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POLYMIN 2005 number is then defined as: ta Dak = tr ∆L Rk = v C k ∆t (23) The product of the Courant number and the Damköhler number is used by Zysset and Stauffer (1992) to express the relationship between the reaction rate and the characteristic concentration of a component. In the case of equilibrium reactions, the equivalent quantity is the reactive mass ratio ρ k , which can be defined relative to the characteristic (background or input) concentration C k B , as: B B = Co = Rk ρ k • Dak (24) B C k Alternatively, the reactive mass ratio can be defined relative to the actual point concentration at the end of the physical step C k phys , as: C = Rk ρ k = Co • Dak (25) phys Ck Since the reactive mass depends on the time step ∆t, either of these relationships can be used to define a time step constraint. The value of such a constraint will depend on the nature of the chemical reactions as well as the characteristics of the particular chemical reaction routine used. For fast reversible reactions, Zysset and Stauffer (1992) recommend ρ k B ≤ 0.01. The MINTEQ-based model generally reached much higher values (see applications below), for the scenarios investigated. The reactive mass ratio ρ k C defined by eq. (23) represents the mass generated or consumed relative to the mass present at the end of the physical step. Since the mass consumed (R k ≤ 0) cannot exceed the mass present, ρ k C ≥ - 1. Upper limits on ρ k B and ρ k C have not yet been defined; it is to be expected that any such limits will depend on the ability of the geochemical model to equilibrate a perturbed system. By monitoring the performance of the model for various scenarios under different chemical environments, we expect eventually to be able to define appropriate constraints. 18
POLYMIN 2005 2.3 Primary Variables and their Dimensions The following variables must be dimensioned large enough to accommodate the chosen grid size. These values are set in the PARAMETER statement within the main program. Array dimension limits: (see parm.inc, parmt.inc, mintran.inc, minteq.inc) maxne .... maxnn .... maxn .... maxna .... laa .... Nxdim … Nydim … Nrdim … maxbt .... maxtim .... maxpt … Maximum number of elements in the transport grid. Maximum number of nodes in the transport grid. Maximum number of degrees of freedom (= maxnn - # of fixed nodes). Total number of non-zero matrix entries in condensed matrix. (As a conservative approximation, use maxna = 14 * maxn). PCG solver matrix dimension. (As a conservative approximation, use laa = 3*maxn+maxna). maximum number of components maximum number of aqueous species maximum number of solid species Maximum number of "wells" at which breakthrough curves are generated Maximum number of time steps maximum number of print times Note these values all represent maximum limits, they can be equal to, or greater than, the actual number required. A conservative estimate for maxna is 14 x maxn, and since this parameter reserves memory for one of the largest real arrays, it should be minimized if available computer RAM is limited. POLYMIN computes the minimum vector length (maxna) required by the flow and transport problems and writes this information to the listing file (look for "vector length"). For more efficient memory use, these values can be substituted into the PARAMETER statement. To do this, the model must first be run using an initial estimate for maxna (and hence laa), at least until the correct vector lengths are computed. The minimum vector length and new value for laa is then entered into the program, which is then recompiled and rerun for the full simulation. The code will detect if the given array limits are too small, in which case the execution will terminate with an error message. 19
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 and 12: POLYMIN 2005 model involves three s
Page 13 and 14: POLYMIN 2005 The three basic mathem
Page 15 and 16: POLYMIN 2005 Solution Strategy POLY
Page 17: POLYMIN 2005 Discretization Criteri
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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