Application of a constructive method in solving the composite reservoir model of dual-porosity media with fractal characteristics

Abstract In this paper, we apply a constructive method to solve the extended Bessel differential equations with boundary value problem(BVP). Considering wellbore storage and skin effects, a dual-porosity composite reservoir model with fractal characteristics and three typical exterior boundary conditions is established. After symbolic comparison, the reservoir model is identical to the BVP proposed above, and the solving of the reservoir model is naturally reduced to the solving of the BVP. Based on the Laplace transform and a constructive method, the Laplacian space solutions of fracture system pressure and wellbore pressure in the two zones are obtained. The type curves of wellbore pressure and the pressure derivative are plotted with the aid of the Stehfest numerical inversion technique, the flow regimes are identified, and the effects of fractal and reservoir parameters on the type curves are analyzed. Compared with the traditional method, the similar constructive method is more efficient and fast in solving complex reservoir models, which is of great value in designing and implementing well-test analysis algorithms for complex reservoirs.