Integral transform solutions for describing transient fluid flow in fractured media

The joint Laplace-Hankel transform is used in order to add new solutions of fluid flow in a fractured reservoir for applications in oilfield production or groundwater studies. We consider four cases resulting from the following combination of boundary conditions of a reservoir model: constant terminal pressure or constant terminal rate and constant pressure or influx recharge at the external boundary. We observe that the convergence of the obtained solutions is speed up by using the closed formula of the time-independent part of the inversion formulas and that the inner boundary condition is achieved only when all terms of the infinite series are considered. In addition, we establish that when Neumann-Neumann boundary conditions are imposed, a quasi-stationary solution must be incorporated in order to obtain the correct solution. Finally, we observe matching between the numerical and exact results.