Compressibility Effects on Transient Gas Pipe Flow

Abstract

Abstract Methods of iterative solution for the partial-differential equations governing the transient flow of gases in pipelines are obtained by using the method of characteristics and linear finite-difference techniques. Solutions are developed for (1) a constant gas compressibility factor throughout transient conditions, and (2) a variable gas compressibility factor at constant temperature, dependent upon pressures encountered during transient flow. Theoretical studies are made to compare results using both approaches for pipelines operating at various constant flowing temperatures. Results show greater differences between the two methods at lower values of flowing temperature due to the more rapidly changing compressibility factor as a function of variable pressure. Introduction The partial-differential momentum and mass equations describing transient gas pipe flow have been solved by various numerical methods. Among the techniques frequently employed in recent studies are implicit finite-differences and the method of characteristics. While these studies have been concerned with the numerical techniques and stability criteria required in transient flow solutions, few investigations have examined the effect of a variable gas compressibility factor on transient behavior. The purpose of this study is to develop and apply the numerical equations of transient gas pipe flow based on (1) a constant gas compressibility factor evaluated at the average of inlet and outlet pressures at initial time, and (2) a gas compressibility factor completely dependent upon the gas pressures encountered in the pipeline during steady- and unsteady-state flow. For both approaches, digital computer solutions of the partial-differential equations describing gas pipe flow are made possible by application of the characteristics transformation and linear finite-difference approximations. The theoretical results, based on both constant and variable gas compressibility, are compared graphically for various transient flow conditions with particular emphasis placed upon temperature effects. Numerous limiting assumptions are required in the development of any steady- or unsteady-state flow equations. In this study, the following assumptions are made.