This is an attempt to develop the hydrodynamic theory of upscaling for complex flows through highly heterogeneous porous media. The basic consequence of high heterogeneity is the change of the equation type after homogenization that is associated, first of all, with the appearance of various non-local phenomena on the macroscale. All components of the upscaling procedure are examined for single-phase flow, immiscible two-phase and miscible multi-component flow. This book includes the modification of homogenization techniques, classification of flows, deduction of new effective models of flow, definition of the macroscale parameters and function, description of dynamic or non-equilibrium effects, solution of the cell problems, reduction of the two-phase cell problems to the saturation-independent ones, development of some effective tools to compute the effective functions in disordered highly heterogeneous media, computational analysis of the deduced models and applications to some problems of the oil industry.
