Linear general rate model of chromatography for core–shell particles: Analytical solutions and moment analysis

Qamar, Shamsul; Abbasi, Javeria Nawaz; Mehwish, Aqsa; Seidel‐Morgenstern, Andreas

doi:10.1016/j.ces.2015.06.053

Cited by 24 publications

(52 citation statements)

References 55 publications

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“…Our research group has solved analytically the linear one-dimensional (1D) and two-dimensional (2D) models of nonreactive and reactive chromatography. [11][12][13][14][15][16] The current work extends our previous analysis on 1D-GRM 17 to the analysis of linear two-component reactive 2D-GRM considering both axial and radial concentration gradients. Analytical solutions of the model for irreversible and reversible reactions are derived by applying the Hankel transformation, the Laplace transformation, the eigendecomposition technique, and the conventional solution technique for ordinary differential equations (ODEs).…”

Section: Introductionmentioning

confidence: 91%

“…Most notable among them are the equilibrium dispersive model, the lumped kinetic model, and the general rate model (GRM). 4,5,[7][8][9][10][11] All these models are characterized by different levels of complexities used in them. Our research group has solved analytically the linear one-dimensional (1D) and two-dimensional (2D) models of nonreactive and reactive chromatography.…”

Section: Introductionmentioning

confidence: 99%

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Analysis of two‐dimensional models for liquid chromatographic reactors of cylindrical geometry

Uche

Qamar

Seidel‐Morgenstern

2019

Int J of Chemical Kinetics

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This work presents the analytical solutions of two-dimensional isothermal reactive general rate models for liquid chromatographic reactors of cylindrical geometry. Both irreversible and reversible reactions are considered. The model equations form a linear system of convection-diffusion-reaction partial differential equations coupled with algebraic equations for isotherms. Analytical solutions are derived by integrated implementation of finite Hankel transform, Laplace transform, eigen-decomposition technique, and conventional ordinary differential equations solution technique. To verify the analytical results, a high-resolution finite volume scheme is also applied to numerically approximate the model equations. The current results can be very useful to optimize and upgrade the liquid chromatographic reactors. K E Y W O R D S analytical solutions, general rate model, liquid chromatography, numerical solutions, reactions and separations Int J Chem Kinet. 2019;51:563-578.

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Section: Introductionmentioning

confidence: 91%

Section: Introductionmentioning

confidence: 99%

Analysis of two‐dimensional models for liquid chromatographic reactors of cylindrical geometry

Uche

Qamar

Seidel‐Morgenstern

2019

Int J of Chemical Kinetics

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“…[20][21][22] Recently, we have also derived analytical solutions and moments of the linear GRM for core-shell particles. [23] In all these derivations, the Laplace transformation was applied as a basic tool to derive analytical solutions. As analytical Laplace inversion was not possible in most of the cases.…”

Section: Introductionmentioning

confidence: 99%

“…These moments can be used to measure retention times, band broadenings, front asymmetries and kurtosis of the elution profiles. Moment analysis and matching is wellknown and instructive in the literature, [2,23,[26][27][28][29][30][31][32][33][34][35][36][37][38][39] and references therein. A high resolution finite volume scheme (HRFVS) was also applied to numerically approximate the linear and nonlinear GRM for fully-porous and core-shell particles.…”

Section: Introductionmentioning

confidence: 99%

“…A high resolution finite volume scheme (HRFVS) was also applied to numerically approximate the linear and nonlinear GRM for fully-porous and core-shell particles. [23,40] This manuscript focuses on the derivation of relations among the essential kinetic parameters of the GRM and the two simpler LKM and EDM models for usage of columns packed with core-shell particles. These relations are derived by matching the corresponding temporal moments of the mentioned three models for linear isotherms.…”

Section: Introductionmentioning

confidence: 99%

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Relations between kinetic parameters of different column models for liquid chromatography applying core-shell particles

Qamar

Bashir

Perveen

et al. 2019

Journal of Liquid Chromatography & Related Technologies

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This article presents analytical solutions of the general rate model (GRM), the lumped kinetic model (LKM), and the simpler equilibrium dispersive model (EDM) for core-shell particles and linear adsorption isotherms. The solutions in the Laplace domain are applied to derive analytical expressions for the temporal moments of these models. The results provide relations between the model specific kinetic parameters by matching one or more of the temporal moments. Several case studies are considered for illustration. The results show that simpler models are in many cases as good as the most detailed GRM if their kinetic parameters fulfill the matching relations. Thus, it is possible to reliably predict elution profiles using the simpler models. The derived analytical expressions can also be utilized to efficiently estimate model parameters from experimentally observed elution profiles to further optimize core-shell particles and to identify suitable column sizes and operating conditions. GRAPHICAL ABSTRACT 0 10 20 30 40 50 60 70 80 90 0 0.1 0.2 0.3 0.4 0.5 t [min] c [g/l] GRM LKM EDM u = 1 cm/min KEYWORDS Core-shell particles; Liquid chromatography; mathematical models; moment analysis; matching relations; semi-analytical solutions rate model (GRM), the lumped kinetic model (LKM), and the equilibrium dispersive model (EDM). [1,2] Hereby, the GRM is the most detailed model, while the LKM and EDM have less degrees of freedom and are simpler. It accounts for various mass transfer kinetics that influence the band profiles, namely external mass transfer resistance and intraparticle diffusion. In addition axial dispersion is

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Modeling of Chromatographic Processes*

Seidel‐Morgenstern¹

2020

Preparative Chromatography

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Linear general rate model of chromatography for core–shell particles: Analytical solutions and moment analysis

Cited by 24 publications

References 55 publications

Analysis of two‐dimensional models for liquid chromatographic reactors of cylindrical geometry

Analysis of two‐dimensional models for liquid chromatographic reactors of cylindrical geometry

Relations between kinetic parameters of different column models for liquid chromatography applying core-shell particles

Modeling of Chromatographic Processes*

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