Department of Chemical Engineering, Vrije Universiteit Brussel, Brussels, Belgium.
Department of Chemical Engineering, Vrije Universiteit Brussel, Brussels, Belgium; Department of Chemical Engineering, Process and Environmental Technology Lab (PETLab), KU Leuven, Sint-Katelijne-Waver, Belgium.
J Chromatogr A. 2020 Dec 20;1634:461710. doi: 10.1016/j.chroma.2020.461710. Epub 2020 Nov 13.
The present study proposes a ready-to-use analytical expression to calculate the mobile zone mass transfer contribution (h) in packed bed columns. For this purpose, first high-accuracy computations of the band broadening in a perfectly ordered sphere array (fcc-arrangement, external porosity ε=0.40) were made using computational fluid dynamics (CFD), covering a broad range of zone retention factors (2≤k''≤18) and reduced velocities (0≤ν≤48). Subsequently, these data were used to determine the value of the geometrical constants in a number of possible analytical expressions for the h-contribution. This fitting exercise showed the traditional literature approach, using the Wilson-Geankoplis correlation to calculate the dimensionless Sherwood (Sh) number for the mass transfer, leads to fitting errors on the h-term as large as 150%. Instead, a new correlation for Sh is established. In addition, we also explored the difference in fitting accuracy between h-expressions based on either a plug-flow or a laminar flow profile assumption. Surprisingly, no significant difference in fitting accuracy between both assumptions was observed. Finally, a best-fit analytical expression is proposed that can represent the CFD-computed band broadening data with an average absolute fitting error of Δh=0.005, corresponding to a relative error of 2.5% on the h-term and of only 0.3% on the total plate height in a perfectly ordered sphere packing. Defining the presently investigated fcc-ordered sphere array with external porosity=40% as the reference geometry for a perfect sphere packing, the established expression can be used as a new yardstick expression against which the degree of eddy-dispersion can be measured.
本研究提出了一种可用于计算填充床塔中移动区域传质贡献（h）的即用型分析表达式。为此，首先使用计算流体动力学（CFD）对完美有序球型阵列（fcc 排列，外部孔隙率 ε=0.40）中的带宽展宽进行了高精度计算，涵盖了广泛的区域保留因子（2≤k''≤18）和降速（0≤ν≤48）。随后，这些数据用于确定多个可能的 h 贡献分析表达式中的几何常数的值。拟合结果表明，传统文献方法使用 Wilson-Geankoplis 相关关系计算传质的无因次 Sherwood（Sh）数，会导致 h 项的拟合误差高达 150%。相反，建立了一个新的 Sh 相关关系。此外，我们还研究了基于活塞流或层流假设的 h 表达式在拟合精度上的差异。令人惊讶的是，两种假设之间的拟合精度没有明显差异。最后，提出了一个最佳拟合的分析表达式，可以用平均绝对拟合误差 Δh=0.005 来表示 CFD 计算的带宽展宽数据，这对应于 h 项的相对误差为 2.5%，在完美有序球型填充中总板高的相对误差仅为 0.3%。将目前研究的外部孔隙率=40%的 fcc 有序球型阵列定义为完美球型填充的参考几何形状，所建立的表达式可用作新的标准表达式，用于衡量涡流扩散程度。
