In this paper, we are interested in the displacement of a single compressible phase in Darcy-Brinkman's flow in porous media. The equations are obtained by the conservation of mass and by considering the Brinkman regularization velocity of the standard Darcy infiltration velocity. This model is treated in its general form with the whole nonlinear terms. In first part, we prove the existence in one dimensional space of a solution for the Dracy-Brinkman system, and in the second one we treat this system with Bear hypothesis in multidimensional spaces.