  The paper deals with homogenization of a model problem describing an
immiscible compressible two-phase flow in random statistically homogeneous
porous media. We derive the effective (macroscopic) problem and prove the
convergence of solutions. Our approach relies on stochastic two-scale
convergence techniques, the realization-wise notion of stochastic two-scale
convergence being used. Also, we exploit various a priori estimates as well as
monotonicity and compactness arguments.
