Modeling the extra column volume of a micro simulated moving bed chromatography system: Introducing the equivalent radial flow rate distribution

Abstract

Recently, the focus in chromatography model development has expanded to include the modeling of extra column volume (ECV), particularly in small- and lab-scale systems where ECV can constitute a significant portion of the total volume. Typically, ECV is modeled with 1D approaches, for example with combinations of dispersed plug flow reactors (DPFRs) and continuously stirred tank reactors (CSTRs). However, radial inhomogeneities in the ECV concentration profile necessitate higher-dimensional models for more accurate predictions. Searching for a suitable modeling approach for a micro simulated moving bed chromatography ($\mu$SMB) system, we investigated whether the 2D laminar flow model can be extended to account for additional dispersion effects, such as Dean vortices, through an equivalent radial flow rate distribution (eqFRD). For this purpose, we conducted 3D CFD simulations of the respective ECV and adapted the radial flow rate profile of a 2D simulation to match the residence time distribution observed in the CFD results. Applying the eqFRD model led to a significant improvement in prediction accuracy for isolated ECV segments, increasing from 90% to 97% compared to traditional ECV models. However, when these models were applied to the full $\mu$SMB system, the choice of ECV model had minimal impact on overall results as long as retention time within the ECV was accurately predicted. This suggests that, in the studied system, the column has a greater influence on peak shape than the ECV, allowing simpler ECV models to suffice in certain contexts. Despite these advances, significant deviations between predicted and experimental results were observed, indicating that factors such as the transition between the column and ECV, as well as detector effects, should be considered in future research. The results underscore the importance of selecting an ECV model in the context of the entire system, balancing accuracy with computational efficiency.