# Experimental Analysis of Shale Cuttings Migration in Horizontal Wells
## 4 Theoretical Model and Validation
### Validation
#### 4.3.2 Rotation of the Drill Tool  
When the drill tool was rotating, the theoretical model's predictions remained within a reasonable error range. The average error between the calculated and experimental results was approximately 11.94%. This discrepancy can be attributed to factors such as equipment vibration, variations in fluid dynamics caused by rotation, and fluctuations in fluid rate during the experiments, which made it easier for the cuttings to start moving. Despite these challenges, the relative error between the theoretical and experimental values remained within an acceptable range, indicating that the model is robust enough to predict cuttings movement even under conditions involving drill tool rotation. As with the non-rotating case, larger eccentricities and particle sizes resulted in higher start-up velocities, and the model's accuracy was maintained across different test conditions. Tables 5-7 further demonstrate that, for spherical particles, the model tends to overestimate the start-up velocity by about 13.10% to 19.87%. However, for non-spherical particles, the model's predictions are more accurate, with an error range of 9.44% to 14.55%. This indicates that the model is effective in predicting the behavior of irregularly shaped particles, which are more complex to model than spherical particles. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{3}{*}{**Eccentricity**} & \multirow{3}{*}{**Drilling Fluid Rate**} & \multirow{3}{*}{**Experimental**} & \multicolumn{4}{c}{**Calculated Data**} \\ \cline{3-6}  & & & **Spherical Particle** & **Error (\%)** & **Non-Spherical Particle** & **Error (\%)** \\ \hline  
\hline \hline \end{tabular}
\end{table} 
Table 4: Experimental and calculation data of critical start-up velocity (Type 3, non-rotating). Figure 16 illustrates the impact of different drilling parameters, such as fluid flow rate, drill tool rotation speed, and annular eccentricity, on cuttings return velocity during the migration experiments. Each curve in the figure represents the relationship between a specific drilling parameter and the changes in cuttings migration. To better visualize the range of data, an 80% confidence interval was chosen. The 80% confidence interval was chosen to balance data reliability while allowing for some variability. This level of confidence helps exclude extreme values but still reflects a reasonable range of data fluctuation. It provides a solid basis for interpreting the experimental results, offering a credible range to assess the stability of the cuttings migration under different parameter conditions. As the fluid flow rate increases, the figure shows a gradual reduction in the height of the cuttings bed, with the confidence intervals becoming narrower. This indicates that higher fluid flow rates lead to a more stable cuttings migration process, with less variability in the data. This suggests that higher flow rates are more effective at clearing cuttings, thus reducing the formation of cuttings beds. Increasing the rotation speed of the drill tool also helps to lower the height of the cuttings bed. Although the effect is not as significant as the fluid flow rate, the confidence \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{3}{*}{**Eccentricity**} & \multirow{3}{*}{**Drilling Fluid Rate**} & \multicolumn{6}{c}{**Critical Start-Up Velocity**} \\ \cline{3-6}  & & & \multicolumn{3}{c}{**Calculated Data**} \\ \cline{3-6}  & & **Depical Particle** & **Spherical Particle** & **Error (\%)** & **Non-Spherical Particle (m/s)** & **Error (\%)** \\ \hline
0 & 4.20 & 0.22 & 0.17 & 22.73 & 0.26 & 18.18 \\
0.1 & 5.13 & 0.26 & 0.21 & 19.23 & 0.29 & 11.54 \\
0.2 & 5.69 & 0.29 & 0.24 & 17.24 & 0.33 & 13.79 \\
0.3 & 6.59 & 0.34 & 0.28 & 17.65 & 0.39 & 14.71 \\ \hline  & & & \multicolumn{3}{c}{Average} & 19.21 & Average & 14.55 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Experimental and calculation data of critical start-up velocity (Type 3, rotating).