REGULARIZED LATTICE BOLTZMANN METHOD FOR MULTI-COMPONENT AND MULTI-PHASE PENG-ROBINSON FLUIDS

To enhance the oil recovery and also to protect the environment, it is necessary to deeply study the transport mechanism and the interface behavior of the multi-component and multi-phase petroleum mixture in the reservoir. The Peng-Robinson equation of state, which is widely used in the oil reservoir and chemical engineering, is more accurately in the modeling of hydrocarbon mixtures. In this work, according to the diffuse interface theory and Peng-Robinson free energy model, the hydrodynamic equations of multi-component and multi-phase Peng-Robinson fluids can be got, which include the mass conservation equations of each component and the momentum equation. Through the thermodynamic relationship, the potential form based momentum balance equation can be derived. The cross diffusion term and the high nonlinearly of the Peng-Robinson free energy model bring great challenges to the numerical method. In this work, based on the lattice Boltzmann method, which has been developed as a powerful tool for modeling complex fluid systems, a regularized lattice Boltzmann method with multi-distribution function is developed for the mass balance equation of each species. Furthermore, a regularized lattice Boltzmann method, which can remove the spurious currents, is proposed to solve the potential form momentum balance equation. Through the multi-scale Chapman-Enskog analysis, the proposed regularized lattice Boltzmann method can recover the hydrodynamic equations correctly. At last, through a series of numerical experiments, including the two-phase coexistence density, the spurious currents test, the gas-liquid equilibrium of the systems of propane and n-pentane, methane and ethane and so on. The numerical results show that the reduction consistent and the thermodynamic consistent can be satisfied by the proposed regularized lattice Boltzmann method. Furthermore, compared with the LBGK model, the numerical stability is improved by the proposed regularized lattice Boltzmann method. In addition, the spurious velocity can be removed and the thermodynamic properties and the interface behavior can also be described accurately by the proposed regularized lattice Boltzmann method.