developed. Analogous to work of G. Dagan & P. Indelman, the energy criterion is used for upscaling of absolute permeability. The fine-scale energy equality to approximated value corresponding to tensor coefficients is required for cells containing fractures. The resulting effective tensor is symmetric and physically consistent since the flux approximation is assured. Two classes of methods are applied to determine the pseudo relative permeability tensor. First one is the stationary capillary equilibrium method which is applicable in capillary trapping zones far from wells. Furthermore, analysis of relations between phase and absolute permeability tensors is carried out using this method. Samples of relative permeability curves are obtained for media with orthotropic and monocline symmetries. The influence of connectivity property on the functions is shown and the saturation dependence of direction of principal axes for phase permeability tensor is investigated. Thereby the misalignment of phase and absolute permeability tensors is shown. The second class is a dynamic pseudo-function approach which uses the multiscale method for water flooding simulation. The method combines the Fedorenko finite superelement method and the Samarskii support operator method and belongs to the high-resolution methods class. The technique developed allows to incorporate fractures of complex geometry, accurately accounts the anisotropy for two-phase flows, and as opposed to dual parameters model doesn’t require the connectivity of fractures system and avoids doubling the number of unknowns. The method is successfully applied for simulation of the China and West Siberia fractured reservoirs.


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