The dead zone in a catalyst particle for fractional‐order reactions

Garcı́a-Ochoa, Félix; Salvador, Alfredo

doi:10.1002/aic.690341120

Cited by 9 publications

(4 citation statements)

References 6 publications

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“…Unfortunately, there is not enough available information on sufficient conditions. They have been published only for powerlaw type kinetics by York (2011) and much earlier by Garcia-Ochoa and Romero (1988) for the simplest reaction (A→R), and for more complex cases (e.g., consecutive parallel reaction) by Andreev (2013). One can conclude that, in many practical cases, sufficient conditions for dead zone formation are unavailable.…”

Section: Foundations Of the Dead Zone Problemmentioning

confidence: 99%

Efficient numerical method for solution of boundary value problems with additional conditions

Szukiewicz

2017

Braz. J. Chem. Eng.

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-An efficient numerical method for solution of boundary value problems with additional condition is presented. The approach is based on the shooting method but the procedure of seeking "the proper shot" allows one to satisfy "additional" boundary conditions. General considerations are illustrated by a real example. The computational example concerns the "dead zone" regime for the non-linear diffusion-reaction equation in heterogeneous catalysis. Accuracy and efficiency of the presented method confirm results obtained for a wide range of changes of process parameters, including the vicinity of a critical point. Calculations were performed with the use of the Maple® program.

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Section: Foundations Of the Dead Zone Problemmentioning

confidence: 99%

Efficient numerical method for solution of boundary value problems with additional conditions

Szukiewicz

2017

Braz. J. Chem. Eng.

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“…Next, the following authors analyzed the problems of existence and formation of the dead core theoretically: Diaz and Hernandez, 3 Bandle and Stackgold, 4 Bobisud 5 . Different generation terms were tested by Bobisud and Royalty, 6 Fedotov, 7 Garcia‐Ochoa and Romero, 8 and then it led to the formulation of conditions that have to be satisfied for a dead zone formation for selected kinetic equations (so‐called necessary conditions of a dead zone formation). The sufficient conditions of a dead zone formation for the simplest kinetic equation were presented by Garcia‐Ochoa and Romero 8 .…”

Section: Introductionmentioning

confidence: 99%

“…Different generation terms were tested by Bobisud and Royalty, 6 Fedotov, 7 Garcia‐Ochoa and Romero, 8 and then it led to the formulation of conditions that have to be satisfied for a dead zone formation for selected kinetic equations (so‐called necessary conditions of a dead zone formation). The sufficient conditions of a dead zone formation for the simplest kinetic equation were presented by Garcia‐Ochoa and Romero 8 . Extended results of this topic were also published by Andreev 9 and Szukiewicz et al 10 The theoretical prediction of a dead zone formation was confirmed experimentally both for the heterogeneous catalysis processes (e.g., for methanol steam reforming over Cu/ZnO/Al 2 O 3 catalyst by Lee et al, 11 for hydrogenation of benzene over nickel‐alumina catalyst by Jiracek et al, 12 for acetic acid oxidation by Levec et al 13 and Look and Smith, 14 for hydrogenation of propylene reaction carried out on commercial Ni catalyst pellets by Szukiewicz et al 15 ) and the bioprocesses (for cephalosporin C production processes by Araujo et al, 16 Cruz et al, 17 for the process of Penicillin G enzymatic hydrolysis by Cascaval et al, 18 for the process of 3‐chloro‐1,2‐propanediol degradation by Konti et al, 19 in an anaerobic fixed‐bed reactor by Zaiat et al, 20 in catalytic particles containing immobilized enzymes for the Michaelis–Menten kinetics by Pereira and Oliveira 21 ).…”

Section: Introductionmentioning

confidence: 99%

An efficient and robust method for numerical analysis of a dead zone in catalyst particle and packed bed reactor

Kaczmarski

Szukiewicz

2021

Engineering Reports

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Zones without reactants inside a catalyst pellet, the so‐called dead zones (DZs), have been reported in the case of catalysis and biocatalysis, two processes of fundamental importance. The presence of the DZ results from diffusional transport limitations when an apparent reaction order is in the range: −1 to 1. The formation of a DZ reduces the effectiveness of a catalyst and affects packed bed reactor productivity. For a simple reaction kinetic model, the width of a DZ inside a pellet can be predicted analytically by solving the appropriate differential mass balance model. However, for more complex kinetic models, the analytical solution is unknown, and a DZ position can be established only by applying a numerical method. The problem with the DZ appearance belongs to problems with moving boundaries. Its solution requires the application of a particular numerical procedure and a relatively long CPU time. In this work, a simple, high‐speed numerical method for the calculation of a DZ position inside a pellet is proposed. The proposed method, combined with the orthogonal collocation on finite elements can be applied to analyze a packed bed reactor operation.

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“…On the other hand, negative concentration values in the analytical solution are avoided by introducing a pellet dead zone where chemical reaction is inactive. The idea of using a particle dead zone is borrowed from studies of a fractional order reaction in catalyst particles where a nonactive region within the particle may exist. − Similar to the method reported by Szukiewicz and Petrus, the result is an implicit EF estimate where two nonlinear equations on the average concentration and the dead-zone position must be solved numerically. Illustrations by means of numerical simulations show that the incorporation of a dead zone adds an important improvement in the prediction of EF when compared with previously reported results. , …”

Section: Introductionmentioning

confidence: 99%

Short-Cut Method for the Estimation of Isothermal Effectiveness Factors

Ochoa‐Tapia

Valdés‐Parada

Álvarez‐Ramírez

2005

Ind. Eng. Chem. Res.

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The computation of effectiveness factors (EFs) is commonly used for simplifying heterogeneous models of catalytic processes. To do this, the reaction rate in a catalyst pellet is expressed by its rate under surface/bulk conditions multiplied by a functional factor, namely, the EF. When many EF evaluations are required, it is desirable to dispose of short-cut methods to alleviate the computational burden. Existing short-cut methods are based on the availability of analytical solutions for a related linear, but nonhomogeneous, approximation to the nonlinear kinetics. However, the nonhomogeneous term can lead to spurious solutions, such as the presence of negative concentration values. This paper proposes a derivation of the EF short-cut method as an iteration procedure in the average concentration. On the other hand, aimed at avoiding negative concentration values, the proposed linear boundary-value problem is equipped with a nonactive region. In this way, the short-cut method is composed of two nonlinear equations on the average concentration and the position of the boundary between the active and nonactive regions. Numerical results show that such a modification increases the prediction capacity of EF short-cut methods for a practically acceptable Thiele modulus region.

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The dead zone in a catalyst particle for fractional‐order reactions

Cited by 9 publications

References 6 publications

Efficient numerical method for solution of boundary value problems with additional conditions

Efficient numerical method for solution of boundary value problems with additional conditions

An efficient and robust method for numerical analysis of a dead zone in catalyst particle and packed bed reactor

Short-Cut Method for the Estimation of Isothermal Effectiveness Factors

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