# Assessment of Changes in the Abrasiveness of Solid Particles in Hydraulic Mixtures Pumped with ESPs
## 3 Results  
In accordance with the diagram shown in Figure 2, the values of the coefficients of sphericality, \(K_{s}\), and roundness, \(K_{r}\), of the particles of the mechanical impurities were determined; the particle size distribution was studied; and the average particle diameter, \(D_{f}\), was determined. The value of the abrasiveness index, \(Al\), was calculated with Equation (3). The results obtained from the studies of water-abrasive mixtures that contained particles of artificial quartz sand and river sand are shown in Figure 6.  
Analysis of the obtained graphs showed that the coarse sand particles were subjected to intensive grinding, passing through 40 working stages of the electric centrifugal pump (Figure 6a, position 1, 2), to the average diameter of \(D_{f}\) = 0.25... 0.3 mm, after which the particle size remained almost unchanged. Particles of fine river sand with an average particle diameter of \(D_{i}\) = 0.26 mm (Figure 6a, position 3) were crushed very slightly, to \(D_{f}\) = 0.2 mm.  
Figure 5: Particle shape and granulometric composition of model mechanical impurities: (**a**–**c**)—initial shape and composition; (**d**–**f**) after passing through 80 working stages, 7A-150, of the tested section of the electric centrifugal pump; (**a,d**) particles of artificial quartz sand; (**b,e**) particles of river sand; and (**c,e**) prop  
The products of grinding sand of artificial and natural origin have an elongated plate shape (Figure 5a,b,d,e), which determines a decrease in the coefficients of roundness and sphericality of ground particles compared to the particles of the initial model mechanical impurities (Figure 6c,d), causing an increase in their abrasion index (Figure 6b) as they passed through the working stages of the tested pumping section. The minimum increase in the abrasion index as the fluid passed through the working stages of the pumping section in the test was characterized with sand with an initial average particle diameter of \(D_{i}=0.26\) mm [34].  
The obtained conclusions were confirmed via the results of durability tests of a similar pumping section assembled from 20 working stages, 7A-150. In circulation of a hydroabrasive mixture in which river sand with an average particle diameter of \(D_{i}=0.58\) mm and a concentration of \(C=3\) g/L was used as mechanical impurities, an increase in the wear of the support washers of the impellers of the stages along the flow from the inlet to the outlet of the pumping section was observed for 4 h. Thus, the support washers of the working stages farther along the flow path were worn out from crushed mechanical impurities more intensely than were the support washers of the stages closest to the flow inlet of the pumping section (Figure 7) [35].  
Figure 6: Changes in the average diameter (**a**), abrasiveness index (**b**), roundness coefficient (**c**) and sphericity coefficient (**d**) of sand particles contained in the hydroabrasive mixture during passing through the pump stages of the electric centrifugal pump: 1—quartz sand of artificial origin, \(D_{i}=1.1\) mm; 2—river sand, \(D_{i}=0.58\) mm; 3—river sand, \(D=0.26\) mm.  
The results of experiments in which water with proppant was used as a hydroabrasive mixture showed that the proppant particles, passing with the flow of liquid through the stages of the tested pumping section, were practically not ground. Upon contact with the metal of the wheels and guide vanes, the upper layers of the proppant granules were removed, while the seal-destruction product, metal and corrosion particles were added to the circulating water-abrasive mixture (Figure 5f) [36,37]. With an increase of more than \(C=3\) g/L in the proppant concentration in the model hydraulic abrasive mixture, there was almost instantaneous destruction of the support washers of the impellers of the first stages along the flow path and jamming of the rotor of the tested pump section.