An investigation of the use of pseudotime in transient test analysis of gas wells

Abstract

The differential equation describing flow of real fluids through porous media is, in general, nonlinear. For gases, the nonlinearity is particularly strong. In order to obtain analytical solutions to the flow equation for gases, the equation must first be linearized to give it the form of the diffusivity equation. To achieve the desired linearization, two approximate linearizations have been proposed--the use of pseudopressure as the dependent variable, and the use of pseudotime as the independent variable. Empirically it has been observed that use of pseudopressure alone is adequate for drawdown test analysis, while both pseudopressure and pseudotime must be used during buildup. In this study, the pseudopressure-pseudotime linearization is studied using both analytical and numerical methods. The pseudopressure-time linearization is exact for steady-state flow; the pseudopressure-pseudotime linearization is exact for the case of uniform pressure, as long a porosity remains constant. Wellbore storage is shown to be described exactly by the pseudopressure-pseudotime linearization. Drawdown is shown to be dominated at the wellbore by flow very similar to steady-state flow. Buildup is shown to be dominated by storage phenomena, with nearly uniform pressure near the wellbore. For buildup when producing time effects become important, the correct producing pseudotime is shown to be that obtained by dividing the producing time by the initial viscosity-compressibility product