Modeling wetting-phase relative permeability hysteresis based on subphase evolution

A recently introduced subphase framework for modeling the nonwetting phase relative permeability is extended to the wetting phase. Within this framework, the wetting phase is divided into four subphases, which are distinguished by their connectivity; backbone, dendritic, isolated and corner-film subphases. The subphase saturations evolve according to inter-subphase volume transfer terms, which require modeling. An advantage of distinguishing the subphases is that wetting phase relative permeability relations as functions of these constituent subphases can be developed. In order to develop models for the inter-subphase volume transfer and the wetting phase relative permeability in a strongly wetted system, quasi-static flow simulations in pore networks were conducted to analyze the evolution of the wetting subphases during drainage and imbibition. The simulation results suggest that hysteresis trends apparent in experimentally obtained wetting phase relative permeability curves for Berea sandstone may be explained by accounting for corner-film flow.