多相多组分Peng-Robinson流体的正则化格子Boltzmann方法研究及模拟

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

为了提高石油、天然气等能源的采收率,并最大限度地保护环境.需要对油藏储层内的多相多组分石油混合物的热力学性质和界面行为进行深入研究.Peng-Robinson状态方程被广泛应用于描述和预测烷烃类混合物的热力学性质.文章根据扩散界面理论和Peng-Robinson自由能模型,得到描述多相多组分流体热力学性质和界面行为的流体动力学方程组.该耦合方程组中的交叉扩散项和Peng-Robinson自由能模型的强非线性,给数值求解带来了极大的挑战.文章基于格子Boltzmann方法,针对每个组分的质量守恒方程,构建了带有多分布函数的正则化格子Boltzmann方法.针对势形式的动量守恒方程,构建了能有效降低两相界面虚假速度的正则化格子Boltzmann方法.通过Chapman-Enskog多尺度分析,能够准确恢复至耦合的流体动力学方程组.最后,通过一系列的数值实验,如气-液两相共存线,丙烷和戊烷、甲烷和乙烷共存时的相平衡状态等,验证所发展的多相多组分正则化格子Boltzmann方法满足还原一致性和热力学一致性,同时具有较好的数值稳定性.此外,该正则化格子Boltzmann方法能够有效消除两相界面处的虚假速度,并能准确刻画多相多组分流体的热力学性质和界面行为.

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.