An Investigation into Apparent Differences Between Injection Transmissibility and Falloff Transmissibility in Oil Reservoirs Subject to Water Injection

Abstract

When water is injected into an oil reservoir, estimates of fluid transmissibility from the respective log-log plots show substantial differences between magnitudes out of injection and falloff models. This observation appears to be anomalous when compared to the cases of producing wells where there are no marked differences in transmissibility estimated from drawdown and buildup models. This study investigates the reason behind the differences in fluid transmissibility estimated from injection and falloff models. We have developed high-resolution, numerical models to illustrate differences in log-log plots observed in the injection and falloff periods. To explain the anomalous behavior, we have reviewed the fundamental principle of superposition which is particularly applicable in production wells. However, we have found that the principle of superposition falls apart while applying during injection periods due to a lack of static equilibrium of the transmissibility distribution around the injection wells. In contrast, the principle of superposition is still applicable during the falloff period following a period of water injection. As a result, differences in injection and falloff models appear on the log-log plots. The requirement of linearity on the part of the principle of superposition breaks down due to changing transmissibility in the vicinity of the injection wells during the injection periods. This invalidates the method of estimating the fluid transmissibility during the injection periods. But during the falloff periods, the transmissibility distribution in the reservoir gets back to its equilibrium condition. Hence the estimates of the mobility from the models during the falloff periods on the log-log plot are valid as demonstrated with isothermal and non-isothermal cases. This study is to show how it is misleading in estimating the mobility from injection-pressure data contrary to conventional wisdom. With this knowledge, reservoir engineers will be able to steer clear of the trap of wrongful analysis of transient-pressure data.