Semi-Analytical Solutions for a Partially Penetrated Well with Wellbore Storage and Skin Effects in a Double-Porosity System with a Gas Cap

We have studied the effect of a constant top pressure on the pressure transient analysis of a partially penetrated well in an infinite-acting fractured reservoir with wellbore storage and skin factor effects. Semi-analytical solutions of a two-dimensional diffusivity equation have been obtained by using successive applications of the Laplace and modified finite Fourier sine transforms. Both pseudo-steady-state and transient exchanges between the matrix and the fractures have been considered. Solutions are presented that can be used to generate type curves for pressure transient analysis or can be used as a forward model in parameter estimation. The presented analysis has applications in well testing of fractured aquifers and naturally fractured oil reservoirs with a gas cap.