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Abstract

The real gas flow equation is effectively linearized for drawdown when expressed in terms of pseudopressure and time. Two time functions have pseudopressure and time. Two time functions have been proposed to linearize the flow equation for buildup: pseudotime and normalized time.

This paper compares the use of pseudotime and normalized time for a variety of different analysis techniques. The study focuses on buildup following constant rate drawdown for systems in which the reservoir is still infinite acting. For radial flow, analysis methods considered include log-log type curve matching and Horner analysis. Analysis methods for wells with infinite conductivity vertical fractures include linear flow analysis, log-log type curve matching, and Horner analysis.

Except for wellbore storage, no major difference in accuracy is found between pseudotime and normalized time.

Also compared are two different methods for treating producing time effects when using pseudotime or normalized time. A new method of pseudotime or normalized time. A new method of calculating the equivalent drawdown time function is presented which is independent of initial pressure. presented which is independent of initial pressure

Introduction

Constant rate solutions to the flow equation are important tools in the analysis of oil well drawdown and buildup tests. The use of pseudopressure as the dependent variable allows the liquid solutions to be used to analyze gas drawdown tests. As found independently by Agarwal and by Scott, the use of pseudopressure and time does not adequately linearize the gas flow equation for the case of buildup following constant rate drawdown.

Agarwal proposed a new time plotting function, which he called pseudotime, to allow liquid drawdown solutions for fractured wells to be used to analyze buildup tests on gas wells. To achieve the same objective, Scott proposed a similar function, called the normalized time.

Lee and Holditch showed that the use of pseudopressure and pseudotime led to a modified pseudopressure and pseudotime led to a modified wellbore storage constant with no pressure dependence. They found the pseudopressure-pseudotime formulation useful in analyzing both drawdown and buildup tests when wellbore storage is present. They also presented an expression for the terms neglected presented an expression for the terms neglected when the gas flow equation is linearized using pseudopressure and pseudotime. pseudopressure and pseudotime. Spivey showed that the proper choice of the producing pseudotime allowed good results to be producing pseudotime allowed good results to be obtained from Horner analysis for permeability, skin, and original pressure when the reservoir is still infinite acting.

Reynolds, Bratvold, and Ding compared the use of pseudotime and normalized time for semilog analysis. They found either time function to give good results for permeability using Horner analysis, using a slightly different Horner time ratio from that used by Spivey. They were also able to estimate average reservoir pressure using the MBH liquid functions with either pseudotime or normalized time.

Thus, both pseudotime and normalized time have been found useful for analyzing gas well buildup tests for a variety of geometries. Pseudotime has been used with success for wells with radial symmetry during wellbore storage, the middle time region, and the late time region.