Lattice Boltzmann simulation of near/supercritical CO₂ flow featuring a crossover formulation of the equation of state

In this work, we have incorporated a crossover equation of state into the pseudopotential multiphase Lattice Boltzmann Model (LBM) to improve the prediction of thermodynamic properties of fluids and their flow in near-critical and supercritical regions. Modeling carbon dioxide (CO₂) properties in these regions is of increasing interest for industrial processes such as CO₂ storage and heat transfer where CO₂ is used as a working fluid. Despite the importance of accurately modeling near-critical and supercritical fluids, popular classical cubic equations of state (EoS) are not accurate. The proposed crossover EoS is a proven hybrid equation which uses the original classical EoS far from the critical point where it is valid, and near the critical point, it asymptotically switches to using non-analytic scaling laws. It also transforms into the ideal gas EoS as the density approaches zero. In order to demonstrate the validity and versatility of the crossover approach in the prediction accuracy of LBM in near-critical flows, this formulation was incorporated into the Peng-Robinson (P-R) EoS. First, 2D static droplets of CO₂ and water at vapor-liquid equilibrium were modeled using both P-R EoS and its crossover formulation, and the numerically predicted results were then compared against the experimental data. The results demonstrate that the model accuracy in representing the thermodynamic behavior of the fluid in near-critical region is improved after adopting the crossover formulation with respect to the classical analytical EoS. The crossover P-R EoS was further applied to study several two-phase CO₂ flows in mini-channels at near-critical temperatures. The flow patterns showed a good qualitative agreement with the experimental data in the near-critical region. The study is further extended to multi-component multiphase systems, specifically to water droplet penetration into porous media filled with CO₂.