A Unique Approach to Oil-Production Decline Curve Analysis with Applications
Authors: Locke C.D. , Schrider L.A. , Romeo M.K. 
Published: December 2007

American Institute of Mining, Metallurgical, and Petroleum Engineers, Inc.
This paper was prepared for the 43rd Annual Fall Meeting of the Society of Petroleum Engineers of AIME, to be held in Houston, Tex., Sept. 29-Oct. 2, 1968. 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 paper is presented. Publication elsewhere after publication in the JOURNAL OF PETROLEUM TECHNOLOGY or the SOCIETY OF PETROLEUM ENGINEERS JOURNAL is usually granted upon request to the Editor of the appropriate journal provided agreement to give proper credit is made. 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 discussion may be presented at the above meeting and, with the paper, may be considered for publication in one of the two SPE magazines.

Abstract
A unique method of decline-curve analysis has been developed which greatly facilitates the estimation of future performance of an individual well or field while maintaining a high degree of mathematical accuracy. A computer program has been written which allows the user to obtain the best approximation to hyperbolic or exponential decline curves with a minimum amount of effort. A unique part of the hyperbolic curve fit is that initial approximations to unknown constants are not necessary—the constants are generated internally. Thus, the program allows the user greater freedom of operation, a high degree of mathematical accuracy, and the ability to update information with a minimum of effort. Field data studies are included to show the accuracy and versatility of the method. The technique is shown to be superior to two other methods investigated.

Introduction
one of the oldest and most useful methods for evaluating reservoirs is decline-curve analysis. Cutler treated the subject extensively in 1924. In his paper, Cutler discussed the use of semilog and log-log graph paper for straightening and extrapolating production decline plots. Arps has shown that equations for the semilog and log-log plots could be derived from the same basic differential equation. The Arps equations for production rate as a function of the time are:
-t/a(semi-log) q=q e ............…[1]0 -1/b and (log-log) q = q [1 +(b/a)t] [2]0 0
where q = production rate, t = time, qa = - ,dq/dt
qddq/dtb = - ,dt
and a0 and q0 are the values of a and q when t = 0.
The constant a in Eq. 1 is called the loss ratio. The constant b in Eq. 2 is the first derivative of the loss ratio. Eqs. 1 and 2 are, respectively, the familiar exponential and hyperbolic equations that have become industry standards for extrapolating production decline.
While the hyperbolic equation is generally accepted as more representative of the production characteristics of most reservoirs, use of the exponential equation is probably more common.