Transient Flow in Gas Transmission Lines

Abstract

Introduction The transient flow of gases in long pipe lines is a problem of industrialinterest. The present discussion deals with the application of the conservationof momentum and material to the transient flow of gas in conduits which arelong with respect to their diameter. Solutions of the resulting equationsinclude consideration of variations in friction and specific volume of thefluid as functions of time and position along the conduit. The changes in statealong the pipe line are established as a function of time. The methods proposedmay be extended to other situations. The flow of compressible fluids under steady conditions has been consideredin detail. Primary emphasis was placed on the development of simple means oftaking into account the non-uniform flow realized in long conduits under suchconditions. Binder discussed the essential differences between the flow ofcompressible and noncompressible fluids. Bonilla proposed direct methods ofsolution for equations describing isothermal flow in long pipes. Similarconsiderations limited to steady flow have been discussed by Ruth. Palsgrovesuggested a graphical means of solving specific problems relating to the flowof gases in conduits of uniform section. Some of the basic concepts of the flowof a compressible viscous fluid in straight tubes have been described by Kuo.Problems of this type require knowledge of the equation of state of the fluid.In many cases it has been convenient to assume that the fluid follows therelationship ascribed to a perfect gas. The treatment of unsteady flow of compressible fluids is less complete. Thisstate of affairs results from the fact that the differential equations relatingpressure and flow rate with time and position for unsteady flow are nonlinearin character. Muskat and Wyckoff presented an excellent treatment of thesituation in laminar flow where inertia forces were not of controllingimportance. Somewhat earlier Hurst discussed the unsteady flow of fluids inpetroleum reservoirs. Hetherington, MacRoberts, and Huntington establishedexperimentally the pressure distribution and accumulative flow rate of naturalgas through an unconsolidated sand. Recently Joffe considered the specificproblem of the flow of natural gas in relatively long pipe lines for unsteadyconditions with emphasis upon the economic feasibility of the storage of gas insuch a reservoir. These discussions were based upon approximations of thepartial differential equations applying to the conditions of flow. The resultswere descriptive of the physical situation and indicated the effectiveness oflarge pipe lines as cyclic storage facilities for natural gas. T.P. 3081