Operating conditions to accomplish the movement of a specified volume of natural gas from a set of supply locations to required delivery locations are among the most critical aspects of the business activities of Williams Natural Gas Company (WNG). We have developed an Optimum Operating Pressure Settings (OOPS) model that minimizes the total cost of transmission of natural gas in a network. The work being presented here is to describe an algorithm or model that has been developed to select compressor stations that should be running and the operating pressures to be used to minimize total cost of fuel to move a given steady state volume of gas. The problem solved by this system is a non-linear unitized programming problem. Pressure loss in a natural gas pipeline is non-linear and the unitized variables determine whether a station has compressors running or it gets bypassed. The procedure is to alternately calculate pressures from flow volumes and optimize a pressure network distribution problem and use the solutions of each as input to the other. Optimum is converged upon to within some preset tolerance of pressure changes between two successive pressure distribution problem solves. The program is coded in FORTRAN and runs on a DEC VAX computer system.


OOPS is a non-linear unitized programming approach to the minimization of fuel in a natural gas flow problem. The program described in this document determines the optimum operating pressure settings for the achievement of desired steady state flow rates in a pipeline network. The presentation is intended to convey a concept for solving gas flow problems in a network and there is no intent to dwell on specifics.


The approach to gas flow optimization described in this paper is to alternately solve a volume flow problem and a pressure distribution problem. The solution to each problem is used for regeneration of the other. The process continues until the problems generated do not vary more than some acceptable amount. The solution obtained is not necessarily the global optimum solution. The volume flow portion of the problem is solved using the fundamental equation of flow in a pipe, a horsepower equation and the equations of flow through the cylinders. The solution of the volume flow problem is used to generate a pressure network distribution problem that is then solved with a minimal cost network flow solver that also solves for unitization variables and handles extra linear programming constraints. The network problem solution is then used to create a new volume flow calculation problem. The network solution is least cost for the total pressure produced at all stations for the volume flow problem last generated. Regeneration of the problems is required because the flow rate is a non-linear function of the pressures. The unitization variables are required because they determine whether or not a station is bypassed and for staying in the proper utilization range for those that are operating.

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