document

SPE Member

Abstract

A new algorithm for hyperbolic decline curve fitting is presented. The new algorithm is self starting, and converges very rapidly. The algorithm minimizes the sum of squares of the deviations of the logarithm of the producing rate from the predicted value.

Introduction

The hyperbolic decline equation has been used for many years to predict future well performance from production records. Many different methods have been developed to determine the decline curve parameters. The techniques reported in the parameters. The techniques reported in the literature fall into two broad categories: those suited to manual use; and those suited to batch mode processing on mainframe computers. processing on mainframe computers. The introduction of the microcomputer to the petroleum industry gives the individual engineer petroleum industry gives the individual engineer computing power approaching that of the minicomputer. Along with the microcomputer has come a new way of using its power. In contrast to the typical mainframe batch mode processing by computer professionals, the microcomputer is used by the engineer professionals, the microcomputer is used by the engineer in an interactive mode. Interactive processing, in turn, has encouraged the user to try more "what if" scenarios to see how the computed results are affected.

In decline curve fitting, the engineer can see a graphical display of the historical production data, select a range of data points to fit with a decline curve, ignore data points that do not follow the trend, and fit a decline curve to the remaining points, all in a matter of seconds. This interactive method places a premium on the speed of the decline curve fitting algorithm.

The algorithm introduced in this paper is particularly well suited to implementation on the particularly well suited to implementation on the microcomputer. It requires no starting estimates of the parameters, as do some methods, and it converges very rapidly compared to general purpose least squares fitting techniques.

REVIEW OF EXISTING METHODS

A wide variety of approaches to the problem of decline curve fitting have been presented in the petroleum literature. These include graphical petroleum literature. These include graphical methods, approximate methods requiring little computation, least squares methods developed especially for the decline equation, and general nonlinear least squares methods.

Graphical Methods

Perhaps the first graphical method for hyperbolic decline curve analysis was described by Cutler. By introducing a time shift of the plot on log-log paper, the rate-time decline plot could be straightened. Trial and error was used to determine the necessary time-shift. The resulting straight line could be used to extrapolate production data. production data. Arps summarized the important developments in decline curve analysis through 1945. In addition, he presented a graphical slide rule method for extrapolating semilog plots of rate versus time. lie also developed special graph paper leaving a linear horizontal axis and vertical axes for rate versus time and rate versus cumulative production.

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