## 2 Factors Impacting the Intensity of Hydroabrasive Wear of the Pumping Stages of the ESP
Intensive development of abrasive wear of the guide apparatus of the VNN5A-100 pumping stage in area 1 is determined by the impact of particles of mechanical impurities separated from the main flow and accumulated under the lower impeller disk. At the same time, a complex of forces acts on abrasive particles moving in the liquid:  
* forces co-directional to the rotation of the impeller and caused by the friction of the liquid against the bottom disk of the impeller;  
Figure 1: Change in wear of thrust washers of VNN5A-100 in relation to the grain size \(R\) of mechanical impurities: 1—\(R\) = 800... 1000 \(\mu\)m; 2—\(R\) = 20... 30 \(\mu\)m [9]. Figure 2: Hydroabrasive wear of the VNN5A-100 stage after the tests. * centrifugal forces, which press the particles of the mechanical impurities against the walls of the guide apparatus;
* forces directed towards the center of the stage and arising from fluid overflow through the seals. The aforementioned factors determine the formation of vortices in the cavity \(1\). Their presence causes the intensive movement of particles of mechanical impurities along the walls of the guide apparatus and, as a consequence, abrasive wear of the metal. The intensity of the wear increases with the size of the vortices. Hydroabrasive wear in the areas 2-4 and 6 is slower than that in area \(1\). The accumulation of the particles of mechanical impurities and the formation of vortices is caused by the change in the direction (rotation) of the pumped fluid flow. The presence of fluid overflow in the pumping stage between the bush of the guide apparatus and the middle thrust washer of the impeller is the reason for the development of the wear in the area \(5\). The fluid containing the particles of mechanical impurities flows from the pumping stage into the previous stage along the direction of the flow and destroys the impeller thrust washers. This process develops most intensively at higher rotation velocities of the drive shaft of the ESP (\(\approx\)6 thousand rpm), which causes the destruction of impellers, i.e., the cutting of disks and their separation from the hub sleeve. The American Petroleum Institute (API) methodology considers the influence of geometric parameters and physical-mechanical properties of particulate mechanical impurities on their wearing capacity. This is evaluated by the value of the complex abrasiveness index of mechanical impurities, which is generally described by Equation (2):  
\[AI=f(R,F,\rho,H_{c}), \tag{2}\]  
where \(AI\)--abrasiveness index of mechanical impurities. The quantitative value of the abrasiveness index is determined empirically by Equation (3):  
\[AI=10(2-K_{r}-K_{s})+0.3M_{-0.25\%}+0.25\big{(}M_{ir\%}+M_{q\%}\big{)}, \tag{3}\]  
where \(K_{r}\)--roundness coefficient of the particles of mechanical impurities, defined according to the \(API\) methodology; \(K_{s}\)--the spherical shape factor of the particles of mechanical impurities, defined according to the \(API\) methodology; \(M_{-0.25\%}\)--mass fraction of abrasive particles of mechanical impurities with the grain size less than 0.25 mm, %; \(M_{ir\%}\)--mass fraction of the particles of mechanical impurities insoluble in acid (mass fraction of insoluble residue), %; \(M_{q\%}\)--fraction of quartz particles in the total mass of mechanical impurities, % [7; 24; 25]. Analysis of Equation (3) shows that the greatest influence on the abrasion ability and the abrasiveness of the particles of mechanical impurities interacting with the parts of submersible pumping equipment is the shape of the solid particles, i.e., their roundness and spherical factor. The graph used for visual determination of values of roundness coefficients \(K_{\rm o}\) and spherical shape factors \(K_{\rm s}\) of solid particles of mechanical impurities is presented in Figure 3[26; 27].