Decline Curve Analysis using Combined Linear and Nonlinear Regression

Abstract

Abstract The varieties of methods for predicting oil well performance are material balance analysis, decline curve analysis and numerical reservoir simulation. Among the techniques, the decline curves have been found quite simple and accurate to forecast oil well performance in the absence of known reservoir parameters. The basic concept of the Arps' hyperbolic decline curve analysis is nonlinear curve fitting. However, the difficulty of finding a proper nonlinear algorithm to tune the Arps' hyperbolic decline equation to match historical oil production has forced analysts to use the exponential and harmonic declines, which are adjudged the approximate limiting cases of the Arps' hyperbolic decline. So, this study advocates a shift in paradigm; that is the use of nonlinear regression algorithm to tune the Arps hyperbolic decline equation initialized from linear curve fitting. The hyperbolic equation was expressed as a linear relationship in terms of the first derivative of production rate with respect to time. The first derivative was obtained from natural spline interpolation which greatly improved the quality of the initialized decline parameters and the accuracy of the decline curve analysis.