Pore-Network Simulation of Unstable Miscible Displacements in Porous Media

We develop a comprehensive pore-network model for simulation of miscible displacements in laboratory-scale porous media. The goal is to study the effect of pore-scale heterogeneity, and in particular pore-size distribution and pore connectivity, as well as mobility ratio M on miscible displacements, and compute the effective longitudinal dispersion coefficient as a function of M. At the pore level the phenomenon is described by the convective-diffusion equation with a Taylor–Aris dispersion coefficient. Extensive simulations indicate the strong effect of the connectivity and broadness of the pore-size distribution on the efficiency of the displacement process. Moreover, the model enables us to compute the effective dispersion coefficient as a function of the mobility ratio of the two fluids that, to our knowledge, has not been calculated before. Simple generalization of the model will make it possible to study more complex related phenomena, and in particular injection of CO2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm{CO}_2$$\end{document} into a pore space that contains saline water.