A mixing ratios‐based formulation for multicomponent reactive transport

Abstract

Chemical reactions are driven by disequilibrium, which is often caused by mixing. Therefore quantification of the mixing rate is essential for evaluating the fate of solutes in natural systems, such as rivers, lakes, and aquifers. We propose a novel mixing ratios‐based formulation to evaluate solute concentrations and reaction rates when equilibrium aqueous reactions and precipitation/dissolution of minerals are driven by mixing of different end‐members. Each end‐member corresponds to a water from a given source with a specific chemical signature. The approach decouples the solute transport and chemical speciation problems, so that mixing ratios can be first obtained from the solution of conservative transport and then be used in general speciation codes to obtain the concentration of reacting species. One key finding is a general expression for reaction rates which demonstrates that the amount of reactants evolving into products depends on the rate at which solutions mix. Our formulation constitutes a general framework according to which one can design and interpret experimental analyses devoted to study mixing‐driven reactive processes and obtain transverse dispersion coefficients. The formulation is also proposed as a useful tool to derive analytical solutions of reactive transport problems and may result computationally advantageous when compared to previous approaches to reactive transport modeling. We apply the developed formulation to provide an analytical solution of the reactive transport process resulting from mixing different CaCO$_{3}$‐saturated waters in a two‐dimensional setup.

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