The purpose of this paper is to give engineers responsible for making forecasts and determining reserves for numerous operated or nonoperated wells some guidelines and fundamental concepts to allow them to make these forecasts and determinations more quickly and accurately.
Decline-curve analysis, based on the Arps equations, has always been considered to be purely empirical with no basis on physical laws governing the flow of oil and gas through the formation. The works of Fetkovich and others have attempted to place decline-curve analysis on a sound, fundamental basis using the constant wellbore pressure analytical solution and simple combinations of material-balance equations and pseudosteady-state rate equations to derive rate/time decline equations for oil and gas wells. (See additional references listed in Ref. 14.) The derivations illustrate under what circumstances specific values of the hyperbolic decline exponent, b, should result. It is from these derivations that the variables in Arps equations can be expressed in terms of reservoir variables and reservoir engineering concepts. Decline-curve analysis, or more specifically rate/time analysis, is not simply an art based on applying a purely empirical equation to be analyzed with statistical approaches. Reliance on a statistical analysis, void of reservoir engineering concepts, often leads to unrealistic and unreliable forecasts and reserve estimates.
Arps Equations. Conventional decline-curve analysis is based on the empirical equations of Arps. In his work, Arps proposed a set of equations described by an exponent, b, having a range between 0 and 1. The resulting rate time and cumulative production equations are shown in Table 1 (see also Ref. 14).