The saturation history dependent relative permeability (kr) data have been reported frequently in the laboratory investigations. Accurate estimation of kr data with hysteresis effects is crucial, specifically in Water Alternating Gas (WAG) injection which involves a sequence of drainage and imbibition cycles. Although there are a few methods to model the hysteresis effects in three-phase systems, the predicted values are still not adequate to simulate the hysteresis observed in experiments.
In this study, a generalized three-phase hysteresis model was developed to simulate the observed hysteresis in the WAG experiments performed at Heriot-Watt University. It is discussed that the use of Land trapping coefficient in the hysteresis models is doubtful since it originates from the observed behaviour in two-phase systems which reach residual saturations. Hence, the new hysteresis model is developed based on innovative techniques to predict the oil and water saturation at the end of each injection cycle. Moreover, in the developed model, the formulations for estimation of hysteresis in water and gas kr data are updated to capture the observed behaviors in WAG experiments.
The suggested hysteresis model was evaluated by comparing the simulation results with the available experimental data. The results showed that the developed model is able to simulate oil, water and gas production more accurately. Based on the results, the model can simulate the pressure behaviours observed in the experiments with dominated hysteresis. In addition, the developed model can predict the oil, water and gas saturations at the end of each cycle with higher accuracy compared to the available methods in the literature.
The significant impacts of the hysteresis phenomenon on designing the best WAG injection scenario require a reliable hysteresis model for performing accurate reservoir simulations. The use of the suggested model elevates the accuracy of any feasibility analysis performed to evaluate the WAG injection scenario.