Macroscopic modeling of double-porosity reservoirs

This paper deals with the seepage of a fluid through a fractured porous medium. It summarizes important results obtained using the homogenization method for periodic structures. Thereby, unlike the phenomenological approaches, the macroscopic behaviors are deduced from the physics at the microscopic scales, without any prerequisite. Two cases have been investigated: flow of gas through a rigid medium and flow of incompressible fluid through a deformable matrix. In both situations, it turns out that the ratio between the two separations of scales (macroscopic scale/fissure scale and fissure scale/pore scale) plays an essential role. The macroscopic description depends upon the separations of scales, and the coupling effects between the two porous systems are maximum when the scales are equally separated. Then, the homogenization result is compared to classical phenomenological models for slightly compressible fluid flow through a rigid double-porosity medium. Pseudo-steady-state phenomenological models are shown to give a rough description for transient excitations and finally a correction is proposed giving a more accurate short-time behavior.