The objective of optimal gas pipeline design is to determine the optimal number of compressor stations and their locations; to select the model, number and configuration of compressor units in each station; and to select the optimal pipe diameter and MAOP (maximum allowable operating pressure). For capacity expansions, only pipe loopings, new compressor stations, and/or possible additional compressors need to optimized. Nonlinear objective function and nonlinear constraints make pipeline design optimization complicated. A number of different methods have been proposed and tried with limited success. The method proposed is a modification to Bellman's Dynamic Programming. Each stage of the optimization procedure is based on a potential location for a compressor station. However, the distance covered is variable and can be fixed only if the compressor station location considered establishes an optimal trajectory.
McClure(Ref. 1) has observed that can cost over a million dollars."Thus, a reduction in cost of only a few percent due to a system design optimization effort is generally more than sufficient to compensate for the cost of the effort. Each root may be a supply source. The terminals are gas consumers. The system has to be capable of supplying a specified maximum amount of gas to each consumer. However, the operating cost is a function of the composite load profile for consumers located downstream. pipeline. Each station contains one or more centrifugal or reciprocating compressor units, and auxiliary equipment to generate electricity, cool discharge gas, control the station, etc. It is possible to configure two or more compressors at a station in parallel or in series. Use of larger compression ratios is prohibited because gas temperature increases with larger ratios which eventually exceed the pipe coating thermal limitations. In order to reduce the temperature, air or water cooling systems can be used or a lower compression ratio can be specified. Pipes of different diameters and wall thicknesses and materials can be used depending upon the flow rate, anticipated pressure and temperature distributions within the system, and the proximity of populated areas. However, diameter changes must be compatible with pigging plans. It is not uncommon to have two or more pipes in parallel. In most cases, parallel pipes are used only when the capacity of the pipeline was or is to be increased after installation by looping to reduce hydraulic resistance.
Let us call the portion of the pipeline between two nodes a "section". Each section may be divided into many auxiliary stages. It is possible that one section has no compressor stations while another has many. First, tree networks with only m e root, the gas supply node, will be analyzed. Of course, real gas pipelines usually do have many sources and many consumers, so they must be considered as multiroot directed trees. For convenience, some terminology from data structures is used(Ref. 4). The pipeline system in Fig.1 has 13 sections (arcs) and 14 nodes where node 14 is the ROOT NODE.