Hyperbolic Theory for Flow in Permeable Media with pH-Dependent Adsorption

A theory for the solution of the Riemann problem for a one-dimensional, quasi-linear, 2$\times$2 system of conservation laws describing reactive transport in a permeable medium with pH-dependent adsorption is developed. The system is strictly hyperbolic and nongenuinely nonlinear because the adsorption isotherms are not convex functions. The solution comprises nine fundamental structures, which are a concatenation of elementary and composed waves. In the limit of low pH, the isotherms reduce to convex two-component Langmuir isotherms considered in chromatography, and the solution comprises only four fundamental structures, as in classical theory. Semianalytical solutions and highly resolved numerical simulations show good agreement in all cases.

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