Efficient and accurate simulation methods are essential for analyzing and optimizing chromatographic processes, which are governed by partial differential equations (PDEs) and characterized by the propagation of steep concentration fronts. These fronts often cause numerical dispersion and high computational costs in conventional finite-volume or finite-difference schemes. In this paper, a fast and accurate simulation method for highly efficient chromatographic columns with negligible axial dispersion, linear and nonlinear non-competitive adsorption isotherms is proposed. The simulation approach is based on the propagation of discrete concentration values using characteristic velocities. In the linear case, the method is exact, and only the graphical representation of the solution depends on the discretization of the concentration coordinate. In the nonlinear case, an approximation is proposed to capture the possible formation of discontinuities efficiently. Nevertheless, it is shown that good agreement with reference solutions is achieved even for a relatively low number of discrete concentration values. Applications of the proposed methods are demonstrated for different multi-column simulated moving bed processes. The results show that the computational effort can be significantly reduced compared to the popular cell model, which represents a first-order finite-volume approximation of the underlying PDEs. The proposed approach thus enables rapid process design and parameter exploration for both linear and nonlinear non competitive adsorption isotherms for SMB chromatography separations with highly efficient columns.
Pishkari et al. (Sat,) studied this question.