Merits of Decline Equations Based on Production History of 90 Reservoirs
Authors: Higgins R.V. , Lechtenberg H.J. 
Published: December 2007

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
Four different equations were tested to determine which would generate a curve that would best fit the production decline curves of 90 California fields. Two conventional equations [the Arps and semilog] and two novel equations [extreme C and double semilog] were tested. The curves were fitted to the first 9 years of production data and then extrapolated for the next 6 years of data. The generated curves were also extended beyond available data to give the rate of production and time necessary until the total cumulative production would equal estimated reserves. The semilog equation resulted in the best fit to production data for the first 9 years, but the Arps and extreme C produced a better fit for the extrapolated data for the period of 9 to 15 years. The Arps and extreme C also gave more realistic production rates when extended until cumulative production rates when extended until cumulative production equaled reserves. production equaled reserves. Extrapolation of empirical performances of fields or wells to forecast their future performances has probably been used since a performances has probably been used since a production decline was first observed. Even production decline was first observed. Even with all the modern fluid mechanics and electronic computers to process data, often their use is restricted by the expense of computation or the absence of knowledge of the physical properties of the reservoirs. As a result, the properties of the reservoirs. As a result, the future performances of wells and fields often are forecasted by extrapolation, using the past performance as a guide. Equations have been performance as a guide. Equations have been proposed and investigated to accomplish this proposed and investigated to accomplish this extrapolation. The merits of these equations have been difficult to evaluate, except on a few fields. Many fields are needed to eliminate the possibility of overgeneralizing from few data.
From a previous study, the authors have on magnetic tape the production history of more than 400 California fields or zones. It was logical to use these data to investigate the merits of equations for forecasting the performances of fields. Ninety of the more than performances of fields. Ninety of the more than 400 fields on the magnetic tape had a 15-year production history. During this 15-year period, production history. During this 15-year period, the wells were flowing at their maximum efficient rate. Therefore the fluid mechanics relating to their performances was virtually under the control of nature, which made the fields suitable candidates for decline investigations. In this study, the electronic computer was used to make the calculations.
The volume of oil reserves in the reservoir also aids in the decline performance studies. The reserves can be compared with those obtained by extrapolation, and the differences are a measure of the merits of the equations to forecast the future performances of fields. ate reserves for the 90 California fields had been published and were used in the study. published and were used in the study. Equations investigated were the hyperbolic Arps, extreme C, double semilog and semilog.