Abstract In this work, the method of volume averaging is applied for the mathematical modeling of transport and adsorption of benzene, toluene, and xylene in a packed bed of activated particles. One benefit of this approach is that it allows one to directly incorporate measured microscale information into macroscale models for predicting the effective transport and adsorption process. This work is novel in that it combines two levels of upscaling and a nonlinear adsorption process. The first level of upscaling develops an effective model for the mass transport and reaction in an activated carbon particle; within the particle, only diffusion and reaction are considered because of the very small pore sizes. The second level of upscaling develops the effective model for a collection of carbon particles forming the porous medium contained in a fixed-bed reactor; here, convection, diffusion, and dispersion are considered. The resulting model resembles a classical mobile-immobile representation of the transport and adsorption process. As part of the upscaling process, we develop the homogenized transport equations and their associated effective parameters using two different averaging volume support scales (i.e., at two disparate length scales). The effective parameters are all diffusion or dispersion tensors. These include (1) the effective diffusion tensor defining diffusion in the homogenized carbon particle, (2) the effective diffusion tensor for the immobile phase in the two-region representation of the medium, and (3) the effective hydrodynamic dispersion tensor (which included diffusion and dispersion) for the mobile region of the porous catalyst bed. Each of these effective parameters are determined by numerically solving closure problems over an idealized spatially periodic model of a porous medium. One novel feature of these particular closure problems is that they describe nonlinear adsorption at the microscale, which is a problem that is not currently represented in the literature. Once derived, the two-scale, two-equation mobile-immobile model was applied to predict experimentally-measured concentration breakthrough curves from packed bed columns with activated carbon from coconut shell as the adsorbent to the removal of petrochemical contaminants (BTX) by adsorption. There were no adjustable parameters in this modeling effort; the only modeling choice was whether the mass transfer coefficient should be computed from the correlations of Wakao and Funazkri (1978) for BTX components. The equations from closure problems and Darcy’s scale of transport of this work were discretized using the finite volumes method and the solutions are found numerically through of a computational code and some packages from the free software OpenFOAM®, version 2.2.x. This work has been selected by the Editors as a Featured Cover Article for this issue.

中文翻译：

---

BTX 化合物碳吸附的多尺度模型：体积平均理论与实验测量的比较

摘要 在这项工作中，体积平均法应用于苯、甲苯和二甲苯在活化颗粒填充床中的传输和吸附的数学建模。这种方法的一个好处是它允许人们直接将测量到的微观信息整合到宏观模型中，以预测有效的传输和吸附过程。这项工作的新颖之处在于它结合了两个级别的放大和非线性吸附过程。第一级放大为活性炭颗粒中的传质和反应开发了有效模型；在颗粒内，由于孔径非常小，只考虑扩散和反应。第二级放大开发了形成固定床反应器中多孔介质的碳颗粒集合的有效模型；这里考虑了对流、扩散和扩散。由此产生的模型类似于传输和吸附过程的经典移动-固定表示。作为升级过程的一部分，我们使用两个不同的平均体积支持尺度（即，在两个不同的长度尺度）开发了均质传输方程及其相关的有效参数。有效参数都是扩散或色散张量。这些包括 (1) 定义均质碳颗粒中扩散的有效扩散张量，(2) 介质的两区域表示中固定相的有效扩散张量，(3) 多孔催化剂床移动区域的有效流体动力分散张量（包括扩散和分散）。这些有效参数中的每一个都是通过在多孔介质的理想化空间周期模型上数值求解闭合问题来确定的。这些特定闭合问题的一个新特征是它们描述了微观尺度上的非线性吸附，这是目前文献中未提及的问题。推导出后，应用两尺度、两方程的移动-固定模型来预测填充床柱的实验测量浓度突破曲线，该柱以椰壳活性炭作为吸附剂，通过吸附去除石化污染物 (BTX)。在这个建模工作中没有可调整的参数；唯一的建模选择是是否应根据 Wakao 和 Funazkri (1978) 对 BTX 组分的相关性计算传质系数。封闭问题的方程和这项工作的达西输运尺度使用有限体积方法离散化，并通过计算代码和免费软件 OpenFOAM® 2.2.x 版中的一些软件包以数值方式找到解决方案。这项工作已被编辑选为本期的特色封面文章。封闭问题的方程和这项工作的达西输运尺度使用有限体积方法离散化，并通过计算代码和免费软件 OpenFOAM® 2.2.x 版中的一些软件包以数值方式找到解决方案。这项工作已被编辑选为本期的特色封面文章。封闭问题的方程和这项工作的达西输运尺度使用有限体积方法离散化，并通过计算代码和免费软件 OpenFOAM® 2.2.x 版中的一些软件包以数值方式找到解决方案。这项工作已被编辑选为本期的特色封面文章。