## 4 Conclusions  
The hydrodynamics and thermodynamics of a reactor with a fluidized bed of particles of polydisperse catalyst and inert material were simulated. The particle layer was located in a distribution device, which is a grid of vertical baffles. To reduce the fluidization effect, the baffles were divided into four sections, where in each section the particles were located in cells of 90 \(\times\) 90 \(\times\) 60 mm. It was determined that with this design of the distribution device and these particle parameters (particle density is 2350 kg/m\({}^{3}\), particle diameter is 1.5-4 mm), the following fluidization regimes are implemented. When the velocities of the liquefying medium are close to the minimum fluidization velocity (1 m/s), an undesirable slugging fluidization is observed. At a velocity of 3 m/s of the liquefying medium, a turbulent fluidization is observed in the lowest particle layer, and the bubbling fluidization is observed on subsequent particle layers. With an increase in the velocity of the liquefying medium over 3 m/s, the entrainment of particles and their impacts on the support grid of the next layer are observed. Since this would lead to particle erosion and destruction, this fluidization regime was also considered undesirable. Therefore, 3 m/s was taken as the optimal fluidization velocity. It was shown that the decrease in the density of the liquefying medium from 1.205 kg/m\({}^{3}\) to 0.383 kg/m\({}^{3}\) when heated in the temperature range of many catalytic chemical processes from 298 K to 923 K does not significantly affect the type of time dependence of the particle bed's hydraulic resistance, and therefore does not change the fluidization regime.  
Based on the obtained results, it can be stated that the obtained model is optimal for such problems and is suitable for the further description of experimental data. In the future, using the obtained model, simulation of the hydrodynamics and heat transfer in a reactor with a fluidized bed of polydispersed catalyst mixture and inert material, having taken into account heterogeneous catalytic reactions, is planned. The accompanying side processes are as follows: the release of additional heat during the reaction, the coking of the catalyst particles, etc., which can significantly affect the reactor regime. Similar studies are presented in [70; 71; 72]. However, these and other works do not consider the effect of internals or design features of the reactor on its hydrodynamics and, consequently, on the chemical process as a whole. The description of this effect will be the focus of further research and verification of the obtained model.  
Conceptualization, N.V.U. and K.E.K.; methodology, N.V.U., K.E.K. and Y.O.M.; software, I.S.R. and K.A.A.; validation, N.V.U., K.A.T., I.S.R. and K.A.A.; formal analysis, N.V.U., K.A.T., K.E.K. and Y.O.M.; investigation, N.V.U., K.A.T., I.S.R., K.A.A. and D.A.S.; resources, K.A.A. and Y.O.M.; data curation, N.V.U., K.A.T., D.A.S., K.E.K. and Y.O.M.; writing--original draft preparation, N.V.U., K.A.T., I.S.R., K.A.A., D.A.S., K.E.K. and Y.O.M.; writing--review and editing, N.V.U., K.A.T., I.S.R., D.A.S. and Y.O.M.; visualization, I.S.R., K.A.A. and D.A.S.; supervision, N.V.U. and Y.O.M.; project administration, N.V.U. and D.A.S.; funding acquisition, N.V.U. All authors have read and agreed to the published version of the manuscript. This research was funded by the Russian Science Foundation (project No. 22-13-00461, [[https://rscf.ru/project/22-13-00461](https://rscf.ru/project/22-13-00461)]([https://rscf.ru/project/22-13-00461](https://rscf.ru/project/22-13-00461))) (accessed on 6 May 2024).  
Not applicable.  
**Data Availability Statement:** The raw data supporting the conclusions of this article will be made available by the authors on request.