Chromatographic separation processes need efficient simulation methods, especially for nonlinear adsorption isotherms such as the Langmuir isotherms which imply the formation of concentration shocks. The focus of this paper is on the space–time conservation element/solution element (CE/SE) method. This is an explicit method for the solution of systems of partial differential equations. Numerical stability of this method is guaranteed when the Courant–Friedrichs–Lewy condition is satisfied. To investigate the accuracy and efficiency of this method, it is compared with the classical cell model, which corresponds to a first-order finite volume discretization using a method of lines approach (MOL). The evaluation is done for different models, including the ideal equilibrium model and a mass transfer model for different adsorption isotherms—including linear and nonlinear Langmuir isotherms—and for different chromatographic processes from single-column operation to more sophisticated simulated moving bed (SMB) processes for the separation of binary and ternary mixtures. The results clearly show that CE/SE outperforms MOL in terms of computational times for all considered cases, ranging from 11-fold for the case with linear isotherm to 350-fold for the most complicated case with ternary center-cut eight-zone SMB with Langmuir isotherms, and it could be successfully applied for the optimization and control studies of such processes.

中文翻译：

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使用保留元素/溶液元素方法对色谱过程进行高效模拟

色谱分离过程需要有效的模拟方法，尤其是对于非线性吸附等温线，例如Langmuir等温线，这暗示了浓度激波的形成。本文的重点是时空守恒元素/解元素（CE / SE）方法。这是求解偏微分方程组的一种显式方法。当满足Courant–Friedrichs–Lewy条件时，可以保证此方法的数值稳定性。为了研究该方法的准确性和效率，将其与经典单元模型进行了比较，经典单元模型对应于使用线法（MOL）的一阶有限体积离散化。针对不同的模型进行了评估，包括理想的平衡模型和传质模型，适用于不同的吸附等温线（包括线性和非线性Langmuir等温线），以及适用于从单柱操作到更复杂的模拟移动床（SMB）工艺分离二元和三元混合物的色谱方法。结果清楚地表明，对于所有考虑的案例，CE / SE在计算时间方面均优于MOL，范围从线性等温线案例的11倍到三元中心切八区SMB的最复杂案例的350倍。 Langmuir等温线，可以成功地用于此类过程的优化和控制研究。