Filtration of bubbly fluids

Abstract

We investigate the macroscopic seepage law of a bubbly fluid through a rigid porous medium when the capillary forces are taken into account. For this purpose we use a method of multiple scale asymptotic developments. Starting from the pore scale it gives the macroscopic equivalent description without any prerequisite at the macroscopic scale. It makes use of the presence of well-separated scales and it permits the investigation of the interactions between them. We study two cases. The first one concerns bubble sizes of the order of the pore size. This case presents only two characteristic separated scales, the pore scale and the macroscopic scale. The second one considers bubble sizes much smaller than the pore size. It presents three characteristic scales. The two cases give Darcy laws at the macroscopic scale. But the large bubble case, the more frequent, does not show an intrinsic permeability and the conductivity depends on the capillary pressure. The macroscopic description is not classical and is strongly non linear.