Comparative assessment of three-phase oil relative permeability models

We assess the ability of 11 models to reproduce three-phase oil relative permeability (kro) laboratory data obtained in a water-wet sandstone sample. We do so by considering model performance when (i) solely two-phase data are employed to render predictions of kro and (ii) two and three-phase data are jointly used for model calibration. In the latter case, a Maximum Likelihood (ML) approach is used to estimate model parameters. The tested models are selected among (i) classical models routinely employed in practical applications and implemented in commercial reservoir software and (ii) relatively recent models which are considered to allow overcoming some drawbacks of the classical formulations. Among others, the latter set of models includes the formulation recently proposed by Ranaee et al. (2015), which has been shown to embed the critical effects of hysteresis, including the reproduction of oil remobilization induced by gas injection in water-wet media. We employ formal model discrimination criteria to rank models according to their skill to reproduce the observed data and use ML Bayesian model averaging to provide model-averaged estimates (and associated uncertainty bounds) of kro by taking advantage of the diverse interpretive abilities of all models analyzed. The occurrence of elliptic regions is also analyzed for selected models in the framework of the classical fractional flow theory of displacement. Our study confirms that model outcomes based on channel flow theory and classical saturation-weighted interpolation models do not generally yield accurate reproduction of kro data, especially in the regime associated with low oil saturations, where water alternating gas injection (WAG) techniques are usually employed for enhanced oil recovery. This negative feature is not observed in the model of Ranaee et al. (2015) due to its ability to embed key effects of pore-scale phase distributions, such as hysteresis effects and cycle dependency, for modeling kro observed during WAG.