Secondary effectiveness factors for catalytic reactions in series: extension to slab, cylindrical, and spherical geometries

Zadeh, Armin Shayesteh; Peters, Baron

doi:10.1039/d0re00242a

Cited by 13 publications

(3 citation statements)

References 11 publications

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“…Indeed, realistic models have many aspects and can include complex reaction mechanisms as well as nonisothermal particles. Particular cases include consecutive and parallel reactions [23,29], reaction orders different than unity [18,19,24], absorption [14], geometrical aspects [16,35], isothermal and nonisothermal Langmuir-Hinshelwood kinetics [20,26,34,38], possibly with dissociative adsorption [31]. One class of distinct important BVPs arises when one accounts for mass and heat transfer by convection at the surface of the catalyst particle.…”

Section: Industrial Processes Main Reaction Catalysts Usagesmentioning

confidence: 99%

Solving boundary value problems in heterogeneous catalysis with orthogonal collocation and arc‐length continuation

Von‐Held Soares,

Binous,

Peixoto

et al. 2023

Comp Applic In Engineering

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An important part of the education of chemical engineers involves the design and assessment of heterogeneous catalytic reactions. They pose fundamental phenomena and constitute invaluable industrial processes. Progressing in this field, especially in graduate‐level courses, entails solving nonlinear differential equations systems, which can only be achieved by using efficient and reliable numerical techniques. In this work, we solve nonisothermal one‐dimensional reaction‐diffusion BVP considering convection in the boundary conditions, by applying orthogonal collocation and arc‐length continuation. Particularly, we predict the effectiveness factor as a function of the Thiele modulus for the main three particle geometries: plane slab, cylinder, and sphere. For chemical engineering students, such problems are at the zenith of the discipline, and the results of such calculations can elucidate basic and advanced concepts of mass and heat transfer as well as chemical reaction engineering. Both Chebyshev and shifted Legendre polynomials were used to transform the boundary value problem into a set of algebraic nonlinear equations. In addition, we also compare our findings against the available analytic solutions whenever possible. Codes in Scilab, Matlab®, and Mathematica© were developed for the solution of such problems and are available in the Supporting Information. There are two possible approaches to compute effectiveness factors: (a) integration as per definition versus (b) differentiation and nonlinear system. It is demonstrable that software performance is dependent on the approach, and that the differentiation approach yields better results.

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Section: Industrial Processes Main Reaction Catalysts Usagesmentioning

confidence: 99%

Solving boundary value problems in heterogeneous catalysis with orthogonal collocation and arc‐length continuation

Von‐Held Soares,

Binous,

Peixoto

et al. 2023

Comp Applic In Engineering

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show abstract

“…Yet, Peters et al successfully developed an analytical solution for the reaction-diffusion model for two reactions in series A->B->C occurring within a slab in which the secondary effectiveness factor was derived and deployed in a plug flow and stirred batch framework for theoretical prediction of solvent−solid phase partitioning and interior mass transfer limitations in catalytic reactions in series 27 . In his follow-up paper, the analytical solution was extended to spherical and cylindrical geometries 28 . In the same year, a system of reaction-diffusion model equations involving multiple reactions was also solved analytically using eigen analysis by Lattanzi et al 26 , with the internal effectiveness factor obtained by integrating the concentration profile using the multistep effectiveness vector (MEV) and DNS.…”

Section: Introductionmentioning

confidence: 99%

Strategy to enhance selectivity in a two-step reaction using the R1-R2-D reactions-diffusion phenomena

Najimu

Adamu

Kareem

et al. 2023

Preprint

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An analytically derived criterion for R1-R2 phenomenon is combined with the Weisz criterion for R1-D phenomenon to allow the development of assignment criteria for the overall controlling factors in R1-R2-D phenomena. The overall assignment criteria are found to be dependent on the internal effectiveness factors η_1 and η_2, as well as the rate of the individual reactions at the surface of the catalyst particle. Applying the developed criteria to a two-step methanol oxidation reaction suggests that the selectivity of the formaldehyde intermediate species can be enhanced at high reaction temperature when catalysts are specifically designed to enhance the rate of formaldehyde formation. However, CO formation needs to be suppressed to enhance selectivity towards formaldehyde at moderately low temperature. This reaction-diffusion theoretical framework provides guidance for the development of highly selective catalyst for two-reactions-in-series systems and can be extended for higher-number multiple reactions in series and in parallel.

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“…Recently, Peters 10 calculated the effectiveness factor for the second step in a A → B → C reaction sequence with first‐order kinetics and slab geometry. In a subsequent work, 11 the model was generalized for the other two main geometries. Olatunde et al 12 .…”

Section: Introduction and Problem Statementmentioning

confidence: 99%

The influence of dissociative adsorption on effectiveness factors of porous catalysts

Soares

2022

Int J of Chemical Kinetics

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The actual concentration profile of a reacting fluid inside a porous catalyst is something of a mystery. However, there are powerful models to predict the concentration distribution, and effectiveness factor as a function of the Thiele modulus. This work provides a model for the porous catalyst particle considering heterogeneous kinetics for steady‐state Langmuir‐Hinshelwood rate expressions, including the cases when adsorption stoichiometry is other than 1:1, as for dissociative adsorption (1:2), which have not been covered by the preceding literature. The isothermal and the non‐isothermal particles are considered. Numerical solutions for the concentration profile of a limiting reactant were calculated by three methods: finite differences with Newton‐Raphson recursion, Chebyshev orthogonal collocation, and integration by Adams method as done by Weisz and Hicks. The Weisz‐Hicks method outperformed the other two. Plots show the results for specific cases, which are briefly discussed. Adsorption stoichiometry and pellet geometry are of paramount importance for the assessment of effectiveness factors. The results demonstrate that the effectiveness of a catalyst pellet with prevalent dissociative adsorption of a reactant is always inferior to the effectiveness with prevalent simple adsorption.

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Secondary effectiveness factors for catalytic reactions in series: extension to slab, cylindrical, and spherical geometries

Abstract: ‘Secondary’ effectiveness factors are developed for reactions in series that are useful for controlling the yield of the intermediate product (B).

Cited by 13 publications

References 11 publications

Solving boundary value problems in heterogeneous catalysis with orthogonal collocation and arc‐length continuation

Solving boundary value problems in heterogeneous catalysis with orthogonal collocation and arc‐length continuation

Strategy to enhance selectivity in a two-step reaction using the R1-R2-D reactions-diffusion phenomena

The influence of dissociative adsorption on effectiveness factors of porous catalysts

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