## 5 Results and Discussion
### Estimation of the Residence Time of Solid Particles in the Overlayer Space  
It is difficult to identify the true residence time of solid particles in the weighted layers with different structures. That is why the authors propose a calculation method for estimating the average residence time of particles in a layer weighted above a shelf. As can be seen from the trajectories of solid-phase motion in the photographs (Figure 7), the weighted layer can be divided into two zones: the solid particle motion zone on the surface of the shelf and the particle motion zone in the overshelf space. For the first zone, the residence time of the particles is calculated by the formula:  
\[\tau_{1}=\frac{L_{sh}}{u_{p}\cdot\left(1-\beta\right)^{m}}=\frac{L_{dev}- \frac{L_{cl}}{L_{dec}}}{u_{p}\cdot\left(1-\beta\right)^{m}}, \tag{20}\]  
where \(u_{p}\) is the velocity of solid particles motion on the shelf surface, m/s; \(\beta\)--the volume concentration of the solid phase in the weighted layer, m\({}^{3}\)/m\({}^{3}\); \(m\)--the experimental coefficient; \(m\) = 4.4-4.5--for the \"weighted layer\" mode; \(m\) = 10-10.2--for the \"gravitationally falling layer\" mode. The following empirical correlation is proposed to find the volume concentration of the solid phase in the weighted layer:  
\[\beta=n\cdot G_{ex}^{0.95}\left(\frac{W}{W_{o.s.}}\right)^{0.6}, \tag{21}\]  
where \(G_{ex}\) is the mass flow rate concentration, kg/kg; \(G_{ex}\) = \(G_{p}\)/\(G_{gas}\); \(G_{p}\)--mass flow rate of the material, kg/s; \(G_{gas}\)--mass flow rate of gas, kg/s; \(W\)--velocity of the gas flow in free cross-section, m/s; \(W_{o.s. }\) is the velocity of medium diameter particles, m; \(n\) is the experimental coefficient; \(n\) = 0.25-0.35 for the \"weighted layer\" mode; \(n\) = 0.1-0.15--for the \"gravitationally falling layer\" mode. There is no weighted layer in the space above the shelf for the \"gravitationally falling layer\" mode, as can be seen from the photograph (Figure 7a). Therefore, the second zone is typical only for the \"weighted layer\" mode (photograph, Figure 7c). When particles pass along the shelf length, they meet with a gas jet, formed by the outloading gap. Particles with a velocity less than the velocity of the gas jet are carried up into space above the shelf. The velocity of the gas jet decreases in height. The particles with a velocity greater than the velocity of the gas are lowered down to the shelf surface. Only small particles are carried out by the gas flow from the device. Thus, in the second zone, the particles move up the trajectory to the upper boundary of the weighted layer and downward trajectory to the surface of the shelf. Then the residence time of the particles is calculated as the following:  
\[\tau_{2}=\frac{L_{tr}}{\theta_{r}}=\frac{2\cdot k\cdot B_{dev}}{\theta_{r}}, \tag{22}\]where \(L_{tr}\) is the length of the trajectory, m; \(\vartheta_{r}\) is the pulsation velocity of the solid particle, m/s; \(k\) is the experimental coefficient; \(k\) = (1.5-3)\(\cdot B_{dev}\). The pulsation velocity of a solid particle in a weighted layer is determined by the empirical dependence:  
\[\vartheta_{r}=bW,\ 0\ <\ W<\ 3.5\ \text{m/s}, \tag{23}\]  
where \(b\) is the experimental coefficient; \(b\) = 0.06 (defined according to the regression with correlation coefficient of 0.844).