Analysis of Warm-Back Data After Cold-Fluid Injection Into Multilayer Reservoirs

Abstract

Summary Determining the rate distribution over multilayer injection zones (i.e., injection profiling) is critical to the optimization of injection operations. With the recent advancements in deployment of fiber-optic distributed-temperature-sensing (DTS) technology, temperature data can be achieved at high resolution and at relatively low cost along the wellbore length. During injection of cooler fluids into a higher-temperature injection zone, the temperature at the wellbore and near-wellbore region decreases. During a shut-in period when the injection operation is paused, the temperature at the wellbore sandface and near-wellbore region experiences “warm back” that is caused by the heat flux from the warmer inswept region of the injection zone. A slower warm back is observed for a layer that admits larger amount of cooler fluid during injection. As a result, the sandface warm-back temperature can be analyzed to determine the injection rate per layer, and hence the thermal-front extent per layer. In this work, we develop an analytical model to determine the temporal and spatial temperature variation for a single-phase reservoir during a warm-back period following a constant-rate-injection period. The analytical solution is developed for a single-layer reservoir and extended to multilayer reservoirs. The solution considers heat transfer by conduction and convection during the injection period and conduction during the shut-in warm-back period. The solution is verified by comparison with synthetic numerical-simulation results obtained using a thermally coupled numerical simulator for single-layer and multilayer cases. Graphical interpretation techniques are introduced by recasting the analytical solution into desirable forms. The graphical techniques are applied to synthetic warm-back data to illustrate their application and accuracy in obtaining the injection rate, thermal-front extent, and initial geothermal temperature per each layer.