Analytical approach for injection profiling through warm-back analysis in multilayer reservoirs

Abstract

Injection profiling in multilayer (stratified) reservoirs is essential for successful water flooding and effective reservoir management. When possible, injection profiling may be achieved via production logging tools (PLT). An alternative approach is to utilize real-time temperature obtained e.g. via fiber optic distributed temperature sensing (DTS) to obtain the injection profiles. Development of modelling tools is required to enable analyzing temperature data to obtain the injection profiling.In this work, an analytical solution is developed to determine the transient temperature distribution in the reservoir during the warm-back period that follows cold fluid injection. The analytical model is used to introduce a temperature inversion approach to obtain the injection profile. The analytical solution is developed for single- and multi-layer reservoirs considering single-phase flow at constant rate over the injection period. The solution considers heat transfer by conduction and convection during the injection period. Warm-back is attained during the subsequent shut-in period through heat transfer by conduction in the reservoir (thermal equilibration) as well as the heat exchange between the completed layers and the surroundings. Heat transfer with the surrounding layers affects the warm-back rate the most for relatively thin layers. The analytical solution is verified through comparison against numerical simulation results obtained using a thermally coupled numerical simulator for single- and multi-layer reservoir cases. Graphical interpretation techniques are introduced by recasting the analytical solution into convenient forms. The graphical techniques are applied to synthetic warm-back data to illustrate their reliability and accuracy in obtaining the injection profile and the thermal front extent (per layer) during the injection period.