On the 30th anniversary of PSIG it seems appropriate to review the status of Dynamic Programming after 30 years of use in the pipeline industry. Dynamic programming (DP) has been one of the workhorse techniques of pipeline optimization since the late 1960s. Originally applied to gunbarrel systems, it gained popularity due to it's fast computational speed on such sequential systems and it's insensitivity to simulation nonlinearities, noise, and modeling discontinuities. In the late 1980s hybrid DP/Enumeration/Annealing methods were produced which could optimize more general branched and looped networks. Although these were very successful at optimizing pipelines - sometimes by a large percentage - the hybrid nature of the methods sometimes cause long runtimes or reduced accuracy in solving the discretized problem. Recent advances have allowed us to perform pure DP directly to general branched and looped systems. Not only is full solution accuracy thereby assured, but the pure DP method have been up to 10 times faster than hybrid methods in our tests on complex networks. This allows rapid turn around of optimization runs during design and feasibility studies. We illustrate these results with real-world examples. We cap off our historical perspective by comparing DP solutions to those generated by another class of methods that have gained support in recent years: Genetic Algorithms.

1 Introduction

In the United States, natural gas consumption is over 60,000 MMCFD, much of it being transported from well head to market over cross-country pipelines. Worldwide consumption is approximately three times this amount. As an accepted rule of thumb, three to five percent of this gas is burned to power the transportation of the remaining amount. At current prices, this is the equivalent of roughly 2 billion dollars per year _ of wasted gas in the US. Moreover, compressor fuel gas is only one of the costs of operating a transmission pipeline. In these days of increased competition and uncertainty, control of these cost factors and lost profits become even more essential than they have been in the past.

1.1 Optimization on gunbarrel systems.

Let us consider a simple, straight line transmission pipeline, often referred to as a gunbarrel pipeline. What quantities can we optimize? What variables do we manipulate to achieve this optimum? Consider a steady-state model of a gunbarrel gas transmission pipeline with n compressor stations and a specified flow, as shown in Figure (1). Hydraulically, this model allows a different pressure to be set at N points to totally specify the state of the system. Two off these points are at the ends of the system, and the remaining points are between the compressors. For gunbarrel pipehnes, N = n + 1. We will refer to these N pressure set points as decision variables. Although simplified in our diagram, the physical system of pipes between the compressor stations can be quite complicated with parallel loops and extensive side branches, without affecting the results of this paper.

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