Some Practical Aspects of Unsteady-State Gas Flow Related to Gas-Well Performance
Authors: Jones Kevin R. , Pearson Walter C. , Riley Homer G. 
Published: December 2007

Abstract
Predictions of gas-well performance utilizing commonly accepted methods and short-term well test data can lead to serious errors due to the effects of unsteady-state flow. A computer program providing a numerical solution of tile differential equation for unsteady-state radial flow under varying conditions of both gas and reservoir properties was used to investigate these effects on gas-well performance. By systematic variation of flow parameters in computer solutions of well performance, the magnitude of error imposed by short-term test data became apparent. These errors are most serious in determining reserves by material balance and in making long-range performance predictions. Within the range of conditions investigated, gas-well recovery efficiencies are nearly independent of flow capacity. Conversely, the time required for depletion is directly related to the flow capacity of a well.

Introduction
The original objective of this study was to develop long-range gas- well performance predictions from short-term well test data. It was believed that by trial-and-error matching of actual short-term performance and well test data a unique solution of the parameters governing the unsteady-state flow from tight reservoirs could be accomplished. These factors were then to be utilized as the basis for long-range predictions of pressure and flow-rate performance. The unsteady-state flow of gas through low-permeability reservoirs may be described by a second-order nonlinear partial differential equation, for which several approximate solutions have been developed. This investigation was undertaken with a computer program designed to provide a numerical solution of the nonlinear differential equation through the use of finite- difference equations. This approach, as presented in the Appendix, is quite similar to others described in the literature, except that provision was made for broad variation of gas properties in addition to variation of both formation and fracture permeability as well as fracture radius. Published correlations of gas viscosity and compressibility as functions of pressure and temperature were used to prepare tables for a range of gas specific gravities from 0.6 to 0..9. The arrangements for variation of reservoir rock properties are described in the Appendix. Facility to handle any desired variation of each of these parameters was not available from earlier general solutions of this complex equation for unsteady-state gas flow. Numerous computer solutions of long-term performance based on short-term test data indicated that the desired unique solution for the parameters-such as fractional porosity, fracture radius and permeability, and interwell permeability-which govern flow might not be obtained. A unique solution would have been extremely beneficial because accurate values of these reservoir parameters are unknown in most instances. Short-term performance could be matched by mere alteration of imposed permeability and fracture conditions over extremely wide ranges of porosity, pay thickness and drainage radius. Short-term well test data proved to be very insensitive to the factors which determine gas in place, such as porosity and drainage radius. Because long-range predictions of gaswell performance are vitally dependent on gas in place, the original objective was not fully realized. Observations made during this work did provide many benefits to the handling of other phases of the over-all problem discussed later. By systematically varying the flow parameters while making computer solutions of well performance, a great deal was accomplished in evaluating quantitatively the magnitude of error imposed by the unsteady nature of short-term well tests in low-permeability reservoirs. Table 1 Illustrates the range of reservoir conditions investigated. Gas-well potentials from short-term tests appear to be controlled almost entirely by permeability and condition ratios imposed by formation fracturing. Condition ratio (CR) as used herein may be defined as the ratio of a gas well's steady-state flow capacity compared to the theoretical flow capacity were no fracture or wellbore damage present. Conversely, recoverable gas volumes are fixed by porosity and pay thickness, with only limited variations introduced by the factors controlling producing capacity.
JPT
P. 41^