## 3 Results
### Effect of Nano-Silica Additive under Different Standoff Distances  
In this group of experiments, the dimensionless standoff distances, \(S\), was normalized by the nozzle diameter, and increased from one, to 10. The inlet pressure was set at a constant value of 50 MPa, the ambient pressure was set at 15 MPa, and the fluid temperature was set at 340 K. The mass fractions of the nano-silica additive were 0 wt %, 3 wt %, 6 wt %, 12 wt %, and 18 wt %, respectively.  
As is clearly shown in Figure 6, the standoff distance significantly affects the rock erosion ability of the SC-CO\({}_{2}\) jet, which is demonstrated by evaluating the erosion volume of the cavity for each specimen. Regardless of the mass fraction of the nano-silica additive, each jet has an optimum standoff distance, at which position the erosion volume reaches a maximum value. This signals that the existence of an optimum standoff distance could be a typical feature of the SC-CO\({}_{2}\) jets for erosion. This is because, the undeveloped jet and backflow resistance at small standoff distances, lead to a large energy loss and a poor erosion intensity. Moreover, a standoff distance larger than the optimal value, results in the significant entrainment of the jet flow, and large energy dissipation [21]. The curves suggest that the optimal standoff distance is about three times the nozzle diameter of the pure SC-CO\({}_{2}\) jet, while it is about five times the nozzle diameter of the nano-silica SC-CO\({}_{2}\) jets. It is inferred that the nano-silica SC-CO\({}_{2}\) jets need a larger distance to reach their maximum erosion capacity. This is most likely due to the fact that the nano-silica particles in the jet flow require a longer time and distance to speed up to a velocity that causes a strong erosion effect, effectively damaging the rock [39; 40; 41]. In addition, after the standoff distance exceeds the optimum value, the erosion ability of the jets greatly decreases.  
Furthermore, it can be observed in Figure 6 that, although the curves of the different mass fractions show a similar trend with an increase in the standoff distance, the jets with different mass fractions of nano-silica additive have different erosion capabilities at the same standoff distance. Specifically, the erosion volumes of the nano-silica SC-CO\({}_{2}\) jets with a mass fraction of 3 wt %, 6 wt %, 9 wt %, and 12 wt %, are enhanced at all of the tested standoff distances. For mass fractions less than or equal to 12 wt %, an increase of the nano-silica mass fraction can increase the enhancement of the erosion capability. The maximum erosion volume is 595.13 mm\({}^{3}\) with a mass fraction of 12 wt %, which is 1.8 times that of the pure SC-CO\({}_{2}\) jet. For the mass fraction of 15 wt %, a reduction in the enhancement can be seen, when compared with that of 12 wt %. In terms of the mass fraction of 18 wt %, the erosion volumes of the nano-silica SC-CO\({}_{2}\) jet are smaller than that of the pure jet, at most standoff distances. This indicates that the excessive addition of the nano-silica additive can attenuate the erosion capability enhancement generated by the nano-silica particles, and has an adverse effect on the erosion ability of the SC-CO\({}_{2}\) jet.  
Figure 5: Photos of rock specimens after erosion: top ones for the nano-silica SC-CO\({}_{2}\) jet with a mass fraction of 12 wt %, bottom ones for the pure SC-CO\({}_{2}\) jet, \(P_{in}\) = 50 MPa, \(P_{am}\) = 15 MPa, \(T_{f}\) = 340 K.