Basis swapping procedure

Conveniently, perhaps even miraculously, the equations developed in Chapter 5 to accomplish basis swaps can be used to balance chemical reactions automatically. Once the equations have been coded into a computer program, there is no need to balance reactions, compute equilibrium constants, or even determine equilibrium equations by hand. Instead, these procedures can be performed quickly and reliably on a small computer. 

Such a method has seldom been used with systems containing an aqueous fluid, probably because the complexity of the solution s free energy surface and the wide range in aqueous solubilities of the elements complicate the numerics of the calculation (e.g., Harvie el al., 1987). Instead, most models employ a procedure of elimination. If the calculation described fails to predict a system at equilibrium, the mineral assemblage is changed to swap undersaturated minerals out of the basis or supersaturated minerals into it, following the steps in the previous chapter the calculation is then repeated. 

Once there are no undersaturated minerals, the procedure checks for supersaturated minerals. If any exist, the most supersaturated mineral, identified by the largest Qi/K[, is swapped into the basis and the governing equations are solved. Precipitating a new mineral, however, may dissolve another away, so now the process begins anew by checking for undersaturated minerals. Once a solution has been found that includes neither undersaturated nor supersaturated minerals, the true equilibrium state has been located. 

To calculate the model with react, we swap C02(g) and 02(g) into the basis in place of H+ and 02(aq), and constrain each basis member. The procedure is... 

The calculation procedure in react is to swap sphalerite and barite into the basis in place of 02(aq) and Ba++... 

The model then swaps aqueous species Aj into the basis locations Ak held by the mineral components. The technique for swapping the basis is explained in Chapter 5, and a method for selecting an appropriate species Aj to include in the basis is described in Chapter 4. When the procedure is complete, the equilibrium system contains only the original fluid. 

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