Optimum Location of Trunklines in Oil and Gas Fields
Authors: Coats Keith H. 
Published: December 2007

COATS, KEITH H., JERSEY PRODUCTION RESEARCH CO., TULSA, OKLA. JUNIOR MEMBER AIME

Introduction
In many oil and gas fields, significant investments are required in piping networks for collection, injection and disposal of various fluids. A single field may concurrently require piping systems for gathering of oil, gathering of gas, injection of water or gas and disposal of salt water. Two problems arise in the consideration of any one of these networks. The first involves the sizing of the various segments of the network to minimize piping and compression costs. The second problem, treated herein, is that of optimally locating the trunkline(s) for a given piping system to minimize the total length of pipe connecting the individual wells or lease batteries to the trunkline. This minimization problem may arise in field automation if it involves replacement of individual lease batteries by a central field battery which will require trunklines and connecting pipelines to individual wells. The problem also aims in connecting a gas pipeline through a subsidiary trunkline to wells in a gas storage field.The first analysis given below treats the case of a single trunkline and of separate connecting lines for all field units.* The analysis is then extended to consider multiple trunklines and common connecting lines for groups of field units. Varying sizes, and therefore costs, of the connecting lines are taken into account. A simplified development is given to illustrate the manner in which line sizing calculations may be integrated with the line placement problem. This study is primarily directed toward the placement of straight trunklines, although for certain field shapes or well distributions curved trunklines might be preferable. Some mathematical consideration is therefore given to the placement of a curved trunkline in a field.The determination of optimal locations for two or more trunklines involves some difficulties which are discussed below. The need for further research in this area is emphasized.
The problem of a single trunkline is solved in relation to an actual oil field. The problem of optimally locating two trunklines in the same field is also treated and the results are compared to the single-trunkline case. All calculations reported were performed on an IBM 7072 digital computer.The importance of right-of-way, roads and terrain in locating trunklines and connecting lines is realized. The present analysis is advanced on the premise that in planning piping networks one should start with the optimal conditions whenever possible and proceed therefrom.

PHYSICAL AND MATHEMATICAL CONSIDERATIONS
If an x-y coordinate system is imposed over a plan view of an oil or gas field, each field unit will be represented by a point (x, y). A single trunkline can be represented by a straight line of slope in and intercept b, given as
(1)
The method of least squares determines m and b so the sum of the squares of the vertical or horizontal distances between the field units and trunkline is a minimum. Application of this method yields
(2)
If this function of m and b is to be a minimum, then the partial derivatives with respect to m and b must both equal zero.
JPT
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