Microscale Investigations of Mixing in a Matrix-Fracture Medium for Intermixing Displacement

Abstract

A finite element method was developed to solve the Navier-Stokes equation and the convectiondiffusion equation in a matrix-fracture medium. Using this method, the effect of molecular diffusion coefficient, fluid velocity, matrix porosity, and fracture space on the mixing pattern was investigated. The results indicate that the dispersion pattern is dominated by convection in the fracture and by diffusion in both the matrix and the fracture. It was discovered that the level of mixing is directly proportional to the molecular diffusion coefficient, matrix porosity, and fracture space, and inversely proportional to the fluid velocity.