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POLYMIN 2005 2+ + 3+ Fe +1/4 O2 + H ⇒ Fe +1/2 H 2 O 3+ 2- + Fe S 2 +1/2 H 2 O +15/4 O2 ⇒ Fe + 2 SO4 + H The rate of these oxidation reactions, however, is controlled by the availability of oxygen at, and within the mineral grains. A common approach for modeling this process, and that adopted here, is the shrinking core model (Levenspiel, 1972) which assumes the sulphide mineral is uniformally distributed within each spherical grain. Derivations for this model have been presented by Davis and Ritchie (1986; 1987), Wunderly et al. (1996), and Gerke et al. (1998), and are not repeated here. The shrinking core model provides the oxygen sink term Q o in equation (4), defined by 3 ( 1 - θ ) ⎛ r ⎞ [ O 2 ] R ⎝ r ⎠ H c o = 2 2 ⎜ R - ⎟ c Q D a (6) where D 2 is the effective diffusion coefficient incorporating the characteristic diffusion properties of both the water film and the oxidized shell of the pyrite particle, R is the average radius of the soil particles, r c is the average radius of the unreacted core, and [O 2 ] a is the oxygen concentration in the air phase in contact with the particle. From the computed change in the oxidized grain radius (r c ), and knowing the fraction of sulfide minerals in the grain f s , (M Su /M solids ), the bulk density ρ b [ML -3 ], and ε, the mass ratio of oxygen to sulphur consumed on the basis of the reaction stoichiometry, the mass of each oxidation product can be determined for each oxidation time step ∆t oxid (Gerke et al., 1998). Geochemical Equilibrium Equations The chemical equilibrium reactions are those provided in the geochemical equilibrium model MINTEQA2 (Felmy et al., 1983; Allison et al., 1990). MINTEQA2 was derived from combining the geochemical equilibrium model MINEQL (Westall et al., 1976) with the data base of the WATEQ2 model (Ball et al., 1979). The reactions considered are chemical speciation, acid-base reactions, mineral precipitationdissolution, oxidation-reduction, and adsorption. The chemical model uses the general transformation-of-the-bases mathematical approach to solve the chemical equilibrium problem for all of the chemical reaction types (Felmy et al., 1983). The ion-association equilibriumconstant approach is used to represent the geochemical reactions. The ion-association aqueous 10
POLYMIN 2005 model involves three separate constituents; the masses of aqueous species and complexes, equilibrium constants which relate these complexes in solution, and the individual ion-activity coefficients for each species. These constituents are related through a system of algebraic equations that solve for the individual ion activities in a solution, which are in turn used to predict chemical reaction equilibrium. Chemical Speciation, Acid-Base Reactions and Redox Reactions In a solution, there exists a set of chemical components and species. The set of chemical components is the minimum number of species that uniquely describe a solution and that is required to be reaction invariant (Mangold and Tsang, 1991). The component mass remains constant, regardless of the distribution between chemical species in both the aqueous and solid phases. This mass conservation principle yields a set of linear algebraic equations, with one equation for each component (Cederberg, 1985). The total component concentration T k (moles/1000g H 2 O) is the sum of the aqueous-phase concentration C k and the solid-phase concentration S k , of component k: T k = Ck + S k (7) where C S k k naq alk ∑ cl (8) l=1 = k = 1, ... N = naq blk ∑ s k = 1,... l N (9) l=1 and where c l is the concentration of species l in the aqueous phase (moles/1000g H 2 0), s l is the concentration of species l in the solid phase (moles/1000g H 2 O), a lk is the stoichiometric coefficient of component k in species c l , b lk is the stoichiometric coefficient of component k in species s l , n aq is the number of species in the aqueous phase, and n s is the number of species in the solid phase. The total mass of each chemical component must be known to describe a solution. The distribution of the species included in the component concentrations is estimated by mass-action equations that form a set of nonlinear algebraic equations, with one equation for each chemical species. For the aqueous-phase species, these equations are: N c alk χ = K ∏ χ naq (10) l cl k=1 k while for the solid-phase species, they are: l = 1,... 11
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: POLYMIN 2005 where S k is the solid
Page 13 and 14: POLYMIN 2005 The three basic mathem
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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