Numerical Simulations by Homogenization of Two-Phase Flow Through Randomly Heterogeneous Porous Media
Aurelian F. Badea, Alain P. Bourgeat · Notes on numerical fluid mechanics · 1997
We consider the behavior of incompressible two-phase flow in heterogeneous reservoirs with randomly placed heterogeneities; that is, a porous medium with permeability A and porosity Ф which are statistically homogeneous random fields oscillating at the dimensionless scale ε. Using the tools of stochastic homogenization we get the nonlinear effective equations which govern the flow behavior in a homogeneous medium being equivalent, in the sense of homogenization theory, to the original one. The computation of the effective permeability tensor A hom is done by solving auxiliary stochastic problems, similar to the ones for the linear one-phase flow case. Under ergodicity assumption, and using the primal and dual formulation of these auxiliary problems, we design a numerical algorithm computing both the effective parameters and the minimal volume on which these effective properties are valid. The validity of our algorithm is tested on a two-phase groundwater flow with injection of one-phase from a well.