A NUMERICAL MODEL FOR THE EVOLUTION OF THE CARBON

SYSTEM GEOCEEMETRY AT THE PROPOSED NUCLEAR WASTE

REPOSITORY AT YUCCA MOUNTAIN, NEVADA, USA

William M. Murphy'**, Chrisropher J. Freitas2, Peter C. LichmerlJ

'Center for Nuclear Waste Regulatory Analyses, and

'Southwest Research Institute. 6220 Culebra Rd, San Antonio, TX 78238 USA

Abstract, Carbon system geccnemistry in the near-field zone of the proposed nuclear

waste repository at Yucca Mountain, Nevada, can affect isolation perfonnance through

controls on solution pH. radioeiement solubility, speciation, and sorption. A liquid and

gas phase transport model has Deen developed that couples local equilibrium carbon

system chemistry and txanspon KO an independent heat and two phase fluid flow model

for the partially saturated host rock This new algorithm implements a model of the

rnspon of chemical species and local equilibrium chemistry through an operator

splitting technique which a i l o ~ s for iterative solution of species transport equations

and local equilibrium mass amon relations.

Model results for the p p s e d repository site indicate that major excursions in

carbon system chemistry from ambient conditions may occur as a result of repository

heating and fluid flow. With irsreasing temperature in the near field, CO, exsolves

from the aqueous phase, whch is the major carbon reservoir, to the gas phase.

Consequently, solution pH rises with temperature, the dominant aqueous carbon

1

speciation shifts from HC03- to CO?--, and calcite (CaC03) precipitates in the vicinity

o i the repository horizon and from the edge of the repository horizon down to the

water table. Liberated CO, is transponed in the gas phase to the cooler far field. CO,

fumeroles are predicted to be an ear& chemical manifestation of the repository at the

-ground surface. Bicarbonate and carbonate are dominant aqueous complexing

compounds for many radioactive waste species in the Yucca Mountain groundwater

system. The thermal impact on carbon system chemistry and pH can alter radioelement

solubilities and solid-liquid disaibudon coefficients by orders of magnitude. Carbon 14

rcleased from the engineered bamer system will mix as a trace component in the

multiphase carbon system of the repository environment. Hence, the carbon system

model ais0 permits assessment ot‘ “C migration.

Introduction

Yucca Mountain, Nevada. is under investigation as a proposed high-level

nuclear waste (HLW) repository sire. The repository horizon is in silicic volcanic

strata approximately 375 meters below the ground surface and 225 meters above the

groundwater table (DOE, 1988). In general, bedded and zeolitized rocks at the site

have porosities of 20 to 35 percent which are 20 to 50 percent saturated with water,

and welded units are 5 to 20 percent porous and 60 to 90 percent sanuated (Nelson

and Anderson, 1992; Kwicklis et al.. 1994). Groundwater chemistry is dilute and

oxidizing (McKinley et ai., 1991).

Carbon system geochemisrp at Yucca Mountain may exext multiple controls on

radionuclide migration. Bicarbonate (HCO,-) is the dominant anion in tuffaceous

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groundwaters at Yucca Mountain (McKinley et al., 1991); calcite (CaCO,) occurs as a

fracture and void filling mineral in many rocks (Bish and Chipera, 1989; Carlos et al.,

1991); and the gas of the vadose zone is enriched in CO, relative to the atmosphere

(Thorstenson et ai., 1990). Thermal loading due to radioactive decay of HLW is

expected to enhance gas and liquid flow (e.g., Buscheck and Nitao, 1994 Pruess and

Tsang, 1994) and chemical reactions (e.g., Murphy, 1993) leading to migration of

aqueous and gaseous carbon species. and precipitation and dissolution of calcite.

Hydrolysis and complexing with carbonate species previously has been shown

to have dominant effects on aqueous speciation of radioactive waste elements in

repository groundwaters (e.g.. Clark et al., 1994). Thermal effects on carbon system

chemistry and pH can alter radioelement solubilities by orders of magnitude with

potentially large effects on the source term for radionuclide migration. Solid-liquid

distribution coefficients also depend strongly on aqueous speciation and pH (e.g..

Beneni et al., 1995) and can vary by large factors due to chemistry changes.

Variations in distribution coefficients affect retardation of radionuclide migration.

Although silicate system chemistry is not included in the carbon system model

developed in this study, depletion of aqueous Ca2+ due to calcite precipitation may

destabilize calcic clinoptilolite, which is a major natural alteration product of the

silicic tuffs at Yucca Mountain with significant sorption capacity.

Radioactive 14C is a constituent of nuclear waste proposed for disposal at

Yucca Mountain (Van Konynenburg, 1994). 14C released from breached waste

containers as I4CO2 would mix as a mice component in the multiphase carbon system

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of the repository environment W i i n isotopic fractionation having a negligible effect

with regard to radionuclide rmgmon. Given a source term for 14C release (e.g..

Codell, 1993), transport of “ C Arcugh the geologic repository can be modeled for the

purposes of performance assessment to be proportional to tmsport of carbon (e.g.,

Codell and Murphy, 1992).

This article reports deveiopment of a coupled thenno-hydro-geochemical

reactive transport model to simuiar,e rhe evolution of the carbon system in the near-

field zone of the proposed reposirory and to aid assessments of radionuclide migration.

The model segregates transport ana equdibrium chemistry by operator splitting.

Independent transport of gaseous CO- and aqueous species is modeled, then mass

action relations for local equiibrium are solved. This paper presents the theoretical

framework of the model along ~1r.h results for a repository scale simulation.

Previous studies

The evolution of the carbon system geochemistry in the proposed nuclear waste

repository at Yucca has been sruciid previously. primarily in relation to 14C release.

Knapp (1990) solved an approxmre equation for transport of 14C as a brealung

kinematic wave. Retardation of “ C transport was assumed to be controlled by the

isotopic equilibrium

H 12~0,- -:‘co2(g) = H 14~0; +12C02(g) (1)

Numerous simplifications in this marhematical model, such as neglecting the effects of

diffusion and temperature variations. lead to approximate results.

Light et al. (1990) calculated gaseous and aqueous carbonate equilibrium

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relations to yield a dimensioniss dsmbution coefficient for carbon between gas and

aqueous phases. The dsmbuccn coefficient was shown to be a strong function of

temperature (25-100 "C) ma ?H i7-9), with values ranging from less than one to

several hundred for likely r e m ~ r a n u e and pH conditions in the Yucca Mountain

repository. A reference value ci three was used in their calculations of 14C fluxes and

concentrations. Their calculations indicated that diffusion of carbon would tend to

homogenize 14C concentrations m a rock matrix containing a static liquid at a value

near equilibrium with a gas flosmg sufficiently slowly in nearby fractures. They

concluded, therefore, that an eaurvalent porous medium approximation to the fractured,

unsaturated system can be accurately implemented for the appropriate conditions. Light

et al. (1990) performed calcuhons of 14C transport using the nominal values of

hydrologic properties and the quivalent porous medium approximation. Their results

indicate that release of 14C at rt;c land surface depends strongly on the amount of I4C

released from the waste packagm. and only slightly on the timing of waste package

release.

Ross (1988) develop a conceptual model relating I4C transport to the

carbonate system at Yucca Mounmn which emphasizes gas-water-rock equilibria and

gas phase transport of CO,. - X relatively realistic water chemistry model was

recognized in this study as a q m m e n t for modeling 14C retardation.

Codell and Murphy ( 1992) developed a one-dimensional model with gas phase

transport of CO, and local eqdirium chemistry as a function of time and space. The

model for local equilibrium presented by Codell and Murphy (1992) is equivalent to

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the chemical model presented in tlus paper. Gas flow was approximated for that model

by uruiorm, time dependent vertical flow generally consistent with results of two

Olmensional thennohydrologic modeling. Major excursions from ambient conditions

were predicted to occur in carbon system chemistry due to repository heating and fluid

flow. With increasing temperature, CO, exsolved from the aqueous phase, which is the

major carbon reservoir, to the gas phase. Solution pH was shown to rise with

temperature, and the dominant aqueous carbon speciation shifted €?om HCO,' to CO,,.

Lncreasing pH, increasing temperature, and evaporation all promoted calcite

precipitation. However, the maximum mass of calcite to precipitate was small because

it is limited by the supply of aqueous Ca2'. The aqueous concentration of Ca2+

dropped to low values in areas of elevated tempera- and calcite precipitation.

Gas phase transport in the model of Codell and Murphy (1992) led to carbon

redsmbution on the scale of the mountain. Carbon was shown to be transported

hundreds of meters in hundreds of years. Although transport was limited to gas flow,

most carbon remained in the aqueous phase, so its migration rate was retarded by the

rano of its aqueous to gas phase distribution. Carbon precipitated in calcite did not

migate, but its mass was small compared to that in fluid phases. CO, liberated from

the aqueous phase in the hotter near field was transported in the gas phase to the

cooler far field where it condensed As the near field temperature diminished the water

chemistry slowly reverted toward initial conditions and calcite dissolved.

The present model is an extension of the model developed by Codell and

llurphy (1992) incorporating more realistic gas and liquid phase flow models,

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diffusive as well as advective transport, use of a radially symmetric geometxy, and an

implementation of higher-order convective modeling techniques developed by Freitas

(1985).

Mathematical Model for Carbon System Chemistry and Transport

The Carbon System T R U I S ~ ~ K Code (CST) is a standalone numerical model

that simulates the transport of aqueous and gas phase species and performs chemical

equilibrium calculations at each grid point. CST uses as input the state variables of

temperature, saturation, pressure, and aqueous and gas phase velocity fields, all as

functions of time and space. Cumntly, these values are obtained through a transient

simulation performed using the CTOUGH code (Lichtner and Walton, 1994), a version

of VTOUGH (Nitao, 1989 and Pruess, 1987). In the course of a CTOUGH simulation.

data at specified instants of time record the spatial distribution of all variables. CST

then reads these data and performs linear interpolations between discrete times to

obtain intermediate values of the state variables at any arbitrary time as determined by

the CST time step scheme. In this way, CST is not restricted to the time scales

inherent in the CTOUGH data files but rather can perform a sub-cycle calculation at a

finer time scale than that represented by the data files. Obviously, the ability of CST

to resolve critical temporal and spatnl events is dictated by the level of temporal

refinement of the instantaneous CTOUGH data fiies and their spatial resolution.

Finally, CST calculates a time step size which maintains the maximum Courant

number in the flow domain to be less than 0.75. This is done primarily to achieve

optimal temporal accuracy in the transport simulations.

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An operator splitting algorithm is used to coupled transport of aqueous and

gaseous species and chemical reactions. In this approach species YZ transported over a

sinele time step by advection and diffusion according to the nonrcxtive transport

equations. At the end of each time step, the reacting species are equilibrated at each

node. The operator splitting approach restricts the maximum time step that is possible

by the Courant condition which allows the fluid to move at most one node point in a

given time step.

The thermohydrologic model used here was taken from Lichmer and Walton

(19941. The repository was treated as a cylindrically symmetrical system with a 2 km

radius and 600 m height representing the zone from the water table to the ground

surface. Uniform thermal and hydraulic properties characteristic of Yucca Mountain

were assigned. An equivalent continuum representation was used for the tuff host rock

with manix and fracture permeabilities of 1.9~10-l~ m2 and 10'" rn'. respectively.

Porosities of 0.1 for the matrix and 0.0018 for the fracture network were used. Values

for other material parameters are given in Lichmer and Walton I 1994). The initial

thermal loading at the repository horizon was 28,000 kW/km2 ( 1 14 kW/acre) over an

area of 3 km2. Thermohydroiogic model results indicate that the near field zone is

heated to a maximum temperature of approximately 180 "C within tens of years after

repository closure. Heat flow, which is dominated by conduction. raises far field

temperatures as the near field cools over a long time period. Transient heat pipes, with

counter flow of gas and liquid, develop above and below the repository during the first

1 ,OOO yr. Gas flow was downward across the repository horizon for the first 1.000 yr.

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Following this period gas flow was towards the repository horizon in the immediate

neighborhood both above and below the repository. These results could be different

with different assumptions for material properties.

Temperature, gas and liquid velocities, water saturation, and pressure from

CTOUGH wen used as input to the finite volume based diffusive and advective,

reactive transport model. Temperam dependent three-phase reaction chemistry was

coupled to species transport by optrator splitting. Effects of chemical reactions on the

thennohydrologic system, other than evaporation and condensation of water, were

neglected. Complete desiccation oi the system was permitted in the chemistry model,

although high ionic stnngth chemistry was not modeled explicitly. Instead, remaining

solutes were precipitated as unspecrfied salts when saturation dropped below 1 percent.

Five key reactions affecting carbon chemistry in the Yucca Mountain unsaturated

- mundwater system wen considend These reactions account for aqueous carbon

speciation, water hydrolysis (and pH), distribution of CO, between aqueous and gas

phases. and dissolution and precipitation of calcite. The Na+ ion was also modeled as

the dominant aqueous cation. Mass action, mass conservation, and aqueous charge

conservation were used as constramu to compute conditions of local equilibrium as a

function of time and space. Reacuons in this model system are npid relative to most

other changes in geochemical systems, e.g., silicate system reactions. Natural

groundwater and ground gas systems are comonly in equilibrium with respect to

aqueous carbonate speciation, CO? - pressure, and calcite. Therefore, local equilibrium

for h s model system is a reasonable assumption. Initial chemical conditions were

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selected to closely represent the amDient system at Yucca Mountain. The initial water

was dilute with intermeciute pH and slightly undersaturated with respect to calcite.

Carbon System Chemisrrp

A relatively simpie geochemical model incorporating reactions of primary

si@icance to the carbon system and "C transport at Yucca Mountain is based on

local chemical equilibrium and mass and charge conservation in a representative

elementary volume. Chermcal reactions and corresponding mass action relations

included in the model are:

H' - OH-= H - 0

H20(l) - COJaq) = H + HCO,

CO&) + HzOfl) = HCO; - H'

caco3(cc) + H = Cai* - HCO;

= %' acoj2-

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where (1). (aq), (g), and (cc) refer to liquid, aqueous, gas, and calcite phases,

respectively, denotes the thermodynamic activity of the subscripted species, fq

stands for the fugacity of gaseous CO,, and PCo2 stands for the reference fugacity of

CO,, which equals 1 bar. In addition to the aqueous species in reactions (2) to (6).

Na' is included in the model to represent generally other basic aqueous cations.

Sodium is the dominant cation in groundwaters from the tuffaceous aquifer at Yucca

Mountain, and calcium is second in molal concentration. Consequently, the simplified

water chemistry closely resembles the natural waters, and the 5 reactions above

represent the carbon system at Yucca Mountain nearly completely.

Local charge balance in the model aqueous phase is represented by

mH+ + mNat + 2 mca2+ - m HCO, + mco:- + mOH- (7)

where m, stands for the molality of the subscripted species. Local mass conservation

for carbon can be expressed as

"COicB, + n COZ(9, +nco;- + ncaco,(cc) = "c (8)

where I+ stands for the number of moles of the subscripted species in the

representative volume, and nc denotes the total number of moles of carbon in the

volume. Similarly,

"ca (9) ca=03(,) nca2- + n

gives the mass conservation condition for calcium. In the case that the aqueous

solution is undersaturated with respect to calcite and no calcite exists locally, ncAco~(cc)

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_--

is Zero, and Eq. (9) is mvial. The. mass of sodium is conserved in the aqueous phase.

The mass of 5 0 is conserved ma H,O maintains equilibrium between the gas and

liquid phases. Its distribution is caiculated in the thennohydrologic model. No

oxidation-reduction reactions are rtlevant to this model system, which is completely

oxidized.

Thermodynamic activities in the mass action relations (2) - (6) are related to

moles and molalities in Eqs. (7) - (9 ) by

where yi represents the activity cceiiicient of aqueous species i, and WHzo stands for

the mass of H20(1) in the representative volume. Activity coefficients are calculated

according to

I 2 7 -A zi I

log i", = + B O 1 I

where A, ai. B, and Bo are empirical parameters, 3 stands for the charge of species i,

and I denotes the ionic strength (Heleeson, 1969). The activity coefficient for neutral

aqueous CO,(aq) is taken to be one. Calcite and H,0(1) are assumed not to deviate

sigmfkantly from their standard states, so activity coefficients for both are also set at

unity.

Assuming Dalton's law is vahd for the the low pressure gas phase, the CO,

fugacity is related to the number o i moles of gaseous CO, by the ideal gas law

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where pc4 stands for the p d pressure of CO,, R denotes the ideal gas constant, T

represents the absolute temperam, and Vg stands for the volume of the gas phase in

the representative volume. The gas phase volume Vg is related geometrically to the

representative volume V by

v, = v $ (I-S) (13)

where 4 stands for the total (gzs and liquid) porosity, and the saturation, S, denotes

the fraction of porosity occupied by the liquid phase. The mass of water can be

expressed in similar terms by

where pHzo stands for the mass Of q0 per volume of liquid.

Substituting Eqs. (2)-(5) and (10)-(14) in Eq. (8) and solving for - yields COY

Substituting the same equations in (7) and solving for aH+ yields

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Component Aqueous Calcium

Aqueous Sodium Aqueous Carbon

PH Fugacity - fco2

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Concentration (rn~les/rn~,~,)

0.40

1.17 2.00

8 0.0012 bar

These substitutions reduce the chemical equilibrium problem to a set of two equations

to be solved simultaneously in the absence of calcite. Once solved the saturation state

of the system with respect to calcite is checked, and if the solution is supersaturated,

then Eqs. (6) and (10) are substituted in Eq. (9) and solved

In this case Eq. (16) contains a modified term for the mass

is obtained by sirmlar substitutions yielding

r

for ncaco, *

t 17)

of aqueous calcium, which

If calcite is present Eqs. (15), (17), and (18) must be solved simultaneously. These

Table 1. Initial Geochemical Conditions

of two or three equations are solved for each point in the domain, at each time by a

Xewton-Raphson technique using masses (e.g.. nNa. nca) provided by the transport

model. Activity coefficients are used from the initial condition or previous time step to

simphfy computations, introducing negligible error. Thermodynamic data are derived

from the EQ3/6 data base R16.com (Wolexy and Daveler, 1992). Equilibrium constants

as a function of temperature are consistent with data reported by Johnson et al. (1992).

Initial conditions for the chemistry model are given in Table 1.

Carbon System Transport

The form of the non-reactive transport equation for both gas and aqueous phase

species, in cylindrical coordinates, is

where the independent variables are time t (s), radial coordinate r (m) and vertical

coordinate z (m). The dependent variables are c, the transported species concentration

(rnoles/m3), D the effective diffusion coefficient (m2/s), the Darcy velocity field,

defined by u and v (ds) and 7 is defined as S for liquid phase saturation and (13)

. for gas phase saturation. Equation (19) results from an operator splitting approach in

which the chemical constituents are first transported non-reactively, hence the zero on

the right-hand-side of Eq. (19). This transport step is then followed by a chemical

equilibrium calculation at each node.

The diffusion coefficients are assumed to be isotropic and homogeneous, and

are therefore, scalar valued functions. Mechanical dispersion is neglected in this

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analysis. For aqueous species uanspoxt, the diffusion coefficient is taken as a function

of tempemure only and is calculated as

E D.?" = A exp (--) RTi.j '.J

where A = 1.02e-06 m h , E = 1.66e44 Jlmole, R - 8.31441 J/mole-K, and Ti j is the

local absolute temperam. This equation is an empirical regression based on data for

sodium ions (Oelkers and Heigeson, 1988). For gas phase species transport the

diffusion coefficient is calculated here as

where the diffusion constant Do = 1.44e-05 m2/s, Po is standard atmospheric pressure

in Pascals (-1.013e+05 Pa). To is the temperature at standard conditions (-273.15 K),

and Pi,j and Ti,j are the local values of pressure and temperam, respectively. This

equation is taken from Bird Stewart, and Lightfoot (1960) and was developed for

calculating the diffusivity of CO, in fke air.

The uanspon equation for a species concentration c is solved by integrating

Eq. (19) over a nodal control volume. This control volume surrounds a single

computational node which is centered within the volume (Figure I). The result of this

integration is a semi-discrete form of Eq. (19) and is written as

where the subscripts e, w, R, s refer to different faces of the control volume. The

volume (rArAz) and facial areas (rAz or r&) of the control volume are scaled by the

porosity and saturation, such that only that area or volume open to flow are used for

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n rArAz (c.? - Ciqj) - + (rAz c , - (rAz u ) ~ t, I*J At

either liquid and gas phase transport.

The tlux coefficients represent the volume flu across each 5ce of the control

voiume. They are defrned as (refer to Figure 1 for definition of gecmemc terms and

nodal locations o i variables)

where again. the flux cross-sectional areas have been scaled by the prosity and

saturation ievels.

The spaual gradient terms in Eq. (22) are defined by cenreza differences of the

form

which resuits in the following definitions for the diffusion coeffcicm

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Substim&I L ----,Tc& 'ps into Eq. (22) results in the discrete form of

Eq. (19), which is

Once c,, c,, c - . .. r . . =x XE k r l and substituted into Eq. (27). terms associated

with each of the n x i ;--re f : LY collected, resulting in a system of algebraic

equations of the f r

ap.: :-- = 2 L - - >=: ..j . c. I- 1.j + ani,j Ci . j+~ + aSij Ci,j-1 + S%.j (28)

where we defme

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rArAz + FLE - FLW + FLN - FLS + -

At + aRj - aeij + awij + aq,j

n L ~ A Z s q j = c.. - At

The definition of the coefficients aeij, awiVj. aq j , and asij are determined by the

convective interpolation scheme.

Two methods are used to represent the facial values of the species

concentration associated with the convective fluxes in Eq. (27). The first uses a

combination of centered interpolation (second-order) with first-order upwinding, and

the second uses first-order upwinding only. This first method is the HYBRID scheme

of Spalding (1972) and is also hown as the “high-late& flux mMication” to the

second-order centered interpolation scheme. A third and more promising method was

developed here based on a third-order convective scheme. This method is a derivative

of the QUICK Scheme (Leonard, 1979; Freitas et al., 1985). However, typical of

higher-order convective methods, spurious overshoots and undershoots at steep

gradients have limited the applicability of this method to solving reactive transport

problems. The authors are presently working on a monotomicity-preserving form of

this scheme which should allow for solution of reactive transport problems.

The HYBRID method segregates the interpolation process into three regions,

defmed by the magnitude of the cell Peclet number. The cell Peclet number is defined

as the ratio of the flux coefficient to the diffusion coefficient; i.e., on the e face of the

control volume the Peclet number is FLE/DIE. The HYBRID scheme uses fxst-order

upwinding if the magnitude of the Peclet number is greater then 2; and for Peclet

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numbers between 2 and -2, it uses second-order central differencing. Mathematically,

c, is calculated as

A compact method to represent this scheme, which eliminates conditional

checking on the direction of the velocity across a face, is to define a set of flux

parameters for each face of the ccnuol volume. For example, the e face flux

parameters are

FPE = 0.5 (FLE + IFLEI) (31) FDE = 0.5 (FLE - IFLEI)

For a positive flux, FLEA), FPE is equal to FLE, and FDE is zero. For a negative

flux, FLE<O, FDE is equal to FLE. and FPE is zero. These flux parameters turn on

and off the various terms for each component of the interpolation function which are

dependent on velocity direction. With these definitions, the HYBFUD scheme may be

compactly represented by

dmy.

&i+l.j - max [-FDE, DIE - FLE ( 2 1 1 a%j

dmq . &i,j

awij = max I p W , DIW + FLW (>)I

a q j = max [-FDN, DIN - FLN (>)I dmv. .

dzi,j+l dmv- .

. - ma^ [Fps, DIS + FLS (L)] dzij

1.J

The first tern within the brackets of these expressions represents the first-order

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upwinding contribution. um z: =End term is the second-order central interpolation

contribution. By simply 50~,3-~- -2 expressions of Eq. 32 one can use either central.

interpolation, fmt-order u p - z g . 3r HYBRID to model the convective fluxes. The

equivalent expressions fcr 5z-c~~ upwinding only are

z:. 1 DIE - FDE L X : : - DIW + FPW 3: -DIN - FDN 5: - DIS + FPS

-1 -,

-J

-1

and for second-order cenrn i ==ia.rion they are

(33)

In the expressions for h-xx :?-Inding, a physical diffusion contribution is

present, while this term 1s e;--y-w m the HYBRID formulation. This is done in the

HYBRID scheme in an sump 12 compensate for the spurious numerical diffusion

introduced by fust-order up-. In the simulations that follow, calculations are

made using the HYBRID Sciz Eq. 32) and fmt-order upwinding (Eq. 33). The

algebraic equation systems xii x i - e i using an SLOR matrix solver.

Model results

To illustrate the capc!;-rrt c i the CST model, results are presented for times

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ICQ and 600 yr following inuoducuon of the heat source. This is a period of rapid and

m:or changes in the near field zone. Temperature, pressure, and saturation distribution

arc 2ustrated in Figs. 2-4. These results are initially derived from CTOUGH.

Terzperature rises to over 150°C at the repository horizon in 100 yr, but is still close

to ;%tial conditions at the model boundanes. At 600 yr temperature gradients have

mc&rated as the near field cools. Saturations go to zem around the repository horizon,

k a v q a nearly desiccated interval approximately 50 m thick at 600 yr. Pressure

incp3es to 1.5 times ambient at 100 yr at the repository horizon, but decreases to 1.2

tirzlts ambient at 600 yr.

Similar excmions from ambient conditions occur in carbon system chemistry

due :o repository heating and fluid flow as observed in the model of Codell and

M-ny (1992). With increasing temperature. CO, exsolves from the aqueous phase to

the gas phase. Solution pH rises with temperature, and aqueous carbon speciation

sh15~ from HC03- to CO,*-. Increasing pH, increasing temperature, and evaporation

all ?mote calcite precipitation. The maximum mass of calcite distribution to

pE:pitate is limited by the suppiy of aqueous Ca2'. The aqueous concentration of

Ca-' drops to iow values in areas of elevated temperature.

Aqueous and gas phase carbon and calcite concentration are illustrated in Figs.

5- - . These calculations were pe~ormed using the HYBRID scheme. Evaporation

(voiatllization) and gas phase nanspon cause rapid carbon redistribution on the scale

of ke mountain resulting in steep _madents in carbon. Carbon is transported hundreds

o i ;~efers in hundreds of yean. Although transport is dominated by rapid gas flow,

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most carbon remains in the aqueous phase in the absence of dessication, so its

migration rate is retarded by the ratio of its aqueous to gas phase distribution. The

mass of carbon precipitated in calcite is small compared to that in fluid phases except

in nearly desiccated areas. CO, liberated horn the aqueous phase in the near field is

transported in the gas phase to the cooler far field both above and below the repository

horizon where it panially condenses in the aqueous phase. Evaporation and gas phase

flow nearly decarbonate the near field.

Figure 5 illustrates that the total aqueous carbon is not strongly affected in the

region above the zone of drying, although the dismbution of carbon species shifts due

to pH changes (see below). Below the repository a greater increase in aqueous carbon

is predicted. In part this effect is due to the no-flow boundary condition at the water

table, which prohibits escape of carbon purged from the near field and the effects of

gravity on water dismbution.

Figure 6 illustrates that a CO, enriched plume of gas moves upward from the

repository horizon. Maximum concentrations in the gas phase are over 10 times greater

than ambient values at 100 yr in an area above the advancing temperature and

dessication fronts. (Ambient CO, pressures in the subsurface are themselves

approximately 4 times atmospheric values.) Similarly at 600 yr the CO, gas

concentrations are over 20 times ambient values near the ground surface over the

center of the repository in an area minimally affected by temperature or saturation

variations. These results indicate that an early surface manifestation of the repository

will be gas springs of CO, enriched gas eminating at the surface, Le., repository

’

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induced CO, fumaroles. Hetemgeneous gas flow in fractures is likely to accelerate and

m a w local manifestations of CO, fumeroles. This early chemical manifestation of

the repository at the ground surface may have biological consequences. The initial

CO, plume will also tend to acidify groundwater solutions promoting reactions in the

silicate system, which are not represented in the model.

The distribution of calcite (Figure 7) is a complicated function of retrograde

solubility, pH variation with CO, pressure changes, and calcium transport by liquid

flow and concentration by evaporation. Solutions are initially undersaturated with

respect to calcite, but by 100 yr quantities of calcite approaching the initial aqueous

calcium content precipitates within tens of meters of the repository horizon. By 600 yr

notable calcite precipitation occurs in the immediate area of the repository horizon and

also in a zone extending from the repository edge to the groundwater table. This edge

effect is apparently a consequence of liquid flow shed off the edge of the repository

carrying calcium into regions of higher temperature and higher pH. Concentration of

calcite precipitation due to this edge effect could have consequences for fluid flow.

However, such effects were not included in the model.

Finally, Figure 8 displays a comparison of the pH distribution at 600 yr as

calculated by the HYBRID scheme and the fmt-order upwind scheme. Clearly seen in

these figures are the spurious dissipative effects of fmt-order upwinding on pH

gradients. This behavior is exhibited in all the transported quantities. pH gradients

above and below the repository an smeared out by fmt-order upwinding, while the

HYBRID scheme maintains them to a greater extent. Although the HYBRID scheme is

24

W II

not fully second-order. it does h i t , to a degree, the artificial smoothing of gradients

introduced by first-order upwinding. Certainly a third- or higher-order convective

scheme would resolve these p d i e n t even more accurately.

Conclusions

Carbon system chemisn?; an affect performance of the proposed nuclear waste

repository at Yucca Mountain, Szvada, through controls on solution pH, radioelement

solubility and speciation. retardation of xadionuclide migration by sorption, stability of

sorptive phases, and “C mi-&on. A gas and liquid phase reactive transport code

(CST) has been developed to model the carbon system chemistry and pH. It has the

capability to provide constraints for performance modeling of radionuclide release and

retardation of radionuclide migation. The CST code incorporates HYBRID and fmt-

order upwind schemes for convective transport modeling. The results presented here

demonstrate the superior ability o i the HYBRID scheme to resolve sharp gradients.

Preliminary results demonstrate the capabilities of the numerical model and

give indications of extensive ma large scale variations in carbon system chemistry due

to heat and fluid flow in the reFsitory. The results presented here could change if, for

example, different mated properties were used to represent the tuff host rock.

Furthermore, the applicability o i the equivalent continuum model needs to be more

fully investigated for species uanspon. A more detailed and longer term repository

model is in preparation for pexformance assessment applications. And, the author are

working on the formulation of a thud-order convection scheme that eliminates

spurious overshoots and underSnoots that are typical of these higher-order methods.

’

25

Acknowledgments. Richard B. Codell assisted with model development. The report

documents work performed at rhe Center for Nuclear Waste Regulatory Analyses

(CNWRA) for the Nuclear Regulatory Commission (NRC) under contract NRC-02-93-

005. The paper is an independent product of the CNWRA and does not necessarily

reflect the views or regulatory position of the NRC.

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32

'u,

Fi-eue Captions.

1. Definition of geomemc terms for a cell centered control volume.

2 . Temperature ("C) distribution at 100 years (A) and 600 years (B). Vertical scale is the same as horizontal scale.

3. Pressure (Pa) distribution at 100 years (A) and 600 years (B). Vertical scale is the same as horizontal scale.

4. Saturation distribution at 100 years (A) and 600 years (B). Vertical scale is the same as horizontal scale.

5 . Distribution of total aqueous carbon (moles/&) at 100 years (A) and 600 years (B). Vertical scale is the same as horizontal scale.

6. Distribution of gas phase carbon (moles/&) at 100 years (A) and 600 years (B). Vertical scale is the same as horizontal scale.

7. Distribution of calcite (rnoles/d) at 100 years (A) and 600 years (B). Vertical scale is the same as horizontal scale.

8. Comparison of pH distribution at 600 years, calculated by HYBRID (A) and first-order upwind (B). Vertical scale is the same as horizontal scale.

33

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