Minimized Capillary End Effect During CO₂ Displacement in 2-D Micromodel by Manipulating Capillary Pressure at the Outlet Boundary in Lattice Boltzmann Method

We propose a new outflow boundary condition to minimize the capillary end effect for a pore-scale CO₂ displacement simulation. The Rothman-Keller lattice Boltzmann method with multi-relaxation time is implemented to manipulate a nonflat wall and inflow-outflow boundaries with physically acceptable fluid properties in 2-D microfluidic chip domain. Introducing a mean capillary pressure acting at CO₂ -water interface to the nonwetting fluid at the outlet effectively prevents CO₂ injection pressure from suddenly dropping upon CO₂ breakthrough such that the continuous CO₂ invasion and the increase of CO₂ saturation are allowed. This phenomenon becomes most pronounced at capillary number of logCa = −5.5, while capillary fingering and massive displacement of CO₂ prevail at low and high capillary numbers, respectively. Simulations with different domain length in homogeneous and heterogeneous domains reveal that capillary pressure and CO₂ saturation near the inlet are reproducible compared with those with a proposed boundary condition. The residual CO₂ saturation uniquely follows the increasing tendency with increasing capillary number, corroborated by experimental evidences. The determination of the mean capillary pressure and its sensitivity are also discussed. The proposed boundary condition is commonly applicable to other pore-scale simulations to accurately capture the spatial distribution of nonwetting fluid and corresponding displacement ratio.