Prediction of Bypassed Oil With Correlations in Side-Water Drive Reservoirs
Authors: Hernandez J.C. , Wojtanowicz A.K. 
Published: March 2010

Abstract
Efficient management of oil reserves involves an understanding of the mechanisms that control the bypassing of oil in water drive reservoirs. The existing analytical models of water front advancement in side-water reservoirs do not account for the combined effects of water underruning and coning. This paper gives correlations for the prediction of the amount of bypassed oil in side-water systems. The correlations have been developed using numerical simulation and an experimental design framework. Considered in the correlations are the effects of dip angle, vertical- to-horizontal permeability ratio, oil viscosity, production rate, oil density, and well penetration.

Introduction
Displacement of oil by water in side-water systems is controlled by viscous forces, gravity forces, capillary forces, and heterogeneities. These mechanisms or forces may interact with each other during the displacement, originating the formation of multiple fingers, water channeling, and/or gravity underrunning (formation of a water tongue). For low flow velocities, gravity forces tend to dominate the displacement and a stable (constant slope) interface occurs(1). A stable front is desirable because it results in high recovery factors. However, the required flow velocity may be so low that the corresponding critical production rate would not be economical. Generally, production rates needed for economical recovery exceed the critical rates. Therefore, the front becomes unstable and a (gravity) water tongue develops along the bottom of the dipping structure, causing early water breakthrough and oil bypassing. In fact, simulation studies have shown that up to 69% of the oil could be bypassed in side-water systems with unfavourable mobility ratios(1, 2). Also, most of the well's production life is plagued by very high water cut.
Knowledge of the motion of the oil-water interface is needed in reservoir engineering in order to determine the amount of oil that will be recovered by the end of the well's operation. The most well known analytical models for the determination of the motion of the oil-water interface are the models presented by Richarson and Blackwell(3), Dake(4), Dietz(5), Outmans(6), and Sheldon and Fayers(7). Potential use of these models for predicting a well's recovery is important due to the simplicity of calculations as compared to reservoir simulations, which become quite complex in modelling individual wells. Recently, the analytical models were verified for stable and unstable cases(1). The results indicated that Dake and Dietz are the best models because of their accuracy and ease of use(1).
Despite convenience, analytical models are poor estimators of the water breakthrough time(1). Moreover, Dake's and Dietz's models are based on assumptions that may not represent the real physics of the displacement of oil by water in dipping structures. For example, the models assume isotropic reservoirs. They also assume completely segregated flow, i.e., consider the thickness of the capillary transition zone negligibly smaller than the thickness of the pay zone. In addition, these analytical models are two-dimensional, so they ignore the physical size of a well at the producing end of the dipping structure.