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POLYMIN 2005 sl = K N c blk ∏ χ k ns (11) sl k=1 l = 1,... where K cl is the equilibrium formation constant for species c l , K sl is the equilibrium formation constant for species s l in the solid phase, χ k is the activity of component k (moles/1000g H 2 0), and χ l is the activity of species l (moles/1000g H 2 0). The stoichiometric mass-balance equations for the components are written in terms of component concentrations, while the mass action equations are expressed in terms of activities. The activities, χ l , are related to concentrations, c l , through the individual ionic activity coefficients, γ l , using the approximation χ = cl (12) l γ l The activity coefficients are calculated using the WATEQ, extended Debye-Hückel or Davies equations (Felmy et al. 1983). The specific equation used is dependent on the availability of specific solute parameters. These equations form a set of algebraic equations which are used in the ion-association model to solve for the individual ion activities given the total component concentrations in solution. The interrelationships between the species concentrations and activities and the ionic strength cannot be solved for explicitly but require an iterative solution. MINTEQ uses the Newton-Raphson iterative technique. Chemical reactions involving the hydrogen and hydroxide ion are simulated in the chemical model using the proton condition (Westall et al., 1976; Felmy et al., 1983; Allison et al., 1990). The proton condition, representing the total analytical component concentration of H + , is the primary variable used in the transport solution. The H + -value may theoretically be negative because it does not have the physical interpretation of a total mass of hydrogen but is the change in H + activity from the reference condition. Similarly, the total calculated mass of H 2 O can also be negative. Oxidation-reduction reactions are calculated with MINTEQ using the external redox couple approach. This approach requires that the initial distribution of the specified redox couples is known before the chemical equilibrium problem can be solved. This distribution can be determined from the initial solution component chemistry and the solution pe. MINTEQ permits selection of redox couples that are set in equilibrium with the solution pe. Other electroactive species may be considered independent of the pe. Thus, the multivalent species can be reacted with their respective solid mineral phases without requiring interactions with other multivalent species. In the present transport model, the total dissolved concentration of each redox state is transported separately, and the new solution pe is calculated using the activities calculated for the specified redox couples at the new location. The electron activity, therefore, is not transported independently. Sorption 12
POLYMIN 2005 The three basic mathematical forms of sorption reaction models, namely isothermal, massaction/ion-exchange, and surface complexation/electrostatic models, have been incorporated into MINTEQ (Allison et al., 1990). The isothermal models included are the activity K d adsorption model, the activity Langmuir adsorption model, and the Freundlich model. The electrostatic adsorption models available are the constant-capacitance model, the diffuse-layer model, and the triple-layer model. To date only the ion-exchange model has been verified in the combined mass-transport chemical-equilibrium model. Ion-exchange sorption reactions are simulated using the Gaines and Thomas model for ion exchange (Allison et al., 1990). This model assumes that the surface site is initially occupied by an exchangeable ion that is released into solution during the exchange process, that the charge on the surface of the solid remains constant, and that the number of surface sites available for sorption, expressed as the cation exchange capacity (C.E.C.), is fixed. The ion-exchange reaction is written as: vA vB B + AB(ad) ⇔ B A(ad) + A (13) v A v v v B where v A and v B are the change on components A and B respectively, A(ad) and B(ad) are the adsorbed mass of components A and B. The mass action equation for the above expression is K AB ⎛ A(ad) = ⎜ vA ⎝ [A ] ⎞ ⎟ ⎠ vB vB ⎛ [B ] ⎜ ⎝ B(ad) ⎞ ⎟ ⎠ vA (14) where the square brackets represent solution activity, and K AB is the selectivity coefficient of species A with respect to species B. Mineral Precipitation and Dissolution Mass-action equations, which relate ion activities and a solid specific solubility product, describe mineral precipitation and dissolution reactions. These reactions can be written as follows (Walter et al., 1994a): A a B b(s) ⇔ aA (aq) + bB (aq) (15) The subscripts (s) and (aq) refer to solid and aqueous phases respectively. The thermodynamic solubility product for a given solid is described by: K sp a A B = [ ] [ ] [ AB] a b b (16) where K sp is the solubility product for the solid. 13
Page 1 and 2: POLYMIN Version 3.0 2D REACTIVE MAS
Page 3 and 4: POLYMIN 2005 TABLE OF CONTENTS page
Page 5 and 6: POLYMIN 2005 1. INTRODUCTION 1.1 Ov
Page 7 and 8: POLYMIN 2005 1.3 Software Support I
Page 9 and 10: POLYMIN 2005 where S k is the solid
Page 11: POLYMIN 2005 model involves three s
Page 15 and 16: POLYMIN 2005 Solution Strategy POLY
Page 17 and 18: POLYMIN 2005 Discretization Criteri
Page 19 and 20: POLYMIN 2005 2.3 Primary Variables
Page 21 and 22: POLYMIN 2005 2.5 Input/Output File
Page 23 and 24: POLYMIN 2005 Table 3. Summary of tr
Page 25 and 26: POLYMIN 2005 4. SAMPLE DATA SET The
Page 27 and 28: POLYMIN 2005 Input options 1.0 0.5
Page 29 and 30: POLYMIN 2005 Data Block 1 0 0 0 ;IS
Page 31 and 32: POLYMIN 2005 Tolerance and relative
Page 33 and 34: POLYMIN 2005 Background aqueous che
Page 35 and 36: POLYMIN 2005 Input File: Bkgrndpoly
Page 37 and 38: POLYMIN 2005 5. STEP BY STEP INSTRU
Page 39 and 40: POLYMIN 2005 6. TIPS AND TECHNIQUES
Page 41 and 42: POLYMIN 2005 8. REFERENCES Aachib,
Page 43 and 44: POLYMIN 2005 Molson, J.W., Fala, O.
Page 45 and 46: POLYMIN 2005 Example 1: Geochemical
Page 47 and 48: POLYMIN 2005 Bkgrndpoly.min (from E
Page 49 and 50: POLYMIN 2005 Input Data file for Ex
Page 51: POLYMIN 2005 500 1.386E-03 ;NA " 41

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