THERMAL SCIENCE

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Numerical approximation of nonlinear chromatographic models considering Bi-Langmuir isotherm

ABSTRACT
In this research article, two standard models of liquid chromatograophy, namely the dispersive equilibrium model (DEM) and the kinetic lumped model (KLM) are approximated numerically. We studied the transport of multi components in a single column of chromatography considering non linear adsorption thermodynamics. The models are analyzed for standard Bi-Langmuir and generalized Bi-Langmuir types adsorption equilibrium isotherms using Danckwert (Robin) boundary conditions. Mathematically, the model equations form a non linear system of partial differential equations accounting for the phenomena of advection and diffusion, paired with an algebraic equation or a differential equation for adsorption isotherm. An extended semi-discrete high-resolution finite volume scheme is employed to obtain the approximate solutions of the governing model equations. The method has second to third order accuracy. Several test case studies are conducted to examine the influence of various critical parameters on the process performance. The contemplated case studies incorporate the elution process of liquid chromatography with an increasing number of components. In particular, single component, two component and three component mixtures are considered for the assessment of process performance. The formulated numerical algorithm provide an efficacious mechanism for investigating the retention behavior and the influence of mass transfer kinetics on the shapes of elution profiles.
KEYWORDS
PAPER SUBMITTED: 2020-08-17
PAPER REVISED: 2020-09-01
PAPER ACCEPTED: 2020-09-04
PUBLISHED ONLINE: 2020-10-10
DOI REFERENCE: https://doi.org/10.2298/TSCI200817298K
REFERENCES
  1. Guiochon, G., Preparative liquid chromatography, J. Chromatogr. A ., 965 (2002), pp. 129-161.
  2. Guiochon, G., Lin, B., Modeling for preparative chromatography, Academic Press., Amsterdam, 2003.
  3. Guiochon, G., Felinger, A., Shirazi, D. G., Katti, A.M., Fundamentals of preparative and nonlinear chromatography, 2nd ed., ELsevier Academic press, New York, 2006.
  4. Ruthven, D.M., Principles of Adsorption and Adsorption Processes, John Wiley and Sons, Wiley-Interscience, New York, 1984.
  5. Lieres, E.V., Andersson, J., A Fast and accurate solver for the general rate model of column liquid chromatography, J. Comput. & Chem. Eng., 34, (2010), 8, pp. 1180-1191.
  6. Javeed, S., Qamar, S., Seidel-Morgenstern, A., Warnecke, G., Efficient and accurate numerical simulation of nonlinear chromatographic processes, J. Comput. Chem. Eng., 35, (2011), 11, pp. 2294-2305.
  7. Qamar, S., Perveen, S., Seidel-Morgenstern, A., Numerical approximation of nonlinear and non-equilibrium twodimensional model of chromatography, J. Comput. Chem. Eng., 94, (2016), pp. 411-427.
  8. Javeed, S., Qamar, S., Seidel-Morgenstern, A., Warnecke, G., A discontinuous Galerkin method to solve chromatographic models, J. Chromatogr. A., 1218, (2011), 40, pp. 7137-7146.
  9. Püttmann, A., Nicolai, M., Behr, M., von Lieres, E., Stabilized space-time finite elements for high-definition simulation of packed bed chromatography, Finite Elem. Anal. Des., 86, (2014), pp. 1-11.
  10. Püttmann, A., Schnittert, S., Leweke, S., von Lieres, E., Utilizing algorithmic differentiation to efficiently compute chromatograms and parameter sensitivities, Chem. Eng. Sci., 139, (2016), pp. 152-162.
  11. Qamar, S., Sattar, F.A., Abbasi, J.N., Seidel-Morgenstern, A., Numerical simulation of nonlinear chromatography with core-shell particles applying the general rate model, Chem. Eng. Sci., 147, (2016), pp. 54-64.
  12. Rouchon, P., Schonauer, M., Valentin, P., Guiochon, G., Numerical Simulation of Band Propagation in Nonlinear Chromatography, Sep. Sci. Technol., 22, (1987), 8-10, pp. 1793-1833.
  13. Cruz, P., Santos, J.C., Magalhaes F.D., Mendes, A., Simulation of separation processes using finite volume method, J. Comput. & Chem. Eng., 30, (2005), 1, pp. 83-98.
  14. Webley, P.A., He, J., Fast solution-adaptive finite volume method for PSA/VSA cycle simulation; 1 single step simulation, J. Comput. & Chem. Eng., 23, (2000), 11-12,pp. 1701-1712.
  15. LeVeque, R.J., Numerical methods for conservation laws, Birkhaüser Verlag, Bassel, Germany, 1992.
  16. Leer, B.V., Towards ultimate conservative finite difference scheme.IV. A new approach to numerical convection. scheme, J. Comput. Phys., 23, (1997), 3, pp. 276-299.
  17. Koren, B., A robust upwind discretization method for advection, diffusion and source terms, Notes on Numerical Fluid Mechanics, chapter 5, in: Numerical Methods for Advection-Diffusion Problems, C.B. Vreugdenhil, B. Koren, Vieweg Verlag, Braunschweig, 45, 1993, pp. 117-138
  18. S. Gottlie., C.-W. Shu., Total Variation Diminishing Runge-Kutta Schemes, Mathematics of Computation., 67, (1998), 221, pp. 73-85.
  19. Dondi, Francesco., Guiochon, G., Theoretical Advancement in Chromatography and Related Separation Techniques, Springer Science+Business Media Dordrecht., Ferrara, Italy, 1992.
  20. Ortner, F., Jermann, S., Joss, L., Mazzotti, M., Equilibrium Theory Analysis of a Binary Chromatographic System Subject to a Mixed Generalized Bi-Langmuir Isotherm., Ind. Eng. Chem. Res., 54, (2015), 45, pp. 11420-11437.
  21. Gritti, F., Guiochon, G., Analytical Solution of the Ideal Model of Chromatography for a Bi-Langmuir Adsorption Isotherm., Anal. Chem., 85, (2013), 81, pp. 8552-8558.
  22. Demin. A. A., Melenevsky.T.A., Bi-Langmuir Isotherms' Applicability for Description of Interaction of Ion-Exchange Sorbents with Protein Mixtures., J. Chromatogr. Sci.., 44, (2006),pp. 181-186.
  23. Mazzotti, M., Local equilibrium theory for the binary chromatography of species subject to a generalized langmuir isotherm Ind. Eng. Chem. Res., 45, (2006), 15, pp. 5332-5350.
  24. Mazzotti, M., Nonclassical composition fronts in nonlinear chromatography: Delta-shock. Ind. Eng. Chem. Res., 48, (2009),16, pp. 7733-7752.
  25. Danckwerts, P.V., Continuous flow system Distribution of residence times, J. Chem. Eng. Sci., 2, (1953), 1, pp. 1-13.
  26. Sweby, P.K., High resolution schemes using flux limiters for hyperbolic conservation laws, SIAM J. Numer. Anal., 21, (1984), 5, pp. 995-1011.
  27. Roe, P.L., Characteristic-based schemes for the Euler equations, Annual Review of Fluid Mechanics., 18, (1986), pp. 337-365.
  28. Leer, B.V., Towards ultimate conservative finite difference scheme.2. Monotonicity and conservation combined in a second-order scheme, J. Comput. Phys., 14, (1974), 4, pp. 361-370.
  29. Kondrat, S., Zimmermam, O., Wiechert, W., von-Lieres, E., Discrete-continuous reaction-diffusion model with mobile point-like sources and sinks, Eur. Phys. J. E., 39, (2016), 1, pp. 11.
  30. Leweke, S., von-Lieres, E., Fast arbitrary order moments and arbitrary precision solution of the general rate model of column liquid chromatography with linear isotherm, Comput & Chem. Eng., 84, (2015), pp. 350-362.
  31. Ghosh, P., Vahedipour, K., Leuthold, M., von-Lieres, E., Model-based analysis and quantitative prediction of membrane chromatography: Extreme scale-up from 0.08 ml to 1200 ml. J. Chromatogr. A., 1332, (2014), pp. 8-13.