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2 938 Transport of Multiple Reactive Chemical Species C. Carnahan and J. Noorishad SUMMARY either linear or axisymmetric cylindrical. The CHEMTRN program has been widely circulated and has been used in a large number of applications to reactive chemical transport problems. However, further experience with these problems led to recognition of a need to extend modeling capabilities beyond those of CHEMTRN. In particular, capabilities were needed to treat systems with variable temperature and oxidation potential as well as systems supporting nonequilibrium chemical reactions and coupled transport processes. Recent research on the simulation of reactive chemical transport at Lawrence Berkeley Laboratory has led to significant extensions of the CHEMTRN methodology in the forms of two newer programs called THCC and CHMTRNS. Our concurrent research on coupled transport processes has resulted in a program called TIP; recently, we have extended the capabilities of TIP by incorporating chemical reactions, following the same approach used in THCC. Our research on transport of reactive chemicals in ground water has followed two paths which recently have converged. On one path, we have developed computer programs (CHEMTRN, THCC, CHMTRNS ) that have focused on incorporating rigorous treatment of chemical reactions, both homogeneous and heterogeneous, directly into the solution of equations of multiple-species mass transport. These programs are based on fundamental chemical thermodynamic and kinetic principles and avoid the restrictions and pitfalls associated with empirical formulations of chemical interactions. On the other path, we have focused on the complete description of physical processes affecting transport of heat and fluid as well as reactive solutes. This has led to development of a computer program (TIP) capable of simulating coupled transport processes, such as chemical osmosis and thermal osmosis, that can be important in a variety of natural settings and engineering applications. The two paths have converged with the incorporation of our reactive chemical transport modeling methods into the TIP program. The resulting program extends our chemical transport modeling abilities to considerably more complex problems. THE THCC PROGRAM The CHEMTRN program is constrained to operate under conditions of constant temp6rature (although temperature can be varied from simulation to.simulation) and constant (or unspecified) oxidation potential. However, certain important applications (e.g., hydrothermal regions, geological repositories for nuclear wastes) require consideration of effects of temperature gradients and possible mixing of fluids with different temperatures and compositions on transport ofreactive solutes. In addition, certain important materials (e.g., the actinide elements) can exist in several oxidation states that exhibit distinctly different chemical behaviors. These considerations led to the development of the THCC program. In the THCC program, equilibrium constants are temperature-dependent and are calculated from thermodynamic expressions. During simulations in which temperature varies with time, the equation of heat transport is solved at each new time level. Simulations can be done of systems with fixed gradients of ternperature, of systems with evolving thermal fields due to mixing of fluids having different temperatures, and of isotliermal systems. Oxidationreduction reactions are treated by either of two methods. One meth6d assumes that the oxidation potential of the simulated system is determined solely by chemical reactions included in the simulation. The other method assumes that the oxidation potential is controlled externally, either by poising by one or more dominant redox couples not included explicitly in the simulation or by an imposed electrical potential. Functions of the THCC program and the method of solution used have been described in detail elsewhere [Carnahan, 986a, 987a,b,c], and examples of applications have been given [ Camahan, 987b; 988a,b]. One example [ Carmahan, 987b] is described briefly here. INTRODUCTION In recent years, considerable progress has been made in the development of computer programs that simulate multicomponent chemical transport with chemical reactions occurring together with mass transport processes. These programs, in general, treat specific chemical reactions occurring in a single fluid phase whose components are subject to diffusion, advection, and possibly other mass transport processes. Chemical reactions are described quantitatively by use of thermodynamic data (usually equilibrium constants) or kinetic rate constants or both. Thus, these programs are based rigorously on chemical principles and in this sense are distinguishable from solute transport programs that rely on Ki's or other empirical formulations. A significant advance in capability for solving complex problems of Inulticomponent, reactive chemical transport occurred with the development at Lawrence Berkeley Laboratory of the CHEMTRN program [Miller, 983; Miller and Benson, 983]. This program assumes all chemical reactions to be at equilibrium at constant temperature and oxidation potential and uses the "direct" method of solution in which the equations of transport are solved simultaneously with thermodynamic mass action relations. Chemical reactions simulated are speciation and variable ph in the aqueous phase, precipitation, cation exchange, and surface complexation. Mass transport processes simulated are advection with constant fluid velocity, hydrodynamic dispersion, and chemical diffusion in one-dimensional geometry, 7

3 The THCC program was used to simulate transport of aqueous uranium species within a porous matrix in the presence of a radial temperature distribution varying from 9 C at the inner boundary to 5 C at a distance of m. A constant flux of uranium dissolved in a source fluid enters a porous matrix in a field of flow having a pore fluid velocity of 3 x -8 In/s (approximately m/y), with a dispersivity of.5 m and a diffusion coefhcient of l x - m/s. The fluid present in the porous matrix has an initial temperature of 5 C and an initial composition approximating a basalt ground water, with ph equal to, Eh equal to -.36 v, total carbonate equal to 9 x -4 M, and ionic strength equal to.6 M, and is saturated with respect to amorphous silica. The source fluid has a temperature of 9 C, 9x-4 M total carbonate and ionic strength equal to.6 M, but no dissolved silica, and is assumed in equilibrium with solid uraninite [U(c)] at a ph of 6 and an Eh of. v. It is assumed that oxidation potentials in the initial and influent fluids are poised by redox reactions external to the simulation. Figure shows the temperature profile, constant during the simulation, and profiles of oxidation potential and total dissolved uranium concentrations at a simulated time of l x 7 s ( approximately.3 y). Also shown is the theoretical solubility of collinite [USi4 (c)] calculated for prevailing values of ph, Eh, and temperature. Filled symbols in the uranium concentration curve designate finite-difference nodes where precipitates of coffinite exist. The uranium species in the source fluid are predominantly UOCO and U(C3 )t- with smaller concentrations of UOH+, UOi, and U(OH ). At the simulated time of lx7 s, cofhnite (more stable here than uraninite) has precipitated at the first four nodes beyond the source, lowering dissolved uranium concentrations by a factor of more than 4, relative to the source concentration. Because of decrease of oxidation potential, the dominant solution species of uranium within the domain of transport is U(OH)5. An interesting feature of Figure is the minimum in the concentration profileof dissolved uranium near the source. This has happened because of precipitation of coffinite in the near-source region followed by further lowering of uranium concentrations caused by upstream diffusion of reducing species and silicic acid. precipitation of calcite in flowing ground water [Noorishad et al, 985]. In this and later versions of CHMTRNS all existing functions of CHEMTRN were retained. Further additions to CHMTRNS consisted of capabilities to simulate kinetic dissolution or precipitation of various silica phases and irreversible dissolution of glass. Capabilities to treat variable temperatures and variable oxidation potentials in the manner of the THCC program were added. An especially interesting addition is the capability to simulate fractionation of 3C during transport with both equilibrium and nonequilibrium reactions involving carbonate species [Noori3had et al., 986]. Detailed descriptions of the functions of the CHMTRNS program, the method of solution used, and several example simulations have been given by Noori8had et at. [987. One example is described briefly here, The CHMTRNS program was used to simulate the fractionation of 3C in recharging water containing dissolved C gas as the water percolates through, and reacts with, marine carbonate rocks. The 63C values are assumed to be -5/ in the water initially and / in the rock. When this rock-water system has come to equilibrium with respect to the chemical reaction (g) + H + CaC3(c) = Ca+ + HCO3, the 63C value in the aqueous solution is expected to be -.5 /. Three scenarios were simulated: () batch kinetic dissolution of calcite, () equilibrium dissolution with transport, and (3) kinetic dissolution with transport. The batch scenario simply contacts the initial recharging water, having P(( ) = -.5 atm, PH = 5, and 6 3C = -5/, with calcite having 63 C = / and allows the system to proceed to equilibrium without any transport. In the two scenarios with transport the recharging water, having the same chemical characteristics as in the batch scenario, flows into a one-dimensional domain in which water with PH = 5 and zero 3( has been allowed to come into chemical equilibrium with calcite; the influent recharging water mixes with and displaces the initial water and reacts with the calcite either instantaneously ( equilibrium scenario) or in finite time (kinetic scenario). Figure shows plots of 6 3C in the fluid phase vs. time for the three scenarios; for the two transport scenarios, results are shown at a point located. m downstream from the inlet where recharging water enters the system. In the batch kinetic and equilibrium transport scenarios the 63C in the fluid phase has reached the equilibrium value of -.5 / by a time of one year. However, in the kinetic transport scenario the 83 C at. In has decreased to -8 / at this time; the rate of dissolution of calcite is evidently too slow, relative to the influx of water light' in 3C, to allow achievement of equilibrium at this location and time. THE CHMTRNS PROGRAM Laboratory and field investigations have shown that imposing the constraint of equilibrium on chemical reactions can be a serious deficiency when modeling certain chemical systems. For example, comparison of computer simulations that assume chemical equilibrium with observed geothermal fluid compositions and associated mineral assemblages has revealed dissimilarities indicative of kinetic hindrance of certain reactions. Thus, for many problems the slowness of reaction rates necessitates the implementation in computer programs of time-dependent, nonequilibrium chemical calculations. This necessity led to the development of the CHMTRNS program. The CHMTRNS program began as a modification of the CHEMTRN program to simulate kinetic dissolution or THE TIP PROGRAM Certain earth materials are known to exhibit properties of semipermeability. These materials include naturally 7

4 I : occurring clays and shales as well as clays that might be used in engineering applications stich as linings of waste disposal pits and packing around nuclear waste canisters. In the presence of gradients of temperature, pressure, or fluid composition, coupled transport processes - thermal osmosis, thermal filtration, chemical osmosis, and ultraflltration - can occur in semipermeable materials simultaneously with the direct processes - heat conduction, advection and chemical diffusion - expressed by Fourier's law, Darcy's law, and Fick's law. The computer program TIP is based on the theory of the thermodynamics of irreversible processes and solves the coupled equations of heat, fluid and solute flow under conditions of spatially and temporally varying fields of temperature, pressure, and composition. The TIP program was developed to investigate the significance of the coupled transport processes relative to the direct processes in various natural and artificial applications. Accounts of the theoretical background and particular applications of the TIP program have been given by Carnahan'[984,985, 986)] and Jacobsen and Carnahan [986]. In its original form, the TIP program did not account for chemical reactions. Recently, however, capabilities to simulate equilibrium chemical reactions, using the methodology of the THCC program, have been added to TIP [JacobBen and Carnahan, 988]. Currently, TIP will simulate formation of aqueous-phase complexes, ionization of water, and cation exchange; the ability to simulate reversible precipitation will be added in the near future. Because the chemical version of TIP retains all functions of the original version, it is a very powerful tool, extending the chemical transport capabilities of the THCC program to applications involving variable fluid flow fields. The chemical-tip program is being used in an ongoing investigation of the effects of major ground-water cations on the cation-exchanging properties of sodium bentonite used as packing around waste canisters. Results of simulations of alteration of the sorbed-phase composition of sodium bentonite by ground-water components have been reported [Jacobaen and Carnahan, 988] and are described briefly here. ACKNOWLEDGEMENT This work was supported by the U. S. Department of Energy under contract No DE-AC3-76SF98. REFERENCES Carnahan, C L, Thermodynamic coupling of heat and matter flows in near field regions of nuclear waste repositories, in Sc:ent:,#c Basis for Nuclear Waste Management VII, Mater. Ra. Soc. Symp. Proc., vol. 6, edited by G L McVay, pp. 3-3, NorthHolland, New York, 984. Carnahan, C L, Thermodynamically coupled mass transport processes in a saturated clay, in Scientific Ba88 for Nuclear Waste Management VIII, Mater. Res. Soc Symp Proc, vol 44, edited by C. M. Jantzen, J A Stone, and R C Ewing, pp , Materials Research Society, Pittsburgh, Pa., 985. Carnahan, C L,A simulator of solute transport in saturated porous media incorporating variable temperature and oxidation potential (abstract), Eos a,w. AGU, 67, 965, 986a Carnahan, C L, Thermal osmosis near a buried heat source, Int Comm Heat Mass Transfer, 3, , 986b Carnahan, C L, Simulation of chemically reactive solute transport under conditions of changing temperature, in Conpkd Processes ABBociated luith Nuclear Wade Repos:torzes, edited by C.-F. Tsang, pp , Acaderruc Press, Orlando, Fla., 987a. Carnahan, C L, Simulation of uranium transport with variable temperature and oxidation potential: the computer program TIICC, in Scientijic Ba8iJ for Nudear Waste Management X, Mater. Ra. SOC. Symp. Proc, vol 84, edited by J. K. Bates and W. B. Seefeldt, pp. 73 7, Materials Research Society, Pittsburgh, Pa., 987b. Carnahan, C. L., Simulation of oxidation-reduction reactions in multicomponent solute transport (abstract), Eos Trans. AGU, 68, 74,987c. Carnahan, C. L., Some effects of data base variations on numerical simulations ofuranium migration, Radiochimica Acta, in press, 988a. Carnahan, C. L., Simulation of effects of redox and precipitation on diffusion of uranium solution species in backfill, in Scient:Bc Basis for Nuclear Wa,Bte Management XI, edited by M. J. Apted and R. E. Westerman, Materials Research Society, Pittsburgh, Pa., in press, 988b. Jacobsen, J. S., and C. L. Carnahan, Chemical osmosis and thermal osmosis near a heat source buried in a saturated, semi-permeable medium (abstract), Eos it ans. AGU, 67,965, 986. Jacobsen, J. S., and C. L. Carnahan, Numerical simulation of alteration of sodium bentonite by diffusion of groundwater components, in Scientijic Basia for Nuclear Waste Management XI, edited by M. J. Apted and R. E. Westerman, Materials Research Society, Pittsburgh, Pa., in press, 988. Noorishad, J., C. L. Carnahan, and L. V. Benson, Development of a kinetic-equilibrium chemical transport code An annulus of sodium bentonite with inner radius of.35 m and outer radius of.85 m is equilibrated with a ground water containing the following initial concentrations of cations (M): Na+,.76; K+,.5x-3; Ca' +,.6; Mg+,.7x -4. The equilibration displaces Na+ from the exchange sites on the bentonite, replacing it with,varying quantities of the other cations. Cations from the original ground water are then allowed to diffuse radially into the bentonite from the outer boundary, where cationic concentrations are held constant. At the inner boundary, cationic concentrations and composition of the sorbed phase are held fixed at the values resulting from the initial equilibration. Figure 3 shows the composition of the sorbed phase in the bentonite as a function of radius at years after diffusion has started. It is seen that strong sorption of Ca+, accompanied by significant displacement of Na+, has occurred in the outermost. m of the annulus. Further inward from this region, decreased concentrations of diffusing Ca+ allow increased sorption of K+ and Mg+. I 73

5 (abstract), Eos YFans. AGU, 66, 74,985. Noorishad, J., C. L. Carnahan, and L. V. Benson, Simulation of fractionation of 3C during nonequilibrium reactive solute transport in geologic systems (abstract), Ew Traw. AGU, 67, 939, 986. Noorishad, J., C. L. Carnahan, and L. V. Benson, Development of the non-equilibrium reactive chemical transport code CHMTRNS, report LBL-36, Lawrence Berkeley Laboratory, Berkeley, Ca., & TRANSPORT EQUILIBRIUM ', 8 - eo CO 4 BATCH KINETIC 6. 8 t < KINETIC TRANSPORT, LOG TIME, years Fig.. 63 in aqueous phase vs. time for three scenarios. 9C TEMPERATURE a.e 8 7 O.OO OXIDATION POTENTIAL.- > -. LU_E ) E TOTAL URANIUM CONC 57/ -9- USi4(c) solubility L. / E simulation Z -i. BEZ - M -... ' -3. : DISTANCE, m Fig.. Temperature, oxidation potential, and total uranium concentrations vs. distance at time x 7 s. Fillid symbols denote presence of USi4(c). Q 5 ' 8CD CK (/) - 8 'cr- :i Na+ V ":.A,X «-«««««««,f 3 ( VIVV V. Mg RADIAL DISTANCE, m Fig. 3. Moles of cations sorbed on bentonite per din3 of aqueous phase vs. radial distance at time years. 74 "