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A kind of problems of radially symmetric transient fluid flow in a mediumwith a geometry similar to a hollow-disk can be addressed using the finiteHankel transform. However, the inverse Hankel transform [G. Cinelli, Int. J.Engng. Sci., 3, 539 (1965)] works well only for homogeneous boundaryconditions. We use the finite Hankel transform, together with the Laplacetransform, to solve partial dfferential equations with inhomogeneous boundaryconditions. With this aim, we propose a method to obtain an analytical solutionof the problem of fluid flow in a finite naturally fractured reservoir withinner and outer boundaries having constant and time-dependent conditions,respectively. We assume that the reservoir has a producing well, with eitherconstant terminal pressure or constant terminal rate, while the outer boundaryhas either an influx recharge or constant pressure. Using these case studies,we show that a part of the inverse transformation given by Cinelli can beexpressed as closed formulas for long time solutions, at the same time thatmake it possible to capture the inhomogeneous condition and speed up theconvergence of solutions. For Neumann-Neumann conditions, we show that theinverse expression of Cinelli is incomplete. In addition, an analysis of theflow characteristic curves in a reservoir with influx recharge is presented.The drawdown pressure curves are used to elucidate the statement that thepressure drop of a single-porosity reservoir with influx recharge resembles theflow behavior in a double-porosity closed reservoir, establishing a criteria todistinguish between both.

Analytical solutions from integral transforms for transient fluid flow in naturally fractured porous media with and without boundary flux