Efficient Simulation of Chromatographic Processes Using the Conservation Element/Solution Element Method

Valentin Plamenov Chernev,Alain Vande Wouwer,Achim Kienle

doi:10.3390/pr8101316

Abstract

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.

Highlights

Chromatographic separation processes are used for the separation of temperature-sensitive mixtures and mixtures of components with very similar physical properties, making them difficult to separate via other cheaper methods
The results clearly show that conservation element/solution element (CE/SE) outperforms method of lines (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 simulated moving bed (SMB) with Langmuir isotherms, and it could be successfully applied for the optimization and control studies of such processes
The focus was placed on the equilibrium model without axial dispersion which can be used for the simulation of highly efficient columns

Summary

Introduction

Chromatographic separation processes are used for the separation of temperature-sensitive mixtures and mixtures of components with very similar physical properties, making them difficult to separate via other cheaper methods These types of processes are frequently used in the chemical and the pharmaceutical industries ranging from small-scale batch separations of highly valuable pharmaceutically active compounds to large-scale continuous separations of isomer mixtures in the petroleum industries [1]. Mathematical modeling of such processes usually leads to a system of partial differential equations (PDEs) [1]. Depending on the modeling assumptions, different types of models are available and frequently used including equilibrium models, which assume thermodynamic equilibrium between the solid and the fluid phase, or mass transfer models with finite mass transfer resistance between both phases.

Methods

Results

Conclusion