Mathematical Model of Synthesis Catalyst with Local Reaction Centers

• Published in: Matematika i matematicheskoe modelirovanie no. 3; pp. 13 - 31
• Main Authors: I. V. Derevich, A. Yu. Fokina
• Format: Journal Article
• Language: Russian
• Published: MGTU im. N.È. Baumana 01.07.2017
• Subjects: catalytic reactions; cobalt catalyst; fischer-tropsch synthesis; heat explosion; legendre polynomials; porous catalyst granule; synthesis gas; thermal effect of synthesis reactions
• ISSN: 2412-5911
• DOI: 10.24108/mathm.0317.0000071

The article considers a catalyst granule with a porous ceramic passive substrate and point active centers on which an exothermic synthesis reaction occurs. A rate of the chemical reaction depends on the temperature according to the Arrhenius law. Heat is removed from the pellet surface in products of synthesis due to heat transfer. In our work we first proposed a model for calculating the steady-state temperature of a catalyst pellet with local reaction centers. Calculation of active centers temperature is based on the idea of self-consistent field (mean-field theory). At first, it is considered that powers of the reaction heat release at the centers are known. On the basis of the found analytical solution, which describes temperature distribution inside the granule, the average temperature of the reaction centers is calculated, which then is inserted in the formula for heat release. The resulting system of transcendental algebraic equations is transformed into a system of ordinary differential equations of relaxation type and solved numerically to achieve a steady-state value. As a practical application, the article considers a Fischer-Tropsch synthesis catalyst granule with active cobalt metallic micro-particles. Cobalt micro-particles are the centers of the exothermic reaction of hydrocarbons macromolecular synthesis. Synthesis occurs as a result of absorption of the components of the synthesis gas on metallic cobalt. The temperature distribution inside the granule for a single local center and reaction centers located on the same granule diameter is found. It was found that there is a critical temperature of reactor exceeding of which leads to significant local overheating of the centers - thermal explosion. The temperature distribution with the local reaction centers is qualitatively different from the granule temperature, calculated in the homogeneous approximation. It is shown that, in contrast to the homogeneous approximation, the temperature of the granule surface with local centers cannot serve as a reliable criterion for the thermal state of the synthesis centers inside the granule.This work was supported by RFBR grant № 17-08-00376.