An asymptotic analysis of the steady process of saturation of a laminated porous material

The propagation of a steady saturation front in a double-layer porous material, situated between impenetrable walls, is investigated. The closed system of equations and boundary conditions are written on the assumption that the displacing and displaced phases, the viscosities of which differ considerably, are connected, and that the capillary pressure on the interface is constant. The features of the behaviour of the interface in the neighbourhood of the boundary of the layers are investigated in the case when the layer thicknesses differ considerably. When the permeabilities of the layers differ considerably, asymptotic expressions are obtained for the pressure and shape of the interface, and a comparison is made with the results of a numerical solution of the complete problem and with the known asymptotic relations obtained when using a simplified boundary condition at the interface.