Analytical solutions for flow in porous media with multicomponent cation exchange reactions

Multicomponent cation exchange reactions have important applications in groundwater remediation, disposal of nuclear wastes as well as enhanced oil recovery. The hyperbolic theory of conservation laws can be used to explain the nature of displacements observed during flow with cation exchange reactions between flowing aqueous phase and stationary solid phase. Analytical solutions have been developed to predict the effluent profiles for a particular case of heterovalent cations (Na⁺, Ca²⁺ and Mg²⁺) and an anion (Cl^-) for any combination of constant injection and constant initial composition using this theory. We assume local equilibrium, neglect dispersion and model the displacement as a Riemann problem using mass action laws, the charge conservation equation and the cation exchange capacity equation. The theoretical predictions have been compared with experimental data available at two scales - the laboratory scale and the field scale. The theory agrees well with the experimental data at both scales. Analytical theory predictions show good agreement with numerical model, developed using finite differences. Key Points Analytical model for cation exchange reactions (Na, Mg, and Ca) with transport Composition space analysis for intermediate compositions and effluent profiles Ternary cation exchange transport model matches laboratory and field measurements