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The presence of natural fractures can significantly affect the quality of hydraulic fracturing operations in tightsand and shale or oil/gas formations. This paper describes the procedure used to model natural fractures with continuum damage tensor and the resulting orthotropic permeability tensor. A damage model that uses damage variable in tensor form is presented. In the procedure presented, a nonnegligible angle is assumed to exist between directions of principal stresses in the formation and in the natural-fractures-related damage tensor, and this difference in orientation is modeled by introducing local directions in the model. A damage-dependent permeability tensor in tabular form is then proposed. A second case scenario when the directions of principal stresses and natural fractures align is also analyzed. Numerical results of fracture distribution are presented for both cases, and differences can be seen from the computed contour of the damage variable. The results indicate that the model can effectively simulate the fracture propagation phenomena during hydraulic fracturing.

Damage Model for Reservoirs with Multisets of Natural Fractures and Its Application in the Simulation of Hydraulic Fracturing