A mathematical formulation for reactive transport that eliminates mineral concentrations

We present a concise and general mathematical formulation for reactive transport in groundwater for general applications. By means of linear algebraic manipulations of the stoichiometric coefficients of the chemical reactions we are able to reduce the number of unknowns of the equations to be solved to the number of degrees of freedom according to thermodynamic rules. We present six formulations that differ from each other by number and type of unknowns and discuss their advantages and disadvantages with respect to the two most important numerical solution methods, the Sequential Iteration Approach (SIA) and the Direct Substitution Approach (DSA). Our conclusion is that the proposed reduction of the number of variables is of special interest for the DSA. We have applied one of these formulations to an example of the flushing of saline water by fresh water.

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