## 4 Results
### Effect of the Concentration of Solid Particles  
To understand the impact of the concentration of the slurry particles, five different values of particle concentration were studied in the present work, i.e., 5%, 10%, 15%, 20%, and 25%, as indicated in Table 1. Figures 8-11 shows particle concentration profiles, wall stress, particle's momentum source, and erosion rate density along the casing walls from point P1 to P11 for different inlet volumetric concentrations of particles. For all these simulations, particle size distribution A and an exit pressure head of 2.6 bar were employed. Figure 8: Variation of the concentration of particles along the casing wall with different values of volumetric concentration of the solid particles. Figure 9: Wall stress profiles along the casing wall with different values of volumetric concentration of the solid particles. Figure 8 shows that profiles for all particle concentrations, except \(\mathrm{P_{vc}}=5\%\), had two peaks of volume concentration. One was near the casing tongue while the second was where the curvature of the casing's profile suddenly becomes zero. The first peak (around point \(\mathrm{P_{3}}\)) was attributed to the smaller cross-section in the region, while the 2 nd peak (around point \(\mathrm{P_{8}}\)) was due to the sudden change in the casing's profile. It should be noted that the 2 nd peak was much larger than the first. This was because the casing profile changed the direction of the fluid suddenly; however, the particles tended to follow a motion in a straight line as the momentum of the solid particles was higher compared to fluid parties of the same size due to their higher densities. This, in turn, leads to a local cluster of particles in that region after hitting the casing wall. It is interesting to note here that volume concentration at the casing wall increased initially with the increase in the volume concentration imposed at the inlet boundary (e.g., \(\mathrm{P_{vc}}=5\) to 10); however, with the additional increase in the value of \(\mathrm{P_{vc}}\) at the inlet, the concentrations of the particles on the wall started falling. This could be explained based  
Figure 11: Variation of erosion rate density along the casing wall with different values volumetric concentration of the solid particles. Figure 10: Variation of particles momentum source along the casing wall with different values volumetric concentration of the solid particles. on the fact that with an increase in volume concentration beyond 10%, solid particles from larger chunks, under the action of gravity, started accumulating at the bottom of the casing. As all quantities were measured on the polyline (red polylines in Figure 1) located at the sidewalls, the values of the volumes concentration on the side walls dropped when the inlet value of \(\mathrm{P_{vc}}\) increased. Figure 9 shows wall stress profiles along the casing wall with different volumetric concentrations of the solid particles. A similar trend for the wall stress could be observed for the volume concentration, as discussed above. A maximum value of wall stress was observed for \(\mathrm{P_{vc}}\) = 10%, while the minimum values were observed for the full volume concentrations, i.e., \(\mathrm{P_{vc}}\) = 25%. The wall stress profiles for \(\mathrm{P_{vc}}\) = 5%, 15%, and 20% were identical in terms of values of stress and the location of the two peaks discussed above. Figure 10 shows the values of the particle momentum source due to the interaction between the two phases. The displayed results suggested that momentum transfer from the water to solid particles changed significantly for the \(\mathrm{P_{vc}}\) values of 5% and 10% along the casing wall (\(\mathrm{P_{1}}\) to \(\mathrm{P_{11}}\)). However, the profiles corresponding to both values of \(\mathrm{P_{vc}}\) were quite different from each other.