# Assessment of Changes in the Abrasiveness of Solid Particles in Hydraulic Mixtures Pumped with ESPs
## 2 Materials and Methods  
Hydroabrasive wear is a common phenomenon in many fields of technology. It occurs when a pumped liquid that contains solid impurity particles (a water-abrasive mixture) interacts with pipelines, pump parts, valves, switchgear assemblies, etc. [14; 15]. The abrasive particles contained in borehole fluids are classified based on origin, as follows:  
* Loose proppant after hydraulic fracturing;
* Particles of reservoir rocks;
* Corrosion products of downhole equipment;
* Solid particles from well-kill solutions;
* Sediment particles formed during mixing of chemically incompatible waters [16; 17]. The composition of a mechanical impurity can be single- or multicomponent, and its concentration, as a rule, is not a constant value. High content of mechanical impurities in pumped liquid is typical for the stages of well development, startup after current and  
Figure 1: Hydroabrasive wear of the guide vanes (**a**) (the arrow points to areas of local hydroabrasive wear of the ESP guide apparatus, the dotted line shows its original cross-sectional shape) and the consequences of cutting the housings of electric submersible pumps (**b**,_c_) (arrows show the consequences of hydro-abrasion—cutting of the ESP housing). overhaul. A short-term increase in concentration of mechanical impurities is observed during the startups of ESP units that operate in periodic modes, as well as during changing of the parameters of reservoir-pressure maintenance systems. It is known that intensive hydroabrasive wear is accompanied by operation of electric centrifugal pumps at the following concentrations of mechanical impurities in pumped well fluid:  
* For pumps in the normal version--\(C=1\) g/m\({}^{3}\);
* For pumps in the wear-resistant version--\(C=3\) g/m\({}^{3}\). If the concentration of mechanical impurities in a well fluid is more than \(C=5\) g/m\({}^{3}\), in addition to hydroabrasive wear, the corresponding ESP-unit operation will be accompanied by significant vibrations and a high probability of pump-rotor jamming [16; 18; 19; 20; 21]. The wear of the working stages of electric centrifugal pumps under the influence of abrasive particles of mechanical impurities is a multifactorial process, the intensity of which in general can be determined with Equation (1):  
\[\frac{dK_{i}}{dt}=f(R,F,\rho,H_{c},C,K,H_{d},F_{d},\omega) \tag{1}\]  
where \(K_{i}\)--relative change in the mass of a wearing part of the working stage of an ESP; \(t\)--time of action of abrasive particles on this wearing part; \(dK_{i}/dt\)--rate of hydroabrasive wear; \(R\), \(F\), \(\rho\), \(H_{c}\) and \(C\)--size, shape, density, hardness and concentration of abrasive particles of mechanical impurities, respectively; \(K\)--corrosiveness of the medium; \(H_{d}\)--hardness of the surface of the wearing part; \(F_{d}\)--surface shape of the wearing part; and \(\omega\)--rotation frequency of the pump drive shaft [18]. The influence of geometric parameters and physical and mechanical properties of particles of mechanical impurities on wear capacity is taken into account in the methodology of the American Petroleum Institute (API) and estimated via the value of the complex index of abrasiveness of mechanical impurities, which is generally described with Equation (2):  
\[AI=f(R,F,\rho,H_{c}) \tag{2}\]  
where \(AI\)--abrasiveness index of mechanical impurities,%.