Determination of Saturation Distributions in Water Displacement by Analytical Models

Abstract

Water is injected in the hydrocarbon reservoir to serve two purposes, to maintain reservoir pressure and to displace oil as production proceeds in the reservoir. In recent years, smart wells coupled with reservoir simulation models are used to improve the results of water injection performance. High frequency data (pressure, flow rate, etc.) that is a product of the smart wells provide the basis for a closed-loop, fast track updating of the dynamic reservoir models. While high frequency updating of the reservoir model remains a challenge, there are emerging technologies that can make such objectives achievable. An integrated approach that combines analytical and numerical solutions with artificial intelligence and data mining is proposed to ultimately achieve the closed-loop, fast track updating system. This study is the first step in that direction. In this work the ability of analytical solutions to calculate reservoir water saturation profiles from field water cut data are investigated. Different flow regimes and reservoir geometries are considered during this study. Diffuse, segregated and capillary influenced flow models are analyzed in both one and two dimensional water injection using a commercial numerical simulator. Different analytical formulations are applied for each flow regime in order to reproduce simulation production data. For each model a specific relative permeability relation is assigned and tuned with the aim of matching water breakthrough time and water cut history. An accurate match is achieved between water saturation profiles generated by the analytical models and the results by the reservoir simulator. The influence of simple reservoir heterogeneity on the robustness of the analytical models is studied.