Convergence of the homogenization process for a double-porosity model of immiscible two-phase flow.

*(English)*Zbl 0866.35018The so-called dual-porosity model for immiscible incompressible two-phase flow in a natural fractured reservoir is derived rigorously from the mathematical point of view. Physically such a model for a porous medium consists of an equivalent coarse-grained porous medium, in which the fissures play the role of “pores” and the blocks of porous media play the role of “grains”. Mathematically the model consists in solving of a nonlinear system of coupled equations with parabolic degeneracy.

Assuming periodic distribution of cells in the microscopic model (each cell contains only one matrix) and using the two-scale convergence method (developed as, for instance, by G. Allaire) the authors prove a convergence of the “total velocity” and of the “reduced pressure” to the solution of the appropriately defined macroscopic (homogenized) model. During this homogenization process the volume fractions of the fissured part and nonfissured part are kept as constants and of the same order.

Assuming periodic distribution of cells in the microscopic model (each cell contains only one matrix) and using the two-scale convergence method (developed as, for instance, by G. Allaire) the authors prove a convergence of the “total velocity” and of the “reduced pressure” to the solution of the appropriately defined macroscopic (homogenized) model. During this homogenization process the volume fractions of the fissured part and nonfissured part are kept as constants and of the same order.

Reviewer: Z.Denkowski (Kraków)