Advanced Theoretical Analysis in Chemical Engineering

Constales, Denis; Yablonsky, Gregory S.; D’hooge, Dagmar; Thybaut, Joris; Marin, Guy

doi:10.1016/b978-0-444-59485-3.00011-4

Cited by 6 publications

(4 citation statements)

References 22 publications

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“…The deduction of chemical models from experimental observations is a central problem of current chemical kinetics [1][2][3][4][5][6][7][8][9]. In practice, elementary reactions can seldom be investigated without the interference of other processes as kinetic coupling is a very common phenomenon.…”

Section: Introductionmentioning

confidence: 99%

Double Exponential Evaluation under Non-Pseudo-First-Order Conditions: A Mixed Second-Order Process Followed by a First-Order Reaction

Kiss

Ősz

2017

Int. J. Chem. Kinet.

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In this paper, a double exponential approximating approach is described for a quite common kinetic model (mixed second‐order formation of an intermediate followed by its first‐order decay) under non‐pseudo–first‐order conditions (i.e., when the initial ratio of the two reactants is between 1 and 10). For the evaluation, first the exact kinetic curves predicted by the two‐step model were calculated and then fitted to a double exponential function. The goodness of the fits and the estimated parameters of the double exponential function for both I and P concentrations were determined as a function of the rate constants and initial concentrations in the two‐step model. It was found that the fit of the double exponential function is acceptable or very good under these conditions despite the fact that none of the reagents is in a large excess. Since UV–vis absorption spectroscopy is probably the most common technique to follow kinetic traces, we also made efforts to deal with the typical properties of monitoring the process through UV–vis. It was found that the experimental curves can be fitted quite well with a double exponential function if the reagents have minor absorption compared to the intermediate and/or product. The connection between the observed rate constants and the rate constants of the above‐mentioned mechanism is also studied.

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Section: Introductionmentioning

confidence: 99%

Double Exponential Evaluation under Non-Pseudo-First-Order Conditions: A Mixed Second-Order Process Followed by a First-Order Reaction

Kiss

Ősz

2017

Int. J. Chem. Kinet.

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“…A graph is a combination of nodes (points) and edges (lines) [2], while a cyclic graph involves finite sequences of edges with the single node (from where it begins and ends).…”

Section: Linear Algebra and Graph Theorymentioning

confidence: 99%

Complex Reactions and Dynamics

Shahzad¹,

Sultan²

2018

Advanced Chemical Kinetics

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Starting from the general idea of reaction kinetics, their classification, concentrations, and chemical equilibrium, we will focus on their activation energy and complexity arising during the chemical reaction. As in complex and higher-dimensional chemical problems, we need special arrangements, specifically, in the case when a system attains different completion paths or several routes. The stiffness of the system can be removed if we distinctly measure their available reaction routes and get a comparison between them and overall reactions. Secondly, the construction and comparison of the invariant region of the manifold based on the modern decomposition techniques in different available reaction routes allow us to discuss the dynamical properties of the system.

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“…It is particularly demonstrated that by contrast to the model based on the standard Fick's diffusion, dead-core solutions exist in the case of first-order reactions. Also, the relationship between critical Thiele moduli for models based on the generalized and standard Fick's diffusion fluxes is established.Nonlinear diffusion-reaction equations are important mathematical tools to understand and quantify phenomena arising in heterogeneous catalysis [1][2][3][4][5][6][7][8][9][10][11] . In petrochemical and chemical industries, chemical reactions are commonly carried out in reactors containing catalyst pellets 12,13 .…”

mentioning

confidence: 99%

“…Nonlinear diffusion-reaction equations are important mathematical tools to understand and quantify phenomena arising in heterogeneous catalysis [1][2][3][4][5][6][7][8][9][10][11] . In petrochemical and chemical industries, chemical reactions are commonly carried out in reactors containing catalyst pellets 12,13 .…”

mentioning

confidence: 99%

Analysis of dead-core formation in catalytic reaction and diffusion processes with generalized diffusion flux

Skrzypacz

Kabduali

Kadyrbek

et al. 2022

Sci Rep

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Dead-core and non-dead-core solutions to the nonlinear diffusion–reaction equation based on the generalized diffusion flux with gradient-dependent diffusivity and the power-law reaction kinetics in catalyst slabs are established. The formation of dead zones where the reactant concentration vanishes is characterized by the critical Thiele modulus that is derived as a function of reaction order and diffusion exponent in the generalized diffusion flux. The effects of reaction order and diffusion exponent on the reactant concentration distribution in the slab and dead-zone length are analyzed. It is particularly demonstrated that by contrast to the model based on the standard Fick’s diffusion, dead-core solutions exist in the case of first-order reactions. Also, the relationship between critical Thiele moduli for models based on the generalized and standard Fick’s diffusion fluxes is established.

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Advanced Theoretical Analysis in Chemical Engineering

Cited by 6 publications

References 22 publications

Double Exponential Evaluation under Non-Pseudo-First-Order Conditions: A Mixed Second-Order Process Followed by a First-Order Reaction

Double Exponential Evaluation under Non-Pseudo-First-Order Conditions: A Mixed Second-Order Process Followed by a First-Order Reaction

Complex Reactions and Dynamics

Analysis of dead-core formation in catalytic reaction and diffusion processes with generalized diffusion flux

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