Steady-State Analysis of Gas Production, Transmission and Distribution Systems
Authors: Stoner Michael A. 
Published: December 2007

Abstract
This paper presents a new method for obtaining a steady-state solution of an integrated gas system model made up of pipelines, compressors, control valves and storage fields. By use of this very flexible solution technique, it is possible to solve directly for system facility parameters when pressure and flow specifications have been given. The mathematical model of a system consists of node continuity equations which are solved by the n-dimensional Newton-Raphson method.
Introduction
Natural gas systems are becoming more and more complex as the use of this energy source increases. The burden of this complexity must be borne by the persons responsible for the design and operation of these systems. Mathematical modeling is one of the more important tools used to aid in design and operation studies. The systems under consideration actually operate in an unsteady nature, and although much effort has been and continues to be spent on unsteady mathematical models, many design problems can and will be solved by steady-state modeling. It is, therefore, desirable to extend the steady-state modeling capabilities to accommodate these complex systems in their entirety. This paper presents a steady-state model and one solution technique for this model which has two important features. First, the method can be used to simulate an integrated system composed of all the elements found in a gas system [i.e., pipelines, compressors, control valves, production fields and peak shaving elements such as storage fields and peak shaving elements such as storage fields and LNG plants]. This systems' analysis approach to modeling gas systems allows the designer to perform a much more comprehensive study than perform a much more comprehensive study than with previous methods. With this model the designer can measure the interaction of any system component all in the same simulation program. Second, to the author's knowledge, program. Second, to the author's knowledge, published network analysis methods have been published network analysis methods have been restricted to determining system pressures and flows. By treating the equations which represent the model in a very general way, it is possible to include system element parameters possible to include system element parameters other than pressure and flow as unknowns. Parameters of the model such as pipe diameter, Parameters of the model such as pipe diameter, compression horsepower, valve settings and number of storage field wells can be determined when appropriate pressure and flow specifications are made. This feature is of great importance to the system designer, since system parameters can be obtained directly instead of parameters can be obtained directly instead of determining them by trial-and-error procedures.
The model proposed in this paper is constructed by writing the continuity equation at each node in the system. The flow equation for each element connected to the node is then substituted to eliminate the element flow. This results in a set of nonlinear simultaneous equations which constitute the system model.