Simulation of large‐scale transport of variable density and viscosity fluids using a stochastic mean model

Abstract

Previous results of stochastic analysis of variable density and viscosity fluids in heterogeneous isotropic porous media show that longitudinal macrodispersivity is a function of mean concentration and concentration gradient. The dependence of macrodispersivity on mean concentration and concentration gradient gives rise to a nonlinear mean solute transport equation. To evaluate this behavior, a one‐dimensional finite difference formulation of the mean solute transport equation that incorporates the analytically derived expression for longitudinal macrodispersivity is used to simulate a step input problem. This approach allows effects of a spatially and temporally varying macrodispersivity on breakthrough curves to be observed and effects on dispersed‐zone width to be calculated. Simulation results show that, for solute concentrations of environmental significance, density effects give rise to macrodispersivities up to several orders of magnitude larger (for the unstable (fingering) case) or smaller (for the stable case) than would be predicted by analysis of an ideal tracer, and the smaller the velocity, the greater the effect. In miscible secondary petroleum recovery, where the displaced and displacing fluids differ in concentration by as much as 100%, viscosity effects have the predominant influence on macrodispersivity; in this case, simulations illustrate that viscous fingering effects give rise to macrodispersivities that are several orders of magnitude larger than predicted by classical analysis. Qualitatively these results agree with fine‐grid numerical simulations of viscous fingering and laboratory column experiments in that similar trends are observed for the effects of displacement orientation, velocity, and density and viscosity contrasts on dispersed‐zone width.