The article offers a systematic approach to the method of developing mathematical models of a chemical-technological system (CTS) in conditions of deficit and fuzziness of initial information using available data of various types. Based on the results of research and processing of the collected quantitative and qualitative information, mathematical models of the reactor are constructed. Formalized and obtained mathematical statements of the control problem for choosing effective modes of operation of technological systems are based on mathematical modeling. Based on the obtained expert information, linguistic variables were described and a database of rules describing the operation of the input parameters of the reactor unit of the catalytic cracking unit was obtained.

The results of the mathematical modeling of a liquid flow in a mixing vessel with a turbine impeller are presented in the paper. The calculations were carried out using the numerical codes of Computat

The paper presents results of numerical simulations and experimental investigations of a cyclone with a square inlet and different dimensions of a vortex finder. Investigations were conducted for five, different cyclone models. The main goal of the research was to determine the influence of cyclone vortex finder geometry (diameter, length) on key parameters for a cyclone operation, such as: gas flow pattern, gas velocity and pressure distribution, pressure drop and collection efficiency. The analysis of flow pattern inside the cyclone was carried out with the use of CFD (Computational Fluid Dynamics) simulations, verified using CTA (Constant Temperature Anemometry). Similarly, pressure distributions, pressure drop and collection efficiency for cyclones were determined numerically and with measurements. The study demonstrated that dimensions of the vortex finder have a significant effect on a cyclone performance. The numerical visualisations of flow showed some unfavorable and beneficial effects and phenomena that may occur in cyclones. Moreover, the smallest pressure drop (305 Pa) was predicted for the cyclone with a maximum diameter of the vortex finder ($D_e$ = 0.105 m), the largest (358 Pa) when this diameter was the smallest ($D_e$ = 0.075 m). The tests did not show any significant influence of the vortex finder length on the pressure drop in a cyclone. A different tendency was observed in the case of collection efficiency. The maximum value of this parameter (89.5%) was predicted for the cyclone with the shortest vortex finder (s = 0.060 m), minimum (85.5%) when the vortex finder was the longest (s = 0.220 m). In this case, however, tests did not show a significant impact of an outlet diameter on the collection efficiency. Results and conclusions presented in this paper can be practically used for design optimization of cyclone separators, and also to select their operating parameters.