Stochastic Analysis of the Effects of Fluid Density and Viscosity Variability on Macrodispersion in Heterogeneous Porous Media

Publisher Website
Google Scholar
Abstract
Both porous medium heterogeneities and fluid density and viscosity contrasts affect solute transport in miscible fluid displacement. The effects of interaction of these processes on large‐scale mixing are evaluated using spectral‐based perturbation theory. A three‐dimensional, statistically isotropic, exponential log permeability autocovariance is used to represent the spatial variability of the porous medium. State equations linearly relating log density and log viscosity perturbations to concentration perturbations represent the density and viscosity variability and strongly couple the flow and solute transport perturbation equations. Analytical expressions for longitudinal macrodispersivity, derived for one‐dimensional mean solute transport, are functionally dependent on mean displacement distance, mean concentration and concentration gradient, density and viscosity differences, mean velocity, gravity, and correlation scale and variance of the log permeability process. Transient analysis shows that longitudinal macrodispersivity grows exponentially in time (or mean displacement distance) without bound for the case where instabilities due to viscous or gravity fingering arise (the “unstable” or “fingering” case) and that it grows at early time then decreases exponentially to an asymptotic value close to that of local dispersivity for the case where density or viscosity contrasts produce a stabilizing effect (the “stable” case).