Optimal Route for Pipelines in Two-Phase Flow
Authors: Shamir Uri 
Published: December 2007

Abstract
A technique is described, which makes it possible to select the optimal route for a pipeline designed to carry oil and gas in two-phase flow. The pipeline is assumed to operate under the pressure differential naturally available between the source and the point of delivery. point of delivery. A discrete grid is established to describe the corridor through which the pipeline is to pass. Topograpbic and terrain data are given for all grid points. Cost data is given for all factors which points. Cost data is given for all factors which affect the capital cost of the pipeline. The equation for the two-phase flow becomes a global constraint, to be satisfied by the selected route. Dynamic programming is then used to solve the minimization programming is then used to solve the minimization problem. problem. A computer program is described, with which a sample problem was solved, and the results that were obtained are also presented.

Introduction
Great sums of money are spent annually on the construction of pipelines for the oil industry. Many of these pipelines are designed to carry gas and oil in simultaneous two-phase flow from wells to various collecting and processing facilities. The procedures for selecting the route for such pipelines procedures for selecting the route for such pipelines have followed the traditional approach of engineering judgment and selection of the cheapest among a few alternative routes laid out by hand on maps and aerial photos. Aerial photo interpretation, to yield soil types, tree cover, existence of swamps and muskeg, and other factors affecting costs, is being used in route selection. Geologists and soil engineers are brought in to evaluate soil conditions on the basis of aerial photos, as well as by examination of the route itself and soil samples. This data is then used to select a route and to design the pipeline. The present project was undertaken with the objective of improving the engineering practice. We sought to proceed beyond the stage of mere trial and error and to develop a rigorous method for determining the optimal route by using the techniques of systems engineering. The over-all problem of conveying fluids in one-and two-phase flow pipelines was reviewed. It ranges from a single pipe carrying a single-phase fluid, through two-phase flow lines, to gathering systems containing networks of pipes and other equipment, such as valves and compressors, to collect the products of a large number of wells and deliver the mixed product to processing plants. All these were considered part of the over-all project, which deals with optimal design of pipeline systems. Initially, one aspect of the over-all project had to be selected. It was decided to tackle the problem of optimizing the route for a single pipeline carrying two-phase flow. This problem presents some complications, and it was felt that if it could be solved, single-phase pipelines would present no added difficulties.

TWO-PHASE FLOW PIPELINES
It is common practice in the oil industry to use a single pipe to carry both oil and gas from producing wells to collecting facilities and plants. The alternative is to separate the two phases at the source and carry them in separate pipelines. Economics of the two alternatives should be the basis for a choice between them. The present work is therefore a useful tool for making a better choice possible by yielding the optimal solution for the possible by yielding the optimal solution for the two-phase line alternative. As will be shown later, the method, as well as the computer programs, can also be used to determine the optimal route for a pipeline carrying flow of a single fluid. pipeline carrying flow of a single fluid.

COMPUTING SIMULTANEOUS FLOW OF LIQUID AND GAS IN A PIPELINE
The regime of flow in a pipeline carrying both liquid and gas depends on many parameters. The regime, in turn, determines the pressure losses along the pipeline. The procedures for computing the two-phase flow are both elaborate and rather inaccurate. No attempt is made in the present work to change or to improve the existing methods, as this is beyond its scope. We do need, however, to modify the sequence of the computations to suit the requirements of the optimization problem.
SPEJ
P. 215