Influence of capillary end effects on steady-state relative permeability estimates from direct pore-scale simulations

We investigate and characterize the influence of capillary end effects on steady-state relative permeabilities obtained in pore-scale numerical simulations of two-phase flows. Our study is motivated by the observation that capillary end effects documented in two-phase laboratory-scale experiments can significantly influence permeability estimates. While numerical simulations of two-phase flows in reconstructed pore-spaces are increasingly employed to characterize relative permeabilities, a phenomenon which is akin to capillary end effects can also arise in such analyses due to the constraints applied at the boundaries of the computational domain. We profile the relative strength of these capillary end effects on the calculation of steady-state relative permeabilities obtained within randomly generated porous micro-structures using a finite volume-based two-phase flow solver. We suggest a procedure to estimate the extent of the regions influenced by these capillary end effects, which in turn allows for the alleviation of bias in the estimation of relative permeabilities.