Numerical Simulation and Homogenization of Diphasic Flow in Heterogeneous Reservoir
Brahim Amaziane, Alain P. Bourgeat, Joe Koebbe · 1990
By mean of the so called homogenization theory, see for instance [16], we derive mathematically rigorous “effective” reservoir equations from exact local equations of incompressible two-phase flow (miscible or immiscible) in a heterogenous reservoir. The main result is that “effective” equations are exactly of the same type as the original ones. In general cases the effective permeability tensor is given only as a mathematical limit. In some special cases where there is some additional knowledge on the heterogeneities repartition as for instance a spatial periodic repartition, we may really compute the effective parameters and then numerically compare both behaviour in a heterogeneous or in a homogenized reservoir. In [1] and [12], we have presented some simulation of stratified medium; in [2] and [12] we have presented several simulations on spatially periodic heterogeneities. Herein we are presenting only one of such a simulation to illustrate our results.