Simulating the Operation of ANatural Gas Distribution System With Linear Flow Models
Authors: Slater G.E. , Erdie J.C. , Raphael D.L. 
Published: March 2010

Abstract
The energy crisis has created a need for more efficient operation of every sector of the energy industry. Shortages of natural gas, federal regulations and increasing demand have imposed special hardships on natural gas distribution (NGD) companies. Management personnel and engineers are in search of economical and practical methods to simulate the operation of gas distribution 8YStem s to allow economic studies to be made of alternative operating policies.
This paper presents research conducted to refine a previous attempt at simulating NGD systems with linear flow models (LFM). A new method of constructing the transaction matric of an NGD system LFM is presented. The new method allows the calculation of storage field leakage volumes and compressor fuel requirements for steady-state operation.
Application of the model to an existing system is described. The validity of the model is verified through comparison of metered and predicted gas flows and pressures. A comparison of historic economic data with model-predicted data is presented to further substantiate model validity. A discussion of model uses is presented, including an example compressor fuel reduction problem. A general compressor fuel minimization procedure is proposed.

Introduction
THE BELATED RECOGNITION of an "energy crisis" throughout the world has focused attention on the energy production and transportation industry. Efficient operation of every sector of the energy industry has become a necessity as a consequence of impending raw material (i.e. oil and gas in particular) shortages and cost increases. NGD companies form one sector of the energy industry which is especially aware of increased difficulties brought about by the energy crisis. Natural gas is in short supply and increased wellhead prices are inevitable. Federal regulations in the United States do not permit gas distribution companies to pass along increased costs to customers without lengthy and costly court hearings before the Federal Power Commission. As a result of increased operating costs and restrictive governmental regulation, gas distribution company management personnel are in search of economical and practical techniques which will enable them to simulate the operation of gas delivery systems to permit the study of alternative operating policies.

Literature Review
Early work on gas flow simulation concentrated on the study of steady-state flow in single line segments(1,2,3,4,5,6). In the early fifties, the study of transient flow in single lines was initiated by Olds and Sage(7). Many others have since studied transient gas flow(8,9,10,11).
Stoner"" published one of the first papers on the steady-state analysis of integrated gas networks. The n-dimensional Newton-Raphson iterative procedure was used to solve the nonlinear equations which result from the problem formulation. A refinement of Stoner's work was published by Evrenos et al.(13). Transient analysis of complex pipeline systems has been studied recently by several authors(14,15,16,17) Rachford et al.(18) described a gas pipeline system transient flow model utilizing variational methods.
LFM's, as described by Rosenblatt(9), were first used to describe the American economy by Leontief(20). Extensions of this original work continue today.