Optimization of the Design and Operation of Natural Gas Pipeline Systems
Authors: Martch Henry B. , McCall Norman J. 
Published: December 2007

This paper was prepared for presentation at the 47th Annual Fall Meeting of the Society of Petroleum Engineers held in San Antonio, Tex., Oct. 8–11, 1972. Permission to copy is restricted to an abstract of not more than 300 words. Illustrations may not be copied. The abstract should contain conspicuous acknowledgment of where and by who the paper is presented. Publication elsewhere after publication in the JOURNAL paper is presented. Publication elsewhere after publication in the JOURNAL OF PETROLEUM TECHNOLOGY or the SOCIETY OF PETROLEUM ENGINEERS JOURNAL is usually granted upon request to the Editor of the appropriate journal provided agreement to give proper credit is made. provided agreement to give proper credit is made. Discussion of this paper is invited. Three copies of any discussion should be sent to the Society of Petroleum Engineers office. Such discussion may be presented at the above meeting and, with the paper, may be considered for publication in one of the two SPE magazines.

Abstract
A natural gas pipeline system is herein defined as an arrangement of pipeline and compressor stations connected in some arbitrary manner so as to permit the steady-state flow of gas from one or more points of supply to on or more points of delivery. A network is code in nodal notation to provide the description of the existing facilities (pipelines and compressors). The network thus defined must be of the form of a tree, i.e., the flow rate through each facility is known. Pipelines operating in parallel with each other, having common endpoint pressures are permitted.
At each source of supply, the available flow rate and a maximum available pressure are known. At each point of delivery, except the terminal, the flow rate and the minimum delivery pressure are known. The pressure at the pressure are known. The pressure at the terminal is constant, and the flow rate at the terminal is calculated from material balance and fuel considerations.
The objective of optimization is to minimize the annual cost of owning and operating the facilities required to transport gas through the system. If the existing facilities are adequate, the sum of the annual costs to operate the existing facilities is minimized, i.e., previous sunk, fixed costs are constant and ignored. If the existing facilities are inadequate, new facilities are added to the system in such a manner that the sum of the annual costs of owning and operating the new facilities plus the operating cost of the existing facilities is minimal. A form of dynamic programming is used as the optimizer.

Introduction
The design of natural gas pipelines systems requires that a set of pipeline facilities be selected that will permit the flow of gas from points of supply to points of demand. In points of supply to points of demand. In general, there are many solutions (sets of facilities), each of which will satisfy or solve the design problem of interest. The engineer, having defined the design problem, usually employs the following procedure in his effort to develop a solution:
assume a set of independent variables and assign these values, solve the appropriate set of equations for values of the dependent variables, determine if the resultant solution is feasible, i.e., all restraints are satisfied, and perhaps estimate the cost of All required facilities, either accept the solution or revalue one or more of the independent variables and repeat Steps 2 through 4.
Computer programs have been written that mechanize the computational and data processing aspects of the problem.