Methods for Predicting Gas Well Performance

Abstract

Abstract The depletion performance of gas wells has been investigated bymathematical simulation techniques. The gas well model which was studiedconsisted of a single well located in the center of a bounded, cylindrical, homogeneous reservoir. Dependency of gas compressibility and viscosity onpressure was considered in studies of well performance at both constant massflow rate and constant flowing pressure conditions. To carry out theinvestigation, the nonlinear, second-order, partial differential equation whichdescribes Darcy flow of a nonideal gas through porous media was solvednumerically. Some of the previous investigations of gas well performance have been oflimited general use, because assumptions were introduced to simplify either thegas properties or the basic differential equation. Other studies have beenrigorous in these respects but have presented a very limited set of calculatedresults. The present study was attempted to present a rigorous theoreticalmodel and sufficient numerical results to permit meaningful conclusions to bedrawn. It was found that all terms must be retained in the partial differentialequation to make accurate predictions. The neglect of higher-order terms, e.g., terms of the order of the "gradient squared", leads to serious material balanceerrors at large times and to conservative estimates of gas well performance. The higher the gas flow rate and/or the lower the permeability-thicknessproduct of the formation, the more pronounced are these deviations. Forexample, in a well draining 640 acres in a 25-md-ft formation (8,120 MMcf gasin place) at a constant rate of 993 Mcf/D, the rigorous solution predicts abottom-hole pressure decline from 4,000 to 1,000 psia in 8.7 years. Ifhigher-order terms are neglected in the differential equation, this decline inpressure is predicted to occur in 5.3 years. With the results of the numerical solution of the differential equationas a basis, simple, easy-to-use approximations for predicting gas wellperformance for Darcy flow conditions have been developed. These simpleapproximations are based on the familiar equations for flow of a single, slightly compressible fluid. The approximate methods possess a high degree ofaccuracy and enable the prediction of long-term gas well performance to be madequickly and accurately without the use of a digital computer. Both transientand stable flow period approximations were developed. Introduction In recent years income from the sale of natural gas and associated productshas represented an ever-increasing fraction of the industry's total revenuefrom operations. To meet the surge in demand for natural gas, the industry hasdepended heavily upon established reserves and has actively pursued developmentof new reserves. This search has progressively led to reservoirs whichyesterday were too tight and/or deep to yield the desired return on investedcapital. More than ever before, evaluation accuracy is now required to forecastthe criteria upon which engineering recommendations and management decisionsare based. Considerable effort has been expended by both research and operationspersonnel on the development and application of methods for analyzing andpredicting the performance of gas wells. Fundamentally, the problem is thefamiliar one of extracting data during the drilling, testing and earlyproduction life of a well and applying these data within an accurate simulationmodel to predict long-term behavior. During the past 30 or more years avoluminous literature dealing specifically with gas field problems has beengenerated. A recent book1 lists a comprehensive bibliography of publishedmaterial through 1959. Over 1,200 references are cited. Since then 39additional articles on natural gas technology have been published inTransactions volumes of the Society of Petroleum Engineers of AIME. Most existing theory for predicting gas well performance requires that oneor more idealizations (e.g., steady-state flow, ideal gas of constantviscosity, small and constant compressibility and constant-viscosity fluid) beapplied. Although existing theory may apply directly or be adapted by variousartifices to describe specific gas well and reservoir behavior, no widelyapplicable method is available, and existing methods appear to be subject toappreciable error unless better limits of applicability are defined.