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Modelling binary non-linear chromatography using discrete equilibrium data

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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.

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Abbreviations

b :

Equilibrium constant in Langmuir isotherm (L \(\text {g}^{-1}\))

c :

Fluid phase concentration of solute (g \(\text {L}^{-1}\))

\(D_{\text {L}}\) :

axial dispersion coefficient (\({\text {cm}}^{2}\, \text {s}^{-1}\))

H :

Henry constant

L :

Length of column (cm)

m :

Dimensionless flow rate ratio

Pu :

Target product purity (%)

Q :

Volumetric flow rate (\({\text {cm}}^{3}\, \text {s}^{-1}\))

q :

Solid phase concentration of solute (g \(\text {L}^{-1}\))

\(q^*\) :

Solid phase equilibrium concentration of solute (g \(\text {L}^{-1}\))

t :

Time (s)

\(t^*\) :

Switch time (s)

v :

Interstitial velocity (cm \(\text {s}^{-1}\))

x :

Molar fraction on the solid phase

z :

Axial coordinate (cm)

D:

Desorbent

E:

Extract

F:

Feed

i :

Component

j :

SMB section

R:

Raffinate

sat:

Saturation

tot:

Total

\(\varepsilon\) :

Column void fraction

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Acknowledgements

Funding from Natural Science and Engineering Research Council, Canada through Discovery Grants program, Project Number RGPIN-2019-5018, is acknowledged.

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Authors and Affiliations

  1. Department of Chemical and Materials Engineering, Donadeo Innovation Centre for Engineering, University of Alberta, 9211-116 Street NW, Edmonton, AB, T6G 1H9, Canada

    Arvind Rajendran & Rafael Teruo Maruyama

  2. Max Planck Institute for Dynamics of Complex Technical Systems, Sandtorstr. 1, 39106, Magdeburg, Germany

    Héctor Octavio Rubiera Landa & Andreas Seidel-Morgenstern

  3. Georgia Institute of Technology, School of Chemical & Biomolecular Engineering, 311 Ferst Drive N. W., Atlanta, 30332-0100, USA

    Héctor Octavio Rubiera Landa

  4. Otto-von-Guericke-Universität / Lehrstuhl für Chemische Verfahrenstechnik, Universitätsplatz 2, 39106, Magdeburg, Germany

    Andreas Seidel-Morgenstern

Authors
  1. Arvind Rajendran
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  2. Rafael Teruo Maruyama
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  3. Héctor Octavio Rubiera Landa
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  4. Andreas Seidel-Morgenstern
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Correspondence to Arvind Rajendran.

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Rajendran, A., Maruyama, R.T., Landa, H.O.R. et al. Modelling binary non-linear chromatography using discrete equilibrium data. Adsorption 26, 973–987 (2020). https://doi.org/10.1007/s10450-020-00220-9

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  • DOI: https://doi.org/10.1007/s10450-020-00220-9

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