Modelling Relative Permeability Hysteresis Based on Subphase Evolution

A recently introduced subphase framework for modeling immiscible two phase flow in porous media has been extended. In this framework the nonwetting and wetting phases are divided into subphases distinguished by their connectivity. The nonwetting phase is divided into three subphases: backbone, dendritic, and trapped subphases. Similarly, the wetting phase is divided into four subphases; backbone, dendritic, film, and isolated subphases. The subphase saturations evolve according to volume transfer terms, which require modeling. Within this framework, relative permeability models can be developed, which take into account the contributions of the different subphases appropriately. For example, only the nonwetting backbone subphase contributes to nonwetting relative permeability. Quasi-static flow network simulations of several drainage-imbibition cycles are conducted to analyze the evolution of the subphases in three different pore-networks. Furthermore, a relative permeability model for the wetting phase as a function of the subphase saturations is proposed. The resulting model can capture complex hysteretic behavior present in relative permeability-saturation curves.