Stress Dependent Anisotropy of Relative Permeabilities in Naturally Fractured Reservoirs

Relative permeabilities of fracture networks as used in dual-continua simulations determine predicted producer behavior and ultimately a field’s achievable recovery. We present numerically derived ensemble (upscaled) relative permeability curves as obtained from discrete fracture and matrix (DFM) imbibition simulations. Our flow simulations are based on unstructured finite element grids and fully capable to account for capillary forces which determine the fluid transfer between fractures and adjacent matrix. Joint aperture distributions are obtained for various trends of maximum horizontal stress using finite element analysis assuming a matrix obeying linear-elasticity and accounting for fracture dilation due to normal stress and displacement. Results obtained from two-phase flow simulations show that relative permeability curves for the case of dominant fracture flow and medium to high flow rates cannot be matched by conventional analytic relationships. A strong anisotropy of relative permeability curve is found - not only as a result of fracture set orientation and degree of percolation, but very much due to the stress dependent ratio between matrix and fracture flow. This result reflects the ability of displacing phase to invade small fractures dependent on stress induced opening/closing. Fracture surface area where capillary transfer processes take place hence strongly depends on stress orientation.