## 1 Introduction
With an increase in the gas velocity, the frequency of gas bubble formation will increase, the size of the bubbles will increase, and the bubbles will begin to merge occupying the entire cross-section of the apparatus, which is called a slugging fluidization [1; 3; 4; 5; 9; 10; 11; 17]. This regime has an extremely negative effect on the heat and mass transfer between the gas and the particles of the bed [1; 3; 4; 5; 9; 10; 11; 17]. With a further increase in the gas velocity, the clear interface between the bed of particles and gas bubbles is blurred, vortices are formed and partial entrainment of particles from the apparatus occurs. This regime is called turbulent (Figure 1D) [1; 3; 4; 5; 9; 10; 11; 17]. A further increase in the gas velocity leads to a constant entrainment of particles from the apparatus and the transition of the fluidization to fast fluidization (Figure 1E) and then to pneumatic conveyance (Figure 1F), and the clearly distinguishable boundary of the particle bed disappears [1; 3; 4; 5; 9; 10; 11; 17]. Fluidization was first used for coal gasification in the 1920s [6]. The process immediately attracted a lot of attention due to the following advantages [1; 3; 6; 18]. 1. Intensive mixing of particles provides high mass and heat transfer rates between the medium and the particles (for instance, in the case of an exothermic reaction occurring on the surface of the particles), and, as a result, improves heat removal through the reactor wall. 2. Since the fluidized particle bed has some liquid properties, it is possible to design apparatuses with a circulating particle bed and use various remote devices. 3. The simple hardware design of the fluidization allows for their use in many industries. Along with the above advantages, a reactor with a fluidized bed has certain disadvantages: contamination of the medium and loss of the catalyst; erosion of the walls of the reactor vessel and installed internals; agglomeration of particles, leading to the defluidization of the particle bed (i.e., transition to a stationary state); and the bypassing of agents in the bubbles of the medium [1; 6; 18; 19; 20]. Despite these disadvantages, fluidization has achieved widespread industrial application in many spheres, especially in the chemical and petrochemical industries. It is used for many non-catalytic processes, such as efficient fuel combustion [21], roasting of ones [22], drying [23], adsorption [24], coating [25], granulation [26], etc., but it has become most widespread in the petrochemical industry in a number of catalytic processes, such as the cracking [27] and reforming of hydrocarbons [28], carbonation [29] and coal gasification [30], Fischer-Tropsch synthesis [31], pyrolysis (including pyrolysis of biomass) [32], and hydrogenation and dehydrogenation of hydrocarbons [12; 13; 14; 20; 33; 34]. A large range of processes based on fluidization and the features of their development and application are presented in the monograph [3]. An important stage in the design of the fluidized bed reactor is the determination of its hydrodynamic parameters by performing experiments in the laboratory and pilot units, and simulation by means of the computational fluid dynamics (CFD) approach. By measuring the hydraulic resistance of the particle bed, it is possible to determine the critical fluidization velocity or some parameters of the fluidization regime: the frequency of formation and size of gas slugs, the velocity of bubble movements, etc. [5; 35]. The hydraulic resistance is measured by installing pressure sensors at the full height of the reactor, the first sensor being installed before the particle bed [5; 8; 35]. In [15], it was determined that the fluidization is affected by the reactor design, the gas and particle properties, the velocity, the gas pressure and temperature, and the design of various internals used to build the particle bed [15].