Analytical Solution of Fractional Order Diffusivity Equation With Wellbore Storage and Skin Effects

Abstract

This paper addresses the model, solution, and analysis of fluid flow behavior in fractal reservoirs considering wellbore storage and skin effects (WS–SE). In the light of the fractional calculus (FC), the general form of fluid flow model considering the history of flow in all stages of production is presented. On the basis of Bessel functions theory, analytical solutions in the Laplace transform domain under three outerboundary conditions, assuming the well is producing at a constant rate, are obtained. Based on the analytical solutions, various examples, discussing the pressuretransient behavior of a well in a fractal reservoir, are presented.