Abstract

In this paper, a discontinuous-Galerkin finite-element method (DG-FEM) is applied for the numerical solution of multi-component, non-equilibrium, lump kinetic model of liquid chromatography under nonlinear conditions. The model is analyzed for standard Bi-Langmuir type adsorption isotherms using Danckwert boundary conditions. Packed bed processes of liquid chromatography are modeled as convection-diffusion partial differential equations (PDE). In these models, the diffusion term is strongly dominated by the convection term. Therefore simulation of packed bed chromatographic processes requires specialized numerical techniques. In this study, the (DG-FEM) is utilized for the space discretization and the resulting semi-discrete system of ordinary differential equations is solved numerically by using a total variation bounded (TVB) Runge–Kutta method. This technique resolves sharp discontinuities and achieves a high order accuracy. To inspect the impact of different parameters, the results of the proposed method are authenticated against the high-resolution finite-volume scheme (HR-FVS). These numerical results include a single-solute flow, two-component mixture flow, and three-component mixture flow. The developed numerical results could be helpful in optimal predictive control, systematic monitoring and efficient operation of chromatographic processes.

摘要

在本文中，非连续伽辽金有限元法（DG-FEM）被应用于非线性条件下液相色谱的多组分非平衡块动力学模型的数值解。使用 Danckwert 边界条件分析该模型的标准 Bi-Langmuir 型吸附等温线。液相色谱的填充床过程被建模为对流-扩散偏微分方程 (PDE)。在这些模型中，扩散项主要受对流项支配。因此，填充床色谱过程的模拟需要专门的数值技术。在本研究中，(DG-FEM) 用于空间离散化，并通过使用总变分有界 (TVB) Runge-Kutta 方法对所得常微分方程的半离散系统进行数值求解。这种技术解决了尖锐的不连续性并实现了高阶精度。为了检查不同参数的影响，所提出方法的结果针对高分辨率有限体积方案（HR-FVS）进行了验证。这些数值结果包括单溶质流、二组分混合物流和三组分混合物流。开发的数值结果有助于色谱过程的最佳预测控制、系统监测和有效操作。和三组分混合物流。开发的数值结果有助于色谱过程的最佳预测控制、系统监测和有效操作。和三组分混合物流。开发的数值结果有助于色谱过程的最佳预测控制、系统监测和有效操作。