An analytical model for production data analysis of under saturated oil reservoirs subjected to edge aquifer

Abstract

Analysis of production data is an important method for estimating recoverable reserves and probable life of the reservoirs. Robust techniques for analysis of production data have been developed and widely used for many years. These methods range from the traditional Arps decline method to modern production data analysis. The most recent techniques are based on material balance time to account for variable operating conditions. In these methods, production rate and flowing bottom hole pressure must be known. A major limitation of many existing modern techniques is volumetric assumption of the reservoir. This paper presents a new model that accounts for non-volumetric effects of edge aquifers on production data analysis of single phase oil reservoirs by defining a new material balance time function. This new time function and material balance time help us to introduce flowing material balance (FMB) equations for such reservoirs. Validity of these equations is justified using analytical solutions. For development of analytical solutions, special simplifying assumptions are considered. To justify these assumptions, comparison is made using a commercial numerical reservoir simulator across some ranges of reservoir parameters. Furthermore, based on the validated FMB equations and obtained analytical flow equations, specific procedures are developed for parameter estimation of such reservoirs. The use of these procedures in estimation of oil in place and reservoir external radius is demonstrated using synthetic examples. On the basis of the considered assumptions, the proposed procedures cannot be applied to multi-phase flow conditions, reservoirs with other types of aquifer (such as bottom aquifer), and gas reservoirs. We also show that the given FMB equations are applicable for any irregularly shaped reservoir which is partially contacted with a non-cylindrical limited edge aquifer. For such reservoir geometries, numerical solution is used for justification. This is followed by introducing a simple equation for predicting average reservoir pressure.