Computer simulations of miscible displacement processes in disordered porous media

Abstract

The results of a detailed study of miscible displacement processes (MDP) in disordered porous media are presented. The main goal is to develop efficient computer simulation methods for investigating the effect of disordered morphology of the pore space on the MDP. A two-dimensional network of interconnected tubes with distributed effective radii is used as a model of the pore space. We use a percolation network to study the effect of random topology on the displacement processes, and the effect of the geometry of the pore space is investigated by using various probability density functions for the effective radii of the tubes. We study MDP over a wide range of values of the mobility ratio, and several quantities of interest, such as the sweep efficiency of the process and its dependence on the length of the porous medium, and the fractal dimension characterizing MDP are determined and compared with the experimental data and previous predictions obtained by other methods. The results show the strong effect of the disordered morphology of the porous medium on MDP. In addition, it is shown that MDP are sensitive to the length scale over which the porous medium is macroscopically homogeneous. If MDP take place over a length scale that is smaller than a certain characteristic length scale over which the porous medium is macroscopically homogeneous, the macroscopic continuum equations which are usually used to describe MDP may not be valid. In addition, we are able to map the problem onto an equivalent random-walk problem for any value of mobility ratio and any type of disorder. The laws governing this random-walk are derived from the flow equations. The predictions of the random-walk model are in agreement with the results of direct simulations, and they both agree quantitatively with the available experimental data. The effect of dispersion on MDP is briefly discussed, and two models are proposed for studying the effect of dispersion on MDP.