## 2 Experimental
### Experimental Results  
By simulating the actual situation of coiled tubing solid-liquid erosion, the surface of the sample was impacted at a flow rate of 6.63 m/s, 13.27 m/s, 19.90 m/s, and 26.54 m/s. Figure 4: Erosion test equipment physical map. Figure 3: Erosion test equipment schematic diagram. 1. Test rig; 2. Nozzle; 3. Control valve; 4. Liquid mixer; 5. Electromagnetic flow meter; 6. Temperature sensor; 7. Pressure sensor; 8. Mortar pump. The erosion time was 2 h, the sand concentration was 50 kg/m\({}^{3}\), and the jet injection angle was 30\({}^{\circ}\), 45\({}^{\circ}\), 60\({}^{\circ}\), and 90\({}^{\circ}\). The erosion pattern of the coiled tubing sample was obtained, as shown in Figure 5.  
After erosion, all the coiled tubing samples had a visibly damaged appearance which was scratched and washed by particles. The common erosion morphology of the erosion center was that the sand particles repeatedly impacted to form a clear and identifiable pit, mainly scratches. The damage of the test sample mainly included the impact of the normal component of the impact velocity of the sand on the test sample, and the scratches that had a long time of contact with the surface of the coiled tubing sample for the sand with a small normal velocity component. The observation of the coiled tubing erosion test in solid-liquid two-phase flow showed that the erosion phenomenon on the surface of the coiled tubing sample was mainly caused by multi-particle impact. The erosion damage degree of coiled tubing surface varied with the impact angle. In addition, with the change in impact velocity, the erosion damage of the pipeline surface also differed. The weight loss method can be used to calculate the weight loss of coiled tubing samples under different conditions, so as to determine the erosion rate of the pipe wall, as shown in Table 1. The results show that the erosion rate increases with the increase in impact velocity between 0.04 mm/h and 0.1 mm/h. It is worth noting that the erosion rate of coiled tubing reached a peak near the erosion angle of 45\({}^{\circ}\). Figure 5: Erosion morphology of coiled tubing sample. A series of erosion experiments were conducted in this study to investigate the correlation between erosion rate and impact angle, impact velocity, sand diameter, and sand concentration. The experimental findings are summarized as follows. Figure 6 showed the erosion rate changes in the coiled tubing samples at different impact velocities. Under the four impact velocities, the samples demonstrated a trend of initially increasing, then decreasing, and ultimately stabilizing the erosion rate. At an impact angle of 45\({}^{\circ}\), the erosion rate of the sample reaches its maximum. The analysis suggested that the most significant erosion-thinning effect occurred due to the equality of shear and normal stress at a 45\({}^{\circ}\) impact angle. Figure 7 shows the erosion rate changes in the coiled tubing samples at different impact angles. Under the six impact angles, the erosion rate showed good consistency with the impact velocity, exhibiting a gradual increase as the velocity increased. The greatest increase in erosion rate was observed when the velocity increased from 12.0 m/s to 16.9 m/s. The analysis suggested that, as the impact velocity increased, the kinetic energy of the sand particles increased, resulting in stronger cutting and impact actions, leading to greater damage to the coiled tubing. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Impact Velocity** & **Impact Angle** & **Weight Before** & **Weight After** & **Weight Loss** & **Erosion Rate** \\
**(m/s)** & (\({}^{\circ}\)) & **(g)** & **(g)** & **(g)** & **(mm/h)** \\ \hline
6.63 & 30 & 9.8391 & 9.8128 & 0.0263 & 0.042  
Figure 8 shows the erosion rate changes in coiled tubing samples at different sand concentrations. Within the concentration range of 30-45 kg/m\({}^{3}\), the erosion rate increased with an increase in sand concentration.