- Email: [email protected]
PASSIPHIC: A program for solubility calculations involving complex solids
PII:
Computers & Geosciences Vol. 24, No. 9, pp. 839±846, 1998 # 1998 Elsevier Science Ltd. All rights reserved Printed in Great Britain S0098-3004(98)00064-8 0098-3004/98/$ - see front matter
PASSIPHIC: A PROGRAM FOR SOLUBILITY CALCULATIONS INVOLVING COMPLEX SOLIDS SUSANNE BOÈRJESSON*, and ALLAN EMREÂN Department of Nuclear Chemistry, Chalmers University of Technology, 412 96 Goteborg, Sweden (Received 2 May 1997; revised 30 March 1998) AbstractÐIn modelling solid±water interactions, where the solid consists of many phases, more phases may be present than is allowed according to the phase rule. The problem becomes even more complex if one or more of the phases are solid solutions. Examples of such solids are rock and cement. To simplify the calculations, these solids may be presented independently of the water solution as a set of dierent phases; pure minerals and/or solid solutions. The PASSIPHIC program has been developed to handle the interaction of pure solids and solid solutions with an aqueous phase. SOLISOL and PHREEQE are among the sub-programs forming the program package PASSIPHIC. The program SOLISOL was originally developed to handle ideal solid solution±aqueous solution reactions only. The program has now been modi®ed to handle non-ideal binary solid solutions as well. In the equilibrium calculations the program PHREEQE is used. The input data to PASSIPHIC are the composition and amount of each phase, secondary minerals that may form, parameters in Guggenheim's excess free enthalpy of mixing equation (for non-ideal binary solid solutions) and the composition of the aqueous phase. The result gives the equilibrium composition of the dierent phases in the solid and the aqueous phase. To test the PASSIPHIC concept, the solubility of the gel phase in cement has been modelled. # 1998 Elsevier Science Ltd. All rights reserved Code available at http://www.iamg.org/CGEditor/index.htm Key Words: Solid solution, SOLISOL, Activity coecient, Cement, PHREEQE.
INTRODUCTION
In the performance assessment of an underground repository for radioactive waste, computer simulations are tools for predicting the interactions of groundwater with dierent barriers. These barriers may for example be the rock itself, cement-based systems or bentonite clay (e.g. the Swedish concept as described in SKB, 1983). All these solid barriers may consist of mixtures of pure minerals and solid solutions. A program frequently used in solubility calculations is the thermodynamic equilibrium program PHREEQE (Parkhurst, Thorstenson and Plummer, 1990). The standard version of PHREEQE considers all solids as pure minerals, dissolving congruently according to their stoichiometry. Because solid solutions have variable compositions, the standard PHREEQE program alone is not suitable for solid solution±aqueous solution (SSAS) equilibrium calculations. Solid solutions often have a miscibility gap that causes the solid solution in this region to be described with two solid solutions of dierent compositions. When modelling such a two-phase *Corresponding author. Fax: +46-21-772-2931; E-mail: [email protected]. {Pure phAses and Solid Solutions In PHREEQE equIlibrium Calculations. 839
system with a composition in the miscibility gap, phase rule violation will occur in the PHREEQE calculations. Muller, Parkhurst and Tasker (1986) used a modi®ed version of PHREEQE to model solid solutions in equilibrium calculations. In their approach, the solid solutions are handled as pseudo-elements and special de®nitions of aqueous species are made. An ideal solid solution or a constant activity model is considered in the calculations and the program handles one binary solid solution at a time. The PHRQXL code developed by Glynn and Parkhurst (1992) calculates equilibrium reaction paths in a binary non-ideal SSAS system. The authors use the modi®cations of PHREEQE as proposed by Muller, Parkhurst and Tasker (1986). In addition to these modi®cations, subroutines were added to PHRQXL to make it possible to handle regular and sub-regular binary solid solutions. One of the subroutines originates from the MBSSAS code (Glynn, 1991) and allows the program to calculate characteristic features of a binary SSAS system such as miscibility and spinodal gaps. The PHRQXL program handles one solid solution at a time together with any pure solids. The PASSIPHIC{ package presented in this work is developed to be used in water interactions with
840
S. BoÈrjesson and A. EmreÂn
Figure 1. Conceptual model of PASSIPHIC program
complex solids. It is designed to handle one or more solid solutions together with pure minerals in equilibrium calculations with standard PHREEQE. The PASSIPHIC program is able to handle multi component solid solutions with the restriction that the activity coecients have to be constant. For binary solid solutions, a sub-regular model can be used. It should be noted that the PASSIPHIC program does not have the ability to determine the parameters needed. For this purpose the MBSSAS program may be used (Glynn, 1991). PASSIPHIC calculates the equilibrium state for any given start composition. In the situation of phase separation, ®nal phase compositions are determined automatically. Besides the problem with solid solutions when using standard PHREEQE in equilibrium calculations, an apparent phase rule violation may occur in calculations with complex solids. This is taken care of by PASSIPHIC. The sub-program SOLISOL is called by PASSIPHIC to perform SSAS equilibrium calculations. The original version of SOLISOL could handle ideal solid solutions only (BoÈrjesson and EmreÂn, 1993). It has now been extended to handle also non-ideal binary solid solutions. To test the PASSIPHIC program, the solubility of the binding phase in cement, the amorphous calcium silicate hydrate (denoted C±S±H in cement chemistry), was modelled. The C±S±H phase can be modelled as a binary solid solution with the components (end-members) Ca(OH)2 and CaH2SiO4 as proposed by Greenberg and Chang (1965). It has
been indicated that the C±S±H phase has a miscibility gap (Kersten, 1996; BoÈrjesson, EmreÂn and Ekberg, 1997) where the upper boundary in this region has a composition close to pure Ca(OH)2(s). Thus, to model a metastable C±S±H gel in the miscibility gap will cause an apparent violation of the phase rule in PHREEQE calculations. CONCEPTUAL MODEL AND PROGRAM OVERVIEW
The PASSIPHIC program has been developed to determine equilibrium in systems where an aqueous phase is in equilibrium with a complex solid. Further, the program is able to perform a number of leaching steps, where the aqueous solution is replenished in every new step. A complex solid is here de®ned as a solid, which macroscopically looks like one homogeneous substance, but which at a closer look is found to consist of several solid phases. Some of these phases may be pure minerals, whereas others are solid solutions. Examples of complex solids are arti®cial materials such as cement and spent nuclear fuel. There are also naturally occurring substances that are complex in a similar way, e.g. clay and soil. Solid solutions are treated in terms of endmembers and, since a mineral may be an endmember in several solid solutions and also present as a pure mineral, an apparent violation of Gibb's phase rule occurs frequently in such systems. Sometimes, a real phase rule violation is present in the initial (metastable) system.
Passiphic: A program for solubility calculations involving complex solids
To avoid problems from real or apparent phase rule violations, the PASSIPHIC program treats each solid solution separately and also separated from all pure phases. The water reacting with the solid is subdivided into fractions (cf. Fig. 1), each of which reacts with one solid solution or with pure phases only. Such a water fraction in contact with a solid phase will be referred to as a reaction cell. When each water fraction has been equilibrated with its solid system, all the water fractions are mixed without any mineral reactions occurring. The resulting mixture is then once again subdivided into fractions and allowed to react with the solid phases. This procedure is repeated until no more changes occur in the system. Meanwhile, some phases may have been consumed and disappeared, while a secondary phase may have formed. Since the ®nal free enthalpy of a spontaneous reaction is always lower than the initial one, the ®nal state corresponds to a minimum in free enthalpy and thus to equilibrium in the system. In the present version of the program, the reaction cells are conceptual in nature. Since two solid phases cannot be at the same place, an obvious future extension of the program is letting the reaction cells correspond to real tiny volumes and including transport between the cells as well as kinetic phenomena inside the individual cells.
solution is 2 ai,ideal Xi : For a non-ideal solid solution the activity of component i is related to its mole fraction by the activity coecient, gi, ai Xi gi :
3
Introducing Equation (3) into Equation (1) we get mi m*i RT ln Xi gi :
4
The main concept of the SOLISOL program is to calculate a saturation index, SIi (=log(ion activity product/solubility product)) for each component i in the solid solution, cf. Equation (5): SIi log
IAPi Ks,i
5
For a pure solid substance in equilibrium with an aqueous solution, SI equals zero. One should note that SI primarily is a property of the aqueous solution and not of the solid with which it may react. Normally, the composition of an aqueous solution in equilibrium with a solid solution diers from that of an aqueous solution in equilibrium with a pure solid phase. This means that the SI value of a component of a solid solution in equilibrium with an aqueous phase mostly diers from zero. As has been shown elsewhere (BoÈrjesson and EmreÂn, 1993), such a saturation index is given by log Xi gi SIi :
THEORY
The standard version of the PHREEQE program can not handle minerals with a variable composition, such as solid solutions, in equilibrium calculations. This drawback was eliminated by introducing the program SOLISOL (BoÈrjesson and EmreÂn, 1993). Originally the program was able to handle ideal solid solutions only. Soon it was extended to take care of solid solutions with constant activity coecients of the end-members. To improve the ability of SOLISOL to handle non-ideal binary solid solutions, an expression for the activity coecient of each endmember as a function of the composition has been added to the program, as is discussed in the next section. THERMODYNAMICS OF SOLID SOLUTIONS
The chemical potential of the ith component in an ideal solid solution at a given temperature and pressure is given by mi m*i RT ln ai
841
1
where ai is the activity of component i. The relationship between the activity and the mole raction, Xi, of component i for an ideal solid
6
SOLISOL makes the SIi available for PHREEQE to be used in the equilibrium calculation. The use of constant activity coecient values limits the use of the program somewhat. Thus, the ability to handle variable coecients has been included. The choice of approach has been the use of a truncated series expansion. Equation (4) can be rewritten as mi m*i RT ln Xi RT ln gi :
7
Considering the total free enthalpy of a non-ideal solid solution we get X X X non-ideal G Xi m0i Xi RT ln Xi Xi RT ln gi : i
i
i
8 The last term on the right-hand side is the excess free enthalpy of mixing, Gexcess. This term is the dierence between the free enthalpy of the nonideal solid solution and that of the ideal solid solution (Prausnitz, 1969) (at the same T, P and Xi) X excess G non-ideal ÿ G ideal RT Xi ln gi : G 9 i
Knowledge about the excess free enthalpy of mixing makes it possible to describe the thermodynamic properties of a non-ideal solution.
S. BoÈrjesson and A. EmreÂn
842
Figure 2. Hierarchical structure of PASSIPHIC package
Several empirical expressions exist for modelling the excess energy of mixing as a function of composition (Glynn, 1991). They are of the Margules type, meaning that the Gexcess is expressed with a power series of the mole fractions of the components constituting the solid solution (Prausnitz, 1969; Saxena, 1973; Glynn, 1991; Nordstrom and Munoz, 1994). One of these Gexcess ®tting functions for a non-ideal binary solid solution is the polynomial given by Guggenheim (Saxena, 1973): excess X1 X2 A0 A1 X1 ÿ X2 A2 G X1 ÿ X2 2 A3 X1 ÿ X2 3 . . .:
10
The parameters A0, A1, . . . depend on temperature and pressure. If the series is terminated after two terms we get excess X1 X2 A0 A1 X1 ÿ X2 : G
11
The partial excess free enthalpy of mixing for component i in a solid solution is related to the activity coecient by (Prausnitz, 1969) excess,i RT ln gi : G
12
To express the activity coecient for component i as a function of composition, the following expression given by Prausnitz can be used excess @ nT G RT ln gi 13 @ ni T,P,nj where ni and nT are the number of moles of component i and the total number of moles, respectively. The subscripts T, P and nj mean that the temperature, pressure and number of moles of all other components than i, respectively, are kept constant. Considering a binary mixture and applying Equation (13) to the expression for Gexcess given by Equation (11), the activity coecient as a function of composition for a component becomes RT ln g1 X 22 A0 A1 3X1 ÿ X2 :
14
PROGRAM DESCRIPTION
The PASSIPHIC program package consists of several sub-programs, all written in the program
language C with the exception of PHREEQE which is written in FORTRAN. A hierarchical structure of the PASSIPHIC package is given in Figure 2. Information is transferred between the manager, PASSIPHIC, and the sub-programs, either through the execute command or by data ®les. Such communication may also be used between sub-programs. Listed below is a short description of the function of the programs in Figure 2. PASSIPHIC: The main program that controls and distributes tasks to the other programs. It also extracts and stores aqueous solution data from equilibrium calculations with each cell. After each leaching cycle, ®les containing equilibrium composition of the solids in each cell are stored together with the aqueous phase. SETUP: This program generates the input data needed for the simulation. It is a menu program where the user interactively gives information on the system to be studied, e.g. aqueous composition, contents of the cells and possible secondary minerals. If calculations with non-ideal binary solid solutions are to be performed, the parameters A0 and A1 will be given here. MKINFILE: Creates aqueous input ®le to SOLISOL. SOLISOL: Handles solid solution±aqueous solution equilibrium calculations. PHREEQE: Calculates aqueous speciation and performs dissolution, precipitation and mixing reactions. SOL1: A sub-program to SOLISOL. Prepares the starting input ®le for the equilibrium calculation to be performed by PHREEQE on the solid solution± aqueous solution system. SOL3: A sub-program to SOLISOL. Extracts information from PHREEQE equilibrium calculation, such as the aqueous solution composition and the dissolved or precipitated amount of each end-member in the solid solution. The results are used to produce input data to PHREEQE. The mathematical model for non-ideal binary solid solutions is a sub-routine in the SOL3 program. TESTPURE: If no cell with pure minerals is present, the aqueous solution is checked to determine whether or not it is oversaturated with respect to any secondary mineral suggested.
Passiphic: A program for solubility calculations involving complex solids
843
Figure 3. Flow charts of PASSIPHIC (A), SOLISOL (B) and SOLVPURE (C)
SOLVPURE: Performs equilibrium calculations with the cell consisting of the pure minerals. Also checks for any secondary mineral to be formed. MAKEIN: A sub-program to SOLVPURE. Creates input ®le for PHREEQE. MIXING: Mixes the equilibrium solutions obtained from each cell±water interaction. The solutions are mixed in equal proportions. The programs SETUP, MKINFILE, MAKEIN and MIXING are modi®ed and/or further developed versions of programs originally developed for the CRACKER program (EmreÂn, 1998). Flow charts of PASSIPHIC, SOLISOL and SOLVPURE are shown in Fig. 3(A±C), respectively. The PASSIPHIC program starts with calling the sub-program SETUP (cf. Fig. 3A). This program makes preparations needed for the other programs. As seen in Figure 3, PASSIPHIC uses SOLISOL and SOLVPURE in an iteration loop to ®nd equilibrium. Once equilibrium has been reached and all leaching steps have been performed, PASSIPHIC ends. The equilibrium calculations for solid solutions are performed with SOLISOL (cf. Fig. 3B). Several iterations may be needed to reach equilibrium. The iteration loop consists of PHREEQE and SOL3. These programs will be called by SOLISOL until equilibrium has been reached and the program ends. The SOLVPURE program (which handles pure minerals) starts with calling the sub-program MAKEIN that creates an input ®le for PHREEQE (cf. Fig. 3C). After the equilibrium calculation with PHREEQE, the function Control checks whether the aqueous solution is oversaturated with respect to any secondary mineral. If so, the mineral will be
added to the present cell. An additional equilibrium calculation is performed. The PHREEQE program can not handle mass balances for minerals involved in the equilibrium calculations. This is taken care of by the programs SOLISOL and SOLVPURE. These programs do not allow dissolution of a larger quantity of a mineral than is available.
TEST CASE
The PASSIPHIC program has been tested on a simpli®ed model for water-cement interaction. The calcium silicate hydrate phase (C±S±H) was used as a simple model for cement. The C±S±H gel is the binding phase in cement and is likely to determine the pH in the cement pore water over a long time (Atkinson, 1985), initially giving a pH of 012.5. This environment serves as a good immobiliser for many radionuclides (Atkins and Glasser, 1992), especially the actinides (Albinsson and others, 1996). Thus, to model the solubility behaviour of the C±S±H phase is of great interest and a subject treated by many authors (Atkinson, Henson and Knights, 1987; Glasser, Macphee and Lachowski, 1987; Berner, 1992; Reardon, 1992; Kersten, 1996). The calcium silicate hydrate gel Hydrated cement is a complex solid consisting of crystalline and amorphous solid phases as well as an aqueous phase (pore water). Examples of pure minerals are portlandite (Ca(OH)2) and ettringite (3CaOAl2O33CaSO432H2O). Many of the solid phases in cement are multi-component solid solutions. The most important solid solution, however,
S. BoÈrjesson and A. EmreÂn
844
Table 1. Composition of C±S±H gel together with thermodynamic data used in calculations Phase
Reaction
log Ks 22.70 (CHEMVAL6, 1995) ÿ7.07 (Greenberg and Chang, 1965) 22.70 (CHEMVAL6, 1995)
Solid solution End-members
Ca(OH)2(s)
Ca(OH)2+2H+=Ca2++2H2O
Pure mineral
CaH2SiO4(s) Ca(OH)2(s)
CaH2SiO4=Ca2++H2SiO2ÿ 4 Ca(OH)2+2H+=Ca2++2H2O
is the amorphous C±S±H phase which is the binding phase in cement. In contact with water, the phases constituting thecement react in dierent ways. Dissolution and precipitation processes as well as the formation of secondary phases occur. These processes are governed by metastable equilibria, diusion and mixing processes, kinetics and surface area. This complexity makes it necessary to simplify the modelling of cement±water interaction. The C±S±H gel is amorphous and has a variable composition given by the Ca/Si molar ratio of the gel. The gel phase can be modelled as a binary solid solution consisting of the end-members Ca(OH)2(s) (portlandite) and CaH2SiO4(s) (Greenberg and Chang, 1965). These are the end-members used by Berner (1992) in his model of the C±S±H gel. For high Ca/Si molar ratios (>1.4±1.8), portlandite (Ca(OH)2(s)) has been observed together with the gel and coexistence has therefore been assumed (Greenberg and Chang, 1965; Atkinson, Hearne and Knights, 1987; Berner, 1992; Reardon, 1992). In the model proposed by Kersten, the gel has a miscibility gap assumed to exist in the region 0.67
boundary of the miscibility gap starts at XCa OH 2 =0.30. Kersten's assumption of the upper boundary (XCa OH 2 =0.95) agrees reasonably well with our results. The modelling work was performed according to two dierent methods, the ®rst for gels with Ca/Si mole ratios greater than 1.43 (XCa OH 2 >0.30) and the second for XCa OH 2 R 0.30. This procedure is not necessary but was followed in order to make the numerical calculations faster. The compositions used were the same as those reported for Kalousek (1952) in the experimental data compilation made by Berner (1992). In the ®rst method PASSIPHIC was used in the calculations. The initial solid was a (metastable) gel phase. SOLISOL calculations for this phase give concentrations of Ca far higher than the observed values. Portlandite was given to the PASSIPHIC program as a possible secondary phase. The PASSIPHIC simulations were performed as onestep leaching (no water replacement). During the simulations, phase separation occurred and the ®nal concentrations were close to the observed values (the plateau in Fig. 4). In the second method (XCa OH 2 R 0.30) no phase separation is expected and thus the full PASSIPHIC program is not needed. Rather, the
RESULTS AND DISCUSSION
In the model calculations, pure water was used as initial aqueous phase and the temperature was 258C. The database used was HATCHES 5.0 (Bond and others, 1992) extended with data on the minerals in Table 1. The equilibrium constant for CaH2SiO4(s) was derived from Greenberg and Chang (1965). Values on A0 and A1 used in the model, A0=3.262 kJ/mol and A1=13.44 kJ/mol, were obtained from BoÈrjesson and others (1997) where component activities were calculated by PHREEQE from experimental element concentrations in aqueous phases (Kalousek, 1952 referred to by Berner, 1992). This resulted in values of activity coecients for the components of the gel as functions of the mole fractions. By ®tting those values to Equation (14), values of the parameters A0 and A1 were determined. From the parameters it was concluded that a miscibility gap exists in which the gel coexists with almost pure portlandite (X>0.99). The lower
Figure 4. Calcium concentration in aqueous phase as function of Ca/Si molar ratio of C±S±H gel. Kalousek's data (Kalousek, 1952) from compilation by Berner (1992). Model results are shown as curves
Passiphic: A program for solubility calculations involving complex solids
new version of SOLISOL was used as a stand alone program. With SOLISOL and PASSIPHIC functioning well, it can be expected that the resulting element concentrations will be close to observed values. That this indeed happens is seen in Figure 4 where the results of the simulations are plotted together with the experimental data (Kalousek, 1952) from the data compilation made by Berner (1992) on which the parameters A0 and A1 were based. For comparison, results from calculations with the earlier version of SOLISOL (BoÈrjesson, 1994) and with the model developed by Berner (1992) are plotted in Figure 4. Figure 4 shows that the addition of the binary non-ideal solid solution algorithm to the SOLISOL program, together with the use of the PASSIPHIC package, has improved the modelled solubility behaviour of the C±S±H gel signi®cantly.
CONCLUSIONS
The tasks of this work were: (1) To modify the former version of the SOLISOL program in order to be able to use nonideal binary solid solutions in equilibrium calculations. (2) To develop a program to be used in solid phase±water interactions, where the solid phase could be considered to consist of solid solutions and pure minerals. To achieve the ®rst of these tasks, subroutines were added to SOLISOL based on the mixing model proposed by Guggenheim, the Guggenheim two-parameter equation. The model makes use of the excess free enthalpy to express a relationship between the activity coecient and the mole fraction for each end-member. To be able to use the solubility model for non-ideal binary solid solutions, it is necessary to estimate values for the parameters A0 and A1; otherwise an ideal solid solution is assumed in the calculations. (The computer program MBSSAS developed by Glynn, 1991 can be a tool to obtain values on A0 and A1 for binary SSAS systems.) For the second task, the PASSIPHIC program, was developed. To test PASSIPHIC and the present version of SOLISOL, the solubility behaviour of C±S±H was modelled. The results in Figure 4 show that the agreement between the experimental data and the model is satisfactory, representing an improvement on an earlier model by the PASSIPHIC package. Further, the use of PASSIPHIC makes it possible to overcome the apparent phase rule violation in the equilibrium calculations for compositions in the miscibility gap. The PASSIPHIC program may be down-loaded via Internet at the location http://www.nc.chal-
mers.se/sta/sb/sannebo.htm, or by FTP from the server IAMG.ORG.
845
anonymous
FUTURE WORK
As mentioned earlier, some interesting features are still missing in the program package. Some of them are desirable to incorporate in the model whereas others are best added as external programs. In the present version of the program, pure minerals but not solid solutions are able to be formed as new secondary phases. This is an obvious limitation and, thus, the formation of new solid solutions is of primary interest for future improved versions of PASSIPHIC. Another feature that needs further investigation is how to handle kinetics, both in the dissolution and in the precipitation process. At present, kinetics may be modelled by the mixing proportions, i.e. if a mineral dissolves easily and there are no mass limitations, the faster kinetics may be described by a larger proportion of the corresponding aqueous solution in the mixing step. Another obvious modi®cation is to use PHREEQC (Parkhurst, 1995) in the PASSIPHIC package. PHREEQC is a new version of PHREEQE written in the programming language C. It includes some properties that will increase the eciency of the PASSIPHIC program. The aforementioned features will be incorporated into the program itself. The eect of transport, on the other hand, will be added to the PASSIPHIC program package as a separate program. AcknowledgmentsÐThe authors would like to thank G. Skarnemark, J.O. Liljenzin and C. Ekberg for their comments on the manuscript. We would also like to thank A. édegaard-Jensen for valuable comments during the programming work. This work was funded by the Swedish Nuclear Power Inspectorate (SKI).
REFERENCES Albinsson, Y., Andersson, K., BoÈrjesson, S. and Allard, B. (1996) Diusion of radionuclides in concrete and concrete±bentonite systems. Journal Contaminant Hydrology 21, 189±200. Atkins, M. and Glasser, F. P. (1992) Application of Portland cement-based materials to radioactive waste immobilization. Waste Management 12(2±3), 105±131. Atkinson, A. (1985) The time dependence of pH within a repository for radioactive waste disposal. UK Atomic Energy Authority Report AERE-R-11777, 11 pp. Atkinson, A., Hearne, J. A. and Knights, C. F. (1987) Aqueous chemistry and thermodynamic modelling of CaO±SiO2±H2O gels. UK Atomic Energy Authority Report AERE-R-12548, 35 pp. Berner, U. (1992) Evolution of pore water chemistry during degradation of cement in a radioactive waste repository environment. Waste Management 12(2±3) , 201±219. Bond, K. A., Moreton, A. D. and Heath, T. G. (1992) HATCHES 5.0: The HARWELL/NIREX
846
S. BoÈrjesson and A. EmreÂn
DATABASE. Harwell Laboratory, Oxfordshire OX11 ORA, UK. BoÈrjesson, S. (1994) Chemical interactions in concrete systems. Licentiate Thesis, Chalmers University of Technology, GoÈteborg, Sweden, 40 pp. BoÈrjesson, K. S. and EmreÂn, A. T. (1993) SOLISOL, a program using PHREEQE to solve solid solution/aqueous equilibria. Computers & Geosciences 19(8), 1065± 1070. BoÈrjesson, S., EmreÂn, A. and Ekberg, C. (1997) A thermodynamic model for the calcium silicate hydrate gel, modelled as a non-ideal binary solid solution. Cement Concrete Research 27(11), 1649±1657. CHEMVAL6 (1995) Thermodynamic Database, version 6. Provided by Dr. S. Duerden, HMIP P3/008A, 2 Marsham Street, London SW1P 3EB, England. EmreÂn, A.T. (1998) CRACKER: a program coupling inhomogeneous chemistry and transport. Computers & Geosciences, in press. Glasser, F.P., Macphee, D.E. and Lachowski, E.E. (1987) Solubility modelling of cements: implication for radioactive waste immobilisation. Materials Research Society Symposia Proceedings, vol. 84. Boston, Massachusetts, USA, pp. 331±341. Glynn, P. D. (1991) MBSSAS: A code for the computation of Margules parameters and equilibrium relations in binary solid-solution aqueous-solution systems. Computers & Geosciences 17(7), 907±966. Glynn, P.D. and Parkhurst, D.L. (1992) Modelling nonideal solid-solution aqueous-solution reactions. Proceedings 7th International Symposium on Water± Rock Interaction-WRI-7. Park City, Utah, USA, pp. 175±179. Greenberg, S. A. and Chang, T. N. (1965) Investigation of colloidal hydrated calcium silicates. II. Solubility relationships in the calcium oxide±silica±water system at 258C. Journal Physical Chemistry 69(1), 182±188. Kalousek, G.L. (1952) Application of dierent thermal analysis in a study of the system lime±silica±water.
Proceedings 3rd International Symposium on Chemistry of Cements. London, England, pp. 296±311. Kersten, M. (1996) Aqueous solubility diagrams for cementitious stabilization systems. 1. The C±S±H solid-solution system. Environmental Science and Technology 30(7), 2286±2293. Muller, A.B., Parkhurst, D.L. and Tasker, P.W. (1986) The use of the PHREEQE code in modelling environmental geochemical problems encountered in performance assessment modelling. Proceedings of the Symposium on Groundwater Flow and Transport Modeling for Performance Assessment of Deep Geologic Disposal of Radioactive Waste: A Critical Evaluation of the State of the Art, May 20±21, 1985. Albuquerque, New Mexico, pp. 303±319. Nordstrom, D.K. and Munoz, J.L. (1994) Geochemical Thermodynamics, 2nd ed. Blackwell Scienti®c Publications, Boston, 493 pp. Parkhurst, D.L. (1995) User's guide to PHREEQC: a computer program for speciation, reaction-path, advective-transport and inverse geochemical calculations. U.S Geological Survey Water Research Investigation Report 95-4227, 143 pp. Parkhurst, D.L., Thorstenson, D.C. and Plummer, L.N. (1990) PHREEQE: a computer program for geochemical calculations. U.S Geological Survey Water Research Investigation Report 80±96, 195 pp. Prausnitz, J.M. (1969) Molecular Thermodynamics of Fluid-phase Equilibria. Prentice-Hall, Engelwood Clis, New Jersey, 523 pp. Reardon, E. J. (1992) Problems and approaches to the prediction of the chemical composition in cement/ water systems. Waste Management 12(2±3), 221±239. Saxena, S.K. (1973) Thermodynamics of Rock-forming Crystalline Solutions. Springer-Verlag, Berlin, 188 pp. SKB (1983) Final storage of spent nuclear fuel: KBS-3. Swedish Nuclear Fuel and Waste Management Co., Box 5864, S-102 48 Stockholm, 71 pp.
Computers & Geosciences Vol. 24, No. 9, pp. 839±846, 1998 # 1998 Elsevier Science Ltd. All rights reserved Printed in Great Britain S0098-3004(98)00064-8 0098-3004/98/$ - see front matter
PASSIPHIC: A PROGRAM FOR SOLUBILITY CALCULATIONS INVOLVING COMPLEX SOLIDS SUSANNE BOÈRJESSON*, and ALLAN EMREÂN Department of Nuclear Chemistry, Chalmers University of Technology, 412 96 Goteborg, Sweden (Received 2 May 1997; revised 30 March 1998) AbstractÐIn modelling solid±water interactions, where the solid consists of many phases, more phases may be present than is allowed according to the phase rule. The problem becomes even more complex if one or more of the phases are solid solutions. Examples of such solids are rock and cement. To simplify the calculations, these solids may be presented independently of the water solution as a set of dierent phases; pure minerals and/or solid solutions. The PASSIPHIC program has been developed to handle the interaction of pure solids and solid solutions with an aqueous phase. SOLISOL and PHREEQE are among the sub-programs forming the program package PASSIPHIC. The program SOLISOL was originally developed to handle ideal solid solution±aqueous solution reactions only. The program has now been modi®ed to handle non-ideal binary solid solutions as well. In the equilibrium calculations the program PHREEQE is used. The input data to PASSIPHIC are the composition and amount of each phase, secondary minerals that may form, parameters in Guggenheim's excess free enthalpy of mixing equation (for non-ideal binary solid solutions) and the composition of the aqueous phase. The result gives the equilibrium composition of the dierent phases in the solid and the aqueous phase. To test the PASSIPHIC concept, the solubility of the gel phase in cement has been modelled. # 1998 Elsevier Science Ltd. All rights reserved Code available at http://www.iamg.org/CGEditor/index.htm Key Words: Solid solution, SOLISOL, Activity coecient, Cement, PHREEQE.
INTRODUCTION
In the performance assessment of an underground repository for radioactive waste, computer simulations are tools for predicting the interactions of groundwater with dierent barriers. These barriers may for example be the rock itself, cement-based systems or bentonite clay (e.g. the Swedish concept as described in SKB, 1983). All these solid barriers may consist of mixtures of pure minerals and solid solutions. A program frequently used in solubility calculations is the thermodynamic equilibrium program PHREEQE (Parkhurst, Thorstenson and Plummer, 1990). The standard version of PHREEQE considers all solids as pure minerals, dissolving congruently according to their stoichiometry. Because solid solutions have variable compositions, the standard PHREEQE program alone is not suitable for solid solution±aqueous solution (SSAS) equilibrium calculations. Solid solutions often have a miscibility gap that causes the solid solution in this region to be described with two solid solutions of dierent compositions. When modelling such a two-phase *Corresponding author. Fax: +46-21-772-2931; E-mail: [email protected]. {Pure phAses and Solid Solutions In PHREEQE equIlibrium Calculations. 839
system with a composition in the miscibility gap, phase rule violation will occur in the PHREEQE calculations. Muller, Parkhurst and Tasker (1986) used a modi®ed version of PHREEQE to model solid solutions in equilibrium calculations. In their approach, the solid solutions are handled as pseudo-elements and special de®nitions of aqueous species are made. An ideal solid solution or a constant activity model is considered in the calculations and the program handles one binary solid solution at a time. The PHRQXL code developed by Glynn and Parkhurst (1992) calculates equilibrium reaction paths in a binary non-ideal SSAS system. The authors use the modi®cations of PHREEQE as proposed by Muller, Parkhurst and Tasker (1986). In addition to these modi®cations, subroutines were added to PHRQXL to make it possible to handle regular and sub-regular binary solid solutions. One of the subroutines originates from the MBSSAS code (Glynn, 1991) and allows the program to calculate characteristic features of a binary SSAS system such as miscibility and spinodal gaps. The PHRQXL program handles one solid solution at a time together with any pure solids. The PASSIPHIC{ package presented in this work is developed to be used in water interactions with
840
S. BoÈrjesson and A. EmreÂn
Figure 1. Conceptual model of PASSIPHIC program
complex solids. It is designed to handle one or more solid solutions together with pure minerals in equilibrium calculations with standard PHREEQE. The PASSIPHIC program is able to handle multi component solid solutions with the restriction that the activity coecients have to be constant. For binary solid solutions, a sub-regular model can be used. It should be noted that the PASSIPHIC program does not have the ability to determine the parameters needed. For this purpose the MBSSAS program may be used (Glynn, 1991). PASSIPHIC calculates the equilibrium state for any given start composition. In the situation of phase separation, ®nal phase compositions are determined automatically. Besides the problem with solid solutions when using standard PHREEQE in equilibrium calculations, an apparent phase rule violation may occur in calculations with complex solids. This is taken care of by PASSIPHIC. The sub-program SOLISOL is called by PASSIPHIC to perform SSAS equilibrium calculations. The original version of SOLISOL could handle ideal solid solutions only (BoÈrjesson and EmreÂn, 1993). It has now been extended to handle also non-ideal binary solid solutions. To test the PASSIPHIC program, the solubility of the binding phase in cement, the amorphous calcium silicate hydrate (denoted C±S±H in cement chemistry), was modelled. The C±S±H phase can be modelled as a binary solid solution with the components (end-members) Ca(OH)2 and CaH2SiO4 as proposed by Greenberg and Chang (1965). It has
been indicated that the C±S±H phase has a miscibility gap (Kersten, 1996; BoÈrjesson, EmreÂn and Ekberg, 1997) where the upper boundary in this region has a composition close to pure Ca(OH)2(s). Thus, to model a metastable C±S±H gel in the miscibility gap will cause an apparent violation of the phase rule in PHREEQE calculations. CONCEPTUAL MODEL AND PROGRAM OVERVIEW
The PASSIPHIC program has been developed to determine equilibrium in systems where an aqueous phase is in equilibrium with a complex solid. Further, the program is able to perform a number of leaching steps, where the aqueous solution is replenished in every new step. A complex solid is here de®ned as a solid, which macroscopically looks like one homogeneous substance, but which at a closer look is found to consist of several solid phases. Some of these phases may be pure minerals, whereas others are solid solutions. Examples of complex solids are arti®cial materials such as cement and spent nuclear fuel. There are also naturally occurring substances that are complex in a similar way, e.g. clay and soil. Solid solutions are treated in terms of endmembers and, since a mineral may be an endmember in several solid solutions and also present as a pure mineral, an apparent violation of Gibb's phase rule occurs frequently in such systems. Sometimes, a real phase rule violation is present in the initial (metastable) system.
Passiphic: A program for solubility calculations involving complex solids
To avoid problems from real or apparent phase rule violations, the PASSIPHIC program treats each solid solution separately and also separated from all pure phases. The water reacting with the solid is subdivided into fractions (cf. Fig. 1), each of which reacts with one solid solution or with pure phases only. Such a water fraction in contact with a solid phase will be referred to as a reaction cell. When each water fraction has been equilibrated with its solid system, all the water fractions are mixed without any mineral reactions occurring. The resulting mixture is then once again subdivided into fractions and allowed to react with the solid phases. This procedure is repeated until no more changes occur in the system. Meanwhile, some phases may have been consumed and disappeared, while a secondary phase may have formed. Since the ®nal free enthalpy of a spontaneous reaction is always lower than the initial one, the ®nal state corresponds to a minimum in free enthalpy and thus to equilibrium in the system. In the present version of the program, the reaction cells are conceptual in nature. Since two solid phases cannot be at the same place, an obvious future extension of the program is letting the reaction cells correspond to real tiny volumes and including transport between the cells as well as kinetic phenomena inside the individual cells.
solution is 2 ai,ideal Xi : For a non-ideal solid solution the activity of component i is related to its mole fraction by the activity coecient, gi, ai Xi gi :
3
Introducing Equation (3) into Equation (1) we get mi m*i RT ln Xi gi :
4
The main concept of the SOLISOL program is to calculate a saturation index, SIi (=log(ion activity product/solubility product)) for each component i in the solid solution, cf. Equation (5): SIi log
IAPi Ks,i
5
For a pure solid substance in equilibrium with an aqueous solution, SI equals zero. One should note that SI primarily is a property of the aqueous solution and not of the solid with which it may react. Normally, the composition of an aqueous solution in equilibrium with a solid solution diers from that of an aqueous solution in equilibrium with a pure solid phase. This means that the SI value of a component of a solid solution in equilibrium with an aqueous phase mostly diers from zero. As has been shown elsewhere (BoÈrjesson and EmreÂn, 1993), such a saturation index is given by log Xi gi SIi :
THEORY
The standard version of the PHREEQE program can not handle minerals with a variable composition, such as solid solutions, in equilibrium calculations. This drawback was eliminated by introducing the program SOLISOL (BoÈrjesson and EmreÂn, 1993). Originally the program was able to handle ideal solid solutions only. Soon it was extended to take care of solid solutions with constant activity coecients of the end-members. To improve the ability of SOLISOL to handle non-ideal binary solid solutions, an expression for the activity coecient of each endmember as a function of the composition has been added to the program, as is discussed in the next section. THERMODYNAMICS OF SOLID SOLUTIONS
The chemical potential of the ith component in an ideal solid solution at a given temperature and pressure is given by mi m*i RT ln ai
841
1
where ai is the activity of component i. The relationship between the activity and the mole raction, Xi, of component i for an ideal solid
6
SOLISOL makes the SIi available for PHREEQE to be used in the equilibrium calculation. The use of constant activity coecient values limits the use of the program somewhat. Thus, the ability to handle variable coecients has been included. The choice of approach has been the use of a truncated series expansion. Equation (4) can be rewritten as mi m*i RT ln Xi RT ln gi :
7
Considering the total free enthalpy of a non-ideal solid solution we get X X X non-ideal G Xi m0i Xi RT ln Xi Xi RT ln gi : i
i
i
8 The last term on the right-hand side is the excess free enthalpy of mixing, Gexcess. This term is the dierence between the free enthalpy of the nonideal solid solution and that of the ideal solid solution (Prausnitz, 1969) (at the same T, P and Xi) X excess G non-ideal ÿ G ideal RT Xi ln gi : G 9 i
Knowledge about the excess free enthalpy of mixing makes it possible to describe the thermodynamic properties of a non-ideal solution.
S. BoÈrjesson and A. EmreÂn
842
Figure 2. Hierarchical structure of PASSIPHIC package
Several empirical expressions exist for modelling the excess energy of mixing as a function of composition (Glynn, 1991). They are of the Margules type, meaning that the Gexcess is expressed with a power series of the mole fractions of the components constituting the solid solution (Prausnitz, 1969; Saxena, 1973; Glynn, 1991; Nordstrom and Munoz, 1994). One of these Gexcess ®tting functions for a non-ideal binary solid solution is the polynomial given by Guggenheim (Saxena, 1973): excess X1 X2 A0 A1 X1 ÿ X2 A2 G X1 ÿ X2 2 A3 X1 ÿ X2 3 . . .:
10
The parameters A0, A1, . . . depend on temperature and pressure. If the series is terminated after two terms we get excess X1 X2 A0 A1 X1 ÿ X2 : G
11
The partial excess free enthalpy of mixing for component i in a solid solution is related to the activity coecient by (Prausnitz, 1969) excess,i RT ln gi : G
12
To express the activity coecient for component i as a function of composition, the following expression given by Prausnitz can be used excess @ nT G RT ln gi 13 @ ni T,P,nj where ni and nT are the number of moles of component i and the total number of moles, respectively. The subscripts T, P and nj mean that the temperature, pressure and number of moles of all other components than i, respectively, are kept constant. Considering a binary mixture and applying Equation (13) to the expression for Gexcess given by Equation (11), the activity coecient as a function of composition for a component becomes RT ln g1 X 22 A0 A1 3X1 ÿ X2 :
14
PROGRAM DESCRIPTION
The PASSIPHIC program package consists of several sub-programs, all written in the program
language C with the exception of PHREEQE which is written in FORTRAN. A hierarchical structure of the PASSIPHIC package is given in Figure 2. Information is transferred between the manager, PASSIPHIC, and the sub-programs, either through the execute command or by data ®les. Such communication may also be used between sub-programs. Listed below is a short description of the function of the programs in Figure 2. PASSIPHIC: The main program that controls and distributes tasks to the other programs. It also extracts and stores aqueous solution data from equilibrium calculations with each cell. After each leaching cycle, ®les containing equilibrium composition of the solids in each cell are stored together with the aqueous phase. SETUP: This program generates the input data needed for the simulation. It is a menu program where the user interactively gives information on the system to be studied, e.g. aqueous composition, contents of the cells and possible secondary minerals. If calculations with non-ideal binary solid solutions are to be performed, the parameters A0 and A1 will be given here. MKINFILE: Creates aqueous input ®le to SOLISOL. SOLISOL: Handles solid solution±aqueous solution equilibrium calculations. PHREEQE: Calculates aqueous speciation and performs dissolution, precipitation and mixing reactions. SOL1: A sub-program to SOLISOL. Prepares the starting input ®le for the equilibrium calculation to be performed by PHREEQE on the solid solution± aqueous solution system. SOL3: A sub-program to SOLISOL. Extracts information from PHREEQE equilibrium calculation, such as the aqueous solution composition and the dissolved or precipitated amount of each end-member in the solid solution. The results are used to produce input data to PHREEQE. The mathematical model for non-ideal binary solid solutions is a sub-routine in the SOL3 program. TESTPURE: If no cell with pure minerals is present, the aqueous solution is checked to determine whether or not it is oversaturated with respect to any secondary mineral suggested.
Passiphic: A program for solubility calculations involving complex solids
843
Figure 3. Flow charts of PASSIPHIC (A), SOLISOL (B) and SOLVPURE (C)
SOLVPURE: Performs equilibrium calculations with the cell consisting of the pure minerals. Also checks for any secondary mineral to be formed. MAKEIN: A sub-program to SOLVPURE. Creates input ®le for PHREEQE. MIXING: Mixes the equilibrium solutions obtained from each cell±water interaction. The solutions are mixed in equal proportions. The programs SETUP, MKINFILE, MAKEIN and MIXING are modi®ed and/or further developed versions of programs originally developed for the CRACKER program (EmreÂn, 1998). Flow charts of PASSIPHIC, SOLISOL and SOLVPURE are shown in Fig. 3(A±C), respectively. The PASSIPHIC program starts with calling the sub-program SETUP (cf. Fig. 3A). This program makes preparations needed for the other programs. As seen in Figure 3, PASSIPHIC uses SOLISOL and SOLVPURE in an iteration loop to ®nd equilibrium. Once equilibrium has been reached and all leaching steps have been performed, PASSIPHIC ends. The equilibrium calculations for solid solutions are performed with SOLISOL (cf. Fig. 3B). Several iterations may be needed to reach equilibrium. The iteration loop consists of PHREEQE and SOL3. These programs will be called by SOLISOL until equilibrium has been reached and the program ends. The SOLVPURE program (which handles pure minerals) starts with calling the sub-program MAKEIN that creates an input ®le for PHREEQE (cf. Fig. 3C). After the equilibrium calculation with PHREEQE, the function Control checks whether the aqueous solution is oversaturated with respect to any secondary mineral. If so, the mineral will be
added to the present cell. An additional equilibrium calculation is performed. The PHREEQE program can not handle mass balances for minerals involved in the equilibrium calculations. This is taken care of by the programs SOLISOL and SOLVPURE. These programs do not allow dissolution of a larger quantity of a mineral than is available.
TEST CASE
The PASSIPHIC program has been tested on a simpli®ed model for water-cement interaction. The calcium silicate hydrate phase (C±S±H) was used as a simple model for cement. The C±S±H gel is the binding phase in cement and is likely to determine the pH in the cement pore water over a long time (Atkinson, 1985), initially giving a pH of 012.5. This environment serves as a good immobiliser for many radionuclides (Atkins and Glasser, 1992), especially the actinides (Albinsson and others, 1996). Thus, to model the solubility behaviour of the C±S±H phase is of great interest and a subject treated by many authors (Atkinson, Henson and Knights, 1987; Glasser, Macphee and Lachowski, 1987; Berner, 1992; Reardon, 1992; Kersten, 1996). The calcium silicate hydrate gel Hydrated cement is a complex solid consisting of crystalline and amorphous solid phases as well as an aqueous phase (pore water). Examples of pure minerals are portlandite (Ca(OH)2) and ettringite (3CaOAl2O33CaSO432H2O). Many of the solid phases in cement are multi-component solid solutions. The most important solid solution, however,
S. BoÈrjesson and A. EmreÂn
844
Table 1. Composition of C±S±H gel together with thermodynamic data used in calculations Phase
Reaction
log Ks 22.70 (CHEMVAL6, 1995) ÿ7.07 (Greenberg and Chang, 1965) 22.70 (CHEMVAL6, 1995)
Solid solution End-members
Ca(OH)2(s)
Ca(OH)2+2H+=Ca2++2H2O
Pure mineral
CaH2SiO4(s) Ca(OH)2(s)
CaH2SiO4=Ca2++H2SiO2ÿ 4 Ca(OH)2+2H+=Ca2++2H2O
is the amorphous C±S±H phase which is the binding phase in cement. In contact with water, the phases constituting thecement react in dierent ways. Dissolution and precipitation processes as well as the formation of secondary phases occur. These processes are governed by metastable equilibria, diusion and mixing processes, kinetics and surface area. This complexity makes it necessary to simplify the modelling of cement±water interaction. The C±S±H gel is amorphous and has a variable composition given by the Ca/Si molar ratio of the gel. The gel phase can be modelled as a binary solid solution consisting of the end-members Ca(OH)2(s) (portlandite) and CaH2SiO4(s) (Greenberg and Chang, 1965). These are the end-members used by Berner (1992) in his model of the C±S±H gel. For high Ca/Si molar ratios (>1.4±1.8), portlandite (Ca(OH)2(s)) has been observed together with the gel and coexistence has therefore been assumed (Greenberg and Chang, 1965; Atkinson, Hearne and Knights, 1987; Berner, 1992; Reardon, 1992). In the model proposed by Kersten, the gel has a miscibility gap assumed to exist in the region 0.67
boundary of the miscibility gap starts at XCa OH 2 =0.30. Kersten's assumption of the upper boundary (XCa OH 2 =0.95) agrees reasonably well with our results. The modelling work was performed according to two dierent methods, the ®rst for gels with Ca/Si mole ratios greater than 1.43 (XCa OH 2 >0.30) and the second for XCa OH 2 R 0.30. This procedure is not necessary but was followed in order to make the numerical calculations faster. The compositions used were the same as those reported for Kalousek (1952) in the experimental data compilation made by Berner (1992). In the ®rst method PASSIPHIC was used in the calculations. The initial solid was a (metastable) gel phase. SOLISOL calculations for this phase give concentrations of Ca far higher than the observed values. Portlandite was given to the PASSIPHIC program as a possible secondary phase. The PASSIPHIC simulations were performed as onestep leaching (no water replacement). During the simulations, phase separation occurred and the ®nal concentrations were close to the observed values (the plateau in Fig. 4). In the second method (XCa OH 2 R 0.30) no phase separation is expected and thus the full PASSIPHIC program is not needed. Rather, the
RESULTS AND DISCUSSION
In the model calculations, pure water was used as initial aqueous phase and the temperature was 258C. The database used was HATCHES 5.0 (Bond and others, 1992) extended with data on the minerals in Table 1. The equilibrium constant for CaH2SiO4(s) was derived from Greenberg and Chang (1965). Values on A0 and A1 used in the model, A0=3.262 kJ/mol and A1=13.44 kJ/mol, were obtained from BoÈrjesson and others (1997) where component activities were calculated by PHREEQE from experimental element concentrations in aqueous phases (Kalousek, 1952 referred to by Berner, 1992). This resulted in values of activity coecients for the components of the gel as functions of the mole fractions. By ®tting those values to Equation (14), values of the parameters A0 and A1 were determined. From the parameters it was concluded that a miscibility gap exists in which the gel coexists with almost pure portlandite (X>0.99). The lower
Figure 4. Calcium concentration in aqueous phase as function of Ca/Si molar ratio of C±S±H gel. Kalousek's data (Kalousek, 1952) from compilation by Berner (1992). Model results are shown as curves
Passiphic: A program for solubility calculations involving complex solids
new version of SOLISOL was used as a stand alone program. With SOLISOL and PASSIPHIC functioning well, it can be expected that the resulting element concentrations will be close to observed values. That this indeed happens is seen in Figure 4 where the results of the simulations are plotted together with the experimental data (Kalousek, 1952) from the data compilation made by Berner (1992) on which the parameters A0 and A1 were based. For comparison, results from calculations with the earlier version of SOLISOL (BoÈrjesson, 1994) and with the model developed by Berner (1992) are plotted in Figure 4. Figure 4 shows that the addition of the binary non-ideal solid solution algorithm to the SOLISOL program, together with the use of the PASSIPHIC package, has improved the modelled solubility behaviour of the C±S±H gel signi®cantly.
CONCLUSIONS
The tasks of this work were: (1) To modify the former version of the SOLISOL program in order to be able to use nonideal binary solid solutions in equilibrium calculations. (2) To develop a program to be used in solid phase±water interactions, where the solid phase could be considered to consist of solid solutions and pure minerals. To achieve the ®rst of these tasks, subroutines were added to SOLISOL based on the mixing model proposed by Guggenheim, the Guggenheim two-parameter equation. The model makes use of the excess free enthalpy to express a relationship between the activity coecient and the mole fraction for each end-member. To be able to use the solubility model for non-ideal binary solid solutions, it is necessary to estimate values for the parameters A0 and A1; otherwise an ideal solid solution is assumed in the calculations. (The computer program MBSSAS developed by Glynn, 1991 can be a tool to obtain values on A0 and A1 for binary SSAS systems.) For the second task, the PASSIPHIC program, was developed. To test PASSIPHIC and the present version of SOLISOL, the solubility behaviour of C±S±H was modelled. The results in Figure 4 show that the agreement between the experimental data and the model is satisfactory, representing an improvement on an earlier model by the PASSIPHIC package. Further, the use of PASSIPHIC makes it possible to overcome the apparent phase rule violation in the equilibrium calculations for compositions in the miscibility gap. The PASSIPHIC program may be down-loaded via Internet at the location http://www.nc.chal-
mers.se/sta/sb/sannebo.htm, or by FTP from the server IAMG.ORG.
845
anonymous
FUTURE WORK
As mentioned earlier, some interesting features are still missing in the program package. Some of them are desirable to incorporate in the model whereas others are best added as external programs. In the present version of the program, pure minerals but not solid solutions are able to be formed as new secondary phases. This is an obvious limitation and, thus, the formation of new solid solutions is of primary interest for future improved versions of PASSIPHIC. Another feature that needs further investigation is how to handle kinetics, both in the dissolution and in the precipitation process. At present, kinetics may be modelled by the mixing proportions, i.e. if a mineral dissolves easily and there are no mass limitations, the faster kinetics may be described by a larger proportion of the corresponding aqueous solution in the mixing step. Another obvious modi®cation is to use PHREEQC (Parkhurst, 1995) in the PASSIPHIC package. PHREEQC is a new version of PHREEQE written in the programming language C. It includes some properties that will increase the eciency of the PASSIPHIC program. The aforementioned features will be incorporated into the program itself. The eect of transport, on the other hand, will be added to the PASSIPHIC program package as a separate program. AcknowledgmentsÐThe authors would like to thank G. Skarnemark, J.O. Liljenzin and C. Ekberg for their comments on the manuscript. We would also like to thank A. édegaard-Jensen for valuable comments during the programming work. This work was funded by the Swedish Nuclear Power Inspectorate (SKI).
REFERENCES Albinsson, Y., Andersson, K., BoÈrjesson, S. and Allard, B. (1996) Diusion of radionuclides in concrete and concrete±bentonite systems. Journal Contaminant Hydrology 21, 189±200. Atkins, M. and Glasser, F. P. (1992) Application of Portland cement-based materials to radioactive waste immobilization. Waste Management 12(2±3), 105±131. Atkinson, A. (1985) The time dependence of pH within a repository for radioactive waste disposal. UK Atomic Energy Authority Report AERE-R-11777, 11 pp. Atkinson, A., Hearne, J. A. and Knights, C. F. (1987) Aqueous chemistry and thermodynamic modelling of CaO±SiO2±H2O gels. UK Atomic Energy Authority Report AERE-R-12548, 35 pp. Berner, U. (1992) Evolution of pore water chemistry during degradation of cement in a radioactive waste repository environment. Waste Management 12(2±3) , 201±219. Bond, K. A., Moreton, A. D. and Heath, T. G. (1992) HATCHES 5.0: The HARWELL/NIREX
846
S. BoÈrjesson and A. EmreÂn
DATABASE. Harwell Laboratory, Oxfordshire OX11 ORA, UK. BoÈrjesson, S. (1994) Chemical interactions in concrete systems. Licentiate Thesis, Chalmers University of Technology, GoÈteborg, Sweden, 40 pp. BoÈrjesson, K. S. and EmreÂn, A. T. (1993) SOLISOL, a program using PHREEQE to solve solid solution/aqueous equilibria. Computers & Geosciences 19(8), 1065± 1070. BoÈrjesson, S., EmreÂn, A. and Ekberg, C. (1997) A thermodynamic model for the calcium silicate hydrate gel, modelled as a non-ideal binary solid solution. Cement Concrete Research 27(11), 1649±1657. CHEMVAL6 (1995) Thermodynamic Database, version 6. Provided by Dr. S. Duerden, HMIP P3/008A, 2 Marsham Street, London SW1P 3EB, England. EmreÂn, A.T. (1998) CRACKER: a program coupling inhomogeneous chemistry and transport. Computers & Geosciences, in press. Glasser, F.P., Macphee, D.E. and Lachowski, E.E. (1987) Solubility modelling of cements: implication for radioactive waste immobilisation. Materials Research Society Symposia Proceedings, vol. 84. Boston, Massachusetts, USA, pp. 331±341. Glynn, P. D. (1991) MBSSAS: A code for the computation of Margules parameters and equilibrium relations in binary solid-solution aqueous-solution systems. Computers & Geosciences 17(7), 907±966. Glynn, P.D. and Parkhurst, D.L. (1992) Modelling nonideal solid-solution aqueous-solution reactions. Proceedings 7th International Symposium on Water± Rock Interaction-WRI-7. Park City, Utah, USA, pp. 175±179. Greenberg, S. A. and Chang, T. N. (1965) Investigation of colloidal hydrated calcium silicates. II. Solubility relationships in the calcium oxide±silica±water system at 258C. Journal Physical Chemistry 69(1), 182±188. Kalousek, G.L. (1952) Application of dierent thermal analysis in a study of the system lime±silica±water.
Proceedings 3rd International Symposium on Chemistry of Cements. London, England, pp. 296±311. Kersten, M. (1996) Aqueous solubility diagrams for cementitious stabilization systems. 1. The C±S±H solid-solution system. Environmental Science and Technology 30(7), 2286±2293. Muller, A.B., Parkhurst, D.L. and Tasker, P.W. (1986) The use of the PHREEQE code in modelling environmental geochemical problems encountered in performance assessment modelling. Proceedings of the Symposium on Groundwater Flow and Transport Modeling for Performance Assessment of Deep Geologic Disposal of Radioactive Waste: A Critical Evaluation of the State of the Art, May 20±21, 1985. Albuquerque, New Mexico, pp. 303±319. Nordstrom, D.K. and Munoz, J.L. (1994) Geochemical Thermodynamics, 2nd ed. Blackwell Scienti®c Publications, Boston, 493 pp. Parkhurst, D.L. (1995) User's guide to PHREEQC: a computer program for speciation, reaction-path, advective-transport and inverse geochemical calculations. U.S Geological Survey Water Research Investigation Report 95-4227, 143 pp. Parkhurst, D.L., Thorstenson, D.C. and Plummer, L.N. (1990) PHREEQE: a computer program for geochemical calculations. U.S Geological Survey Water Research Investigation Report 80±96, 195 pp. Prausnitz, J.M. (1969) Molecular Thermodynamics of Fluid-phase Equilibria. Prentice-Hall, Engelwood Clis, New Jersey, 523 pp. Reardon, E. J. (1992) Problems and approaches to the prediction of the chemical composition in cement/ water systems. Waste Management 12(2±3), 221±239. Saxena, S.K. (1973) Thermodynamics of Rock-forming Crystalline Solutions. Springer-Verlag, Berlin, 188 pp. SKB (1983) Final storage of spent nuclear fuel: KBS-3. Swedish Nuclear Fuel and Waste Management Co., Box 5864, S-102 48 Stockholm, 71 pp.