Revisiting the analytical solution approach to mixing-limited equilibrium multicomponent reactive transport using mixing ratios: identification of basis, fixing an error, and dealing with multiple minerals

Abstract

Multicomponent reactive transport involves the solution of a system of nonlinear coupled partial differential equations. A number of methods have been developed to simplify the problem. In the case where all reactions are in instantaneous equilibrium and the mineral assemblage is constant in both space and time, de Simoni et al. (2007) provide an analytical solution that separates transport of aqueous components and minerals using scalar dissipation of Multicomponent reactive transport involves the solution of a system of nonlinear coupled partial differential equations. A number of methods have been developed to simplify the problem. In the case where all reactions are in instantaneous equilibrium and the mineral assemblage is constant in both space and time, de Simoni et al. (2007) provide an analytical solution that separates transport of aqueous components and minerals using scalar dissipation of "mixing ratios" between a number of boundary/initial solutions. In this approach, aqueous speciation is solved in conventional terms of primary and secondary species, and the mineral dissolution/precipitation rate is given in terms of the scalar dissipation and a chemical transformation term, both involving the secondary species associated with the mineral reaction. However, the identification of the secondary species is nonunique, and so it is not clear how to use the approach in general, a problem that is keenly manifest in the case of multiple minerals which may share aqueous ions. We address this problem by developing an approach to identify the secondary species required in the presence of one or multiple minerals. We also remedy a significant error in the de Simoni et al. (2007) approach. The result is a fixed and extended de Simoni et al. (2007) approach that allows construction of analytical solutions to multicomponent equilibrium reactive transport problems in which the mineral assemblage does not change in space or time and where the transport is described by closed-form solutions of the mixing ratios.

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