TECHNICAL SUPPORT DOCUMENT FOR SECTION 194.23
                    TECHNICAL REVIEW OF SALT AGGREGATE, DISTURBED
                  ROCK ZONE, AND OPEN DRIFT HEALING CHARACTERISTICS

                            Contract Number: EP-D-10-042
                              Work Assignment No. 5-12
      Prepared for:U.S. Environmental Protection AgencyOffice of Radiation and Indoor AirCenter for Waste Management and RegulationsWashington, DC 20460Kathleen EconomyWork Assignment ManagerPrepared by:S. Cohen & Associates1608 Spring Hill Road Suite 400Vienna, Virginia 22182

                                      June 2017

PREFACE
The U.S. Department of Energy (the DOE) is required to submit a Compliance Recertification Application (CRA) to the U.S. Environmental Protection Agency (EPA) for the Waste Isolation Pilot Plant (WIPP) facility every five years including an updated assessment of future WIPP performance. During the EPA's review of the DOE's CRA-2014 performance assessment (PA), events associated with the February 2014 repository fire and radionuclide release have resulted in closed portions of the underground facility. This closure has created a situation where certain parts of the underground facility could not be accessed for ground control. Panel 9 may be abandoned along with plans to install panel closures in panels 3, 4, 5 and 6.
Because the CRA performance assessments are predictions of post-closure repository performance and the EPA knows there will be modifications to the current repository design, modifying the CRA-2014 PA at this time to incorporate alternative parameter values would not add more reality to predictions of repository post-closure performance. Consequently, the EPA adopted the CRA-2014 PA as originally submitted by the DOE as the baseline, rather than have the DOE conduct a revised PA baseline calculation (PABC). In lieu of requesting a PABC-2014, the EPA requested that the DOE the DOE conduct a set of sensitivity studies to address some of the significant technical concerns arising from the EPA's CRA-2014 review. The inputs to these sensitivity studies broadly address many of the EPA's technical concerns that could potentially impact long-term repository performance. The Agency has reviewed the results of these studies and determined that there exists an adequate level of confidence -- that is, a reasonable expectation -- that the repository will continue to comply with EPA regulations.
Additionally, the EPA recommends further work that can be conducted to evaluate many of the technical concerns identified in the EPA's review of the CRA-2014 PA, as well as incorporate future repository design changes. The EPA will work with the DOE to determine the best path forward for resolution of EPA's concerns, which could include additional data reviews, independent technical reviews, and possibly additional sensitivity analyses to reach a consensus for the next CRA. It is anticipated that the results of these efforts will be incorporated into the CRA-2019 PA or otherwise be made available during the EPA's review of the CRA-2019 PA.

EXECUTIVE SUMMARY

In 2013 the EPA approved a request by the DOE to replace the previously approved waste panel closure design with a new design consisting of a run-of-mine (ROM) salt aggregate plug between two steel ventilation control bulkheads. The salt aggregate is produced during the process of excavating the underground rooms and can be easily emplaced in the waste panel access drifts. The previous design consisted of a relatively porous concrete monolith and explosion wall in each access drift that allowed the slow seepage of brine and flow of gas throughout the WIPP underground facility. Although explosion walls have been installed in three waste panels, no concrete monoliths have been installed. The creep characteristics of salt allow it to flow under pressure and seal an access drift or an excavated room within a few hundred years to very low porosity and permeability. The new seals will almost completely isolate the WIPP waste panels by essentially eliminating brine and gas flow between them and between the panels and the WIPP operations and experimental area drifts. Salt creep will also close the operations and experimental area drifts to similarly low porosity and permeability even though they are not planned to be filled with ROM salt.

The waste panel closures are currently modeled in WIPP performance assessment as not completely healing and the operations and experimental areas are currently modeled as remaining open and not creep closing for the entire 10,000-year regulatory period. The current models therefore predict considerably more transfer of brine and gas between waste panels than will actually occur. The principal impact of salt healing is expected to be an increase in gas pressure that drives the important direct brine and spallings release pathways.

The relatively high brine and gas mobility in the current modeling approach is appropriate for the relatively porous panel closures of the previous concrete monolith design but may not be appropriate for the new design. In view of the essential elimination of this mobility under DOE's new panel closure design, the Agency requested the DOE to perform three sensitivity studies to evaluate the effects of this design change on repository performance. This report describes the technical basis for the parameter value changes made by the Agency in these sensitivity studies. The results of these studies are documented in a separate report (EPA 2017).

This report describes the results of field and laboratory studies of the creep closure characteristics of open rooms, rooms filled with ROM salt aggregate, and adjacent disturbed rock zones around mined entries in bedded salt. Many of these field and laboratory studies were conducted since the initial development of the WIPP performance assessment models in the 1990s. They include studies specific to the WIPP facility as well as investigations by European scientists in countries where disposal of radioactive waste in bedded salt is also being planned. The results have better quantified the porosity and permeability reductions due to salt creep and have enhanced an understanding of the relatively rapid rate at which these reductions can occur. Current results indicate that a drift filled with ROM salt may consolidate and approach the very low porosity and permeability of intact halite within 100 years; an initially open drift is expected to fill with roof fall rubble and similarly consolidate within 200 years; and the disturbed rock zones around those drifts could heal and approach the properties of intact halite within 500 years. These time frames indicate that essentially complete isolation of the WIPP waste panels could occur within a short time compared with the 10,000-year period of regulatory concern.
                               TABLE OF CONTENTS

PREFACE	ii
EXECUTIVE SUMMARY	iii
1.0 INTRODUCTION	1
2.0 POROSITY AND PERMEABILITY OF CONSOLIDATING ROM SALT	3
2.1 Overview of Consolidation Mechanisms in ROM Salt	3
2.2 First and Second Phase Consolidation of ROM Salt	6
2.2.1 Consolidation Mechanisms	6
2.2.2 Consolidation Rates	7
2.3 Third and Fourth Phase Consolidation of ROM Salt	10
2.3.1 Backpressure Buildup	10
2.3.2 Fluid-Assisted Deformation	11
2.3.3 Consolidation Rates	11
2.4 Empirical Porosity  -  Permeability Relationships for ROM Salt	13
2.5 Recommended Porosity and Permeability Modeling Values for ROM Salt	14
3.0 POROSITY AND PERMEABILITY OF A HEALING DRZ	19
3.1 Overview of Consolidation Mechanisms in a DRZ	19
3.2 Healing of the DRZ Adjacent to a WIPP ROM Salt PCS	20
3.3 PCS DRZ Porosity and Permeability	20
3.4 Sensitivity Study Porosity and Permeability Modeling Values for the PCS DRZ	22
4.0 TWO PHASE FLOW PROPERTIES IN ROM SALT	24
4.1 Introduction to Two-Phase Flow in Salt Aggregates	24
4.2 Overview of Two-Phase Flow in ROM Salt	25
4.3 Two-Phase Flow in WIPP PA	27
4.4 Residual Saturation and Capillary Pressure Experimental Data for ROM Salt	28
4.5 Recommended Residual Saturation Modeling Values for ROM Salt	31
4.5.1 T0 and T1 Time Periods (-5 to 50 years)	31
4.5.2 T2 Time Period (50 to 100 years)	32
4.5.3 T3 Time Period (100 to 10,000 years)	33
4.6 Equations for Two-Phase Flow in BRAGFLO	33
4.7 Threshold Pressure and Pore Size Distribution Modeling Values for ROM Salt	34
4.7.1 Overview of Threshold Pressure in Salt	34
4.7.2 Overview of Pore Size Distribution in Salt	35
4.7.3 Threshold Pressure and Pore Size Distribution Modeling Values	35
5.0 TWO PHASE FLOW PROPERTIES IN THE PCS DRZ	36
5.1 Introduction to Two-Phase Flow in a DRZ	36
5.2 Residual Saturation Modeling Values	36
5.3 Threshold Pressure and Pore Size Distribution Modeling Values	37
6.0 SUMMARY TABLES OF SEN3 SENSITIVITY STUDY PARAMETER VALUES	37
7.0 SPECIAL CONSIDERATION OF THE PROPERTIES OF THE FIRST PANEL CLOSURES SOUTH OF THE SHAFTS	41
8.0 SPECIAL CONSIDERATION OF THE PROPERTIES OF THE PANEL CLOSURES AND DRZ IN THE BRAGFLO_DBR MODEL	41
9.0 CREEP CLOSURE OF EMPTY ROOMS	41
9.1 Flow Properties for the Operations and Experimental Areas	45
9.2 Flow Properties for the DRZ Adjoining the Operations and Experimental Areas	47
9.3 Summary Tables	49
REFERENCES	52

                                LIST OF FIGURES

Figure 1. Backfill resistance vs. void ratio for oedometer tests on crushed Asse salt.
Figure 2. Multistep oedometer test results for dry and wetted granular salt samples with dashed line extrapolations to asymptotic porosity values.
Figure 3. ROM salt consolidation in WIPP PCS intake and exhaust drifts.
Figure 4. Estimated duration for consolidation from 6% porosity to 2% porosity of Asse crushed salt under triaxial compaction with linear extrapolation to 10 MPa applied stress.
Figure 5. Porosity  -  permeability datasets for crushed salt and mixtures showing the EPA empirical relationship for WIPP ROM salt as a dashed line.
Figure 6. Porosity  -  permeability datasets for crushed salt showing the EPA empirical relationship for WIPP ROM salt as a dashed line.
Figure 7. General relative imbibition (IM) and draining (DR) permeability curves vs brine saturation.
Figure 8. Changes in pore structure of salt aggregate during compaction.
Figure 9. Brine saturation vs. capillary pressure.
Figure 10. Brine saturation vs. suction (capillary pressure) for salt aggregates at 5% and 10% porosity.
Figure 11. Brine saturation versus capillary pressure on Asse salt aggregate compacted to 7.33% porosity.
Figure 12. Calculated deformation of an open room after 195 years.
Figure 13. Calculated volume reduction of an open room with respect to time due to creep closure.
                                LIST OF TABLES

Table 1. Empirical Porosity  -  Permeability Relationship for a Brine-Wetted ROM WIPP Salt
Table 2. Porosity and Permeability Parameter Values for Modeling the ROM Salt PCS
Table 3. Porosity of Microfracture-Damaged WIPP Salt Samples
Table 4. Permeability of Microfracture-Damaged WIPP Salt Samples
Table 5. Porosity and Permeability Parameter Values for Modeling the DRZ Adjacent to a WIPP     ROM Salt PCS
Table 6. Parameter Values for ROM Salt to be used in the PCS Sensitivity Study
Table 7. Parameter Values for the PCS DRZ to be used in the PCS Sensitivity Study
Table 8. Parameter Values for Operations and Experimental Area Rooms to be used in SEN1 and SEN2 Sensitivity Studies
Table 9. Parameter Values for DRZs Adjoining Operations and Experimental Area Rooms
to be used in SEN1 and SEN2 Sensitivity Studies

                               LIST OF ACRONYMS

            CCA		Compliance Certification Application
            CCDF		Complementary Cumulative Distribution Function
            CFR		Code of Federal Regulations
            CRA		Compliance Recertification Application
		DBR		Direct Brine Release
		DOE		U.S. Department of Energy
            DRZ		Disturbed Rock Zone
            EPA		Environmental Protection Agency
		FADT		Fluid Assisted Diffusion Transfer
            FR		Federal Register
            PA 		Performance Assessment
		PABC		Performance Assessment Baseline Calculation
            PCS		Panel Closure System
		RCRA		Resource Conservation and Recovery Act
		ROM		Run-of-Mine
            SEN		Sensitivity
		SNL		Sandia National Laboratories
		SPDV		Site and Preliminary Design Validation
            TRU		Transuranic
		TSD		Technical Support Document
		VOC		Volatile Organic Compound
		WIPP		Waste Isolation Pilot Plant

                               Glossary of Terms

40 CFR Part 191
Environmental Radiation Protection Standards for the Management and Disposal of Spent Nuclear Fuel, High Level and Transuranic Radioactive Wastes; Final Rule (EPA, 1993).
40 CFR Part 194
Criteria for the Certification and Re Certification of the Waste Isolation Pilot Plant's Compliance with the 40 CFR Part 191 Disposal Regulations: Certification Decision; Final Rule (EPA, 1998a).

Run-of-mine (ROM) salt
Salt produced from mining operations in the WIPP facility underground without undergoing any additional treatment.

1.0 INTRODUCTION

The U.S. Department of Energy (DOE) developed the Waste Isolation Pilot Plant (WIPP) repository for the permanent disposal of transuranic (TRU) waste. The repository is located in deeply buried deposits of bedded salt in the Salado Formation in southeastern New Mexico. The U.S. Environmental Protection Agency (EPA or the Agency) regulates containment of TRU waste at WIPP in accordance with the radioactive waste disposal standards at Code of Federal Regulations (CFR) Title 40, Parts 191 and 194. EPA first certified the WIPP as complying with these standards and approved it for TRU waste disposal in 1998. The regulations require recertification of WIPP at five year intervals following the first waste shipment in 1999, with the most recent recertification application occurring in 2014. EPA's decision to recertify WIPP is based in part on the results of an assessment of the projected ability of the facility to meet the Agency's waste isolation standards over the 10,000-year post-closure regulatory time frame. The ability to meet these standards is determined by the results of numerical modeling conducted for the DOE by Sandia National Laboratories (SNL). This modeling simulates the repository's future performance in a process called Performance Assessment (PA). The most recent assessment was included in DOE's 2014 Compliance Recertification Application (CRA) and is called the CRA-2014 PA.

Prior to 2013 the EPA required the DOE to install a concrete monolith and explosion wall in the waste panel drifts -- denoted as the Option D Panel Closure System (PCS) design. Emplacing a panel closure in the waste panel drifts is a requirement of the Resource Conservation and Recovery Act (RCRA) for closure of a waste panel and is required by New Mexico Environment Department in permitting the WIPP underground facility during the operational period. The purpose of the PCS is to protect workers from gas build-up and potential explosions of Volatile Organic Compounds (VOCs). In 1998 EPA placed a condition on DOE's WIPP certification which stipulated that all waste panels closures were to use the Option D design. This requirement was a regulatory component written as Condition 1 in Appendix A of 40 CFR Part 194 (EPA 1998). Consequently, the Option D PCS design was represented in DOE's subsequent CRA-2004 and CRA-2009 PA calculations submitted to the Agency.

In September 2011 the Department requested EPA to eliminate the requirement for the Option D design PCS because such a rigorous structure was not needed for worker safety and protection, and secondarily, the high cost to install (DOE 2011). The Department indicated the same protection can be achieved by using ROM salt in the PCS design rather than the concrete monolith called for in Option D. The ROM salt PCS design consists of loose salt aggregates emplaced in the waste panel drifts.  The aggregate is produced during the process of excavating the underground drifts and can be easily emplaced in the waste panel access drifts.

For EPA to approve this design change a modification to 40 CFR Part 194 would be needed.  Prior to doing so, the Agency needed to determine the impact of using the ROM salt PCS on repository performance and compare it to that using the Option D design.  Consequently, the Agency asked the Department to perform a comparison PA. The intention was to compare long-term repository performance using a ROM salt PCS design, rather than that of Option D, and determine whether compliance with the regulatory components of 40 CFR Part 191 would still be met. The EPA requested DOE conduct a comparison PA that used inputs submitted by DOE from the PABC-2009 that had been previously reviewed and approved by EPA. For the comparison PA all inputs would be the same as that of PABC-2009 with the exception of parameters representing the PCS. The PCS in this PA represented properties of ROM salt rather than those of Option D. Because there were many uncertainties related to how the ROM salt would be emplaced in the drifts, DOE adopted a broad range of parameter values to represent this material in this PA. This comparison PA was denoted as the PCS-2012 PA. The DOE argued that using this large range was appropriate because how the ROM salt would be emplaced in the drifts was still undergoing considerations ((e.g., moist or dry, packed or loose) and the final design had yet to be approved. The Agency agreed to this wide range of values for ROM salt over the 10,000-year modeled time frame as proof-of-principle test case to support whether eliminating the Option D design would still comply with repository performance specified in 40 CFR Part 191, with the understanding, that once the ROM salt PCS design was final, more representative parameter values would be expected in any upcoming PAs.

The outcome of the PCS-2012 PA demonstrated that using a panel closure design other than that of Option D would not adversely affect repository performance.  In 2013 the EPA approved removing Condition 1 as a component 40 CFR Part 194 and eliminated any specific design requirement for a PCS in the waste panels (EPA 2013).  EPA's Technical Support Document (TSD) supporting that decision evaluated the parameter values DOE had adopted to represent the ROM salt over the 10,000-year time frame.  In that document the Agency stated that it may reevaluate the parameter values for ROM salt in the upcoming CRA-2014 PA to be more representative of the long-term properties of ROM salt PCS, as well as couple the properties of the adjoining disturbed rock zone (DRZ) to those of the ROM salt PCS (EPA 2013, Appendix A Quality Assurance Review, p. 34).

      "As described above, the Agency accepted retention in the PCS-2012 PA of several parameter values from the PABC-2009 PA to simplify comparison of results by focusing only on parameter value changes that were potentially significant and resulted directly from the proposed changes in PCS design. However, when agreeing with the parameter values for the PCS-2012 PA in June 2012, the Agency noted that although the multi-phase flow and other parameters in BRAGFLO could remain as they have been in past PAs, they may be re-evaluated for appropriateness in the 2014 recertification PA."

The DOE has not updated the parameter values for ROM salt in its CRA-2014 from those used in the PCS-2012 PA. The Agency believes some of those values are not representative of the long-term properties of ROM salt, the adjacent DRZ, or of the creep closure characteristics of the open operational and experimental area drifts. Consequently, the Agency conducted an independent review of laboratory and field investigations of salt consolidation and healing to provide an updated basis for evaluating long-term repository performance.

Since the PCS-2012 PA the Agency has become aware of a significant amount of information that indicates the ROM salt and open drifts will creep close and heal relatively quickly to properties reflective of intact halite. Parameter values for ROM salt, such as permeability, porosity, and two-phase flow, will change soon after being emplaced in the panel closure drifts as the salt consolidates and is compressed due to the stresses imposed on it. Using parameter values for the healed PCS and open drifts that the EPA believes are more representative of the majority of the regulatory time-frame essentially eliminates brine and gas flow between waste panels and increases their isolation from one another. In contrast, the PCS parameter values adopted in the CRA-2014 maintain a connection between waste panels via the PCS and adjacent DRZ and are not representative of ROM salt during both the short- and long-time regulatory period. The Agency does not question that ROM salt is a suitable material to be used in the PCS, but rather questions the range of values the DOE has adopted as being representative of ROM salt over the majority of the regulatory time frame.

This report describes the Agency's comprehensive review of laboratory and numerical studies of the behavior of salt aggregate as it consolidates and is compressed within the repository setting, the behavior of open drifts as they creep close, and the application of those studies to WIPP repository conditions. This report also describes the Agency's review of studies evaluating the long-term behavior of the adjacent DRZs. The results of this review were used to identify and explain the basis for the parameter values selected by the Agency for three sensitivity studies, denoted as the SEN1, SEN2, and SEN3 studies in this report. The results of those studies are described in EPA (2017).

2.0 POROSITY AND PERMEABILITY OF CONSOLIDATING ROM SALT

2.1 Overview of Consolidation Mechanisms in ROM Salt

ROM salt has been proposed as a useful material for backfilling and sealing drifts excavated in natural halite deposits for disposal of nuclear waste (Cinar et al. 2006; Castagna 2007). At the WIPP site, ROM salt is planned to be used for sealing access drifts to waste panels as part of the WIPP Panel Closure System (PCS). The WIPP ROM salt panel closures are expected to consolidate under their own weight as well as under applied stresses from possible roof falls and creep of the surrounding intact halite. The consolidation of salt aggregates is influenced by the primary factors of moisture content, temperature, applied stress, initial porosity, halite purity  (mixture of halite with anhydrite, clays, and other minerals), and grain size. Other, less important factors include grain size distribution, load cycling, and brine chemistry (see, for example, Davidson and Dusseault, 1996). Different factors influence consolidation at different times. Under WIPP conditions, moisture content and compressive stress have strong influences at all times and are the primary factors considered in this review. The sensitivity of WIPP performance to healing of the ROM salt and adjacent DRZ was studied in the SEN3 analysis.

Compressive stress on the ROM salt will occur due to the weight of the salt itself and from applied stresses resulting from roof falls and creep of the surrounding halite. The WIPP ROM salt panel closures are therefore expected to consolidate under their own weight as well as under externally applied stresses. Other factors such as initial porosity, grain size, and grain size distribution primarily influence early time consolidation and are less important because, as discussed below, such consolidation is expected to occur quickly relative to the 10,000-year period of regulatory concern. Ambient WIPP temperatures are not high enough (less than 100°C) to have significant impacts. Load cycling effects due to gas generation and release are not expected to significantly affect the PCS as demonstrated by the U.S. Department of Energy (DOE) in response to an Agency concern associated with the 2012 PCS PA (EPA 2013, Section <IP_ADDRESS>). Correlations with impurity content (additional minerals within a predominantly halite matrix) and brine chemistry will be inherently incorporated where possible through the use of WIPP-specific data in selecting flow parameter values and ranges.

Laboratory tests on crushed salt that simulate the ROM salt aggregates have shown that consolidation of those aggregates occurs in two phases, identified (for example) by Cinar et al. (2006, p. 214) as the `high rate' phase for porosities greater than 10% and the `low rate' phase for porosities less than 10%. For purposes of this report, these two phases have been separated by a transition phase representing the increase in backpressure buildup and shift in consolidation mechanisms that occur as the porosity drops from 10% to about 5%. Very little backpressure buildup occurs during the `high rate' phase. The rate of backpressure buildup increases during the transition phase and becomes very high during the `low rate' phase as the porosity drops below 5% and resistance to further consolidation increases rapidly.

Examples of backpressure buildup with decreasing crushed salt void ratio are shown in Figure 1. The figure shows backpressure vs. void ratio. The void ratio (e) is the volume of voids divided by the volume of solids whereas the porosity (Φ) is the volume of voids divided by the total volume, thus Φ = e/1+e. The porosity and void ratio are essentially equal below void ratios of 0.05. For purposes of this review, reference is made to the green curve on the figure because it is supported by the largest data set and represents moisture (1% wt brine) and temperature (33°C) conditions similar to those at WIPP. This figure also illustrates the difference in behavior between oven-dried samples and so-called "wet" samples that contain small amounts of moisture. Additional discussion of the influences of available moisture on consolidation of salt aggregates is presented later.

The green curve on Figure 1 begins at a void ratio of about 30% (porosity of 23%) and shows that the backpressure of the salt aggregate remains low (less than 2 MPa) until the void ratio drops to about 0.10 (porosity of 9.1%). At void ratios below 0.10 the backpressure begins to increase and at void ratios below 0.05 (porosity of 4.8%) the rate of backpressure buildup increases significantly. This indicates that at void ratios (or porosities) below about 5% the salt aggregate is returning to a very low porosity, low compressibility state approaching that of intact halite.

For purposes of this review, ROM salt consolidation is considered to occur in three phases with a fourth and final stage representing fully consolidated salt in isotropic equilibrium with the lithostatic stress of the surrounding intact halite. The ROM salt consolidates rapidly during the first phase and exerts little backpressure on the applied load. This phase is consistent with Cinar et al's. (2006, p. 214) `high rate' consolidation phase and generally coincides with porosities greater than 10% and backpressures less than 2 MPa. As discussed later in this report, consolidation of a WIPP ROM salt PCS during this first phase is initially due to compaction from settlement of the salt under its own weight followed by compression exerted by creep closure of the surrounding drift.

Figure 1. Backfill resistance vs. void ratio for oedometer tests on crushed Asse salt (from Hansen et al. 2014, Figure 3.3c).

Second phase consolidation represents a transition between the high rate, low backpressure consolidation of the first phase and the reduced rate, high backpressure consolidation of the third phase. Second phase consolidation is characterized by increasing backpressures and decreasing porosities as the salt is further compressed by drift creep closure. This phase generally coincides with porosities between about 5 and 10% and backpressures between about 3 and 5 MPa. These ranges are approximate because of the strong correlation of test results with test conditions but are considered reasonably applicable to conditions at WIPP.

Third phase consolidation is characterized by rapidly increasing backpressures above 5 MPa as the porosity drops below about 5%. As further discussed below, the rate of third phase consolidation depends strongly on moisture content. At a given applied load, consolidation progresses relatively slowly in dry salt but increases rapidly when even a small amount of moisture (as low as about 1% wt) is present. As further described below, the presence of moisture enables additional processes that enhance the consolidation rate.

The fourth phase begins when the backpressure exerted by the ROM salt comes into equilibrium with the surrounding lithostatic stress and is therefore site-specific. During this phase the ROM salt is considered to have `healed' with properties essentially the same as the undisturbed Salado halite. At WIPP this fourth phase is consistent with a backpressure of about 15 MPa.

2.2 First and Second Phase Consolidation of ROM Salt

2.2.1 Consolidation Mechanisms

The first phase of consolidation occurs as the salt aggregates are compacted from a loose, uncompacted state at a porosity of about 33 to 35% down to a porosity on the order of 10%. As will be seen below, under a constant load in laboratory tests, this first phase consolidation occurs relatively rapidly.

The ROM salt PCS is planned to be emplaced without compaction and at an initial porosity of 33 to 35% (U.S. Department of Energy and Nuclear Waste Partnership 2012, Item 1, Appendix B, Attachment G-1, Section 2.2.2). As previously noted, consolidation during the first phase is the result of the application of relatively low, unconfined stresses due to self-settlement under gravity, possible roof falls, and creep of the surrounding Salado halite. This initial consolidation is characterized by rearrangement of individual aggregate grains due to sliding and rotation, and to cataclastic deformation due to brittle compression or shear failure of grains from local stress concentrations or frictional slip.

Evaporation caused by the WIPP ventilation system may reduce the initial moisture content of the ROM salt to about 0.25% wt (Hurtado et al. 1997).  However, following repository closure and shutdown of the ventilation system, brine inflow and an increase in humidity will lead to higher moisture content reflective of in-situ conditions of 0.5 to 1% wt (Hansen et al. 1995). These relatively higher moisture contents will be obtained in a relatively short time and are sufficient to support moisture-sensitive consolidation characteristics. In the presence of even a small amount of moisture, the dissolution  -  precipitation mechanism significantly increases the rate of consolidation as compared with the rates that occur in artificially dried salt (Olivella and Gens 2002).

As discussed below, laboratory results and WIPP drift closure rate and moisture content data indicate that under WIPP stress conditions the consolidation of a ROM salt PCS to near in situ conditions may require only a few decades. For the WIPP ROM salt, moisture content and applied stress will therefore have strong influences at all times.

The stress on the WIPP ROM salt is initially expected to be essentially uniaxial due to self-settlement, compaction from roof falls, and vertical creep of the rock-bolted roof beam. Lateral stress will build as the ROM salt is vertically compacted and expands laterally into the room side walls, while the sidewalls simultaneously expand laterally into the ROM salt. The simultaneous lateral movements will increase backstress on the ROM salt and move consolidation into the second phase where the stress on the ROM salt transitions from uniaxial to triaxial. During the second phase the importance of largely mechanical, cataclastic deformation also decreases and the role of moisture dependent mechanisms increases. These fluid-assisted mechanisms become predominant during third phase consolidation and are described in Section 2.3. The effective porosity and permeability are expected to remain sufficiently high and the load application rate sufficiently low throughout the first phase consolidation process that the influence of fluid pressure on effective stress is negligible.

Both laboratory test results and modeling simulations of ROM salt consolidation are strongly influenced by such components as the edges of the testing apparatus or grid limitations that would influence the long-term representative values. Because of these influences, the relevance of the results to the consolidation of WIPP ROM salt panel closures depends on the extent to which these conditions are consistent with field conditions.

2.2.2 Consolidation Rates

Information on first and second phase consolidation rates is available from laboratory tests, drift creep closure measurements, and numerical modeling results. Examples of each of these information sources are discussed below.

Oedometer Laboratory Tests

The oedometer test is a constant load, laboratory creep test consisting of a loaded piston compressing a salt sample encased in a thick-walled cylinder (Hansen et al. 2014, Figure 3.1). The average load on the salt is equal to the constant applied load on the piston minus friction from the lateral load on the cylinder wall. The results of such uniaxial tests can provide a reasonable approximation of early-time ROM salt consolidation under constant applied loads when lateral stresses are low. However, oedometer tests have limitations, primarily related to the scale and time restrictions of the tests (limited to only a few years rather than tens-of-years) that result in the sample achieving less than steady-state stress fields. The sample measurements often result in backstresses at the center being less than those at the edges. With time the samples can approach in situ conditions, but given time constraints, researchers have to extrapolate to predict end-state stress conditions. Concomitantly, the variability in porosity and permeability measured from the edges to the center are reflective of the variation in the stress field propagated from the sample exterior to the interior. This difference results in higher average porosity and permeability values across the sample that would not be seen in the field and not directly applicable to the time and space scales of a WIPP panel access drift.

One set of oedometer test results is shown in Figure 2 (Hansen et al. 2014, Figure 3.5; also see Czaikowski et al. 2012). Manually extrapolating the oedometer results in the figure to asymptotic porosity values at the given loads shows that, for a sample wetted to about 1% wt under stepped loadings of 1, 2, and 4 MPa, the porosity of an initially granular salt could be reduced from 30% to about 6% in about 1,000 days or approximately 3 years. This porosity reduction encompasses the entire first phase consolidation period as well as part of the second phase transition period and likely would be even shorter if the 4 MPa load had been applied from the beginning. This same porosity reduction is expected to take longer under WIPP conditions than in the oedometer test because of a slower buildup in the applied load. As discussed below, a WIPP-specific engineering calculation and WIPP-specific FLAC3D modeling both estimate a duration of approximately 30 years to achieve a similar porosity reduction in the ROM salt.

Figure 2 also shows that consolidation rates for a dried sample and for a sample with very low natural water content were much slower even when greater loads were applied. Although the extrapolated test results in Figure 2 are approximate, it is apparent that porosity reductions in granular salt can occur quickly under relatively low loads and moisture contents.

Figure 2. Multistep oedometer test results for dry and wetted granular salt samples with dashed line extrapolations to asymptotic porosity values (modified from Hansen et al. 2014, Figure 3.5).

WIPP-Specific JAS3D Modeling

WIPP-specific conditions were incorporated into JAS3D modeling of ROM salt PCS consolidation by Herrick (2012). The JAS3D modeling predicted that under WIPP in-situ conditions it would take about 120 years for the porosity of the ROM salt to drop from 30% to 6% and at that time the backpressure of the ROM salt would be about 3 MPa (Herrick 2012, Figures 4 and 11). This porosity reduction again encompasses the entire first phase consolidation period as well as part of the second phase transition period. The Agency considers the correlation to be very good between Herrick's prediction of a backpressure of 3 MPa as consistent with a ROM salt porosity of 6% and the 4 MPa (minus sidewall friction) backpressure identified in the aforementioned oedometer test required to produce essentially the same porosity.

Although Herrick's (2012) porosity  -  backpressure relationship is consistent with the oedometer test results, his predicted consolidation times are much longer than the oedometer test results would suggest. This difference may in part result from a lower modeled loading rate than was used in the oedometer test; however, the Agency's review of the modeling assumptions described by Herrick noted that even though a 3-dimensional geomechanical model was used in his analysis, the model was configured to simulate 2-dimensional, plane strain geomechanical conditions combined with a 3-dimensional volumetric creep constitutive model for the ROM salt. According to Herrick (2012, p. 2), the plane strain model was selected to accommodate a simplified stratigraphic cross section used in earlier geomechanical numerical analyses at WIPP.

A plane strain condition assumes that all deformation occurs in the plane of the drift cross-section and that there is no deformation in the out-of-plane direction along the length of the drift. In plane strain calculations, the stresses in the third (longitudinal) dimension along the length of the drift must therefore be adjusted to maintain the plane strain assumption for materials, such as the salt, that deform volumetrically in three dimensions.

In applying a volumetric constitutive model for the salt to the plane strain conditions in the PCS drift, the stresses in the salt at the end of the previous time step are typically used to calculate new nodal point locations for the next time step. These new locations are then used to calculate new trial stresses in the salt using the volumetric (elastic) part of the salt constitutive model. The volumetric part of the salt constitutive model is three-dimensional and therefore calculates compression of the salt in every direction, including the out-of-plane direction along the length of the drift. However, the plane strain assumption does not allow for volume changes due to strain in the out-of-plane direction, so the new trial stresses must correct for the out-of-plane compression by applying a tensile stress in that direction to pull the salt back to zero strain. This tensile stress increases the volume and porosity of the salt, and therefore increases the time required for the porosity to decrease to a prescribed value. Because of this effect, the Agency believes that the model predictions of Herrick (2012) are likely to have overestimated the time required for ROM salt consolidation.

WIPP-Specific Engineering Estimate

An alternative approach for calculating WIPP-specific consolidation rates was developed by Hansen and Thompson (2002), who made an engineering estimate of room closure rates based on measurements of roof-to-floor and wall-to-wall closure in the WIPP waste disposal panel entries. The closure rates were found to have remained stable and uniform for more than 20 years at a volume closure of about 1% per year. Projecting forward and ignoring the effects of ROM salt backpressure buildup on slowing the closure rate, a volume reduction of 30% would decrease the porosity from 33% to 4% in about 30 years. Thus, based on this engineering estimate, the first and second phase consolidation of the ROM salt would be essentially completed in about thirty years. Hansen and Thompson (2002) cautioned that slower consolidation might be expected as backpressure develops. From this engineering estimate, it can be concluded that under WIPP in-situ conditions the first phase consolidation and possibly part of the second phase transition may be completed to a porosity of less than 10% within approximately 30 years.

WIPP-Specific FLAC3D Modeling

WIPP-specific conditions were also incorporated into FLAC3D modeling of ROM salt PCS consolidation by RockSol (2012). These modeling results were used in a DOE Permit Modification Request to the New Mexico Environment Department to use ROM salt instead of a concrete monolith for WIPP panel closures (U.S. Department of Energy and Nuclear Waste Partnership 2012, Item 1, Appendix B). The FLAC3D modeling also incorporated drift closure rate data that was updated from data used in the engineering approach of Hansen and Thompson (2002).  The FLAC3D analysis simulated the ROM salt PCS and adjacent drifts as fully 3-dimensional half-spaces of the intake and exhaust drifts of a generic waste panel that took advantage of longitudinal axial symmetry, thereby avoiding the quasi-2-dimensional plane strain assumptions that appear to have affected the aforementioned JAS3D results. Plan views of the intake and exhaust drift FLAC3D model areas are presented in RockSol (2012, Figures 3-2 and 3-3). Note that the PCS is identified as the WPC (Waste Panel Closure) in the figures.

The consolidation rates predicted by the FLAC3D modeling are shown in Figure 3. The modeling assumed ROM salt emplacement would occur 5 years after waste panel excavation and that external loading of the ROM salt would occur due to progressive vertical creep of an intact drift roof. The effects of rock falls due to roof failure were not included in the modeling. The occurrence of rock falls would likely locally increase the early time loading and possibly decrease the later time loading of the ROM salt. However, predicting the occurrence of rock falls and their effects is difficult and unlikely to significantly change the overall modeling results. The Agency therefore accepts the FLAC3D modeling as providing a reasonable approximation of early time consolidation of the ROM salt.

The results of the FLAC3D modeling predict a ROM salt porosity decrease from 35% to 6% (equivalent to a fractional density increase from 65% to 94%) in 30 years after emplacement and are consistent with the aforementioned engineering estimate of Hansen and Thompson (2002). The FLAC3D results also indicate an initial, rapid self-settlement of the ROM salt under its own weight that is essentially complete after about 2 years. Beginning with an initial porosity of 35% and a drift height of 4 m, the porosity of the ROM salt is predicted to drop to about 25% within the first year after emplacement due to self-settlement alone. When projecting these modeling results from porosities of 6% to 5%, the porosity is predicted to drop to about 5% in 32 years and essentially encompass both first and second phase consolidation. The Agency considers these FLAC3D modeling results to provide a useful, corroborated approximation of the time to completion of first phase consolidation as well as the transition to third phase consolidation of the WIPP ROM salt PCS.

2.3 Third and Fourth Phase Consolidation of ROM Salt

2.3.1 Backpressure Buildup

During third phase consolidation the ROM salt completes the transition from a porous material to the equivalent of an intact solid, attaining a very low porosity and permeability in the fourth phase lithostatic state (Hansen et al. 2014, p. 2-9). Third phase consolidation is characterized by rapid backpressure buildup due to decreasing salt compressibility at void ratios (or porosities) below about 0.05, as shown in Figure 1. As the void ratio drops further the backpressure increases above about 5 MPa and reaches the WIPP lithostatic stress of about 15 MPa at a void ratio of about 0.02. This void ratio is equivalent to a porosity of about 2% and approximates equilibrium stress conditions for completely consolidated ROM salt at WIPP with a backpressure equal to the maximum applied lithostatic stress. This test result is comparable with estimated fourth phase porosities on the order of less than 1% to 2% for intact Salado halite (Stormont and Daemen 1992).

As the effective porosity drops below 1 to 2%, individual pores will become increasingly isolated resulting in reduced interconnected pore-space where flow occurs, thus reducing the effective porosity and intrinsic permeability to near zero. As the permeability becomes very low and the pores lose their interconnection, pressure buildup may occur in individual pores and locally affect stresses but because those pressurized pores are isolated, they do not contribute to an overall reduction in effective stress of the rock mass (Hansen et al. 2014, p. 2-16).

2.3.2 Fluid-Assisted Deformation

Fluid-assisted salt deformation processes related to the increased stress conditions become dominant during third phase consolidation. Thin water films are ubiquitous along grain boundaries and support fluid-assisted diffusion transfer (FADT), pressure solution  -  reprecipitation creep processes, and fluid-assisted plastic deformation that change the shapes of the grains and strongly modify the geometry of the pores (Schenk et al. 2006; Czaikowski, et al. 2012). The plastic deformation includes dislocation motion accommodated by glide and cross slip along the dodecahedral {110} planes (Hansen 1985). Empirical evidence indicates that fluid-assisted transport processes will be operative in ROM salt aggregates derived from typical bedded salt even if no construction moisture is added due to the availability of adequate moisture to sustain those processes from negative crystals, grain boundary fluid, and hydrous minerals (Spiers et al. 1990; Callahan et al. 1996). As previously noted, these fluid-assisted consolidation mechanisms occur with moisture contents as low as 1% wt.

2.3.3 Consolidation Rates

The observed rapid increase in salt backpressure at low porosities suggests that the consolidation rate might decrease considerably as the backfill resistance approaches host rock fluid pressure. However, the presence of even a small amount of moisture significantly increases consolidation rates throughout the consolidation process. During third phase consolidation, the fluid-assisted creep deformation mechanisms that come to dominate continue to accelerate the rate of consolidation (Czaikowski er al. 2012). Due to the long time periods required for testing, little analytical information on third phase consolidation under in- situ drift closure conditions is available.  However, as discussed below, extrapolation of available test results and analogue information indicate that the final consolidation of an ROM salt aggregate from a porosity of 5% down to 1 to 2% under WIPP conditions could occur within a few tens of years and would be similar in duration to the initial phase consolidation.

During third phase consolidation the stress on the ROM salt is initially triaxial but transitions to an isotropic state under lithostatic stress when equilibrium with in situ conditions is reached at the end of the phase. Triaxial and isotropic laboratory stress test results are therefore most applicable to studying third phase consolidation rates.

Figure 3. ROM salt consolidation in WIPP PCS intake and exhaust drifts (from U.S. Department of Energy and Nuclear Waste Partnership 2012, Figure G1-10).

Estimates of third phase consolidation rates can be developed from the results of a series of triaxial compaction tests described by Hansen et al. (2014, p. 3-10 and Figure 3.6). The test sample was preconsolidated under a uniaxial load to a void ratio 19.7% and then compacted at increasing isotropic stresses ranging from 10.3 MPa to 20.4 MPa. Each stress cycle lasted about 300 days. The results of the tests at 18.4 MPa and 20.4 MPa were manually extrapolated by Hansen et al. to represent possible behavior down to porosities approaching those of the host salt. These extrapolations indicated that under a constant 18.4 MPa triaxial load the void ratio would drop from 6% to 2% (porosities of 5.7% to 2.0%) in about 8 years and under a constant 20.4 MPa load the same drop in void ratio would occur in about 1.5 years.

The foregoing test durations are plotted against applied stress in Figure 4. As discussed above, during third phase consolidation the applied stress at WIPP will increase from about 5 MPa to the lithostatic stress of about 15 MPa, with an average applied stress of about 10 MPa. If the duration of third phase consolidation from the foregoing test is assumed to be linearly related to the applied stress, extrapolation of the test results to an average applied stress of 10 MPa indicates that third phase consolidation under WIPP conditions would be essentially completed and further consolidation would cease in about 35 years. Although the validity of a linear extrapolation cannot be supported based on only two data points and the actual duration is expected to be longer, these results do indicate that third phase consolidation can occur relatively quickly when moisture is present and over a duration that may not significantly exceed the first and second phase consolidation. The Agency considers the extrapolated third phase duration of 35 years to be a possible but uncertain value and will accommodate this uncertainty when parameterizing the data for analysis.

2.4 Empirical Porosity  -  Permeability Relationships for ROM Salt

The permeability of granular salt has been successfully correlated with a wide range of porosities using a simple empirical equation of the following type (see, for example, Cinar et al. (2006), Table III):

k = aΦ[n]

where Φ is the effective porosity (expressed as a percentage), k is the intrinsic permeability in m[2], and a and n are empirical curve-fitting parameters. Figure 5 provides examples that demonstrate the appropriateness of this relationship as applied to laboratory test results. The figure shows porosity  -  permeability relationships for porosities down to 1% and permeabilities down to 10[-21] m[2]. These limits approach the ranges of porosity (<1% to 2%) and permeability (10[-2][4] to 10[-2][1] m[2]) of intact halite at WIPP.

Based on the foregoing exponential equation, the Agency developed the following empirical relationship between porosity and permeability for the Agency's SEN3 sensitivity analysis:

kWIPP = 1.5x10[-23.5] Φ[8.5]

This equation is intended to provide an empirical approximation of the relationship between porosity and permeability for a consolidating, brine-wetted ROM WIPP salt. Examples of the porosity  -  permeability relationships predicted by this equation are provided in Table 1. This approximation is consistent with the generally assumed high ROM salt permeabilities on the order of 10[-12] to 10[-11] m[2] for high porosity, loosely emplaced ROM salt and also with low permeabilities on the order of 10[-24] to 10[-21] m[2] for ROM salt that has healed and has properties approaching those of intact halite.  The curve generated by this equation is plotted as a dashed line on Figure 5. The results lie within and slightly to the right of the range shown in the figure for brine-wetted ROM salt. This positioning of the curve relative to data for other crushed salts may be related to a slightly higher impurity content found in the Salado salt beds.

Figure 4. Estimated duration for consolidation from 6% porosity to 2% porosity of Asse crushed salt under triaxial compaction with linear extrapolation to 10 MPa applied stress (data from Hansen et al. 2014, p. 3-11 and Figure 3.6).

A comparison of the curve generated by this equation with WIPP-specific laboratory data is presented in Figure 6. The figure shows data from several sets of laboratory tests on crushed salt and includes tests on crushed WIPP salt by IT Corporation (1987; also presented in Case et al. 1987, Figure 1), Mellegard et al. (1999), and Brodsky (1993; the Brodsky data are taken from Mellegard et al. 1999, Appendix B). As can be seen from the figure, the Agency's curve falls roughly in the center of the range of results and is therefore considered to provide an adequate approximation for consolidating WIPP ROM salt.

2.5 Recommended Porosity and Permeability Modeling Values for ROM Salt

Given the constraints of WIPP performance assessment modeling and the uncertainties in the duration of third phase consolidation at WIPP, the modeling approximations shown in Table 2 have been developed for the sensitivity study. The sampled ranges of porosity and permeability take into account uncertainties the applicability of laboratory test and modeling results to field conditions, variabilities associated with extrapolating short-term test results to the long-term third phase durations and conditions, and the effects of uncertain repository conditions such as such as waste panel gas pressure fluctuations that could slow ROM salt consolidation.

Figure 5. Porosity  -  permeability datasets for crushed salt and mixtures showing the EPA empirical relationship for WIPP ROM salt as a dashed line (modified from Hansen 2015,
Figure 7).

           Table 1. Empirical Porosity  -  Permeability Relationship
                       for a Brine-Wetted ROM WIPP Salt

                                Porosity Φ (%)
                           Permeability kWIPP (m[2])
                         Permeability kWIPP log(m[2])
                                       1
                                  4.74E-24[1]
                                    -23.32
                                       2
                                   1.72E-21
                                    -20.77
                                       3
                                   5.39E-20
                                    -19.27
                                       5
                                   4.14E-18
                                    -17.38
                                      7.5
                                   1.30E-16
                                    -15.89
                                      10
                                   1.50E-15
                                    -14.82
                                      15
                                   4.71E-14
                                    -13.33
                                      20
                                   5.43E-13
                                    -12.27
                                      25
                                   3.62E-12
                                    -11.44
                                      35
                                   6.32E-11
                                    -10.20

Note: The permeability values in the table are based on the relationship k = 1.5E[-23.5] Φ[8.5]
	   	   [1]1E-24 = 1 x 10-24

kWIPP ≈ 1.5*10[-23.5] Φ[8.5]

Figure 6. Porosity  -  permeability datasets for crushed salt showing the EPA empirical relationship for WIPP ROM salt as a dashed line (modified from U.S. Department of Energy and Nuclear Waste Partnership 2012, Item 1, Appendix B, Attachment G, Figure G1-13).

The basis for the ROM salt porosity and permeability values, ranges and distributions in Table 2 takes into account the following considerations.

ROM Salt Porosity and Permeability in Time Period T0
 Purpose: Used to establish initial conditions for WIPP PA models
 Duration: Same as in CRA-2014 PA
 Porosity - 30%: Approximates initial ROM salt porosity assuming PCS installation prior to time period T0
 Permeability - 1E-10 m[2]: Value used in CRA-2014; approximates high initial ROM salt permeability

ROM Salt Porosity and Permeability in Time Period T1
 Purpose: Represents first and partial second phase ROM salt consolidation
 Duration  -  50 years: Approximates engineering and FLAC3D modeling estimates of about 30 years plus an allowance for uncertainty (Sections 2.2.3 and 2.2.4)
 Porosity - 7.5 to 20%: Low end is midpoint of 5 to 10% porosity range for the second phase, transition consolidation (see Section 2.1). High end is the expected porosity 12 years after PCS installation based on FLAC3D model results and accounts for installation of most ROM salt panel closures before final repository closure. Range reflects uncertainty in the degree of compaction and in the porosity value representative of the time duration, and is similar to the T1 porosity range in the CRA-2014 PA of 6 to 18%. A uniform, maximum entropy distribution is selected because little is known about the actual parameter distribution.
 Permeability - Calculated as function of porosity: The Agency considers this calculation to provide a reasonable approximation for ROM WIPP salt. The sampled T1 permeability must be conditioned to always be greater than the sampled T2 permeability. Range reflects uncertainty in the permeability value representative of the sampled porosity. A triangular distribution is selected with a mode equal to the calculated permeability value. This distribution is consistent with an increased confidence in the calculated value based on comparisons with both non-WIPP and WIPP-specific data sets as shown in Figures 5 and 6.

ROM Salt Porosity and Permeability in Time Period T2
 Purpose: Represents partial second phase and third phase ROM salt consolidation
 Duration  -  50 years: Approximates a linearly extrapolated estimate of 35 years plus an allowance for uncertainty (Section 3.3)
 Porosity 2 to 7.5%: Low end approximates the porosity of completely healed WIPP halite and the completion of third phase consolidation (see Section 2.3.1). High end is the low end of the previously established porosity range for Time Period T1. The sampled T2 porosity must be conditioned to always be greater than the sampled T3 porosity. Range reflects uncertainty in the degree of compaction and in the porosity value representative of the time duration.  A uniform, maximum entropy distribution is selected because little is known about the actual parameter distribution.
 Permeability - Calculated as function of porosity: As in Time Period T1, the Agency considers this calculation to provide a reasonable approximation for ROM WIPP salt. The sampled T2 permeability must be conditioned to always be greater than the sampled T3 permeability. Range reflects uncertainty in the permeability value representative of the sampled porosity. As in Time Period T1, a triangular distribution is selected with a mode equal to the calculated permeability value.

ROM Salt Porosity and Permeability in Time Period T3
 Purpose: Represents final healed state of ROM salt.
 Duration  -  9,900 years: Balance of the regulatory time frame.
 Porosity: Same as sampled porosity value for intact halite in CRA-2014 PA.
 Permeability: Same as sampled permeability value for intact halite in CRA-2014. The healed permeability of the ROM salt is considered equal to the rock mass permeability of the Salado halite because the greater purity of the ROM salt mined from the repository horizon and the homogenization of that salt during the mining process would tend to lower the healed permeability below that of the Salado rock mass (which contains higher permeability clay seams), but this is expected to be offset by increases in permeability of the ROM salt due to potentially incomplete healing during the regulatory time frame.

Table 2. Porosity and Permeability Parameter Values for Modeling the ROM Salt PCS

                              Time Period (years)
                                   Duration
                                    (years)
                                 Porosity Φ
                                      (%)
                                Permeability k
                                    (m[2])
                                Time Period T0
                                    -5 to 0
                                       5
                                ΦROM T0 = 30
                                kROM T0 = 1E-10
                                Time Period T1
                                    0 to 50
                                      50
                             ΦROM T1 = 7.5 to 20
                       kROM T1 = 1.5E-23.5 ΦROM T1[8.5]
                           +- 1 order of magnitude;
                         must be greater than kROM T2
                                 Distribution

                                    Uniform
              Triangular  -  mode is calculated value of kROM T1
                                Time Period T2
                                   50 to 100
                                      50
                             ΦROM T2 = 2 to 7.5;
                         must be greater than ΦROM T3
                            and less than ΦROM T1
                       kROM T2 = 1.5E-23.5 ΦROM T2[8.5]
                           +- 1 order of magnitude;
                         must be greater than kROM T3
                             and less than kROM T1
                                 Distribution

                                    Uniform
              Triangular  -  mode is calculated value of kROM T2
                                Time Period T3
                                 100 to 10,000
                                     9,900
          ΦROM T3 = Sampled porosity of intact halite in CRA-2014 PA
        kROM T3 = Sampled permeability of intact halite in CRA-2014 PA
                                 Distribution

                            Same as in CRA-2014 PA
                            Same as in CRA-2014 PA

Both porosity and permeability will be decreasing over time as the ROM salt consolidates and this decrease will be reflected in the selection of parameter values. The long-term, healed values will take precedence and the earlier time values will be conditioned to be greater than the healed values. The potential exists for sampling earlier permeability values that are less than the later values. In such case, the sampled value will be rejected and the earlier value will be set equal to the later value.

3.0 POROSITY AND PERMEABILITY OF A HEALING DRZ

3.1 Overview of Consolidation Mechanisms in a DRZ

Numerous laboratory and field tests indicate that damage occurring during salt dilatation is reversible through crack closure and healing during subsequent compression (Hansen 2003, Sections 4.5 and 4.6). As far back as the late 1980s it was acknowledged that a disturbed rock zone (DRZ) surrounding an excavated drift in salt would heal due to creep closure of the drift. Costin and Wawersik (1980) tested salt fracture healing under confining pressures ranging from 10 to 35 MPa for 3 to 4 days at temperatures between 22 to 100[o] C. These tests included those representative of WIPP repository ambient temperature and pressure conditions (28[o] C and a lithostatic stress of 14.9 MPa). The majority of test specimens healed to within 70 to 80% of original tensile strength in this brief period.

IT Corporation (1987) conducted permeability tests on salt cores with both longitudinal-tension and saw tooth fractures at confining pressures between about 3.5 and 20 MPa. The cores initially had tensile induced fractures, but once 20 MPa backpressures were imposed on them for 8 days their measured endpoint permeabilities were within the same order of magnitude or less than the intact permeabilities. Cores with induced tensile fractures had lower end-point permeabilities than saw tooth fractures. The authors speculated that the tensile fracture cores healed more readily because the fractured surfaces of each half had similar paired geometries.

Brodsky (1990) tested fracture healing and microstructure hardening of induced damaged salt cores at pressures of 5, 10, and 15 MPa. Brodsky concluded that fracture closure and complete healing will occur if compressive pressures persist for an extended period of time (within a few tens of years). Fractures healed more quickly and effectively for those cores where fracture geometries were similar in shape and did not shear but conformed to the shape created during fracture formation.  Healing of the DRZ due to compressive stresses ranging from 2.5 to 14.5 MPa has been demonstrated in triaxial laboratory tests (Stormont and Daemon 1992). Stormont and Daemon concluded that the DRZ will readily heal to in situ values when stresses are applied to the samples representative of in situ conditions.

However, DRZ healing will only occur if a rigid body is able to impose compressive stresses on it.  For a drift filled with ROM salt, DRZ healing will therefore only occur once the ROM salt has reached porosities and densities similar to intact halite. Hansen et al. (1993, p. 7) report that when crushed salt aggregates have fractional densities less than about 0.9 the salt will produce minimal back stresses on adjoining DRZ and healing will be minimal.  However, once ROM salt aggregate achieves fractional densities approaching 0.9 the DRZ healing will begin to occur. This is corroborated by Hansen and Thompson (2002, p. 2) and Hansen (2003, pp. 10 and 27) who indicate that as the ROM PCS porosity is reduced to the target value of 0.05 (a fractional density of 0.95), healing of the DRZ will occur.

Other lines of evidence support the relatively rapid healing of a DRZ when compressive stresses are imposed on it. Pfeifle and Hurtado (1998) performed healing experiments on stress-induced fractures in both argillaceous and `clean' salt applying compressive pressures of 1, 5, 10 and 15 MPa to the fractures.  Their results showed that the stress induced fractures healed within a few years when compressive stresses imposed on them were between 10 and 15 MPa.  The experiments predicted that fracture healing will also occur when applied stresses are below 10 MPa but will take a longer time.  The authors estimate that DRZ healing at imposed compressive stresses below 10 MPa would take between 200 to 300 years. Because the imposed compressive stress at WIPP can reach lithostatic values of 15 MPa, the rate of healing would be faster. The previously cited measurements of the `regained' tensile strength provide another line of evidence that halite grain boundaries along the fracture faces re-bond, closing fractures and reducing permeability to near in-situ values.

3.2 Healing of the DRZ Adjacent to a WIPP ROM Salt PCS

DRZ healing phenomena have been clearly documented by results from laboratory tests (see, for example, Popp et al. 2012) and substantiated by field investigations (see, for example, Bechthold et al. 2004). Taken collectively, the above empirical data indicate that as the ROM salt porosity is reduced and the density increases, the ROM salt will impose an increasing back stress on the adjacent DRZ.  Once the ROM salt PCS has consolidated to end point porosities and densities the imposed back stress on the DRZ will become significant and will quickly approach the WIPP lithostatic pressure of 14.9 MPa. Full reconsolidation of the adjoining DRZ will therefore occur once the ROM salt panel closure is itself fully reconsolidated and stress equilibrium is achieved. The higher density and low compressibility of the healed ROM salt will transfer large compressive stresses to the adjoining DRZ at repository depths. These compressive stresses are expected to close stress-induced fractures and heal the DRZ within tens of years to properties approaching or equal to those of undisturbed halite. It is therefore reasonable to assume that the DRZ will readily heal soon after the properties of the ROM salt approach those of a rigid body.

In conclusion, creep closure will heal the multiple fractures and micro-fractures created by dilatory stresses along separation and alignment planes of the DRZ adjacent to an ROM salt PCS.  End-point healing will occur relatively soon after the ROM salt PCS is compressed into a rigid, solid body capable of exerting significant back pressure on the DRZ.  Because of the foregoing evidence that the ROM salt will heal to a rigid solid within less than 100 years post closure, it can be assumed that the DRZ will heal within roughly the same time frame. Therefore, it is reasonable to assume that final DRZ end point healing will be essentially achieved by 100 years post closure. Two-phase flow parameters in the now healed DRZ will be similar to those of intact, pre-damaged conditions.

3.3 PCS DRZ Porosity and Permeability

Laboratory tests on WIPP halite performed by Pfeifle and Hurtado (1998) provide the basis for the DRZ porosity and permeability values to be used in the sensitivity study. Triaxial compression creep tests were performed on salt specimens designated by Pfeifle and Hurtado as either "clean" or "argillaceous" to induce microfracturing similar to the damage created around an open drift in intact halite. The tests were performed at a temperature of 25°C, a stress difference of 20 MPa, and a confining pressure of either 3 or 4 MPa. As discussed above, this confining pressure is approximately the same as the 3 to 5 MPa confining pressure on the ROM salt during the transition period following first phase consolidation. This transition confining pressure appropriately approximates the end of first phase consolidation, the beginning of third phase consolidation, the beginning of significant ROM salt backpressure increases, and therefore the beginning of rapid DRZ healing.

Pfeifle and Hurtado's (1998) tests were designed to promote the accelerated creep resulting from the accumulation of microfracture-induced damage known as tertiary creep. The induced damage levels were consistent with the damage levels expected to occur in the DRZ around a typical WIPP opening. The tests were terminated before the damage accumulation led to sample failure (except in one test) by invoking a test termination criterion based on accumulated dilatant volumetric strain. The goal of the termination criterion was to produce specimens with dilatant volumetric strains ranging between 0 and about 0.5 percent that could be used in compression tests of DRZ healing.

The sample conditions at the end of the triaxial compression creep tests and before subsequent compression tests were used by the Agency to approximate the porosity and permeability of the DRZ during time periods T0 and T1, before significant backpressure buildup occurs in the ROM salt. Because of the relatively short test durations (approximately 10 to 60 days), data from Pfeifle and Hurtado's (1998) healing stage compression tests were not used. Rather, the Agency accepted the sampled porosity for Material DRZ_PCS in the CRA-2014 PA as providing a reasonable representation of DRZ porosity during the healing process. Consistent with the foregoing conclusions that DRZ healing is relatively rapid and closely follows healing of the ROM salt, the DRZ surrounding the ROM salt PCS is assumed by the Agency to heal to approximate the properties of intact halite by the end of the 50-year T2 time period.

The microfractures in a DRZ around an open drift are preferentially oriented parallel to the direction of maximum principal stress, leading to permeabilities that are likely anisotropic (Popp et al. 2012). Pfeifle and Hurtado's (1998) constant head synthetic brine and nitrogen gas permeability measurements were made in the axial direction of applied principal stress and are therefore considered maximum values for the damaged specimens.

The results of the compression tests indicated greater creep in the argillaceous specimens than in the clean specimens at a given load (Pfeifle and Hurtado 1998, Figure 2). This was attributed to the potential role of clay and other impurities as sources for microcrack initiation. Damage to cleaner salt would be less at a given load and the induced porosities and permeabilities would also be less. This observation is generally substantiated by Pfeifle and Hurtado's test results. However, Pfeifle and Hurtado also point out that comparison of dilatant volumetric strain / permeability data pairs with those presented by Pfeifle et al. (1998) suggests that the permeability of clean WIPP salt is approximately the same as the permeability of argillaceous WIPP salt for identical levels of dilatant volumetric strain.

Porosity data are presented by Pfeifle and Hurtado (1998, Table 2) for four clean samples and four argillaceous samples. These results are summarized in Table 3.

         Table 3. Porosity of Microfracture-Damaged WIPP Salt Samples

                               Sample Condition
                               Number of Samples
                                Porosity Range
                                      (%)
                                 Mean Porosity
                                      (%)
                           Sample Standard Deviation
                                      (%)
Clean
                                       4
                                 0.37 to 1.44
                                     0.84
                                     0.36
Argillaceous
                                       4
                                 1.15 to 3.32
                                     2.40
                                     0.74
All Samples
                                       8
                                 0.37 to 3.32
                                     1.62
                                     1.01
Data from Pfeifle and Hurtado (1998, Table 2)

Permeability data are presented by Pfeifle and Hurtado (1998, Table 3) for seven clean samples and three argillaceous samples. These results are summarized in Table 4.

       Table 4. Permeability of Microfracture-Damaged WIPP Salt Samples

                               Sample Condition
                               Number of Samples
                              Permeability Range
                                    (m[2])
                              Permeability Range
                                   log(m[2])
                               Mean Permeability
                                   log(m[2])
                           Sample Standard Deviation
                                   log(m[2])
                                     Clean
                                       7
                             1.77E-16 to 3.36E-13
                                   -15.75 to
                                    -12.47
                                    -14.30
                                     1.04
                                 Argillaceous
                                       3
                                  2.45E-16 to
                                   1.19E-13
                                   -15.61 to
                                    -12.92
                                    -14.05
                                     1.14
                                  All Samples
                                      10
                             1.77E-16 to 3.36E-13
                                   -15.75 to
                                    -12.47
                                    -14.22
                                     1.08
Data from Pfeifle and Hurtado (1998, Table 3)

3.4 Sensitivity Study Porosity and Permeability Modeling Values for the PCS DRZ

Porosity and permeability values for modeling the DRZ surrounding the ROM salt PCS in the sensitivity study are given in Table 5. These values are based on the foregoing results of Pfeifle and Hurtado's (1998) laboratory studies of damaged samples of WIPP salt. The sampled values and ranges are intended to take into account the range of Pfeifle and Hurtado's results and uncertainties in the applicability of laboratory tests to field conditions, as well as uncertainties in the time required for healing to occur. Because the Salado consists of clean as well as argillaceous halite, the sensitivity study parameter values reflect the combined properties of all Pfeifle and Hurtado's triaxial compression creep test results and will be used to represent the initial condition of the DRZ prior to healing in the Agency's sensitivity study.

Both the porosity and permeability of the DRZ will be decreasing over time as healing occurs and these decreases will be reflected in the selection of parameter values. The long-term, healed values will take precedence and the earlier time values will be conditioned to be greater than the healed values. The potential exists for sampling earlier values that are less than the later values. In such case, the sampled value will be rejected and the earlier value will be set equal to the later value.

The basis for the DRZ porosity and permeability values, ranges and distributions takes into account the following considerations.

PCS DRZ Porosity and Permeability in Time Period T0
 Purpose: Used to establish initial conditions for PA models when the DRZ is assumed to be in an unhealed, damaged state.
 Duration: Same as in CRA-2014 PA.
 Porosity: Equals the rounded mean porosity of 1.6% for all eight Pfeifle and Hurtado samples +- the rounded sample standard deviation of 1.0. The sampled T0 porosity must be conditioned to always be greater than the sampled T2 porosity. The uniform, maximum entropy distribution is selected because little is known about the actual parameter distribution.
 Permeability: Equals the rounded mean permeability of -14.22 log(m[2]) (6E-15 m[2]) for all ten Pfeifle and Hurtado samples +- the rounded sample standard deviation of 1.0 log(m[2]), equivalent to +- 1 order of magnitude. The sampled T0 permeability must be conditioned to always be greater than the sampled T2 permeability. The loguniform distribution is selected because the results encompass several orders of magnitude but only a few data sets are available for DRZs and little is known about the actual parameter distribution.

PCS DRZ Porosity and Permeability in Time Period T1
 Purpose: Represents first phase and part of the second phase ROM salt consolidation. The DRZ is assumed to remain in an unhealed, damaged state because ROM salt backpressure is low throughout most of T1.
 Duration  -  50 years: Approximates engineering and FLAC3D modeling estimates of about 30 years for ROM phase one consolidation plus an allowance for uncertainty (Section 2.2.2)
 Porosity  -  Same as T0 sampled value.
 Permeability  -  Same as T0 sampled value.

PCS DRZ Porosity and Permeability in Time Period T2
 Purpose: Represents third phase and part of second phase ROM salt consolidation and backpressure buildup, during which time DRZ healing closely follows healing of the ROM salt and is relatively rapid.
 Duration  -  50 years: Same as T2 for ROM salt and includes an allowance for uncertainty for healing times of both ROM salt and DRZ.
 Porosity  -  Same as porosity for Material DRZ_PCS as sampled in CRA-2014 PA. However, the sampled T2 porosity must be conditioned to always be greater than the sampled T3 porosity. By adopting the properties of Material DRZ_PCS, the sampled T2 porosity will represent intermediate values between the unhealed and the fully healed state.
 Permeability  -  Same as permeability for Material DRZ_PCS as sampled in CRA-2014 PA. However, the sampled T2 permeability must be conditioned to always be greater than the sampled T3 permeability. By adopting the properties of Material DRZ_PCS, the sampled T2 permeability will represent intermediate values between the unhealed and the fully healed state.
PCS DRZ Porosity and Permeability in Time Period T3
 Purpose: Represents final healed state of the DRZ.
 Duration  -  9,900 years: Balance of the regulatory time frame.
 Porosity: Same as sampled porosity value for intact halite in CRA-2014 PA.
 Permeability: Same as sampled permeability value for intact halite in CRA-2014. The healed permeability of the DRZ is considered equal to the rock mass permeability of the Salado halite.

     Table 5. Porosity and Permeability Parameter Values for Modeling the
                      DRZ Adjacent to a WIPP ROM Salt PCS

                                  Time Period
                                   Duration
                                    (years)
                                  Porosity Φ
                                      (%)
                                Permeability k
                                    (m[2])
                                Time Period T0
                                 -5 to 0 years
                                       5
                            ΦDRZ T0 = 1.6 +- 1.0;
                         must be greater than ΦDRZ T2
                                kDRZ T0 = 6E-15
                            +- 1 order of magnitude
                                 Distribution

                                    Uniform
                                  Loguniform
                                Time Period T1
                                 0 to 50 years
                                      50
                             ΦDRZ T1 =  ΦDRZ T0
                               kDRZ T1 = kDRZ T0
                                Time Period T2
                                50 to 100 years
                                      50
            ΦDRZ T2 =  Sampled porosity of DRZ_PCS in CRA-2014 PA;
                         must be greater than ΦDRZ T3
                            and less than ΦDRZ T0
           kDRZ T2 = Sampled permeability of DRZ_PCS in CRA-2014 PA;
                         must be greater than kDRZ T3
                             and less than kDRZ T0
                                 Distribution

                            Same as in CRA-2014 PA
                            Same as in CRA-2014 PA
                                Time Period T3
                                 100 to 10,000
                                     9,900
          ΦDRZ T3 = Sampled porosity of intact halite in CRA-2014 PA
        kDRZ T3 = Sampled permeability of intact halite in CRA-2014 PA
                                 Distribution

                            Same as in CRA-2014 PA
                            Same as in CRA-2014 PA

4.0 TWO PHASE FLOW PROPERTIES IN ROM SALT

4.1 Introduction to Two-Phase Flow in Salt Aggregates

Two-phase flow properties in porous media vary over a wide range of values depending on the mineralogy, size and shape of pores and pore throats, fluid connectivity between pores, irregularity of granular textures (surfaces), and fluid pressures between each pore. Prior to the mid-1990s, two-phase flow measurements in salt were few. As a result, the WIPP CCA PA used sandstone as an analog material in developing parameter values for two-phase flow. Since the CCA timeframe, additional two-phase flow laboratory experiments have been conducted on salt aggregates. These experiments coupled with consolidation and compression experiments, highlight the unique two-phase flow properties of salt, especially loose, granular salt as it undergoes consolidation under its own weight and compression due to applied stress (e.g., salt creep).  These experimental results indicate that sandstone is a weak analog for determining the changing two-phase flow properties of a salt aggregate as it consolidates and compresses under pressure toward a healed end-point state. This is primarily because sandstone does not exhibit the unique creep characteristics of salt when compressed and consolidating.

Salt consolidation and compression affect permeability, porosity, pore shapes and textures, and grain configurations that in turn affect salt's two-phase flow properties. Consequently, when modeling two-phase flow in salt, it is important to consider the evolution of these physical characteristics and their effect on residual brine and gas saturations and threshold pressures as the salt transforms from a loose mixture of aggregates into a solid and healed salt `block.'  A summary of the updated experimental work that can support the selection of appropriate two-phase flow parameter values as the ROM salt properties evolve through time is given below.

Krg_DR
Krg_IM
Krw_DR
Krw_IM

4.2 Overview of Two-Phase Flow in ROM Salt
Fluid movement depends on a connected pathway between pores and whether the fluid is draining (exiting the pore space) or imbibing (entering the pore space). For two fluids simultaneously residing in a medium, the permeability of each fluid is a function of the degree of saturation.

Figure 7. General relative imbibition (IM) and draining (DR) permeability curves vs brine saturation (from Hansen et al. 2014, Figure 4.2a).

Figure 7 is a general representation of relative permeability related to degree of saturation and whether the fluid is imbibing or draining the medium.  Flow ceases when the fluid enters dead-end pores and is no longer able to move out of the pore and into another; this is its residual saturation point. At this point the permeability of the medium to that fluid becomes essentially zero. Residual saturation is affected in part by the fluid's viscosity and density. Generally, it takes more energy for a denser and more viscous fluid to move between pores. Because water (or brine in the WIPP case) is denser and more viscous than gas it will have a higher residual saturation than gas. The appropriate residual saturations and threshold pressures for both gas and brine in the ROM salt PCS depend on the time-dependent porosity and permeability of the ROM salt, as well as whether each fluid is draining or imbibing in the pore space.

Because the ROM salt PCS will be emplaced without any added moisture its gas permeability will first follow the gas draining curve (curve krg_DR) as the pores become filled with brine. The incoming brine will follow the imbibition curve (curve krw_IM) and displace the gas.  Incoming brine must overcome the gas capillary pressure, via a threshold pressure, to enter the pore space. What complicates determining two-phase flow parameter values is that the ROM salt PCS porosity will be reduced with time due to consolidation and compression. Therefore, as the ROM salt porosity is reduced the degree of saturation will change and depend, in part, on whether brine or gas is being drained or imbibed.

At the time of emplacement, the ROM salt will be primarily gas saturated. Brine saturation will be low, in the range of 0.5 to 1.0 % wt (Arhens and Hansen 1995). There will be few connected brine pathways resulting in low relative brine permeability. In contrast, relative gas permeability will be high. Initially the loose ROM salt will have highly interconnected porosity for gas with less tortuous paths and fewer dead-end pore spaces. At this point the residual gas saturation will be relatively low.  Within approximately 30 to 40 years the salt is predicted to consolidate under its own weight and be compressed due to creep closure of the host rock (U.S. Department of Energy and Nuclear Waste Partnership 2012, Item 1, Appendix B, Attachment G1, Section 3.2.6).  Both mechanisms will `suture' the individual grains together and reduce porosity.

During this consolidation and compression phase, gas will be easily `squeezed' out of the pore space.  Concurrently, brine will begin to seep into the ROM salt PCS from the anhydrite units and the DRZ (DOE 2014, Appendix PA, p. PA-2.1.1). Because salt is hydrophilic, incoming brine will tend to `film flow' along grain boundaries, preferentially creating interconnected films along grain edges. This will provide an interconnected film flow path between pores. Simultaneous consolidation and compression of the ROM salt PCS will constrict pore spaces and create `deadend pores' that will entrap fluid. Because of the reduction in porosity and creation of more constricted pore spaces, total brine saturation will increase and the areas of less mobile brine will also increase in the salt aggregates.

As discussed in Section 2, in addition to consolidation and compression, small amounts of moisture contacting grain edges will modify the grains via two mechanisms. These are: 1) fluid assisted diffusion transfer (FADT) and 2) pressure dissolution and re-precipitation. FADT can occur when salt aggregates are exposed to either small amounts of brine (less than 1% wt) or very low humidity (Spiers et al. 1988).  These mechanisms alter pore structures, sizes, and surface textures. They also globally constrict pore shapes, narrow pore throats, and reduce total porosity and permeability (Maartje et al. 2011 as reported in Hansen 2012, pp 2-14 to 2-16). Additionally, during compression salt aggregates and crystals will undergo plastic deformation that will narrow pore throats creating more impedance for brine to pass between pores, reduce relative permeability, and increase residual brine saturation. Illustrations of these mechanisms are given in Figure 8. All these mechanisms need to be taken into consideration when determining two-phase flow properties in ROM salt.

      Figure 8. Changes in pore structure of salt aggregate during compaction
      (from Hansen et al. 2014, p. 2-7).

Brine saturation versus capillary measurements have been made on Salado materials but these were on anhydrite samples rather than halite (Howarth and Christian-Frear 1996).  Because anhydrite is brittle and is characterized as a semi-fractured medium containing numerous fracture networks, measured residual saturations would be lower than for ROM salt.  Since the late 1990s there have been two-phase flow laboratory experiments conducted on salt aggregates. Results from a few of these experiments are given below and should be taken into consideration in adopting two-phase flow parameters values for the ROM salt.

4.3 Two-Phase Flow in WIPP PA

The CRA-2014 values adopted for the ROM salt PCS residual saturations, capillary pressures, and threshold pressures were developed in the early 1990s for the 1992 preliminary WIPP PA calculations and are documented as estimated values in Webb (1992). At that time, emphasis was placed on flow through the more brittle and fractured anhydrite units. Little consideration was given to ROM salt properties because the use of ROM salt in panel closures was not yet part of the repository design. Parameter estimates for ROM salt were mainly based on values applicable to the anhydrite units and not the properties of ROM salt.

The estimated values developed by Webb (1992) were intended to broadly include parameter values relevant to the anhydrites, halite and shaft seals, and were recognized as such by Webb.  Additionally, these estimates were acknowledged as being put together in a short time period. The values provided in Webb's memo were caveated as: a) based on best-guess estimates, and b) derived in order to blend both the Brooks-Corey and the van Genuchten models together.

Webb also provided estimates for effective saturation Se, which was needed to perform the preliminary calculations. The effective saturation represents the pore space occupied by the mobile portion of both brine and gas, and excludes the pore space occupied by the immobile residual gas and brine saturations. The assigned value for Se was not intended to represent any specific material and was set at 0.5 in order to create similar curve fitting parameters between the two models. This means that the residual brine saturation cannot exceed 0.5, which is not realistic for tight, compressed and contorted salt aggregates.

Webb acknowledged that his recommended two-phase flow parameter values were broad and not specific to one unit or material, but were intended to capture all possible values for all Salado lithologies.

4.4 Residual Saturation and Capillary Pressure Experimental Data for ROM Salt

Saturation versus capillary pressure measurements on salt plugs packed with fine grain salt have been reported by Cinar et al. (2006) and the results are plotted in Figure 9. The salt plugs were of uniform grain size packed at porosities of 5.02 and 4.82%, and respective permeabilities were measured at log -14.5 m2 and log -14.7 m[2]. The plugs were first brine saturated and then subjected to a stepped drainage process to measure saturation at given capillary pressures. Because saturation versus capillary pressure was based on the brine draining the pores, residual brine saturation would be slightly lower than if brine was entering the pore spaces. For this test, the residual, irreducible brine saturation was slightly below 0.2 at a capillary pressure of approximately 0.4 MPa.

Pore throat sizes and shapes were also measured by Cinar et al. (2006) and compared to those found in tight sandstones. The salt pore structures were almost four times longer, more tortuous, narrower and more slit like (aligning along grain boundaries), and less `rounded' than those in sandstones. Because of these differences in pore shapes the authors speculated that salt aggregates will have higher residual saturations and capillary pressures than those of sandstones with similar porosity.

Saturation versus pressure measurements on salt aggregates were reported by Olivella et al. (2011). In these experiments, brine saturations and capillary pressures were measured on initially brine saturated aggregate salt cylinders compressed to porosities of 5 and 10 %, and the results are illustrated in Figure 10. The data were curve-fitted using a van Genuchten two phase flow model. Generally, air-entry pressures, capillary pressures and degree of saturation increased as porosity decreased. No residual brine saturation was measured below 0.10; most values clustered between 0.15 and 0.20 and brine flow effectively stopped around 50 kPa (0.05 MPa), indicating drainage ceases at relatively low capillary pressures and the maximum threshold pressure for these porosities would be less than 1 MPa. Both curves illustrate trends toward higher residual saturations and capillary pressures as porosity decreases.  (Note, for the curve fitted line, lambda (), and Po were derived using the Van Genuchten model, where Po is the brine pressure and  is the pore size distribution parameter).

Figure 9. Brine saturation vs. capillary pressure (from Cinar et al. 2006, Figure 5). (MRSM = steady-state modified restored-state method; CPDM = dynamic constant pressure desaturation method)

Other, but preliminary results, for threshold pressure versus saturation have been conducted on Asse salt aggregates and reported by Kröhn (2015). Saturations versus capillary pressures were measured on a core sample packed to a porosity of 7.33%, with a measured permeability of (log) ~10[- 15] m[2].  Results are depicted in Figure 11. Residual saturations were found to be 0.35 at capillary threshold pressures of approximately 2 MPa. These results indicate relatively high residual saturations (~ 0.35) at relatively high porosities and permeabilities for salt aggregate.  This could be because of the FADT process creating dead-end pores -- zones where brine cannot easily flow out of one pore space to another.

If all these measurements are taken collectively, both residual brine and gas saturation will be above 0.0 in the ROM salt PCS throughout the 10,000-year modeled period. Furthermore, the data indicate that as the ROM salt PCS consolidates and compresses to lower permeability and porosity the residual saturations for both gas and brine will increase.

Consolidated sandstone can be used as an approximate analogue material to capture data gaps and uncertainty ranges in estimating two-phase flow properties for salt when data measured on ROM salt are sparse; however, using data from sandstone should be caveated. At a minimum the permeabilities and porosities of the sandstone analogue should be similar to those of ROM salt if sandstone residual saturations are adopted for ROM salt. EPA believes that sandstone analogues should only be used if they meet these criteria for a specific time frame during the ROM salt consolidation process.

Figure 10. Brine saturation vs. suction (capillary pressure) for salt aggregates at 5% and 10% porosity (from Olivella et al. 2011, Figure 9).

Based on the foregoing criteria, only a subset of residual saturations for consolidated sandstone reported in Hurtado et al. (1997, Table 3-1) are appropriate analogs for ROM salt. The consolidated Berea and Hygiene sandstones appear to be the most suitable analogues for ROM salt. The Berea sandstone has a porosity that ranges between 12.5 to 15.6% and permeabilities ranging between 2 to 15.2 md (Jackson 1985; equivalent to log -14.7 m2 and log -13.82 m[2]). The Hygiene sandstone porosity and hydraulic conductivity are reported at 0.250 and 108 cm/d (van Genuchten, 1980), respectively. Assuming water was the permeant fluid used in the conductivity tests, the Hygiene sandstone permeability equates to approximately log -11.9 m[2].   These two materials have porosities and permeabilities similar to those for consolidating ROM salt and could therefore be deemed as suitable analogs for estimating residual saturations for ROM salt during the consolidation process.

xxx
Figure 11.  Brine saturation versus capillary pressure on Asse salt aggregate compacted to 7.33 % porosity. (Kröhn 2015; the authors are investigating the cause of the anomalous values given by the open diamonds).

4.5 Recommended Residual Saturation Modeling Values for ROM Salt

The evolving characteristics of the ROM salt PCS from the time of emplacement through the 10,000-year regulatory period will affect residual saturation, threshold pressure, and capillary pressure. Therefore, it is reasonable to assume the following:
4.5.1 T0 and T1 Time Periods (-5 to 50 years)

Soon after emplacement the ROM salt will be loose and unconsolidated with a relatively high porosity of 30 to 35% and a permeability ranging from 10[-10] to 10[-12] m[2]. The sizes of WIPP ROM salt aggregates are reported to range between to 0.05 to 75 mm (Holcomb and Shields 1987; Case et al. 1987; Pettigrew and Associates, 1993). However, many of these size measurements excluded larger aggregates due to sieve size limitations and no single distribution can be cited with confidence.  During WIPP site inspections, EPA staff have observed ROM salt chunks much larger than 100 mm.  From the recorded sieve analyses and direct observations, EPA concludes that WIPP ROM salt contains a wide range of particle sizes. This variability will create an array of pore sizes with the larger pores filled with smaller particles that are able to wedge into and between pore throats. This alone enhances the production of dead end pore spaces and creates areas where fluid becomes entrapped.  The wider range of grain sizes produces a relatively broad range of residual saturations.

At emplacement, the ROM salt will be close to fully gas saturated and brine saturation will be low.  The resulting high porosities and gas permeabilities are due to relatively large and wide pore throats and longer, less contorted paths between pores. Because ROM salt at emplacement will be a `porous medium' with various grain sizes it will have `dead-end' pore space where brine or gas can become entrapped.  Because gas is less viscous and less dense than brine and the medium will be originally gas saturated, it will be less likely to be `entrapped' in the dead-end pores. Since there are no two-phase flow parameters measured on salt aggregates at these relatively high porosities and permeabilities, analog values will have to be used derived from material with similar permeabilities and porosities.

The above reasoning supports using unconsolidated and fragmented sandstone, with properties similar to the high porosity and permeability characteristics of ROM salt, as an appropriate analog material. A list of suitable analog materials can be found in Hurtado et al. (1997, Table 3-1). From this list the materials that best match the properties of pre-consolidated ROM salt are sand and fragmented Fox Hill Sandstone. The Fox Hill Sandstone residual saturation ranges between 0.110 and 0.300. A value of 0.0, given for sandy porous media from Parker et al. (1987) is not used because it was a value estimated by the researchers in order to curve-fit their newly developed numerical model.  A direct examination of the journal article found that there were no values measured this low.

Flow occurs in the non-dead-end pore space and this space is defined as the effective saturation, Se. It is in this pore space that both brine and gas flow occurs because flow bypasses the dead-end, residual brine or gas pore space.  Effective saturation is defined by the following equation:

Se = 1  -  (Sgr+Sbr)

Because the pore spaces are large and not constricted, there will be a larger area for brine or gas to flow between pores. Therefore the difference between residual brine and gas saturation will be larger at these higher porosities. For purposes of this sensitivity study, residual gas saturation will be a function of residual brine saturation using the equation in the following tabulation. These and similar relationships established below are based on the following physical constraints: Sbr and Sgr should be consistent with relevant data; Sbr should be greater than Sgr because of the greater mobility of gas; Sbr and Sgr should be greater than zero in a porous medium because of capillary effects that constrain mobility; Sbr and Sgr should be increasing as porosity decreases because of the decreasing mobility of both brine and gas with decreasing porosity; and Sbr + Sgr < 1 because Se should be greater than zero.

                   T0 and T1 - ROM Salt Residual Saturation
                                  Time Period
                                    (years)
                                   SAT_RBRN
                                     (Sbr)
                                   SAT_RGAS
                                     (Sgr)
                                   -5 to 50
                                   T1 Sbr =
                                  0.1 to 0.2
                               Sampled - Uniform
                                   T1 Sgr =
                                (1-T1 Sbr)*0.05
            Sbr = residual brine saturation
            Sgr = residual gas saturation

4.5.2 T2 Time Period (50 to 100 years)

During compression and consolidation the more mobile gas will flow out of the ROM pore space and porosity and permeability will be reduced.  As the ROM salt compresses and consolidates, the salt grains become deformed and create smaller pore spaces and narrower pore throats causing an increase in residual saturation. The second time period coincides with porosities less than 5% and permeability below 10[-17] m[2].  EPA considers it reasonable to increase the original residual brine saturation values by either 0.15 or 0.2 due to decreasing porosity. This increase in residual brine saturation is accompanied by an increase the residual gas saturation due to decreased mobility of both brine and gas. The effective saturation will also be reduced because more gas and brine will be entrapped in dead-end pores. This increase captures measured residual brine saturations for salt aggregates reported by Olivella et al. (2011) and Cinar et al. (2006) for salt having similar permeabilities and porosities. For time period T2, residual gas saturation will be a function of residual brine saturation using the equation in the following tabulation based on the physical constraints described above.

                       T2 -ROM Salt Residual Saturation
                                  Time Period
                                    (years)
                                   SAT_RBRN
                                     (Sbr)
                                   SAT_RGAS
                                     (Sgr)
                                   50 to 100
                                   T2 Sbr =
                                  T1 Sbr + x
                                   T2 Sgr =
                                (1-T2 Sbr)*0.2
            x is sampled and is either 0.15 or 0.2
            Sbr = residual brine saturation
            Sgr = residual gas saturation

4.5.3 T3 Time Period (100 to 10,000 years)

As ROM porosity is reduced and pore throats become more constricted, the relative volume of the remaining non-mobile brine, the brine residual saturation, will increase and approach values nearing the total porosity because a large portion of the pore space will have immobile fluid. This is corroborated by underground tests measuring gas flow through damaged halite reported by Stormont and Daemon (1992). These tests found that when pore throats are pinched, conditions are created where brine becomes less mobile and residual saturation increases. With additional constriction, residual saturation will approach a point where most of the saturated pore space is filled with immobile brine, or by implication, with immobile gas. For time period T3, residual gas saturation will be a function of residual brine saturation using the equation in the following tabulation based on the physical constraints described above.

                       T3 - ROM Salt Residual Saturation
                                  Time Period
                                    (years)
                                   SAT_RBRN
                                     (Sbr)
                                   SAT_RGAS
                                     (Sgr)
                                 100 to 10,000
                                   T3 Sbr =
                                 T2 Sbr + 0.25
                                   T3 Sgr =
                                (1-T3 Sbr)*0.8
            Sbr = residual brine saturation
            Sgr = residual gas saturation

4.6 Equations for Two-Phase Flow in BRAGFLO

This section presents a brief review of the two-phase flow equations used in the WIPP BRAGFLO PA model. In the current PA, threshold pressure, Pt, is first estimated and represented by the equation given below (DOE 2014, Appendix PA, Equation PA.41).

Pt=akn
Threshold pressure is a function of permeability, k. The constants a and exponent n are estimates provided in Webb (1992) and adopted from Davies (1991) (as cited in DOE 2014, Appendix PA, Table PA-3).

Capillary pressure is derived from threshold pressure. The formula for capillary pressure is given below (DOE 2014, Appendix PA, Equation PA.38).

Pc= Pt (k)/  Se21/λ
The above formula assumes a modified Brooks-Corey two-phase flow model. Input parameters for Pc are pore-size distribution, λ (the relative abundance of pore sizes in a representative volume) and effective saturation, Se2. The suggested range for λ in the 1992 Webb memo was 0.7 to 10 and was based on values collected over a wide range of porous media; however, no values were available for halite (Hurtado et al. 1997, Table 3-2). The assumed effective brine saturation, Se2, was set to 0.5. Webb admits this value was estimated based on very limited data. Additionally, Webb's recommended range for both residual gas and brine saturation was 0.0 to 0.4, with the value of `0.0' intended to force possible fingering to be simulated in the modeled fractured anhydrites. EPA believes updates to these values are needed that are aligned with the time-varying characteristics for ROM salt during the modeled period.

The recommended two-phase flow parameters values to be used in this sensitivity study take into consideration relevant empirical data specific to capillary and threshold pressures in ROM salt as it evolves with time. The changing properties of ROM salt as it undergoes compression, consolidation, and modifications to pore shapes and structures creates a situation that necessitates modifying two-phase flow parameter values that represent the evolving structure of the medium as it is compressed and consolidated. These unique components and mechanisms relevant to salt indicate that using sandstone as a common analog for salt properties should be accompanied with caveats and such use is only appropriate when other data related to salt properties are not available, especially when developing two-phase flow properties in ROM salt as it evolves with time.

4.7 Threshold Pressure and Pore Size Distribution Modeling Values for ROM Salt

4.7.1 Overview of Threshold Pressure in Salt

Davies (1991) provided an in-depth report on threshold pressures for bedded salt and highlighted the inverse correlation between threshold pressure and permeability for Salado salt beds: as permeability decreases threshold pressure increases. Because bedded salt is nearly impermeable, Davies suggested threshold pressures in the Salado would have to be well above hydrostatic pressure and, in some instances, approach formation pressures for one fluid to displace another.   Results from early field tests (Stormont 1990) corroborated Davies' assumption  -  that threshold pressures of intact Salado halite would be close to or above formation pressures.

4.7.2 Overview of Pore Size Distribution in Salt

Pore-size distribution is a measure of the variability of pore sizes in a porous medium. Capillary and threshold pressures are functions of the pore-size distribution. Smaller values for pore-size distribution result in larger values for both capillary and threshold pressures. No measurements are available for pore size distributions in ROM salt, therefore values of the pore-size distribution parameter need to be adopted from analog materials. Hurtado et al. (1997, Table 3-2) list pore-size distribution values for multiple types of geologic materials. The most suitable values applicable for ROM salt as it goes through consolidation and compression would be those that lie between loose and unconsolidated sandstone.

4.7.3 Threshold Pressure and Pore Size Distribution Modeling Values

The aforementioned inverse correlation between threshold pressure and permeability postulated by Davies (1991) and corroborated in the field by Stormont (1990) is supported by the relationship of both parameters to porosity. As porosity decreases and pore sizes become smaller, permeability will decrease and capillary pressures in partially saturated media will increase, thereby increasing the threshold pressure required for one fluid to displace another. As noted above, threshold pressure Pt is a function of a linear parameter a and an exponential parameter n. The Agency determined that the values assigned these parameters in WIPP PA (a = 0.56 and n = -0.346) are consistent with field data for Pt and permeability k over a wide range of values and therefore accepts the use of these values in the Agency's sensitivity study.

Capillary pressure is an important parameter in two-phase flow and, as shown above, is modeled as a function of threshold pressure Pt, effective saturation Se2, and pore-size distribution λ. The Agency's modeling values for brine and gas effective saturations are given above. The modeling values for pore-size distribution are developed in the following paragraph.

For this sensitivity study, appropriate ranges for the ROM salt pore-size distribution were estimated by starting with the assigned value in the CRA-2014 PA for intact halite (0.7) for the T3 time period, and then stepping backward in time. The ROM salt is being consolidated under increasing pressure during time period T2. From the T3 value, the appropriate T2 value was estimated from a range of values representative of consolidated materials with a higher porosity and permeability than for ROM salt during T3, but with lower porosity and permeability than expected for ROM salt during T1. The intermediate pore-size distribution value of 1.4 assigned to the T2 time period was based on simply doubling the T3 value for intact halite and comparing that value with those listed in Hurtado et al. (1997, Table 3-2). The pore-size distribution value of 1.4 falls within the majority of values for consolidated sandstones listed in Hurtado et al.'s table. The value of 2.1 for the pore-size distribution of relatively loose ROM salt during the T1 time period was estimated by simply tripling the value for T3. This value lies within the majority of values listed for loose sand in Hurtado et al.'s table.

5.0 TWO PHASE FLOW PROPERTIES IN THE PCS DRZ

5.1 Introduction to Two-Phase Flow in a DRZ

The damage zone comprising the DRZ will have discrete large, open fractures near the drift walls that quickly grade to the microfractures present within the bulk of the DRZ's volume. As shown in Table 3, the porosity increase associated with DRZ microfracture damage is very low and typically less than 2%. The low porosity increase and the ease of re-mating parted microfracture surfaces under compressive stress combine to promote rapid healing to very low porosities and permeabilities.
5.2 Residual Saturation Modeling Values

Brine and gas are expected to flow in the open fractures in an unhealed DRZ down to very low saturations. Residual brine and gas saturations are therefore expected to initially be low and to increase as the PCS DRZ consolidates and heals under pressure.
For the T0 and T1 time periods, residual brine saturations ranging from 0.05 to 0.1 were selected from the high end of the range of values for salt surrogates listed in Hurtado et al. (1997, Table 3-1). These values do not go to zero because there is expected to be a minimum brine saturation at which flow ceases, even in a network of open fractures. This range will be sampled from a uniform distribution because little is known about the actual distribution. Residual gas saturation for this same time period will be calculated as a function of the sampled residual brine saturation using the relationship
Sgr = (1-Sbr)*0.04
This relationship meets the foregoing physical constraints and assures that the residual gas saturation will always be less than the residual brine saturation but will also not be zero.

For the T2 time period, the residual brine saturation sampled for T1 will be incremented by either 0.1 or 0.2. The incremented amount will be randomly sampled and each amount will be given equal weight. This sampling will assure that the residual brine saturation is greater during T2 than during T1. The increase in residual brine saturation is consistent with a decrease in pore sizes during the DRZ healing process that occurs in the T2 time period. Residual gas saturation during T2 will be calculated as a function of the sampled residual brine saturation using the relationship

Sgr = Sbr*0.5
This relationship meets the foregoing physical constraints and assures that the T2 residual gas saturation will always be less than the T2 residual brine saturation but will be greater than the T1 residual gas saturation.

For the T3 time period, the residual brine and gas saturations will be the same as the residual brine and gas saturations for ROM salt shown in Section 4.5.3. The residual saturations are the same for both ROM salt and the PCS DRZ because both materials are expected to be fully healed at the beginning of time period T3.
5.3 Threshold Pressure and Pore Size Distribution Modeling Values

The Agency's acceptance of the threshold pressure calculation for ROM salt discussed in Section 4.7.3 also applies to threshold pressure calculations for the PCS DRZ. The values assigned to the linear parameter a and the exponential parameter n are consistent with field data for Pt and permeability k over a wide range of values and the Agency therefore accepts the use of these values for the PCS DRZ.

In the T0 and T1 time periods the PCS DRZ will have discrete large and small fractures and fracture networks in a large matrix of relatively tight and intact halite. During these time periods the pore size distribution for the DRZ may be bi-modal. One mode would represent the range of fracture porosity and the other would represent the relatively tight and intact matrix porosity. No data for a DRZ are available for this parameter.  Consequently, data must be adopted from analog materials. The properties of fragmented Fox Hill sandstone in Hurtado et al. (1997, Table 3-2) are most representative of an un-healed DRZ because this sandstone represents a material that includes fractures in a relatively intact matrix. Pore size distribution values from two samples of this sandstone provide an average of 2.27 that will be used for time periods T0 and T1.

During the T2 time period, drift creep closure will cause the ROM salt PCS to impose considerable back pressures on the DRZ, causing DRZ fractures and fracture networks to eventually close and heal. However, it is more representative of the T2 time period to assume that some fractures are not completely healed and an intermediate pore-size distribution of 1.4 for the PCS DRZ is used.

At the beginning of the T3 time period, compressive forces from the ROM PCS and drift creep closure will have healed all fractures and fracture networks in the PCS DRZ to values representative of intact halite. Therefore the appropriated `healed' PCS DRZ pore-size distribution will be 0.7, the same as intact halite.

6.0 SUMMARY TABLES OF SEN3 SENSITIVITY STUDY PARAMETER VALUES
A summary of parameter values representing progressive creep closure and salt healing of the ROM salt panel closures is presented in Tables 6 and 7. The parameter values in these tables were intended to be used in EPA's SEN3 sensitivity study. The Agency's initial plan for SEN3 was to model the progressive creep closure of the backfilled waste panel access drifts and surrounding DRZs over time. This approach would have simulated the decreases in porosity and permeability as the access drifts and surrounding DRZs were compressed and consolidated by creep flow of the surrounding halite. However, in an attempt to similarly model progressive creep closure of the WIPP operations and experimental area drifts it was found that WIPP's BRAGFLO Salado flow model could not properly converge when simulating both progressive closure and the capillary effects inherent in the originally proposed parameter values. As a result, the parameter values in Tables 6 and 7 could not be used and the sensitivity study was instead run assuming the ROM salt panel closures and surrounding DRZ were already fully healed to time period T3 intact halite conditions at the beginning of the study. The sensitivity study was also run assuming the operations and experimental area drifts and surrounding DRZs were fully
Table 6. Parameter Values for ROM Salt to be used in the SEN3 Sensitivity Study

                                     Years
                               Porosity[1] ΦROM
                                      (%)
                                 PERMX [1][,2]
                                 kROM  (m[2])
                                 Use equation
k T(x)= 1.5x10-23.5 ΦT(x)[8.5],
 with sampled value of  ΦROM  as the input variable for that time period (Tx).
                                   COMP_RCK
                                   POR_DISP
                                    CAP_MOD
                                     PCT_A
                                    PCT_EXP
                                   RELP_MOD
                                   SAT_IBRN
                                   SAT_RBRN
                                    SROMBR
                              SAT_RGAS[3] SROMGR
                            (a function of SROMBR)
T-0
(-5 to 0)
                                      30
                                     1E-10
                                       0
                                      2.1
                                       2
                                     0.56
                                    -0.346
                                       4
                                     0.95
                                    Sampled
                                  0.1 to 0.2
                                    Uniform
=  (1- SROMBR T0) *0.05
T-1
(0 to 50)
                                    Sampled
                                   7.5 to 20
                                    Uniform
                                  = k(ΦT1),
                            then adjust +- 1 OM[4]

                                  Triangular

                                 Assure that
                                 kT2 <  kT1
                                  = S_HALITE
                                      2.1
                                       2
                                     0.56
                                    -0.346
                                       4
                                      NA
                                     = T0
                                     = T0
T-2
(50 to 100)
                                    Sampled
                                   2 to 7.5
                                    Uniform

                                 Assure that,
                             ΦT1>ΦT2>ΦT3

                                  = k(ΦT2),
                              then adjust +- 1 OM

                                 Triangular[5]

                                  Assure that
                              kT1 >kT2>kT3
                                  = S_HALITE
                                      1.4
                                       2
                                     0.56
                                    -0.346
                                       4
                                      NA
                                   Sampled
                           = T1 + either 0.15 or 0.2
                             = (1- SROMBR T2) *0.2

T-3
(100 to 10,000)
                                 = ΦS_HALITE
                                  = kS_HALITE
                                  = S_HALITE
                                      0.7
                                       2
                                     0.56
                                    -0.346
                                       4
                                      NA
                                  = T2 + 0.25
                             = (1- SROMBR T3) *0.8
1 For each vector, assure that both porosity and permeability always decrease with time.
[2] Sample for ΦROM as an input variable for that time period to derive kROM for that same time period.
3 SROMGS is a function of SROMBR at all times.
4 OM = Order of magnitude
5 Mode of triangular distribution for kROM is the calculated value of kROM
PERMX = PERMY = PERMZ

 Table 7. Parameter Values for the PCS DRZ to be used in the SEN3 Sensitivity Study

                                     Years
                              Porosity ΦDRZ [1]
                                      (%)
                                   PERMX [1]
                                     kDRZ
                                    (m[2])
                                   COMP_RCK
                                   POR_DISP
                                    CAP_MOD
                                     PCT_A
                                    PCT_EXP
                                   RELP_MOD
                                   SAT_IBRN
                                   SAT_RBRN
                                    SDRZBR
                               SAT_RGAS 2 SDRZGR

T-0
(-5 to 0)
                                    Sampled
                                 = 1.6 +- 1.0
                                    Uniform
                                    Sampled
                                 =  6x10[-15]
                                  +- 1 OM[3]
                                  Loguniform

                                  = S_HALITE
                                     2.27
                                       2
                                     0.56
                                    -0.346
                                       4
                                     0.95
                                   Sampled
                                 = 0.05 to 0.1
                                    Uniform
                             = (1-SDRZBR T0) *0.04
T-1
(0 to 50)
                                     = T0

                                     = T0

                                   =S_HALITE
                                     2.27
                                       2
                                     0.56
                                    -0.346
                                       4
                                      NA
                                     = T0
                                     = T0

T-2
(50 to 100)
                                  =  DRZ_PCS

                              Assure that ΦDRZ

                                T1>T2>T3

                                  = DRZ_PCS

                               Assure that kDRZ

                                T1>T2>T3

                                  = S_HALITE
                                      1.4
                                       2
                                     0.56
                                    -0.346
                                       4
                                      NA
                           = T1 + either 0.1 or 0.2
                                = SDRZBR T2*0.5
 T-3
(100 to 10,000)
                                  = S_HALITE
                                  = S_HALITE
                                  = S_HALITE
                                      0.7
                                       2
                                     0.56
                                    -0.346
                                       4
                                      NA
                                 = T3 ROMBR