PA-1.0  Introduction

This appendix presents the mathematical models used to evaluate performance of the Waste Isolation Pilot Plant (WIPP) disposal system and the results of these models for the 2009 Compliance Recertification Application (CRA-2009) Performance Assessment (PA).  The term PA signifies an analysis that (1) identifies the processes and events that might affect the disposal system; (2) examines the effects of these processes and events on the performance of the disposal system; and (3) estimates the cumulative releases of radionuclides, considering the associated uncertainties, caused by all significant processes and events (40 CFR § 191.12 [U.S. Environmental Protection Agency 1993]).  PA is designed to address three primary questions about the WIPP:

Q1:        What processes and events that might affect the disposal system could take place at the WIPP site over the next 10,000 years?

Q2:        How likely are the various processes and events that might affect the disposal system to take place at the WIPP site over the next 10,000 years?

Q3:        What are the consequences of the various processes and events that might affect the disposal system that could take place at the WIPP site over the next 10,000 years?

In addition, accounting for uncertainty in the parameters of the PA models leads to a further question:

Q4:        How much confidence should be placed in answers to the first three questions?

These questions give rise to a methodology for quantifying the probability distribution of possible radionuclide releases from the WIPP repository over the next 10,000 years and characterizing the uncertainty in that distribution due to imperfect knowledge about the parameters contained in the models used to predict releases. The containment requirements of 40 CFR § 191.13 require this probabilistic methodology.

This appendix is organized as follows: Section PA-2.0 gives an overview and describes the overall conceptual structure of the CRA-2009 PA.  The WIPP PA is designed to address the requirements of section 191.13, and thus involves three basic entities:  (1) a probabilistic characterization of different futures that could occur at the WIPP site over the next 10,000 years, (2) models for both the physical processes that take place at the WIPP site and the estimation of potential radionuclide releases that may be associated with these processes, and (3) a probabilistic characterization of the uncertainty in the models and parameters that underlies the WIPP PA.  Section PA-2.0 is supplemented by Appendix SCR-2009, which documents the results of the screening process for features, events, and processes (FEPs) that are retained in the conceptual models of repository performance.

Section PA-3.0 describes the probabilistic characterization of different futures.  This characterization plays an important role in the construction of the complementary cumulative distribution function (CCDF) specified in section 191.13.  Regulatory guidance and extensive review of the WIPP site identified exploratory drilling for natural resources and the mining of potash as the only significant disruptions at the WIPP site with the potential to affect radionuclide releases to the accessible environment.  Section PA-3.0 summarizes the stochastic variables that represent future drilling and mining events in the PA.  The results of the PA for CRA-2009, as documented in Section PA-7.0, Section PA-8.0, and Section PA-9.0 of this appendix, confirm that direct releases from drilling intrusions are the major contributors to radionuclide releases to the accessible environment.

Section PA-4.0 presents the mathematical models for both the physical processes that take place at the WIPP and the estimation of potential radionuclide releases. The mathematical models implement the conceptual models as prescribed in 40 CFR § 194.23 (2004), and permit the construction of the CCDF specified in section 191.13.  Models presented in Section PA-4.0 include two-phase (i.e., gas and brine) flow in the vicinity of the repository; radionuclide transport in the Salado Formation (hereafter referred to as the Salado); releases to the surface at the time of a drilling intrusion due to cuttings, cavings, spallings, and direct brine releases (DBRs); brine flow in the Culebra Dolomite Member of the Rustler Formation (hereafter referred to as the Culebra); and radionuclide transport in the Culebra.  Section PA-4.0 is supplemented by Appendices MASS-2009, TFIELD-2009, and PORSURF-2009.  Appendix MASS-2009 discusses the modeling assumptions used in the WIPP PA.  Appendix TFIELD-2009 discusses the generation of the transmissivity fields (T fields) used to model groundwater flow in the Culebra.  Appendix PORSURF-2009 presents results from modeling the effects of excavated region closure, waste consolidation, and gas generation in the repository.

Section PA-5.0 discusses the probabilistic characterization of parameter uncertainty, and summarizes the uncertain variables incorporated into the CRA-2009 PA, the distributions assigned to these variables, and the correlations between variables.  Section PA-5.0 is supplemented by Fox (2008) and Appendix SOTERM-2009.  Fox (2008) catalogs the full set of parameters used in the CRA-2009 PA, previously referred to as the CCA Appendix PAR and the CRA-2004, Appendix PA, Attachment PAR.  Appendix SOTERM-2009 describes the actinide (An) source term for the WIPP performance calculations, including the mobile concentrations of actinides that may be released from the repository in brine.

Section PA-6.0 summarizes the computational procedures used in the CRA-2009 PA, including sampling techniques (i.e., random and Latin hypercube sampling (LHS)); sample size, statistical confidence for mean CCDF, generation of sample, generation of individual futures, construction of CCDFs, calculations performed with the models discussed in Section PA-4.0, construction of releases for each future, and the sensitivity analysis techniques in use.

Section PA-7.0 presents the results of the PA for an undisturbed repository.  Releases from the undisturbed repository are determined by radionuclide transport in brine flowing from the repository to the land withdrawal boundary (LWB) through the marker beds (MBs) or shafts.  Releases in the undisturbed scenario are used to demonstrate compliance with the individual and groundwater protection requirements in 40 CFR Part 191 (40 CFR § 194.51 and 40 CFR § 194.52).

Section PA-8.0 presents PA results for a disturbed repository.  As will be discussed in Section PA-2.3.1, the only future events and processes in the analysis of disturbed repository performance are those associated with mining and deep drilling.  Release mechanisms include direct releases at the time of the intrusion via cuttings, cavings, spallings, and DBR, and long-term releases via radionuclide transport up abandoned boreholes to the Culebra and thence to the LWB.

Section PA-9.0 presents the set of CCDFs resulting from the CRA-2009 PA.  This material supplements 40 CFR § 194.34, which demonstrates compliance with the containment requirements of section 191.13.  Section PA-9.0 presents the most significant output variables from the PA models, accompanied by sensitivity analyses to determine which subjectively uncertain parameters are most influential in the uncertainty of PA results.

The overall structure of the CRA-2009 PA does not differ from that presented in the first WIPP Compliance Certification Application (CCA) (U.S. Department of Energy 1996), the CRA-2004 (U.S. Department of Energy 2004) or the CRA-2004 Performance Assessment Baseline Calculation (PABC) (Leigh et al. 2005).  This recertification application appendix follows the approach used by Helton et al. (1998) to document the mathematical models used in the CCA PA and the results of that analysis.  Much of the content of this appendix derives from Helton et al. (1998); these authors’ contributions are gratefully acknowledged.

PA-2.0  Overview and Conceptual Structure of the PA

Because of the amount and complexity of the material presented in Appendix PA-2009, an introductory summary is provided below, followed by detailed discussions of the topics in the remainder of this section, which is organized as follows:

Section PA-2.1 – Overview of PA and the results

Section PA-2.2 – The conceptual structure of the PA used to evaluate compliance with the containment requirements

Section PA-2.3 – The overall methodology used to develop FEPs, the screening methodology applied to the FEPs, the results of the screening process, and the development of the scenarios considered in the system-level consequence analysis

The U.S. Department of Energy (DOE) continues to use the same PA methodology as in the CCA and CRA-2004 because changes that have been made since the U.S. Environmental Protection Agency (EPA) certified WIPP do not impact PA methodology.  A corresponding detailed presentation for the CRA-2004 PA methodology is provided in the CRA-2004, Chapter 6.0, Section 6.1, and a detailed presentation for the CRA-2004 PABC implementation is provided in Leigh et al. (2005).  A corresponding detailed presentation for the CCA PA methodology is provided in Helton et al. (1998, Section 2).

PA-2.1  Overview of Performance Assessment

A demonstration of future repository performance was required by the disposal standards in Part 191.  The EPA required a PA to demonstrate that potential cumulative releases of radionuclides to the accessible environment over a 10,000-year period after disposal are less than specified limits based on the nature of the materials disposed (section 191.13).  The PA is to determine the effects of all significant processes and events that may affect the disposal system, consider the associated uncertainties of the processes and events, and estimate the probable cumulative releases of radionuclides.

A PA was included in the CCA.  This was the first demonstration of compliance by the DOE with the EPA’s disposal standards.  The EPA required a verification PA based on the CCA PA that included revised parameters and distributions.  This PA was termed the CCA Performance Assessment Verification Test (PAVT) (Trovoto 1997).  The EPA based the original certification of the WIPP on the information in the CCA and the results of the CCA PAVT (U.S. Environmental Protection Agency 1998a).  The CCA PAVT is documented in Sandia National Laboratories (SNL) 1997 and U.S. Department of Energy 1997.

The WIPP is required to be recertified every five years after first waste receipt (Public Law 02-579).  A revised PA was included in the first recertification application in 2004.  This PA is termed the CRA-2004 PA, and is documented in the CRA-2004, Chapter 6.0.  The EPA again required a verification PA using revised modeling assumptions and parameters (Cotsworth 2005).  This PA was termed the CRA-2004 PABC and was documented in Leigh et al. (2005).

As part of the five-year recertification cycle, a PA is included in the CRA-2009.  The CRA-2009 PA is a culmination of the previous PAs and is not significantly different from the CRA-2004 PABC, as the methodologies, conceptual models, and assumptions have not changed.  Updates to parameters and improvements to computer codes are incorporated in the CRA-2009.

PA-2.1.1  Changes in the CRA-2009 PA

A list of changes to PA since the CRA-2004 and citations for where they are discussed is shown in Table PA-1. In addition to the changes discussed in Table PA-1, the terminology used to describe uncertainty has been updated to reflect the usage now prevalent in the risk assessment literature. Previously, uncertainty in model parameters was referred to as “subjective uncertainty,” and that due to stochastic processes was referred to as “stochastic uncertainty.” In the years since these terms were first employed, these concepts have matured, and the term “epistemic uncertainty” is now used to describe uncertainty from lack of knowledge, while the term “aleatory uncertainty” now describes uncertainty due to natural variability, e.g. uncertainty arising from future events whose occurrence can be defined in terms of probabilities. In this text, the terms epistemic uncertainty and aleatory uncertainty are used in place of the terms subjective uncertainty and stochastic uncertainty, respectively.

Table PA-1.  WIPP Project Changes and Cross References

 

From this assessment, the DOE has demonstrated that the WIPP continues to comply with the containment requirements of section 191.13.  The containment requirements are stringent and state that the DOE must demonstrate a reasonable expectation that the probabilities of cumulative radionuclide releases from the disposal system during the 10,000 years following closure will fall below specified limits.  The PA analyses supporting this determination must be quantitative and consider uncertainties caused by all significant processes and events that may affect the disposal system, including future inadvertent human intrusion into the repository.  A quantitative PA is conducted using a series of loosely coupled computer models in which epistemic parameter uncertainties are addressed by a stratified Monte Carlo sampling procedure on selected input parameters, and uncertainties related to future intrusion events are addressed using simple random sampling.

As required by regulation, results of the PA are displayed as CCDFs showing the probability that cumulative radionuclide releases from the disposal system will exceed the values calculated for scenarios considered in the analysis.  These CCDFs are calculated using reasonable and, in some cases, conservative conceptual models based on the scientific understanding of the disposal system’s behavior.  Parameters used in these models are derived from experimental data, field observations, and relevant technical literature.  Changes to the CCA and CRA-2004 parameters and models since the original certification have been incorporated into the CRA-2009 PA (Clayton 2008a).  The overall mean CCDF continues to lie entirely below the specified limits, and the WIPP therefore continues to be in compliance with the containment requirements of 40 CFR Part 191 Subpart B (see Section PA-2.1.6).  Sensitivity analysis of results shows that the location of the mean CCDF is dominated by radionuclide releases that could occur on the surface during an inadvertent penetration of the repository by a future drilling operation (Section PA-9.0).  Releases of radionuclides to the accessible environment from transport in groundwater through the shaft seal systems and the subsurface geology are negligible, with or without human intrusion, and do not significantly contribute to the mean CCDF.  No releases are predicted to occur at the ground surface in the absence of human intrusion. The natural and engineered barrier systems of the WIPP provide robust and effective containment of transuranic (TRU) waste, even if the repository is penetrated by multiple boreholes.

PA-2.1.2  Conceptual Basis for PA

The foundations of PA are a thorough understanding of the disposal system and the possible future interactions of the repository, waste, and surrounding geology.  The 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.

The progression of compliance applications document these aspects of PA leading up to the CRA-2009 PA (i.e., the CCA, the CCA PAVT [Sandia National Laboratories 1997 and U.S. Department of Energy 1997], the CRA-2004 PA, and the CRA-2004 PABC [Leigh et al. 2005]).

The interactions of the repository and waste with the geologic system, and the response of the disposal system to possible future inadvertent human intrusion, are described in Section PA-2.1.4.

PA-2.1.3  Undisturbed Repository Performance

An evaluation of undisturbed repository performance, which is defined to exclude human intrusion and unlikely disruptive natural events, is required by regulation (see 40 CFR § 191.15 and 40 CFR § 191.24).  Evaluations of past and present natural geologic processes in the region indicate that none has the potential to breach the repository within 10,000 years (see the CCA, Appendix SCR, Section SCR.1).  Disposal system behavior is dominated by the coupled processes of rock deformation surrounding the excavation, fluid flow, and waste degradation.  Each of these processes can be described independently, but the extent to which they occur is affected by the others.

Rock deformation immediately around the repository begins as soon as excavation creates a disturbance in the stress field.  Stress relief results in some degree of brittle fracturing and the formation of a DRZ, which surrounds excavations in all deep mines including the WIPP repository.  For the WIPP, the DRZ is characterized by an increase in permeability and porosity, and it may ultimately extend a few meters (m) from the excavated region.  Salt will also deform by creep processes resulting from deviatoric stress, causing the salt to move inward and fill voids.  Salt creep will continue until deviatoric stress is dissipated and the system is once again at stress equilibrium (see the CRA-2004, Chapter 6.0, Section 6.4.3.1).

The ability of salt to creep, thereby healing fractures and filling porosity, is one of its fundamental advantages as a medium for geologic disposal of radioactive waste, and one reason it was recommended by the National Academy of Sciences (see the 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 CRA-2004, Chapter 6.0, Section 6.4.3).

Characterization of the Salado indicates that fluid flow from the far field does not occur on time scales of interest in the absence of an artificially imposed hydraulic gradient (see the CRA-2004, Chapter 2.0, Section 2.1.3.4 for a description of Salado investigations).  This lack of fluid flow is the second fundamental reason for choosing salt as a medium for geologic disposal of radioactive waste.  Lack of fluid flow is a result of the extremely low permeability of evaporite rocks that make up the Salado.  Excavating the repository has disturbed the natural hydraulic gradient and rock properties, resulting in fluid flow.  Small quantities of interstitial brine present in the Salado move toward regions of low hydraulic potential, and brine seeps are observed in the underground repository.  The slow flow of brine from halite into more permeable anhydrite MBs, and then through the DRZ into the repository, is expected to continue as long as the hydraulic potential within the repository is below that of the far field.  The repository environment will also include gas, so the fluid flow must be modeled as a two-phase process. Initially, the gaseous phase will consist primarily of air trapped at the time of closure, although other gases may form from waste degradation.  In the PA, the gaseous phase pressure will rise due to creep closure, gas generation, and brine inflow, creating the potential for flow from the excavated region (see also the CRA-2004, 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 CRA-2004, Chapter 6.0, Section 6.4.3.3 for historical perspective, and Leigh et al. 2005, Section 2.3 and Section 2.4 for changes):

1.     The generation of hydrogen (H₂) gas by anoxic corrosion of steels, other iron (Fe)-based alloys, and aluminum (Al) and Al-based alloys

2.     The generation of carbon dioxide (CO₂), hydrogen sulfide (H₂S), and methane (CH₄) by anaerobic microbial consumption of waste containing CPR materials

Coupling these gas-generation reactions to fluid-flow and salt-creep processes is complex.  Gas generation will increase fluid pressure in the repository, thereby decreasing the hydraulic gradient and deviatoric stress between the far field and the excavated region and inhibiting the processes of brine inflow and salt creep.  Anoxic corrosion will also consume brine as it breaks down water to oxidize steels and other Fe-based alloys and release H₂.  Thus, corrosion has the potential to be a self-limiting process, in that as it consumes all water in contact with steels and other Fe-based alloys, it will cease.  Microbial reactions also require water, either in brine or the gaseous phase.  It is assumed that microbial reactions will result in neither the consumption nor production of water.

The total volume of gas generated by corrosion and microbial consumption may be sufficient to result in repository pressures that approach lithostatic.  Sustained pressures above lithostatic are not physically reasonable within the disposal system, because the more brittle anhydrite layers are expected to fracture if sufficient gas is present.  The conceptual model implemented in the PA causes anhydrite MB permeability and porosity to increase rapidly as pore pressure approaches and exceeds lithostatic.  This conceptual model for pressure-dependent fracturing approximates the hydraulic effect of pressure-induced fracturing and allows gas and brine to move more freely within the MBs at higher pressures (see the CRA-2004, Chapter 6.0, Section 6.4.5.2).

Overall, the behavior of the undisturbed disposal system will result in extremely effective isolation of the radioactive waste.  Concrete, clay, and asphalt components of the shaft seal system will provide an immediate and effective barrier to fluid flow through the shafts, isolating the repository until salt creep has consolidated the compacted crushed salt components and permanently sealed the shafts.  Around the shafts, the DRZ in halite layers will heal rapidly because the presence of the solid material within the shafts will provide rigid resistance to creep.  The DRZ around the shaft, therefore, will not provide a continuous pathway for fluid flow (see the CRA-2004, Chapter 6.0, Section 6.4.4).  Similarly, the panel closure will rigidly resist creep, leading to a build-up of compressive stress which in turn will cause a rapid elimination of the DRZ locally.  In PA, it is conservatively assumed that the DRZ does not heal around either the disposal region or the operations and experimental regions, and pathways for fluid flow may exist indefinitely to the overlying and underlying anhydrite layers (e.g., 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.  These pressures will not significantly exceed lithostatic because the more brittle anhydrite layers will fracture and provide a pathway for gas to leave the repository.  Fracturing due to high gas pressures may enhance gas and brine migration from the repository, but gas transport will not contribute to the release of actinides from the disposal system.  Brine flowing out of the waste disposal region through anhydrite layers may transport actinides as dissolved and colloidal species.  However, the quantity of actinides that may reach the accessible environment boundary through the interbeds during undisturbed repository performance is insignificant and has no effect on the compliance determination.  No migration of radionuclides is expected to occur vertically through the Salado (see Section PA-7.0, and Ismail and Garner 2008).

PA-2.1.4  Disturbed Repository Performance

The WIPP PA is required by the performance standards to consider scenarios that include intrusions into the repository by inadvertent and intermittent drilling for resources.  The probability of these intrusions is based on a future drilling rate. This rate was calculated using the method outlined in 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 (40 CFR § 194.41). Passive institutional controls (PICs) were assumed in the CCA to effectively reduce the drilling rate by two orders of magnitude for the 600-year period following 100 years of active control.  However, in certifying the WIPP, the EPA denied credit for the effectiveness of passive controls for 600 years (U.S. Environmental Protection Agency 1998a). Although the CRA-2009 PA does not include a reduced drilling intrusion rate to account for PICs, future PAs may do so.  Future drilling practices are assumed to be the same as current practice, also consistent with regulatory criteria.  These practices include the type and rate of drilling, emplacement of casing in boreholes, and the procedures implemented when boreholes are plugged and abandoned (see 40 CFR § 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.     Long-term brine releases, which include the contaminated brine that may flow through a borehole after it is abandoned

The first four mechanisms immediately follow an intrusion event and are collectively referred to as direct releases.  The accessible environment boundary for these releases is the ground surface.  The fifth mechanism, An transport by long-term groundwater flow, begins when concrete plugs are assumed to degrade in an abandoned borehole and may continue throughout the regulatory period.  The accessible environment boundary for these releases is the lateral subsurface limit of the controlled area (CRA-2004, Chapter 6.0, Section 6.0.2.3).

Repository conditions prior to intrusion will be the same as those for undisturbed repository performance, and all processes active in undisturbed repository performance will continue to occur following intrusion.  Because an intrusion provides a pathway for radionuclides to reach the ground surface and enter the geological units above the Salado, additional processes will occur that don’t in the undisturbed repository performance.  These processes include the mobilization of radionuclides as dissolved and colloidal species in repository brine and groundwater flow, and subsequent An transport in the overlying units.  Flow and transport in the Culebra are of particular interest because it is the most transmissive unit above the repository.  Thus, the Culebra is a potential pathway for lateral migration of contaminated brine in the event of a drilling intrusion accompanied by significant flow up the intrusion borehole (see the CRA-2004, Chapter 6.0, Section 6.4.6.2).

PA-2.1.4.1  Cuttings and Cavings

In a rotary drilling operation, the volume of material brought to the surface as cuttings is calculated as the cylinder defined by the thickness of the unit and the diameter of the drill bit.  The quantity of radionuclides released as cuttings is therefore a function of the activity of the intersected waste and the diameter of the intruding drill bit.  The DOE uses a constant value of 0.31115 m (12.25 inches [in]), consistent with bits currently used at the WIPP depth in the Delaware Basin (see the CRA-2004, Chapter 6.0, Section 6.4.12.5).  The intersected waste activity may vary depending on the type of waste intersected.  The DOE considers random penetrations into remote-handled (RH) transuranic (TRU) (RH-TRU) waste and each of the 690 different waste streams (Leigh, Trone, and Fox 2005, Section 4.4) identified for contact-handled (CH) transuranic (TRU) (CH-TRU) waste (569 and 693 waste streams were used in the CCA and the CRA-2004, respectively; see the CRA-2004, Chapter 6.0, Section 6.0.2.3.1).

The volume of particulate material eroded from the borehole wall by the drilling fluids and brought to the surface as cavings may be affected by the drill bit diameter, effective shear resistance of the intruded material, speed of the drill bit, viscosity of the drilling fluid and rate at which it is circulated in the borehole, and other properties related to the drilling process.  The most important of these parameters, after drill bit diameter, is the effective shear resistance of the intruded material (Leigh et al. 2005, Section 7.2).  In the absence of data describing the reasonable and realistic future properties of degraded waste and magnesium oxide (MgO) backfill, the DOE used conservative parameter values based on the properties of fine-grained sediment.  Other properties are assigned fixed values consistent with current practice.  The quantity of radionuclides released as cavings depends on the volume of eroded material and its activity, which is treated in the same manner as the activity of cuttings (see also Section PA-4.5 and Section PA-6.8.2.1).

PA-2.1.4.2  Spallings

Unlike releases from cuttings and cavings, which occur with every modeled borehole intrusion, spalling releases will occur only if pressure in the waste-disposal region exceeds the hydrostatic pressure in the borehole.  At lower pressures, below about 8 megapascals (MPa), fluid in the waste-disposal region will not flow toward the borehole.  At higher pressures, gas flow toward the borehole may be sufficiently rapid to cause additional solid material to enter the borehole.  If spalling occurs, the volume of spalled material will be affected by the physical properties of the waste, such as its tensile strength and particle diameter. The DOE based the parameter values used in the PA on reasonable and conservative assumptions.  Since the CCA, a revised conceptual model for the spallings phenomena has been developed (see the CRA-2004, Appendix PA, Section PA-4.6 and Appendix PA, Attachment MASS, Section MASS-16.1.3). Model development, execution, and sensitivity studies necessitated implementing parameter values pertaining to waste characteristics, drilling practices, and physics of the process.  The parameter range for particle size was derived by expert elicitation (U.S. Department of Energy 1997).

The quantity of radionuclides released as spalled material depends on the volume of spalled waste and its activity.  Because spalling may occur at a greater distance from the borehole than cuttings and cavings, spalled waste is assumed to have the volume-averaged activity of CH-TRU waste, rather than the sampled activities of individual waste streams.  The low permeability of the region surrounding the RH-TRU waste means it is isolated from the spallings process and does not contribute to the volume or activity of spalled material (see also Section PA-4.6 and Section PA-6.8.2.2 for more description of the spallings model).

PA-2.1.4.3  Direct Brine Flow

Radionuclides may be released to the accessible environment if repository brine enters the borehole during drilling and flows to the ground surface.  The quantity of radionuclides released by direct brine flow depends on the volume of brine reaching the ground surface and the concentration of radionuclides contained in the brine.  As with spallings, DBRs will not occur if repository pressure is below the hydrostatic pressure in the borehole.  At higher repository pressures, mobile brine present in the repository will flow toward the borehole.  If the volume of brine flowing from the repository into the borehole is small, it will not affect the drilling operation, and flow may continue until the driller reaches the base of the evaporite section and installs casing in the borehole (see also Section PA-4.7 and Section PA-6.8.2.3).

PA-2.1.4.4  Mobilization of Actinides in Repository Brine

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, and—in the case of plutonium (Pu)—only the lower-solubility oxidation states (Pu(III) and Pu(IV)) will persist.  Microbial activity will also help create reducing conditions.  Solubilities also vary with pH.  The DOE is therefore emplacing MgO in the waste-disposal region to ensure conditions that reduce uncertainty and establish low An solubilities.  MgO consumes CO₂ and buffers pH, lowering An solubilities in WIPP brines (see Appendix SOTERM-2009 and Appendix MgO-2009).  Solubilities in the PA are based on the chemistry of brines that might be present in the waste-disposal region, reactions of these brines with the MgO engineered barrier, and strongly reducing conditions produced by anoxic corrosion of steels and other Fe-based alloys.

The waste contains organic ligands that could increase An solubilities by forming complexes with dissolved An species.  However, these organic ligands also form complexes with other dissolved metals, such as magnesium (Mg), calcium (Ca), Fe, lead (Pb), vanadium (V), chromium (Cr), manganese (Mn), and nickel (Ni), that will be present in repository brines due to corrosion of steels and other Fe-based alloys.  The CRA-2009 PA speciation and solubility calculations include the effect of organic ligands but not the beneficial effect of competition with Fe, Pb, V, Cr, Mn, and Ni.  (Appendix SOTERM-2009, Section SOTERM-2.3.6 and Section SOTERM-4.6, and Brush and Xiong 2005).

Colloidal transport of actinides has been examined, and four types of colloids have been determined to represent the possible behavior at the WIPP.  These include microbial colloids, humic substances, An intrinsic colloids, and mineral fragments.  Concentrations of An mobilized as these colloidal forms are included in the estimates of total An concentrations used in PA (Appendix SOTERM-2009, Section SOTERM-3.8.1 and Section SOTERM-4.7, and Garner and Leigh 2005).

PA-2.1.4.5  Long-Term Brine Flow up an Intrusion Borehole

Long-term releases to the ground surface or groundwater in the Rustler Formation (hereafter referred to as the Rustler) or overlying units may occur after the borehole has been plugged and abandoned.  In keeping with regulatory criteria, borehole plugs are assumed to have properties consistent with current practice in the basin.  Thus, boreholes are assumed to have concrete plugs emplaced at various locations. Initially, concrete plugs effectively limit fluid flow in the borehole.  However, under most circumstances, these plugs cannot be expected to remain fully effective indefinitely.  For the purposes of PA, discontinuous borehole plugs above the repository are assumed to degrade 200 years after emplacement.  From then on, the borehole is assumed to fill with a silty-sand-like material containing degraded concrete, corrosion products from degraded casing, and material that sloughs into the hole from the walls.  Of six possible plugged borehole configurations in the Delaware Basin, three are considered either likely or adequately representative of other possible configurations; one configuration (a two-plug configuration) is explicitly modeled in the flow and transport model (see Section PA-3.7 and Appendix MASS-2009, Section MASS-16.3).

If sufficient brine is available in the repository, and if pressure in the repository is higher than in the overlying units, brine may flow up the borehole following plug degradation.  In principle, this brine could flow into any permeable unit or to the ground surface if repository pressure were high enough.  For modeling purposes, brine is allowed to flow only into the higher-permeability units and to the surface.  Lower-permeability anhydrite and mudstone layers in the Rustler are treated as if they were impermeable to simplify the analysis while maximizing the amount of flow into units where it could potentially contribute to disposal system releases.  Model results indicate that essentially all flow occurs into the Culebra, which has been recognized since the early stages of site characterization as the most transmissive unit above the repository and the most likely pathway for subsurface transport (see also the CRA-2004, Chapter 2.0, Section 2.2.1.4.1.2).

PA-2.1.4.6  Groundwater Flow in the Culebra

Site characterization activities in the units above the Salado have focused on the Culebra.  These activities have shown that the direction of groundwater flow in the Culebra varies somewhat regionally, but in the area that overlies the repository, flow is southward.  These characterization and modeling activities conducted in the units above the Salado confirm that the Culebra is the most transmissive unit above the Salado.  The Culebra is the unit into which actinides are likely to be introduced from long-term flow up an abandoned borehole.  Regional variation in the 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.  Site characterization activities have provided no evidence of karst groundwater systems in the controlled area, although groundwater flow in the Culebra is affected by the presence of fractures, fracture fillings, and vuggy pore features (see Appendix HYDRO-2009 and the CRA-2004, Chapter 2.0, Section 2.1.3.5).  Other laboratory and field activities have focused on the behavior of dissolved and colloidal actinides in the Culebra.

Basin-scale regional modeling of three-dimensional groundwater flow in the units above the Salado demonstrates that it is appropriate, for the purposes of estimating radionuclide transport, to conceptualize the Culebra as a two-dimensional confined aquifer (see the CRA-2004, Chapter 2.0, Section 2.2.1.1).  Uncertainty in the flow field is incorporated by using 100 different geostatistically based T fields, each of which is consistent with available head and transmissivity data (Appendix PA-2009, Appendix TFIELD-2009).

Groundwater flow in the Culebra is modeled as a steady-state process, but two mechanisms considered in the PA could affect flow in the future.  Potash mining in the McNutt Potash Zone (hereafter referred to as the McNutt) of the Salado, which occurs now in the Delaware Basin outside the controlled area and may continue in the future, could affect flow in the Culebra if subsidence over mined areas causes fracturing or other changes in rock properties (see the CRA-2004, 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 CRA-2004, Chapter 6.0, Section 6.4.9 and the CCA, Appendix CLI).

Consistent with regulatory criteria of 40 CFR § 194.32, mining outside the controlled area is assumed to occur in the near future, and mining within the controlled area is assumed to occur with a probability of 1 in 100 per century (adjusted for the effectiveness of AICs during the first 100 years after closure).  Consistent with regulatory guidance, the effects of mine subsidence are incorporated in PA by increasing the transmissivity of the Culebra over the areas identified as mineable by a factor sampled from a uniform distribution between 1 and 1000 (U.S. Environmental Protection Agency 1996a, p. 5229).  T fields used in PA are therefore adjusted and steady-state flow fields calculated accordingly; once for mining that occurs only outside the controlled area, and once for mining that occurs both inside and outside the controlled area (Appendix TFIELD-2009, Section 9.0).  Mining outside the controlled area is considered in both undisturbed and disturbed repository performance.

The extent to which the climate will change during the next 10,000 years and how such a change will affect groundwater flow in the Culebra are uncertain.  Regional three-dimensional modeling of groundwater flow in the units above the Salado indicates that flow velocities in the Culebra may increase by a factor of 1 to 2.25 for reasonably possible future climates (see the CCA, Appendix CLI).  This uncertainty is incorporated in PA by scaling the calculated steady-state specific discharge within the Culebra by a sampled parameter within this range.

PA-2.1.4.7  Actinide Transport in the Culebra

Field tests have shown that the Culebra is best characterized as a double-porosity medium for estimating contaminant transport in groundwater (see the CRA-2004, Chapter 2.0, Section 2.2.1.4.1.2 and Appendix HYDRO-2009).  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 low-permeability dolomite matrix.  Transported species, including actinides (if present), will diffuse into this porosity.

Diffusion from the advective porosity into the dolomite matrix will retard An transport through two mechanisms.  Physical retardation occurs simply because actinides that diffuse into the matrix are no longer transported with the flowing groundwater.  Transport is interrupted until they diffuse back into the advective porosity.  In situ tracer tests have demonstrated this phenomenon.  Chemical retardation also occurs within the matrix as actinides are sorbed onto dolomite grains.  The relationship between sorbed and liquid concentrations is assumed to be linear and reversible.  The distribution coefficients (K_ds) that characterize the extent to which actinides will sorb on dolomite were based on experimental data (see the CRA-2004, Chapter 6.0, Section 6.4.6.2).

PA-2.1.4.8  Intrusion Scenarios

Human intrusion scenarios evaluated in the PA include both single intrusion events and combinations of multiple boreholes.  Two different types of boreholes are considered:  those that penetrate a pressurized brine reservoir in the underlying Castile Formation (hereafter referred to as the Castile), and those that do not.

The presence of a brine reservoir under the repository is speculative, but on the basis of current information cannot be ruled out.  A pressurized brine reservoir was encountered at the WIPP-12 borehole within the controlled area to the north of the disposal region, and other pressurized brine reservoirs associated with regions of deformation in the Castile have been encountered elsewhere in the Delaware Basin (see the CRA-2004, Chapter 2.0, Section 2.2.1.2.2).  Based on a geostatistical analysis of the geophysical data of brine encounters in the region, the DOE estimates that there is a 0.08 probability that a random borehole penetrating waste in the WIPP will also penetrate an underlying brine reservoir (see the CCA, Appendix MASS, Attachment 18-6).  Upon their review of the CCA, the EPA determined that the DOE should treat this probability as uncertain, ranging from 0.01 to 0.60 in the CCA PAVT.  The EPA also required the DOE to modify the assumptions concerning Castile properties to increase the brine reservoir volumes (U.S. Environmental Protection Agency 1998b; Technical Support Document for 194.23:  Parameter Justification Report, Section 5).  The EPA determined that changing the rock compressibility and porosity of the Castile effectively modified the sampled brine reservoir volume to include the possibility of larger brine reservoir volumes like those encountered by the WIPP-12 borehole.

The primary consequence of penetrating a pressurized reservoir is to provide an additional source of brine beyond that which might flow into the repository from the Salado.  Direct releases at the ground surface resulting from the first repository intrusion would be unaffected by additional Castile brine, even if it flowed to the surface, because brine moving straight up a borehole will not significantly mix with waste.  However, the presence of Castile brine could significantly increase radionuclide releases in two ways.  First, the volume of contaminated brine that could flow to the surface may be greater for a second or subsequent intrusion into a repository that has already been connected by a previous borehole to a Castile reservoir.  Second, the volume of contaminated brine that may flow up an abandoned borehole after plug degradation may be greater for combinations of two or more boreholes that intrude the same panel if one of the boreholes penetrates a pressurized reservoir.  Both processes are modeled in PA.

PA-2.1.5  Compliance Demonstration Method

The DOE’s approach to demonstrating continued compliance is the PA, which is based on the criteria indicated in section 194.34.  The PA process comprehensively considers the FEPs relevant to disposal system performance (see Appendix SCR-2009).  Those FEPs shown by screening analyses to potentially affect performance are included in quantitative calculations using a system of loosely coupled computer models to describe the interaction of the repository with the natural system, both with and without human intrusion.  Uncertainty in parameter values is incorporated in the analysis by a Monte Carlo approach, in which multiple simulations (or realizations) are completed using sampled values for the imprecisely known input parameters (see the CRA-2004, Chapter 6.0, Section 6.1.5).  Distribution functions characterize the state of knowledge for these parameters, and each realization of the modeling system uses a different set of sampled input values.  A sample size of 300 results in 300 different values of each parameter.  Thus, there are 300 different sets (vectors) of input parameter values.  These 300 vectors were divided among 3 replicates.  Quality assurance activities demonstrate that the parameters, software, and analysis used in PA were the result of a rigorous process conducted under controlled conditions (40 CFR § 194.22).

Of the FEPs considered, exploratory drilling for natural resources was identified as the only disruption with sufficient likelihood and consequence of impacting releases from the repository. For each vector of parameters values, 10,000 possible futures (realizations) are simulated, where a single future is defined as a series of intrusion events that occur randomly in space and time (Section PA-2.2). Each of these futures is assumed to have an equal probability of occurring; hence a probability of 0.0001.  Cumulative radionuclide releases from the disposal system are calculated for each future, and CCDFs are constructed by sorting the releases from smallest to largest and then summing the probabilities across the future.  Mean CCDFs were then computed for the three replicates of sampled parameters (Section PA-2.2).

PA-2.1.6  Results of the PA

This section summarizes the results of the CRA-2009 PA and demonstrates that the WIPP continues to comply with the quantitative containment requirements in 40 CFR § 191.13(a).  The CRA-2009 PA is different than the original certification PA in the CCA and the PA in the CRA-2004 PABC because it includes additional information, changes, and new data required by 40 CFR § 194.15 recertification application requirements.  Table PA-1 details the changes and new information included in this PA.

The results of the CRA-2009 PA demonstrate that the repository continues to comply with the disposal standards.  The key metric for regulatory compliance is the mean CCDF.  Figure PA-1, which compares the overall mean CCDF for the CRA-2009 PA to the overall mean CCDF for the CRA-2004 PABC, demonstrates two key points.  First, the overall mean CCDF lies entirely below the limits specified in section 191.13(a).  Thus, the WIPP is in compliance with the containment requirements of Part 191.  Second, for any probability, the expected releases in the CRA-2009 PA are only slightly higher than those in the CRA-2004 PABC, primarily because of the increased drilling rate.

Figure PA-1.      Overall Mean CCDFs for Total Normalized Releases:  CRA-2009 PA and CRA-2004 PABC

Detailed results of the CRA-2009 PA are contained in Section PA-9.0, which describes sensitivity analyses conducted as the final step in the Monte Carlo analysis.  These sensitivity analyses indicate the relative importance of each sampled parameter in terms of its contribution to uncertainty in estimating disposal system performance.  Analyses also examine the sensitivity of intermediate performance measures to the sampled parameters.  Examples of such intermediate performance measures include the quantity of radionuclides released to the accessible environment by any one mechanism (for example, cuttings or DBRs), and other model results that describe conditions of interest, such as disposal region pressure.

Section PA-9.0 presents CCDF distributions for each replication of the analysis, mean CCDFs, and an overall mean CCDF with the 95% confidence interval estimated from the 3 independent mean distributions. All 300 individual CCDFs, as well as the overall mean CCDF determined from the 3 replicates, lie entirely below and to the left of the limits specified in section 191.13(a) (see Figure PA-79).  Thus, the WIPP continues to comply with the containment requirements of Part 191.  Comparing the results of the 3 replicates indicates that the sample size of 100 in each replicate is sufficient to generate a stable distribution of outcomes (see Figure PA-80).  Within the region of regulatory interest (that is, at probabilities greater than 10 ^-3/10⁴ year [yr]), the mean CCDFs from each replicate are essentially indistinguishable from the overall mean.

As discussed in Section PA-9.1, Section PA-9.2, and Section PA-9.3, examining the normalized releases from cuttings and cavings, spallings, and DBRs provides insight into the relative importance of each release mode’s contribution to the mean CCDF’s location and the compliance determination.  Releases from cuttings and cavings dominate the mean CCDF at high probabilities, while DBRs dominate the mean CCDF at low probabilities.  Spallings are less important and have very little effect on the location of the mean.  Subsurface releases from groundwater transport are less than 10 ^-6 EPA units and make no contribution to the mean CCDF’s location.

Uncertainties characterized in the natural system and the interaction of waste with the disposal system environment show little variation between the location of the mean CCDFs of the three replicates, providing additional confidence in the compliance determination.  The natural and engineered barrier systems of the WIPP provide robust and effective containment of TRU waste even if the repository is penetrated by multiple borehole intrusions.

PA-2.2  Conceptual Structure of the PA

This section outlines the conceptual structure of the WIPP PA.  First, a discussion of the regulatory requirements is given.  The requirements of section 191.13 and section 194.34 (summarized in Section PA-2.2.1) lead to the identification of three main PA components:

1.      A probabilistic characterization of the likelihood for different futures to occur at the WIPP site over the next 10,000 years

2.      A procedure for estimating the radionuclide releases to the accessible environment associated with each possible future that could occur at the WIPP site over the next 10,000 years

3.      A probabilistic characterization of the uncertainty in the parameters used to estimate potential releases

The probabilistic methods employed in WIPP PA give rise to the CCDF specified in section 191.13(a) and the distributions specified by 40 CFR § 194.34(b).

PA-2.2.1  Regulatory Requirements

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, High-Level and Transuranic Radioactive Wastes (Part 191) (U.S. Environmental Protection Agency 1993), which is divided into three subparts.  40 CFR Part 191 Subpart A applies to a disposal facility prior to decommissioning and establishes standards for the annual radiation doses to members of the public from waste management and storage operations.  Part 191 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 (40 CFR § 191.14).  Part 191 Subpart B also sets limits on radiation doses to members of the public in the accessible environment for 10,000 years of undisturbed repository performance (section 191.15).  40 CFR Part 191 Subpart C limits radioactive contamination of groundwater for 10,000 years after disposal (section 191.24).  In this recertification application, the DOE must demonstrate a reasonable expectation that the WIPP will continue to comply with the requirements of Part 191 Subparts B and C.

The following is the central requirement in Part 191 Subpart B, and the primary determinant of the PA methodology (U.S. Environmental Protection Agency 1985, p. 38086).

§ 191.13 Containment Requirements:

(a) Disposal systems for spent nuclear fuel or high-level or transuranic radioactive wastes shall be designed to provide a reasonable expectation, based upon performance assessments, that cumulative releases of radionuclides to the accessible environment for 10,000 years after disposal from all significant processes and events that may affect the disposal system shall:

(1) Have a likelihood of less than one chance in 10 of exceeding the quantities calculated according to Table 1 (Appendix A); and

(2) Have a likelihood of less than one chance in 1,000 of exceeding ten times the quantities calculated according to Table 1 (Appendix A).

(b) Performance assessments need not provide complete assurance that the requirements of 191.13(a) will be met.  Because of the long time period involved and the nature of the events and processes of interest, there will inevitably be substantial uncertainties in projecting disposal system performance.  Proof of the future performance of a disposal system is not to be had in the ordinary sense of the word in situations that deal with much shorter time frames.  Instead, what is required is a reasonable expectation, on the basis of the record before the implementing agency, that compliance with 191.13(a) will be achieved.

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. Environmental Protection Agency 1985, Appendix A).  Table 1 of Appendix A specifies allowable releases (i.e., release limits) for individual radionuclides and is reproduced as Table PA-2.  The WIPP is a repository for TRU waste, which is defined as “waste containing more than 100 nanocuries of alpha-emitting TRU isotopes, with half-lives greater than twenty years, per gram of waste” (U.S. Environmental Protection Agency 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 10,000-year period following closure of the repository (curies [Ci]), L_i is the release limit for radionuclide i given in Table PA-2 (Ci), and C is the amount of TRU waste emplaced in the repository (Ci).  In the CRA-2009 PA, C = 2.32 ´ 10⁶ Ci (Leigh and Trone 2005, Section 3).  Further, “accessible environment” means (1) the atmosphere, (2) land surfaces, (3) surface waters, (4) oceans, and (5) all of the lithosphere beyond the controlled area.  “Controlled area” means (1) a surface location, to be identified by PICs, that encompasses no more than 100 square kilometers (km²) and extends horizontally no more than 5 kilometers (km) in any direction from the outer boundary of the original radioactive waste’s location in a disposal system, and (2) the subsurface underlying such a location (section 191.12).

PAs are the basis for addressing the containment requirements.  To help clarify the intent of Part 191, the EPA promulgated 40 CFR Part 194 (2004), Criteria for the Certification and

Table PA-2.       Release Limits for the Containment Requirements (U.S. Environmental Protection Agency 1985, Appendix A, Table 1)

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 methodology for PA uses information about the disposal system and waste to evaluate performance over the 10,000-year regulatory time period.  To accomplish this task, the FEPs with potential to affect the future of the WIPP are first defined (Section PA-2.3.1).  Next, scenarios that describe potential future conditions in the WIPP are formed from logical groupings of retained FEPs (Section PA-2.3.2).  The scenario development process results in a probabilistic characterization for the likelihood of different futures that could occur at the WIPP (Section PA-2.2.2).  Using the retained FEPs, models are developed to estimate the radionuclide releases from the repository (Section PA-2.2.3).  Finally, uncertainty in model parameters is characterized probabilistically (Section PA-2.2.4).

PA-2.2.2  Probabilistic Characterization of Different Futures

As discussed in Section PA-2.3.1, the CCA PA scenario development process for the WIPP identified exploratory drilling for natural resources as the only disruption with sufficient likelihood and consequence of impacting releases from the repository (see the CCA, Appendix SCR).  In addition, Part 194 specifies that the occurrence of mining within the LWB must be included in the PA.  This has not changed for the CRA-2009 PA.  As a result, the projection of releases over the 10,000 years following closure of the WIPP is driven by the nature and timing of intrusion events.

The collection of all possible futures x_st forms the basis for the probability space (S_st, S_st, p_st) characterizing aleatory uncertainty, where S_st = {x_st : x_st is a possible future of the WIPP}, S_st is a suitably restricted collection of sets of futures, called “scenarios” (Section PA-3.10), and p_st is a probability measure for the elements of S_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, CH-TRU waste, RH-TRU waste, and, for CH-TRU 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 letters st are retained for historical context. The subscript i indicates that the future x_st is one of many sample elements from S_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 (CH-TRU and RH-TRU) as well as to encounter different waste streams in the CH-TRU 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 PA-3.0.

PA-2.2.3  Estimation of Releases

Based on the retained FEPs (Section PA-2.3.1), release mechanisms include direct transport of material to the surface at the time of a drilling intrusion (i.e., cuttings, spallings, and brine flow) and release subsequent to a drilling intrusion due to brine flow up a borehole with a degraded plug (i.e., groundwater transport). The quantities of releases are determined by the state of the repository through time, which is determined by the type, timing, and sequence of prior intrusion events.  For example, pressure in the repository is an important determinant of spallings, and the amount of pressure depends on whether the drilling events that have occurred penetrated brine pockets and how long prior to the current drilling event the repository was inundated.

Computational models for estimating releases were developed using the retained FEPs; these models are summarized in Figure PA-2.  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 PA-4.0.  Most of the computational models involve the numerical solution of partial differential equations (PDEs) used to represent processes such as material deformation, fluid flow, and radionuclide transport.

The collection of computation models can be represented abstractly as a function f (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 (S_st, S_st, 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 PA-3.  The CCDF represents the probability that a release from the repository greater than R will be observed, where R is a point on the abscissa (x-axis) of the graph (Figure PA-3).

Formally, the CCDF depicted in Figure PA-3 results from an integration over the probability space (S_st, S_st, 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 (S_st, S_st, 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, is generated from S_st consistent with the probability distribution p_st.  Using this random sample, Equation (PA.3) is numerically evaluated as

                                                  (PA.4)

The models in Figure PA-2 are too complex to permit a closed-form evaluation of the integral in Equation (PA.4) that defines the CCDF specified in Part 191.  In WIPP PA, these probability distribution functions (PDFs) are constructed using Monte Carlo simulation to sample the entire possible set of release outcomes. As long as the sampling is conducted properly and a sufficient number of samples is collected, the PDF of the sample should successfully approximate the PDF of the sample “universe” of all possible releases.

Figure PA-2.  Computational Models Used in PA

Figure PA-3.  Construction of the CCDF Specified in 40 CFR Part 191 Subpart B

In PA, the number of samples nR used to construct a CCDF is 10,000. However, the models in Figure PA-2 are also too computationally intensive to permit their evaluation for each of these 10,000 futures.  Due to this constraint, the models in Figure PA-2 are evaluated for a relatively small number of specific scenarios, and the results of these evaluations are used to construct CCDFs.  The representative scenarios are labeled E0, E1, E2, and E1E2, and are defined in Section PA-3.10; the procedure for constructing a CCDF from these scenarios is described in Section PA-6.0.

PA-2.2.4  Probabilistic Characterization of Parameter Uncertainty

If the parameters used in the process-level models of Figure PA-2 were precisely known and if the models could accurately predict the future behavior of the repository, the evaluation of repository performance alone would be sufficient to answer the first three questions related to repository performance. However, the models do not perfectly represent the dynamics of the system and their parameters are not precisely known. Therefore, it is necessary to estimate the confidence one has in the CCDFs being constructed. The confidence in the CCDFs is established using Monte Carlo methods to evaluate how the uncertainty in the model parameters impacts the CCDFs or releases. The probabilistic characterization of the uncertainty in the model parameters is the outcome of the data development effort for the WIPP (summarized in Section 8.0 in Fox 2008).

Formally, uncertainty in the parameters that underlie the WIPP PA can be characterized by a second probability space (S_su, S_su, p_su), where the sample space S_su is defined by

                                  S_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; the letters su are retained for historical context.  An element v_su Î S_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 PA-5.0.

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 10,000-year 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 PA-4) 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.

WIPP PA uses a Monte Carlo procedure for evaluating the effects of epistemic uncertainty on releases. The procedure involves sampling the distributions assigned to the uncertain parameters and generating a CCDF of releases based on the results of the process-level models generated using those parameters values.  By repeating this process many times, a distribution of the

Figure PA-4.      Distribution of CCDFs Resulting from Possible Values for the Sampled Parameters

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 PA-4) (a formal definition is provided in Helton et al. 1998).  In addition, confidence limits on the mean are computed using standard t-statistics (Figure PA-5).  The proximity of these curves to the boundary line in Figure PA-3 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 (Figure PA-6).

WIPP PA uses a stratified sampling design called LHS (McKay, Beckman, and Conover 1979) to generate a sample v_su, i = 1, …, nLHS, from S_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. Environmental Protection Agency 1996b, p. 8-41).

Figure PA-5.      Example Mean Probability of Release and the Confidence Limits on the Mean from CRA-2009 PA

Figure PA-6.  Example CCDF Distribution From CRA-2009 PA (Replicate 1)

The DOE has chosen to demonstrate repeatability of the mean and to address the associated criteria of Part 194 using an operational approach of multiple replication, as proposed by 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).

PA-2.3  PA Methodology

This section addresses scenarios formed from FEPs that were retained for PA calculations, and introduces the specification of scenarios for consequence analysis.

PA-2.3.1  Identification and Screening of FEPs

The EPA has provided criteria concerning the scope of PAs in 40 CFR § 194.32.  In particular, criteria relating to the identification of potential processes and events that may affect disposal system performance are provided in 40 CFR § 194.32(e), which states

Any compliance application(s) shall include information which:

(1)  Identifies all potential processes, events or sequences and combinations of processes and events that may occur during the regulatory time frame and may affect the disposal system;

(2)  Identifies the processes, events or sequences and combinations of processes and events included in performance assessments; and

(3)  Documents why any processes, events or sequences and combinations of processes and events identified pursuant to paragraph (e)(1) of this section were not included in performance assessment results provided in any compliance application.

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 CRA-2004, Chapter 6.0, Section 6.2 discusses the development of a comprehensive initial FEPs set used in the CCA, the methodology and criteria used for screening, the method used to reassess the CCA FEPs for the CRA-2004, and a summary of the FEPs retained for scenario development.  Changes to FEPs since the CRA-2004 are outlined in Section 32 and Appendix SCR-2009 of this application.

The original FEPs generation and screening were documented in the CCA, and the resulting FEPs list became the FEPs compliance baseline.  The baseline contained 237 FEPs and was documented the CCA, Appendix SCR.  The EPA compliance review of FEPs was documented in EPA’s Technical Support Document 194.32:  Scope of PA (U.S. Environmental Protection Agency 1998c).  The EPA numbered each FEP with a different scheme than the DOE used for the CCA.  The DOE has since adopted the EPA’s numbering scheme.

PA-2.3.2  Scenario Development and Selection

Logic diagrams illustrate the formation of scenarios for consequence analysis from combinations of events that remain after FEP screening (Cranwell et al. 1990) (Figure PA-7).  Each scenario shown in Figure PA-7 is defined by a combination of occurrence and nonoccurrence for all potentially disruptive events.  Disruptive events are defined as those that create new pathways or significantly alter existing pathways for fluid flow and, potentially, radionuclide transport within the disposal system.  Each of these scenarios also contains a set of features and nondisruptive events and processes that remain after FEP screening.  As shown in Figure PA-7, undisturbed repository performance (UP) and disturbed repository performance (DP) scenarios are considered in consequence modeling for the WIPP PA.  The UP scenario is used for compliance assessments (40 CFR § 194.54 and 40 CFR § 194.55).  Important aspects of UP and DP scenarios are summarized in this section.

PA-2.3.2.1  Undisturbed Repository Performance

The UP scenario is defined in 40 CFR § 191.12 to mean “the predicted behavior of a disposal system, including consideration of the uncertainties in predicted behavior, if the disposal system is not disrupted by human intrusion or the occurrence of unlikely natural events.”  For compliance assessments with respect to the Individual and Groundwater Protection Requirements (section 191.15; Appendix IGP-2009), it is only necessary to consider the UP scenario.  The UP scenario is also considered with DP scenario for PA with respect to the containment requirements (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 M scenario involves future mining within the controlled area. The disturbed repository E scenario involves at least one deep drilling event that intersects the waste disposal region. The M scenario and the E scenario may both occur in the future. The DOE calls a future in which both of these events occur the ME scenario.  More detailed descriptions are found in Section PA-2.3.2.2. 

The only natural features and waste- and repository-induced FEPs retained after screening that are excluded in the UP scenario, but included in the DP scenario, are those directly associated with the potential effects of future deep drilling within the controlled area.  Among the most significant FEPs that will affect the UP scenario within the disposal system are excavation-induced fracturing, gas generation, salt creep, and MgO in the disposal rooms.

·       The repository excavation and consequent changes in the rock stress field surrounding the excavated opening will create a DRZ immediately adjacent to excavated openings.  The DRZ will exhibit mechanical and hydrological properties different than those of the intact rock.

Figure PA-7.  Logic Diagram for Scenario Analysis

·       Organic material in the waste may degrade because of microbial activity, and brine will corrode metals in the waste and waste containers, with concomitant generation of gases.  Gas generation may result in pressures sufficient to both maintain or develop fractures and change the fluid flow pattern around the waste disposal region.

·       At the repository depth, salt creep will tend to heal fractures and reduce the permeability of the DRZ and the crushed salt component of the long-term shaft seals to near that of the host rock salt.

·       The MgO engineered barrier emplaced in the disposal rooms will react with CO₂ and maintain mildly alkaline conditions.  Metal corrosion in the waste and waste containers will maintain reducing conditions.  These effects will maintain low radionuclide solubility.

Radionuclides can become mobile as a result of waste dissolution and colloid generation following brine flow into the disposal rooms.  Colloids may be generated from the waste (humics, mineral fragments, and An intrinsic colloids) or from other sources (humics, mineral fragments, and microbes).

Conceptually, there are several pathways for radionuclide transport within the undisturbed disposal system that may result in releases to the accessible environment (Figure PA-8).  Contaminated brine may migrate away from the waste-disposal panels if pressure within the panels is elevated by gas generated from corrosion or microbial consumption.  Radionuclide transport may occur laterally, through the anhydrite interbeds toward the subsurface boundary of the accessible environment in the Salado, or through access drifts or anhydrite interbeds to the base of the shafts.  In the latter case, if the pressure gradient between the panels and overlying strata is sufficient, contaminated brine may migrate up the shafts.  As a result, radionuclides may be transported directly to the ground surface, or laterally away from the shafts through permeable strata such as the Culebra, toward the subsurface boundary of the accessible environment.  These conceptual pathways are shown in Figure PA-8.

Figure PA-8.   Conceptual Release Pathways for the UP Scenario

The modeling system described in Section PA-4.0 includes potential radionuclide transport along other pathways, such as migration through Salado halite.  However, the natural properties of the undisturbed system make radionuclide transport to the accessible environment via these other pathways unlikely.

PA-2.3.2.2  Disturbed Repository Performance

Assessments for compliance with section 191.13 need to consider the potential effects of future disruptive natural and human-initiated events and processes on the performance of the disposal system.  No potentially disruptive natural events and processes are considered sufficiently likely to require inclusion in analyses of either the UP or DP scenario.  The only future human-initiated events and processes retained after FEP screening are those associated with mining and deep drilling (but not the subsequent use of a borehole) within the controlled area or LWB when institutional controls cannot be assumed to eliminate the possibility of such activities (Section PA-3.2 and the CRA-2004, Chapter 6.0, Section 6.4.12.1).  In total, 21 disturbed repository FEPs associated with future mining and deep drilling have been identified.  These FEPs were assigned a screening designator of the DP scenario.

For evaluating the consequences of disturbed repository performance, the DOE has defined the mining scenario (M), the deep drilling scenario (E), and a mining and drilling scenario (ME).  These scenarios are described in the following sections.

PA-2.3.2.2.1  Disturbed Repository M Scenario

The M scenario involves future mining within the controlled area.  Consistent with the criteria stated by the EPA in 40 CFR § 194.32(b) for PA calculations, the effects of potential future mining within the controlled area are limited to changes in hydraulic conductivity of the Culebra that result from subsidence (as described in Section PA-3.9).

Radionuclide transport may be affected in the M scenario if a head gradient between the waste-disposal panels and the Culebra causes brine contaminated with radionuclides to move from the waste-disposal panels to the base of the shafts and up to the Culebra.  The changes in the Culebra T field may affect the rate and direction of radionuclide transport within the Culebra.  Features of the M scenario are illustrated in Figure PA-9.

The three disturbed repository FEPs labeled M in the CRA-2004, Chapter 6.0, Table 6-9 are related to the occurrence and effects of future mining.  The modeling system used for the M scenario is similar to that developed for the UP scenario, but with a modified Culebra T field in the controlled area to account for the mining effects.

PA-2.3.2.2.2  Disturbed Repository E Scenario

The disturbed repository E scenario involves at least one deep drilling event that intersects the waste disposal region.  The EPA provides criteria for analyzing the consequences of future drilling events in PA in 40 CFR § 194.33(c).

Performance assessments shall document that in analyzing the consequences of drilling events, the Department assumed that:

(1) Future drilling practices and technology will remain consistent with practices in the Delaware Basin at the time a compliance application is prepared.  Such future drilling practices shall include, but shall not be limited to: the types and amounts of drilling fluids; borehole depths, diameters, and seals; and the fraction of such boreholes that are sealed by humans; and

Figure PA-9.  Conceptual Release Pathways for the Disturbed Repository M Scenario

(2) Natural processes will degrade or otherwise affect the capability of boreholes to transmit fluids over the regulatory time frame.

Consistent with these criteria, there are several pathways for radionuclides to reach the accessible environment in the E scenario.  Before any deep drilling intersects the waste, potential release pathways are identical to those in the undisturbed repository scenario.

If a borehole intersects the waste in the disposal rooms, releases to the accessible environment may occur as material entrained in the circulating drilling fluid is brought to the surface. Particulate waste brought to the surface may include cuttings, cavings, and spallings.  Cuttings are the materials cut by the drill bit as it passes through waste.  Cavings are the materials eroded by the drilling fluid in the annulus around the drill bit.  Spallings are the materials forced into the circulating drilling fluid if there is sufficient pressure in the waste disposal panels.  During drilling, contaminated brine may flow up the borehole and reach the surface, depending on fluid pressure within the waste disposal panels.

When abandoned, the borehole is assumed to be plugged in a manner consistent with current practices in the Delaware Basin as prescribed in 40 CFR § 194.33(c)(1).  An abandoned intrusion borehole with degraded casing and/or plugs may provide a pathway for fluid flow and contaminant transport from the intersected waste panel to the ground surface if the fluid pressure within the panel is sufficiently greater than hydrostatic.  Additionally, if brine flows through the borehole to overlying units, such as the Culebra, it may carry dissolved and colloidal actinides that can be transported laterally to the accessible environment by natural groundwater flow in the overlying units.

Alternatively, the units intersected by an intrusion borehole may provide sources for brine flow to a waste panel during or after drilling. For example, in the northern Delaware Basin, the Castile, which underlies the Salado, contains isolated volumes of brine at fluid pressures greater than hydrostatic (as discussed in the CRA-2004, Chapter 2.0, Section 2.2.1.2.2).  The WIPP-12 penetration of one of these reservoirs provided data on one brine reservoir within the controlled area.  The location and properties of brine reservoirs cannot be reliably predicted; thus, the possibility of a deep borehole penetrating both a waste panel and a brine reservoir is accounted for in consequence analysis of the WIPP, as discussed in the CRA-2004, Chapter 6.0, Section 6.4.8.  Such a borehole could provide a connection for brine flow from the Castile to the waste panel, thus increasing fluid pressure and brine volume in the waste panel.

A borehole that is drilled through a disposal room pillar, but does not intersect waste, could also penetrate the brine reservoir underlying the waste disposal region.  Such an event would, to some extent, depressurize the brine reservoir, and thus would affect the consequences of any subsequent reservoir intersections.  The PA does not take credit for possible brine reservoir depressurization.

The DOE has distinguished two types of deep drilling events by whether or not the borehole intersects a Castile brine reservoir.  A borehole that intersects a waste disposal panel and penetrates a Castile brine reservoir is designated an E1 event.  A borehole that intersects a waste panel but does not penetrate a Castile brine reservoir is designated an E2 event. The consequences of deep drilling intrusions depend not only on the type of a drilling event, but on whether the repository was penetrated by an earlier E2 event or flooded due to an earlier E1 event.  The PA also does not take credit for depressurization of brine reservoirs from multiple drilling intrusions.  These scenarios are described in order of increasing complexity in the following sections.

PA-2.3.2.2.3  The E2 Scenario

The E2 scenario is the simplest scenario for inadvertent human intrusion into a waste disposal panel.  In this scenario, a panel is penetrated by a drill bit; cuttings, cavings, spallings, and brine flow releases may occur; and brine flow may occur in the borehole after it is plugged and abandoned.  Sources for brine that may contribute to long-term flow up the abandoned borehole are the Salado or, under certain conditions, the units above the Salado.  An E2 scenario may involve more than one E2 drilling event, although the flow and transport model configuration developed for the E2 scenario evaluates the consequences of futures that have only one E2 event.  Features of the E2 scenario are illustrated in Figure PA-10.

Figure PA-10.    Conceptual Release Pathways for the Disturbed Repository Deep Drilling E2 Scenario

PA-2.3.2.2.4  The E1 Scenario

Any scenario with exactly one inadvertent penetration of a waste panel that also penetrates a Castile brine reservoir is called E1.  Features of this scenario are illustrated in Figure PA-11.

Sources of brine in the E1 scenario are the brine reservoir, the Salado, and, under certain conditions, the units above the Salado.  However, the brine reservoir is conceptually the dominant source of brine in this scenario.  The flow and transport model configuration developed for the E1 scenario evaluates the consequences of futures that have only one E1 event.

Figure PA-11.    Conceptual Release Pathways for the Disturbed Repository Deep Drilling E1 Scenario

PA-2.3.2.2.5  The E1E2 Scenario

The E1E2 scenario is defined as all futures with multiple penetrations of a waste panel of which at least one intrusion is an E1.  One example of this scenario, with a single E1 event and a single E2 event penetrating the same panel, is illustrated in Figure PA-12.  However, the E1E2 scenario can include many possible combinations of intrusion times, locations, and types of event (E1 or E2).  The sources of brine in this scenario are those listed for the E1 scenario, and multiple E1 sources may be present.  The E1E2 scenario has a potential flow path not present in the E1 or E2 scenarios: flow from an E1 borehole through the waste to another borehole.  This flow path has the potential to (1) bring large quantities of brine in direct contact with waste and (2) provide a

Figure PA-12.    Conceptual Release Pathways for the Disturbed Repository Deep Drilling E1E2 Scenario

less restrictive path for this brine to flow to the units above the Salado (via multiple boreholes) compared to either the individual E1 or E2 scenarios.  It is both the presence of brine reservoirs and the potential for flow through the waste to other boreholes that make this scenario different from combinations of E2 boreholes in terms of potential consequences.  Estimates from flow and transport modeling are used to determine the extent of flow between boreholes and whether modeled combinations of E1 and E2 boreholes at specific locations in the repository should be treated as E1E2 scenarios or as independent E1 and E2 scenarios in the consequence analysis.

PA-2.3.2.3  Disturbed Repository ME Scenario

The M scenario and the E scenario may both occur in the future.  The DOE calls a future in which both of these events occur the ME scenario.  The occurrence of both mining and deep drilling do not create processes beyond those already described separately for the M and E scenarios.  For example, the occurrence of mining does not influence any of the interactions between deep boreholes and the repository or brine reservoirs, nor does the occurrence of drilling impact the effects of mining on Culebra hydrogeology.

PA-2.3.2.4  Scenarios Retained for Consequence Analysis

The scenarios described in Section PA-2.3.2.1, Section PA-2.3.2.2, and Section PA-2.3.2.3 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 PA-2.3.3.

PA-2.3.3  Calculation of Scenario Consequences

Calculating scenario consequences requires quantitative modeling.  This section discusses the conceptual and computational models and some parameter values used to estimate the consequence of the scenarios described in Section PA-2.3.2.  Additional discussion of conceptual models and modeling assumptions is provided in Section PA-4.0.  Additional descriptions of sampled parameter values are included in Fox (2008).

A single modeling system was used to represent the disposal system and calculate the CCDFs.  The modeling system, however, can be conveniently described in terms of various submodels, with each describing a part of the overall system.  The models used in the WIPP PA, as in other complex analyses, exist at four different levels.

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 closed-form solutions.

4.     The complexity of the system requires computer codes to solve the numerical models.  The implementation of the numerical model in the computer code with specific initial and boundary conditions and parameter values is generally referred to as the computational model.

Data are descriptors of the physical system being considered, normally obtained by experiment or observation. Parameters are values necessary in mathematical, numerical, or computational models.  The distinction between data and parameters can be subtle. Parameters are distinct from data, however, for three reasons:  (1) Data may be evaluated, statistically or otherwise, to generate model parameters to account for uncertainty in data.  (2) Some parameters have no relation to the physical system, such as the parameters in a numerical model to determine when an iterative solution scheme has converged.  (3) Many model parameters are applied at a different scale than one directly observed or measured in the physical system.  The distinction between data and parameter values is described further in Fox (2008) and Tierney (1990), where distribution derivations for specific parameters are given.  The interpretation and scaling of experimental and field data are discussed in Fox (2008) for individual and sampled parameters, as appropriate.

PA-3.0  Probabilistic Characterization of Futures

The PA for the WIPP identifies uncertainty in parameters and uncertainty in future events as distinctly different entities and requires sampling to be conducted in two dimensions. One dimension focuses on characterizing the uncertainty in terms of the probability that various possible futures will occur at the WIPP site over the next 10,000 years.  The other dimension characterizes the uncertainty due to lack of knowledge about the precise values of model parameters appropriate for the WIPP repository.  Each dimension of the analysis is characterized by a probability space.  Monte Carlo methods are used with the WIPP PA modeling system to sample each of the two probability spaces. 

Characterizing the probability distribution for the first dimension of the PA depends on identifying the kinds of events that could impact releases from the repository over the next 10,000 years. Screening analyses of possible future events concluded that the only significant events with the potential to affect radionuclide releases to the accessible environment are drilling and mining within the LWB (Appendix SCR-2009, Section SCR-5.0).  Consequently, modeling the future states of the repository focuses on representing the occurrences and effects of these two events. CCDFGF uses stochastic processes to simulate intrusion events by drilling and the occurrence of mining for natural resources. CCDFGF assembles the results from the deterministic models and selects the most appropriate scenario data provided by these models to use as the simulation of a 10,000-year future progresses.  Ten thousand potential futures are simulated and used to create distributions of potential releases, and then compiled into a single CCDF of potential releases.

WIPP PA is required not only to estimate the likelihood of future releases, but to establish confidence in those estimates.  Confidence is established using the second dimension of the analysis, which is based on the evaluation of uncertainty in the values of some of the parameters of the deterministic models.  This uncertainty is assumed to represent a lack of knowledge about the true values of the parameters, and is labeled epistemic uncertainty.  Epistemic uncertainty can be viewed as the representation of potential systematic errors in the results.  The impact of epistemic uncertainty on the results is determined by generating 300 sets of parameter values using a stratified random sampling design, LHS, and then running the deterministic models and CCDFGF with each set of sampled parameters.  Thus, 300 CCDFs are generated by CCDFGF. One set of parameters is often referred to as a vector.  The 300 simulations are organized as 3 replicates of 100 vectors each.  Because the uncertainty assigned to the parameters represents a lack of knowledge, this epistemic uncertainty could theoretically be reduced by collecting data to improve knowledge about the parameters.  Epistemic uncertainty is represented in the projections of potential releases from the repository by the variability among the 300 CCDFs.

The WIPP PA modeling system consists of a set of loosely coupled deterministic models (BRAGFLO, PANEL, NUTS, SECOTP2D, and CUTTINGS_S) that provide scenario-specific results to the code CCDFGF (Figure PA-2).  CCDFGF is, in contrast, a stochastic simulation model used to simulate potential futures of repository performance where drilling and mining intrusions can impact the state of the repository and produce release events. CCDFGF implements intrusions as stochastic events, thus incorporating the aleatory uncertainty associated with projections of future events.  This section describes how aleatory uncertainty is implemented in PA.  Epistemic uncertainty is discussed in Section PA-6.0.

PA-3.1  Probability Space

As discussed in Section PA-2.2.2, aleatory uncertainty is defined by the possible futures x_st,i  conditional on the set i of parameters used in Equation (PA.2).  Section PA-3.2, Section PA-3.3, Section PA-3.4, Section PA-3.5, Section PA-3.6, Section PA-3.7, Section PA-3.8, and Section PA-3.9 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 PA-3.10.  The procedure used to sample the individual elements x_st,i is described in Section PA-6.5.

PA-3.2  AICs and PICs

AICs and PICs will be implemented at the WIPP site to deter human activity detrimental to repository performance.  AICs and PICs are described in detail in the CRA-2004, Chapter 7.0 and in appendices referenced in Chapter 7.0.  In this section, the impact of AICs and PICs on PA is described.

AICs will be implemented at the WIPP after final facility closure to control site access and ensure that activities detrimental to disposal system performance do not occur within the controlled area.  The AICs will preclude human intrusion in the disposal system.  A 100-year limit on the effectiveness of AICs in PA is established in 40 CFR § 191.14(a).  Because of the regulatory restrictions and the nature of the AICs that will be implemented, PA assumes there are no inadvertent human intrusions or mining in the controlled area for 100 years following repository closure.

PICs are designed to deter inadvertent human intrusion into the disposal system.  Only minimal assumptions were made about the nature of future society when designing the PICs to comply with the assurance requirements.  The preamble to Part 194 limits any credit for PICs in deterring human intrusion to 700 years after disposal (U.S. Environmental Protection Agency 1996a, p. 5231).  Although the DOE originally took credit for PICs in the CCA PA, but has not taken credit since.  Not including PICs is a conservative implementation, as no credit is taken for a beneficial process.

PA-3.3  Drilling Intrusion

As described in Section PA-2.3.2.2, drilling intrusions in PA are assumed to occur randomly in time and space following a Poisson process.  Specifically, the drilling rate considered within the area marked by a berm as part of the system for PICs (Fox 2008, Table 46) is 5.85 ´ 10^-3 intrusions per square kilometer per year (km²/yr).  AICs are assumed to prevent any drilling intrusions for the first 100 years after the decommissioning of the WIPP (Section PA-3.2).  In the computational implementation of PA, it is convenient to represent the Poisson process for drilling intrusions by its corresponding rate term l_d( t) for intrusions into the area marked by the berm.  Specifically,

                                                                                      (PA.6)

where 0.6285 km² is the area enclosed by the berm (Fox 2008, Table 45) and t is elapsed time 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 sampled to define the times between successive drilling intrusions (Figure PA-13, Section PA-6.5).  A key assumption of the exponential distribution is that events are independent of each other, so the occurrence of one has no effect on the occurrence of the next event.  The process giving rise to such events is sometimes called a Poisson process because the distribution of such events over a fixed interval of time is a Poisson distribution. Due to the 10,000-year regulatory period specified in 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-13.  CDF for Time Between Drilling Intrusions

PA-3.4  Penetration of Excavated/Nonexcavated Area

The variable e_j is a designator for whether or not the j^th drilling intrusion penetrates an excavated, waste-filled area of the repository:  e_j = 0 or 1 implies penetration of 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)

                                                                                (PA.8)

where 0.1273 km² and 0.6285 km² are the excavated area of the repository and the area of the berm, respectively (Fox 2008, Table 45).

PA-3.5  Drilling Location

Locations of drilling intrusions through the excavated, waste-filled area of the repository are discretized to the 144 locations in Figure PA-14.  Assuming that a drilling intrusion occurs within the excavated area, it is assumed to be equally likely to occur at each of these 144 locations.  Thus, the probability pL_k that drilling intrusion j will occur at location l_k, k = 1, 2, ¼, 144 in Figure PA-14 is

                           (PA.9)

Figure PA-14.  Discretized Locations for Drilling Intrusions

PA-3.6  Penetration of Pressurized Brine

The conceptual models for the Castile include the possibility that pressurized brine reservoirs underlie the repository (Section PA-4.2.10).  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 PA, the probability pB₁ = P[b_j = 1] is sampled from a uniform distribution ranging from 0.01 to 0.60 (see GLOBAL:PBRINE in Table PA-19).

PA-3.7  Plugging Pattern

Three borehole plugging patterns, p_k, are considered in PA:  (1) p₁, a full concrete plug through the Salado to the Bell Canyon Formation (hereafter referred to as Bell Canyon), (2) p₂, a two-plug configuration with concrete plugs at the Rustler/Salado interface and the Castile/Bell Canyon interface, and (3) p₃, a three-plug configuration with concrete plugs at the Rustler/ Salado, Salado/Castile, and Castile/Bell Canyon interfaces.  The probability that a given drilling intrusion will be sealed with plugging pattern p_k, k= 1, 2, 3, is given by pPL_k, where pPL₁ = P[k = 1] = 0.015, pPL₂ = P[k = 2] = 0.696, pPL₃ = P[k = 3] = 0.289 (Fox 2008, Table 46).

PA-3.8  Activity Level

The waste intended for disposal at the WIPP is represented by 767 distinct waste streams, with 690 of these waste streams designated as CH-TRU waste and 77 designated as RH-TRU waste (Leigh, Trone, and Fox 2005, Section 4.4).  For the CRA-2009 PA, the 77 separate RH-TRU waste streams are represented by a single, combined RH-TRU waste stream.  The activity levels for the waste streams are given in Fox (2008, Table 48 and Table 49).  Each waste container emplaced in the repository contains waste from a single CH-TRU waste stream.  Waste packaged in 55-gallon (gal) drums is stacked 3 drums high within the repository.  Although waste in other packages (e.g., standard waste boxes, 10-drum overpacks, etc.) may not be stacked 3 high, PA assumes that each drilling intrusion into CH-TRU waste intersects 3 different waste streams.  In contrast, all RH-TRU waste is represented by a single waste stream, and so each drilling intrusion through RH-TRU waste is assumed to intersect this single waste stream.  Appendix MASS-2009, Section MASS-21.0 examines the sensitivity of PA results to the assumption that three waste streams are intersected by each drilling intrusion into CH-TRU waste.

The vector 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 RH-TRU is penetrated                          (PA.11)

                         a_j = [iCH_j1, iCH_j2, iCH_j3] if e_j = 1 and CH-TRU is penetrated           (PA.12)

where iCH_j1, iCH_j2, and iCH_j3 are integer designators for the CH-TRU 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 690).

Whether the j^th intrusion penetrates a nonexcavated or excavated area is determined by the probabilities pE₀ and pE₁ discussed in Section PA-3.4.  The type of waste penetrated is determined by the probabilities pCH and pRH.  The excavated area used for disposal of CH-TRU waste (aCH) is 1.115 ´ 10⁵ square meters (m²) and the area used for disposal of RH-TRU waste (aRH) is 1.576 ´ 10⁴ m² (Fox 2008, Table 45), for a total disposal area of aEX = aCH + aRH = 1.273 ´ 10⁵ m².  Given that the j^th intrusion penetrates an excavated area, the probabilities pCH and pRH of penetrating CH-TRU and RH-TRU waste are given by

                                                                                                                                         (PA.13)

                                                                                                                                         (PA.14)

As indicated in this section, the probabilistic characterization of a_j depends on a number of individual probabilities.  Specifically, pEx₀ and pEx₁ determine whether a nonexcavated or excavated area is penetrated (Section PA-3.5); pCH and pRH determine whether CH-TRU or RH-TRU waste is encountered, given penetration of an excavated area; and the individual waste stream probabilities in Fox (2008, Table 48 and Table 49), determine the specific waste streams iCH_j1, iCH_j2, and iCH_j3 encountered given a penetration of CH-TRU waste. The probability of encountering a particular CH-TRU waste stream is computed as the ratio of the volume of that waste stream to the volume of CH-TRU waste.

PA-3.9  Mining Time

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 the absence of institutional controls is specified as following a Poisson process with a rate of l_m = 1 ´ 10 ^-4 yr ^-1 (Fox 2008, Table 46).  However, this rate can be reduced by AICs and PICs.  Specifically, AICs are assumed to result in no possibility of mining for the first 100 years after decommissioning of the WIPP.  In PA, PICs do not affect the mining rate. Thus, the mining rate l_m( t) is

                                                                                   (PA.15)

                                                                (PA.16)

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 10,000-year 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.

PA-3.10  Scenarios and Scenario Probabilities

A scenario is a subset of the sample space for aleatory uncertainty.  The underlying goal of scenario definition is to define the state of repository conditions prior to and following intrusion events.  Scenarios are specific cases of inputs or system states that are selected to cover the range of possible cases.  Given the complexity of the futures 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 PA-2.2.3 limits evaluation to only a few intrusion scenarios.  As presented in Section PA-2.3.2, PA considers four fundamental intrusion scenarios:

           E0  =  no drilling intrusion through an excavated area of the repository

           E1  =  a drilling intrusion through an excavated area of the repository that penetrates pressurized brine in the Castile

           E2  =  a drilling intrusion through an excavated area of the repository that does not penetrate pressurized brine in the Castile

      E1E2  =  two or more previous intrusions, at least one of which is an E1 intrusion

These definitions of intrusion scenarios capture the most important events impacting the state of the repository:  whether or not the repository is inundated by the penetration of a brine pocket, and whether or not there exists a possible route of release upward via a borehole. The state of the repository is also designated as E0, E1, E2, or E1E2. Scenarios for some of the process-level models consist of a single intrusion scenario occurring at specific times.  CCDFGF is used to simulate multiple intrusions over 10,000 years.

If only the intrusion scenarios controlled the state of the repository, then the state would be defined by the sequence of drilling events alone.  However, CCDFGF also considers the impact of plugging pattern on boreholes.  A borehole with a full plugging pattern that penetrates the waste area is also assumed to have no impact, and leaves the repository in its previous state, including the undisturbed state (see Section PA-6.8.4.1 and Figure PA-41 for more details).  Thus, an E2 intrusion event into an E0 repository will result in an E0 state if a full plugging pattern is used, or an E2 state otherwise.  An E1 intrusion subsequent to an E2 intrusion will leave the repository in an E1E2 state, where it will remain, regardless of subsequent intrusions.  It is therefore important to distinguish between the type of intrusion, listed above, and the state of the repository.

The probability that no excavated area will be penetrated during the 10,000-year interval can be computed using a distribution of the number of penetration events and the probability that a drilling event will penetrate the excavated area.  For the Poisson distribution of drilling events, the probability of there being n events in the 10,000-year history is

                                                                         (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 pEx₀ⁿ, or specifically 0.797ⁿ.  Thus, the probability of having only events in the nonexcavated area over 10,000 years, i.e., having no drilling intrusions into the excavated area, is just the sum across all n of the products of the probability of having exactly n drilling events and the probability that all n events penetrate the unexcavated area:

                                                                                                (PA.18)

The calculated probability becomes

                                                                             (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 pB₁ takes on its mean value of 0.305 (see Section PA-3.6), and ignoring the impact of the plugging pattern, for a constant rate of drilling, l_d, these equations are

                                                                    (PA.20)

and

                                                                   (PA.21)

respectively, where (pEx₁ × l_d)represents the annual rate of drilling into the excavated region of the repository which is multiplied by 9900 to give the rate per 9,900 years.  The probability of an intrusion into the excavated area is subsequently multiplied by the probability of hitting or missing a brine pocket.  In this form, it can be seen that the term for the probability for intrusion is equivalent to the PDF of the Poisson distribution for n = 1:

                                                                                                                  (PA.22)

The expressions defining the probability of being in the E0 state after 10,000 years and of having a single E1 or E2 intrusion event after 10,000 years are relatively simple because the scenarios E0, E1, and E2 are relatively simple.  The scenario E1E2 is more complex and, as a result, computing its probability is also more complex.  Closed-form formulas for the probabilities of quite complex scenarios can be derived, but they are very complicated and involve large numbers of iterated integrals (Helton 1993).  These probabilities of single E1 and E2 intrusions are relevant to the scenarios used by the process-level models.

PA-3.11  CCDF Construction

CCDFGF simulates histories that can have many intrusion events (WIPP Performance Assessment 2003a).  The process-level models evaluate the releases at a small number of specific times for each of the four intrusion scenarios.  Releases from the repository are calculated using results from these fundamental scenarios (Section PA-6.7 and Section PA-6.8).  Releases for an arbitrary future are estimated from the results of these fundamental scenarios (Section PA-6.8); these releases are used to construct CCDFs by Equation (PA.4).

Previous WIPP PAs have used 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 CRA-2009 PA uses the same approach as the CRA-2004 PA.

PA-4.0  Estimation of Releases

This section describes how releases to the accessible environment are estimated for a particular future in PA.

PA-4.1  Results for Specific Futures

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) ~ two-phase 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,i)) 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 2003a), uses a sample of size nS = 10,000 in PA.  The individual programs that estimate releases do not run fast enough to allow this many evaluations of f.  As a result, a two-step procedure is being used to evaluate f in calculating the summation in Equation (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 PA-6.7 and Section PA-6.8, and produce the evaluations of f(x_st) that are actually used in Equation (PA.23).

For notational simplicity, the functions on the right-hand side of Equation (PA.23) will typically be written with only x_st as an argument (e.g., f_SP(x_st) 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 two-phase flow in the vicinity of the repository as modeled by BRAGFLO (i.e., f_B) (Section PA-4.2), radionuclide transport in the vicinity of the repository as modeled by NUTS (i.e., f_MB, f_DL, f_S, f_NP) (Section PA-4.3), radionuclide transport in the vicinity of the repository as modeled by PANEL (i.e., f_NP) (Section PA-4.4), cuttings and cavings releases to the surface as modeled by CUTTINGS_S (i.e., f_C) (Section PA-4.5), spallings releases to the surface as modeled by DRSPALL and CUTTINGS_S (i.e., f_SP) (Section PA-4.6), DBRs to the surface as modeled by BRAGFLO (i.e., f_DBR) (Section PA-4.7), brine flow in the Culebra as modeled by MODFLOW (i.e., f_MF) (Section PA-4.8), and radionuclide transport in the Culebra as modeled by SECOTP2D (i.e., f_ST) (Section PA-4.9).

PA-4.2  Two-Phase Flow:  BRAGFLO

Quantifying the effects of gas and brine flow on radionuclide transport from the repository requires a two-phase (brine and gas) flow code.  The two-phase flow code BRAGFLO is used to simulate gas and brine flow in and around the repository (Nemer 2007b and 2007c).  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.

PA-4.2.1  Mathematical Description

Two-phase flow in the vicinity of the repository is represented by the following system of two conservation equations, two constraint equations, and three equations of state:

Gas Conservation

                               Ñ×           (PA.24)

Brine Conservation

                                 Ñ×             (PA.25)

Saturation Constraint

                                                                                                                      (PA.26)

Capillary Pressure Constraint

                                                                                                        (PA.27)

Gas Density

       r_g (determined by Redlich-Kwong-Soave (RKS) equation of state; see Equation (PA.51))
                                                                                                                                         (PA.28)

Brine Density

                                                                                              (PA.29)

Formation Porosity

                                                                                                  (PA.30)

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/m³/s])

         q_l  =  rate of injection (or removal, if negative) of fluid l (kg/m³/s)

         S_l =  saturation of fluid l (dimensionless)

           t  =  time (s)

         a  =  geometry factor (m)

         r_l =  density of fluid l (kg/m³)

         m_l =  viscosity of fluid l (Pa s)

          f  =  porosity (dimensionless)

         f₀ =  reference (i.e., initial) porosity (dimensionless)

       P_b0   =  reference (i.e., initial) brine pressure (Pa), constant in Equation (PA.29) and spatially variable in Equation (PA.30)

         r₀  =  reference (i.e., initial) brine density (kg/m³)

         c _f  =  pore compressibility (Pa^-1)

         c_b  =  brine compressibility (Pa^-1)

         K  =  permeability of the material (m²), isotropic for PA (Howarth and Christian-Frear 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 formation-dependent constants.  Values of a = -0.3410 and b = 0.2710 were determined from data obtained for MB 139 (Christian-Frear 1996), with these values used for all regions in Figure PA-15.

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 two-phase fluid flow within the two-dimensional region shown in Figure PA-15.  The details of this system are now discussed.

The a term in Equation (PA.24) and Equation (PA.25) is a dimension-dependent geometry factor and is specified by

a  =  area normal to flow direction in one-dimensional flow (i.e., DyDz; units = m²)
    =  thickness normal to flow plane in two-diemensional flow (i.e., Dz; units = m)
    =  1 in three-dimensional flow (dimensionless)                                              (PA.32)

PA uses a two-dimensional geometry to compute two-phase flow in the vicinity of the repository, and as a result, a is the thickness of the modeled region (i.e., Dz) normal to the flow plane (Figure PA-15).  Due to the use of the two-dimensional grid in Figure PA-15, a is spatially dependent, with the values used for a defined in the column labeled “Dz.”  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 PA-16 and ensures that the total volume surrounding the repository is conserved in the numerical grid.  The equations and method used to determine a  for the grid shown in Figure PA-15 are described in detail by 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 1266 in Figure PA-17).  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 Equations (PA.24) through (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 PA-17) 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 PA-3.

Values for f₀ and c _f (Equation (PA.30)) are also given in Table PA-3.  Initial porosity f₀ for the DRZ is a function of the uncertain parameter for initial halite porosity f_0H (HALPOR; see Table PA-19) and is given by Martell (1996a) and Bean et al. (1996), Section 4):

                                                                f₀ = f_0H + 0.0029                                            (PA.34)

Initial porosity f₀ of the Castile brine reservoir is calculated from the uncertain sampled parameter for the bulk Castile rock compressibility (BPCOMP; see Table PA-19), 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 m³/Pa.  The productivity ratio PR is computed by

                                                                                                          (PA.36)

where V is the volume of the grid block representing the Castile brine reservoir in Figure PA-15. Because of this relationship, the initial porosity of the brine reservoir ranges from 0.1842 to 0.9208.  This range of porosity is not meant to represent an actual reservoir, but rather allows a reservoir to supply a volume of brine to the repository in the event of an E1 intrusion consistent with observed brine flows in the Delaware Basin.

The compressibility c _f in Equation (PA.30) and Table PA-3 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 f₀ 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 Brooks-Corey model (Brooks and Corey 1964).  In this model, P_c, k_rb, and k_rg are defined by

                                                                                                          (PA.38)

Figure PA-15.  Computational Grid Used in BRAGFLO for PA

Figure PA-16.  Definition of Element Depth in BRAGFLO Grid

 

Figure PA-17.  Identification of Individual Cells in BRAGFLO Grid

 

 

 

                                                                                                              (PA.39)

                                                                                     (PA.40)

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 PA-3.  The statement that the Brooks-Corey model is in use means that P_c, k_rb, and k_rg are defined by Equation (PA.38) through Equation (PA.40).

In the anhydrite MBs, either the Brooks-Corey model or the van Genuchten-Parker model is used as determined by the subjectively uncertain parameter ANHBCVGP (see Table PA-19).  A linear model is used to represent two-phase flow in an open borehole (i.e., for the first 200 years after a drilling intrusion for boreholes with two-plug or three-plug configurations, in the open cavities [CAVITY_1, . . , CAVITY_4], and for the experimental and operations areas).  This is discussed further below.

In the van Genuchten-Parker model, P_c, k_rb, and k_rg are defined by (van Genuchten 1978)

                                                                                               (PA.44)

                                                                                        (PA.45)

                                                                                     (PA.46)

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_e2 = 0.5 (Webb 1992).  The van Genuchten-Parker 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 Brooks-Corey model (Table PA-3).

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 PA-4.2.2) and the experimental and operations areas (t = 0 to 10,000 years) which, in PA, are modeled without a time-dependent creep closure:

                                                                                                     (PA.48)

                                                                         (PA.49)

                                                                                             (PA.50)

where l = gas or brine and tol is a tolerance (slope) over which the relative permeability changes linearly from 0 to 1.  In PA, tol = 1 ´ 10^-2 (dimensionless).  Thus, the relative permeabilities are ~ 1 for saturations away from residual saturation.

Capillary pressure P_c for both the van Genuchten-Parker and Brooks-Corey 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 ´ 10⁸ Pa in selected regions (Table PA-4).

Gas density is computed using the RKS equation of state, with the gas assumed to be pure H₂.  For a pure gas, the RKS equation of state has the form (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 (m³ mol ^-1)

             a  =  0.42747/P_crit

             b  =  0.08664 RT_crit  /P_crit

Table PA-4.  Models for Relative Permeability and Capillary Pressure in Two-Phase Flow

Material	Relative Permeabilitya (RELP_MOD)	Capillary Pressureb (CAP_MOD)	Material	Relative Permeabilitya (RELP_MOD)	Capillary Pressureb (CAP_MOD)
S_HALITE	4	2	WAS_AREA	12	1
DRZ_0	4	1	DRZ_1	4	1
S_MB139	ANHBCVGPc	2	DRZ_PCS	Sampled	1
S_ANH_AB	ANHBCVGPc	2	CONC_PCS	4	2
S_MB138	ANHBCVGPc	2	UNNAMED	4	1
CAVITY_1	11	1	TAMARISK	4	1
CAVITY_2	11	1	FORTYNIN	4	1
CAVITY_3	11	1	DRF_PCS	12	1
CAVITY_4	11	1	REPOSIT	12	1
IMPERM_Z	4	1	CONC_MON	4	2
CASTILER	4	2	SHFTU	4	1
OPS_AREA	11	1	SHFTL_T1	4	1
EXP_AREA	11	1	SHFTL_T2	4	1
CULEBRA	4	2	CONC_PLG	4	1
MAGENTA	4	2	BH_OPEN	5	1
DEWYLAKE	4	2	BH_SAND	4	1
SANTAROS	4	1	BH_CREEP	4	1
a   Relative permeability model, where 4 = Brooks-Corey model given by Equation (PA.38) through Equation (PA.40), 5 = linear model given by Equation (PA.47), 11 = linear model given by Equation (PA.48) through Equation (PA.50), 12 = modified Brooks-Corey model to account for cutoff saturation (Nemer 2007c),  and ANHBCVGP ~ use of Brooks-Corey or van Genuchten-Parker model treated as a subjective uncertainty. b    Capillary pressure model, where 1 = capillary pressure is unbounded, 2 = Pc bounded above by 1 ´ 108 Pa as Sb approaches Sbr. c    See ANHBCVGP in Table PA-19.

 

            a  = 

                 »  for H₂ (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 H₂ (Graboski and Daubert 1979)

In order to account for quantum effects in H₂, effective critical temperature and pressure values of T_crit  = 43.6 K and P_crit = 2.047 ´ 10⁶ 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 H₂ (i.e., 2.01588 ´ 10 ^-3 kg/mol; see Weast 1969, p. B-26).

Brine density r_b is defined by Equation (PA.29), with r_b0= 1230.0 kg/m³ at a pressure of P_b0 = 1.0132 ´ 10⁵  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 PA-4.2.3) and in the DRZ and MBs subsequent to fracturing (see Section PA-4.2.4).  The values of f₀ and c _f used in conjunction with Equation (PA.30) are listed in Table PA-3.  The reference pressure P_b0 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 PA-4.2.2). 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 long-term 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 PA-4.7, q_g and q_b are used to describe injection and production wells in the DBR grid.

In PA, no gas consumption occurs through the term q_rg (see below), and gas production has the potential to occur (due to corrosion of steel or microbial degradation of CPR materials) only in the waste disposal regions of the repository (i.e., Waste Panel, South RoR, and North RoR in Figure PA-15).  Thus,

            q_rg ³ 0  in waste disposal regions of Figure PA-15

= 0  elsewhere                                                                                                (PA.53)

Gas consumption occurs due to the reaction of CO₂ with MgO in the waste panels, and potentially from the sulfidation of steel.  This gas consumption is not modeled using q_rg, but is accounted for by reducing the gas generation rate q_rg, as discussed in Section PA-4.2.5.  Finally, no brine production occurs, and brine consumption has the potential to occur (due to the consumption of brine during steel corrosion) only in the waste disposal regions of the repository.  Thus,

            q_rb   £ 0  in waste disposal regions of Figure PA-15

= 0  elsewhere                                                                                                (PA.54)

More detail on the definition of q_rg and q_rb is provided in Section PA-4.2.5.

PA-4.2.2  Initial Conditions

In each two-phase flow simulation, a short period of time representing disposal operations is simulated.  This period of time is called the start-up period, and covers 5 years from t = -5 years to 0 years, corresponding to the amount of time a typical panel is expected to be open during disposal operations.  All grid locations require initial brine pressure and gas saturation at the beginning of the simulation (t = -5 years).

The Rustler and overlying units (except in the shaft) are modeled as horizontal with spatially constant initial pressure in each layer (see Figure PA-15).  Table PA-5 lists the initial brine pressure, P_b, and gas saturation, S_g, for the Rustler.

The Salado (Mesh Rows 3–24 in Figure PA-15) is assumed to dip uniformly q = 1 degree downward from north to south (right to left in Figure PA-15).  Except in the repository excavations and the shaft, brine is initially assumed (i.e., at -5 years) to be in hydrostatic equilibrium relative to an uncertain initial pressure P_b,ref (SALPRES; see Table PA-19) at a reference point located at shaft center at the elevation of the midpoint of MB 139, which is the center of Cell 1266 in Figure PA-17.  This gives rise to the condition

                                                                          (PA.55)

                                           (PA.56)

                               (PA.57)

                                                          (PA.58)

                                                                                                          (PA.59)

Table PA-5.  Initial Conditions in the Rustler

Name	Mesh Row (Figure PA-15)	Pb (x, y, -5), Pa	Sg (x, y, -5)
Santa Rosa c	33	1.013250 ´ 105	1 - Sb = 0.916 (Sb = SANTAROS:SAT_IBRN)a
Santa Rosa c	32	1.013250 ´ 105	1 - Sb  = 0.916 (Sb = SANTAROS:SAT_IBRN)a
Dewey Lakec	31	1.013250 ´ 105	1 - Sb = 0.916 (Sb = SANTAROS:SAT_USAT)a
Dewey Lakec	30	7.355092 ´ 105	1 - Sb = 0.916 (Sb = SANTAROS:SAT_USAT)a
Forty-ninerc	29	1.47328 ´ 106	0b
Magenta	28	9.465 ´ 105 (MAGENTA:PRESSURE)	0b
Tamariskc	27	1.82709 ´ 106	0b
Culebra	26	9.141 ´ 105 (CULEBRA:PRESSURE)	0b
Los Medaños c	25	2.28346 ´ 106	0b
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.55) below, using the brine density of 1220 kg/m3.  See subsequent discussion taking θ = 0 and the reference point (xref, yref) at the top of the Dewey Lake.  See the ALGEBRA input file ALG1_BF_CRA09.INP in library LIBCRA09_BF, class CRA09-1 on the WIPP PA cluster for details.  See Nemer and Clayton (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/m³ (BRINESAL:DNSFLUID)

            c_b  =  3.1 ´ 10 ^-10 Pa ^-1 (BRINESAL:COMPRES)

             g =  9.80665 m/s²

        P_b,ref  =  1.01325 ´ 10⁵ Pa (BRINESAL:REF_PRES)

          P_b0  =  sampled far-field 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 rest of Castile and has a different initial pressure which is a sampled parameter.  Specifically, outside the brine reservoir, pressure is calculated using Equation (PA.55) above 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 PA-19).  Initial gas saturation S_g( x, y, -5) = 0.

Within the shaft (areas Upper Shaft, Lower Shaft, and CONC_MON) and panel closures (areas CONC_PCS and DRF_PCS), P_b( x, y, -5) = 1.01325 ´ 10⁵ Pa and S_g( x, y, -5) = 0.  Within the excavated areas (Waste Panel, South RoR, and North RoR, Ops and Exp), P_b( x, y, -5) = 1.01325 ´ 10⁵ Pa and S_g( x, y, -5) = 0.

At the end of the initial five-year start-up period and the beginning of the regulatory period (t = 0 years), brine pressure and gas saturation are reset in the shaft, panel closures, and excavated areas.  In the shaft (areas Upper Shaft, Lower Shaft, and CONC_MON) and panel closures (areas CONC_PCS and DRF_PCS), P_b( x, y, 0) = 1.01325 ´ 10⁵ Pa and S_g( x, y, 0) = 1 ´ 10 ^-7 (see CONC_MON:SAT_IBRN).  In the waste disposal regions (areas Waste Panel, South RoR, and North RoR), P_b( x, y, 0) = 1.01325 ´ 10⁵ Pa and S_g( x, y, 05) = 0.985 (see WAS_AREA:SAT_IBRN).  In the other excavated areas, P_b( x, y, 0) = 1.01325 ´ 10⁵ Paand S_g( x, y, 0) = 1.0.

PA-4.2.3  Creep Closure of Repository

Salt creep occurs naturally in the Salado halite in response to deviatoric stress.  Inward creep of rock is generally referred to as creep closure.  Creep closure of excavated regions begins immediately from excavation-induced deviatoric stress.  If the rooms were empty, closure would proceed to the point where the void volume created by the excavation would be eliminated as the surrounding formation returned to a uniform stress state.  In the waste disposal region, inward creep of salt causes consolidation of the waste, and this waste consolidation continues until loading in the surrounding rock is uniform, at which point salt creep and waste consolidation ceases.  The amount of waste consolidation that occurs and the time it takes to consolidate are governed by the waste properties (e.g., waste strength, modulus, etc.), the surrounding rock properties, the dimensions and location of the room, and relative quantities of brine and gas present.

The porosity of the waste disposal regions and neighboring access drifts (i.e., Waste Panel, South RoR, North RoR, and DRF_PCS in Figure PA-15) is assumed to change through time due to creep closure of the halite surrounding the excavations.  The equations on which BRAGFLO is based do not incorporate this type of deformation.  Therefore, the changes in repository porosity due to halite deformation are modeled in a separate analysis with the geomechanical program SANTOS, which implements a quasi-static, large-deformation, finite-element procedure (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.

For more information on the generation of the porosity surface for BRAGFLO in PA, see Appendix PORSURF-2009.

PA-4.2.4  Fracturing of MBs and DRZ

Fracturing within the anhydrite MBs (i.e., regions MB 138, Anhydrite AB, and MB 139 in Figure PA-15) and in the DRZ (region DRZ in Figure PA-15) is assumed to occur at pressures slightly above lithostatic pressure, and is implemented through a pressure-dependent compressibility c_r( P_b) (Mendenhall and Gerstle 1995).  Specifically, MB fracturing begins at a brine pressure of

                                                                                                                (PA.60)

where P_bi and P_b0 are spatially dependent (i.e., P_b0 = P(x, y, 0) as in Section PA-4.2.2) and DP_i = 2 ´ 10⁵ Pa (see S_MB138:PI_DELTA in Fox 2008, Table 30)

Fracturing ceases at a pressure of

                                                                                                               (PA.61)

and a fully fractured porosity of

                                                                                                   (PA.62)

where DP_a = 3.8 ´ 10⁶ Pa (see S_MB138:PF_DELTA in Fox 2008, Table 30), f₀ is spatially dependent (Table PA-3), and Df_a = 0.04, 0.24, and 0.04 for anhydrite materials S_MB138, S_ANH_AB, and S_MB139, respectively (see S_MB138:DPHIMAX in Fox 2008, Table 30).

Once fractured, compressibility c_r becomes a linear function

                                                                             (PA.63)

of brine pressure for P_bi £ P_b £ P_ba, with c_ra defined so that the solution f of

                                                (PA.64)

satisfies f (P_ba) = f_a; specifically, c_ra is given by

                                                       (PA.65)

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

                                                                                                     (PA.66)

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 m² (i.e., n is a function of k, which is an uncertain input to the analysis; see ANHPRM in Table PA-19).  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 PA-15.  The fracture model implementation is the same as for the anhydrite materials.  In this case, fracturing would be in halite rather than anhydrite, but because of the limited extent of the DRZ and the proximity of the nearby interbeds, this representation was deemed acceptable by the Salado Flow Peer Review panel (Caporuscio, Gibbons, and Oswald 2003).

PA-4.2.5  Gas Generation

Gas production is assumed to result from anoxic corrosion of steel and the microbial degradation of CPR materials.  Thus, the gas generation rate q_rg in Equation (PA.24) is of the form

                                                                                                            (PA.67)

where q_rgc is the rate of gas production per unit volume of waste (kg/m³/s) due to anoxic corrosion of Fe-base metals, and q_rgm is the rate of gas production per unit volume of waste (kg/m³/s) due to microbial degradation of CPR materials.  Furthermore, q_rb in Equation (PA.25) is used to describe the consumption of brine during the corrosion process.

Gas generation takes place only within the waste disposal regions (i.e., Waste Panel, South RoR, and North RoR in Figure PA-15) and all the generated gas is assumed to have the same properties as H₂ (see discussion in Appendix MASS-2009, Section MASS-3.2).  In PA, the consumable materials are assumed to be homogeneously distributed throughout the waste disposal regions (i.e., the concentration of Fe-base metals and CPR materials in the waste is not spatially dependent).  A separate analysis examined the potential effects on PA results of spatially varying Fe-base metal and CPR material concentrations, and concluded that PA results are not affected by representing these materials with spatially varying concentrations (see Appendix MASS-2009, Section MASS-21.0).

The rates q_rgc, q_rb, and q_rgm (kg/m³/s) are defined by

gas generation by corrosion

                                                       (PA.68)

brine consumption by corrosion

                                                                       (PA.69)

and microbial gas generation

                                                       (PA.70)

where

                          D_s    = surface area concentration of steel in the repository (m²  surface area steel/ m³ disposal volume)

                          D_c  =  mass concentration of cellulosics in the repository (kg biodegradable material/m³ disposal volume)

                       =  molecular weight of H₂ (kg H₂/mol H₂)

                    =  molecular weight of water (H₂O) (kg H₂O/mol H₂O)

                          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 C₆H₁₀O₅/kg C₆H₁₀O₅/s)

                         R_mh  =  rate of cellulose biodegradation under humid conditions (mol C₆H₁₀O₅/kg C₆H₁₀O₅/s)

                        S_b,eff  =  effective brine saturation due to capillary action in the waste materials (see Equation (PA.90) in Section PA-4.2.6)

                          = 

            =  stoichiometric coefficient for gas generation due to corrosion of steel, i.e., moles of H₂ produced by the corrosion of 1 mole of Fe (mol H₂/mol Fe)

        =  stoichiometric coefficient for brine consumption due to corrosion of steel, i.e., moles of H₂O consumed per mole of H₂ generated by corrosion (mol H₂O/mol H₂)

               =  average stoichiometric factor for microbial degradation of cellulose, i.e., the moles of H₂ generated per mole of carbon consumed by microbial action (mol H₂/mol C)

                         r_Fe  =  molar density of steel (mol/m³)

                          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 products R_ci  D_s  r_Fe X_c , R_ch  D_s  r_Fe X_c, R_mi  D_c  y, and R_mh in Equation (PA.68) and Equation (PA.70) define constant rates of gas generation (mol/m³/s) that continue until the associated substrate (i.e., steel or cellulose) is exhausted (i.e., zero order kinetics are assumed).  The terms S_b,eff and  in Equation (PA.68) and Equation (PA.70), which are functions of location and time, correct for the amount of substrate exposed to inundated and humid conditions, respectively.  All the corrosion and microbial action is assumed to cease when no brine is present, which is the reason that 0 replaces S_g = 1 in the definition of .  In PA, R_ch = 0 and R_ci, R_mh, and R_mi are defined by uncertain variables (see WGRCOR, WGRMICH, WGRMICI in Table PA-19).  However, R_mh is now sampled based on the sampled value of R_mi: see Nemer and Clayton (2008, Section 5.1.3).  Further, M_{H 2} = 2.02 ´10 ^-3 kg/mol (Lide 1991, pp. 1-7, 1-8), M_{H 2O} = 1.80 ´ 10 ^-2 kg/mol (Lide 1991, pp. 1-7, 1-8), r_Fe = 1.41 ´ 10⁵ mol/m³ (Telander and Westerman 1993), and D_s, D_c, X_c(H₂O|H₂), X_c(H₂|Fe), and y(H₂| C) are discussed below.

The concentration D_s in Equation (PA.68) is defined by

                                                                                                               (PA.71)

where

         A_d  =  surface area of steel associated with a waste disposal drum (m²/drum)

        V_R  =  initial volume of a single room in the repository (m³)

         n_d  =  ideal number of waste drums that can be close-packed into a single room

In PA, A_d = 6 m²/drum (REFCON:ASDRUM), V_R = 3,644 m³ (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.

During the CRA-2004 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.  In the CRA-2004, the probability that microbial gas generation could occur was assigned a value of 0.5.  To comply with the EPA’s letter, in the CRA-2004 PABC and the CRA-2009 PA the parameter WMICDFLG was changed so that the probability that microbial gas generation could occur was set to 1 while preserving the previous probability distribution on whether CPR could be degraded.  This is summarized in Table PA-6, and is discussed further in Nemer and Stein

Table PA-6.    Probabilities for Biodegradation of Different Organic Materials (WAS_AREA:PROBDEG) in the CRA-2009 PA and the CRA-2004 PA

 

(2005, Section 5.4).  Because there are significant uncertainties in whether the experimentally observed gas-generation rates could be realized in the WIPP repository, during the CRA-2004 PABC the EPA agreed to allow the DOE to multiply the sampled microbial rates by a parameter (WAS_AREA:BIOGENFC) uniformly sampled from 0 to 1.  This is discussed further in Nemer, Stein, and Zelinski (2005, Section 4.2.2).

In cases where biodegradation of rubbers and plastics occur, rubbers and plastics are converted to an equivalent quantity of cellulosics based on their carbon equivalence (Wang and Brush 1996a). This produces the density calculation

	for biodegradation of cellulosics only	(PA.72)
	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).

In the CRA-2009 PA, the emplacement materials (cellulose and plastic) have been added to m_cel and m_p.  This is discussed further in Nemer and Clayton (2008, Section 5.1.1).  Density values for CPR materials can be found in Fox (2008, Table 34).

The most plausible corrosion reactions after closure of the WIPP are believed to be (Wang and Brush 1996a)

                                                        Fe + 2H₂O = Fe(OH)₂  + H₂                                     (PA.73)

and

                                                         3Fe + 4H₂O = Fe₃O₄ + 4H₂                                     (PA.74)

When normalized to 1 mole of Fe and linearly weighted by the factors x and , the two preceding reactions become

                                     (PA.75)

where x and  are the fractions of Fe consumed in the reactions in Equation (PA.73) and Equation (PA.74), respectively.  Although magnetite (Fe₃O₄) has been observed to form on Fe as a corrosion product in low-Mg anoxic brines at elevated temperatures (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 Fe₃O₄ were to form, H₂ 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 H₂ in excess of the amount of Fe consumed.  Therefore, the stoichiometric factor x in Reaction (PA.75) is set to 1.0 (i.e., x = 1), which implies that Reaction (PA.73) represents corrosion. Thus, the stoichiometric factor for corrosion is

                                                                            (PA.76)

which implies that one mole of H₂ is produced for each mole of Fe consumed, and the stoichiometric factor for brine consumption is

                                                                     (PA.77)

which implies that two moles of H₂O are consumed for each mole of H₂ produced.

The most plausible biodegradation reactions after closure of the WIPP are believed to be (Wang and Brush 1996a)

denitrification             C₆H_1OO₅ + 4.8H⁺ + 4.8NO₃ ^- = 7.4H₂O + 6CO₂ + 2.4N₂                (PA.78)

sulfate reduction              C₆H_1OO₅ + 6H⁺ + 3SO₄^{2 -} = 5H₂O + 6CO₂ + 3H₂S                    (PA.79)

methanogenesis                            C₆H_1OO₅ + H₂O = 3CH₄ + 3CO₂                                  (PA.80)

Accumulation of CO₂ produced by the above reactions could decrease pH and add carbonate to increase An solubility in the repository (Wang and Brush 1996b).

However, in the CRA-2004 PABC, the EPA (Cotsworth 2005) directed the DOE to remove methanogenesis (Equation (PA.80)) from PA.  The EPA cited the presence of calcium sulfate as gypsum and anhydrite in the bedded salt surrounding the repository as possible sources of sulfate.  These sources of sulfate would, if accessible, promote sulfate reduction (Equation (PA.82)), which is energetically and kinetically favored over methanogenesis.  In response, the DOE removed methanogenesis from PA.  Additionally, the DOE removed Fe sulfidation from PA as a gas-consuming reaction because sulfidation of steel produces one mole of H₂ for every mole of H₂S consumed,

                                                              Fe + H₂S = FeS + H₂                                          (PA.81)

This and the removal of methanogenesis are discussed fully in Nemer and Zelinski (2005).

To provide added assurance of WIPP performance, a sufficient amount of MgO is added to the repository to remove CO₂ (Bynum et al. 1997).  MgO in polypropylene “supersacks” is emplaced on top of the three-layer waste stacks to create conditions that reduce An solubilities in the repository (see Appendix MgO-2009 and Appendix SOTERM-2009, Section SOTERM-2.3).  If brine flows into the repository, MgO will react with water in brine and in the gaseous phase to produce brucite (Mg[OH]₂).  MgO will react with essentially all of the CO₂ that could be produced by complete microbial consumption of the CPR materials in the waste, and will create hydromagnesite with the composition Mg₅(CO₃)₄(OH)₂·4H₂O (Appendix MgO-2009; Appendix SOTERM-2009, Section SOTERM-2.0).  The most important MgO hydration and carbonation reactions that will occur in the WIPP are

                                                MgO + H₂O(aq and/or g) → Mg(OH)₂                            (PA.82)

                                5Mg(OH)₂ + 4CO₂(aq and/or g) → Mg₅(CO₃)₄(OH)₂×4H₂O            (PA.83)

In these equations, “aq and/or g” indicates that the H₂O or CO₂ that reacts with MgO and/or brucite could be present in the aqueous phase (brine) and/or the gaseous phase.  The removal of CO₂ by MgO is not explicitly modeled as a separate reaction in PA.  Rather, the effect of CO₂ consumption is accounted for by modifying the stoichiometry of Reaction (PA.78), Reaction (PA.79), and Reaction (PA.80) to remove the CO₂ from the mass of gas produced by microbial action.

The average stoichiometry of Reaction (PA.78) , Reaction (PA.79), and Reaction (PA.80), is

                                                      (PA.84)

where the average stoichiometric factor y in Reaction (PA.84) represents the number of moles of gas produced and retained in the repository from each mole of carbon consumed.  This factor y depends on the extent of the individual biodegradation pathways in Reaction (PA.84), and the consumption of CO₂ by MgO.  A range of values for y is estimated by considering the maximum mass of gas that can be produced from consumption of cellulosics (M_cel) and Fe-base metals (M_Fe), and is derived as follows (Wang and Brush 1996b).  Estimates of the maximum quantities M_cel and M_Fe (mol) of cellulosics (i.e., C₆H₁₀O₅) and steels that can be potentially consumed in 10,000 years are given by

                                                                  (PA.85)

                                                                (PA.86)

where m_cel and m_Fe are the masses (kg) of cellulosics (see Equation (PA.72) for definition) and steels initially present in the repository.  The mass of cellulosics that can be consumed is determined by the uncertain parameter WMICDFLG (see Table PA-19).  The mass of steels m_Fe = 5.16 ´ 10⁷ kg; this value is calculated as

                                                              (PA.87)

where V_CH and V_RH are the volumes of CH-TRU and RH-TRU waste, r_WCH  and r_WRH are the Fe densities in CH-TRU and RH-TRU waste, and r_CCH and r_CRH  are the Fe densities of the containers of CH-TRU and RH-TRU waste (see Fox 2008, Table 34).  The terms 6000 m_cel/162 and 1000 m_Fe/56 in Equation (PA.85) and Equation (PA.86) equal the inventories in moles of cellulosics and steel, respectively.  The terms 3.2 ´ 10¹¹  R_m m_cel and 4.4 ´ 10¹⁶  R_ci A_d n_d equal the maximum amounts of cellulosics and steel that could be consumed over 10,000 years.  In Equation (PA.85), R_m = max{R_mh, R_mi}, where R_mh and R_mi are defined by uncertain variables (see WGRMICH and WGRMICI in Table PA-19, respectively), and 3.2 ´ 10¹¹ = (3.15569 ´ 10⁷ s/yr) (10⁴ yr).  In Equation (PA.86), A_d n_d is the total surface area of all drums (m²) and the factor 4.4 ´ 10¹⁶ = (3.15569 ´ 10⁷ s/yr) (10⁴ yr) (1.41 ´ 10⁵ mol/ m³), where r_Fe = 1.41 ´ 10⁵ mol/m³ (see Equation (PA.72)) (Telander and Westerman 1993), converts the corrosion rate from m/s to mol/m²/s.

A range of possible values for the average stoichiometric factor y in Reaction (PA.84) can be obtained by considering individual biodegradation pathways involving M_cel and accounting for the removal of CO₂ by the MgO. 

In the absence of methanogenesis and steel sulfidation, y from Equation (PA.84) becomes

                                                                           (PA.88)

                                                                                           (PA.89)

where  is the quantity of NO₃ ^- (mols) initially present in the repository.  Specifically, = 4.31 ´ 10⁷ mol (Fox 2008, Table 39).

PA-4.2.6  Capillary Action in the Waste

Capillary action (wicking) is the ability of a material to carry a fluid by capillary forces above the level it would normally seek in response to gravity.  In the current analysis, this phenomena is accounted for by defining an effective saturation given by

                                                                                                                                         (PA.90)

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 waste-filled areas

          α  =  smoothing parameter = -1000

The effective saturation given by Equation (PA.90) differs from that in the CRA-2004 PA in that S_b,eff  now 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 could be quite long.  In order to speed up the code and increase robustness, the parameter S_min was added.  For PA, S_min = 0.015, which was small enough to not affect the results, while greatly reducing run time.  This is explained fully in 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 PA-15).  The wicking saturation, S_wick, is treated as an uncertain variable (see WASTWICK in Table PA-19).  The effective brine saturation S_b,eff is currently used only to calculate the corrosion of steel (Equation (PA.68)) and the microbial degradation of cellulose (Equation (PA.70)), and does not directly affect the two-phase flow calculations indicated.

PA-4.2.7  Shaft Treatment

The WIPP excavation includes four shafts that connect the repository region to the surface: the air intake shaft, salt handling shaft, waste handling shaft, and exhaust shaft. In PA, these four shafts are modeled as a single shaft.  The rationale for this modeling treatment is set forth in SNL (Sandia National Laboratories 1992, Volume 5, Section 2.3).

The shaft seal model included in the PA grid (Column 43 in Figure PA-15) is the simplified shaft model used in the CRA-2004 PA and the CRA-2004 PABC.  The simplified shaft seal model used in PA is described by Stein and Zelinski (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 short-term and long-term fluid flow through the Salado portion of the shafts.  For the CCA PA, each material in the shaft seal was represented in the BRAGFLO grid.  Analysis of the flow results from the CCA PA and the subsequent CCA PAVT (Sandia National Laboratories 1997 and U.S. Department of Energy 1997) indicated that no significant flows of brine or gas occurred in the shaft during the 10,000-year regulatory period.  As a result of these analyses, a simplified shaft seal model was developed for the CRA-2004 PA.

A conceptual representation of the simplified shaft seal system used in PA is shown in Figure PA-18.  The simplified model divides the shaft into three sections:  an upper section (shaft seal above the Salado), a lower section (within the Salado), and a concrete monolith section within the repository horizon.  A detailed discussion of how the material properties were assigned for the simplified shaft seal model is included in James and Stein (2003).  The permeability value used to represent the upper and lower sections is defined as the harmonic mean of the component materials’ permeability in the detailed shaft seal model (including permeability adjustments made for the DRZ assumed to surround the lower shaft seal section within the Salado).  Porosity is defined as the thickness-weighted mean porosity of the component materials.  Other material properties are described in James and Stein (2003).

The lower section of the shaft experiences a change in material properties at 200 years.  This change simulates the consolidation of seal materials within the Salado and significantly decreases permeability.  This time was chosen as a conservative overestimate of the amount of time expected for this section of the shaft to become consolidated.  The concrete monolith section of the shaft is unchanged from the CCA PA and is represented as being highly permeable for 10,000 years to ensure that fluids can access the north end (operations and experimental areas) in the model.  In three thin regions at the stratigraphic position of the anhydrite MBs, the shaft seal is modeled as MB material (Figure PA-18).  This model feature is included so that fluids flowing in the DRZ and MB fractures can access the interbeds to the north of the repository “around” the shaft seals.  Because these layers are so thin, they have virtually no effect on the effective permeability of the shaft seal itself.

The simplified shaft model was tested in the AP-106 analysis (Stein and Zelinski 2003), which supports the Salado Flow Peer Review (Caporuscio, Gibbons, and Oswald 2003).  The results of the AP-106 analysis demonstrate that vertical brine flow through the simplified shaft model is comparable to brine flows seen through the detailed shaft model used in the CCA PA and subsequent CCA PAVT calculations.

PA-4.2.8  Option D Panel Closures

PA includes panel closures models that represent the Option D panel closure design (see the CRA-2004, Chapter 6.0, Section 6.4.3), which are unchanged from the CRA-2004.  Option D closures (Figure PA-19) are designed to allow minimal fluid flow between panels.  PA explicitly represents selected Option D panel closures in the computational grid using a model approved by the Salado Flow Peer Review Panel (Caporuscio, Gibbons, and Oswald 2003).  The Option D panel closure design has several components: an SMC monolith, which extends into the DRZ in all directions; an empty drift section; and a block and mortar explosion wall (Figure PA-19). Each set of panel closures are represented in the BRAGFLO grid by 4 materials in 13 grid cells (Figure PA-20):

Figure PA-18.    Schematic View of the Simplified Shaft Model (numbers on right indicate dimensions in meters)

Figure PA-19.  Schematic Side View of Option D Panel Closure

·       Six cells of panel closure concrete (area CONC_PCS, material CONC_PCS)

·       One cell above and one cell below the concrete material consisting of MB anhydrite (areas MB 139 and Anhydrite AB, materials S_MB139 and S_ANH_AB, respectively)

·       Two cells of healed DRZ above Anhydrite AB and the panel closure system (PCS) (area DRZ_PCS, material DRZ_PCS)

·       Three cells of empty drift and explosion wall (area DRF_PCS, material DRF_PCS)

Figure PA-20.  Representation of Option D Panel Closures in the BRAGFLO Grid

Properties for the materials making up the panel closure system are listed in Table PA-3.

PA-4.2.8.1  Panel Closure Concrete

The Option D panel closure design requires the use of a salt-saturated concrete, identified as SMC, as specified for the shaft seal system.  The design of the shaft seal system and the properties of SMC are described in the CCA, Appendix SEAL.  The BRAGFLO grid incorporates the material CONC_PCS, which is assigned the material properties of undegraded SMC and is used to represent the concrete portion of the Option D panel closure system (Figure PA-15).  A double-thickness concrete segment represents the northernmost set of panel closures (between the north RoR and the operations area).  This feature represents the two sets of panel closures in series that will be emplaced between the waste-filled repository and the shaft.

PA-4.2.8.2  Panel Closure Abutment with MBs

In the BRAGFLO grid, regions where the Option D panel closures intersect the MBs are represented as blocks of MB material (Figure PA-15).  This representation is warranted for two reasons:

1.   The MB material has a very similar permeability distribution (10 ^-21 to 10 ^-17.1 m²) to the concrete portion of the Option D panel closures (10 ^-20.699  to 10 ^-17 m²), and thus, assigning this material as anhydrite MB in the model has essentially the same effect as calling it concrete, as long as pressures are below the fracture initiation pressure.

2.   In the case of high pressures, it is expected that fracturing may occur in the anhydrite MBs and flow could go “around” the panel closures and out of the two-dimensional plane considered in the model grid.  In this case, the flow would be through the MB material, which incorporates a fracture model, as described above.

PA-4.2.8.3  DRZ Above the Panel Closure

After constructing the concrete portion of the panel closure, the salt surrounding the monolith will be subjected to compressive stresses, which will facilitate the rapid healing of disturbed halite.  The rounded configuration of the monolith creates a situation very favorable for concrete durability:  high compressive stresses and low stress differences.  In turn, the compressive stresses developed within the salt will quickly heal any damage caused by construction excavation, thereby eliminating the DRZ along this portion of the panel closure.  The permeability of the salt immediately above and below the rigid concrete monolith component of Option D will approach the intrinsic permeability of the undisturbed Salado halite.

To represent the DRZ above the monoliths, PA uses the material DRZ_PCS in the BRAGFLO grid (Figure PA-15).  The values assigned to DRZ_PCS are the same as those used for the DRZ above the excavated areas (material DRZ_1, see Table PA-3), except for the properties PRMX_LOG, PRMY_LOG, and PRMZ_LOG, the logarithms of permeability in the x, y, and z directions, respectively.  These permeability values are assigned the same distributions used for the material CONC_PCS.  In this instance, the values are based on the nature of the model setup, not directly on experimental data (although the general range of the distribution agrees with experimental observations of healed salt).  The use of these permeabilities ensures that any fluid flow is equally probable through or around the Option D panel closures, and represents the range of uncertainty that exists in the performance of the panel closure system.

PA-4.2.8.4  Empty Drift and Explosion Wall Materials

The DRF_PCS is the material representing the empty drift and explosion wall.  For simplicity, this material is assumed to have hydrologic properties equivalent to the material representing the waste panel and is used for the three sets of panel closures represented in the grid (Figure PA-15).  The creep closure model is applied to this material to be consistent with the neighboring materials.  The assignment of a high permeability to this region for the PA calculations, which contains the explosion wall, is justified because the explosion wall is not designed to withstand the stresses imposed by creep closure beyond the operational period and will be highly permeable following rapid room closure.

PA-4.2.9  Borehole Model

The major disruptive event in PA is the penetration of the repository by a drilling intrusion.  In the undisturbed scenario (see Section PA-6.7.1), these blocks have the material properties of the neighboring stratigraphic or excavated modeling unit, and there is no designation in the borehole grid except for the reduced lateral dimensions of this particular column of grid blocks.

In the scenarios simulating drilling disturbance, these cells start out with the same material properties as in the undisturbed scenario, but at the time of intrusion, the borehole grid blocks are reassigned to borehole material properties.  The drilling intrusion is modeled by modifying the permeability of the grid blocks in Column 26 of Figure PA-15 (values listed in Table PA-7).  Furthermore, the drilling intrusion is assumed to produce a borehole with a diameter of 12.25 in. (0.31 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 PA-3).  When a borehole that penetrates pressurized brine in the Castile is simulated (i.e., an E1 intrusion), the permeability modifications indicated in Table PA-7 extend from the ground surface (i.e., Grid Cell 2155 in Figure PA-17) to the base of the pressurized brine (i.e., Grid Cell 2225 in Figure PA-17).  When a borehole that does not penetrate pressurized brine in the Castile is under consideration (i.e., an E2 intrusion), the permeability modifications indicated in Table PA-7 stop at the bottom of the lower DRZ (i.e., Grid Cell 1111 in Figure PA-17).

PA-4.2.10  Castile Brine Reservoir

High-pressure Castile brine was encountered in several WIPP-area boreholes, including the WIPP-12 borehole within the controlled area and the ERDA-6 borehole northeast of the site.  Consequently, the conceptual model for the Castile includes the possibility that brine reservoirs underlie the repository.  The E1 and E1E2 scenarios include borehole penetration of both the repository and a brine reservoir in the Castile.

Unless a borehole penetrates both the repository and a brine reservoir in the Castile, the Castile is conceptually unimportant to PA because of its expected low permeability.  Two regions are specified in the disposal system geometry of the Castile horizon:  the Castile (Rows 1 and 2 in

Table PA-7.  Permeabilities for Drilling Intrusions Through the Repository

 

Figure PA-15) and a reservoir (Row 1, Columns 23 to 45 in Figure PA-15).  The Castile region has an extremely low permeability, which prevents it from participating in fluid flow processes.

It is unknown whether a brine reservoir exists below the repository.  As a result, the conceptual model for the brine reservoirs is somewhat different from those for known major properties of the natural barrier system, such as stratigraphy.  The principal difference is that a reasonable treatment of the uncertainty of the existence of a brine reservoir requires assumptions about the spatial distribution of such reservoir and the probability of intersection (see Attachment MASS-2009, Section MASS.18.1).  A range of probabilities for a borehole hitting a brine reservoir is used (see Section PA-3.6).

In addition to the stochastic uncertainty in the location and hence in the probability of intersecting reservoirs, there is also uncertainty in the properties of reservoirs.  The manner in which brine reservoirs would behave if penetrated is captured by parameter ranges and is incorporated in the BRAGFLO calculations of disposal system performance.  The conceptual model for the behavior of such a brine reservoir is discussed below.  The properties specified for brine reservoirs are pressure, permeability, compressibility, and porosity, and are sampled from parameter ranges (see Table PA-19).

Where they exist, Castile brine reservoirs in the northern Delaware Basin are believed to be fractured systems, with high-angle fractures spaced widely enough that a borehole can penetrate through a volume of rock containing a brine reservoir without intersecting any fractures, and therefore not producing brine.  Castile brine reservoirs occur in the upper portion of the Castile (Popielak et al. 1983).  Appreciable volumes of brine have been produced from several reservoirs in the Delaware Basin, but there is little direct information on the areal extent of the reservoirs or the existence of the interconnection between them.  Data from WIPP-12 and ERDA-6 indicate that fractures have a variety of apertures and permeabilities, and they deplete at different rates.  Brine occurrences in the Castile behave as reservoirs; that is, they are bounded systems.

PA-4.2.11  Numerical Solution

Determining gas and brine flow in the vicinity of the repository requires solving the two nonlinear PDEs in Equation (PA.24) through Equation (PA.30) on the computational domain in Figure PA-15, 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) through 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 PA-4.2.2.  As indicated there, the calculation starts at time t = −5 years, with a possible resetting of values at t = 0 years, which corresponds to final waste emplacement and sealing of the repository.  The boundary conditions are such that no brine or gas moves across the exterior grid boundary (Table PA-8).  This Neumann-type boundary condition is maintained for all time.  Further, BRAGFLO allows the user to maintain a specified pressure and/or saturation at any grid

Table PA-8.  Boundary Value Conditions for P_g and P_b

 

block.  This is not a boundary condition and is not required to close the problem.  This feature is used to specify Dirichlet-type conditions at the surface grid blocks (Columns 1-68, Row 33, Figure PA-15) and at the far-field locations in the Culebra and Magenta (Columns 1 and 68, Row 26, and Columns 1 and 68, Row 28, Figure PA-15).  These auxiliary conditions are summarized in Table PA-9.

A fully implicit finite-difference procedure is used to solve Equation (PA.24) through Equation (PA.30).  The associated discretization of the gas mass balance equation is given by