Dynamic programming (DP) has had a successful 40-year history in the field of optimizing pipeline operations so as to minimize fuel consumption. One of the drawbacks of DP is that it is usually based on a discrete representation of the possible states of each pump (or compressor) station. In reality, the station suction and discharge pressures and pump speeds might have any value from the least allowed operating pressure (LAOP) to the maximum allowed operating pressure (MAOP), they are not limited to a discrete mesh (e.g. 100 psi, 105 psi, 110 psi, etc.) This inaccuracy can lead to accumulated roundoff errors that become significant over the length of a pipeline, and can also cause the solver to be unnecessarily slow in order to achieve the desired accuracy. This article discusses a new approach to DP-based optimization that correctly represents the possible pressures as continua. There are two main advantages to this approach: the accuracy of the optimum can be enforced directly through adaptive mesh techniques that use a detailed description of the pressures where it is necessary, and the speed of the solver can be improved by using a less detailed description where the behavior of the system is linear. This paper discusses the theory behind the new method, compares this approach with the usual DP formulation, and talks about an installed application of this method to a crude-oil pipeline and a products pipeline.

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