Numerical solution of the bivariate population balance equation for the interacting hydrodynamics and mass transfer in liquid¿liquid extraction columns
Numerical solution of the bivariate population balance equation for the interacting hydrodynamics and mass transfer in liquid¿liquid extraction columns
复制标题
液体中流体动力学和传质的双变量总体相互作用平衡方程的数值解¿
DOI：
10.1016/j.ces.2004.12.055
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发表时间：
2006
影响因子：
4.7
通讯作者：
N. Faqir
中科院分区：
文献类型：
--
作者：
Menwer Attarakih;H. Bart;N. Faqir
在空间分布的粒子数平衡方程的基础上，根据关于液滴直径和溶质浓度的二元数密度函数，建立了预测相互作用流体力学和传质的综合模型。两种宏观(液滴破碎和合并)和微观(相间传质)液滴现象通过分散界面张力相互作用。由此得到的模型方程是由一组以对流为主的偏微分方程组和代数方程组组成的，因此需要一种专门的离散化方法。利用实验验证的液滴输运和相互作用函数，将模型方程应用于RDC柱的实验室段。除了模型的空间离散化外，还扩展了两种液滴直径的离散化方法，以包括液滴溶质浓度。这两种方法是广义固定枢轴技术(GFP)和矩的求积方法(QMOM)。两种扩展方法得到的数值结果基本一致，且两种方法的计算时间都是可以接受的，因此这两种方法被扩展到模拟全尺寸的液-液萃取塔。
A comprehensive model for predicting the interacting hydrodynamics and mass transfer is formulated on the basis of a spatially distributed population balance equation in terms of the bivariate number density function with respect to droplet diameter and solute concentration. The two macro- (droplet breakage and coalescence) and micro- (interphase mass transfer) droplet phenomena are allowed to interact through the dispersion interfacial tension. The resulting model equations are composed of a system of partial and algebraic equations that are dominated by convection, and hence it calls for a specialized discretization approach. The model equations are applied to a laboratory segment of an RDC column using an experimentally validated droplet transport and interaction functions. Aside from the model spatial discretization, two methods for the discretization of the droplet diameter are extended to include the droplet solute concentration. These methods are the generalized fixed-pivot technique (GFP) and the quadrature method of moments (QMOM). The numerical results obtained from the two extended methods are almost identical, and the CPU time of both methods is found acceptable so that the two methods are being extended to simulate a full-scale liquid–liquid extraction column.