Modeling Hysteresis Effect in Three-Phase Relative Permeability

Simulation and fluid flow prediction of many petroleum enhanced oil recovery methods as well as environmental processes such as carbon dioxide (CO2) geological storage requires accurate modeling and determination of relative permeability under different saturation histories. Based on this critical need, there has been several different three-phase relative permeability models developed to predict the hysteresis effects in relative permeability, most of which requiring many different parameters which introduce extreme complexity to the models for practical purposes. In this work, we experimentally measured three-phase, water/oil/gas, relative permeability in a 1-m long water-wet sand pack, under several different flow histories. We measured the in-situ saturations along the sand pack using a CT scanner. We then determined the relative permeabilities directly from the measured in-situ saturations, using unsteady-state method. Based on our results, good estimation of residual saturations yields in excellent three-phase relative permeability estimations by just using the simple, standard relative permeability models such as, Saturation Weighted Interpolation (SWI), Corey's and Stones. Our results show that, the key parameter to model the hysteresis in three-phase relative permeability (effect of saturation history) is the residual saturations. Once the residual saturations were correctly determined for each specific saturation path, the standard relative permeability models can predict the three-phase relative permeabilities perfectly.