Some remarks on simplified double porosity model of immiscible incompressible two-phase flow

The paper is devoted to the derivation, by linearization, of simplified (fully homogenized) homogenized models of an immiscible incompressible two-phase flow in double porosity media in the case of thin fissures. In a simplified dual porosity model derived previously by the authors the matrix-fracture source term is approximated by a convolution type source term. This approach enables to exclude the cell problem, in form of the imbibition equation, from the global double porosity model. In this paper we propose a new linear version of the imbibition equation which leads to a new simplified dual porosity model. We also present numerical simulations which show that the matrix-fracture exchange term based on this new linearization procedure gives a better approximation of the exact one than the corresponding exchange term obtained earlier by the authors.