Viscous fingering, gravity segregation and permeability heterogeneity in two-dimensional and three-dimensional flows.

摘要

A hybrid finite-difference/particle-tracking numerical simulator for unstable flow in the presence of density and viscosity differences in heterogeneous domains was developed for a Single Instruction, Multiple Data (SIMD) parallel machine. High resolution two-dimensional (2D) and three-dimensional (3D) simulations were performed to investigate the interplay of viscous fingering and gravity segregation in both homogeneous and heterogeneous porous media.; In both 2D and 3D flow, there is a transition from gravity-dominated flow at low values of the ratio of viscous to gravity forces ({dollar}Rsb{lcub}v/gsb{lcub}z{rcub}{rcub}{dollar}) to flow dominated by viscous fingering at high values of {dollar}Rsb{lcub}v/gsb{lcub}z{rcub}{rcub}{dollar}. In homogeneous porous media, a single gravity tongue forms when {dollar}Rsb{lcub}v/gsb{lcub}z{rcub}{rcub}{dollar} is {dollar}{lcub}cal O{rcub}{dollar}(1) in both the 2D and the 3D flows. In 3D flow, however, gravity effects are important over a significantly wider range of {dollar}Rsb{lcub}v/gsb{lcub}z{rcub}{rcub}{dollar}. When the flow is 3D, buoyancy remains a significant transport mechanism for values of {dollar}Rsb{lcub}v/gsb{lcub}z{rcub}{rcub}{dollar} that are nearly an order of magnitude larger that the {dollar}Rsb{lcub}v/gsb{lcub}z{rcub}{rcub}{dollar} values for which the 2D flow is dominated by viscous fingering.; Permeability heterogeneity disrupts vertical flow that is essential for buoyancy to be effective, and it enhances the transport in the mean flow direction. Whether the flow is 2D or 3D, the presence of heterogeneity shifts the {dollar}Rsb{lcub}v/gsb{lcub}z{rcub}{rcub}{dollar} range for which gravity segregation is effective to smaller values.; For a 2D domain that has a permeability correlation structure that can be described as nearly equivalent to a 3D structure, tracer and viscous fingering flows display similar characters in 2D and 3D. In the presence of density differences, however, the 3D flow is always more affected by gravity segregation than the 2D flow.; The simulation results demonstrate that there are many flow situations for which 2D simulations do not represent adequately the combined effects of viscous fingering and gravity segregation. For such flows, 3D simulations are required.