Analysis of Linear General Rate Model of Reactive Chromatography for Core–Shell Adsorbents

Qamar, Shamsul; Bashir, Seemab; Perveen, Sadia; Seidel‐Morgenstern, Andreas

doi:10.1021/acs.iecr.7b01949

Cited by 5 publications

(10 citation statements)

References 58 publications

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“…The effects of the intraparticle diffusion resistance and the external film mass transfer resistance on the effectiveness factor of an inert-core catalyst are presented in Figures 4a-4c, where effectiveness factor h b as a function of the shell thickness j C for various values of f 2 at Bi ¼ 100 (a), Bi ¼ 10 (b), and Bi ¼ 1 (c), is calculated by Equation (32). The Thiele modulus f stands for the ratio of the reaction rate to the intraparticle diffusion rate which is a measure of whether the process is reaction rate controlled (low f value) or diffusion rate controlled (high f value); the Biot number Bi is the ratio of the intraparticle diffusion resistance to the external film mass transfer resistance, which is characterized by the mass transfer limitations that include the external film mass transfer resistance and the intraparticle diffusion resistance.…”

Section: Resultsmentioning

confidence: 99%

“…However, newly developed batch and fixed bed reactors with applications use inert‐core spherical particles, and those solutions are no longer valid to predict the concentration time relationship or the elution curves for inert‐core catalysts. Some investigations have been done for reactive chromatography for inert‐core adsorbents . It is therefore most desirable to develop a mathematical model and present the analytical solutions for batch and fixed bed reactors with inert‐core catalysts.…”

Section: Introductionmentioning

confidence: 99%

“…Some investigations have been done for reactive chromatography for inert-core adsorbents. [30][31][32] It is therefore most desirable to develop a mathematical model and present the analytical solutions for batch and fixed bed reactors with inert-core catalysts.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Modelling diffusion and reaction for inert‐core catalyst in batch and fixed bed reactors

Xiu²,

Rodrigues

2018

Can J Chem Eng

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New analytical solutions of concentration time curves are derived for an isothermal inert‐core spherical catalyst based on the mathematical models by taking into account first‐order irreversible reaction and mass transfer resistances in batch and fixed bed reactors. The effects of mass transfer resistances and Thiele modulus on catalytic efficiency and conversion of reactant are examined over a wide range of parameters for an inert‐core catalyst. The results show that the inert‐core catalyst can significantly improve the efficiency for fast catalytic reactions, where mass transfer limitations occur; however, the reactant conversion will decrease due to a lower loading ratio of active species of catalyst for inert‐core catalyst.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Modelling diffusion and reaction for inert‐core catalyst in batch and fixed bed reactors

Xiu²,

Rodrigues

2018

Can J Chem Eng

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“…Bashir et al discussed reactive liquid chromatography considering two components for fully porous beads. Qamar et al highlight the impact of core–shell adsorbents on the reactive GRM of liquid chromatography.…”

Section: Introductionmentioning

confidence: 99%

Analysis of Liquid Chromatography Considering a Linear Single-Component Heterogeneous-Type Reactive General Rate Model

Alharbi,

Bashir,

Ramzan

et al. 2023

ACS Omega

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This paper elaborates on the significance of liquid chromatography for a single-component reactive linear general rate model. The model equations consist of a set of two coupled partial differential equations, which include diffusion, interfacial mass transfer, axial dispersion, external and intraparticle pore diffusivity, and heterogeneous chemical reaction of the first order with two sets of boundary conditions. The model equations are solved by the Laplace transformation. The actual time domain solution is obtained by numerical Laplace inversion, as analytical inversion cannot be obtained. The graphical sketch of different physical parameters is presented to analyze the dynamics of the elution profiles. The result indicates that the chromatographic reactor works more efficiently on increasing the value of the heterogeneoustype first-order reaction. To check the analytical results, a second-order high-resolution finite volume scheme is used. Both results are in good agreement and indicate the correctness of the numerical scheme. The current work is also compared with the previously available numerical schemes, which shows that the proposed numerical scheme is better for elaborating the chromatographic reactor performance. A comparison table is also presented to compute error analysis and computational run time for analyzing the efficiency of the reactor. A graphical sketch of the numerical temporal moment analysis is also presented, which gives significant information about the performance and the shape of the concentration profiles.

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“…Eventually, the use of core–shell particles as the stationary phase has been found advantageous over the use of nonporous and porous packing particles for achieving higher efficiencies and greater resolution of the components in a mixture. The thin porous layers on the solid impermeable cores provide shorter intraparticle-diffusion pathways, forcing the peaks of elution curves to be narrow. − ,− ,, Various theoretical studies exist in the literature for analytical chromatography using core–shell particles. ,,,,− , …”

Section: Introductionmentioning

confidence: 99%

Two-Dimensional General Rate Model of Liquid Chromatography Incorporating Finite Rates of Adsorption–Desorption Kinetics and Core–Shell Particles

Brhane

Qamar

Seidel‐Morgenstern

2019

Ind. Eng. Chem. Res.

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A two-dimensional general rate model of liquid chromatography incorporating slow rates of adsorption−desorption kinetics, axial and radial dispersions, and core−shell particles is formulated. Radial concentration gradients are generated inside the column by considering different regions of injection at the inlet. Analytical solutions are obtained for a single-component linear model by simultaneously utilizing the Laplace and Hankel transformations for the considered two sets of boundary conditions. These linear solutions are useful for simulating liquid-chromatographic columns with diluted or small-volume samples and those in which radial concentration gradients are significant. To gain further insight into the process, analytical moments are also deduced from the Laplace−Hankel-domain solutions. For situations of concentrated and large-volume samples, which are not solvable analytically, formulation of nonlinear models is necessary. In this study, a semidiscrete, high-resolution, finite-volume scheme is extended to approximate the resulting nonlinear-model equations for multicomponent mixtures. The performance of the column is analyzed by implementing a specified criterion of performance. A few numerical case studies are conducted to inspect the effects of the model parameters on the elution profiles.

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Analysis of Linear General Rate Model of Reactive Chromatography for Core–Shell Adsorbents

Cited by 5 publications

References 58 publications

Modelling diffusion and reaction for inert‐core catalyst in batch and fixed bed reactors

Modelling diffusion and reaction for inert‐core catalyst in batch and fixed bed reactors

Analysis of Liquid Chromatography Considering a Linear Single-Component Heterogeneous-Type Reactive General Rate Model

Two-Dimensional General Rate Model of Liquid Chromatography Incorporating Finite Rates of Adsorption–Desorption Kinetics and Core–Shell Particles

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