Production of fluids from petroleum reservoirs reduces the pore pressure, increases the net overburden stress, and consequently, reduces the total porosity and permeability of the reservoir rock. This effect is much more significant in low permeability geo-pressured and naturally fractured reservoirs. For well test purpose, the assumption of constant permeability in the diffusivity equation will yield inaccurate estimates of the reservoir properties for any reservoirs in geo-pressured zone. To study the pressure transient behavior in a stress dependent porous media, it is assumed that permeability of the formation is stress dependent. Hence, a new parameter known as the permeability modulus is introduced.

In this study, the effect of stress-sensitivity was incorporated by expressing the permeability as an exponential function of pore pressure in the derivation of a three-dimensional diffusivity equation required to describe the flow of fluid for a horizontal well in a naturally fractured reservoir. The matrix-fracture fluid transfer model considered was the pseudo-steady state flow model. Since pragmatic values for the dimensionless permeability modulus ranges between zero and unity, it was possible to apply the theory of perturbation to develop and solve a system of linear boundary value problem subject to an infinite lateral and bounded vertical boundary condition. Applying the Laplace and finite Fourier cosine transform, an approximate analytical solution in Laplace space was obtained which was inverted numerically. Pressure response curves were generated and analyzed for certain vital parameters.

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