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• W1965497457 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.Elevation changes in the pipeline are negligible.Flow is isothermal and single-phase.Gas composition remains constant throughout each transient flow investigation.Friction factor is constant for a given pipe diameter.All variations in boundary conditions take place at inlet and outlet.Pipeline is of constant cross-sectional area. The first three assumptions are essential for the equation development in this investigation. While the remaining assumptions could be neglected without debasing the integrity of the development, they are accepted here in order to simplify the numerical solution. BASIC DEVELOPMENT Attractive forces existing between gas molecules cause the actual volume of a gas to deviate from those volumes predicted by the ideal gas law. To account for these variations in volume, the gas compressibility factor is applied as a correction term to the ideal gas equation of state. Thus, for methane and natural gas, (1) p V = z n R T (All variables, except for terms requiring specific units, are defined in the Nomenclature.)Since the value of the compressibility factor is essential in gas metering, charts and tables have been devised to aid in its determination; but this procedure usually requires a lengthy calculation involving gas composition, pressure and temperature. SPEJ P. 315ˆ" @default.
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• W1965497457 date "1972-08-01" @default.
• W1965497457 modified "2023-09-27" @default.
• W1965497457 title "Compressibility Effects on Transient Gas Pipe Flow" @default.
• W1965497457 doi "https://doi.org/10.2118/3648-pa" @default.
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