A Method to Determine Optimum Well Spacing
Authors: Tokunaga H. , Hise B.R. 
Published: December 2007

This paper was prepared for the California Regional Meeting of the Society of Petroleum Engineers of AIME, to be held in Santa Barbara, Calif., Nov. 17–18, 1966. Permission to copy is restricted to an abstract of not more than 300 words. Illustrations may not be copied. The abstract should contain conspicuous acknowledgment of where and by whom the paper is presented. Publication elsewhere after publication in the JOURNAL OF PETROLEUM TECHNOLOGY or the SOCIETY OF PETROLEUM ENGINEERS JOURNAL is usually granted upon requested to the Editor of the appropriate journal, provided agreement to give proper credit is made.
Discussion of this paper is invited. Three copies of any discussion should be sent to the Society of Petroleum Engineers Office. Such discussions may be presented at the above meeting and, with the paper, may be considered for publication in one of the two SPE magazines.

Abstract
The selection of the well spacing for the development of an oil accumulation requires both a reservoir and an economic analysis. This paper is concerned with the economic aspects of selecting the optimum well spacing for an oil field. Currently, the economics of the study are conducted by trial and error calculations. This paper introduces a new and more straight-forward method of determining the optimum.
A relationship for the present worth of an oil field is expressed as a function of the well spacing. The derivative of this function is used to find the point of maximum present worth, which is designated as the optimum spacing. The equations are solved graphically, and the technique is quick and easy to apply. Solution procedures are presented for single and multiple completion programs, and example problems are worked for each case.

Introduction
The well density for a field is selected after a study of the engineering, legal and economic considerations, which apply to the situation. The engineering aspects of well spacing have been the source of considerable control in the petroleum literature. The relations are very difficult to express quantitatively are not well known. The legal considerations are usually beyond the oil operator's control. Therefore, the determination of the well spacing for a field is primarily an economic evaluation of the alternatives available.
The type of economic analysis necessary is called an acceleration project. The present worth has been shown to be a good economic criterion for this type of problem. Currently, the optimum economic well spacing is determined by trial-and-error calculations, hereafter called the conventional calculation. In this method the present worth of the production from a reservoir is calculated for selected values of the well spacing, and the results are plotted as present worth vs well spacing. The spacing corresponding to the maximum present worth is found by inspection, and is called the optimum well spacing. A schematic of the conventional calculation procedure is shown in Fig. 1.
A new method to determine this optimum well spacing is the subject of this paper. The new method is developed by formulating a mathematical statement of the present worth as a function of well spacing. A unique mathematical solution to the problem is found for a field with a single oil reservoir and one with multiple oil zones. The method is illustrated by example problems for each situation. The validity of the new method is proved by checking with conventional calculations of the optimum well spacing.