Khan Ambreen, Qamar Shamsul
Department of Mathematics, Air University, Islamabad 44000, Pakistan.
Department of Mathematics, COMSATS University Islamabad, Islamabad 45550, Pakistan.
ACS Omega. 2023 Oct 3;8(41):38301-38312. doi: 10.1021/acsomega.3c04641. eCollection 2023 Oct 17.
This paper presents the numerical approximation of a nonlinear equilibrium-dispersive (ED) model of multicomponent mixtures for simulating single-column chromatographic processes. Using Danckwerts boundary conditions (DBCs), the ED is studied for both generalized and standard bi-Langmuir adsorption isotherms. Advection-diffusion partial differential equations are used to represent fixed-bed chromatographic processes. As the diffusion term is significantly weaker than the advection term, sophisticated numerical techniques must be applied for solving such model equations. In this study, the model equations are numerically solved by using the Runge-Kutta discontinuous Galerkin (RKDG) finite element method. The technique is designed to handle sudden changes (sharp discontinuities) in solutions and to produce highly accurate results. The method is tested with several case studies considering different parameters, and its results are compared with the high-resolution finite volume scheme. One-, two-, and three-component liquid chromatography elutions on fixed beds are among the case studies being considered. The dynamic model and its accompanying numerical case studies provide the initial step toward continuous monitoring, troubleshooting, and effectively controlling the chromatographic processes.
本文提出了一种用于模拟单柱色谱过程的多组分混合物非线性平衡-扩散（ED）模型的数值近似方法。利用丹克维茨边界条件（DBCs），对广义和标准双朗缪尔吸附等温线的ED模型进行了研究。对流-扩散偏微分方程用于表示固定床色谱过程。由于扩散项远弱于对流项，因此必须应用复杂的数值技术来求解此类模型方程。在本研究中，使用龙格-库塔间断伽辽金（RKDG）有限元方法对模型方程进行了数值求解。该技术旨在处理解中的突然变化（尖锐间断）并产生高精度结果。通过考虑不同参数的几个案例研究对该方法进行了测试，并将其结果与高分辨率有限体积格式进行了比较。固定床上的单组分、二组分和三组分液相色谱洗脱是所考虑的案例研究之一。该动态模型及其伴随的数值案例研究为色谱过程的连续监测、故障排除和有效控制迈出了第一步。
