The effect of saturation path on three-phase relative permeability

Abstract

Simulation and fluid flow prediction of many petroleum-enhanced oil recovery methods as well as environmental processes such as carbon dioxide (CO2) geological storage or underground water resources remediation requires accurate modeling and determination of relative permeability under different saturation histories. Based on this critical need, several three-phase relative permeability models were developed to predict relative permeability; however, for practical purposes most of them require a variety of parameters introducing undesired complexity to the models. In this work, we attempt to find out if there is a simpler way to express this functionality. To do so, we experimentally measure three-phase, water/oil/gas, relative permeability in a 1 m long water-wet sand pack, under several saturation flow paths to cover the entire three-phase saturation space. We obtain the in situ saturations along the sand pack using a CT scanner and then determine the relative permeabilities of liquid phases directly from the measured in situ saturations using an unsteady state method. The measured data show that at a specific saturation, the oil relative permeability varies significantly (up to two orders of magnitude), depending on the path through saturation space. The three-phase relative permeability data are modeled using standard relative permeability models, Corey-type, and Saturation Weighted Interpolation (SWI). Our measured data suggest that three-phase oil relative permeability in water-wet media is only a function of its own saturation if the residual oil saturation is treated as a function of two saturations. We determine that residual saturation is the key parameter in modeling three-phase relative permeability (effect of saturation history).