A fully-coupled geo-mechanics and two-phase (oil-water) fluid-flow model is developed to analyze pressure transient problems in naturally fractured reservoirs (or stress-sensitive reservoirs) with deformable anisotropic formation. For fractured reservoirs, the rock is actually dual-porosity media of matrix pores and fractures, fractures are the main storage of oil. Fluid flow is modeled within the context of dual-porosity concept and based on three basic principles: mass conservation, Darcy's law, and equation of state. While geo-mechanics is modeled following Biot's two-phase (fluid and rock), isothermal, linear poroelastic theory, which has three basic principles: stress equilibrium, strain-displacement, and strain-stress-pressure relations. The development follows along the line of the conventional and existing porous single-phase fluid-flow modeling. The interpretation of the pore volumetric changes of the dual continua, fractures and matrix-blocks, and the associated effective stress law for anisotropic double porous media are the most difficult and critical coupling considerations. The model reduces, in the case of isotropic and anisotropic but single-phase response, to that suggested by Li et. al. and Zhao. et al.
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