Optimal Design of Gas Transmission Networks
Authors: Edgar T.F. , Himmelblau D.M. , Bickel T.C. 
Published: December 2007

This study presents a computer algorithm to optimize the design of a gas transmission network. The technique simultaneously determinesthe number of compressor stationsthe diameter and length of pipeline segments, andthe operating conditions of each compressor station so that the capital and operating costs are minimized, or profit is maximized.
The literature has not reported profit is maximized. The literature has not reported the solution of such an open-ended problem, although lesser problems have been solved to determine the operating conditions of the gas network for a given configuration. Two solution techniques were used. One was the generalized reduced gradient method, a nonlinear programming algorithm that could be used directly in instances where the capital costs of the compressors were a function of horsepower output but had zero initial fixed cost. The second method was applied to cases in which the capital costs are comprised of a nonzero initial fixed cost plus some function of horsepower output. Here it was necessary to use a branch-and-bound scheme with the nonlinear programming technique mentioned above. programming technique mentioned above

Introduction
The design or expansion of a gas pipeline transmission system involves a large capital expenditure as well as continuing operation and maintenance costs. Substantial savings have been reposed (Flanigan, Graham et al.) by improving the system design for a given delivery rate. Both the number and location of compressor stations and the operating parameters of each must be determined to obtain the minimum cost configuration. Such a problem involves both integer and continuous variables because the optimal number of compressor stations is unknown at the outset.
Recent developments in nonlinear programming (optimization) algorithms have made available new techniques for solving such a free configuration design problem for a gas transmission system. This paper describes the gas pipeline, its mathematical formulation (a mixed-integer programming problem), the derivation of various cost programming problem), the derivation of various cost functions and constraints, and two techniques for solving the minimum-cost design problem. Two example networks were solved. The first network had gas entry at one point, with delivery to two points. This problem was solved with and without points. This problem was solved with and without an initial fixed charge for the compressors. The second network was more general, consisting of a multiple entry, multiple delivery network. It was solved for the case of a zero fixed initial charge for the compressor. The procedure should aid in the planning and design of gas pipelines, acquisition of construction sites, and justification of system modification.

THE PIPELINE DESIGN PROBLEM
Suppose a gas pipeline is to be designed to transport a specified quantity of gas per time from the gas wellheads to the gas demand points. The initial states (pressure, temperature, and composition) of the gas at the wellheads and the fixed states of the gas at the demand points are both known The following design variables need to be determinednumber of compressor stations;lengths of pipeline segments between compressor stations, that is, station locations;diameters of the pipeline segments; andsuction and discharge pressure at each compressor station.
Most published investigations of the above problem have focused on design problems that fix problem have focused on design problems that fix some of the above variables (subproblems of the one posed above). One of the first investigations of optimal operating conditions for a straight (unbranched) natural gas pipeline with compressors in series was performed by Larson and Wong. Their solution technique was dynamic programming, and they found the optimal suction and discharge pressures of a fixed number of compressor stations. pressures of a fixed number of compressor stations. The length and diameter of the pipeline segments were considered fixed because dynamic programming was unable to accommodate a large number of decision variables, although it readily handled pressure and compression ratio constraints. pressure and compression ratio constraints. A comparison of their approach with the algorithm tested in this paper is discussed later.
SPEJ
P. 96