Pore-scale simulation of dispersion in porous media

Mixing of miscible gas with oil in a reservoir decreases the effective strength of the gas, which can adversely affect miscibility and recovery efficiency. The level of true mixing that occurs in a reservoir, however, is widely debated and often ignored in reservoir simulation where very large grid blocks are used. Large grid blocks create artificially large mixing that can cause errors in predicted oil recovery. This paper examines the mixing that occurs in porous media by solving for single-phase flow in a connected network of pores. This work differs from network models in that we directly solve the Navier-Stokes equation and the convectiondiffusion equation to determine the velocities and concentrations at any location within the pores. Flow in series and layered heterogeneous porous media are modeled by using many grains in different arrangements. We consider both slug, continuous, and partial injection as well as echo tests (single-well tracer tests) and transmission tests (interwell tracer tests). We match the concentrations from the pore-scale simulations to the analytical convection dispersion solution that includes both transverse and longitudinal dispersion coefficients. The results show that for flow in series and in layers, echo and transmission longitudinal dispersivities become equal and reach an asymptotic value if complete mixing over a cross section perpendicular to flow has occurred. In practice, the asymptotic value of dispersivity may never be reached depending on pattern-scale heterogeneity and well spacing. Transverse dispersion coefficients also are scale dependent, but they decrease with traveled distance. We further demonstrate that the classical Perkins-Johnston relationship between longitudinal dispersion coefficient and fluid velocity is obtained. We conclude that echo dispersivities are reliable indicators of true mixing in porous media.