### Date: June 7 , 2012 Operated for the U.S. Department of Energy by the Sandia Corporation Defense Waste Management Programs 4100 National Parks Highway Carlsbad, New Mexico 88220 

### To: Paul Shoemaker

From: R. Chris Camphouse (6211)

Technical Review: Dan Clayton

QA Review: Shelly Nielsen

Management Review : Janis Trone
Subject: An overview of the BRAGFLO two

- phase flow parameters used to model the run

- of

mine salt panel closure s implemented in the PCS

- 2012 PA Introduction

BRAGFLO Version 6.0 is the WIPP PA code used in the PABC

- 2009 to calculate brine and gas flows in and around the repository. Version 6.0 is the most recent qualified version of BRAGFLO, and is the code version that will be used for the PCS

- 2012 PA. BRAGFLO assumes a n i mmiscible water/gas system ( Nemer 2007)

. Immiscible fluids are not capable of mixing and have interfaces across which pressure discontinuities exist. This interfacial tension produces a capillary pressure between the water and gas phases. C apillary pres sure modeling is a component of the overall flow m odeling implemented in BRAGFLO

.
This memo describes the two

- phase flow model and the parameters associated with the run

- of

- mine (ROM) salt panel closures to be implemented in the PCS

- 2012 (Camphouse et al 2012)

. Generally, the
two

- phase flow flags used in BRAGFLO specify the relative permeability model and whether the capillary pressure model is to be used or not for a given material

. Capillary pressure, which is a function of saturation and threshold pre ssure , is used to constrain the brine and gas pressures. Parameters associated with these models must be chosen carefully as they can cause BRAGFLO numerical difficulties. In particular, capillary pressure modeling in BRAGFLO typically causes numerical di fficulties when materials undergo instantaneous changes in permeability. Capillary pressure modeling in BRAGFLO is often disabled for these kinds of materials.

BRAGFLO Capillary Pressure Modeling
Several PA parameters are used as part of the capillary pressure modeling imple mented in BRAGFLO.
T he threshold capillary pressure, P T , characterizes the point at which gas, the non wetting phase
, can start to flow in the porous media saturated with brine , and thus defines the capillary pressure at 100%brine saturation . The capillary pressure must exceed the threshold capillary pressure before the gas

phase can start to drain the porous medium and flow.

Th ere are two BRAGFLO material parameters that are used to calculate the threshold capillary pressure for a given material. These two parameters are named PCT_A and PCT_EXP. In BRAGFLO, t he practice has been to correlate the threshold capillary pressure to permeability according to ( Vaughn 1996)

P T = PCT_A * k PCT_EXP , ( Equation 1)

where k is the brine permeability (m 2 ) in the x direction. A capability was included in BRAGFLO during the preparation of the CCA that provided a dependence of threshold capillary pressure on dynamic changes in permeability. The database parameter KPT is use d as a flag that provides an instruction to BRAGFLO to dynamically update the threshold capillary pressure as k changes temporally. Setting KPT = 1 allows threshold capillary pressure to be updated if permeability changes in the material. The q uantity P T is not updated when KPT is set to 0. KPT has been set to 0 for all BRAGFLO materials in the CCA and every PA performed since , so t hreshold capillary pressure has never been dynamically updated in WIPP
PA.
BRAGFLO solves a system of two mass balance equa tions for brine pressure and gas saturation as well a s two constraint equations for saturation and capillary pressure in the calculation of two

- phase flow ( Nemer 2007 ). Instantaneous changes in permeability , due to material changes in a grid region, cause difficulty in numerically satisfying the convergence criterion for the capillary pressure constraint equation. When the convergence criterion cannot be satisfied , the capillary pressure model is disabled for the responsible materials so that a convergent solution can be obtained from BRAGFLO. The flag for this is to set PCT_A = 0 , which results in t he capillary pressure component be ing disabled. When this occurs, t he convention is to also set PCT_EXP = 0.

BRAGFLO grid regions used to represent the ROM salt panel closures in the PCS

- 2012 will undergo instantaneous changes in p ermeability. Specifically, the permeability prescribed to these BRAGFLO grid regions will change instantaneously at 100 and 200 years as closure materials change from PCS_T1 to PCS_T2 and from PCS_T2 to PCS_T3 (Camphouse et al 2012 ). It is currently planned that capillary pressure modeling will be enabled for these materials. However if numerical convergence difficulties
are encounter ed in BRAGFLO , then capillary pressure modeling will be disabled for them.

In addition to properties PCT_A and PCT_EXP, each material in BRAGFLO has a flag named CAP_MOD associated with it. A value of 1 or 2 is prescribed to CAP_MOD in WIPP PA for all BR AGFLO materials . As illustrated in the BRAGFLO Version 6.0 User’s Manual (see e.g. F igure 18 and Figure 19 ) , capillary pressure can be unbounded as a function of brine saturation, depending on the relative permeability model employed. A value of CAP_MOD = 2 results in the capillary pressure being bounded above by a maximum value which is assigned to material property PC_MAX . PC_MAX is 1 x 10 8 Pa by default for all materials in BRAGFLO. T he convention used in WIPP PA is to set CAP_MOD = 1 for materials that have capillary pressure disabled, and to set CAP_MOD = 2 otherwise. That is, CAP_MOD = 1 for materials that also have PCT_A = 0. Thus, all BRAGFLO materials in which capillary pressure is used have a default value of 1 x 10 8 Pa specified for PC_MAX (and have since the CCA)

.Property CAP_MOD is denoted as KPC inside the actual BRAGFLO Fortran code. T here is a capillary

pressure model number 3 (KPC = 3) include d in the BRAGFLO Fortran code in which a minimum brine
pressure i s defined , denoted by P0_MIN. However, while the c apillary pressure model 3 (CAP_MOD = 3) was developed and coded in BRAGFLO in preparation for the original certification of WIPP, it has never actually been used in any PA, including the original certifica tion PA

. Even though CAP_MOD = 3 has never been used in PA, BRAGFLO still expects a value to be specified for P0_MIN for all materials , so all BRAGFLO materials have a prescribed value of 1.01325 x 10 5 Pa for property PO_MIN,
A summary of the parameters used in BRAGFLO capillary pressure modeling is provided in the following bul leted list and Table 1 :
In WIPP PA, threshold capillary pressure is define d by Equation (1). The threshold capillary pressure is constant, based on the initial permeability of each material, and has never been dynamically updated as a function of temporal permeability changes. Material property flag KPT has been set to 0 for al l BRAGFLO materials since the CCA. Capillary pressure modeling is disabled by setting PCT_A = 0

. The convention used in PA is to set PCT_EXP = 0 when PCT_A = 0. The convention used in PA is to set CAP_MOD = 1 for materials that have the capillary pressure model disabled. CAP_MOD = 2 corresponds to capillary pressure being bounded above by PC_MAX. All BRAGFLO materials have a value of PC_MAX = 1 x 10 8 Pa prescribed to them

. CAP_MOD = 3 corresponds to a capillary pressure model that depends on the minimum brine pressure P0_MIN. This model has never been used in any PA, including the original certification PA. BRAGFLO still expects a value to be specifi ed for P0_MIN for all materials, however. The value used for P0_MIN is 1.01325 x 10 5 Pa.



### Table 1 : Parameters Used for BRAGFLO Capillary Pressure Modeling

Property Description Value C apillary Pressure Model E nabled Value

Capillary Pressure Model Dis abled PCT_A Threshold Capillary Pressure

Linear Parameter Material Dependent Nonzero Value 0 PCT_EXP Threshold Capillary Pressure

Exponential Parameter Material Dependent Nonzero Value 0 CAP_MOD Capillary Pressure Model Number 2 1 PC_MAX (Pa) Maximum Allowable Capillary

Pressure 1 x 10 8 1 x 10 8
KPT Flag for Permeability Determined

Threshold Capillary Pressure 0 0 P0_MIN (Pa) Minimum Brine Pressure for

Capillary Pressure Model 3 (CAP_MOD = 3 has never been used in PA) 1.01325 x 10 5 1.01325 x 10 5BRAGFLO Relative Permeability Modeling

The relative permeability model associated with a given material in BRAGFLO is specif ied by property RELP_MOD. BRAGFLO panel closure materials have been given a value of RELP_MOD = 4 in WIPP PA

. RELP_MOD = 4 corresponds to the Second M odified B rooks

- Corey M odel illustrated in Figure 20 of the BRAGFLO Version 6.0 User’s Manual (Nemer 2007) and the discussion pertaining to that figure. In this model, capillary pressure is a function o f the effective saturation which depends on the current brine saturation and both the residual brine an d gas saturation s

. The model also depends on a pore size distribution parameter, denoted as property PORE_DIS in WIPP PA. The run

- of

- mine (ROM) salt panel closures implemented in the PCS

- 2012 PA , specifically materials PCS_T1, PCS_T2 , and PCS_T3, will be assigned a value of RELP_MOD = 4.
The DRZ has two components for the PCS

- 2012 PA: DRZ_1 and DRZ_PCS. The DRZ region ove rall (i.e. material DRZ_1) used a va lue of RELP_MOD = 4 in the PABC

- 2009

. DRZ_PCS model s the healed DRZ above and below panel closures , and also uses RELP_MOD = 4

. The material properties assigned to material DRZ_PCS are exactly the same as those used for material DRZ_1, with the exception of permeability. The permeabilities are defined by the ir logarithm in the x, y, and z directions, and denoted by PRMX_LOG, PRMY _LOG, and PRMZ_LOG, respectively ( Stein 2002)

. Materials DRZ_1 and DRZ_PCS will also be used in the PCS

- 20 12 PA, and will use the same relative permeability model (R ELP_MOD = 4 ) and permeability parameters as used in the PABC

- 2009

.
References

Camphouse, R., Gross, M., Herrick, C., Kicker, D., and Thompson, B. 2012. Recommendations and Justifications of Parameter Values for the Run

- of

- Mine Salt Panel Closure System Design Modeled in the PCS

- 2012 PA. Memo to WIPP Records Center dated May 3, 2012. Sandia N ational Laboratories. Carlsbad, NM. ERMS 557396

. Nemer, M. 2007

. WIPP PA User’s Manual for BRAGFLO, Version 6.0

. Sandia National Laboratories. Carlsbad, NM. ERMS 545016.
Stein, J. 2002. Parameter Values for new materials CONC_PCS and DRZ_PCS. Memo to Kathryn Knowles dated February 13, 2002. Sandia National Laboratories. Carlsbad, NM. ERMS 520524

. Vaughn, P. 1996. KPT Modeling Feature. Memo to Martin Tierney dated February 19, 1996. Sandia National Laboratories. Carlsbad, NM. ERMS 235271

.