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Mass conservative lattice Boltzmann scheme for a three-dimensional diffuse interface model with Peng-Robinson
Zhonghua Qiao1, Xuguang Yang1,2, Yuze Zhang1
1Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Hong Kong.
Abstract:
Peng-Robinson (P-R) equation of state (EOS) has been widely used in the petroleum industry for hydrocarbon fluids. In this work, a three-dimensional diffuse interface model with P-R EOS for two-phase fluid system is solved by the lattice Boltzmann (LB) method. In this diffuse interface model, an Allen-Cahn (A-C) type phase equation with strong nonlinear source term is derived. Using the multiscale Chapman-Enskog analysis, the A-C type phase equation can be recovered from the proposed LB method. Besides, a Lagrange multiplier is introduced based on the mesoscopic character of the LB scheme so that total mass of the hydrocarbon system is preserved. Three-dimensional numerical simulations of realistic hydrocarbon components, such as isobutane and propane, are implemented to illustrate the effectiveness of the proposed mass conservative LB scheme. Numerical results reach a better agreement with laboratory data compared to previous results of two-dimensional numerical simulations.
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