Methods for Predicting Gas Well Performance

Abstract

The depletion performance of gas wells has been in? vestigated by mathematical simulation techniques. The gas well model which was studied consisted of a single well located in the center of a bounded, cylindrical, homogen? eous reservoir. Dependency of gas compressibility and vis? cosity on pressure was considered in studies of well per? formance at both constant mass flow rate and const!211t flowing pressure conditions. To carr� ou� the 1?vest1ga? . tion, the nonlinear, second-order, partial d1fjerent1al equa? tion which describes Darcy flow of a nonideal gas through porous media was solved numerically. Some of the previous investigations of gas well perform? ance have been of limited general use, because assump? tions were introduced to simplify either the gas properties or the basic differential equation. Other studies have been rigorous in these respects but have presented a very lim? ited set of calculated results. The present study was at? tempted to present a rigorous t�eoretic�I model and �uf? ficient numerical results to permit meaningful conclusions to be drawn. It was found that all terms must be retained in the par? tial differential equation to make accurate predictions. The neglect of higher-order terms, e.g., terms of the order of the "gradient squared", leads to serious material balance errors at large times and to conservative estimates of gas well performance. The higher the gas flow rate and! or the lower the permeability-thickness product of the forma? tion, the more pronounced are these deviations. For ex? ample, in a well draining 640 acres in a 25-md-ft forma? tion (8,120 MMcf gas in place) at a constant rate of 993 Mcfl D, the rigorous solution predicts a bottom-hole pressure decline from 4,000 to I ,OOO psia in 8.7 years. If higher-order terms are neglected in the differential equation, this decline in pressure is predicted to occur in 5.3 years. With the results of the numerical solution of the differ? ential equation as a basis, simple, easy-to-use approxima? tions for predicting gas well performance for Darcy flow conditions have been developed. These simple approxi? mations are based on the familiar equations for flow of a single, slightly compressible fluid. The approximate methods possess a high degree of accuracy and enable the prediction of long-term gas well performance to be made quickly and accurately without the use of a digital com? puter. Both transient and stable flow period approxima? tions were developed.