elative permeability tensors are 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.