Use of Pressure, Pressure-Squared Or Pseudo-Pressure In the Analysis of Transient Pressure Drawdown Data From Gas Wells
Authors: Aziz K. , Mattar L. , Ko S. , Brar G.S. 
Published: March 2010

Abstract
In the analysis of transient pressure drawdown data, it is possible to Plot the data in terms of pressure, pressure-squared or pseudo-pressure.
Equation Available In Full Paper
In this paper, we compare these three approaches and provide some guidelines for the use of each. The use of pseudo-pressure is found to be the only reliable method when large drawdowns exist. We find that any of the three approaches is adequate when drawdowns are small. However, the pressure-squared approach is found to be better than the pressure approach in most wells where these two are different. Our conclusions are based on the comparison of analytical solutions with numerical solutions for several typical gas reservoirs in Alberta.

Introduction
In the reservoir engineering literature, the flow of gas is variously analyzed by using one of three variables - namely, the pressure, the pressure-squared or the pseudo-pressure. There is no clear evidence concerning the conditions of flow under which the use of some of these variables is admissible.
Rawlins and Shellhardt (1935) found empirically that stabilized gas flow could be described in terms of pressure-squared by the well-known deliverability equation Equation (1) Available In Full Paper.
Aronofsky and Jenkins (1954) showed that Darcy flow of an ideal gas in the reservoir could be represented by the diffusivity equation expressed in terms of pressure-squared (instead of pressure, as in the case of oil flow),
Matthews and Russell (1967), in their discussion of pressure buildup and analysis, suggested that using the pressure-squared was unnecessary and that satisfactory results were being obtained by simply using the pressure as the variable in the diffusivity equation.
AI-Hussainy and Ramey (1966) proposed yet a third variable, originally termed the "real gas potential", but later referred to as the "real gas pseudo-pressure." We refer to this simply as the "pseudo-pressure."
There are then three well-known approaches for the plotting and analysis of well data: pressure, pressure-squared and pseudo-pressure. To complicate matters, some pressure data may be analyzed by using any one of these three variables, and give the same answer.
Other data will give a different answer for each of the variables.
Moreover, deliverability tests on gas wells are usually analyzed using the pressure-squared, whereas drill-stem tests or buildup tests are often analyzed using the pressure. This gives rise to the question of consistency of results.
Further complication and confusion results because some of the parameters that must be constant for the application of the analytical solution are actually dependent on pressure. What pressure should these variable parameters be evaluated at? A clear answer to this question is also not available in the literature.
The purpose of this publication is to clarify the relationship between the three systems of analysis, and to indicate clearly when they are consistent with each other and when they are not. We will also consider the question: At what constant (or average) conditions should the variable parameters be evaluated? This study is restricted to constant-rate production from infinite-acting reservoirs.