A Comprehensive Study Of Dimensionless IPR Correlations For Gas Wells
Authors: Ambastha A.K. , Kosarussawadee P. 
Published: March 2010

Abstract
Following the Voge!'s(1) concept of dimensionless Inflow Performance Relation (IPR) for solution-gas-drive reservoirs recent studies have focussed on current and future IPR curves for fractured or unfractured gas wells producing from a homogeneous reservoir. The application of dimensionless IPR correlations for deliverability calculations for gas wells requires data from a single stabilized flow test and a shut-in test. Therefore, dimensionless IPR correlations have been proposed as a simple alternative to elaborate multi-point deliverability testing.
Using an analytical approach, this study evaluates the accuracy of the previously proposed dimensionless IPR correlations. This paper shows that previously proposed linear IPR correlations and all future IPR correlations for fractured gas wells are inaccurate. This work extends the application of dimensionless IPR correlations to low-permeability gas reservoirs and to sour gases. A detailed sensitivity study of dimensionless current and future IPRs is also presented.

Introduction
Deliverability tests are used to predict short- and long-term production behaviour of gas wells. Usually, deliverability tests are multi-point flow tests conducted as flow-after-flow tests(2) (conventional back pressure tests), isochronal tests(3), and/or modified isochronal tests(4). Data from these multi-point flow tests are analyzed using either the empirical U.S. Bureau of Mines (USBM) back pressure equation2 or the Forchheimer Equation(3). Reference 6 presents a detailed description of deliverability testing methods and analysis procedures. Brar and Aziz(7) present analysis techniques for modified isochronal tests to predict the stabilized deliverability potential of gas wells without using stabilized flow data.
Horne and Kuchuk(8) have proposed a computer-automated interpretation of simultaneous flow-rate and pressure measurements to replace isochronal gas well tests. The methods proposed in References 7 and 8 require well-test data of shorter durations than the multi-point flow tests with One or more flow rates maintained to stabilization.
Also, dimensionless IPR correlations(9–11) have been proposed as a simple alternative to elaborate multi-point deliverability testing. The application of dimensionless IPR correlations for deliverability calculations for gas wells requires data from a single stabilized flow test and a shut-in test. A summary of available empirical correlations for current and future IPR curves for fractured or unfractured gas wells producing from a homogeneous reservoir appears in Appendix 1. Tables 1 and 2 present rock and fluid properties used to develop the correlations presented in Appendix A. This study presents the effects of low permeability (k &lt; 10−15 m2) and skin factor (-5 to 20) on current and future inflow performance relations for gas wells. In the following, a brief discussion of the theory used to develop the IPR correlations for gas wells is presented.

Theory
Mishra and Caudle(9) use the following gas deliverability equation under pseudosteady state conditions:
Equations 1–4 (available in full paper)
Details regarding equation (4) are presented in Appendix A of Reference 9. Mishra and Caudle(9) used gas viscosity and z-factor correlations of Lee et al.(13) and Yarborough and Ha1l(14), respectively. This study uses viscosity and z-factor correlations of Carr et al.(15), and Dranchuk et al.(l6), respectively.