Modelling binary non-linear chromatography using discrete equilibrium data
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Modelling binary non‑linear chromatography using discrete equilibrium data Arvind Rajendran1 · Rafael Teruo Maruyama1 · Héctor Octavio Rubiera Landa2,3 · Andreas Seidel‑Morgenstern2,4 Received: 23 November 2019 / Revised: 9 February 2020 / Accepted: 13 March 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract The determination and description of adsorption equilibria is critical for the design of several separation processes. In some instances, the dependence of the solid phase loading on the fluid phase concentration is complex and it is difficult to find a suitable functional form to represent the adsorption equilibria. This difficulty can be overcome by the use of discrete equilibrium data, i.e., using the experimental data of solid phase loadings and the corresponding fluid phase concentrations in its discrete form, without the use of a functional form to describe the adsorption isotherms. In this work we demonstrate how discrete equilibrium data can be used to predict binary competitive equilibria using the ideal adsorbed solution theory. Two approximations to generate data outside the range of measured values are proposed. The effectiveness of these methods in predicting competitive equilibria and elution profile of binary injections is demonstrated using numerical simulations. The application of this framework to estimate the regions of achievable separation for a multi-column simulated moving bed chromatographic separation is also discussed. Keywords Adsorption column dynamics · Chromatography · Discrete equilibrium data · Ideal adsorbed solution theory List of symbols b Equilibrium constant in Langmuir isotherm (L g−1) c Fluid phase concentration of solute (g L−1) DL axial dispersion coefficient ( cm2 s−1) H Henry constant L Length of column (cm) m Dimensionless flow rate ratio Pu Target product purity (%) Q Volumetric flow rate ( cm3 s−1) q Solid phase concentration of solute (g L−1)
* Arvind Rajendran [email protected] 1
Department of Chemical and Materials Engineering, Donadeo Innovation Centre for Engineering, University of Alberta, 9211‑116 Street NW, Edmonton, AB T6G 1H9, Canada
2
Max Planck Institute for Dynamics of Complex Technical Systems, Sandtorstr. 1, 39106 Magdeburg, Germany
3
Georgia Institute of Technology, School of Chemical & Biomolecular Engineering, 311 Ferst Drive N. W., Atlanta 30332‑0100, USA
4
Otto-von-Guericke-Universität / Lehrstuhl für Chemische Verfahrenstechnik, Universitätsplatz 2, 39106 Magdeburg, Germany
q∗ Solid phase equilibrium concentration of solute (g L−1) t Time (s) t∗ Switch time (s) v Interstitial velocity (cm s−1) x Molar fraction on the solid phase z Axial coordinate (cm) Subscripts and superscripts D Desorbent E Extract F Feed i Component j SMB section R Raffinate sat Saturation tot Total Greek symbols 𝜀 Column void fraction
1 Introduction Adsorption and chromatographic separation processes exploit the ability of solids to selectively bind one or more components from a flui
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