Production Decline Analysis using Influence Functions

Abstract

We previously reported (Zais, 1979) that Arps's exponential equation works quite well on geothermal production data. The hyperbolic equation should probably not be used. In this paper we show the progress made in using influence functions to describe reservoir production behavior.

Influence functions arise in many areas of science and engineering under the names of Green's function, memory function, response function, and resistance function. They are used to relate the response of a system to an input. In a geothermal reservoir we can find an influence function relating reservoir pressure to production rate.Once this function is calculated, it can be used to predict the behavior of the reservoir. van Everdingen and Hurst(1949)developed an influence function method for aquifer drive petroleum reservoirs using Laplace transforms. Hutchinson and Sikora(1959) and Jargon and van Poolen (1965) developed algebraic water drive analysis methods for reservoir s and individual wells, respectively.