The present study proposes a ready-to-use analytical expression to calculate the mobile zone mass transfer contribution (h_Cm) 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_i≤48). Subsequently, these data were used to determine the value of the geometrical constants in a number of possible analytical expressions for the h_Cm-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_Cm-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_Cm-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_Cm-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.

本研究提出了一种现成的分析表达式，用于计算填充床塔中的移动区传质贡献（h _Cm）。为此，首先使用计算流体力学（CFD）对完全有序的球形阵列中的谱带展宽进行了高精度计算（fcc排列，外部孔隙率ε= 0.40），涵盖了广泛的区域保留因子（2 ≤k''≤18）和降低的速度（0≤ν_我≤48）。随后，这些数据用于确定h _Cm的许多可能分析表达式中的几何常数的值-贡献。该拟合练习显示了传统的文献方法，使用Wilson-Geankoplis相关性计算质量传递的无量纲舍伍德（Sh）数，导致h _Cm项上的拟合误差高达150％。取而代之的是，建立Sh的新相关性。此外，我们还根据塞流或层流剖面假设探索了h _Cm表达式之间拟合精度的差异。出人意料的是，在两个假设之间都没有观察到拟合精度的显着差异。最后，提出了一个最佳拟合分析表达式，该表达式可以表示CFD计算的谱带展宽数据，其平均绝对拟合误差为Δh= 0.005，对应于h _Cm上的相对误差为2.5％-完美排列的球状填料，仅占板总高度的0.3％。将当前研究的fcc有序球体阵列（外部孔隙率= 40％）定义为理想球体填充的参考几何体，可以将建立的表达式用作新的准绳表达式，可以根据其衡量涡流分散程度。