Hear we present a mathematical approach to averaged description of porous flows. We consider the homogenization of unsaturated flows through a random fractured porous medium. We suppose the non-wetting gas phase occupies the cracks only, and its penetration into porous blocks is impossible. These blocks are supposed to be filled with wetting liquid which can either move trough the system of connected blocks or flow out of them into the cracks. Under these physical assumptions the problem at the microscopic level of blocks and cracks includes Darcy equation inside each block and boundary condition with one-sided constrains on its surface. This problem is well-posed. The homogenization means the asymptotic analysis of this problem when the number of cracks tends to infinity and their sizes simultaneously vanishes. The homogenized problem is found to be a variation inequality which does not equivalent to any differential equation. It is proved rigorously that the leading term of the solution satisfies this problem.
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