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 (S_nwt$S_{nwt}$). 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.

当流动的饱和历史从排水变为吸水或反之时，就会发生两相相对渗透率的滞后现象。吸水率相对渗透率是吸水过程开始时初始非润湿相饱和度的强函数。因此，进行许多实验以测量所有可能的吸收相对渗透率（kr）数据非常耗时。一种替代方法是使用测得的土地诱集系数和一次排水相对渗透率来预测吸水率相对渗透率。商业仿真器中提供了一些文献中找到的预测模型，例如Land，Carlson和Killough的模型。为了预测吸水数据，这些模型需要主要排水kr数据和一组吸水kr数据来计算校正后的陆地诱集系数。然而，吸水率相对渗透率并不总是可用，并且这些模型的不适当使用会在计算中引入重大误差。在这项研究中，讨论了可用模型的局限性，并提出了一种修改方法，该方法仅需要主要排水kr数据和测得的土地诱集系数。

用于预测吸水kr数据的可用模型基于捕获的非润湿饱和度（S _nwt${\mathrm{小号}}_{ñwŤ}$）。因此，在这项研究中，引入了一种改进的方法，该方法改进了对捕获的非润湿相饱和度的估计。使用该改进方法的吸水率相对渗透率的预测值与实验数据吻合良好。结果表明，该方法可以在水和湿介质中作为非润湿相用于天然气和石油。但是，捕获的非润湿阶段是毛细管数的函数，并且Land捕获系数随毛细管数的变化而变化。因此，在压力的剧烈变化导致界面张力（IFT）和流体粘度发生变化的情况下，无法将测得的Land捕集系数假定为常数。