (see Section PA1.1.6). 
Drilling Rate 
The drilling rate increased from 59.8 to 67.3 boreholes per square kilometer (km^{2}) over 10,000 years (see Section PA1.1.7). Borehole plugging pattern probabilities are also updated. 
Refined Water Balance Implementation 
The repository water balance implementation is refined to include the major gas and brine producing and consuming reactions in the existing conceptual model (see Sections PA1.1.8 and PA4.2.5). 
Variable Brine Volume 
Radionuclide concentrations in brine are dependent on the volume of brine in the repository at the time of intrusion (see Section PA1.1.9). 
Radionuclide Solubilities and their Uncertainty 
Radionuclide baseline solubilities are updated to reflect the organic ligand content in the CRA2014 PA waste inventory, and are calculated for several brine volumes. Solubility uncertainties are updated based on recently available results in published literature (see Section PA1.1.10 and SOTERM2014, Section 5.0 ). 
Updated Colloid Parameters 
Colloid parameters in the CRA2014 are updated to reflect data presented in Reed et al. (Reed et al. 2013) (see section PA 1.1.11). 
The CRA2014 PA is comprised of four individual cases, with a subset of the changes listed in Table PA1 incorporated into the first three. This was done in order to evaluate the effects of various individual, and combined, changes. The fourth case includes all changes listed in Table PA1. A thorough description of the four cases, and the changes included in them, is given in Camphouse (Camphouse 2013d). CRA2014 PA results included in this appendix correspond to the fourth case where all changes listed in Table PA1 are included in the PA. Results from each of the individual cases can be found in the appropriate individual CRA2014 PA analysis packages. Citations for this additional documentation are included in the references section of this appendix, and are indicated in the list below.
· Unit Loading Calculation (Kicker and Zeitler 2013a)
· Inventory Screening Analysis (Kicker and Zeitler 2013b)
· Parameter Sampling (Kirchner 2013a)
· Salado Flow (Camphouse 2013c)
· Direct Brine Release Volumes (Malama 2013)
· Cuttings, Cavings, and Spallings (Kicker 2013)
· Radionuclide Transport (Kim 2013a)
· Actinide Mobilization (Kim 2013b)
· CCDF Normalized Releases (Zeitler 2013)
· Run Control (Long 2013)
The WIPP waste panel closures comprise a feature of the repository that has been represented in the WIPP PA regulatory compliance demonstration since the CCA (U.S. DOE 1996). The 1998 rulemaking that certified the WIPP to receive transuranic (TRU) waste required the DOE to implement the Option D PCS at the WIPP. Following the selection of the Option D panel closure design in 1998, the DOE has reassessed the engineering of the panel closure and established a revised design which is simpler, cheaper, easier to construct, and equally effective at performing its operational period isolating function. The DOE has submitted a planned change request to the EPA requesting that EPA modify Condition 1 of the Final Certification Rulemaking for 40 CFR Part 194 (U.S. EPA 1998a) for the WIPP, and that a revised panel closure design be approved for use in all panels (U.S. DOE 2011a). The revised panel closure design, denoted as the ROMPCS, is comprised of 100 feet of runofmine (ROM) salt with barriers at each end. A PA was executed to quantify WIPP repository performance impacts associated with the replacement of the approved Option D PCS design with the ROMPCS (Camphouse et al. 2012a). It was found that longterm WIPP performance with the ROMPCS design is similar to that seen with Option D. The ROMPCS design is implemented in the CRA2014 PA, and is further discussed in Section PA4.2.8.
Following the recertification of the WIPP in November 2010, the DOE submitted a planned change notice to the EPA that justified additional excavation to the WIPP experimental area (U.S. DOE 2011b) for the Salt Disposal Investigations (SDI) project. A performance assessment was undertaken to determine the impact of the additional excavation on the longterm performance of the facility (Camphouse et al. 2011). Impacts were determined via a direct comparison to results obtained in the CRA2009 PABC. It was found that total normalized releases were indistinguishable from those obtained in the CRA2009 PABC, and remained below regulatory release limits. After reviewing the DOE proposal and written responses to questions related to the effects of increasing the mined area, the EPA found that the mining phase of the SDI activities will not adversely impact WIPP waste handling activities, air monitoring, disposal operations, or longterm repository performance (U.S. EPA 2011). An additional excavated volume of 60,335 m^{3} in the WIPP experimental area is included in the CRA2014 PA Salado flow model in an identical fashion to that done in Camphouse et al. (Camphouse et al. 2011).
Penetration into a region of pressurized brine during a WIPP drilling intrusion can have significant consequences with respect to releases. The WIPP PA parameter GLOBAL:PBRINE (hereafter PBRINE) is used to specify the probability that a drilling intrusion into the excavated region of the repository encounters a region of pressurized brine below the repository. Parameter PBRINE has historically been an uncertain parameter in the WIPP PA, and its initial development was the result of an analysis of Time Domain Electromagnetics (TDEM) data (Rechard et al. 1991; Peake 1998). A framework that provides a quantitative argument for refinement of parameter PBRINE has been developed since the CRA2009 PABC (Kirchner et al. 2012). The refinement of PBRINE results from a reexamination of the TDEM data while also including a greatly expanded set of drilling data for locations adjacent to the WIPP site than were available when the original analysis was performed in 1998. The refinement is based on a subregion that has a highdensity cluster of drilling intrusions. The resulting subset of data is used to provide a conservative estimate of the probability of brine pocket intrusion based solely on the drilling data and to estimate a probability of encountering a brine pocket given that a well is drilled into a TDEMidentified region, that is a region with high conductivity. The distribution for PBRINE that results from this framework is used in the CRA2014 PA, and is listed in Kicker and Herrick (Kicker and Herrick 2013), Table 4.
The interaction of steel in the WIPP with repository brines will result in the formation of hydrogen (H _{2} ) gas due to anoxic corrosion of the metal. The rate of H _{2} gas generation will depend on the corrosion rate and the type of corrosion products formed. Wang and Brush (Wang and Brush 1996a) provided estimates of gasgeneration parameters for the longterm WIPP PA based on experimental work of Telander and Westerman (1997). A new series of steel and lead corrosion experiments has been conducted with the aim of determining steel and lead corrosion rates under WIPPrelevant conditions. Telander and Westerman measured H _{2} generation rates directly and from those measurements were able to calculate metal corrosion rates. In contrast, the new experiments directly measure metal corrosion rates. A description of the new experiments and the use of their results to determine an updated steel corrosion rate are presented in Roselle (Roselle 2013). The WIPP PA parameter STEEL:CORRMCO2 represents the anoxic steel corrosion rate for brineinundated steel in the absence of microbially produced carbon dioxide (CO _{2)} . Based on the newly obtained experimental corrosion data and its subsequent analysis, Roselle (Roselle 2013) recommends that both the distribution type and values for parameter STEEL:CORRMCO2 be changed to reflect the new experimental data. The revised steel corrosion parameter is used in the CRA2014 PA, and is listed in Kicker and Herrick (Kicker and Herrick 2013), Table 4.
The WIPP PA includes scenarios in which human intrusion results in a borehole intersecting the repository. During the intrusion, drilling mud flowing up the borehole will apply a hydrodynamic shear stress on the borehole wall. Erosion of the wall material can occur if this stress is high enough, resulting in a release of radionuclides being carried up the borehole with the drilling mud. In this intrusion event, the drill bit would penetrate repository waste, and the drilling mud would flow up the borehole in a predominately vertical direction. In order to experimentally simulate these conditions, a flume was designed and constructed. In the flume experimental apparatus, eroding fluid enters a vertical channel from the bottom and flows past a specimen of surrogate WIPP waste. Experiments were conducted to determine the erosive impact on surrogate waste materials that were developed to represent WIPP waste that is 50%, 75%, and 100% degraded by weight. A description of the vertical flume, the experiments conducted in it, and conclusions to be drawn from those experiments are discussed in Herrick et al. (Herrick et al. 2012). The WIPP PA parameter BOREHOLE:TAUFAIL is used to represent the effective shear strength for erosion of WIPP waste. Based on experimental results that realistically simulate the effect of a drilling intrusion on an accepted surrogate waste material, as well as analyses of existing data, Herrick (Herrick 2013) recommends a refinement to parameter BOREHOLE:TAUFAIL be used in the CRA2014 PA. The refined distribution used for the effective waste shear strength in the CRA2014 PA is listed in Kicker and Herrick (Kicker and Herrick 2013), Table 4.
The waste information used in the CRA2014 PA is updated from that used in the CRA2009 PABC calculations. The Performance Assessment Inventory Report (PAIR)  2012 (Van Soest 2012) was released on November 29, 2012. The PAIR  2012 contains updated estimates to the anticipated radionuclide content and nonradionuclide constituents, scaled to a full repository, based on inventory information collected through December 31, 2011. The WIPP PA inventory parameters are updated in the CRA2014 PA to account for this new information. Waste inventory parameters used in the CRA2014 PA are discussed further in Kicker and Zeitler (Kicker and Zeitler 2013b).
The WIPP regulations require that current drilling practices are assumed for future inadvertent intrusions in WIPP PA. The DOE continues to survey drilling activity in the Delaware Basin in accordance with the criteria established in 40 CFR 194.33. Results for the year 2012 are documented in the 2012 Delaware Basin Monitoring Annual Report (U.S. DOE 2012). Plugging pattern probabilities and the drilling rate are updated in the CRA2014 PA to include information assembled through year 2012, and are developed in Camphouse (Camphouse 2013d). Drilling rate and plugging pattern probabilities correspond to parameters GLOBAL:LAMBDAD, GLOBAL:ONEPLG, GLOBAL:TWOPLG, and GLOBAL:THREEPLG, and their CRA2014 PA values are listed in Kicker and Herrick (Kicker and Herrick 2013), Table 38.
The saturation and pressure history of the repository are used throughout PA. Along with flow in and out of the repository, the saturation and pressure are influenced by the reaction of materials placed in the repository with the surrounding environment. As part of the review of the CRA2009, the EPA noted several issues for possible additional investigation, including the potential implementation of a more detailed repository water balance (U.S. EPA 2010b). The repository water balance implementation is refined in the CRA2014 PA in order to include the major gas and brine producing and consuming reactions in the existing conceptual model. Development of the revised water balance implementation is given in Clayton (Clayton 2013), and is further discussed in Section PA4.2.5.
To date, the minimum brine volume necessary for a DBR has been used as an input to the radionuclide solubility calculation. The entire organic ligand inventory was assumed to be dissolved in the minimum necessary brine volume, and the resulting organic ligand concentrations were then used in the calculation of radionuclide solubilities. As the organic ligand inventory has increased over time, the use of a constant organic ligand concentration in brine that is independent of the actual volume of brine present in the repository has resulted in overall massbalance errors. For large repository brine volumes, the use of ligand concentrations that correspond to the minimum brine volume necessary for a DBR yields greater quantities of dissolved organics in brine than are present in the waste inventory. The result is higher actinide concentrations in brine than are physically attainable when repository brine volumes are large. As a result, the calculation of baseline radionuclide solubilities is extended in the CRA2014 so that they are dependent on the concentration of organic ligands, which vary with the actual volume of brine present in the repository (Brush and Domski 2013a). Brine volumes of 1x, 2x, 3x, 4x, and 5x the minimum requisite repository brine volume for a DBR (17,400 m^{3}) (Clayton 2008b) are used in the calculation of baseline radionuclide solubilities in the CRA2014 (Brush and Domski 2013b). The organic ligand waste inventory is assumed to be dissolved in each of these multiples of the minimum necessary brine volume. The resulting organic ligand concentrations, now dependent on a range of brine volume, are then used to calculate baseline radionuclide solubilities corresponding to each brine volume. This approach keeps ligand mass constant over realized brine volumes, rather than keeping ligand concentration constant over realized brine volumes. The variable brine volume implementation results in five baseline solubilities for actinides in the +III, +IV, and +V oxidation states, with these baseline solubilities being calculated for both Salado and Castile brines (see materials SOLMOD3, SOLMOD4, and SOLMOD5 in Kicker and Herrick (Kicker and Herrick 2013), Table 27). Radionuclide concentrations prescribed for a DBR volume in a given vector realization are obtained by interpolating between concentrations calculated for the integer multiples of the minimum necessary DBR volume (WIPP Performance Assessment 2010).
The solubilities of actinide elements are influenced by the chemical components of the waste (for example, organic ligands). With the release of the PAIR  2012 (Van Soest 2012), updated information on the amount of various chemical components in the waste is available. To incorporate this updated information, parameters used to represent baseline actinide solubilities are updated in the CRA2014 PA. Baseline radionuclide solubilities are calculated in the CRA2014 PA using multiples of the minimum brine volume necessary for a DBR to occur, as discussed in Section PA1.1.9. Additional experimental results have been published in the literature since the CRA2009 PABC, and this new information is used in the CRA2014 PA to enhance the uncertainty ranges and probability distributions for actinide solubilities. More discussion of radionuclide solubilities and their associated uncertainties is given in Brush and Domski (Brush and Domski 2013b and Brush and Domski 2013c) and Appendix SOTERM2014, Section 5.0.
Colloid parameters are updated in the CRA2014 PA to incorporate recently available data given in Reed et al. (Reed et al. 2013). Actinide colloid enhancement parameters were reassessed and updated, as appropriate, to reflect recent literature and more extensive WIPPspecific data. The CRA2014 PA contains no changes to the WIPP colloid model developed for the CCA.
Because of the amount and complexity of the material presented in Appendix PA2014, an introductory summary is provided below, followed by detailed discussions of the topics in the remainder of this section, which is organized as follows:
Section PA2.1  Overview of PA
Section PA2.2  The conceptual structure of the PA used to evaluate compliance with the containment requirements
Section PA2.3  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 systemlevel consequence analysis
A demonstration of future repository performance is required by the disposal standards in Part 191. These standards invoke a PA demonstration that potential cumulative releases of radionuclides to the accessible environment over a 10,000year period after disposal are less than specified limits based on the nature of the materials disposed (section 191.13). The PA is used 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. 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 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.
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 DOE's 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.
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 system's behavior. Parameters used in these models are derived from experimental data, field observations, and relevant technical literature. Parameters updated in the CRA2014 PA are discussed in Section PA1.1 and summarized in Table PA1.
An evaluation of undisturbed repository performance, which is defined to exclude human intrusion and unlikely disruptive natural events, is required by regulation (see section 191.15 and section 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 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 an excavation creates a disturbance in the stress field. Stress relief results in some degree of brittle fracturing and the formation of a disturbed rock zone (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 CRA2004, 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 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 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 CRA2004, 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 CRA2004, 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 some 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 twophase 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 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 repository's 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 CRA2004, Chapter 6.0, Section 6.4.3.3 for historical perspective):
1. The generation of hydrogen (H_{2}) gas by anoxic corrosion of steels, other iron (Fe)based alloys, and aluminum (Al) and Albased alloys
2. The generation of carbon dioxide (CO_{2}) and hydrogen sulfide (H_{2}S) by anaerobic microbial consumption of waste containing cellulosic, plastic, and rubber (CPR) materials
Coupling these gasgeneration reactions to fluidflow and saltcreep processes is complex. Gas generation will increase fluid pressure in the repository, thereby decreasing the hydraulic gradient between the far field and the excavated region and inhibiting the processes of brine inflow. This also reduces the deviatoric stress and will therefore reduce the salt creep. Anoxic corrosion will also consume brine as it breaks down water to oxidize steels and other Febased alloys and release H _{2} . Thus, corrosion has the potential to be a selflimiting process, in that as it consumes all water in contact with steels and other Febased alloys, it will cease. Microbial reactions also require water, either in brine or the gaseous phase. In the CRA2009 PABC, it was assumed that microbial reactions neither consume nor produce water. For the CRA2014 PA, the same biodegradation pathways are included as implemented in the CRA2009 PA, but the consumption or generation of water from reactions other than anoxic corrosion are also considered (see Section PA4.2.5).
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 pressuredependent fracturing approximates the hydraulic effect of pressureinduced fracturing and allows gas and brine to move more freely within the MBs at higher pressures (see the CRA2004, 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 CRA2004, Chapter 6.0, Section 6.4.4). Similarly, the runofmine salt in each panel closure will reconsolidate and resist creep, leading to a buildup of compressive stress which in turn will cause healing 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., MB 139 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. 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. In addition, no migration of radionuclides is expected to occur vertically through the Salado (see Section PA7.0, and Kim (2013a)).
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 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 (section 194.41). 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 (section 194.33).
Human intrusion by drilling may cause releases from the disposal system through five mechanisms:
1. Cuttings, which include material intersected by the rotary drilling bit
2. Cavings, which include material eroded from the borehole wall during drilling
3. Spallings, which include solid material carried into the borehole during rapid depressurization of the waste disposal region
4. DBRs, which include contaminated brine that may flow to the surface during drilling
5. Longterm 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, actinide transport by longterm 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 (CRA2004, Chapter 6.0, Section 6.0.2.3).
Repository conditions prior to intrusion correspond to those of the undisturbed repository. As an intrusion provides a pathway for radionuclides to reach the ground surface and enter the geological units above the Salado, additional processes are included to model the disturbed repository. These processes include the mobilization of radionuclides as dissolved and colloidal species in repository brine and groundwater flow, and subsequent actinide 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 CRA2004, Chapter 6.0, Section 6.4.6.2).
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 0.31115 m (12.25 inches [in]), consistent with bits currently used at the WIPP depth in the Delaware Basin (see the CRA2004, 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 remotehandled transuranic (RHTRU) waste and each of the 451 different waste streams (see Kicker and Zeitler 2013a) identified for contacthandled transuranic (CHTRU) waste.
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. During the intrusion, drilling mud flowing up the borehole will apply a hydrodynamic shear stress on the borehole wall. Erosion of the wall material can occur if this stress is high enough, resulting in a release of radionuclides being carried up the borehole with the drilling mud. In this intrusion event, the drill bit would penetrate repository waste, and the drilling mud would flow up the borehole in a predominately vertical direction. In order to experimentally simulate these conditions, a flume was designed and constructed (Herrick et al. 2012). In the flume experimental apparatus, eroding fluid enters a vertical channel from the bottom and flows past a specimen of surrogate WIPP waste. Experiments were conducted to determine the erosive impact on surrogate waste materials that were developed to represent WIPP waste that is 50%, 75%, and 100% degraded by weight. The DOE used newly available data from these experiments to develop the effective shear strength of WIPP waste in the CRA2014 PA (Camphouse et al. 2013). 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 Section PA4.5 and Section PA6.8.2.1).
Unlike releases from cuttings and cavings, which occur with every modeled borehole intrusion, spalling releases can only occur if pressure in the wastedisposal region is sufficiently high (greater than 10 megapascals (Mpa)). At these high 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. Since the CCA, a revised conceptual model for the spallings phenomena has been developed (see Appendix PA2004, Section PA4.6 , and Attachment MASS2004, Section MASS16.1.3 ). 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 (Carlsbad Area Office Technical Assistance Contractor 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 volumeaveraged activity of CHTRU waste, rather than the sampled activities of individual waste streams. The low permeability of the region surrounding the RHTRU waste means it is isolated from the spallings process and does not contribute to the volume or activity of spalled material (see also Section PA4.6 and Section PA6.8.2.2 for further description of the spallings model).
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. DBRs will not occur if repository pressure is below the hydrostatic pressure in the borehole, assumed to be 8 MPa in the WIPP PA. 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 Section PA4.7 and Section PA6.8.2.3).
Actinides may be mobilized in repository brine in two principal ways:
1. As dissolved species
2. 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 lowersolubility 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 wastedisposal region to ensure conditions that reduce uncertainty and establish low actinide solubilities. MgO consumes CO _{2} and buffers pH, lowering actinide solubilities in the WIPP brines (see Appendix SOTERM2014, Section SOTERM2.3.2 and Appendix MgO2014, Section MgO5.1 ). Solubilities in the PA are based on the chemistry of brines that might be present in the wastedisposal region, reactions of these brines with the MgO engineered barrier, and strongly reducing conditions produced by anoxic corrosion of steels and other Febased alloys.
The waste contains organic ligands that could increase actinide solubilities by forming complexes with dissolved actinide 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 Febased alloys. The CRA2014 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 (Appendix SOTERM2014, Section SOTERM2.3.6 and Section SOTERM4.6, and Brush and Domski (Brush and Domski 2013a)).
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, actinide intrinsic colloids, and mineral fragments. Concentrations of actinides mobilized as these colloidal forms are included in the estimates of total actinide concentrations used in PA (see Appendix SOTERM2014, Section SOTERM3.9 ).
Longterm 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 siltysandlike 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 twoplug configuration) is explicitly modeled in the flow and transport model (see Section PA3.7 and Appendix MASS2014, Section MASS15.3 ).
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 higherpermeability units and to the surface. Lowerpermeability 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 CRA2004, Chapter 2.0, Section 2.2.1.4.1.2).
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 longterm flow up an abandoned borehole. Regional variation in the Culebra's 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. Groundwater flow in the Culebra is affected by the presence of fractures, fracture fillings, and vuggy pore features (see Appendix HYDRO2014 and the CRA2004, 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. Members of the public suggested that karst formation and processes may be a possible alternative conceptual model for flow in the Rustler. Karst may be thought of as voids in nearsurface or subsurface rock created by water flowing when rock is dissolved. Public comments stated that karst could develop interconnected "underground rivers" that may enhance the release of radioactive materials from the WIPP. Because of this comment, the EPA required the DOE to perform a thorough reexamination of all historical data, information, and reports, both those by the DOE and others, to determine if karst features or development had been missed during previous work done at the WIPP. The DOE's findings are summarized in Lorenz (Lorenz 2006a and Lorenz 2006b). The EPA also conducted a thorough reevaluation of karst and of the work done during the CCA (U.S. EPA 2006a). The EPA's reevaluation of historical evidence and recent work by the DOE did not show even the remotest possibility of an "underground river" near the WIPP, nor did it change the CCA conclusions. Therefore, the EPA believed karst was not a viable alternative model at the WIPP. For a more complete discussion of the reevaluation of karst, see CARD 14/15 (U.S. EPA 2006b) and Lorenz (Lorenz 2006a and Lorenz 2006b).
Basinscale regional modeling of threedimensional 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 twodimensional confined aquifer (see the CRA2004, Chapter 2.0, Section 2.2.1.1). Uncertainty in the flow field is incorporated by using 100 different geostatistically based Tfields, each of which is consistent with available head and transmissivity data and with updated information on geologic factors potentially affecting transmissivity in the Culebra (see TFIELD2014).
Groundwater flow in the Culebra is modeled as a steadystate 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 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 CRA2004, Chapter 6.0, Section 6.4.9, and the CCA, Appendix CLI).
Consistent with regulatory criteria of section 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 (U.S. EPA 1996a, p. 5229). Tfields used in PA are therefore adjusted and steadystate 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 (Appendix TFIELD2014, 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 change will affect groundwater flow in the Culebra are uncertain. Regional threedimensional 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 CCA, Appendix CLI). This uncertainty is incorporated in PA by scaling the calculated steadystatespecific discharge within the Culebra by a sampled parameter within this range.
Field tests have shown that the Culebra is best characterized as a doubleporosity medium for estimating contaminant transport in groundwater (see the CRA2004, Chapter 2.0, Section 2.2.1.4.1.2, and Appendix HYDRO2014, Section 7.1 ). Groundwater flow and advective transport of dissolved or colloidal species and particles occurs primarily in a small fraction of the rock's 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 lowpermeability dolomite matrix. Transported species, including actinides (if present), will diffuse into this porosity.
Diffusion from the advective porosity into the dolomite matrix will retard actinide 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 the actinides diffuse back into the advective porosity. In situ tracer tests have demonstrated this phenomenon (Meigs et al. 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 (K_{d}s) that characterize the extent to which actinides will sorb on dolomite were based on experimental data (see the CRA2004, Chapter 6.0, Section 6.4.6.2).
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 region of pressurized brine in the underlying Castile Formation (hereafter referred to as the Castile), and those that do not.
The presence of brine pockets under the repository is speculative, but on the basis of current information cannot be ruled out. A pressurized brine pocket was encountered at the WIPP12 borehole within the controlled area to the north of the disposal region, and other pressurized brine pockets associated with regions of deformation in the Castile have been encountered elsewhere in the Delaware Basin (see the CRA2004, Chapter 2.0, Section 2.2.1.2.2). In the CRA2009 PABC, the DOE represented the probability of encountering a pressurized brine pocket during a drilling intrusion as being uncertain, with a range from 0.01 to 0.60. A framework that provides a quantitative argument for refinement of this probability has been developed since the CRA2009 PABC (Kirchner et al. 2012). The probability of a pressurized brine pocket encounter that results from this refinement is represented as an uncertain parameter, with a range from 0.06 to 0.19.
The primary consequence of penetrating a pressurized brine pocket is the supply of 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 brine pocket. Both processes are modeled in PA.
The DOE uses PA to demonstrate continued regulatory compliance of the WIPP. The PA process comprehensively considers the FEPs relevant to disposal system performance (see Appendix SCR2014). Those FEPs shown by screening analyses to potentially affect performance are included in quantitative calculations using a system of 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 CRA2004, 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 are divided among 3 replicates. Quality assurance activities demonstrate that the parameters, software, and analysis used in PA are the result of a rigorous process conducted under controlled conditions (section 194.22).
Of the FEPs considered, exploratory drilling for natural resources has been 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 are constructed, where a single future is defined as a series of intrusion events that occur randomly in space and time (Section PA2.2). 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 are then computed for the three replicates of sampled parameters (Section PA2.2). The key metric for regulatory compliance is the overall mean CCDF for total releases in combination with its confidence limits (CL).
This section outlines the conceptual structure of the WIPP PA with an emphasis on how its development is guided by regulatory requirements. The conceptual structure of the CRA2014 PA is identical to that of the CRA2009 PA.
The methodology employed in PA derives from the EPA's standard for the geologic disposal of radioactive waste, Environmental Radiation Protection Standards for the Management and Disposal of Spent Nuclear Fuel, HighLevel and Transuranic Radioactive Wastes (Part 191) (U.S. EPA 1993), which is divided into three subparts. 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. Subpart B applies after decommissioning and sets probabilistic limits on cumulative releases of radionuclides to the accessible environment for 10,000 years (section 191.13) and assurance requirements to provide confidence that section 191.13 will be met (section 191.14). 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 (section 191.15). Subpart C limits radioactive contamination of groundwater for 10,000 years after disposal (section 191.24). The DOE must demonstrate a reasonable expectation that the WIPP will continue to comply with the requirements of Part 191 Subparts B and C as a necessary condition for WIPP recertification.
The following is the central requirement in Part 191 Subpart B, and the primary determinant of the PA methodology (U.S. EPA 1985, p. 38086).
§ 191.13 Containment Requirements:
(a) Disposal systems for spent nuclear fuel or highlevel 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.
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 (U.S. EPA 1985, Appendix A). Table 1 of Appendix A specifies allowable releases (i.e., release limits) for individual radionuclides and is reproduced as Table PA2. The WIPP is a repository for TRU waste, which is defined as "waste containing more than 100 nanocuries of alphaemitting TRU isotopes, with halflives greater than twenty years, per gram of waste" (U.S. EPA 1985, p. 38084). The normalized release R for TRU waste is defined by
(PA.1)
where Q
_{i}
is the cumulative release of radionuclide i to the accessible environment during the 10,000year period following closure of the repository (curies [Ci]), L
_{i}
is the release limit for radionuclide i given in Table PA2 (Ci), and C is the amount of TRU waste emplaced in the repository (Ci). In the CRA2014 PA, C = 2.06 ´ 10^{6} Ci (Kicker and Zeitler 2013b, Section 2
). 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 passive institutional controls (PICs), that encompasses no more than 100 square kilometers (km^{2}) and extends horizontally no more than 5 kilometers (km) in any direction from the outer boundary of the original radioactive waste's location in a disposal system, and (2) the subsurface underlying such a location (section 191.12).
Table PA
2. Release Limits for the Containment Requirements (U.S. EPA 1985,
Appendix A, Table 1)
Radionuclide 
Release Limit Li per 1000 MTHM^{a} or Other Unit of Waste^{b} 
Americium241 or 243 
100 
Carbon14 
100 
Cesium135 or 137 
1,000 
Iodine129 
100 
Neptunium237 
100 
Pu238, 239, 240, or 242 
100 
Radium226 
100 
Strontium90 
1,000 
Technetium99 
10,000 
Thorium (Th) 230 or 232 
10 
Tin126 
1,000 
Uranium (U) 233, 234, 235, 236, or 238 
100 
Any other alphaemitting radionuclide with a halflife greater than 20 years 
100 
Any other radionuclide with a halflife greater than 20 years that does not emit alpha particles 
1,000 
a Metric tons of heavy metal (MTHM) exposed to a burnup between 25,000 megawattdays (MWd) per metric ton of heavy metal (MWd/MTHM) and 40,000 MWd/MTHM. b An amount of TRU waste containing one million Ci of alphaemitting TRU radionuclides with halflives greater than 20 years.

PAs are the basis for addressing the containment requirements. To help clarify the intent of Part 191, the EPA promulgated 40 CFR Part 194, Criteria for the Certification and Recertification of the Waste Isolation Pilot Plant's Compliance with the Part 191 Disposal Regulations. There, an elaboration on the intent of 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 DOE's PA methodology uses information about the disposal system and waste to evaluate performance over the 10,000year regulatory time period. To accomplish this task, the FEPs with potential to affect the future of the WIPP are first defined (Section PA2.3.1). Next, scenarios that describe potential future conditions in the WIPP are formed from logical groupings of retained FEPs (Section PA2.3.2). The scenario development process results in a probabilistic characterization for the likelihood of different futures that could occur at the WIPP (Section PA2.2.2). Using the retained FEPs, models are developed to estimate the radionuclide releases from the repository (Section PA2.2.3). Finally, uncertainty in model parameters is characterized probabilistically (Section PA2.2.4).
As discussed in Section PA2.3.1, 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 CCA, Appendix SCR). In addition, Part 194 specifies that the occurrence of mining within the LWB must be included in the PA. These requirements have not changed for the CRA2014 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 x _{st} forms the basis for the probability space ( _{st} , _{sc} , p _{st} ) characterizing aleatory uncertainty, where _{st} = { x _{st} : x _{st} is a possible future of the WIPP}, _{sc} is a suitably restricted collection of sets of futures called "scenarios" (Section PA3.10), and p _{st} is a probability measure for the elements of _{st} . A possible future, x _{st,i} , is thus characterized by the collection of intrusion events that occur in that future:
(PA.2)
where
n is the number of drilling intrusions
t _{j} is the time (year) of the j ^{th} intrusion
l _{j} designates the location of the j ^{th} intrusion
e _{j} designates the penetration of an excavated or nonexcavated area by the j ^{th} intrusion
b _{j} designates whether or not the j ^{th} intrusion penetrates pressurized brine in the Castile Formation
p _{j} designates the plugging procedure used with the j ^{th} intrusion (i.e., continuous plug, two discrete plugs, three discrete plugs)
a _{j} designates the type of waste penetrated by the j ^{th} intrusion (i.e., no waste, CHTRU waste, RHTRU waste and, for CHTRU waste, the waste streams encountered)
t _{min} 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 subscript i indicates that the future x _{st} is one of many sample elements from _{st} .
The probabilistic characterization of n, t _{j} , l _{j} ,and e _{j} 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 b _{j} derives from assessed properties of brine pockets; the probabilistic characterization of a _{j} derives from the volumes of waste emplaced in the WIPP in relation to the volume of the repository; and the probabilistic characterization of p _{j} 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 a _{j} because it is possible for a given drilling intrusion to miss the waste or to penetrate different waste types (CHTRU and RHTRU), as well as to encounter different waste streams in the CHTRU waste. Further, the probabilistic characterization for t _{min} follows from the criteria in 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 l _{m} = 10^{  } ^{4} yr^{  } ^{1}), with all commercially viable potash reserves within the LWB extracted at time t _{min}. In practice, the probability measure p _{st} is defined by specifying probability distributions for each component of x _{st} , as discussed further in Section PA3.0.
Based on the retained FEPs (Section PA2.3.1), 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 Figure PA1. These computational models implement the conceptual models representing the repository system as described in section 194.23 and the mathematical models for physical processes presented in Section PA4.0. 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.
Figure PA 1. Computational Models Used in PA
The collection of computation models can be represented abstractly as a function f ( x _{st}  v _{su} ), which quantifies the release that could result from the occurrence of a specific future x _{st} and a specific set of values for model parameters v _{su} . Because the future of the WIPP is unknown, the values of f ( x _{st}  v _{su} ) are uncertain. Thus, the probability space ( _{st} , _{sc} , p _{st} ), together with the function f ( x _{st}  v _{su} ), give rise to the CCDF specified in section 191.13 (a), as illustrated in Figure PA2. 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 (xaxis) of the graph (Figure PA2).
Figure PA 2. Construction of the CCDF Specified in 40 CFR Part 191 Subpart B
Formally, the CCDF depicted in Figure PA2 results from an integration over the probability space ( _{st} , _{sc} , p _{st} ):
(PA.3)
where d _{R} (f ( x _{st}  v _{su} )) = 1 if f ( x _{st}  v _{su} ) > R, d _{R} (f ( x _{st}  v _{su} )) = 0 if f ( x _{st}  v _{su} ) £ R, and d _{st} ( x _{st}  v _{su} ) is the probability density function associated with the probability space ( _{st} , _{sc} , p _{st} ). In practice, the integral in Equation (PA.3) is evaluated by a Monte Carlo technique, where a random sample x _{st,i} , i = 1, nR, (where nR is the number of releases) is generated from _{st} consistent with the probability distribution p _{st} . Using this random sample, Equation (PA.3) is numerically evaluated as
The models in Figure PA1 are too complex to permit a closedform evaluation of the integral in Equation (PA.4) that defines the CCDF specified in Part 191. In the 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.
In PA, the number of samples nR used to construct a CCDF is 10,000. However, the models in Figure PA1 are also too computationally intensive to permit their evaluation for each of these 10,000 futures. Due to this constraint, the models in Figure PA1 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 Section PA3.10; the procedure for constructing a CCDF from these scenarios is described in Section PA6.6.
If the parameters used in the processlevel models of Figure PA1 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 Section 6.0 of Kicker and Herrick (Kicker and Herrick 2013).
Formally, uncertainty in the parameters that underlie the WIPP PA can be characterized by a second probability space ( _{su} , _{sc} , p _{su} ), where the sample space _{su} is defined by
_{su} = {v _{su}: v _{su} is a sampled vector of parameter values} (PA.5)
The subscript su indicates that epistemic (i.e., subjective) uncertainty is being considered. An element v _{su} Î _{su} is a vector v _{su} = v _{su,1} , v _{su,2} , …, v _{su,N} ) of length N, where each element v _{su,k} is an uncertain parameter used in the models to estimate releases. In practice, the probability measure p _{su} is defined by specifying probability distributions for each element of v _{su} , discussed further in Section PA5.0.
If the actual value for v _{su} were known, the CCDF resulting from evaluation of Equation (PA.4) could be determined with certainty and compared with the criteria specified in Part 191. However, given the complexity of the WIPP site, the 10,000year period under consideration, and the state of knowledge about the natural and engineered system, values for v _{su} are not known with certainty. Rather, the uncertainty in v _{su} is characterized probabilistically, as described above, leading to a distribution of CCDFs (Figure PA3), with each CCDF resulting from one of many vectors of values of v _{su} . The uncertainty associated with the parameters is termed epistemic uncertainty, and has been referred to in WIPP PA documentation as subjective uncertainty.
Figure PA 3. Distribution of CCDFs Resulting from Possible Values for the Sampled Parameters
The 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 processlevel models generated using those parameters values. By repeating this process many times, a distribution of the CCDFs can be constructed. The requirements of 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 (Figure PA3) (a formal definition is provided in Helton et al. 1998). In addition, confidence limits on the mean are computed using standard tstatistics. The proximity of these curves to the boundary line in Figure PA2 indicates the confidence with which Part 191 will be met. Confidence is also established by examining the distribution of the CCDFs in relation to the release limits.
The WIPP PA uses a stratified sampling design called LHS (McKay, Beckman, and Conover 1979) to generate a sample v _{su} , i = 1, …, nLHS, from _{su} consistent with the probability distribution p _{su} . 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 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 (U.S. EPA 1996b, p. 841).
The DOE has chosen to demonstrate repeatability of the mean and to address the associated criteria of Part 194 using an operational approach of multiple replication, as proposed by Iman (Iman 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 section 191.13 (a).
This section addresses scenarios formed from FEPs that were retained for PA calculations, and introduces the specification of scenarios for consequence analysis.
The EPA has provided criteria concerning the scope of PAs in section 194.32. In particular, criteria relating to the identification of potential processes and events that may affect disposal system performance are provided in section 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.
Section 32 of this application fulfills these criteria by documenting the DOE's identification, screening, and screening results of all potential processes and events consistent with the criteria specified in section 194.32(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 FEPs screening arguments used for the CRA2014 PA are described in Section 32 and Appendix SCR2014.
Logic diagrams illustrate the formation of scenarios for consequence analysis from combinations of events that remain after FEP screening (Cranwell et al. 1990) (Figure PA4). Each scenario shown in Figure PA4 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 Figure PA4, 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 (section 194.54 and section 194.55). The M scenario is for future mining within the site boundary. Potash mining outside the site boundary is included in all scenarios. Important aspects of UP and DP scenarios are summarized in this section.
Figure PA 4. Logic Diagram for Scenario Analysis
The UP scenario is defined in section 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 (section 191.15; Appendix IGP2009), 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 (section 191.13).
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 mining scenario (M) involves future mining within the controlled area. The disturbed repository deep drilling scenario (E) 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 mining and drilling scenario (ME). More detailed descriptions are found in Section PA2.3.2.2.
The potential effects of future deep drilling and/or mining within the controlled area are the only natural features and waste (and repository) induced FEPs retained after screening that are included in the DP scenario, but excluded in the UP scenario. Among the most significant FEPs that will affect the UP scenario within the disposal system are excavationinduced 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.
· 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, the crushed salt component of the shaft seals, and the ROM salt in the panel closures to near that of the host rock salt.
· The MgO engineered barrier emplaced in the disposal rooms will react with CO_{2} 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, microbes, and actinide 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 (Figure PA5). Contaminated brine may migrate away from the wastedisposal 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 Figure PA5.
Figure PA 5. Conceptual Release Pathways for the UP Scenario
The modeling system described in Section PA4.0 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.
Assessments for compliance with section 191.13 need to consider the potential effects of future disruptive natural and humaninitiated 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 humaninitiated 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 (Section PA3.2 and the CRA2004, 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 M scenario, the E scenario, and the ME scenario. These scenarios are described in the following sections.
The M scenario involves future mining within the controlled area. Consistent with the criteria stated by the EPA in section 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 Section PA3.9). The modeling system used for the M scenario is similar to that developed for the UP scenario, but with a modified Culebra Tfield in the controlled area to account for the mining effects.
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 Tfield may affect the rate and direction of radionuclide transport within the Culebra. Features of the M scenario are illustrated in Figure PA6.
Three disturbed repository FEPs (H13, H37, and H57 in Appendix SCR2004, Table SCR1 ) are related to the occurrence and effects of future mining.
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 section 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
(2) Natural processes will degrade or otherwise affect the capability of boreholes to transmit fluids over the regulatory time frame.
Figure PA 6. Conceptual Release Pathways for the Disturbed Repository M Scenario
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. 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 section 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 CRA2004, Chapter 2.0, Section 2.2.1.2.2). The WIPP12 borehole penetration of one of these volumes provided data on one pressurized brine pocket within the controlled area. The location and properties of brine pockets 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 CRA2004, 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 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 longterm 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 Figure PA7.
Figure PA 7. Conceptual Release Pathways for the Disturbed Repository Deep Drilling E2 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 Figure PA8.
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 8. Conceptual Release Pathways for the Disturbed Repository Deep Drilling E1 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 Figure PA9. 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 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.
Figure PA 9. Conceptual Release Pathways for the Disturbed Repository Deep Drilling E1E2 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.
The scenarios described in Section PA2.3.2.1, Section PA2.3.2.2, and Section PA2.3.2.3 have been retained for consequence analysis to determine compliance with the containment requirements in section 191.13. The modeling systems used to evaluate the consequences of these undisturbed and disturbed scenarios are discussed in Section PA2.3.3.
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 Section PA2.3.2. Additional discussion of conceptual models and modeling assumptions is provided in Section PA4.0. Additional descriptions of sampled parameter values are included in Kicker and Herrick (Kicker and Herrick 2013).
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.
1. 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.
2. 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.
3. Numerical models are developed to approximate mathematical model solutions because most mathematical models do not have closedform solutions.
4. Computational models generally refer to the implementation of the numerical models in the computer code with specific initial and boundary conditions and parameter values. The complexity of the system requires computer codes to solve the numerical models.
Parameters are values necessary in mathematical, numerical, or computational models. Data are descriptors of the physical system being considered, normally obtained by experiment or observation. 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 Kicker and Herrick (Kicker and Herrick 2013) and Tierney (Tierney 1990), where distribution derivations for specific parameters are given.
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 (Appendix SCR2004, Section SCR5.0 ). 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.
The WIPP PA is required not only to estimate the likelihood of future releases, but to establish statistical 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. 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 coupled deterministic models (BRAGFLO, PANEL, NUTS, SECOTP2D, and CUTTINGS_S) that provide scenariospecific results to the code CCDFGF (Figure PA1). 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 the timing of 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 Section PA6.0.
As discussed in Section PA2.2.2, aleatory uncertainty is defined by the possible futures x _{st,i} conditional on the set i of parameters used in Equation (PA.2). Section PA3.2, Section PA3.3, Section PA3.4, Section PA3.5, Section PA3.6, Section PA3.7, Section PA3.8, and Section PA3.9 describe the individual components t _{j} , e _{j} , l _{j} , b _{j} , p _{j} , a _{j} , and t _{min} of x _{st,i} and their associated probability distributions. The concept of a scenario as a subset of the sample space of x _{st,i} is discussed in Section PA3.10. The procedure used to sample the individual elements x _{st,i} is described in Section PA6.5.
The AICs and PICs will be implemented at the WIPP site to deter human activity detrimental to repository performance. The AICs and PICs are described in detail in the CRA2004, Chapter 7.0 and in appendices referenced in Chapter 7.0. Permanent markers will be constructed to inform future populations of the location of the WIPP, and part of the marker system will be a berm that defines the active areas of the repository. In this section, the impact of AICs and PICs on PA is described.
The 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 100year limit on the effectiveness of AICs in PA is established in section 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.
The 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 Part 194 limits any credit for PICs in deterring human intrusion to 700 years after disposal (U.S. EPA 1996a, p. 5231). Although the DOE originally took credit for PICs in the CCA PA, it has not taken credit since. Not including PICs is a conservative implementation, as no credit is taken for a beneficial component of the system.
As described in Section PA2.3.2.2, 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 (Kicker and Herrick 2013, Table 38) is 6.73 ´ 10^{3} intrusions per square kilometer per year (km^{} ^{2} yr^{1}). AICs are assumed to prevent any drilling intrusions for the first 100 years after the decommissioning of the WIPP (Section PA3.2). In the computational implementation of PA, it is convenient to represent the Poisson process for drilling intrusions by its corresponding rate term l _{d} (t) for intrusions into the area marked by the berm. Specifically,
(PA.6)
where 0.6285 km^{2} is the area enclosed by the berm (Kicker and Herrick 2013, Table 37) and t is the elapsed time (in years) since decommissioning the WIPP.
The function l _{d} (t) defines the parameter of the exponential distribution that gives rise to the times of intrusions, t _{j} of Equation (PA.2). In the computational implementation of the analysis, the exponential distribution is randomly sampled to define the times between successive drilling intrusions (Figure PA10 and Section PA6.5). A key assumption of the exponential distribution is that events are independent of each other, so the occurrence of one event 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 10,000year regulatory period specified in section 191.13, t _{j} is assumed to be bounded above by 10,000 years in the definition of x _{st,i} . Further, t _{j} is bounded below by 100 years as defined in Equation (PA.6).
Figure PA 10. CDF for Time Between Drilling Intrusions
The variable e _{j} is a designator for whether or not the j ^{th} drilling intrusion penetrates an excavated, wastefilled area of the repository: e _{j} = 0 or 1 implies penetration of a nonexcavated or excavated area, respectively. The corresponding probabilities P[e _{j} = 0] and P[e _{j} = 1] for e _{j} = 0 and e _{j} = 1 are
(PA.7)
where 0.1273 km^{2} and 0.6285 km^{2} are the excavated area of the repository and the area of the berm, respectively (Kicker and Herrick 2013, Table 37).
Locations of drilling intrusions through the excavated, wastefilled area of the repository are discretized to the 144 locations in Figure PA11. 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 pL _{k} that drilling intrusion j will occur at location l _{k} , k = 1, 2, ¼, 144 in Figure PA11 is
(PA.9)
Figure PA 11. Discretized Locations for Drilling Intrusions
The conceptual models for the Castile include the possibility that pressurized brine reservoirs underlie the repository (Section PA4.2.10). The variable b _{j} is a designator for whether or not the j ^{th} drilling intrusion penetrates pressurized brine, where b _{j} = 0 signifies nonpenetration and b _{j} = 1 signifies penetration of pressurized brine. In the CRA2014 PA, the probability of encountering pressurized brine during a drilling intrusion has been refined from that used in the CRA2009 PABC. Specifically, the probability pB _{1} = P[b _{j} = 1] in the CRA2014 PA is sampled from a normal distribution ranging from 0.06 to 0.19 (see Section PA1.1.3 and Kirchner et al. 2012).
Three borehole plugging patterns, p _{k} , are considered in PA: (1) p _{1} , a full concrete plug through the Salado to the Bell Canyon Formation (hereafter referred to as Bell Canyon), (2) p _{2}, a twoplug configuration with concrete plugs at the Rustler/Salado interface and the Castile/Bell Canyon interface, and (3) p _{3} , a threeplug configuration with concrete plugs at the Rustler/ Salado, Salado/Castile, and Castile/Bell Canyon interfaces. The DOE continues to survey drilling activity in the Delaware Basin in accordance with the criteria established in section 194.33. Results for the year 2012 are documented in the 2012 Delaware Basin Monitoring Annual Report (U.S. DOE 2012). Drilling parameters are updated in the CRA2014 PA to include information assembled through year 2012. The probability that a given drilling intrusion will be sealed with plugging pattern p _{k} , k= 1, 2, 3, is given by pPL _{k} , where pPL _{1} = P[k = 1] = 0.04, pPL _{2} = P[k = 2] = 0.594, pPL _{3} = P[k = 3] = 0.366 (Kicker and Herrick 2013, Table 38).
The waste intended for disposal at the WIPP is represented by 528 distinct waste streams, with 451 of these waste streams designated as CHTRU waste and 77 designated as RHTRU waste (Kicker and Zeitler 2013a). For the CRA2014 PA, the 77 separate RHTRU waste streams are represented by a single, combined RHTRU waste stream, as has been done in all previous PAs. The activity levels for the waste streams are given in Kicker and Herrick 2013, Tables B1 and B2. Each waste container emplaced in the repository contains waste from a single CHTRU waste stream. Waste packaged in 55gallon (gal) drums is stacked 3 drums high within the repository. Although waste in other packages (e.g., standard waste boxes, 10drum overpacks, etc.) may not be stacked 3 high, PA assumes that each drilling intrusion into CHTRU waste intersects 3 different waste streams. In contrast, all RHTRU waste is represented by a single waste stream, and so each drilling intrusion through RHTRU waste is assumed to intersect this single waste stream. Appendix MASS2014, Section MASS19.0 examines the sensitivity of PA results to the assumption that three waste streams are intersected by each drilling intrusion into CHTRU waste.
The vector a _{j} characterizes the type of waste penetrated by the j ^{th} drilling intrusion. Specifically,
a _{j} = 0 if e j = 0 (PA.10)
(i.e., if the i ^{th} drilling intrusion does not penetrate an excavated area of the repository)
a _{j} = 1 if e_{j} = 1 and RHTRU is penetrated (PA.11)
a _{j} = [iCH_{j1} , iCH_{j2} , iCH_{j3} ] if e_{j} = 1 and CHTRU is penetrated (PA.12)
where iCH _{j1} , iCH _{j2} , and iCH _{j3} are integer designators for the CHTRU waste streams intersected by the j ^{th} drilling intrusion (i.e., each of iCH _{j1} , iCH _{j2} , and iCH _{j3} is an integer between 1 and 451).
Whether the j ^{th} intrusion penetrates a nonexcavated or excavated area is determined by the probabilities pE _{0} and pE _{1} discussed in Section PA3.4. The type of waste penetrated is determined by the probabilities pCH and pRH. The excavated area used for disposal of CHTRU waste (aCH) is 1.115 ´ 10^{5} square meters (m^{2}) and the area used for disposal of RHTRU waste (aRH) is 1.576 ´ 10^{4} m^{2} (Kicker and Herrick 2013, Table 37), for a total disposal area of aEX = aCH + aRH = 1.273 ´ 10^{5} m^{2}. Given that the j ^{th} intrusion penetrates an excavated area, the probabilities pCH and pRH of penetrating CHTRU and RHTRU waste are given by
(PA.13)
As indicated in this section, the probabilistic characterization of a _{j} depends on a number of individual probabilities. Specifically, pEx _{0} and pEx _{1} determine whether a nonexcavated or excavated area is penetrated (Section PA3.5). Probabilities pCH and pRH determine whether CHTRU or RHTRU waste is encountered, given penetration of an excavated area. The individual waste stream volumes in Kicker and Herrick (Kicker and Herrick 2013), Tables B1 and B2 are used to determine the specific waste streams iCH _{j1} , iCH _{j2} , and iCH _{j3} encountered, given a penetration of CHTRU waste. The probability of encountering a particular CHTRU waste stream is computed as the ratio of the volume of that waste stream to the volume of CHTRU waste.
Full mining of known potash reserves within the LWB is assumed to occur at time t _{min} . The occurrence of mining within the LWB in 10,000 years in the absence of institutional controls is specified as following a Poisson process with a rate of l _{m} = 1 ´ 10^{  } ^{4} yr^{  } ^{1} (parameter GLOBAL:MINERT in Kicker and Herrick 2013, Table 38). 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 l _{m} (t) is
(PA.15)
where t is the elapsed time since decommissioning of the WIPP.
In the computational implementation of the analysis, l _{m} (t) is used to define the distribution of time to mining. The use of l _{m} (t) to characterize t _{min} is analogous to the use of l _{d} to characterize the t _{j} , except that only one mining event is assumed to occur (i.e., x _{st,} _{i} contains only one value for t _{min} ) in order to be consistent with guidance given in Part 194 that mining within the LWB should be assumed to remove all economically viable potash reserves. Due to the 10,000year regulatory period specified in section 191.13, t _{min} is assumed to be bounded above by 10,000 years in the definition of x _{st,i} .
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 x _{st,i} (see Equation (PA.2)), many different scenarios can be defined. The computational complexity of the function f(x _{st} v _{su} ) in Section PA2.2.3 limits evaluation to only a few intrusion scenarios. As presented in Section PA2.3.2, 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 processlevel models consist of a single intrusion scenario occurring at specific times. CCDFGF is used to simulate multiple intrusions over 10,000 years (see section PA3.11).
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 Section PA6.8.4.1 and Figure PA33 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 10,000year 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 10,000year history is
(PA.17)
where l _{d} 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 pEx _{0} ^{n}, or specifically 0.797^{n}. 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:
The calculated probability becomes
exp[0.203(4.23×10^{3})(10000100)] = 2.03×10^{4} (PA.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 pB _{1} takes on its mean value of 0.127 (see Section PA3.6), and ignoring the impact of the plugging pattern, for a constant rate of drilling, l _{d} , these equations are
exp[9900 𝝀 _{d} pEx_{1} ](9900 𝝀 _{d} pEx_{1} )pB_{1} = 2.2×10^{4} (PA.20)
and
exp[9900 𝝀 _{d} pEx_{1} ](9900 𝝀 _{d} pEx_{1} )pB_{0} = 1.5×10^{3} (PA.21)
respectively, where (pEx _{1} × l _{d} ) represents the annual rate of drilling into the excavated region of the repository which is multiplied by 9900 to give the frequency 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:
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. Closedform formulas for the probabilities of quite complex scenarios can be derived, but they are very complicated and involve large numbers of iterated integrals (Helton 1993).
CCDFGF simulates histories that can have many intrusion events (WIPP Performance Assessment 2010). The processlevel 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 (Section PA6.7 and Section PA6.8). Releases for an arbitrary future are estimated from the results of these fundamental scenarios (Section PA6.8); these releases are used to construct CCDFs by Equation (PA.4).
The WIPP PA uses the Monte Carlo approach to construct the CCDF indicated in Equation (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 CRA2014 PA uses the same approach as the CRA2009 PA.
This section describes how releases to the accessible environment are estimated for a particular future in PA.
The function f(x _{st,i} ) estimates the radionuclide releases to the accessible environment associated with each of the possible futures (x _{st,i} ) that could occur at the WIPP site over the next 10,000 years. In practice, f(x _{st,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(x _{st,i} ) has the form
(PA.23)
where
x _{st,i} ~ particular future under consideration
~ future involving no drilling intrusions but a mining event at the same time t _{min} as in x _{st}
f _{C}(x _{st,i} ) ~ cuttings and cavings release to accessible environment for x _{st,i} calculated with CUTTINGS_S
f _{B}(x _{st,i} ) ~ twophase flow in and around the repository calculated for x _{st,i} with BRAGFLO; in practice, f _{B} (x _{st,i} ) is a vector containing a large amount of information, including pressure and brine saturation in various geologic members
~ spallings release to accessible environment for x _{st,i} calculated with the spallings model contained in DRSPALL and CUTTINGS_S; this calculation requires repository conditions calculated by f _{B} (x _{st,i} ) as input
~ DBR to accessible environment for x _{st,i} also calculated with BRAGFLO; this calculation requires repository conditions calculated by f _{B} (x _{st,i} ) as input
~ release through anhydrite MBs to accessible environment for x _{st,i} calculated with NUTS; this calculation requires flows in and around the repository calculated by f _{B} (x _{st,i} ) as input
~ release through Dewey Lake to accessible environment for x _{st,i} calculated with NUTS; this calculation requires flows in and around the repository calculated by f _{B} (x _{st,i} ) as input
~ release to land surface due to brine flow up a plugged borehole for x _{st,i} calculated with NUTS; this calculation requires flows in and around the repository calculated by f _{B} (x _{st,i} ) as input
~ flow field in the Culebra calculated for x _{st,} _{0} with MODFLOW; x _{st,} _{0} is used as an argument to f _{MF} because drilling intrusions are assumed to cause no perturbations to the flow field in the Culebra
~ release to Culebra for x _{st,i} calculated with NUTS or PANEL as appropriate; this calculation requires flows in and around the repository calculated by f _{B} (x _{st,i} ) as input
~ groundwater transport release through Culebra to accessible environment calculated with SECOTP2D. This calculation requires MODFLOW results (i.e., f _{MF} (x _{st,0} )) and NUTS or PANEL results (i.e., ) as input
The remainder of this section describes the mathematical structure of the mechanistic models that underlie the component functions of f(x _{st,i} ) in Equation (PA.23).
The Monte Carlo CCDF construction procedure, implemented in the code CCDFGF (WIPP Performance Assessment 2010), 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 twostep procedure is being used to evaluate f in calculating the summation in Equation (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(x _{st} ) for the randomly selected futures x _{st,i} used in the numerical evaluation of the summation in Equation (PA.23) are then constructed from results obtained in the first step. These constructions are described in Section PA6.7 and Section PA6.8, and produce the evaluations of f(x _{st} ) that are actually used in Equation (PA.23).
For notational simplicity, the functions on the righthand side of Equation (PA.23) will typically be written with only x _{st} as an argument (e.g., f _{SP} (x _{st} ) and will be used instead of f _{SP} [x _{st} , f _{B} (x _{st} )]). However, the underlying dependency on the other arguments will still be present.
The major topics considered in this chapter are twophase flow in the vicinity of the repository as modeled by BRAGFLO (i.e., f _{B} ) (Section PA4.2), radionuclide transport in the vicinity of the repository as modeled by NUTS (i.e., f _{MB} , f _{DL} , f _{S} , f _{NP} ) (Section PA4.3), radionuclide transport in the vicinity of the repository as modeled by PANEL (i.e., f _{NP} ) (Section PA4.4), cuttings and cavings releases to the surface as modeled by CUTTINGS_S (i.e., f _{C} ) (Section PA4.5), spallings releases to the surface as modeled by DRSPALL and CUTTINGS_S (i.e., f _{SP} ) (Section PA4.6), DBRs to the surface as modeled by BRAGFLO (i.e., f _{DBR} ) (Section PA4.7), brine flow in the Culebra as modeled by MODFLOW (i.e., f _{MF} ) (Section PA4.8), and radionuclide transport in the Culebra as modeled by SECOTP2D (i.e., f _{ST} ) (Section PA4.9).
Quantifying the effects of gas and brine flow on radionuclide transport from the repository requires a twophase (brine and gas) flow code. The twophase flow code BRAGFLO is used to simulate gas and brine flow in and around the repository (Camphouse 2013a and Camphouse 2013b). 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.
Twophase 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
Ñ × (PA.24)
Brine Conservation
Saturation Constraint
Capillary Pressure Constraint
Gas Density
r
_{g} (determined by RedlichKwongSoave (RKS) equation of state; see Equation (PA.51))
(PA.28)
Brine Density
Formation Porosity
where
g = acceleration due to gravity (meters per second squared [m])
h = vertical distance from a reference location (m)
k rl = relative permeability (dimensionless) to fluid l, l = b (brine), g (gas)
P _{c} = capillary pressure in Pascals (Pa)
P _{l} = pressure of fluid l (Pa)
q rl = rate of production (or consumption, if negative) of fluid l due to chemical reaction (kilograms per cubic meter per seconds [kg/m^{3}/s])
q _{l} = rate of injection (or removal, if negative) of fluid l (kg/m^{3}/s)
S l = saturation of fluid l (dimensionless)
t = time (s)
a = geometry factor (m)
r l = density of fluid l (kg/m^{3})
m l = viscosity of fluid l (Pa s)
f = porosity (dimensionless)
f 0 = reference (i.e., initial) porosity (dimensionless)
P b 0 = reference (i.e., initial) brine pressure (Pa), constant in Equation (PA.29) and spatially variable in Equation (PA.30)
r 0 = reference (i.e., initial) brine density (kg/m^{3})
c _{ f } = pore compressibility (Pa^{1})
c _{b} = brine compressibility (Pa^{1})
K = permeability of the material (m^{2}), isotropic for PA (Howarth and ChristianFrear 1997)
For the brine transport Equation (PA.25), the intrinsic permeability of the material is used. For the gas transport Equation (PA.24), the permeability K is modified to account for the Klinkenberg effect (Klinkenberg 1941). Specifically,
(PA.31)
where a and b are gas and formationdependent constants. Values of a = 0.3410 and b = 0.2710 were determined from data obtained for MB 139 (ChristianFrear 1996), with these values used for all material regions in Figure PA12.
The conservation equations are valid in one (i.e., Ñ = [ ¶ / ¶ x]), two (i.e., Ñ = [ ¶ / ¶ x, ¶ / ¶ y]), and three (i.e., Ñ = [ ¶ / ¶ x, ¶ / ¶ y, ¶ / ¶ z]) dimensions. In PA, the preceding system of equations is used to model twophase fluid flow within the twodimensional region shown in Figure PA12. The details of this system are discussed below.
The a term in Equation (PA.24) and Equation (PA.25) is a dimensiondependent geometry factor and is specified by
a = area normal to flow direction in onedimensional flow (i.e., D y D z; units = m^{2})
= thickness normal to flow plane in twodimensional flow (i.e., D z; units = m)
= 1 in threedimensional flow (dimensionless) (PA.32)
PA uses a twodimensional geometry to compute twophase flow in the vicinity of the repository, and as a result, a is the thickness of the modeled region (i.e., D z) normal to the flow plane (Figure PA12). Due to the use of the twodimensional grid in Figure PA12, a is spatially dependent, with the values used for a defined in the column labeled "D z." Specifically, a 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 Figure PA13 and ensures that the total volume surrounding the repository is conserved in the numerical grid. The equations and method used to determine a for BRAGFLO grids used in the WIPP PA were developed by Stein (Stein 2002).
The h term in Equation (PA.24) and Equation (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., (x _{ref} , y _{ref} ) = (23664.9 m, 378.685 m), which is the center of cell 1272 in Figure PA14). Specifically, h is defined by
(PA.33)
where q 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, q = 1 degree for points within the Salado, and q = 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 Medaños 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 Equation (PA.24), Equation (PA.25), Equation (PA.26), Equation (PA.27), Equation (PA.28), Equation (PA.29) and (PA.30), S _{b} and S _{g} are functions of location and time. Thus, P _{c} , k _{rb} , and k _{rg} are functions of the form P _{c} (x, y, t), k _{rb} (x, y, t), and k _{rg} (x, y, t). In the computational implementation of the solution of the preceding equations, flow of phase l out of a computational cell (Figure PA14) cannot occur when S _{l} (x, y, t) £ S _{lr} (x, y, t), where S _{lr} denotes the residual saturation for phase l. The values used for S _{lr} , l = b, g are summarized in Table PA3.
Figure PA 14. BRAGFLO Grid Cell Indices
Table PA 3. Parameter Values Used in Representation of TwoPhase Flow



Region 
Material 
Material Description 
BrooksCorey Pore Distribution (PORE_DIS)^{a}

Threshold Pressure Linear Parameter (PCT_A)^{a}

Threshold Pressure Exponential Parameter 
Residual Brine Saturation 
Residual Gas Saturation 
Porosity 
Pore Compressibility^{a}

Intrinsic Permeability 


Salado 
S_HALITE 
Undisturbed halite 
0.7 
0.56 
 0.346 
0.3 
0.2 
HALPOR^{b} 
f(HALCOMP)^{b,d} 
10^{x}, x = HALPRM^{b} 


DRZ 
DRZ_0 
DRZ,  5 to 0 years 
0.7 
0.0 
0.0 
0.0 
0.0 
f(HALPOR)^{b,c} 
f(HALCOMP)^{b,d} 
1.0 ´ 1017 


DRZ_1 
DRZ, 0 to 10,000 years 
0.7 
0.0 
0.0 
0.0 
0.0 
f(HALPOR)^{b,c} 
f(HALCOMP)^{b,d} 
10^{x}, x = DRZPRM^{b} 


MB 138 
S_MB138 
Anhydrite MB in Salado 
ANHBCEXP^{b} 
0.26 
 0.348 
ANRBSAT^{b} 
ANRGSSAT^{b} 
0.011 
f(ANHCOMP)^{b,d} 
10^{x}, x = ANHPRM^{b} 


Anhydrite AB 
S_ANH_AB 
Anhydrite layers A and B in Salado 
ANHBCEXP^{b} 
0.26 
 0.348 
ANRBSAT^{b} 
ANRGSSAT^{b} 
0.011 
f(ANHCOMP)^{b,d} 
10^{x}, x = ANHPRM^{b} 


MB 139 
S_MB139 
Anhydrite MB in Salado 
ANHBCEXP^{b} 
0.26 
 0.348 
ANRBSAT^{b} 
ANRGSSAT^{b} 
0.011 
f(ANHCOMP)^{b,d} 
10^{x}, x = ANHPRM^{b} 


Waste Panel

CAVITY_1 
Single waste panel,  5 to 0 years 
NA^{e} 
NA^{e} 
NA^{e} 
0.0 
0.0 
1.0 
0.0 
1.0 ´ 10 ^{  } ^{ 10 } 


WAS_AREA 
Single waste panel, 0 to 10,000 years 
2.89 
0.0 
0.0 
WRBRNSAT^{b} 
WRGSSAT^{b} 
0.848^{f} 
0.0 
2.4 ´ 10 ^{  } ^{ 13 } 


Rest of Repository (SRoR and NRoR) 
CAVITY_2 
RoR,  5 to 0 years 
NA^{e} 
NA^{e} 
NA^{e} 
0.0 
0.0 
1.0 
0.0 
1.0 ´ 10 ^{  } ^{ 10 } 


REPOSIT 
RoR, 0 to 10,000 years 
2.89 
0.0 
0.0 
WRBRNSAT^{b} 
WRGSSAT^{b} 
0.848^{f} 
0.0 
2.4 ´ 10 ^{  } ^{ 13 } 


Ops

CAVITY_3 
Operations area,  5 to 0 years 
NA^{e} 
NA^{e} 
NA^{e} 
0.0 
0.0 
1.0 
0.0 
1.0 ´ 10 ^{  } ^{ 10 } 


OPS_AREA 
Operations area, 0 to 10,000 years 
NA^{e} 
NA^{e} 
NA^{e} 
0.0 
0.0 
0.18 
0.0 
1.0 ´ 10 ^{  } ^{ 11 } 


Exp 
CAVITY_3 
Experimental area,  5 to 0 years 
NA^{e} 
NA^{e} 
NA^{e} 
0.0 
0.0 
1.0 
0.0 
1.0 ´ 10 ^{  } ^{ 10 } 



a Parenthetical parameter names are property names for the corresponding material, as indicated in Table PA17 . b Uncertain variable; see Table PA17. c See Equation (PA.34). d See Equation (PA.37); f _{0} can also be defined by an uncertain variable. e These materials are using relative permeability model = 11; see Table PA4. f Initial value of porosity f _{0}; porosity changes dynamically to account for creep closure (see Section PA4.2.3). g See Equation (PA.35). 


Table PA3. Parameter Values Used in Representation of TwoPhase Flow (Continued) 


Region 
Material 
Material Description 
BrooksCorey Pore Distribution (PORE_DIS)^{a}

Threshold Pressure Linear Parameter (PCT_A)^{a}

Threshold Pressure Exponential Parameter 
Residual Brine Saturation 
Residual Gas Saturation 
Porosity 
Pore Compressibility^{a}

Intrinsic Permeability 


Exp 
EXP_AREA 
Experimental area, 0 to 10,000 years 
NA^{e} 
NA^{e} 
NA^{e} 
0.0 
0.0 
0.18 
0.0 
1.0 ´ 10 ^{  } ^{ 11 } 


Castile 
IMPERM_Z 
Castile 
0.7 
0.0 
0.0 
0.0 
0.0 
0.005 
0.0 
1.0 ´ 10 ^{  } ^{ 35 } 


Castile Brine Reservoir 
CASTILER 
Brine Reservoir in Castile 
0.7 
0.56 
 0.346 
0.2 
0.2 
f(BPCOMP)^{b,g} 
f(BPCOMP)^{b,d} 
10^{x}, x = BPPRM^{b} 


Culebra 
CULEBRA 
Culebra Member of Rustler 
0.6436 
0.26 
 0.348 
0.08363 
0.07711 
0.151 
6.622517 ´ 10 ^{  } ^{ 10 } 
7.72681 ´ 10 ^{  } ^{ 14 } 


Magenta 
MAGENTA 
Magenta Member of Rustler 
0.6436 
0.26 
 0.348 
0.08363 
0.07711 
0.138 
1.915942 ´ 10 ^{  } ^{ 9 } 
6.309576 ´ 10 ^{  } ^{ 16 } 


Dewey Lake 
DEWYLAKE 
Dewey Lake Redbeds 
0.6436 
0.0 
0.0 
0.08363 
0.07711 
0.143 
6.993007 ´ 10 ^{  } ^{ 8 } 
5.011881 ´ 10 ^{  } ^{ 17 } 


Santa Rosa 
SANTAROS 
Santa Rosa Formation 
0.6436 
0.0 
0.0 
0.08363 
0.07711 
0.175 
5.714286 ´ 10 ^{  } ^{ 8 } 
1.0 ´ 10 ^{  } ^{ 10 } 


Los Medaños 
UNNAMED 
Los Medaños Member of Rustler 
0.7 
0.0 
0.0 
0.2 
0.2 
0.181 
0.0 
1.0 ´ 10 ^{  } ^{ 35 } 


Tamarisk 
TAMARISK 
Tamarisk Member of Rustler 
0.7 
0.0 
0.0 
0.2 
0.2 
0.064 
0.0 
1.0 ´ 10 ^{  } ^{ 35 } 


Fortyniner 
FORTYNIN 
Fortyniner Member of Rustler 
0.7 
0.0 
0.0 
0.2 
0.2 
0.082 
0.0 
1.0 ´ 10 ^{  } ^{ 35 } 


DRZ_PCS

DRZ_0 
DRZ, 5 to 0 years 
0.7 
0.0 
0.0 
0.0 
0.0 
f(HALPOR)^{b,c} 
f(HALCOMP)^{b,d} 
1.0 ´ 10 ^{  } ^{ 17 } 


DRZ_1 
DRZ, 0 to 200 years 
0.7 
0.0 
0.0 
0.0 
0.0 
f(HALPOR)^{b,c} 
f(HALCOMP)^{b,d} 
10^{x}, x = DRZPRM^{b} 


DRZ_PCS 
DRZ above/below the panel closures, 200 to 10,000 years 
0.7 
0.0 
0.0 
0.0 
0.0 
f(HALPOR)^{b,c} 
f(HALCOMP)^{b,d} 
10^{x}, x = DRZPCPRM^{b} 


a Parenthetical parameter names are property names for the corresponding material, as indicated in Table PA17 . b Uncertain variable; see Table PA17. c See Equation (PA.34). d See Equation (PA.37); f _{0} can also be defined by an uncertain variable. e These materials are using relative permeability model = 11; see Table PA4. f Initial value of porosity f _{0}; porosity changes dynamically to account for creep closure (see Section PA4.2.3). g See Equation (PA.35). 


Table PA3. Parameter Values Used in Representation of TwoPhase Flow (Continued) 


Region 
Material 
Material Description 
BrooksCorey Pore Distribution (PORE_DIS)^{a}

Threshold Pressure Linear Parameter (PCT_A)^{a}

Threshold Pressure Exponential Parameter 
Residual Brine Saturation 
Residual Gas Saturation 
Porosity 
Pore Compressibility^{a}

Intrinsic Permeability 


ROMPCS 
CAVITY_4 
Panel closures, 5 to 0 years 
NA^{e} 
NA^{e} 
NA^{e} 
0.0 
0.0 
1.0 
0.0 
1.0 ´ 10 ^{  } ^{ 10 } 


PCS_T1 
Panel closures, 0 to 100 years 
T1PDIS^{b} 
0.0 
0.0 
T1SRBRN ^{b} 
T1SRGAS ^{b} 
T1POROS^{b} 
f(T1POROS)^{b,d} 
10^{x}, x = T1PRMX^{b} 


PCS_T2 
Panel closures, 100 to 200 years 
T1PDIS^{b} 
0.0 
0.0 
T1SRBRN ^{b} 
T1SRGAS ^{b} 
T2POROS^{b} 
f(T2POROS)^{b,d} 
f(T2POROS) 


PCS_T3 
Panel closures, 200 to 10,000 years 
T1PDIS^{b} 
0.0 
0.0 
T1SRBRN ^{b} 
T1SRGAS ^{b} 
T3POROS^{b} 
f(T3POROS)^{b,d} 
f(T3POROS) 


CONC_MON

CAVITY_4 
Concrete monolith portion of shaft seals,  5 to 0 years 
NA^{e} 
NA^{e} 
NA^{e} 
0.0 
0.0 
1.0 
0.0 
1.0 ´ 10 ^{  } ^{ 10 } 


CONC_MON 
Concrete monolith portion of shaft seals, 0 to 10,000 years 
0.94 
0.0 
0.0 
SHURBRN^{b} 
SHURGAS^{b} 
0.05 
1.2 ´ 10 ^{  } ^{ 9 } 
1.0 ´ 10 ^{  } ^{ 14 } 


Upper Shaft

CAVITY_4 
Upper portion of shaft seals,  5 to 0 years 
NA^{e} 
NA^{e} 
NA^{e} 
0.0 
0.0 
1.0 
0.0 
1.0 ´ 10 ^{  } ^{ 10 } 


SHFTU 
Upper portion of shaft seals, 0 to 10,000 years 
CONBCEXP^{b} 
0.0 
0.0 
SHURBRN^{b} 
SHURGAS^{b} 
0.005 
2.05 ´ 10 ^{  } ^{ 8 } 
10^{x}, x = SHUPRM^{b} 


a Parenthetical parameter names are property names for the corresponding material, as indicated in Table PA17 . b Uncertain variable; see Table PA17. c See Equation (PA.34). d See Equation (PA.37); f _{0} can also be defined by an uncertain variable. e These materials are using relative permeability model = 11; see Table PA4. f Initial value of porosity f _{0}; porosity changes dynamically to account for creep closure (see Section PA4.2.3). g See Equation (PA.35). 


Table PA3. Parameter Values Used in Representation of TwoPhase Flow (Continued) 


Region 
Material 
Material Description 
BrooksCorey Pore Distribution (PORE_DIS)^{a}

Threshold Pressure Linear Parameter (PCT_A)^{a}

Threshold Pressure Exponential Parameter 
Residual Brine Saturation 
Residual Gas Saturation 
Porosity 
Pore Compressibility^{a}

Intrinsic Permeability 


Lower Shaft

CAVITY_4 
Lower portion of shaft seals,  5 to 0 years 
NA^{e} 
NA^{e} 
NA^{e} 
0.0 
0.0 
1.0 
0.0 
1.0 ´ 10 ^{  } ^{ 10 } 


SHFTL_T1 
Lower portion of shaft seals, 0 to 200 years 
CONBCEXP^{b} 
0.0 
0.0 
SHURBRN^{b} 
SHURGAS^{b} 
0.005 
4.28 ´ 10 ^{  } ^{ 9 } 
10^{x}, x = SHLPRM1^{b} 


SHFTL_T2 
Lower portion of shaft seals, 200 to 10,000 years 
CONBCEXP^{b} 
0.0 
0.0 
SHURBRN^{b} 
SHURGAS^{b} 
0.005 
4.28 ´ 10 ^{  } ^{ 9 } 
10^{x}, x = SHLPRM2^{b} 


Borehole plugs

CONC_PLG 
Concrete borehole plug, before plug degradation 
0.94 
0.0 
0.0 
0.0 
0.0 
0.32 
1.1875 ´ 10^{9} 
10^{x}, x = PLGPRM^{b} 


BH_SAND 
Borehole after plug degradation, 200 years after intrusion 
0.94 
0.0 
0.0 
0.0 
0.0 
0.32 
0.0 
10^{x}, x = BHPRM^{b} 


Upper Borehole

BH_OPEN 
Borehole above repository before plug degradation 
0.7 
0.0 
0.0 
0.0 
0.0 
0.32 
0.0 
1.0 ´ 10 ^{  } ^{ 9 } 


BH_SAND 
Borehole after plug degradation, 200 years after intrusion 
0.94 
0.0 
0.0 
0.0 
0.0 
0.32 
0.0 
10^{x}, x = BHPRM^{b} 


Lower Borehole

BH_OPEN 
Borehole below repository before creep closure 
0.7 
0.0 
0.0 
0.0 
0.0 
0.32 
0.0 
1.0 ´ 10 ^{  } ^{ 9 } 


BH_CREEP 
Borehole below repository after creep closure, 1,000 years after intrusion 
0.94 
0.0 
0.0 
0.0 
0.0 
0.32 
0.0 
10^{x}/10, x = BHPRM^{a} 


a Parenthetical parameter names are property names for the corresponding material, as indicated in Table PA17 . b Uncertain variable; see Table PA17. c See Equation (PA.34). d See Equation (PA.37); f _{0} can also be defined by an uncertain variable. e These materials are using relative permeability model = 11; see Table PA4. f Initial value of porosity f _{0}; porosity changes dynamically to account for creep closure (see Section PA4.2.3). g See Equation (PA.35). 

Values for f _{0} and c _{ f } (Equation (PA.30)) are also given in Table PA3. Initial porosity f _{0} for the DRZ is a function of the uncertain parameter for initial halite porosity f _{0} _{H} (HALPOR; see Table PA17) and is given by Martell (Martell 1996a) and Bean (Bean et al 1996), Section 4:
f _{0} = f _{0H} + 0.0029 (PA.34)
Initial porosity f _{0} of the Castile brine reservoir is calculated from the uncertain sampled parameter for the bulk Castile rock compressibility (BPCOMP; see Table PA17), according to the following relationship:
(PA.35)
where 1.0860 ´ 10^{10} is a scaling constant that ensures that the productivity ratio, PR, remains constant at 2.0 ´ 10^{3} m^{3}/Pa. The productivity ratio PR is computed by
where V is the volume of the grid block representing the Castile brine reservoir in Figure PA12. 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 _{ f } in Equation (PA.30) and 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 C _{r} to pore compressibility C _{ f } is approximated by
(PA.37)
where f _{0} is the initial porosity in the region under consideration.
The primary model used in PA for capillary pressure P _{c} and relative permeability k _{rl} is a modification of the BrooksCorey model (Brooks and Corey 1964). In this model, P _{c} , k _{rb} , and k _{rg} are defined by
(PA.38)
where
l = pore distribution parameter (dimensionless)
P _{t}(k) = capillary threshold pressure (Pa) as a function of intrinsic permeability k (Webb 1992)
= (PA.41)
= effective brine saturation (dimensionless) without correction for residual gas saturation
= (PA.42)
= effective brine saturation (dimensionless) with correction for residual gas saturation
= (PA.43)
The values used for l , a, h , S _{br} , S _{gr} , and k are summarized in Table PA3. The statement that the BrooksCorey model is in use means that P _{c} , k _{rb} , and k _{rg} are defined by Equation (PA.38), Equation (PA.39) and Equation (PA.40).
In the anhydrite MBs, either the BrooksCorey model or the van GenuchtenParker model is used as determined by the subjectively uncertain parameter ANHBCVGP (see Table PA17). A linear model is used to represent twophase flow in an open borehole (i.e., for the first 200 years after a drilling intrusion for boreholes with twoplug or threeplug configurations, in the open cavities [CAVITY_1, . . , CAVITY_4], and for the experimental and operations areas). This is discussed further below.
In the van GenuchtenParker model, P _{c} , k _{rb} , and k _{rg} are defined by (van Genuchten 1978)
(PA.44)
where m = l /(1 + l ) and the capillary pressure parameter P _{VGP} is determined by requiring that the capillary pressures defined in Equation (PA.38) and Equation (PA.44) are equal at an effective brine saturation of S _{e} _{2} = 0.5 (Webb 1992). The van GenuchtenParker model is only used for the anhydrite MBs in the Salado and uses the same values for l , S _{br} , and S _{gr} as the BrooksCorey model (Table PA3).
In the linear model used for the open borehole (RELP_MOD = 5), P _{c} , k _{rb} , and k _{rg} are defined by
P _{c} = 0, k _{rb} = S _{e1}, k _{rg} = 1  S _{e1} (PA.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 Section PA4.2.2) and the experimental and operations areas (t = 0 to 10,000 years) which, in PA, are modeled without a timedependent creep closure:
(PA.48)
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 P _{c} for both the van GenuchtenParker and BrooksCorey models becomes unbounded as brine saturation S _{b} approaches the residual brine saturation, S _{br} . To avoid unbounded values, P _{c} is capped at 1 ´ 10^{8} Pa in selected regions (Table PA4).
Gas density is computed using the RKS equation of state, with the gas assumed to be pure H_{2}. For a pure gas, the RKS equation of state has the form (Walas 1985, pp. 43−54)
(PA.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 (m^{3} mol^{  } ^{1})
a = 0.42747 R ^{2} T ^{2} _{crit} /P _{crit}
b = 0.08664 RT _{crit} /P _{crit}
a =
» for H_{2} (Graboski and Daubert 1979)
T _{crit} = critical temperature (K)
P _{crit} = critical pressure (Pa)
T _{r} = T / T _{crit} = reduced temperature
w = acentric factor
= 0 for H_{2} (Graboski and Daubert 1979)
Table PA 4. Models for Relative Permeability and Capillary Pressure in TwoPhase Flow
Material 
Relative Permeability^{a } (RELP_MOD) 
Capillary Pressure^{b } (CAP_MOD) 
Material 
Relative Permeability^{a } (RELP_MOD) 
Capillary Pressure^{b } (CAP_MOD) 
BH_OPEN 
5 
1 
MAGENTA 
4 
2 
BH_SAND 
4 
1 
OPS_AREA 
11 
1 
BH_CREEP 
4 
1 
PCS_T1 
4 
1 
CASTILER 
4 
2 
PCS_T2 
4 
1 
CAVITY_1 
11 
1 
PCS_T3 
4 
1 
CAVITY_2 
11 
1 
REPOSIT 
12 
1 
CAVITY_3 
11 
1 
SANTAROS 
4 
1 
CAVITY_4 
11 
1 
SHFTU 
4 
1 
CONC_MON 
4 
2 
SHFTL_T1 
4 
1 
CONC_PLG 
4 
1 
SHFTL_T2 
4 
1 
CULEBRA 
4 
2 
S_ANH_AB 
ANHBCVGP^{c} 
2 
DEWYLAKE 
4 
1 
S_HALITE 
4 
2 
DRZ_0 
4 
1 
S_MB138 
ANHBCVGP^{c} 
2 
DRZ_1 
4 
1 
S_MB139 
ANHBCVGP^{c} 
2 
DRZ_PCS 
4 
1 
TAMARISK 
4 
1 
EXP_AREA 
11 
1 
UNNAMED 
4 
1 
FORTYNIN 
4 
1 
WAS_AREA 
12 
1 
IMPERM_Z 
4 
1 



^{a} Relative permeability model, where 4 = BrooksCorey model given by Equation (PA.38) , Equation (PA.39) and Equation (PA.40), 5 = linear model given by Equation (PA.47), 11 = linear model given by Equation (PA.48), Equation (PA.49) and Equation (PA.50), 12 = modified BrooksCorey model to account for cutoff saturation (Camphouse 2013b), and ANHBCVGP = use of BrooksCorey or van GenuchtenParker model treated as a subjective uncertainty. ^{b} Capillary pressure model, where 1 = capillary pressure is unbounded, 2 = P _{ c } bounded above by 1 ´ 10^{8} Pa as S _{ b } approaches S _{ br } . ^{c} See ANHBCVGP in Table PA17. 
In order to account for quantum effects in H_{2}, effective critical temperature and pressure values of T _{crit} = 43.6 K and P _{crit} = 2.047 ´ 10^{6} Pa are used instead of the true values for these properties (Prausnitz 1969). Equation (PA.51) is solved for molar volume V. The gas density r _{g} then is given by
(PA.52)
where M _{w,H} _{ 2 } is the molecular weight of H_{2} (i.e., 2.01588 ´ 10^{  } ^{3} kg/mol; see Weast 1969, p. B26).
Brine density r _{b} is defined by Equation (PA.29), with r _{b} _{0}= 1230.0 kg/m^{3} at a pressure of P _{b} _{0} = 1.0132 ´ 10^{5} Pa and c _{b} = 2.5 ´ 10^{  } ^{10} Pa^{  } ^{1} (Roberts 1996). Porosity, f , is used as defined by Equation (PA.30) with two exceptions: in the repository (see Section PA4.2.3) and in the DRZ and MBs subsequent to fracturing (see Section PA4.2.4). The values of f _{0} and c _{ f } used in conjunction with Equation (PA.30) are listed in Table PA3. The reference pressure P _{b} _{0} in Equation (PA.30) is spatially variable and corresponds to the initial pressures P _{b} (x, y, −5) (here, −5 means at time equal to −5 years; see Section PA4.2.2). The gas and brine viscosities m _{l} , l = g, b in Equation (PA.24) and Equation (PA.25) were assumed to have values of m _{g} = 8.93 ´ 10^{  } ^{6} Pa s (H2:VISCO; see Vargaftik 1975) and m _{b} = 2.1 ´ 10^{  } ^{3} Pa s (BRINESAL:VISCO; see McTigue 1993).
The terms q _{g} , q _{rg} , q _{b} , and q _{rb} in Equation (PA.24) and Equation (PA.25) relate to well injection or removal (i.e., q _{g} , q _{b} ) and reaction, production, or consumption (i.e., q _{rg} , q _{rb} ) of gas and brine, with positive signs corresponding to injection or production and negative signs corresponding to removal or consumption. In the longterm Salado flow calculations, no injection or removal of gas or brine is calculated using q _{g} and q _{b} . Thus, q _{g} and q _{b} 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 Section PA4.7, q _{g} and q _{b} are used to describe injection and production wells in the DBR grid.
More detail on the definition of q _{rg} and q _{rb} is provided in Section PA4.2.5.
In each twophase flow simulation, a short period of time representing disposal operations is simulated. This period of time is called the startup 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 Figure PA12). Table PA5 lists the initial brine pressure, P _{b} , and gas saturation, S _{g} , for the Rustler.
The Salado (Mesh Rows 324 in Figure PA12) is assumed to dip uniformly q = 1 degree downward from north to south (right to left in Figure PA12). 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 P _{b,ref} (SALPRES; see Table PA17) at a reference point located at shaft center at the elevation of the midpoint of MB 139, which is the center of Cell 1272 in Figure PA14. This gives rise to the condition
(PA.53)
Table PA 5. Initial Conditions in the Rustler
Name 
Mesh Row 
P _{b} (x, y, 5), Pa 
S _{g} (x, y, 5) 
Santa Rosa 
33 
1.013250 ´ 10^{5} 
1 
S_{b}
= 0.916 
Santa Rosa 
32 
1.013250 ´ 10^{5} 
1 
S_{b}
= 0.916 
Dewey Lake 
31 
1.013250 ´ 10^{5} 
1 
S_{b}
= 0.916 
Dewey Lake^{c} 
30 
7.355092 ´ 10^{5} 
1 
S_{b}
= 0.916 
Fortyniner^{c} 
29 
1.47328 ´ 10^{6} 
0^{b} 
Magenta 
28 
9.465 ´ 10^{5 } (MAGENTA:PRESSURE) 
0^{b} 
Tamarisk^{c} 
27 
1.82709 ´ 10^{6} 
0^{b} 
Culebra 
26 
9.141 ´ 10^{5} (CULEBRA:PRESSURE) 
0^{b} 
Los Medaños ^{c} 
25 
2.28346 ´ 10^{6} 
0^{b} 
^{a} 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 2008), Section 3.2. ^{c} These pressures are calculated in the ALGEBRA1 step analogously to Equation (PA.53), using the brine density of 1220 kg/m^{3}. See subsequent discussion taking θ = 0 and the reference point (x_{ref} , y_{ref} ) at the top of the Dewey Lake. See the ALGEBRA input file ALG1_BF_CRA09.INP in library LIBCRA09_BF, class CRA091 on the WIPP PA cluster for details. See (Nemer and Clayton 2008), Section 4.1.7 for details on the ALGEBRA1 step. 
where
h(x, y) is defined in Equation (PA.33)
r _{b0} = 1220 kg/m^{3} (BRINESAL:DNSFLUID)
c _{b} = 3.1 ´ 10^{  } ^{10} Pa^{  } ^{1} (BRINESAL:COMPRES)
g = 9.80665 meters per second squared (m/s^{2)}
P _{b,ref} = 1.01325 ´ 10^{5} Pa (BRINESAL:REF_PRES)
P _{b} _{0} = sampled farfield pressure in the undisturbed halite (S_HALITE:PRESSURE)
In the Salado, initial gas saturation S _{g} (x, y, 5) = 0 (see 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 the rest of the Castile and has a different initial pressure, which is a sampled parameter. Specifically, outside the brine reservoir, pressure is calculated using Equation (PA.53) with no dip ( q = 0) in the ALGEBRA1 step. Within the reservoir, P _{b} (x, y, 5) = BPINTPRS, the uncertain initial pressure in the reservoir (see Table PA17). Initial gas saturation S _{g} (x, y, 5) = 0.
Within the shaft (areas Upper Shaft, Lower Shaft, and CONC_MON) and panel closures (areas ROMPCS), P _{b} (x, y, 5) = 1.01325 ´ 10^{5} Pa and S _{g} (x, y, 5) = 1. Within the excavated area (Waste Panel, South RoR, and North RoR, Ops and Exp), P _{b} (x, y, 5) = 1.01325 ´ 10^{5} Pa and S _{g} (x, y, 5) = 1.
At the end of the initial fiveyear startup 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), P _{b} (x, y, 0) = 1.01325 ´ 10^{5} Pa and S _{g} (x, y, 0) = 1 ´ 10^{  } ^{7}. In the panel closures, P _{b} (x, y, 0) = 1.01325 ´ 10^{5} Pa and S _{g} (x, y, 0) = 1  PCS_T1:SAT_RBRN, where PCS_T1:SAT_RBRN is a sampled parameter having a minimum of 0.0 and a maximum of 0.6. In the waste disposal regions (areas Waste Panel, South RoR, and North RoR), P _{b} (x, y, 0) = 1.28039 ´ 10^{5} Pa and S _{g} (x, y, 0) = 0.985 (see WAS_AREA:SAT_IBRN). The initial pressure in the waste disposal regions is greater than atmospheric pressure (1.01325 ´ 10^{5} Pa) to account for the incremental pressure generated by faster initial microbial gas generation rates observed during laboratory experiments (Nemer and Stein 2005, Sections 3.2 and 5.5.2). In the other excavated areas, P _{b} (x, y, 0) = 1.01325 ´ 10^{5} Pa and S _{g} (x, y, 0) = 1.0. The value of initial pressure in the waste disposal regions is identical with that used in the CRA2009 PABC (Clayton et al. 2010).
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 excavationinduced 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 the load on the surrounding rock reached lithostatic, and the deviatoric stress is removed, 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, and North RoR in Figure PA12) 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 quasistatic, largedeformation, finiteelement procedure (Stone 1997). Interpolation procedures are then used with the SANTOS results to define porosity ( f ) within the repository as a function of time, pressure, and gas generation rate.
Fracturing within the anhydrite MBs (i.e., regions MB 138, Anhydrite AB, and MB 139 in Figure PA12) and in the DRZ (region DRZ in Figure PA12) is assumed to occur at brine pressures slightly above lithostatic pressure, and is implemented through a pressuredependent compressibility c _{r} (P _{b} ) (Mendenhall and Gerstle 1995). Specifically, MB fracturing begins at a brine pressure of
(PA.58)
where P _{bi} and P _{b} _{0} are spatially dependent (i.e., P _{b} _{0} = P(x, y, 0) as in Section PA4.2.2) and D P _{i} = 2 ´ 10^{5} Pa (see S_MB138:PI_DELTA in Kicker and Herrick 2013, Table 22)
Fracturing ceases at a pressure of
(PA.59)
and a fully fractured porosity of
where D P _{a} = 3.8 ´ 10^{6} Pa (see S_MB138:PF_DELTA in Kicker and Herrick 2013, Table 22), f _{0} is spatially dependent (Table PA3), and D f _{a} = 0.04, 0.24, and 0.04 for anhydrite materials S_MB138, S_ANH_AB, and S_MB139, respectively (see e.g. S_MB138:DPHIMAX in Kicker and Herrick 2013, Table 22).
Once fractured, compressibility c _{r} becomes a linear function
(PA.61)
of brine pressure for P _{bi} £ P _{b} £ P _{ba} , with c _{ra} defined so that the solution f of
satisfies f (P _{ba} )= f _{a} ; specifically, c _{ra} is given by
The permeability k _{f} ( P _{b} ) of fractured material at brine pressure P _{b} is related to the permeability of unfractured material at brine pressure P _{bi} by
where k is the permeability of unfractured material (i.e., at P _{bi} ) and n is defined so that k _{f} (P _{ba} ) = 1 ´ 10^{  } ^{9} m^{2} (i.e., n is a function of k, which is an uncertain input to the analysis; see ANHPRM in Table PA17). When fracturing occurs, k _{f} (P _{b} ) 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 Figure PA12. 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 (Caporuscio, Gibbons, and Oswald 2003).
Gas production is assumed to result from anoxic corrosion of steel and the microbial degradation of CPR materials. Thus, the gas generation rate q _{rg} in Equation (PA.24) is of the form
(PA.65)
where q _{rgc} is the rate of gas production per unit volume of waste (kg/m^{3}/s) due to anoxic corrosion of Febase metals, q _{rgs} is the rate of gas production per unit volume of waste (kg/m^{3}/s) due to sulfidation of Febase metals, and q _{rgm} is the rate of gas production per unit volume of waste (kg/m^{3}/s) due to microbial degradation of CPR materials. Furthermore, the brine production rate q _{rb} in Equation (PA.25) is of the form
where q _{rbc} is the rate of brine production per unit volume of waste (kg/m^{3}/s) due to anoxic corrosion of Febase metals, q _{rbs} is the rate of brine production per unit volume of waste (kg/m^{3}/s) due to sulfidation of Febase metals, q _{rbm} is the rate of brine production per unit volume of waste (kg/m^{3}/s) due to microbial degradation of CPR materials, q _{rbh} is the rate of brine production per unit volume of waste (kg/m^{3}/s) due to hydration of MgO, and q _{rbhc} is the rate of brine production per unit volume of waste (kg/m^{3}/s) due to hydromagnesite conversion to magnesite (developed in Clayton 2013).
Chemical reactions are assumed to take place only within the waste disposal regions (i.e., Waste Panel, South RoR, and North RoR in Figure PA12) and all the generated gas is assumed to have the same properties as H_{2} (see discussion in Appendix MASS2014, Section MASS3.2 ). In PA, the consumable materials are assumed to be homogeneously distributed throughout the waste disposal regions (i.e., the concentration of Febase metals, CPR materials and MgO in the waste area is not spatially dependent). A separate analysis examined the potential effects on PA results of spatially varying Febase metal and CPR material concentrations, and concluded that PA results are not affected by representing these materials with spatially varying concentrations (see Appendix MASS2014, Section MASS19.0 ).
The rates q _{rgc} , q _{rgs} , q _{rgm} , q _{rbc} , q _{rbs} , q _{rbm} , q _{rbh} , q _{rbhc} (kg/m^{3}/s) are defined by
gas generation by corrosion
(PA.67)
gas generation by sulfidation
microbial gas generation
brine production by corrosion
brine production by sulfidation
microbial brine production
brine production by MgO hydration
brine production by hydromagnesite conversion to magnesite
where
D _{s} = surface area concentration of steel in the repository (m^{2} surface area steel/ m^{3} disposal volume)
D c = mass concentration of cellulosics in the repository (kg biodegradable material/m^{3} disposal volume)
D m = mass concentration of MgO in the repository (kg MgO/m^{3} disposal volume)
D HM = mass concentration of hydromagnesite in the repository (kg hydromagnesite /m^{3} disposal volume)
= molecular weight of H_{2} (kg H_{2}/mol H_{2}), 2.02 ´10^{  } ^{3} kg/mol (Lide 1991, pp. 17, 18)
= molecular weight of water (H_{2}O) (kg H_{2}O/mol H_{2}O), 1.80 ´ 10^{  } ^{2} kg/mol (Lide 1991, pp. 17, 18)
R ci = corrosion rate under inundated conditions (m/s)
R ch = corrosion rate under humid conditions (m/s)
R mi = rate of cellulose biodegradation under inundated conditions (mol C_{6}H_{10}O_{5}/kg C_{6}H_{10}O_{5}/s)
R mh = rate of cellulose biodegradation under humid conditions (mol C_{6}H_{10}O_{5}/kg C_{6}H_{10}O_{5}/s)
R hi = MgO hydration rate under inundated conditions (mol MgO/kg MgO/s)
R hh = MgO hydration rate under humid conditions (mol MgO/kg MgO/s)
R hc = rate of hydromagnesite conversion to magnesite (mol hydromagnesite/kg hydromagnesite/s)
S b,eff = effective brine saturation due to capillary action in the waste materials (see Equation (PA.99) in Section PA4.2.6)
=
= stoichiometric coefficient for gas generation due to corrosion of steel, i.e., moles of H_{2} produced by the corrosion of 1 mole of Fe (mol H_{2}/mol Fe)
= stoichiometric coefficient for gas generation due to sulfidation of steel, i.e., moles of H_{2} produced by the sulfidation of 1 mole of Fe (mol H_{2}/mol Fe)
= stoichiometric coefficient for H_{2}S microbial degradation of cellulose, i.e., moles of H_{2}S generated per mole of carbon consumed by microbial action (mol H_{2}S/mol C)
= stoichiometric coefficient for H_{2} microbial degradation of cellulose, i.e., moles of H_{2} generated per mole of carbon consumed by microbial action (mol H_{2}/mol C)
= stoichiometric coefficient for brine production due to corrosion of steel, i.e., moles of H_{2}O produced per mole of H_{2} generated by corrosion (mol H_{2}O/mol H_{2})
= stoichiometric coefficient for brine production due to sulfidation of steel, i.e., moles of H_{2}O produced per mole of H_{2} generated by sulfidation (mol H_{2}O/mol H_{2})
= stoichiometric coefficient for brine production due to microbial degradation of cellulose, i.e., moles of H_{2}O produced per mole of H_{2} generated by microbial degradation of cellulose (mol H_{2}O/mol H_{2})
= stoichiometric coefficient for brine production due to MgO hydration, i.e., moles of H_{2}O produced per mole of MgO generated by hydration (mol H_{2}O/mol MgO)
= stoichiometric coefficient for brine production due to hydromagnesite conversion to magnesite, i.e., moles of H_{2}O produced per mole of hydromagnesite converted to magnesite (mol H_{2}O/mol hydromagnesite)
r Fe = molar density of steel (mol/m^{3}), 1.41 ´ 10^{5} mol/m^{3} (Telander and Westerman 1993)
B _{fc} = 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 reactions are assumed to continue until the associated substrate (i.e., steel, cellulose, MgO, etc.) is exhausted (i.e., zero order kinetics are assumed). The terms S _{b,eff} and , 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 S _{g} = 1 in the definition of . In PA, R _{ch} = 0 and R _{ci} , R _{mh} , R _{mi} , R_{hi} , R_{hh} , and R_{hc} are defined by uncertain variables (see WGRCOR, WGRMICH, WGRMICI, BRUCITEC, BRUCITES, BRUCITEH and HYMAGCON in Table PA17). However, R _{mh} is now sampled based on the sampled value of R _{mi} : see Nemer and Clayton (Nemer and Clayton 2008, Section 5.1.3 ). The calculations of D _{s} , D _{c} , D _{m} , D _{HM} , X _{c} (H_{2}Fe), X _{s} (H_{2}Fe), X _{m} (H _{2} SC), X _{m} (H_{2}C), X _{c} (H_{2}OH_{2}), X _{s} (H_{2}OH_{2}), X _{m} (H_{2}OH_{2}), X _{h} (H_{2}OMgO), X _{hc} (H_{2}OHM), and B_{fc} are discussed below.
The concentration D _{s} in Equation (PA.67) is defined by
(PA.75)
where
A d = surface area of steel associated with a waste disposal drum (m^{2}/drum)
V R = initial volume of a single room in the repository (m^{3})
n d = ideal number of waste drums that can be closepacked into a single room
In PA, A _{d} = 6 m^{2}/drum (REFCON:ASDRUM), V _{R} = 3,644 m^{3} (REFCON:VROOM), and n _{d} = 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 (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.
In the CRA2004, the probability that microbial gas generation could occur was assigned a value of 0.5. During the CRA2004 PABC, the EPA (Cotsworth 2005) indicated that the probability that microbial gas generation could occur (WMICDFLG) should be set equal to 1 in PA calculations. To comply with the EPA's letter, in the CRA2004 PABC and the CRA2009 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. The same approach is used in the CRA2014 PA. This is summarized in Table PA6, and is discussed further in Nemer and Stein (Nemer and Stein 2005), Section 5.4.
Table PA 6. Probabilities for Biodegradation of Different Organic Materials (WAS_AREA:PROBDEG) in the CRA2014 PA
WAS_AREA:PROBDEG 
Meaning 
Probability CRA2014 
0 
No microbial degradation can occur 
0.0 
1 
Biodegradation of only cellulose can occur 
0.75 
2 
Biodegradation of all CPR materials can occur 
0.25 
Because there are significant uncertainties in whether the experimentally observed gasgeneration rates could be realized in the WIPP repository, during the CRA2004 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 (B_{fc} ). This is discussed further in Nemer, Stein, and Zelinski (Nemer, Stein, and Zelinski 2005), Section 4.2.2. The same approach is used in the CRA2014 PA.
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 (Wang and Brush 1996a). This produces the density calculation
for biodegradation of cellulosics only 
(PA.76 ) 

for biodegradation of CPR materials 
where m _{cel} is the mass of cellulosics (kg), m _{r} is the mass of rubbers (kg), and m _{p} is the mass of plastics (kg).
Mass values for CPR materials can be found in Kicker and Herrick (Kicker and Herrick 2013), Table 26.
The most plausible iron corrosion reactions after closure of the WIPP are believed to be (Wang and Brush 1996a)
Fe + 2H_{2}O = Fe(OH)_{2} + H_{2} (PA.77)
3Fe + 4H_{2}O = Fe_{3}O_{4} + 4H_{2} (PA.78)
When normalized to 1 mole of Fe and linearly weighted by the factors x and , the two preceding reactions become
where x and are the fractions of Fe consumed in the reactions in Equation (PA.77) and Equation (PA.78), respectively. Although magnetite (Fe_{3}O_{4}) has been observed to form on Fe as a corrosion product in lowMg anoxic brines at elevated temperatures (Telander and Westerman 1997) and in oxic brine (Haberman and Frydrych 1988), there is no evidence that it will form at WIPP repository temperatures. If Fe_{3}O_{4} were to form, H_{2} would be produced (on a molar basis) in excess of the amount of Fe consumed. However, anoxic corrosion experiments (Telander and Westerman 1993) did not indicate the production of H_{2} in excess of the amount of Fe consumed. Therefore, the stoichiometric factor x in Reaction (PA.79) is set to 1.0 (i.e., x = 1), which implies that Reaction (PA.77) represents corrosion. Thus, the stoichiometric factor for corrosion is
(PA.80)
which implies that one mole of H_{2} is produced for each mole of Fe consumed, and the stoichiometric factor for brine consumption is
which implies that two moles of H_{2}O are consumed for each mole of H_{2} produced.
The most plausible biodegradation reactions after closure of the WIPP are believed to be (Wang and Brush 1996a)
denitrification C_{6}H_{10}O_{5} + 4.8H^{+} + 4.8NO_{3} ^{  } = 7.4H_{2}O + 6CO_{2} + 2.4N_{2} (PA.82)
sulfate reduction C_{6}H_{10}O_{5} + 6H^{+} + 3SO_{4} ^{2} ^{  } = 5H_{2}O + 6CO_{2} + 3H_{2}S (PA.83)
methanogenesis C_{6}H_{10}O_{5} + H_{2}O = 3CH_{4} + 3CO_{2} (PA.84)
However, in the CRA2004 PABC, the EPA (Cotsworth 2005) directed the DOE to remove methanogenesis (Equation (PA.84)) 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 PA.83), which is energetically and kinetically favored over methanogenesis. In response, the DOE removed methanogenesis from PA. The removal of methanogenesis is discussed fully in Nemer and Zelinski (Nemer and Zelinski 2005). Methanogenesis is also removed in the CRA2014 PA.
The average stoichiometry of Reaction (PA.82), Reaction (PA.83), and Reaction (PA.84), is
C_{6}H_{10}O_{5}/6 + microbes = y (mol) gas + z (mol) H_{2}O + unknowns (PA.85)
where the average stoichiometric factors y and z represent the number of moles of gas (assumed to be H_{2}) and brine produced from each mole of carbon consumed, respectively. In PA, the CO_{2} is ignored, as it is assumed to be consumed by reactions with magnesium materials in the repository. The factors depend on the extent of the individual biodegradation pathways. Then, X _{m} (H_{2}C) is equal to y and X _{m} (H_{2}OH_{2}) is equal to the ratio of z to y.
In the absence of methanogenesis, y and z from Equation (PA.85) become
where F_{NO3} is the fraction of carbon consumed through the denitrification reaction and F_{SO4} is the fraction of carbon consumed by sulfate reduction. F_{NO3} is calculated by comparing the quantity of NO_{3} ^{  } (mols) initially present in the repository ( , 2.74 ´ 10^{7} mol, Kicker and Herrick 2013, Table 31) and the moles of carbon that could be consumed by biodegradation. F_{SO4} is then just one minus F_{NO3} . Since, X _{m} (H _{2} SC) only considers H _{2} S, this stoichiometric factor is
With biodegradation by sulfate reduction, hydrogen sulfide (H _{2} S) is produced. The reactions of iron and its corrosion products with H_{2}S are modeled as
Fe(s) + H_{2}S(g) → FeS(s) + H_{2}(g), (PA.89)
Fe(OH)_{2}(s) + H_{2}S(g) → FeS(s) + 2H_{2}O(l) (PA.90)
In PA it is assumed that Reaction (PA.90) kinetically dominates Reaction (PA.89), and so based on Reaction (PA.90)
To provide added assurance of WIPP performance, a sufficient amount of MgO is added to the repository to remove CO_{2} (Bynum et al. 1997). MgO is emplaced in the repository such that there are at least 1.2 moles of MgO per mole of carbon in the repository (see Appendix MgO2009, Section MgO6.2.4.6 ). MgO in polypropylene "supersacks" is emplaced on top of the threelayer waste stacks to create conditions that reduce actinide solubilities in the repository (see Appendix MgO2014, Section MgO2.1.1 and Appendix SOTERM2014, Section SOTERM2.3 ). The mass concentration of MgO in the repository is calculated by
where
= molecular weight of MgO (kg MgO/mol MgO), 4.03 ´ 10^{  } ^{2} kg/mol (Lide 1997, pp. 468)
= molecular weight of cellulosics (kg cellulosics/mol cellulosics), 2.70 ´ 10^{  } ^{2} kg/mol
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 + H_{2}O(aq and/or g) → Mg(OH)_{2} (PA.94)
In this equation, "aq and/or g" indicates that the H_{2}O reacts with MgO present in the aqueous phase (brine) and/or the gaseous phase and so
The brucite will react with essentially all of the CO_{2} that could be produced by complete microbial consumption of the CPR materials in the waste, and will create hydromagnesite (Appendix MgO2014, Section MgO5.1 and Appendix SOTERM2014, Section SOTERM2.3 )
5 Mg(OH)_{2} + 4 CO_{2}(g) → Mg_{5}(CO_{3})_{4}(OH)_{2} ×4 H_{2}O (PA.96)
Since hydromagnesite is not thermodynamically stable under repository conditions, it is expected to dehydrate to form magnesite.
Mg_{5}(CO_{3})_{4}(OH)_{2}:4 H_{2}O(s) → 4 MgCO_{3}(s) + Mg(OH)_{2}(s) + 4 H_{2}O(l). (PA.97)
and so
The mass concentration of hydromagnesite, D_{HM} , is calculated dynamically and is a function of the biodegradation rate and hydromagnesite conversion to magnesite rate.
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
(PA.99)
where
S b,eff = effective brine saturation
S b = brine saturation
S wick = wicking saturation
S _{min } = minimum brine saturation at which code can run in the wastefilled areas
α = smoothing parameter = 1000
The effective saturation, S _{b,eff,} given by Equation (PA.99) approaches zero as S _{b} approaches a small value S _{min} . In simulations where Fe corrosion dried out the repository, the time required to complete the simulation can be quite long. In order to speed up the code and increase robustness, the parameter S _{min} was added as part of the CRA2009 PA. For PA, S _{min} = 0.015, which is small enough to not affect the results, while greatly reducing run time. This is explained fully in Nemer and Clayton (Nemer and Clayton 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 Figure PA12). The wicking saturation, S _{wick} , is treated as an uncertain variable (see WASTWICK in Table PA17). The effective brine saturation S _{b,eff} is currently used only to calculate chemical reaction rates, and does not directly affect the twophase flow calculations.
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 Sandia National Laboratories (1992), Volume 5, Section 2.3.
The shaft seal model included in the PA grid (Column 43 in Figure PA12) is the simplified shaft model used in the CRA2009 PA. The simplified shaft seal model used in PA is described by Stein and Zelinski (Stein and Zelinski 2003) and is briefly discussed below; this model was approved by the Salado Flow Peer Review Panel (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 CCA, Appendix SEAL). The design is intended to control both shortterm and longterm 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 Performance Assessment Verification Test (PAVT) (Sandia National Laboratories 1997; U.S. DOE 1997) indicated that no significant flows of brine or gas occurred in the shaft during the 10,000year regulatory period. As a result of these analyses, a simplified shaft seal model was developed for the CRA2004 PA.
A conceptual representation of the simplified shaft seal system used in PA is shown in Figure PA15. 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 (James and Stein 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 thicknessweighted mean porosity of the component materials. Other material properties are described in James and Stein (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 (Figure PA15). 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.
Figure PA 15. Schematic View of the Simplified Shaft Model (numbers on right indicate length in meters)
The simplified shaft model was tested in the AP106 analysis (Stein and Zelinski 2003), which supported the Salado Flow Peer Review (Caporuscio, Gibbons, and Oswald 2003). The results of the AP106 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.
The WIPP waste panel closures comprise a feature of the repository that has been represented in WIPP PA regulatory compliance demonstration since the CCA. Following the selection of the Option D panel closure design in 1998, the DOE has reassessed the engineering of the panel closure and established a revised design which is simpler, easier to construct, and equally effective at performing its operationalperiod isolating function. The revised design is the ROMPCS, and is comprised of 100 feet of ROM salt with barriers at each end (Figure PA16). The barriers consist of ventilation bulkheads, and are similar to those used in the panels as room closures. The ventilation bulkheads are designed to restrict air flows and prevent personnel access into wastefilled areas during the operational phase of the repository. The ventilation bulkheads are expected to have no significant impact on longterm performance of the panel closures and are therefore not included in the representation of the ROMPCS. Option D explosion walls fabricated from concrete blocks have been emplaced in the entries of waste panels 1, 2, and 5. It is expected that these walls will not be significant structures after the initial 100year time period, due to the brittle, nonplastic behavior of concrete. The already emplaced explosion walls are therefore expected to have no significant impact on longterm panel closure performance, and so are also not included in the representation of the ROMPCS. Consequently, the ROMPCS is modeled as consisting of 100 feet of ROM salt in the WIPP PA.

(a) Panel closure with 100 feet of ROM salt between two ventilation bulkheads 

(b) Panel closure with 100 feet of ROM salt between a ventilation bulkhead and explosion wall 
Figure PA 16. Schematic Diagram of the ROMPCS
Material parameters and timings used to represent the ROMPCS are developed to account for the following physical processes and accepted rock mechanics principles:
1. Creep closure of the salt rock surrounding panel entries will cause consolidation of ROM salt emplaced in panel entries.
2. Eventually, the ROM salt comprising the closures will approach a condition similar to intact salt.
3. As ROM salt reaches higher fractional densities during consolidation, back stress will be imposed on the surrounding rock mass leading to eventual healing of the DRZ.
4. DRZ healing above and below the ROM salt panel closures will reduce DRZ porosity and permeability in those areas.
ROMPCS properties are based on three time periods (see Camphouse et al. 2012a, Camphouse 2013c, and Camphouse et al. 2013) to capture the temporal dependence of the physical processes listed above. Consequently, the ROMPCS is represented by three materials, with each material representing the ROMPCS for a portion of the 10,000year regulatory period. Material PCS_T1 represents the ROMPCS for the first 100 years after facility closure. Material PCS_T2 models the ROMPCS from 100 to 200 years. Finally, material PCS_T3 represents the ROMPCS from years 200 to 10,000. For the first 200 years postclosure, the DRZ above and below the ROMPCS maintains the same properties as specified to the DRZ surrounding the disposal rooms (PA material DRZ_1). After 200 years, the DRZ above and below the ROMPCS is modeled as having healed, and is represented by material DRZ_PCS(see Figure PA12 and Appendix MASS2014, Section 4.1.3 ). Material DRZ_1 has the same properties in the CRA2014 PA as were assigned to it in the CRA2009 PABC. The permeability of material DRZ_PCS is modified slightly in the CRA2014 PA as compared to the CRA2009 PABC (see Appendix PA2009, Section 4.2.8.3 for a discussion of material DRZ_PCS used in the CRA2009 PABC). The healing of the DRZ region above and below the ROMPCS will not yield a higher permeability than that above the rooms. A relationship is implemented in the CRA2014 PA to enforce that the permeability of material DRZ_PCS is never greater than the permeability of material DRZ_1. The constraint placed on the permeability for DRZ_PCS is that DRZ_PCS:PRMX ≤ DRZ_1:PRMX, and likewise in the y and z directions. If the sampled permeability for DRZ_PCS is greater than that obtained for DRZ_1, then DRZ_PCS retains the DRZ_1 permeability. The uncertainty distributions specified for the permeabilities of materials DRZ_1 and DRZ_PCS in the CRA2014 PA are identical to those used in the CRA2009 PABC.
As developed in Camphouse et al. (Camphouse et al. 2012b), permeability and porosity values are obtained through sampling for ROMPCS material PCS_T1. Porosity values are sampled for materials PCS_T2 and PCS_T3 and then used to calculate permeability values for these materials. The relationship used to calculate the permeability of material PCS_T2 is of the form
where k_{2} is the calculated permeability for PCS_T2, f _{ 2 } is the sampled PCS_T2 porosity value, and α is sampled from a normal distribution having a mean of 0, a standard deviation of 0.86,
and truncated at ±2 standard deviations. An analogous relationship is used for PCS_T3, and is of the form
Overlap in the porosity ranges for materials PCS_T1 and PCS_T2 potentially results in an increase in panel closure porosity during the transition from PCS_T1 to PCS_T2 at 100 years, a nonphysical result. To prevent this possibility, the porosity for PCS_T2 is conditionally sampled so that PCS_T2:POROSITY ≤ PCS_T1:POROSITY for all vectors. For similar reasons, the porosity for material PCS_T3 is conditionally sampled so that PCS_T3:POROSITY ≤ PCS_T2:POROSITY. Similar constraints are placed on the calculated permeabilities for materials PCS_T2 and PCS_T3. The calculated permeability value for PCS_T2 is constrained such that PCS_T2:PRMX ≤ PCS_T1:PRMX. If the calculated permeability for PCS_T2 is greater than the sampled permeability for PCS_T1, then PCS_T2 retains the sampled PCS_T1 permeability. The same is true for the calculated permeabilities in the y and z directions. A similar constraint is placed on the calculated permeability for PCS_T3 in order to prevent nonphysical instantaneous increases in panel closure permeability at 200 years. The constraint placed on the calculated permeability for PCS_T3 is that PCS_T3:PRMX ≤ PCS_T2:PRMX, and likewise in the x and y directions. If the calculated permeability for PCS_T3 is greater than the permeability for PCS_T2, then PCS_T3 retains the sampled PCS_T2 permeability. Uncertain parameters representing the ROMPCS are listed in Kicker and Herrick (Kicker and Herrick 2013), Table 4.
The major disruptive event in PA is the penetration of the repository by a drilling intrusion. The same numerical grid is used for undisturbed and borehole intrusion scenarios. In the undisturbed scenario (see Section PA6.7.1), grid cells corresponding to the intrusion location have the material properties of the neighboring stratigraphic or excavated modeling unit. There is no designation in the borehole grid except for the reduced lateral dimensions of this particular column of grid cells.
In the scenarios simulating drilling disturbance, cells corresponding to the intrusion location start out with the same material properties as in the undisturbed scenario. At the time of intrusion, these cells are reassigned borehole material properties. The drilling intrusion is modeled by modifying the permeability of the grid blocks in Column 26 of Figure PA12 (values listed in Table PA7). Furthermore, the drilling intrusion is assumed to produce a borehole with a diameter of 12.25 in. (0.31115 m) (Vaughn 1996; 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 Table PA3). When a borehole that penetrates pressurized brine in the Castile is simulated (i.e., an E1 intrusion), the permeability modifications indicated in Table PA7 extend from the ground surface (i.e., Grid Cell 2155 in Figure PA14) to the base of the pressurized brine (i.e., Grid Cell 2225 in Figure PA14). 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 Table PA7 stop at the floor of the intruded waste panel (i.e., Grid Cell 1419 in Figure PA14).
Highpressure Castile brine was encountered in several WIPParea boreholes, including the WIPP12 borehole within the controlled area and the U.S. Energy Research and Development Administration (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
Figure PA12) and a reservoir (Row 1, Columns 23 to 45 in Figure PA12). The Castile region has an extremely low permeability, which prevents it from participating in fluid flow processes.
Table PA 7. Permeabilities for Drilling Intrusions Through the Repository
Time After Intrusion 
Assigned Permeabilities 
0200 years 
Concrete 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 Figure PA14) and the Los Medaños 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 Figure PA14). Concrete plugs are assumed to have a permeability loguniformly sampled between 10^{19} m^{2} to 10^{17}m^{2} (see material CONC_PLG in Kicker and Herrick (2013), Table 4). The open portions of the borehole are assumed to have a permeability of 1 ´ 10^{ 9} m^{2}. 
2001200 years 
Concrete plugs are assumed to fail after 200 years (U.S. DOE 1995). An entire borehole is assigned a permeability typical of silty sand loguniformly sampled between 10^{16.3} m^{2} and 10^{11} m^{2} (see parameter BHPRM and material BH_SAND in Kicker and Herrick 2013, Table 4). 
> 1200 years 
Permeability of borehole reduced by one order of magnitude in the Salado beneath the repository due to creep closure of borehole (Thompson et al. 1996) (i.e., k = 10 ^{x} /10, x = BHPRM, in Grid Cells 2225, 1576, 26, 94, 162, 230, 1135, 1142, 1149 of Figure PA14) (see material BH_CREEP in Kicker and Herrick 2013, Table 4). 
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 Appendix MASS2014, Section MASS.17.0 ). A range of probabilities for a borehole hitting a brine reservoir is used (see Section PA3.6).
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 Table PA17).
Where they exist, Castile brine reservoirs in the northern Delaware Basin are believed to be fractured systems, with highangle 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 (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 WIPP12 and ERDA6 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.
Determining gas and brine flow in the vicinity of the repository requires solving the two nonlinear PDEs in Equation (PA.24), Equation (PA.25), Equation (PA.26), Equation (PA.27), Equation (PA.28), Equation (PA.29) and Equation (PA.30) on the computational domain in Figure PA12, along with evaluating appropriate auxiliary conditions. The actual unknown functions in this solution are P _{b} and S _{g} , although the constraint conditions also give rise to values for P _{g} and S _{b} . As two dimensions in space and one dimension in time are in use, P _{b} , P _{g} , S _{b} , and S _{g} are functions of the form P _{b} (x, y, t), P _{g} (x, y, t), S _{b} (x, y, t), and S _{g} (x, y, t).
Solving Equation (PA.24), Equation (PA.25), Equation (PA.26), Equation (PA.27), Equation (PA.28), Equation (PA.29) and Equation (PA.30) requires both initial value and boundary value conditions for P _{b} and S _{g} . The initial value conditions for P _{b} and S _{g} are given in Section PA4.2.2. 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 (Table PA8). This Neumanntype 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 8. Boundary Value Conditions for P _{g} and P _{b}
Boundaries below (Row 1, y = 0 m) and above (Row 33, y = 1039 m) system for 0 £ x £ 46630 m (Columns 168) and 5 yr £ t. Below, j refers to the unit normal vector in the positive y direction. 

× j = 0 Pa / m 
No gas flow condition 
× j = 0 Pa / m 
No brine flow condition 
Boundaries at left (Column 1, x = 0 m) and right (Column 68, x = 46630 m) of system for 0 £ y £ 1039 m (Rows 133) and 5 yr £ t. Below, i refers to the unit normal vector in the positive x direction. 

× i = 0 Pa / m 
No gas flow condition 
× i = 0 Pa / m 
No brine flow condition 
block. This is not a boundary condition and is not required to close the problem. This feature is used to specify Dirichlettype conditions at the surface grid blocks (Columns 168, Row 33,
Figure PA12) and at the farfield locations in the Culebra and Magenta (Columns 1 and 68, Row 26, and Columns 1 and 68, Row 28, Figure PA12
). These auxiliary conditions are summarized in Table PA9.
Table PA 9. Auxiliary Dirichlet Conditions for S _{g} and P _{b}
Surface Grid Blocks 

= 0.08363 
Columns 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 ´ 10^{5} Pa 
Columns 168, row 33, 5 yr £ t 
Culebra and Magenta Far Field 

= 9.14 ´ 10^{5} Pa 
i = 1 and 68, j = 26, 5 yr £ t (Culebra) 
= 9.47 ´ 10^{5} Pa 
i = 1 and 68, j = 28, 5 yr £ t (Magenta) 
A fully implicit finitedifference procedure is used to solve Equation (PA.24), Equation (PA.25), Equation (PA.26), Equation (PA.27), Equation (PA.28), Equation (PA.29) and Equation (PA.30). The associated discretization of the gas mass balance equation is given by
where F represents the phase potentials given by
and
the subscripts are defined by
i = xdirection grid index
j = ydirection grid index
= xdirection grid block interface
= ydirection grid block interface
x _{i} = grid block center in the xcoordinate direction (m)
y _{j} = grid block center in the ycoordinate direction (m)
= grid block length in the xcoordinate direction (m)
= grid block length in the ycoordinate 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 k _{rg} in Equation (PA.100) 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 a r _{g}k _{x} / m _{g} and a r _{g}k _{y} / m _{g} are obtained by harmonic averaging of adjacent grid block values for these expressions. Currently all materials are isotropic, i.e. k _{x} = k _{y} = k _{z} .
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, P _{g} and S _{b} are replaced in the numerical implementation with the substitutions indicated by Equation (PA.27) and Equation (PA.26), respectively. Wells are not used in the conceptual model for longterm Salado flow calculations, but they are used for DBR calculations. Thus, for longterm Salado flow calculations, the terms q _{g} and q _{b} are zero. For longterm 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 Figure PA12).
The resultant coupled system of nonlinear brine and gas mass balance equations is integrated in time using the NewtonRaphson 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.
The Darcy velocity vectors v _{g} (x, y, t) and v _{b} (x, y, t) for gas and brine flow (m^{3}/m^{2}/s = m/s) are defined by the expressions
(PA.101)
and
Values for v _{g} and v _{b} are obtained and saved as the numerical solution of Equation (PA.24), Equation (PA.25), Equation (PA.26), Equation (PA.27), Equation (PA.28), Equation (PA.29) and Equation (PA.30) is carried out. Cumulative flows of gas, C _{g} (t, B), and brine, C _{b} (t, B), from time 0 to time t across an arbitrary boundary B in the domain of (Figure PA12) is then given by
(PA.103)
for l = g, b, where a (x, y) is the geometry factor defined in Equation (PA.32), n(x, y) is an outwardpointing unit normal vector, and denotes a line integral. As an example, B could correspond to the boundary of the waste disposal regions in Figure PA12. The integrals defining C _{g} (t, B) and C _{b} (t, B) are evaluated using the Darcy velocities defined by Equation (PA.101) and Equation (PA.102). Due to the dependence of gas volume on pressure, C _{g} (t, B) is typically calculated in moles or cubic meters at standard temperature and pressure, which requires an appropriate change of units for v _{g} in the calculation of C_{l}(t,B).
Additional information on BRAGFLO and its use in the CRA2014 PA can be found in the BRAGFLO user's manual (Camphouse 2013b), the BRAGFLO design document (Camphouse 2013a) and the analysis package for the Salado flow calculations in the CRA2014 PA (Camphouse 2013c).
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 the shaft, without reaching the surface as a DBR, 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 and to the land surface due to longterm flow are set to zero.
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 radionuclide's full transport is performed (see Section PA6.7.2).
This section describes the model used to compute radionuclide transport in the Salado for E0, E1, and E2 scenarios (defined in Section PA2.3.2). The model for transport in the E1E2 scenario, which is computed using the PANEL code, is described in Section PA4.4.
NUTS models radionuclide transport by advection (see Appendix MASS2014, Section MASS12.5 ). 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 reactionrate 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 Appendix MASS2014, Section MASS12.5.
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 actinide 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, colloidalsized precipitates will behave like mineralfragment 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, 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 Section PA4.2.4). The processes and effects associated with fracture dilation or fracture propagation not already captured by the PA fracture model are negligible (see the CCA, Appendix MASS, Section MASS.13.3 and 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 largeraperture sections of a fracture network with locally high permeabilities. It could locally enhance actinide 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 theportions 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 liquidsaturated 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 actinide transport, however, because actinides of interest are transported only in the liquid phase, which will not displace gas in the relatively highpermeability regions due to capillary effects.
The following system of PDEs is used to model radionuclide transport in the Salado:
 Ñ × (PA.104)
for l = 1, 2, …, n _{R} , where
= Darcy velocity vector (m^{3}/m^{2}/s = m/s) for brine (supplied by BRAGFLO from solution of Equation (PA.102))
C bl = concentration (kg/m^{3}) of radionuclide l in brine
C sl = concentration (kg/m^{3}) 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 Figure PA12)
S l = linkage term (kg/m^{3}/s) due to dissolution/precipitation between radionuclide l in brine and in solid phase (see Equation (PA.106))
f = porosity (supplied by BRAGFLO from solution of Equation (PA.24), Equation (PA.25), Equation (PA.26), Equation (PA.27), Equation (PA.28), Equation (PA.29) and Equation (PA.30))
S b = brine saturation (supplied by BRAGFLO from solution of Equation (PA.24), Equation (PA.25), Equation (PA.26), Equation (PA.27), Equation (PA.28), Equation (PA.29) and Equation (PA.30))
l l = decay constant (s^{ 1}) for radionuclide l
P(l) = {p: radionuclide p is a parent of radionuclide l}
n _{R} = number of radionuclides,
and a is the dimensiondependent geometry factor in Equation (PA.32). PA uses a twodimensional representation for fluid flow and radionuclide transport in the vicinity of the repository, with a defined by the element depths in Figure PA12. Although omitted for brevity, the terms a, v _{b} , C _{bl} , C _{sl} , S _{l} , S _{b} , and f are functions a (x, y), v _{b} (x, y, t), C _{bl} (x, y, t), C _{sl} (x, y, t), S _{l} (x, y, t), S _{b} (x, y, t), and f (x, y, t) of time t and the spatial variables x and y. Equation (PA.104) and Equation (PA.105) are defined and solved on the same computational grid (Figure PA12) used by BRAGFLO for the solution of Equation (PA.24), Equation (PA.25), Equation (PA.26), Equation (PA.27), Equation (PA.28), Equation (PA.29) and Equation (PA.30).
Radionuclides are assumed to be present in both brine (Equation (PA.104)) and in an immobile solid phase (Equation (PA.105)), although radionuclide transport takes place only by brine flow (Equation (PA.104)). Maximum radionuclide concentrations are calculated for elements dissolved in Salado and Castile brines for oxidation states III, IV, and V. Maximum concentrations are dependent on the dissolved solubility (mols per liter mol/L) for each brine type and oxidation state, as well as the uncertainty associated with the dissolved solubility. Dissolved solubilities and their uncertainties are developed in Brush and Domski (Brush and Domski 2013b and Brush and Domski 2013c), and are listed in Kicker and Herrick (Kicker and Herrick 2013), Table 27, Table A8 , and Table A9. Only the maximum concentration corresponding to the minimum brine volume of 17,400 m^{3} is used in Salado transport calculations due to the computational expense associated with NUTS. This approach is conservative as it maximizes the concentration of actinides that are potentially transported across the LWB.
The maximum radionuclide concentration is assumed to equilibrate instantly for each element (Am, Pu, U, Th). Then each individual radionuclide equilibrates between the brine and solid phases based on the maximum concentration of the radionuclide and the mole fractions of other isotopes included in the calculation. The linkage between the brine and solid phases in Equation (PA.104) and Equation (PA.105) is accomplished by the term S _{l} , where
(PA.106)
where
= maximum concentration (kg/m^{3}) 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.
_{ } = 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 Î El(l) only if k is an isotope of element El(l):
= difference (kg/m^{3}) between maximum concentration of element El(l) in brine and existing concentration of element El(l) in brine
MF
pl
= mole fraction of radionuclide l in phase p, where p = b (brine) or
p = s (solid)
CM l = conversion factor (mol/kg) from kilograms to moles for radionuclide l
= Dirac delta function (s^{  } ^{1}) ( d ( t  t) = 0 if t ¹ t and )
The terms S _{l} , S _{b} , C _{p,El(l)} , MF _{pl} , and f are functions of time t and the spatial variables x and y, although the dependencies are omitted for brevity. The Dirac delta function, d( t  t), appears in Equation (PA.106) to indicate that the adjustments to concentration are implemented instantaneously within the numerical solution of Equation (PA.104) and Equation (PA.105) whenever a concentration imbalance is observed.
The velocity vector v _{b} in Equation (PA.104) and Equation (PA.105) is defined in Equation (PA.102) and is obtained from the numerical solution of Equation (PA.24), Equation (PA.25), Equation (PA.26), Equation (PA.27), Equation (PA.28), Equation (PA.29) and Equation (PA.30). If B denotes an arbitrary boundary (e.g., the LWB) in the domain of Equation (PA.104) and Equation (PA.105) (as shown in Figure PA12), the cumulative transport of C _{l} (t, B) of radionuclide l from time 0 to time t across B is given by
(PA.110)
where n (x, y) is an outwardpointing unit normal vector and denotes a line integral over B.
Equation (PA.104) and Equation (PA.105) models advective radionuclide transport due to the velocity vector v _{b} .
Since the solution of Equation (PA.104) and Equation (PA.105) for many radionuclides and decay chains is computationally very expensive, the number of radionuclides for direct inclusion in the analysis is initially reduced using the algorithm shown in Figure PA17. The number of radionuclides included in the transport calculations is then further reduced by combining those with similar decay and transport properties. The CRA2014 PA uses the same reduction algorithm as the CCA PA (see the CCA, Appendix WCA); the algorithm was found to be acceptable in the CCA review (U.S. EPA 1998a, Section 4.6.1.1 ).
Figure PA 17. Selecting Radionuclides for the Release Pathways Conceptualized by PA
Using Figure PA17, the number of radionuclides initially included in the decay calculations is 29. These radionuclides are the same as those in the CRA2009 PABC, and belong to the following decay chains:
(PA.111)
Radionuclides considered in the decay calculations that do not belong to one of the decay chains listed above are ^{147}Pm, ^{137}Cs, and ^{90}Sr. In addition, some intermediates with extremely short halflives, such as ^{240}U, 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, ^{137}Cs and ^{90}Sr 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.
After the reduction of radionuclides outlined inFigure PA17 and the paragraph above, the following 10 radionuclides remained from the decay chains shown:
(PA.115)
^{238}Pu does not significantly affect transport calculations because of its short halflife (87.8 years). The remaining nine radionuclides were then further reduced by combining those with similar decay and transport properties. In particular, ^{234}U, ^{230}Th, and ^{239}Pu were used as surrogates for the groups {^{234}U, ^{233}U}, {^{230}Th, ^{229}Th}, and {^{242}Pu, ^{240}Pu, ^{239}Pu}, with the initial inventories of ^{234}U, ^{230}Th, and ^{239}Pu being increased to account for the additional radionuclide(s) in each group.
In increasing the initial inventories, the individual radionuclides were combined (or "lumped" together) on either a mole or curie basis (i.e., moles added and then converted back to curies, or curies added directly (see Kicker and Zeitler 2013b)). In each case, the method that maximized the combined inventory was used; thus, ^{233}U was added to ^{234}U, ^{240}Pu to ^{239}Pu, and ^{229}Th to ^{230}Th by curies, while ^{242}Pu was added to ^{239}Pu by moles. In addition, ^{241}Pu was added to ^{241}Am by moles because ^{241}Pu has a halflife of 14 years and will quickly decay to ^{241}Am. The outcome of this process was the following set of five radionuclides in three simplified decay chains:
which were then used with Equation (PA.104) and Equation (PA.105) for transport in the vicinity of the repository. The development of these "lumped" radionuclide inventories is done in Kicker and Zeitler (Kicker and Zeitler 2013b), and the results are listed in Kicker and Herrick (Kicker and Herrick 2013), Table 29. These "lumped" radionuclides closely approximate the activity of the total normalized waste inventory (Kim 2013b).
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/m^{3}. 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 10^{7} 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 10^{7} 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 10^{6} EPA units, the smallest release displayed in CCDF construction (Stockman 1996). The largest normalized release would be 9.98 × 10^{7} EPA units, corresponding to 10^{  } ^{7} kg of ^{241}Am if the release was entirely ^{241}Am.
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 (^{241}Am, ^{239}Pu, ^{238}Pu, ^{234}U, and ^{230}Th). These radionuclides represent a larger number of radionuclides; as discussed in Section PA4.3.2, radionuclides were grouped together based on similarities, such as isotopes of the same element and those with similar halflives, to simplify the calculations. For transport purposes, solubilities are lumped to represent both dissolved and colloidal forms. These groupings simplify and expedite calculations.
Equation (PA.104) and Equation (PA.105) are numerically solved by the NUTS program (WIPP Performance Assessment 1997a) on the same computational grid (Figure PA12) used by BRAGFLO for the solution of Equation (PA.24), Equation (PA.25), Equation (PA.26), Equation (PA.27), Equation (PA.28), Equation (PA.29), and Equation (PA.30). In the solution procedure, Equation (PA.104) and Equation (PA.105) are numerically solved with S _{l} = 0 for each time step, with the instantaneous updating of concentrations indicated in Equation (PA.106) and the appropriate modification to C _{sl} in Equation (PA.105) taking place after the time step. The solution is carried out for the five radionuclides indicated in Equation (PA.119).
The initial value and boundary value conditions used with Equation (PA.104) and Equation (PA.105) are given in Table PA10. 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 (PA.106) then immediately adjust the values for C _{bl} (x, y, t) and C _{sl} (x, y, t) for consistency with the constraints imposed by S _{T} (Br, Ox, El) and available radionuclide inventory.
The n _{R} PDEs in Equation (PA.104) and Equation (PA.105) 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 C _{bl}, so that the unknown function is represented by C _{l}.
· A superscript n denotes time t _{n}, with the assumption that the solution C _{l} is known at time t _{n} and is to be propagated to time t _{n+1}.
· The grid indices are i in the xdirection and j in the ydirection, and are the same as the BRAGFLO grid indices.
Table PA 10. Initial and Boundary Conditions for C _{bl}(x, y, t) and C _{sl}(x, y, t)
Initial Conditions for C _{bl}(x, y, t) and C _{sl}(x, y, t) 
= if (x, y) is a point in the repository (i.e., areas Waste Panel, South RoR and North RoR, in Figure PA12), where A_{l} (0) is the amount (kg) of radionuclide l present at time t = 0 and V_{b} (0) is the amount (m^{3}) of brine in repository at time t = 0 (from solution of Equation (PA.24), Equation (PA.25), Equation (PA.26), Equation (PA.27), Equation (PA.28), Equation (PA.29) and Equation (PA.30) with BRAGFLO) for all (x, y). = 0 otherwise. = 0 if (x, y) is a point in the repository. 
Boundary Conditions for C _{bl}(x, y, t) 
= , where B is any subset of the outer boundary of the computational grid in Figure PA12, is the flux (kg/s) at time t of radionuclide l across B, v _{b} (x, y, t) is the Darcy velocity (m^{3}/m^{2}/s) of brine at (x, y) on B and is obtained from the solution of Equation (PA.24) Equation (PA.25), Equation (PA.26), Equation (PA.27), Equation (PA.28), Equation (PA.29), and Equation (PA.30) by BRAGFLO, n (x, y) denotes an outwardpointing 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, v _{b}, f , and S _{b}) every 20 time steps.
The following finitedifference discretization is used for the l ^{th} equation in each grid block (i, j):
(PA.120)
where q _{b} is the grid block interfacial brine flow rate (m^{3}/s) and V _{R} is the grid block volume (m^{3}). The quantity q _{b} is based on and a in Equation (PA.104) and Equation (PA.105), and the quantity V _{R} is based on grid block dimensions (Figure PA12) and a.
The interfacial values of concentration in Equation (PA.120) are discretized using the onepoint upstream weighting method (Aziz and Settari 1979), which results in
(PA.121)
where w derives from the upstream weighting for flow between adjacent grid blocks and is defined by
By collecting similar terms, Equation (PA.121) can be represented by the linear equation
where