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The original Shan-Chen's pseudopotential Lattice Boltzmann Model (LBM) has continuously evolved during the past two decades. However, despite its capability to simulate multiphase flows, the model still faces challenges when applied to multicomponent-multiphase flows in complex geometries with a moderately high-density ratio. Furthermore, classical cubic equations of state usually incorporated into the model cannot accurately predict fluid thermodynamics in the near-critical region. This paper addresses these issues by incorporating a crossover Peng–Robinson equation of state into LBM and further improving the model to consider the density and the critical temperature differences between the CO2 and water during the injection of the CO2 in a water-saturated 2D homogeneous porous medium. The numerical model is first validated by analyzing the supercritical CO2 penetration into a single narrow channel initially filled with H2O, depicting the fundamental role of the driving pressure gradient to overcome the capillary resistance in near one and higher density ratios. Significant differences are observed by extending the model to the injection of CO2 into a 2D homogeneous porous medium when using a flat versus a curved inlet velocity profile. [ABSTRACT FROM AUTHOR]

• Thermodynamic phase transition in nanopores is directly modeled by using a molecular-level approach. • Effects of adsorption and capillary pressure on phase equilibrium in nanoscale are evaluated. • Vapor-liquid contact angle is used to characterize molecular scale fluid–solid interaction. • Phase behavior in a nanoporous medium with chemical heterogeneity is presented. Owing to the strong interaction between fluid molecules and solid surface, thermodynamic phase behavior of fluids in nanopores deviates from that at bulk condition. In this work, a pseudopotential lattice Boltzmann method is employed to directly model phase equilibrium of methane in nanopores. The effects of adsorption and fluid–solid force on confined phase behavior are studied. In the absence of solid walls, our simulation of nanoscale droplets is consistent with prediction from thermodynamic model coupling Peng-Robinson equation of state and capillary pressure. The shifted phase equilibrium is compared with Kelvin equation. When the pore space is confined by solid walls, heterogeneous density distributions in nanopores are developed by adsorption. It is observed that the apparent critical temperature and critical pressure decrease whereas critical density increases in nanopores from the simulated co-existence curves. In addition, it is found that a larger fluid–solid force leads to a more heterogeneous density distribution in nanopores. However, the average liquid/vapor density and apparent critical temperature in confined space are not significantly affected by the strength of fluid–solid force. Density of gas in equilibrium with condensed liquid, on the other hand, is significantly decreased with increasing fluid–solid force. We propose that the phase equilibrium in nanopores under different fluid–solid forces can be characterized by using contact angle. In the end, we extend this method to model the phase equilibrium in a nanoporous medium with chemical heterogeneity. [ABSTRACT FROM AUTHOR]