Computer Simulation of Coke Sediments Burning from the Whole Cylindrical Catalyst Grain
The article is devoted to the development of the mathematical model of oxidative regeneration of the cylindrical catalyst grain. The model is constructed using a diffusion approach to modeling catalytic processes. The model is based on the equations of material and thermal balance. Mass transfer in...
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MDPI AG
2023-01-01
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| author | Olga S. Yazovtseva Irek M. Gubaydullin Elizaveta E. Peskova Lev A. Sukharev Andrey N. Zagoruiko |
| author_facet | Olga S. Yazovtseva Irek M. Gubaydullin Elizaveta E. Peskova Lev A. Sukharev Andrey N. Zagoruiko |
| author_sort | Olga S. Yazovtseva |
| collection | DOAJ |
| description | The article is devoted to the development of the mathematical model of oxidative regeneration of the cylindrical catalyst grain. The model is constructed using a diffusion approach to modeling catalytic processes. The model is based on the equations of material and thermal balance. Mass transfer in the catalyst grain is carried out due to diffusion and the Stefan flow resulting from a decrease in the reaction volume during sorption processes. Chemical transformations of substances are taken into account as a source term in the equation. The thermal balance of the catalyst grain is described by a thermal conductivity equation, with an inhomogeneous term responsible for heating the grain during exothermic chemical reactions. The effective coefficients of heat capacity and thermal conductivity of the catalyst grain, which are determined taking into account the porosity of the grain depending on temperature, were used to calculate the thermal balance of the catalyst grain. The dependencies are approximated using the method of least squares based on experimental data. Different boundary conditions for the developed model allow calculating the main characteristics of the oxidative regeneration process for a whole catalyst grain under different conditions. The mathematical model of oxidative regeneration of a cylindrical catalyst grain is described by a stiff system of differential equations. Splitting by physical processes is applied to avoid computational difficulties. The calculation of flows is carried out sequentially: first, chemical problems are solved using the Radau method, then the diffusion and thermal conductivity equations are solved by the finite volume method. The result of the algorithm implemented in C++ is a picture of the distribution of substances and temperature along the cylindrical grain of the catalyst. |
| first_indexed | 2024-03-11T09:34:11Z |
| format | Article |
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| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-11T09:34:11Z |
| publishDate | 2023-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-3c8e7e5891774097bf65d2caa9f7a2f02023-11-16T17:22:52ZengMDPI AGMathematics2227-73902023-01-0111366910.3390/math11030669Computer Simulation of Coke Sediments Burning from the Whole Cylindrical Catalyst GrainOlga S. Yazovtseva0Irek M. Gubaydullin1Elizaveta E. Peskova2Lev A. Sukharev3Andrey N. Zagoruiko4Faculty of Mathematics and Information Technologies, National Research Mordovia State University, 68 Bolshevistskaya Str., Saransk 430005, RussiaInstitute of Petrochemistry and Catalysis of the Russian Academy of Sciences, Ufa 450075, RussiaFaculty of Mathematics and Information Technologies, National Research Mordovia State University, 68 Bolshevistskaya Str., Saransk 430005, RussiaFaculty of Mathematics and Information Technologies, National Research Mordovia State University, 68 Bolshevistskaya Str., Saransk 430005, RussiaBoreskov Institute of Catalysis SB RAS, Novosibirsk 630090, RussiaThe article is devoted to the development of the mathematical model of oxidative regeneration of the cylindrical catalyst grain. The model is constructed using a diffusion approach to modeling catalytic processes. The model is based on the equations of material and thermal balance. Mass transfer in the catalyst grain is carried out due to diffusion and the Stefan flow resulting from a decrease in the reaction volume during sorption processes. Chemical transformations of substances are taken into account as a source term in the equation. The thermal balance of the catalyst grain is described by a thermal conductivity equation, with an inhomogeneous term responsible for heating the grain during exothermic chemical reactions. The effective coefficients of heat capacity and thermal conductivity of the catalyst grain, which are determined taking into account the porosity of the grain depending on temperature, were used to calculate the thermal balance of the catalyst grain. The dependencies are approximated using the method of least squares based on experimental data. Different boundary conditions for the developed model allow calculating the main characteristics of the oxidative regeneration process for a whole catalyst grain under different conditions. The mathematical model of oxidative regeneration of a cylindrical catalyst grain is described by a stiff system of differential equations. Splitting by physical processes is applied to avoid computational difficulties. The calculation of flows is carried out sequentially: first, chemical problems are solved using the Radau method, then the diffusion and thermal conductivity equations are solved by the finite volume method. The result of the algorithm implemented in C++ is a picture of the distribution of substances and temperature along the cylindrical grain of the catalyst.https://www.mdpi.com/2227-7390/11/3/669oxidative regenerationchemical kineticsdiffusion equationthermal conductivity equationsplitting by physical processesnumerical methods |
| spellingShingle | Olga S. Yazovtseva Irek M. Gubaydullin Elizaveta E. Peskova Lev A. Sukharev Andrey N. Zagoruiko Computer Simulation of Coke Sediments Burning from the Whole Cylindrical Catalyst Grain Mathematics oxidative regeneration chemical kinetics diffusion equation thermal conductivity equation splitting by physical processes numerical methods |
| title | Computer Simulation of Coke Sediments Burning from the Whole Cylindrical Catalyst Grain |
| title_full | Computer Simulation of Coke Sediments Burning from the Whole Cylindrical Catalyst Grain |
| title_fullStr | Computer Simulation of Coke Sediments Burning from the Whole Cylindrical Catalyst Grain |
| title_full_unstemmed | Computer Simulation of Coke Sediments Burning from the Whole Cylindrical Catalyst Grain |
| title_short | Computer Simulation of Coke Sediments Burning from the Whole Cylindrical Catalyst Grain |
| title_sort | computer simulation of coke sediments burning from the whole cylindrical catalyst grain |
| topic | oxidative regeneration chemical kinetics diffusion equation thermal conductivity equation splitting by physical processes numerical methods |
| url | https://www.mdpi.com/2227-7390/11/3/669 |
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