Mathematical Modeling and Simulation of Reactive Transport in Porous Media: Application to CO ₂ Sequestration

Abstract

We present an improved finite volume scheme for reactive transport in porous media, with application to CO2geological sequestration. The method couples advection-dispersion with nonlinear equilibrium adsorption and combines a nonlinear two-point flux approximation with a second-order upwind reconstruction and a regularized limiter. It ensures mass conservation, low numerical diffusion, and robustness on unstructured meshes. Numerical experiments, including a synthetic $C O_{2}$ sequestration test, demonstrate accurate capture of sharp concentration fronts and highlight the influence of the Freundlich adsorption exponent. Specifically, we introduce a regularization step to address the singular behavior of the Freundlich derivative at the origin, a central objective of this work that ensures numerical stability of the proposed scheme.