Journal of Porous Media

Crank-Nicolson Galerkin Model for nonlinearly Coupled Macrophase and Microphase Transport in the Subsurface

ABSTRACT

A subsurface can be considered to consist of two phases—the macrophase and the microphase in the context of contaminant transport. The inter-particle pore spaces constitute the macrophase with the intraparticle pore spaces constituting the microphase. The macrophase transport is oftentimes nonlinearly coupled with the microphase transport. The solution of nonlinearly coupled macrophase and microphase transport is particularly challenging. A Crank-Nicolson Galerkin finite element model has been developed to simulate the macrophase transport nonlinearly coupled with the microphase transport. The model is stable and provides oscillation-free results when the mesh Peclet number ≤ 2.5 and the Courant number ≈ 1. The model prediction was also found to be in excellent agreement with experimental data obtained from the literature.