2016
DOI: 10.1007/s00449-016-1647-0
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Abstract: In this article, the occurrence of dead core in catalytic particles containing immobilized enzymes is analyzed for the Michaelis-Menten kinetics. An assessment of numerical methods is performed to solve the boundary value problem generated by the mathematical modeling of diffusion and reaction processes under steady state and isothermal conditions. Two classes of numerical methods were employed: shooting and collocation. The shooting method used the ode function from Scilab software. The collocation methods in… Show more

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Cited by 12 publications
(13 citation statements)
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“…Michaelis‐Menten kinetics, as was mentioned in the Introduction, is a commonly applied equation to describe enzyme catalyzed reactions. This equation can also be found in dead core models . However, the application of these kinetics to the dead core model can produce ambiguous solutions.…”
Section: Mathematical Considerationsmentioning
confidence: 99%
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“…Michaelis‐Menten kinetics, as was mentioned in the Introduction, is a commonly applied equation to describe enzyme catalyzed reactions. This equation can also be found in dead core models . However, the application of these kinetics to the dead core model can produce ambiguous solutions.…”
Section: Mathematical Considerationsmentioning
confidence: 99%
“…The considered kinetic belongs to the ones that do not meet the necessary condition of dead zone existence. In another study, in the numerical simulation, the authors assumed that, for a sufficiently small value of concentration inside, the bioparticle dead zone will appear. However, the solution depends on the arbitrary accepted value of concentration.…”
Section: Mathematical Considerationsmentioning
confidence: 99%
See 1 more Smart Citation
“…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%
“…Additionally, many popular algorithms for differential equation solving fail in such a case. The tests of a few popular algorithms employed to the dead‐zone problem solution have been presented in the source already cited 21 . Among the troubles reported are: a divergence, a low rate of convergence, and a high complexity of programming.…”
Section: Introductionmentioning
confidence: 99%