Simulation of many enhanced oil recovery (EOR) methods such as water alternative gas (WAG) requires accurate determination of relative permeability (kr) data under different saturation histories. Relative permeability is a function of several factors such as wettability, spreading coefficient and fluid pore occupancy. Experimental measurements of three phase kr data are time consuming and difficult considering infinite possible flow paths in the three-phase flow regime. There are several models in the literature to estimate the oil relative permeability data in three phase systems (3P-Kr models). However, the available models can not accurately estimate the oil production in low oil saturation region observed in WAG experiments.
In this paper, Stone I model has been modified to improve the estimation of oil kr data. To this aim, the behaviors of three phase flow in immiscible and near miscible WAG experiments were considered. It was shown that the Stone model overestimates the oil relative permeability data in the low oil saturation regions. In addition, it was revealed that Stone's exponent model cannot simulate the gradual decreace in the oil kr data. To improve the results, a new coefficient is incorporated into the model to consider the impacts of the disconnected oil clusters during the cyclic injection. In addition, the end-of-cycle residual oil saturation (Som), which was required based on the Stone model, is no longer needed in this modified model.