The method of Distributed Volumetric Sources (DVS) is developed to solve problems of transient and pseudo steady state fluid flow. The basic building block of the method comprises calculation of the analytical response of a rectilinear reservoir with closed outer boundaries to an instantaneous volumetric source, also shaped as a rectilinear body. The solution also provides the well-testing derivative of the response to a continuous source in analytical form. This can be integrated over time to provide the pressure response to a continuous source. For production engineering applications, we cast the results into a transient/pseudo-steady productivity index form. The new method is validated through comparison to results of some of the well known well-testing solutions for simple configurations such as vertical wells with full and partial penetration, horizontal wells with unform flux and infinite conductivity, and fractured wells with uniform flux, finite or infinte conductivity. The results show a very good agreement with the existing models. The main advantage of the new solution is its applicability over the more complex fracture/well configurations, some of which is studied in the paper.
The new method has shown to provide a fast, robust, and reliable way to pressure transient analysis, and well performance prediction whenever complex well/fracture configuration is considered.