llll IIII1 iiII1 - Digital Library/67531/metadc627427/m2/1/high_re… · q30 --SAN D93-7007 Distribution Unlimited Release Category UC-721 Printed October 1993 The SECO Suite of Codes

lllll_IIII1_iiII1_

q30 --

SAN D93-7007 Distribution

Unlimited Release Category UC-721Printed October 1993

The SECO Suite of Codes forSite Performance Assessment*

Patrick J. Roache

Ecodynamics Research AssociatesP.O. Box 9229

Albuquerque, NM 87119

ABSTRACT

Modeling for Performance Assessment of the Waste Isolation Pilot Plant (WIPP) has led todevelopment of the SECO suite of codes for groundwater flow, particle tracking, and transport.Algorithm and code developments include the following areas: facilitation of grid convergence tests inmultiple domains; correct treatment of transmissivity factors for unconfined aquifers; efficientmultigrid algorithms; a formulation of brine Darcy flow equations that uses freshwater head as thedependent variable; boundary-fitted coordinates; temporal high order particle tracking; an efficient andaccurate implicit Finite Volume TVD algorithm for radionuclide transport in (possibly) fracturedporous media; accurate calculation of advection via a flux-based modified method of characteristics;and Quality Assurance procedures.

* Work performed under Contract Number 87-6727 for Performant;e Assessment Division (6342),Sandia National Laboratories.

MASTER_._.

I31gilRi_Uf,(j,t_ (..;;i-:l Piii:. b,...'...,_.;;.,',L?,_i i_ UNLIMITED

PREFACE

This SAND report is a reproduction of the identically titled paper published in:

America,. Nuclear Society and American Society of Civil Engineers. High-Level Waste Management:Proceedings of the Fourth Annual International Conference in Las Vegas, NI,', April 26- 30, 1993.American Nuclear Society, La Grange, IL; American Society of Civil Engineers, New York, NY.

iii

THE SECO SUITE OF CODES

FOR. SITE PERFORMANCE ASSESSMENT *

Patrick J. Roache

Ecodynamics Research AssociatesP.O. Box 9229

Albuquerque, NM 87119(505) 843-?445

ABSTRACT regional and local grid simulations; 2-D and 3-D, carte-sign and boundary-fitted coordinate versions; confined

Modeling for Performance Assessment of the Waste (._rtesian) and unconfined (,water table) conditions, in-Isolation pilot Plant (WIPP) has led to development eluding recharge of dry cel_s mad correct treatment ofof the SECO suite of codes for groundwater flow, parti- transmissivity factors; parameterized climatic variations;cle tracking, and transport. Algorithm and code devel- options for node-on-boundary or cell-edge-on-boundaryopments include the following areas: facilitation of grid configurations; spatial grid packing near features; timeconvergence tests in multiple domains; correct treatment step packing near events; automatic time-step error esti-oftransmissivityfactorsforunconfinedaquifers;efficient marionandadaptivetimestepping;semicoarseningmulti-multigridalgorithms;a formulationofbrineDarcy flow gridsolversforefficiency;and highorderaccuracypar-equationsthatusesfreshwaterhead as the dependent ticletracking.The two-phaseflowproblemsincludethevariable;boundary-fittedcoordinates;temporalhighor- followingfeatures:multicomponentchemistry;unusuallyder particletracking;an efficientand accurateimplicit highcapillarypressuresinverytightformations;complexFinite Volume TVD algorithm for radionuclide transport geometries; and super-critical pressures, above the ther-in (possibly) fractured porous media; accurate c_cula- modynamic dome. Modifications to existing FDM andtion of advection via a flux-b_cd modified method of FEM. codes, as well as development of new codes wherecharacteristics; and Quality Assurancc procedures, necessary, have been accomplished. Verification bench-

INTRODUCTION marking exercises and QA (Quality Assurance) aspectsof the software project are significant factors.

As authorized by Congress (Public Law 96-164, 1979),the U.S. Department of Energy (DOE) is developing the SECO-FLOW CODESWaste Isolation Pilot Plant (WIPP) as a facility for the The SECO-FLOW codes [27, 29] perform groundwa-management, storage, and long-term disposal of defense- ter hydrology simulation by solving the time-dependentrelated transuranic (TRU)wastes. Use of the WIPP for partial differential equation for hydraulic head using awaste disposal is contin.gent on performance, assessments, fully implicit formulation. The guiding philosophy for the(PA) to evaluate compliance with applicable regulatmns SECO codes is to produce solutions of verified accuracy ;of the U.S. Environmental Protection Agency. to utilize modern structured programming; to design for

The WIPP is a full-scale mined geologic repository future maintenance; to make the basic problem defini-for TRU radioactive waste located in southeastern New tion efficient; to make the perturbed problem definition

efficient (e.g. for parametric sensitivity studies}; to facil-Mexico, 655 meters below the surface in 255 million year itate grid convergence studies; and to faciiitatelocal areaold salt deposits. Under support from Sandia National simulations within the larger regional area simulation.Laboratories, Ecodynamics has been involved for severalyears in the Computational Fluid Dynamics (CFD) rood- An important aspect of this philosophy is the decou-cling for performance assessments of the disposal system, piing of the problem definition (rock properties, bound-Compliance with environmental regulations requires con- ary conditions, well descriptions, etc.) from the com-sideration of future inadvertent intrusions due to resource putational grid, and of the problcm discretization in theexploration, and significant gas production in waste ma- regional computational grid from the local computationalterial due to corrosion, bacterial action, and radiolysis, grid, both in space and in time.Performance assessment [10] results in a CCDF (Com-plimentary Cumulative Distribution Function) curve for Additional features include: general boundary con-normalized cumulative releases to the accessible enel- ditions; time truncation error estimation and solutionronment. The modeling problems include single phase adaptive time step; parameterized boundary conditionDarcy flow in the overlying aquifer, and two-phase Darcy variations; confined or water table conditions with cor-flow in the collapsed rooms containing the waste. The rect recharge of dry cells; flexible specification of initial

conditions, boundary conditions, rivers/lakes; variableSECO (Sandia - ECOdynamics) single-phase groundwa-ter flow codes developed include the following features: density and viscosity due to variations in salt concentra-decoupling of the problem definition (,_quifer properties, tion; high accuracy particle tracking via adaptive O(At) sboundary conditions, weUs/from the computational grids; algorithms; efficient semi-coarsening multigrid solvcrs.

.Thc work dcscribcd in this report was performed for Sandia National Laboratories under Contract No. 87-6727.

Animation display of time-dependent 2-D head con- The difference between any two _st-order solutions is it-tours and particle tracking is provided by the SECO- self a first-order accurate error estimator, provided thatVIEW code built for the Silicon Graphics IRIS 4D-25 we accept the premise, not rigorously proven for finiteworkstation, difference or finite volume methods [17]but well estab-

lished by experience for parabolic problems, that the so-Enhancement modules already built and verified in- lutions from a locally O(At '_ method are globally O(At m

elude: 2-D and 3-D non-orthogonal feature-adapted gridgeneration [15]; 2-D and 3-D tensor conductivity in non- also.) The method is very cheap to implement becauseit does not require smother implicit matrix solution, nororthogonal grids [15]; 3-D animation display of head con- even another explicit stencil evaluation. However, it doestours and particle tracking; and brine transport coupled not include the effects of time-dependent boundary con-to Darcy flow. Versions and enhancements to be com- ditions or wells, lt is also used in an adaptive time steppleted in the near term include non-zero Reynolds num- algorithm.ber (Forscheimer) effects and a 3-D stretched cartesiancode. Enhancements to be completed in the far terminclude: automatic estimation of spatial discretization Transmissivity Factors for Unconfined Aquiferserror via completed Richardson extrapolation; and non-orthogonal feature-adapted grid solutions. The SECO-FLOW codes correct an error found in (at

least) two commonly used groundwater flow codes in theFacilitation of Grid Convergence Tests in Multiple treatment of transmissivity factors (TF) for unconfinedDomains

aquifers (water table conditions). TF for a computationalcell is simply the fraction of the cell vertical thickness

Grid convergence tests, or other reliable truncation occupied by water. The inter-cell volume fluxes drivenerror estimators, are important to amyCFD project (e.g., by head (pressure) gradients as obtained from Darcy'ssee [15, 16]). Unfortunately, in groundwater flow model- law must be reduced by TF appropriately averaged atcell faces. Inter-cell conductance terms are typically ob-ing (as i_ other geophysical studies) such elementary buttime-consuming exercises are exceptional. Unavoidable t_ined by harmonic averaging. The motivation for usingharmonic averaging is very strong in l-D, giving the ex-uncertainty in the governing physical parameters is of- act answer for piece-wise constant properties. The errorten used as the rationale for neglecting grid convergence comes from applying harmonic averaging not only to con-tests. The WIPP PA group tries to improve accuracy ductances but also to the transmissivity factors. This iswhenever possible, not simply a matter of choosing between two different

Accordingly, considerable effort has been expended but consistent discretizations; the harmonic averaging ofin the SECO codes to facilitate the performance of grid transmissivity factors is wrong.

convergence tests by the users. Although these features This is easily shown by considering a de-watered cell,involve few algorithmic innovations, they represent a con-siderable improvement and departure from traditional for which TF = 0. Then application of harmonic averag-ing gives TF = 0 at all the faces of that cell, regardlessgroundwater code design. The SECO codes use two do- of 'IF values in neighboring cells. Now all conductancesm_ns, a local grid embedded in a larger regional grid. into the cell are zero, and the head (pressure) can neverThis allows both higher resolution in the local grid di-rectly over the repository, and closer alignment of grid change. Even though neighboring cells might developarbitrarily large heads, no flow can occur into the cell,boundaries with natural features particular to the site. which is now permanently de-watered. The rational and

The aquifer properties are defined in a separate dis- simple solution is to use harmonic averaging only for thecretization (called the aquifer-defining grid) which is not other terms in the conductsmces, but to use linear aver-used for computation. The properties on the computa- aging for the transmissivity factors.tional grids (local and regional) are then obtained auto-matically byinterpolation using a conservation-preserving Multigrid Algorithmsinterpolation method of Dukowitz [28], enhanced by P.Knupp to handle unaligr.ed boundaries. Solution of the implicit matrix equation by direct LU

Likewise, boundary conditions are not specified in the decomposition is still used in many groundwater codes,computational grids but in the continuum, and the loca- in spite of its intimids.ting operation count, especiallytion and properties of production wells, recharge wells, in 3-D. This is another reason for the coarse grids typi-and surface water features (lakes/rivers) are defined only cally used. The potential for gains in efficiency by imple-once in map coordinates, menting multigrid methods were clear, and have indeed

been realized, but only with considerable developmentTime Error Estimation effort. The primary difficulty is the enormous range of

matrix coefEcients. This is due to both variable gridspacings and to the unusual range of physical parame-

The most reliable method of establishing convergence ters which must be considered in the probabalistic inves-in discretization error is the performance of systematic tigation of uncertainties for WIPP Performance Assess-grid convergence tests in space and time. Tne SECO ment (using Monte Carlo techniques with Latin Hyper-code design philosophy is to facilitate such tests, _ noted cube Sa_mpling). Not only is the range enormous, (e.g.above. The codes also include an inexpensive time errorestimator, using the difference between backward and for- six orders of magnitude in conductivity) but the spatialward time inter:ration, implemented as an extrapolation, variation is not necessarily monotone.

S. Schaffer [18[ has developed semicoarsening multi- VE- (O,O,_E/dz) (5)grid algorithms in "2-D and 3-D for the single phase Darcyflow problem (with a Symmetric Positive Definite or SPD Brine concentration also enters into the evaluation of Kmatrix) which are robust and achieve true multigrid per- through viscosity/z. The brine continuity equation !s justformance, even with 12 orders of magnitude variation in

coel_cients, and proved tobe less sensitive to computer Sail! V (6)round-off errs'." accumulation than line SOR, J. Ruge u_ =

$

and S. McCormick also developed variants of AMG (al-gebraic multigrid) methods [19] which were successfully but the specific storativity So depends on true (environ-installed into the STAFF2D [20] finite element code, but mental) head for a.n unconfined aquifer. We assume S, isthe AMG solvers have not proven to be as robust as de- not affected by brine concentration.

The combined equations (4) and (6) are convenientsired on problems with large property variations, in the interior, but some of the appeal may be lost when

The two-phase flow problem at the repository itself boundary conditions are considered. There still is an in-(caused by brine flow in the Formation and gas genera- herent appeal to formulating the equations in such a waytion from the waste) has additional difficulties because a as to isolate the effect of a physically small perturbation.system of two nonlinear equations is involved, Newton- However, we stress that this is not a "small perturbation"Raphson llnearization is used, the ranges of grid spacings equation, in spite of the fact that it looks reminiscent ofand cell aspect ratios are extreme, and again physical the Boussinesq approximation. There is no approxima-l:,arameters vary over orders of magnitude. After much tion involved. Also, to allay the concerns of readers whowork, J. Ruge and J. Jones achieved multigrid perfor- know of misinterpretations caused by [21], we emphasizemance using semicoarsening, that there is nothing mathematically significant, about

using freshwater head as the dependent variable, asideBrine Darcy Flow in Terms of Freshwater Head from convenience of interpretation. Freshwater head in

this formulation is just a normalization of pressu_ e usingthe density of fresh water. The density of mercury could

The use of hydrauhc head, rather than pressure, as just as well have been used, and the equations would stillthe dependent variable in constant density Darcy flow be valid.codes has advantages, not the least of which is that headcan be measured directly in the field. Also, head being Boundary-Fitted Coordinatesthe sum of pressure and elevation, it is the gradient of

head, not pressure, which causes flow. Modules have been developed [15]. for non-orthogonalHowever, for a variable density code, e.g. includ- boundary-fitted (or feature-fitted) discretizations of the

ing variable (unsaturated) brine concentration, pressure head equations. Although the use of non-orthogonal co-is used virtually universally. The well-known paper by ordinates in finite difference and finite volume discretiza-Lusczynski [21] indicates that, even for variable density tions is now commonplace, we paid attention to severalflows, the horizontal flow is driven only by gradients in special aspects of the present problems, notably tensorfreshwater head. Although true, we find this mislead- properties with step discontinuities, strict conservation,ing (like some other theorems). It is true for 3-D flows demonstrated convergence [15], and symmetry. A sur-but only for strictly horizontal coordinates in quasi-2-D prising result by S. Steinberg [24] is a proof that matrixcodes, whereas real aquifers have some dip. symmetry cannot be maintained for a nearest-neighbor

discretization in agrid that is non-orthogonal at a bound-Nevertheless, we find some advantage in formulating ary where Robin (mixed) boundary conditions are crnl-the variable density flow equations using freshwater head

as the dependent variable. This results l'n the addition of unfed to second order accuracy.a bouyancy term involving brine to the usual Darcy equa- Near term enhancements to the SECO-FLOW codestion. With z vertical (colinear with g), define freshwater now also include full tensor conductivity and non-zerohead as Reynolds number (Forscheimer) effects, and plan for

special 2-D enhancements such as aquitard leakanceShavebeen dropped in favor of the full 3-D code, presently un-

H I = P/(p, [g 1) + E (1) der verification.

where P is pressure, Pt is freshwater density, and eleva- SECO-TRACKER

tion E is measured along z. Define the usual hydraulic The SECO-TRACKER code is built to provide tem-conductivity poral high-order particle tracking.

K =-klglpj/# (2) For particle tracking, the SECO-TRACKER codesRun e Kutta Feh_Iberuse a g_- - g ODE integrator [221 com-

and the density perturbation bined withlinear velocity interpolation in space and timeto produce particle tracking with verified accuracy [15]

2 5e = (p- Pf)/Pl. (3) of O((Az) ,(At) ). This may appear to be inconsistent

with the flow field accuracy, but is in fact justifiable.Then the Darcy equation with bouyancy (brine) usingfreshwater head is In an intercomparison study of radionuchde transport

codes [23], surprising variability occured in particle track-V = -K[VH_ + eVE] (4] ing results, much more so than the variability in pressure

and velocity fields. Although this poo: perf,',imance was must be treated carefully.noted several times in the analyses of results, no men-tion was made in any of the calculations about the par- Governing Equationsticle tracking algorithms. One might assume that theparticle tracking was performed with algorithms anal-ogous to those used for the Darcy flow solutions, i.e. The radionuclide transport problem consists of NO((Az)2,(At)) or perha.ps O((Az)2, (At) 2) at most. species equations, k = 1,... ,N:

Although plausible at first glance, further thoughtsuggests that this may be inadequate. The trap is that V. [DVCj, - VC_,] = CRk OCk-Ot + CRk)_Cj,the flow codes are Eulerian, whereas the particle track-ing is intrinsically Lagrangian. For a steady Eulerian - ¢Rk-t,X_,-lCk-i - QCk - F_ (7)velocity field with linear vaxiation in space, there is zerotime truncation error in the velocity field. Yet the (La- where the dependent variables are Ck, the concentration

of the k-th radionuclide. Physical parameters includegrangian) solution for paxticle position involves exponen- D(x, t), a 2 x 2 hydrodynamic dispersion tensor (velocity-tim functions in time. The higher time vaxiability of par-ticle position, compared to Eulerian velocity fields, justi- dependent), V(x, t), the Darcy Velocity, ¢(x), the frac-ties the use of higher accuracy tracking algorithms. See ture system porosity, Rk, the retardation coefficient, ,_,also [30]. the species decay constant, and Ck, the concentration of

the k-th injected radionuclide. The well injection rateSECO..TRANSPORT is Q. Detailed physical descriptions of these terms can

An implicit TVD schen'e h_ been developed to solve be found in [1, 2]. A double-porosity (dual-continuum)the two-dimensional radionuclide transport equation irl model [3, 4, 5] requires the additional source term Fk toa (possibly) fractured porous medium [14]. The scheme represent the flux due to the exchange of contaminantuses a finite volume staggered mesh. The 2-D governing between the fracture and matrix domain. The N equ_-equation is solved using an efficient Approximate Factor- tions are linear and, in the earlier code, wer,_ sequentiallyization procedure with an implicit treatment of boundary coupled. A general Robin boundary condition is used,conditions. This method has been applied to test prob-

lems and was verified to be be second order accurate in aCj, + flOCk,space and time for both high and low mesh Peclet hum- On =: ")' (8)hers.

on a planar rectangular domain f2. For various choiceNumerous codes solve the solute transport equations. ' " " " uof a(x), ft(x), and 7rx), one may obtain Dmchlet, Ne -

Many were written over ten years ago and use outdated mann, or Cauchy Boundary conditions on different por-numerical algorithms and coding practices. Typically, tions of the boundary. For example, the commomy usedthese older codes use upstream differencing, which is iri- flux boundary condition isaccurate, and direct (banded) solvers, which are ineffi-cient. In contrast, the SECO-TRANSPORT code uses VCk- D_Ck = Vf(t.) (9)an implicit TVD scheme with three-level time differenc-

ing and directional splitting to produce an efficient code where / is a known function.that is also second-order accurate both in time and space.Problems with moderately-high Peclet number greatly The flow-field V is assumed to be independent ofbenefit from this scheme by avoiding spurious oscilla- the solute concentration. It is essential that the flowtions commonly associated with the central differencin_ field be consistent with the advection differencing used inschemes or the excessive numerical diffusion associated SECO-TRANSPORT; otherwise, false source terms can

with upstream differencing. The long time-scales of the result. With the wide range of parameters sampled inproblems to which the code is to be applied dictate the the WIPP PA project, single precision VAX calculationsuse of fully-implicit _lgorithms. were marginal. In WIPP practice, the flow-field is ob-

" tained from the SECO-FLOW code in double precision.This AF/TVD algorithm originally developed for aero-

dynamics problems required significant adaptions to the The Transport Algorithmfinite volume (or block-centeredfinite difference) grid, es-pecially in regard to ghost cells, cross-derivative terms,and velocity locations staggered with respect to concen- The transport algorithm developed by Salari [14] usestrations (which proved to be advantageous for TVD). The a finite volume mesh (with ghost cells) where fluxes arefinite volume (or block-centered finite difference) grid evaluated at cell faces and concentrations at cell centers.makes SECO-TRANSPORT compatible with the SECOflow codes, and with MODFLOW [31] and SWIFT II Equation (7) is transformed into a stretched Cartesiancoordinate32], whereas the STAFF2D finite element formulationnvolved an inconsistency with these. I_ --'z 7",

The relevant partial differential equation contains ad- z = z((), (10)vection, dispersion, adsorbtion, source, and decay terms.Mesh Peeler numbers of order one in the nominal case y --- y(r/)

and of order ten in the extreme case are expected in the where metric transformations are _ = dy,_, flu = dz_,present application, indicating that the advection term and d = _,%. The transformed equation, with further

algebraic manipulations, was put into a strong conserva- Table 1: Partial list of schemes available

tion form [6] to ensure mass conservation which is essen- "'0 _o Schemes Truncation errorSial here. The transformed equation is given by 1 0 Baler, implicit O( At )

_t 0 0 - { 0 Trapezoidal, implicit O( At 2 )l 3-point-bac}ward, implicit O( At _ )eR_ (Ck)+bTC_)+ = 1 i

0 . 0 . O 8

At

+CRk:_ + CR___a___O,__+ 0 +fi Oa) +_l-Z_ - F_+ Ct;o_)_+ CE_)_^n.where + (_:i). + CF_,),

k-_+ +fi"]

= -y, i+___[+ eRkAO_-' l (13)

/_ = rh,vC'_, The cross derivative terms are time-lagged to facilitatethe factorization of the right-hand side operator. The er-

j_ _ _Dl_ 0C'j, rot introduced by lagging these terms is corrected throughJ 0_ ' _ intra-time step iteration.

Er.2 _%D1_ 0_Tk The convective t.-rms are modeled using the following= d 0-"_' TVD flux developed for staggered meshes by Sahxri [14_.The flux is a combination of upwind and centered scheme.

F_l = 1

s 0_ E___,_= _(1- ej_,__)[CC_,_+ c__,,_),,L_,__Dm 0(7_, u"L,- r/_ , -(eh-c"

J Or/ _-a,_,) [ i-[,_ []

= Q_____ +_ ___,_(q,_+ c___,_)(_.b__,_,__,_(_4)J ,

g, = -.r where -. 2((.)_,_(_b..,,_2 (_.)_-_,_= (_.)j,,+ (_)__,,_

Equation (11) is solved using an implicit Approximate The function q' is called a limiter function. There are aFactorization procedure [71. The convective terms are number of limiter functions available ranging from verymodeled by TVD [81and the remaining terms by central compressive (Roe superbee) to very dissipative (minmod)differencing. A general two-level implicit finite volume [8].scheme, in delta {orm [7], can be written as After the explicit portion (RHS) of equation (13) has

been evalr _.ed, the solution at the new time level is ob-OAt ., At . ,,

eR_A(7_' = 1+_(¢R_,AC_,)t + _+-_w(¢RkCk)_ tained through the following sequence(I + a=L_)A6'i,_ = RHS, (15)

+I--_(¢R_AO_'-')¢(12) (Z+_L.)A6s,_ = AO,,_, (_6)_"+' "" "" (17)where "-'i.k = Ci., + ACi._,

AC_' = 6"_'+_- 0_' where I is an identity matrix and L,_, L_ are the x andThe AC_' can be thought of as a correction to advance the y operators, respectively. The first sweep in either thesolution to a new time.level (n+l). The time difference x or y direction produces intermediate results, denotedequation (12), with appropriate choice of the parameters by CTi._. The second sweep uses the intermediate results0 and _o, produces many two- and three-level implicit to complete the cycle. The order of the sweep can beschemes as shown in Table 1. Applying equation (12) to symmetrized by alternating the direction. After bothequation CIi) we ha ,. sweeps are complete, the solution is updated.

Th," boundary conditions (Dirichlet, Neumann, at:dRobin)are ali implicitly imple,nented in the 1-D operator

OAt [-(AE")¢ - (A._'"), in both directions. This ensures the second-order accu-eR_A6'_ = 1 +---_ racy of the scheme. Tbe implicit construction of bound-

+ (A/_),, + (AF_). -¢R_,_AC_'] ary conditions requires an intermediate boundary condi-tion for the initial sweep. The intermediate boundary

OAt _E_ )_+ (iF:,).1

Table 2: Convergence results, uniform grid PA transport calculations, even allowing high-resolutionS'ize Az At RMS .....RMS ratio calculations of the effects of clay linings, a problem which

---20x20 .05 .25 7.697E-3 could not be calculated i previous PA's with STAFF2D.

40x40 .025 .125 1.954E-3 3.94 The algorithmic breakthrough consists of a directly80x80 .0125 .0625 4.921E,-4 3.97 coupled (simultaneous, vs. iterative or sequential) solu-160x160 .00625 .03125 1.234E-4 3.99 tion of both the fracture system and matrix equations

within the constrictions of the AF (approximate factor-ization) algorithm. It is analogous to the coupled solutionin STAFF2D, which is itself a fairly complex algorithm.

condition is subtle, and is evaluated by applying either The complicating factors in,the SECO-TRANSPORT al-the x or y operator, depending on the boundary, to the gorithm for incorporation of direct coupling are the stag-equation of the ghost cell. The stencils of these operators gered finite volume mesh (compared to the co-locatedwill be different r.ear the boundaries, variables used in STAFF2D), the use of ghost cells, and

the delta-formulation of the AF algorithm.Transport Accuracy, Single Porosity

With the source term of Equation (7) evaluated asF = -),Dr=, the basic algorithmic steps following Huyakorn

The SECO-TRANSPOP_ code was verified for tem- et. al [4] for the double-porosity solution are as follows.poral and spatial accuracy using an exact solution for anunsteady problem. Details may be found in [14]. Ta- • Algebraically perform forward elimination on dis-ble 2 presents the computed solution at time=25 for four cretized equations to get matrix solution in termsdifferent grid sizes and time steps. By examining the ra- of unknown interface concentration ui.rio of Root Mean Square (RMS) of errors, it is evidentthat the overall solution is secondlorder accurate in time • Express source term as P = ctut +/3, where a andand space. Also in [14] are comparisons with the two- /3 depend on matrix solution.

dimensional convection-dispersion model problem of [9] • Substitute source term in fracture system equation;for both low and moderate mech Peeler numbers (Pe = put ux on operator side of equation.2, 10).

These results are compared to results obtained using • Solve fracture system equations for _.._ each frac-ture system node.imphcit upstream differencing, representative of solutionscomputed by the majority of existing codes. The maxi-mum error usng implicit upstream differencing is about • Perform backward elimination on discretized equa-three times and the RMS about 8 times larger than TVD tions to complete matrix solution.

solution, even for mesh Pe = 2. For moderately high The previously used algorithm [14], like ali sequentialmesh Peclet number, Pe = 10, the difference between the algorithms, was effective only when the coupling betweentwo solutions is dramatic. As expected, the TVD scheme the fracture system and matrix equations was not dotal- -retained a sharp front as opposed to a very diffused front nant. Although each equation was solved efficiently andgenerated by the implicit upstream differencing, stably in the implicit AF algorithm, allowing large time

We have developed an even more accurate transport steps for physically well resolved flows, the s_4uentialalgorithm using a Flux-Based Modified Method of Char- couphng introduced an ezphcit behavior which limitedacteristics (MMOC) methodology thr is fully conserva- the time step. When the coupling dominated, either duetive and allows implementations of various flux limiters to large retardation (R >> 1) or to high resolution ofto avoid spurious oscillations [27, 13]. As yet, it has been the clay linings (Az) << 1 then this exphcit time stepapplied only in 1-D limitation dominated the calculations, reducing the al-

" lowable time step even though the physics became lessTransport E_ciency, Single Porosity consequential, i.e. for R >> 1 the transport shuts down.

The new coupled algorithm solves a somewhat largerCompared to STAFF2D for a single-porosity problem, implicit system than the previous sequential approach,

SECO-TRANSPORT has been benchmarked at 9.6 times but does not require any intra-time step iterations. Evenfaster on a 41x41 grid and 34.5 times faster on an 81x81 for one iteration, the old sequential approach is slower,grid [14]. and for difficult problems it required more than one it-eration. Also, for R >> 1, the new calculation becomes

Direct Solution for the Double-Porosity Equations more stable computationally, even as it does physically.The result is that the previously most difficult cases havenow become the easiest cases.

A major algorithmic development recently built intothe SECO-TRANSPORT code (since [14]) is the direct Performance :or Double Porositysolution for the double-porosity (or dual-continuum) equa.tions. This algorithmic development, with the code run-ning on a modern workstation (IBM Prise/System 0000) With the new algorithm, the complete array of pa-ehminated a former computing bottleneck for the WIPP rameter variations, including highly resolved clay lin-

ings, R >> 1, and dual porosities, are computable, withroughly a factor of 50 increase in speed. (C¢,,npared

to STAFF2D using the same time steps, the new ver- QUALITY ASSURANCE

sion of SECO-TRANSPORT is still roughly a factor of Formal software QA procedures for the WIPP project30 faster.) Some double-porosity cases, with R = 1 are described in [25], and encompass (amongst other tasks)or R > 1, can now be run stably in O(10) time stepswith SECO-TRANSPORT, the same as previously used code Verification studies, establishment oi review com-with STAFF2D. However, as is always the case, accu- mittees, version control, traceability, retrievability, doc-racy must be verified by systematic grid and time-step umentation, etc.convergence studies, which axe now feasible with SECO- SUMMARYTRANSPORT. Note that the operation count for theSECO-TRANSPORT algorithm, which is indicative of This paper has described the SECO suite of codesits execution time, varies optimally with grid size (i.e., for groundwater flow, particle tracldng, and radionuclidelinear with the number of unknowns) whereas the the op- transport, presently used and in ongoing development byeration count for the commonly used direct solvers v,.-ies the WIPP PA. The algorithm and code developments inquadratically, making grid convergence te_:.s expensi, e. the areas of facilitation of grid convergence tests in mul-tiple domains, correct treatment of transmissivity factors

An especially good feature of the ne,_ algorithm is the for unconfined ,_.quifers, efficient multigrid algorithms, ahigh resolution now possible for the clay lining calcula- formulation of brine Darcy flow equations that uses fresh-tions. High resolution r.ear the interface is necessary for wa;er head as the dependent variable, boundary-fittedaccuracy, e.g. 15 nodes in a stretched grid with (Az) = coordinates, temporal high-order particle tracking, an eh1.F_,-06. Like R >> 1, this has the effect _f strongly cou- ficient and accurate implicit Finite Volume TVD algo-piing the fracture system and matrix equations. The new rithm for radionuclide transport in (possibly) fracturedalgorithm allows this calculation to proceed with insignif- porous media, and accurate calculation of advection viaicant penalty in computer time. (A pr,_viously developed a flux-based modified method of characteristics, have ledrepresentation of clay linings by way of a skin resistance to documented significant improvements in both accu-is still a maintained option.) racy and efficiency, making systematic grid convergence

tests feasible, and increasing the confidence in modelingThe 2-D SECO-TRANSPORT, along with the SECO-

FLOW code, has been incorporated into CAMCON [26] computations.(the WIPP PA executive controller _-ystemfor computer Acknowledgement

codes) via a pre- and post-processor af _:,r_;::.chby R. Blaine Thi._ is Sandia National Laboratories report SAND93-lt is now operational and was used !_ the 1992 Prelimi- 7007C. The work was performed for Sandia National Lab-nary Performance Assessment [10], _;.lacing STAFF2D oratories and the United States Department of Energyused in previous years [11, 12]. under Contract DE-AC04-76DP00789.

The verification exercises indicated the importance ofretaining the flow information of the ghost cells, whichare not naturally retained in the CAMCON data base. ReferencesThe post-processor of the SECO flow codes was modi-fied to retain this information. The verification exercises [1] tIuyakorn, P.S. and Pinder, G.F. Computationalbased on the exact solutions have not only demonstrated Methods in Subsurface Flow, Academic Press, New

that the theoretical O((Az. )._,(A_))2 accuracy is actually York, 1983.

attained, but also provide gmdance to the WIPP PA an- [2] Bear, J. and Bachmat, Y. Introduction to Modelingalysts on selection of grid size, grid clustering about thesource (intrusion), time step size, and sensitivity of the of 7_ranspor_ Phenomena in Porous Media, KluwerAcademic Publishers, Dordrecht, Netherlands, 1990.release (integrated mass discharge and pulse shape) to

dispersivities, velocity, porosity, species decay rate, and [3] Streltsova-Adams, T.D. 'Well Hydraulics in Hetero-retardation, geneous Aquifer Formations' Advances in Hydro-

science, Vol. ll,(Ed., Chow, V.T.), pp. 357-423,Computational Dimensionallty Academic Press, New York, 1978.

lt is noteworthy that a 2-D flow problem produces a [4] Huyakorn, P.S., Lester, B.H., and Mercer, J.W.'An Efficient Finite Element Technique for Model-computati_nally 3-D transport problem when the direc- ing Transport in Fractured Porous Media: _;ingletion into the clay lining and matrix blocks is properly Species Transport' Water Res. Res., Vol. 19, No. 3,resolved (i.e., when the analyst does not simply assign pp. 841 -854, 1983.an arbitrary small number of node points in this direc-tion, but actually performs systematic grid convergence [5] Huyakorn, P.S., Lester, B.H., and Mercer, J.W.tests). Likewise, the 3-D S2]CC-FLOW code will give rise 'An Efficient Finite Element Technique for Model-to a 4-D double-porosity transport problem. In addition, ing Transport in Fractured Porous Media: Nuclidethe number of radionuclides present, while not systemat- Decay Chain Transport' Water Res. Res., Vol. 19,ically increased as axe the number of grid points, can be No. 5, pp. 1286-1296, 1983.substantial; presently [10] we are considering 9 radionu-clides. A computation'ally time-dependent 4-D problem [6] Pulliam, T.H. 'Efficient Solutior, Methods for thewith 9 radionuclides run for Monte Carlo analysis, even Navier-Stokes Equations', Lecture Notes for the Vonwith efficient LHS techniques, makes for a computation- Karman Institute for Fluid Dynamics Lecture .%-ally demandin_ study, especially if accuracy is demanded, ties, Brusses, Belgium, 1986.

[7] Fletcher, C.A.J. Computational Techniques for [18] Schaffer, S. 1991. "An Efficient 'Black Box' Semi-Fluid Dynamics, Volumes I and II, Springer-Verlag, coarsening Multigrid Algorithm for Two and Three1988. Dimensional Symmetric Elliptic PDE's with Highly

Varying Coefficients," Proc. Fifth Copper Mountain[8] Yee, H.C. 'Construction of Explicit and Implicit Conference on Multigrid Methods, March 31-April 5,

Symmetric TVD Schemes and Their Applications' 199I. Also, submitted to SIAM Journal of NumericalJ. Comp. Phys., Vol. 68, pp. 151-179, 1987. Analysis.

[9] Javaaadel, I., Doughty, C., az_dTs_mg, C.F. Ground- [19] Ruge, J. and Steuben, K., "Algebraic Multigridwater Transport: Handbook ,f Mathematical Models, (AMG)", IZconiiers in Applied Mathematics, Vol.American Geophysical Union, Washington, D.C., 3: Multigrid Methods, S. McCormick, cd., SIAM,1984. philadelphia, 1987.

[10] WIPP PA (Performance Assessment)Division, Pre- [20] Huyakorn, P. S., White, Jr., H. O. and Panday,liminary Comparison with 40 CFR Part I9I, Sub- S. 1989. "STAFF2D Solute Transport and Frac-part B for the Waste Isolation Pilot Plant, December ture Flow in Two Dimensions", Hydrogeologic, Inc.,I995, Volume I: Methodology and Results. SAND92- Herndon, VA.0700/1, Sandia National Laboratories, Albuquerque,NM. [21] Lusczynski, N. J., "Head and Flow of Ground Wa-

ter of Variable Density", Journal of Geophysical Re-[11] WIPP PA(Performance Assessment) Division, Pre- search, Vol. 66, No. 12, December 1961, pp. 4247-

liminary Comparison with 30 CFR Part 191, Sub- 4256.part B for the Waste Isolation Pilot Plant, DecemberI991, Volume I: Methodology and Results. SAND91- [22] Shampine, L."F., Watts, W. A., and Davenport, S.,0893/1, Sandia National Laboratories, Albuquerque, "Solving Non-stiff Ordinary Differential Equations -NM. The State of the Art", Sandia Laboratories Report

SAND 75-0182, 1975, Sandia National Laboratories,[12] Bertram-Howery, S. G., M. G. Marietta, R.P. Albuquerque, New Mexico. Also, SIAM Review, Vol.

Rechard, P. N. Swift, D. R. Anderson, B. L. Baker, 18, No. 3, pp 376-411, July 1976.J. E. Bean, Jr., W. Beyeler, K. F. Brinster, R. V.Guzowski, J. C. Helton, R. D. McCur_ey, D.K. [23] "The International HYDROCOIN Project, Ground-Rudeen, J. D. Schreiber, and P. Vaughn, Prelimi. water Hydrology Mode_ng Strategies for Perfor-nary Comparison with ,40 CFR Part 19I, Subpart B m_nce Assessment of Nuclear Waste Disposal, Levelfor the Wast, Isolation Pilot Plant, December 1990. 1: Code Verification".SAND90-2347, Sandia National Laboratories, Albu-querque, NM. [24] Steinberg, S. and Roache, P., "Symmetric Operators

in General Coordinates", Ecodynamics Research As-I13] Roache, P. J., "Validation Exercises of a One- sociates, 1990. To be submitted for publication.

Dimensional Flux-Based Modified Method of Char-acteristics", Proc. IX International Conference on [25] Rechetrd, R. P., Roache, P. J., Blaine, R. L.,Computational Methods in Water Resources, Den- Gilkey, A. P., and Rudeen, D. K., "Quality Assur-vet, Colorado, 9-12 June I992, pp. 69-76. ance Procedures for Computer Software Support-

ing Performance Assessments of the Waste Isola-[14] Salari, K., Knupp, P., Roache, P. and Steinberg, S., tion Pilot Plant", SAND90-1240, Sandia National

"TVD Applied to Radionuclide Transport in l,'rac- Laboratories-Albuquerque, April 1991.turcd Porous Media", Proc. IX International Con-ference on Computational Methods in Water Re- [26] Rechard, R. P., "CAMCON: Computer System forsources, Denver, Colorado, 9-12 June 1992, pp. 141- Assessing Regulatory Compliance of the Waste Iso-148. lation Pilot Plant", Proc. Probabalistc Safety and

Management Plan (PSAM) Conf., Beverly Hills,[15] Roache, P. J., Knupp, P. M., Steinberg, S., Blaine, Calif., Feb. 4-7, I991. Elsevier Science publishers,

R. L. 1990. "Experience with Benchmark Test Cases Amsterrdam, pp. 899-904.for Groundwater Flow." A_:ME FED Vol. 93, Bench-mark Test Cases for Computational Fluid D_nam. [27] "Computational Fluid Dynamics Algorithms andics, I. Celik and C. J. Freitas, Eds., Boer No. Codes Developed for WIPP Site Simulations", Com-H00598, June 1990, pp. '19-56. putational Mechanics, Proc. Asian Pacific Conf. on

Computational Mechanics, Hong Kong, 11-13 Dec.[16] Roache, P. J., "Need for Control of Numerical Ac- 1991, Y. K. Cheung, J.H.W. Lee, and A.Y.T.Leung,

curacy", Journal of Spacecraft and Rockets, Vol. 27, eds., A. A. Balkema, Rotterdam, Vol. 2, pp. 1325-No. 2, 1990, pp. 98-102. 1335.

[17] Russell, T. F., and Wheeler, M. F., "Finite Element [28] Dukowitz, J. D., "Conservative Rezoning Algorithmand Finite Difference Methods for Continuous Flows for Generalized Two-Dimensional Meshes", J. Com-in Porous Media", Mathematics of Reservoir Simu- putational Physics, Vol. 59, 1985, pp. 193-199.lation, R. E. Ewing, cd., SIAM Publications, 1983,pp. 35- 106.

[29] Roache, P. J., "Computational Fluid Dynami,:s Al-orithms Developed for WIPP Site Simulatmns",roc. IX International Conference on Computa-

tional Methods in Water Resources, Denver, Col-orado, 9-I2 June 1992, pp. 375-382.

[30] Baptista, A. M., Solution of Advectio_-Dominated7"_ansport by Eulerian-La#rangian Methods using theBackward Methods of Characteristics, Ph.D. Thesis,Dept. of Civil Engineering, M.I.T., 1987.

[31] McDonald, M. G. and Haxbaugh, A. W., A ModttlarThree-Dimensional Finite-Difference Ground- Wa_erFlow Model, Techniques of Water-Resources Inves-tigations of the United States Geological Survey,Book 6, Modeling Techniques, Chapter Al. Scien-tific Software Group, P.O. Box 23401, Washington,D.C. 20026-3041.

[32] Reeves, M., Ward, D. S., Johns, N. D., ;,hd Cran-well, R. M., Theory and Implementation for SWIFTII The Sandia Waste-Isolation Flow,c.nd TransportModel for Fractured Media, SAND8_-l159, SandiaNational Laboratories, Albuquerque, New Mexico,August 1986.

DISTRIBUTION

(Send Distribution list changes to M.M. Gruebel, Dept. 6342, Sandia

National LaboratorJes_ PO Box 5800, Album" _rque, NM 87185-1328)

Fede_lAgencies US Department of EnergyOffice of Environmental Restoration

US Depa"tment of Energy (6) and Waste Management

Office of Civilian Radioactive Waste Attn: S. Schneider, EM-342

Management Trevion II

Attn: Deputy Director, RW-2 Washington, DC 20585-0002Associate Director, RW-IO/50

Office of Program and US Department of Energy (3)Resources Management WIPP Task Force

Office of Contract Business Attn: G.H. Daly

Management S. Fucigna

Director, RW-22, Analysis and B. Bower

Verification Divisiol_ 12800 Middlebrook Rd., Suite 400

Associate Director, RW-30 Germantown, MD 20874

Office of Systems and

Compliance US Department of Energy (4)

Associate Director, RW-40 Office of Environment, Safety and

Office of Storage and Health

Transportation Attn: R.P. Berube, EH-20

Director, RW-4/5 C. Borgstrom, EH-25

Office of Strategic Planning R. Pelletier, EH-231

and International Programs K. Taimi, EH-232

Office of External Relations Washington, DC 20585

Forrestal Building

Washington, DC 20585 US Department of _nergy (6)

WIPP Project Integration Office

US Department of Energy Attn: S. Alcorn

Albuquerque Operations Office W.J. Arthur III

Attn: National Atomic Musenal Library J. Coffey

PO Box 5400 L.W. Gage

Albuquerque, NM 87185 P.J. HigginsD.A. Olona

US Department of Energy (2) PO Box 5400

Office of Environmental Restoration Albuquerque, NM 87115-5400and Waste Management

Attn: Director, EM-I US Department of Energy (2)

C. Frank, EM-50 WIPP Project Integration Satellite

Washington, DC 20585 Office

Attn: Ro Batra

US Department of Energy (3) R. Becket

Office of Environmental Restoration PO Box 3090, Mail Stop 525

and Waste Management Carlsbad, NM 88221-3090Attn: M. Frei, EM-34 / Trevion II

Director, Waste Manageme_it Projects US Department of Energy (i0)

Washington, DC 20585-0002 WIPP Project Site Office (Carlsbad)

Attn" A. Hunt (4)

j US Department of Energy V. Daub (4)

I Office of Environmental Restoration J. Lippisand Waste Management K. Hunter

Attn: J. Lytle, EM-30 / Trevion II PO Box 3090

Washington, DC 20585-0002 Carlsbad, NM 88221-3090

Dist-i

US Department of Energy US Department of Energy (3)

Research & Waste Manageme_l Division Rocky Flats Area OfficeAttn: Director Attn: W.C. Rask

PO Box E G. Huffman

Oak Ridge, TN 37831 T. LukowPO Box 928

US Department of Energy (2) Golden, CO 80402-0928

Idaho Operations Office

Fuel Processing and Waste US Department of Energy

Management Division Los Alamos Area Office

785 DOE Piace 528 35th Street

Idaho Falls, lD 83402 Los Alamos, NM 87544

US Department of Energy US Department of Energy

Savannah River Operations Office Dayton Area Office

Defense Waste Processing Attn: R. Grandfield

Facility Project Office PO Box 66

Attn: W.D. Pearson Miamisburg, OH 45343-0066PO Box A

Aiken, SC 29802 US Bureau of Land ManagementCarlsbad Office

US Department of Energy i01 E. Mermod

Richland Field Office Carlsbad, NM 88220Attn: R.F. Guercia

PO Box 550 / R3-80 US Bureau of Land Management

Richland, WA 99352 New Mexico State Office

PO Box 1449

US Department of Energy Santa Fe, NM 87507

Office of Geologic Disposal.

Yucca Mountain Project Office US Environmental Protection

Attn: Associate Director, RW-20 Agency (2)

PO Box 98608 Radiation Protection Programs

Las Vegas, NV 89].93-8608 Attn: M. OgeANR-460

US Department of Energy (3) Washington, DC 20460

Nevada Operations Office

Attn: J.R. Boland US Environmental Protection

D. Livingston Agency, Region 6

P.K. Fitzsimmons Attn: C. Byrum, 6T-ET

2753 S. Highland Drive 1445 Ross Ave.

Las Vegas, NV 89183-85i8 Dallas, TX 75202

US Department of Energy (2) US Geological Survey (2)Technical Information Center Water Resources Division

PO Box 62 Attn: C. Peters

Oak Ridge, TN 37831 4501 Indian School NE

Suite 200

US Department of Energy (2) Albuquerque, NM 87710

Chicago Operations Office

Attn: J.C. Haugen US Nuclear Regulatory Commission

9800 South Cass Avenue Division of Waste Management

Argonne, IL 60439 Attn: H. Marson

Mail Stop 4-H-3

Washington, DC 20555

Dist-2

US Nuclear Regulatory Commission (4) New Mexico Environment Department

Advisory Committee on Nuclear Waste Secretary of the Environment (3)

Attn: D. Moeller Attn: J. EspinosaM.J. Steindler PO Box 968

P.W. Pomeroy 1190 St. Francis DriveW.J. Hinze Santa Fe, NM 87503-0968

7920 Norfolk Ave.

Bethesda, MD 20814 New Mexico Environment DepartmentAttn: P. McCasland

Defense Nuclear };_cilities Safety WIPP Project Site OfficeBoard PO Box 3090

Attn: D. Winters Carlsbad, NM 88221-3090625 Indiana _ve. NW

Suite 700 New Mexico State Engineer's Office

Washington, DC 20004 Attn: H. ChudnnffPO Box 25102

Nuclear Waste Technical Review Board Santa Fe, NM 87504-5102

Attn: Library (2)

Ii00 Wilson Blvd. Environmental Evaluation Group (5)Suite 910 Attn: R. Neill

Arlington, VA 22209-2297 7007 Wyoming Blvd. NE, Suite F-2

Albuquerque, NM 87109

State Agencies Adviso_ Comm_ee on NuclearFacll_y Safety

New Mexico Bureau of Mines

and Mineral Resources John F. Ahearne

Socorro, NM 87801 Executive Director, Sigma Xi99 Alexander Drive

New Mexico Energy, Minerals and Research Triangle Park, NC 27709

Natural Resources DepartmentAttn: Librarian James E. Martin

2040 South Pacheco 109 Observatory Road

Santa Fe, NM 87505 Ann Arbor, M1 48109

New Mexico Energy, Minerals and WiPP Commiffee, NationalResearch Council'sNatural Resources Department Board on Radioactive Wa_e ManagementNew Mexico Radioactive Task Force (2)

(Governor's WIPP Task Force) National Research Council (2)

Attn: A. Lockwood, Chairman Board on Radioactive Waste Management

C. Wentz, Policy Analyst Attn" C.A. Anderson2040 South Pacheco I.B. Alterman

Santa Fe, NM 87505 2101 Constitution Ave. NWHarris Bldg. HA 456

Bob Forrest Washington, DC 20418

Mayor, City of CarlsbadPO Box 1569 Howard Adler

Carlsbad, NM 88221 Oxyrase, Inc.11020 Solway School Rd.

Carlsbad Department of Development Knoxville, TN 37931Executive Director

Attn: C. Bernard John O. Blomeke

PO Box 1090 3833 Sandy Shore Drive

Carlsbad, NM 88221 Lenoir City, TN 37771-9803

q

Dist-3

John D. Bredehoeft Thomas H. Pigford

Western Region Hydrologist Department of Nuclear EngineeringWater Resources Division 4159 Etcheverry Hall

US Geological Survey (M/S 439) University of California

345 Middlefield Road Berkeley, CA 94720

Menlo Park, CA 94025Thomas A. Cotton

Fred M. Ernsberger JK Research Associates, Inc.1325 NW Tenth Ave. 4429 Butterworth Piace NW

Gainsville, FL 32605 Washington, DC 20016

Rodney C. Ewing Robert J. Budnitz

Department of Geology President, Future Resources

University of New Mexico Associates, Inc.

Albuquerque, NM 87131 2000 Center StreetSuite 418

Charles Fairhurst Berkeley, CA 94704

Department of Civil and Mineral

Engineering C. John Mann

University of Minnesota Department of Geology

500 Pillsbury Dr. SE 245 Natural History Bldg.

Minneapolis, MN 55455-0220 1301 West Green Street

U_L_versity of IllinoisB. John Garrick Urbana, IL 61801

PLG, Incorporated

4590 MacArthur Blvd., Suite 400 Frank W. Schwartz

Newport Beach, CA 92660-2027 Department of Geology and Mineralogy

The Ohio State UniversityLeonard F. Konikow Scott Hall

US Geological Survey 1090 Carmack Rd.431 National Center Columbus, OH 43210

4 Reston, VA 22092National Laboratories

Jeremiah O'Driscoll

Jody, Incorporated Argonne National Laboratory (2)

505 Valley Hill Drive Attn: A. Smith

Atlanta, GA 30350 D. Tomasko9700 South Cass, Bldg. 201

Christopher G. Whipple Argonne, IL 60439

ICF Kaiser Engineers1800 Harrison St. 7th Floor Battelle Pacific Northwest

Oakland, CA 94612-3430 Laboratory (2)Attn: S. Bates

Thomas A. Zordan R.E. Westerman

Zordan Associates, Inc. MSIN P8-44

3807 Edinburg Dr. Battelle Boulevard

Murrysville, PA 15668 Richland, WA 99352

Pe_ormanceAssessmentPeerReview Panel Idaho National Laboratory (2)

Westinghouse-Idaho Nuclear Co.G. Ross Heath Attn: H. Loo

College of Ocean & Fishery Sciences R. Klingler

University of Washington Mail Stop 3422583 Henderson Hall, HN-15 P.O. Box 4000

Seattle, WA 98195 Idaho Falls, lD 83415-3422

Dist-4

Los Alamos National Laboratory (5) Deuel and Associates, Inc.Attn: B. Erdal, INC-12 Attn: R.W. Prindle

M. Ennis, HS-12 7208 Jefferson NE

Mail Stop J900 Albuquerque, NM 87109

S. Kosiewicz, EM-7

Mail Stop J595 Disposal Safety, Inc.L. Soholt, EM-13 Attn: B. Ross

Mail Stop M992 1660 L Street NW, Suite 314

J. Wenzel, HS-12 WashingtGn, DC 20036

Mail Stop K482

PO Box 1663 Ecodynamics (2)Los Alamos, NM 87545 Attn: P. Roache

R. Blaine

Oak Ridge National Laboratory PO Box 9229

Transuranic Waste Manager Albuquerque, NM 87119-9229Attn: D.W. Turner

Bldg. 3047 EG & G Idaho (3)PO Box 2008 1955 Fremont Street

Oak Ridge, TN 37831-6060 Attn: C. AtwoodC. Hertzler

Pacific Northwest Laboratory T.I. Clements

Attn: B. Kennedy Idaho Falls, lD 83415PO Box 999

Richland, WA 99352 Geomatrix

Attn: K. Coppersmith

Westinghouse-Savannah River I00 Pine St., Suite I000

Technology Cente_ (4) San Francisco, CA 94111Attn" N. Bibler

J.R. Harbour Golder Associates, Inc.M.J. Plodinec Attn: R. KossikG.G. Wicks 4104 148th Avenue NE

Aiken, SC 29802 Redmond, WA 98052

Corporations/Members ofthe Public John Hart and Associates, P.A.Attn: J.S. Hart

Battelle Memorial Institute 2815 Candelaria Road NW

Attn: R. Root Albuquerque, NM 87107J. Kircher

505 Marquette NW, Suite I John Har_ and Associates, P.A.Albuquerque, NM 87102 Attn: K. Lickliter

400-C Sth St. hTW

Benchnmrk Environmental Corp. Tacoma, WA 98439Attn: C. Frederickson

4501 Indian School NE, Suite 105 INTERA, Inc.Albuquerque, NM 87110 Attn: A.M. LaVenue

1650 University Blvd. NE, Suite 300

Beta Corporation Int. Albuquerque, NM 87102Attn: E. Bonano

6613 Esther NE INTERA, Inc.Albuquerque, NM 87109 Attn: J.F. Pickens

6850 Austin Center Blvd., Suite 300

City of Albuquerque Austin, TX 78731Public Works Department

Utility Planning Division INTERA, Inc.Attn: W.K. Summers Attn: W. Stensrud

PO Box 1293 PO Box 2123

Albuquerque, NM 87103 Carlsbad, NM 88221

Dist-5

INTERA, Inc. SAIC (3)Attn: W. Nelson Attn: M. Davis

I01 Convention Center Dr. R. Guzowski

Suite 540 J. Tollison

Las Vegas, NV 89109 2109 Air Park Road SE

Albuquerque, NM 87106

lT Corporation (2)

Attn: R.F. McKinney SAIC (2)

J. Myers Attn: J. Young

Regional Office, Suite 700 D. Lester5301 Central Avenue NE 18706 North Creek Parkway, Suite ii0

Albuquerque, NM 87108 Bothell, WA 98011

Lawrence Berkeley Laboratory Southwest Research Institute

Attn: J. Long Nuclear Waste Regulatory Analysis (2)

Building 50 E Attn: P.K. Nair

Berkeley, CA 94720 6220 Culebra RoadSan Antonio, TX 78228-0510

MAC Technical Services Co.

Attn: D.K. Duncan Systems, Science, and Software (2)

8418 Zuni Road SE, Suite 200 Attn: E. Peterson

Albuquerque, NM 87108 P. LagusBox 1620

Newman and Holtzinger La Jolla, CA 92038Attn: C. Mallon

1615 L Street NW, Suite I000 TASC

Washington, DC 20036 Attn: S.G. Oston55 Walkers Brook Drive

RE/SPEC, Inc. (2) Reading, MA 01867Attn: W. Coons

4775 Indian School NE, Suite 300 Tech Reps, Inc. (6)

Albuquerque, NM 87110 Attn: J ChapmanC Crawford

RE/SPEC, Inc. D Marchand

Attn: J.L. Ratigan T PetersonPO Box 725 J Stikar

Rapid City, SD 57709 D Scott5000 Marble NE, Suite 222

Reynolds Electric and Engineering Albuquerque, NM 87110

Company, Inc.Attn: E.W. Kendall Tolan, Beeson & Associates

Building 790 Attn: T.L. TolanWarehouse Row 2320 W. 1Sth Avenue

PO Box 98521 Kennewick, WA 99337

Las Vegas, NV 89193-8521

TRW Environmental Safety Systems (2)SAIC Attn: I. Sacks, Suite 800

Attn: H.R. Pratt L. Wildman, Suite 1300

10260 Campus Point Drive 2650 Park Tower Drive

San Diego, CA 92121 Vienna, VA 22180-7306

SAIC Sanford Cohen and Associates

Attn: C.G. Pflum Attn: J. Channell

I01 Convention Center Dr. 7101 Carriage Rd NE

Las Vegas, NV 89109 Albuquerque, NM 87109

Dist-6

Westinghouse Electric Corporation (5) Universities

Attn: LibraryC. Cox University of California

L. Fitch Mechanical, Aerospace, and

B.A. Howard Nuclear Engineering Department (2)

R.F. Kehrman Attn: W. Kastenberg

PO Bc_ 2078 D. Browne

Carlsbad, NM 88221 5532 Boelter HallLos Angeles, CA 90024

Westinghouse Hanford Company

Attn: D.E. Wood, MSIN HO-32 University of CaliferniaPO Box 1970 Engineering and Applied Science

Richland, WA 99352 Attn: D. Okrent

48-121A Engineering IV

Western Water Consultants Los Angeles, CA 90024-1597

Attn: P.A. Rechard

PO Box 4128 University of California

Laramie, WY 82071 Mine Engineering DepartmentRock Mechanics Engineering

Western Water Consultants Attn: N. Cook

Attn: D. Fritz Berkeley, CA 94720

1949 Sugarland Drive #134

Sheridan, WY 82801-5720 University of Hawaii at HiloBusiness Administration

P. Drez Attn: S. Hora

8816 Cherry Hills Road NE Hilo, HI 96720-4091

Albuquerque, NM 87111University of Illinois

David Lechel Department of Geology

9600 Allende Rd. NE Attn: C. Bethke

Albuquerque, NM 87109 1301 W. Green St.Urbana, IL 61801

C.A. Marchese

PO Box 21790 University of New Mexico

Albuquerque, NM 87154 Geology DepartmentAttn: Library

Arend Meijer Albuquerque, NM 871313821 Anderson SE

Albuquerque, NM 87108 University of New MexicoResearch Administration

D.W. Powers Attn: H. Schreyer

Star Route Box 87 102 Scholes Hall

Anthony, TX 79821 Albuquerque, NM 87131

Shirley Thieda University of Wyoming

PO Box 2109, RR1 Department of Civil Engineering

Bernalillo, NM 87004 Attn: V.R. HasfurtherLaramie, WY 82071

Jack Urich

c/o CARD University of Wyoming144 Harvard SE Department of Geology

Albuquerque, NM 87106 Attn: J.I. DreverLaramie, WY 82071

Dist-7

University of Wyoming Nicolo Cadelli

Department of Mathematics Commission of European Communities

Attn: R.E. Ewing 200, Rue de la LoiLaramie, WY 82071 B-I049 Brussels, BELGIUM

Lib_ries R. Heremans

Organisme Nationale des D_chetsThomas Brannigan Library Radioactifs et des Matidres Fissiles

Attn: D. Dresp (ONDRAF)

106 W. Hadley St. Piace Madou I, Boitec 24/25

Las Cruces, NM 88001 B-lO30 Brussels, BELGIUM

New Mexico State Library J. Marivoet

Attn: N. McCallan Centre d'Etudes de l'Energie325 Don Gaspar Nucl_aire (CEN/SCK)

Santa Fe, NM 87503 Boeretang 200B-2400 Mol, BELGIUM

New Mexico Tech

Martin Speere Memorial Library P. Conlon

Campus Street Waste Management Division

Socorro, NM 87810 Atomic Energy Control Board (AECB)PO Box 1046

New Mexico Junior College Ottawa, Ontario KIP 559, CANADA

Pannell Library

Attn: R. Hill A.G. Wikjord

Lovington Highway Manager, Environmental and SafetyHobbs, NM 88240 Assessment Branch

Atomic Energy of Canada LimitedCarlsbad Municipal Library Whiteshell Research Establishment

WIPP Public Reading Room Pinawa, Manitoba ROE ILO, CANADAAttn: L. Hubbard

I01 S. Halagueno St. Teollisuuden Voima Oy (TVO) (2)Carlsbad, NM 88220 Attn: Timo Aikas

Jukka-Pekka Salo

University of New Mexico Annankatu 42 C

Zimmerman Library SF-O0100 Helsinki Suomi, FINLANDGovernment Publications Department

Albuquerque, NM 87131 Timo VienoTechnical Research Centre of Finland

NEA/Pedormance AssessmentAdvisow (VTT)

Group(PAAG) Nuclear Energy LaboratoryPO Box 208

P. Duerden SF-02151 Espoo, FINLANDANSTO

Lucas Heights Research Laboratories Division de la S4curitd et de la

Private Mail Bag No. I Protection de l'Environment (DSPE)

Menai, NSW 2234 Commissariat d l'Energie Atomique

AUSTRALIA Agence Nationale pour la Gestion desD_chets Radioactifs (ANDRA) (2)

Gordon S. Linsley Attn: G_rald Ouzounian

Division of Nuclear Fuel Cycle and M. Claude RingeardWaste Management Route du Panorama Robert Schuman

International Atomic Energy Agency B.P. No. 38

PO Box I00 F-92266 Fontenay-aux-Roses CedexA-1400 Vienna, AUSTRIA FRANCE

Dist-8

Claudio Pescatore Conny H_ggDivision of Radiation Protection and Swedish Radiation Protection

Waste Management Institute (SSI)

OECD Nuclear Energy Agency Box 6020438, Boulevard Suchet S-104 01 Stockholm, SWEDENF-75016 Paris

FRANCE J. HadermannPaul Scherrer Institute

M. Dominique Greneche Waste Management Programme

Commissariat _ l'Energie Atomique CH-5232 Villigen PSI

IPSN/DAS/SASICC/SAED SWITZERLANDB.P. No. 6

F-92265 Fontenay-aux-Roses Cedex J. Vigfusson

FRANCE HSK-Swiss Nuclear Safety Inspectorate

Federal Office of Energy

Robert Fabriol CH-5232 Villigen-HSK

Bureau de Recherches G_ologiques et SWITZERLAND

Mini_res (BRGM)

B.P. 6009 D.E. Billington

45060 Orl_ans Cedex 2 Departmental Manager-AssessmentFRANCE Studies

Radwaste Disposai R&D Division

P. Bogorinski AEA Decommissioning & Radwaste

Gesellschaft f_r Reaktorsicherheit Harwell Laboratory, B60(GRS) MBH Didcot Oxfordshire OXII ORA

Schwertnergasse I UNITED KINGDOMD-5000 K61n i, GERMANY

P. Grimwood

R. Storck Waste Management Unit

GSF - Institut for Tieflagerung BNFLTheodor-Heuss-Strabe 4 Sellafield

D-3300 Braunschweig, GERMANY Seascale, Cumbria CA20 lPGUNITED KINGDOM

Ferrucio Gera

ISMES S.p.A Alan J. HooperVia del Crociferi 44 UK Nirex Ltd

1-00187 Rome, ITALY Curie Avenue

Harwell, Didcot

Hiroyuki Umeki Oxfordshire, OXII ORH

Isolation System Research Program UNITED KINGDOM

Radioactive Waste Management Project

Power Reactor and Nuclear Fuel Jerry M. Boak

Development Corporation (PNC) Yucca Mountain Project Office

1-9-13, Akasaka, Minato-ku US Department of Energy

Tokyo 107 PO Box 98608

JAPAN Las Vegas, NV 89193

T6nis Papp Seth M. Coplan (Chairman)

Swedish Nuclear Fuel and Waste US Nuclear Regulatory Commission

Management Co. Division of High-Level Waste

Box 5864 Management

S 102 48 Stockholm Mail Stop 4-H-3

SWEDEN Washington, DC 20555

Dist-9

A.E. Van Luik Nils A. Kjellbert

INTERA/M&O Swedish Nuclear Fuel and Waste

The Valley Bank Center Management Company (SKB)I01 Convention Center Dr. Box 5864

Las Vegas, NV 89109 S-I02 48 Stockholm, SWEDEN

NEA/Probabilistic System Assessment Bj_rn Cronhjort

Group(PSAG) Royal Institute of TechnologyAutomatic Control

Shaheed Hossain S-lO0 44 Stockholm, SWEDENDivision of Nuclear Fuel Cycle and

Waste Management Richard A. Klos

International Atomic Energy Agency Paul-Scherrer Institute (PSI)

Wagramerstrasse 5 CH-5232 Villingen PSI, SWITZERLANDPO Box i00

A-1400 Vienna, AUSTRIA Nationale Genossenschaft for die

Lagerung Radioaktiver Abf_lle (2)Alexander Nies (PSAC Chairman) Attn: C. McCombie

Gesellschaft for Strahlen- und F. Van DorpInstitut f_r Tieflagerung Hardstrasse 73

Abteilung for Endlagersicherheit CH-5430 Wettingen SWITZERLANDTheodor-Heuss-Strasse 4

D-3300 Braunschweig N.A. Chapman

GERMANY Intera Information TechnologiesPark View House

Eduard Hofer 14B Burton Street

Gesellschaft for Reaktorsicherheit Melton Mowbray(GRS) MBH Leicestershire LEI3 IAE

Forschungsgel_nde UNITED KINGDOM

D-8046 Garching, GERMANY

Daniel A. Galson

Andrea Saltelli Galson Sciences Ltd.

Commission of the European 35, Market PiaceCommunities Oakham

Joint Resarch Centre of Ispra Leicestershire LEI5 6DT

1-21020 Ispra (Varese) UNITED KINGDOMITALY

David P. Hodgkinson

Alejandro Alonso Intera Information TechnologiesC_tedra de Tecnologia Nuclear 45 Station Road, Chiltern House

E.T.S. de Ingenieros Industriales Henley-on-ThamesJos_ Guti_rrez Abascal, 2 Oxfordshire RG9 IAT

E-28006 Madrid, SPAIN UNITED KINGDOM

ENRESA (2) Brian G.J. Thompson

Attn: M. A. Cu_ado Department of the Environment: Her

F. J. Elorza Majesty's Inspectorate of Pollution

Calle Emilio Vargas, 7 Room A5.33, Romney HouseE-28043 Madrid, SPAIN 43 Marsham Street

London SWIP 2PY, UNITED KINGDOMPedro Prado

CIEMAT Intera Information Technologies

Instituto de Tecnologia Nuclear Attn: M.J.AptedAvenida Complutense, 22 3609 South Wadsworth Blvd.

E-28040 Madrid, SPAIN Denver, CO 80235

Dist-10

US Nuclear Regulatory Commission (2) Christian RavenneAttn: R. Codell Geology and Geochemistry Division

N. Eisenberg Institut Francais du Pdtrole

Mall Stop 4-H-3 i & 4, Av. de Bois-Prdau B.P. 311

Washington, DC 20555 92506 Rueil Malmaison CedexFRANCE

Battelle Pacific Northwest

Laboratories Peter Grindrod

Attn: P.W. Eslinger INTERA Information Technologies Ltd.MS K2-32 Chiltern House

PO Box 999 45 Station Road

Richland, WA 99352 Henley-on-ThamesOxford_hire, RG9 IAT, UNITED KINGDOM

Center for Nuclear Waste Regulatory

Analysis (CNWRA) Alan Gutjahr

Southwest Research Institute Department of Mathematics

Attn: B. Sagar New Mexico Institute of Mining and

PO Drawer 28510 Technology6220 Culebra Road Socorro, NM 87801

San Antonio, TX 78284C. Peter Jackson

Geo_atistics ExpedWorking Group(GXG) Harwell Laboratory

Theoretical Studies Department

Rafael L. Bras Radwaste Disposal Division

R.L. Bras Consulting Engineers Bldg. 424.444 Percy Road Oxfordshire Didcot Oxon OXII ORA

Lexington, MA 02173 UNITED KINDGOM

Jesus Carrera Rae Mackay

Universidad Polit_cnica de Catalu_a Department of Civil Engineering

E.T.S.I. Caminos University of Newcastle Upon Tyne

Jordi, Girona 31 Newcastle Upon Tyne NEl 7RUE-08034 Barcelona, SPAIN UNITED KINGDOM

Gedeon Dagan Steve Gorelick

Department of Fluid Mechanics and Department of Applied Earth Sciences

Heat Transfer Stanford University

Tel Aviv University Stanford, CA 94305-2225PO Box 39040

Ramat Aviv, Tel Aviv 69978 Peter Kitanidis

ISRAEL 60 Peter Coutts Circle

Stanford, CA 94305Ghislain de Marsily (GXG Chairman)

University Pierre et Marie Curie Dennis McLaughlin

Laboratorie de Geologie Applique Parsons Laboratory4, Piace Jussieu Room 48-209

T.26 - 5e etage Department of Civil Engineering

75252 Paris Cedex 05 Massachusetts Institute of Technology

FRANCE Cambridge, MA 02139

Alain Galli Shlomo P. Neuman

Centre de Geostatistique College of Engineering and Mines

Ecole des Mines de Paris Hydrology and Water Resources Dept.

35 Rue St. Honore University of Arizona

77035 Fontainebleau, FRANCE Tucson, AZ 85721

Dist-ll

Yoram Rubin Bunde_anstalt f_r Geowissenschaften

Department of Civil Engineering und Rohstoffe

University of California Attn: M. Langer

Berkeley, CA 94720 Postfach 510 153Do30631 Hannover, GERMANY

Foreign AddressesGesellschaft f_r Anlagen und

Studiecentrum Voor Kernenergie Reaktorsicherheit (GRS) (2)

Centre D'Energie Nucleaire Attn: B. BaltesAttn: A. Bonne W. Muller

SCK/CEN Schwertnergasse i

Boeretang 200 D-50667 Cologne, GERMANYB-2400 Mol, BELGIUM

Institut fur Tieflagerung (2)

Atomic Energy of Canada, Ltd. (3) Attn: K. KuhnWhiteshell Research Establishment Theodor-Heuss-Strasse 4

Attn: M.E. Stevens D-3300 BraunschweigB.W. Goodwin GERMANY

D. Wushke

Pinewa, Manitoba ROE ILO, CANADA Physikalisch-TechnischeBundesanstalt

Juhani Vira Attn: P. Brenneke

Teollisuuden Voima Oy (TVO) Postfach 33 45

Annankatu 42 C D-3300 BraunschweigSF-00100 Helsinki Suomi GERMANY

FINLAND

Shingo Tashiro

Jean-Pierre Olivier Japan Atomic Energy ResearchOECD Nuclear Energy Agency (2) Institute

38, Boulevard Suchet Tokai-Mura, Ibaraki-Ken

F-75016 Paris, FRANCE 319-11, JAPAN

D. Alexandre, Deputy Director Netherlands Energy ResearchANDRA Foundation (ECN)31 Rue de la Federation Attn: L.H. Vons

75015 Paris, FRANCE 3 WesterduinwegPO Box i

Claude Sombret 1755 ZG Petten

Centre D'Etudes Nucleaires THE NETHERLANDSDe La Vallee Rhone

CEN/VALRHO Johan Andersson

S.D.H.A. B.P. 171 Swedish Nuclear Power Inspectorate

30205 Bagnols-Sur-Ceze, FRANCE Statens Karnkraftinspektion (SKI)Box 27106

Commissariat a L'Energie Atomique S-I02 52 StockholmAttn: D. Alexandre SWEDENCentre d'Etudes de Cadarache

13108 Saint Paul Lez Durance Cedex Fred Karlsson

FRANCE Svensk Karnbransleforsorjning AB

Project KBSBundesministerit_ f_r Forschung und Box 5864

Technologie S-I02 48 StockholmPostfach 200 706 SWEDEN

5300 Bonn 2, GERMANY

Dist-12

Nationale Genossenschaft f_r die InternalLagerung Radioaktiver Abf_lle (2) MS OKg.Attn: S. Vomvoris 0101 0001 A Narath

P. Zuidema 0102 0002 O.E JonesHardstrasse 73 0827 1502 P.J Hommert

CH-5430 Wertingen 0827 1511 D.K GartllngSWITZERLAND 0127 4511 D.P Garber

0724 6000 D.L Hartley

AEA T=chnology 1324 6115 P.B DaviesAttn: J.E. Tinson 1324 6115 R.L Beauheim

B4244 Harwell Laboratory 0750 6118 H.R WestrichDidcot, Oxfordshire OXII ORA 1320 6119 E.J Nowak

UNITED KINGDOM 1320 6119 Staff (14)1322 6121 J.R. Tillerson

AEA Technology 1322 6121 Staff (7)Attn" J.H. Rees 1337 6300 D.E. Ellis

DSW/29 Culham Laboratory 1335 6302 L.E. ShephardAbington 1335 6303 S.Y. PickeringOxfordshire OXI4 3DB 1335 6303 W.D. Weart

UNITED KINGDOM 1335 6305 S.A. Go!dstein

1335 6305 A.R. Lappin

AEA Technology 1341 6306 A.L. Stevens

Attn" W.R. Rodwell 1326 6312 F.W. Bingham

O44/A31 Winfrith Technical Centre 1326 6313 L.S. CostinDorchester 1345 6331 P.A. Davis

Dorset DT2 8DH, UNITED KINGDOM 1330 6352 WIPP Central Files (I00)1328 6342 D.R. Andes:son

D.R. Knowles 1328 6342 Staff (_0)

British Nuclear Fuels, plc 1395 6343 V.H. Slaboszewicz

Risley, Warrington 1395 634.3 Staff (3)Cheshire WA3 6AS, 1002607 1341 6345 R.C. Lincoln

UNITED KINGDOM 1341 6345 Staff (9)1341 6347 D.R. Schafer

1341 6348 J.T. Holmes

1341 6348 Staff (4)

1343 6351 R.E. Thompson

1330 6352 S E. Sharpton0736 6400 N R. Ortiz

0746 6613 R M. Cranwell

0746 6613 R L. Iman

0746 66].3 C Leigh0727 6622 M S.Y. Chu

0718 6641 R E. Luna, Acting

0899 7141 Technical Library (5)0619 7151 Technical Publications

0100 7613-2 Document Processing for

DOE/OSTI (i0)9018 8523-2 Central Technical Files

Dist-13