Obtaining reliable relative permeability (kr) values and their variations is difficult particularly in processes involving three-phase flow and flow reversal (e.g. WAG injection) which results in kr hysteresis. The current approach in the industry is to use a three-phase kr correlation (e.g., Stone I, Stone II, Baker) in conjunction with a kr hysteresis model (e.g., Killough, WAG- Hysteresis). However, these models have been mostly developed based on water-wet systems and have rarely been benchmarked against experimental measurements.
In this paper, we present the results of an extensive assessment of different three-phase relative permeability models available in the most widely used reservoir simulators. The input two-phase data needed for using three-phase kr correlations were obtained from core flood experiments. The simulation results were directly compared with WAG injection experiments performed under both water-wet and mixed-wet conditions.
The results show significant differences between the simulation and experimental results of WAG injection. In water-wet rocks, the results show that without considering kr hysteresis, Stone-I model underestimates WAG performance, but it overestimates oil recovery in mixed-wet rocks. SWI and Baker correlations overestimate WAG performance in water-wet rocks while for mixed-wet rocks they significantly underestimate production data. For both wettabilities, Stone-II significantly underestimates oil production. The generated recovery trends by IKU model show a relative advantage over other models but still underestimates the performance of WAG injection especially for later cycles.
Coupling of three-phase kr correlations with hysteresis models (Carlson, Killough and Jargon) generally results in highly overestimated oil recovery predictions especially for mixed-wet conditions. For water-wet systems, coupling Stone-I with WAG-hysteresis model improves the predictions up to the second gas injection period. Nevertheless, serious underestimation is observed for further cycles. The WAG-hysteresis model overestimated WAG performance in mixed-wet systems. To improve its prediction, based on our experimental results, WAG-hysteresis model parameters were adjusted after each cycle. This modified approach improved simulation results in water-wet systems. However, none of the available approaches could adequately reproduce experimental results obtained for mixed-wet conditions. This is a major concern for predication of WAG performance in real reservoirs which are believed to be mixed-wet.