Transient Quasi-Static Gas Flow through a Rigid Porous Medium with Double Porosity

International audienceThe highly compressible fl uid fl ow through a three-scales rigid porous medium (pore, fracture, macroscopic sample) is investigated using a homogenization method. The macroscopic description is strongly dependent on the separation of the different scales, and three cases are considered. The pores either play the role of a compressible fluid reservoir, introduce a memory effect, or are ignored, respectively. The homogenization result is compared to classical phenomenological models that are available in the case of slightly compressible fl uids. Pseudo-steady state models are shown to give a rough description of the phenomenon