The use of effective medium theories for seismic wave propagation and fluid flow in fractured reservoirs under applied stress

Methods for predicting the permeability and elastic properties of hydrocarbon reservoirs containing natural fractures are important for the production optimization and seismic characterization of fractured reservoirs. Effective medium theories may be used for this purpose but need to be validated using numerical calculations of the fluid flow and seismic properties for realistic fracture networks. The prediction of effective permeability and elastic properties using effective medium theories of fractured media are compared with numerical simulations using a discrete fracture network (DFN) containing two sets of non-orthogonal vertical fractures. Discrepancies between the permeability obtained from the simulations and using effective medium theory are attributed to an oversimplified treatment of fracture interconnectivity in the effective medium theory used. The simulations indicate that the effect of interconnectivity on fluid flow varies with stress and flow direction. By contrast, the effective elastic compliances obtained from numerical simulation and effective medium theory are in good agreement, even for relatively complicated fracture networks. Although permeability and seismic anisotropy both vary with stress, the relation between them is not simple. The variation in reflection amplitude with offset and azimuth is found to be sensitive to the ratio of the normal to shear compliance of the fractures, whereas permeability is less sensitive to this ratio. For the DFN studied, the permeability rapidly increases at high level of stress due to dilation of the fractures when the in situ stress field is strongly anisotropic.