Changing the Basis
Changing the Basis
To this point we have assumed the existence of a basis of chemical components that corresponds to the system to be modeled. The basis, as discussed in the previous chapter, includes water, each mineral in the equilibrium system, each gas at known fugacity, and certain aqueous species. The basis serves two purposes: each chemical reaction considered in the model is written in terms of the members of the basis set, and the system’s bulk composition is expressed in terms of the components in the basis. Since we could not possibly store each possible variation on the basis, it is important for us to be able at any point in the calculation to adapt the basis to match the current system. It may be necessary to change the basis (make a basis swap, in modeling vernacular) for several reasons. This chapter describes how basis swaps can be accomplished in a computer model, and Chapter 9 shows how this technique can be applied to automatically balance chemical reactions and calculate equilibrium constants. The modeler first encounters basis swapping in setting up a model, when it may be necessary to swap the basis to constrain the calculation. The thermodynamic dataset contains reactions written in terms of a preset basis that includes water and certain aqueous species (Na+, Ca++, K+, Cl-, HCO-3, SO4- -, H+, and so on) normally encountered in a chemical analysis. Some of the members of the original basis are likely to be appropriate for a calculation. When a mineral appears at equilibrium or a gas at known fugacity appears as a constraint, however, the modeler needs to swap the mineral or gas in question into the basis in place of one of these species. Over the course of a reaction model, a mineral may dissolve away completely or become supersaturated and precipitate. In either case, the modeling software must alter the basis to match the new mineral assemblage before continuing the calculation. Finally, the basis sometimes must be changed in response to numerical considerations (e.g., Coudrain-Ribstein and Jamet, 1989). Depending on the numerical technique employed, the model may have trouble converging to a solution for the governing equations when one of the basis species occurs at small concentration.
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