This study deals with projecting production decline curves. It examines a generalized relationship of cumulative production versus time presented in the literature by Gentry. production versus time presented in the literature by Gentry. A production rate versus time relationship is derived from this general equation. Four methods of determining the constants appearing in both equations is presented. The equations are used to model solution-gas drive production (simulated and actual field case studies). The goal is to determine the utility of using the equations to evaluate solution-gas drive reservoirs.
Several methods have been presented in the literature for mathematically predicting, by extrapolation, the future production rates of a producing property. The extrapolation of the production rate versus time curve (to predict future production rates) is commonly termed decline curve analysis due to the declining nature of primary production.
One of the most important contributions to decline curve analysis was a paper published by Arps in 1945. Arps presented both a production rate - time relationship and a production rate- cumulative production relationship. These empirical relationships are presented in the first four columns of Table 1. The ranges of the decline exponent, 1/h, can be seen for the three classes of declines (exponential, hyperbolic, and harmonic). The equations are all solutions of thin differential equation
where q is the production rate, t is the time, a is the decline parameter, 1/h is the decline exponent, and K is a constants parameter, 1/h is the decline exponent, and K is a constantsGentry presented a simplified method for the solution and extrapolation of hyperbolic production decline equations. The method involves the determination of dimensionless production parameters qi/qt and Np/qi t. The hyperbolic: equations were manipulated to solve for unknowns in terms of the dimensionless production parameters. The equations are presented in columns five and six of Table 1. Figs: 1 and 2 were developed to allow for quick graphical evaluation of the hyperbolic decline exponent, 1/h, and the initial decline rate, qi.
Various reservoir parameters have been studied to determine those which may effect the decline exponent 1/h in the hyperbolic equations. Gentry attributes changes in the decline exponent to changes in production policy, reservoir heterogeneity and other factors. Fetkovich et al. concluded in a study of cases histories that "the misuse of the Arps equation with transient data generally results in overly optimistic forecasts and is technically incorrect." The transient flow period may last as long as three years in certain formations and, in Fetkovich's opinion, must be disregarded if an accurate evaluation is to be generated.