Prediction of Water Influx of Edge-Water Drive Reservoirs Using Nonparametric Optimal Transformations

Abstract

Abstract The accurate estimation of water influx into a petroleum reservoir is very important in many reservoir engineering applications, such as material balance calculation, design of pressure maintenance programs, and advanced reservoir simulation studies. These applications have heavily relied on the classical work of van Everdingen and Hurst for finite and infinite edge-water drive reservoirs. However, for both types of water drive reservoirs, the calculation of water influx is not a straight forward task. Table lookup and interpolation between time entries are needed, and furthermore for finite aquifers, interpolation between tables may be also required. The paper presents nonparametric optimal transformations models for the prediction of dimensionless water-influx and dimensionless pressure drop for finite and infinite edge-water drive reservoirs using Graphical Alternating Conditional Expectation (GRACE). In order to achieve maximum efficiency, all the terms involved in the models are used in dimensionless form. GRACE transformations are totally data driven and do not assume any a priori functional form. The results of the various cases are in excellent agreement with the original tables of van Everdingen and Hurst.