Affiliations: [a] Faculty of Science, University of Zagreb, Bijenička 30, 10000 Zagreb, Croatia | [b] Moscow Institute of Physics and Technology, 9 Institutskiy per., Dolgoprudny, Moscow Region, 141700, Russian Federation | [c] UPPA, Fédération IPRA, Pau, France | [d] Faculty of Mining, Geology and Petroleum Engineering, University of Zagreb, Pierottijeva 6, 10000 Zagreb, Croatia
Abstract: The paper is devoted to the derivation, by linearization, of simplified homogenized models of an immiscible incompressible two-phase flow in double porosity media in the case of thin fissures. In a simplified double 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 double 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.
