Gas Well Testing with Wellbore Storage and Skin: a Line Source Solution Using the Green's Functions Approach

Abstract

Abstract Even when written in terms of a pseudo-pressure function, the diffusivity equation for flow of gases through porous media is, rigorously speaking, non-linear because the viscosity-compressibility product is pseudo-pressure dependent. However, several techniques and analysis procedures neglect such non-linearity. A new methodology for constructing solutions for gas reservoirs through the Green's Function technique has been recently proposed in the literature. Such methodology handles the viscosity-compressibility product variation rigorously and it has been applied to solve several gas well tests problems successfully. However, wellbore storage and skin effects have not been considered yet in this new approach. In this work, the Green's Function technique is applied to obtain a new solution for an infinite homogeneous isotropic gas reservoir being produced through a single vertical well with wellbore storage and skin. The solution, however, does not consider non-Darcy flow effects. Even though the wellbore storage introduces a new non-linearity to an already non-linear problem, this work presents two accurate approximate solutions compared to the results from a commercial numerical simulator. This work also shows that wellbore pseudo-pressure dimensionless solution is a function of the correlating groups CDexp(2S) and tD/CD, exactly like the wellbore dimensionless liquid solutions are. Liquid and gas dimensionless solutions under these correlating groups are not equal, though.