Pore-scale simulation of liquid CO₂ displacement of water using a two-phase lattice Boltzmann model

A lattice Boltzmann color-fluid model, which was recently proposed by Liu et al. (2012) based on a concept of continuum surface force, is improved to simulate immiscible two-phase flows in porous media. The new improvements allow the model to account for different kinematic viscosities of both fluids and to model fluid-solid interactions. The capability and accuracy of this model is first validated by two benchmark tests: a layered two-phase flow with a variable viscosity ratio, and a dynamic capillary intrusion. This model is then used to simulate liquid CO₂ (LCO₂) displacing water in a dual-permeability pore network. The extent and behavior of LCO₂ preferential flow (i.e., fingering) is found to depend on the capillary number (Ca), and three different displacement patterns observed in previous micromodel experiments are reproduced. The predicted variation of LCO₂ saturation with Ca, as well as variation of specific interfacial length with LCO₂ saturation, are both in reasonable agreement with the experimental observations. To understand the effect of heterogeneity on pore-scale displacement, we also simulate LCO₂ displacing water in a randomly heterogeneous pore network, which has the same size and porosity as the simulated dual-permeability pore network. In comparison to the dual-permeability case, the transition from capillary fingering to viscous fingering occurs at a higher Ca, and LCO₂ saturation is higher at low Ca but lower at high Ca. In either pore network, the LCO₂-water specific interfacial length is found to obey a power-law dependence on LCO₂ saturation.