New concepts for modeling connectivity effects in capillary pressure hysteresis in porous media

Continuum models of porous media often characterize microscopic features of the pore space using macroscopic parameters like porosity and tortuosity, and macroscopic state variables like fluid saturations. To account for the effects of pore-scale connectivity between different sized pores, we propose a new parameter, “pore-space accessivity” to contrast serial and parallel arrangements of different sized pores, and a new state variable, “radius-resolved saturation”, to describe the microscopic distribution of fluids. Based on a statistical branching process, we derive a new microscopic constitutive theory of capillary pressure hysteresis for arbitrary drainage-imbibition cycles. Expanding on the classical “capillary bundle” picture by means of providing a useful first approximation for connectivity effects in porous media, these concepts may have much broader utility in continuum modeling of porous media in a variety of applications.