## 3 Materials and Methods  
Experimental research was carried out in the device with a cross-section of \(50\,\times\,100\) mm, and a height of up to \(1\) m with a separation space (Figure 1). Shelf contact elements differ from gas distribution grids of fluidized-bed devices and wedge-shaped elements plates primarily due to the presence of outloading space between the end of the shelf and the wall in the unit (Figure 1). The width of the outloading space is expressed by the ratio \(L_{cl}/L_{dev}\), where \(L_{cl}\) is the distance between the end of the shelf and the wall of the device, and \(L_{dev}\) is the length of the side section of the device. It is possible to influence the gas flow distribution between the outloading space and the holes of the shelf, as well as on the ascending flow velocities in the separation space and the solid phase, moving along the shelf, by varying the \(L_{cl}/L_{dev}\) ratio, the perforation degree of the shelf \(\psi\). The tilt angle of the shelf \(\gamma\) to a lesser extent affects the velocities profile of the gas flows over the outloading space and the holes of the shelf. The optimal tilt angle of the shelves is \(\gamma=25^{\circ}\) to the horizontal plane (Figure 2). The material particles lay on the surface of the shelf at a smaller angle. The particles quickly roll down to the outloading space and do not form a weighted layer above the shelf at a larger angle. The distance between the end of the upper shelf and the beginning of the lower shelf \(L_{s}\) is determined by the ratio between this distance to the length of the lateral part of the section in the device--\(L_{s}/L_{dev}\). If \(L_{s}/L_{dev}<0.5\), the gas flow velocity in the outloading space increases. As a result, the free flow of material particles is impeded through the outloading space to the lower shelf. As the distance \(L_{s}\) increases, the gas flow velocity in the outloading space naturally decreases. When \(L_{s}=L_{dev}\) the flow rate is constant. Therefore, we take \(0.5<L_{s}/L_{dev}\leq 1\) in the construction of the device. Figure 1: Multistage shelf device circuit: \(M\)—raw material; \(G\)—gas; \(G\)DS—gas-dispersed substance; \(FG\)—finished granules. A polydisperse granular superphosphate mixture in the form of a 0.1-5 mm granule with a shape factor of 0.85 was used in the studies. The sieve analysis using wire sieves with aperture sizes (the size of the square hole side) 0.5, 1.0, 1.6, and 2.5 mm defined the granulometric composition of the polydisperse mixture. The sieves were folded in a vertical block with decreasing hole sizes from top to bottom and installed on a vibrating table with a control unit. Sieve analysis was carried out for 15-20 min, corresponding to the measurement accuracy [46]. Several samples were analyzed according to the methodology to assess the accuracy of the measurement [47]. The deviation of the results for each sample did not exceed 1.5-2.0%. The results of the sieve analysis of the initial polydisperse mixture are as follows: +2.5 mm--10%; 2.5 + 1.6 mm--25%; 1.6 + 1 mm--25%; 1 + 0.5 mm--20%; 0.5 mm--20%. According to the reference data, the true and bulk density of superphosphate granules obtained by the noululizing method in a drum granulator was 2250 kg/m\({}^{3}\) and 1100-1200 kg/m\({}^{3}\)[48]. The laboratory unit consisted of a device equipped with a loading hopper with a belt feeder and an unloading hopper, a centrifugal cyclone to capture fine fractions with an unloading hopper, a high-pressure fan for pumping air through the device, and a cyclone. The walls in the device from the front side were transparent for visual observation and filming. The initial mixture of the granulated superphosphate with amount of 3 kg was weighed on an electronic scale with an accuracy of 0.1 g. The mixture was heated to 90-95 \({}^{\circ}\)C in the loading hopper with electric heating elements (it corresponds to the temperature at the outlet of the drum granulator dryer [49]) and fed by the belt feeder into the device on the upper shelf.