Abstract:

The purpose of this paper is to describe the equations which govern the flow of compressible fluids through pipes. Particular emphasis is placed on those used within the natural gas industry in hopes that engineers within that industry can make knowledgeable decisions on how to model pipes. Its thesis is that all practical equations were created to solve intense numerical problems and have been made obsolete by advancing computing technology. It further discusses a new flow formula proposed by the GERG Research project 1.19 A Note Concerning Units: These equations have generally been published in the English system of units. Where appropriate, the alternate equations in metric units have been included, with the names of the metric units being shown in italic type. Since the Pole, Spitzglass, and Weymouth equations are included only for historical interest, only their original published form is presented Biographical Sketch: Don Schroeder, whose present title is Director, Technical Affairs, has been employed by Stoner Associates, Inc. of Carlisle Pennsylvania in various capacities over the past 23 years. During this time he has served as principal author of SAI's gas steady-state and transient offerings as well as being heavily involved in their optimization efforts. Prior to joining Stoner Associates, he worked for the former Columbia Gas System for 12 years: 5 in various engineering capacities within their Pittsburgh Group Companies, and 7 in their Service Corporation's Operations Research Department. Don's academic background includes a Bachelor of Science in Chemical Engineering degree from Carnegie Institute of Technology in its "pre-Melon" days. Don served as secretary of PSIG (Pipeline Simulation Interest Group) from 1971 to 1973, chairman from 1973 to 1975, and has been the immediate past-chairman ever since (this is the longest he ever held a job). He also has served as PSIG treasurer since 1989.

I. The Fundamental Equation

During the almost two centuries that the natural gas industry has been in existence there has always been a need for workable equations to relate the flow of gas through a pipe to the properties of both the pipe and the gas and to the operating conditions such as pressure and temperature. The usefulness of such equations is obvious: systems must be designed and operated with full knowledge of what pressures will result from required flow rates. The purpose of this paper is to describe the ways that this has been accomplished and to provide some practical insight into what the current practice should be. Since nearly every text on fluid mechanics, and they are legion, contains some derivatioof the fundamental equation governing one dimensional, compressible fluid flow, it is not necessary to repeat that derivation here. Excellent derivations are presented in both the Hyman, Stoner, Karnitz and the Finch, Ko papers referenced in the bibliography. Essentially one begins with the partial differential equations of motion along with the equation of state and then starts assuming and integrating.

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