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Thiele modulus having regard to the anomalous diffusion in a catalyst pellet

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  • Zhokh, Alexey
  • Strizhak, Peter

Abstract

In the present paper, Thiele modulus (TM) for a catalytic reaction with the anomalous diffusion of a reagent in a catalyst pellet is introduced. Different cases of the TM are considered related to the anomalous diffusion process governed by a diffusion equation with the space-fractional, time-fractional, and space-time fractional derivatives. In addition, each fractional derivative is used according to the Caputo and the Riemann–Liouville definitions. Closed-form expressions of the TM for each definition of the fractional derivative are provided. For the time-fractional derivative, the TM is obtained under the assumption of the reaction dynamics nonlinearity. We demonstrate and critically discuss the applicability of the TM obtained for the reaction-diffusion equation with non-integer order derivatives to the evaluation of the parameters of the heterogeneous catalytic process.

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  • Zhokh, Alexey & Strizhak, Peter, 2018. "Thiele modulus having regard to the anomalous diffusion in a catalyst pellet," Chaos, Solitons & Fractals, Elsevier, vol. 109(C), pages 58-63.
    • Handle: RePEc:eee:chsofr:v:109:y:2018:i:c:p:58-63
    DOI: 10.1016/j.chaos.2018.02.016
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    1. Bolster, Diogo & Benson, David A. & Singha, Kamini, 2017. "Upscaling chemical reactions in multicontinuum systems: When might time fractional equations work?," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 414-425.
    2. Povstenko, Yuriy, 2015. "Time-fractional thermoelasticity problem for a sphere subjected to the heat flux," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 327-334.
    3. Weberszpil, J. & Lazo, Matheus Jatkoske & Helayël-Neto, J.A., 2015. "On a connection between a class of q-deformed algebras and the Hausdorff derivative in a medium with fractal metric," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 436(C), pages 399-404.
    4. Changpin Li & Deliang Qian & YangQuan Chen, 2011. "On Riemann-Liouville and Caputo Derivatives," Discrete Dynamics in Nature and Society, Hindawi, vol. 2011, pages 1-15, March.
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    Cited by:

    1. Zik, N.A.F.A. & Sulaiman, S. & Jamal, P., 2020. "Biodiesel production from waste cooking oil using calcium oxide/nanocrystal cellulose/polyvinyl alcohol catalyst in a packed bed reactor," Renewable Energy, Elsevier, vol. 155(C), pages 267-277.

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