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