Assessment of two-phase relative permeability hysteresis models for oil/water, gas/water and gas/oil systems in mixed-wet porous media

Accurate determination of relative permeability curves and their hysteresis is vital for reliable prediction of the performance of oil and gas reservoirs under enhanced recovery processes. Two out of the three available approaches to simulate three-phase relative permeability hysteresis are based on two-phase hysteresis. A few options (e.g., Carlson, Killough and Jargon models) are available in commercial reservoir simulators to account for hysteresis in relative permeability curves under two-phase flow. These models are based on the assumptions of water-wet state of the rocks, while most of the reservoir rocks are mixed-wet. As a result the aim of the present work is to evaluate the performance of these hysteresis models for mixed-wet systems. In addition to the above models, more recent ones such as Beattie et al., Kjosavik et al., Spiteri et al. are also evaluated by coupling an in-house MATLAB code with the Eclipse simulator. The assessments of models are performed by comparing their predictions with those of previously reported comprehensive set of experimentally measured relative permeabilities for different two-phase systems. All possible two phase fluid/fluid systems i.e. oil/water, gas/water and gas/oil are considered. The interfacial tension in the case of oil/gas system is extra low (i.e. 0.04 mN.m(-1)) and it represents near-miscible condition. It is concluded that hysteresis models developed by Killough and Carlson are unable to accurately predict hysteresis effect on relative permeability in oil/gas system under extra low IFT and mixed-wettability. However, either of Killough and Carlson models could provide satisfactory results in gas/water and oil/water systems, respectively. Beattie et al. model that is not used in Eclipse gave a better fit to experimental data in oil/gas system, but it couldn't provide a suitable fit with experimental data in the cases of gas/water and oil/water systems. For different fluids systems, Kjosavik et al. model results were approximately close to the Killough model during the imbibition process and Beattie et al. during the drainage process. Even the results of the best models in each category of the two phase systems are not very satisfactorily. This study highlights the lack of a versatile hysteresis model to capture the hysteresis effect in all possible two phase systems for the mixed-wettability. As a result it is vital that modified or even novel hysteresis models in the case of mixed-wet system be developed.