The hysteresis in two phase relative permeability occurs when the saturation history of the flow changes from drainage to imbibition or vice versa. The imbibition relative permeability is a strong function of initial non-wetting phase saturation from which the imbibition process starts. Hence, it is very time-consuming to conduct many experiments for measuring all possible imbibition relative permeability (kr) data. An alternative approach is to predict the imbibition relative permeability using the measured Land trapping coefficient and primary drainage relative permeability. Some predictive models, found in the literature, such as that of Land, Carlson and Killough are available in commercial simulators. For prediction of imbibition data, these models require the primary drainage kr data and one set of imbibition kr data to calculate the corrected Land trapping coefficient. However, the imbibition relative permeability is not always available and the inappropriate use of these models can introduce significant errors in the calculations. In this study, the limitations of the available models are discussed and a modified method is suggested, which only requires the primary drainage kr data and the measured Land trapping coefficient. The available models for prediction of imbibition kr data are based on the calculations of trapped non-wetting saturation (Snwt). Therefore, in this study, a modified method was introduced which improved the estimations of trapped non-wetting phase saturation. The predicted values of imbibition relative permeability using this improved method were in good agreement with the experimental data. It was shown that this method can be used for both gas and oil as non-wetting phases in a water-wet medium. However, the trapped non-wetting phase is a function of capillary number and the Land trapping coefficient changes as the capillary number changes. Hence, the measured Land trapping coefficient cannot be assumed as constant in cases where severe changes in pressure result in changing interfacial tension (IFT) and fluid viscosity.
- Relative permeability
- Saturation history
- Trapped non-wetting saturation
ASJC Scopus subject areas
- Energy Engineering and Power Technology