## 4 Results and Analysis
### Sensitivity Analysis of Cracks and Solution Cavities Characteristics on the Wellbore Stability  
Figure 28 shows the percentage of the maximum change in the equivalent densities of collapse pressure under the circumstances of variations in crack orientation, crack dip angle, crack width, solution cavities size, solution cavities quantity, and the connectivity between cracks and solution cavities. As shown in Figure 28, cracks have a much more significant impact on wellbore stability than solution cavities. When comparing the influencing factors such as the orientation, dip angle, and width of cracks, the wellbore stability is most sensitive to the crack dip angle, followed by the crack width and crack orientation. For example, the equivalent drilling fluid densities of collapse pressure (\(\rho_{\rm c}\)) for a crack dip angle (\(\theta\)) of 90\({}^{\circ}\) is 30.55% higher than that for \(\theta=0^{\circ}\); \(\rho_{\rm c}\) for a crack width (\(L_{\rm d}\)) of 8 mm is 25.47% higher than that for \(L_{\rm f}=30\) mm; and \(\rho_{\rm c}\) for a crack orientation (\(\beta\)) of 0\({}^{\circ}\) is 15.87% higher than that for \(\beta=90^{\circ}\). Regarding the influencing factor of the solution cavity characteristics, the solution cavity size has the greatest impact on the wellbore stability, followed by the connectivity between cracks and solution cavities and the solution cavities quantity. However, the difference in the influence among these solution cavities characteristics factors is smaller than that of the cracks characteristics factors. It should be noted that the sensitivity analysis of cracks and solution cavities characteristics on wellbore stability here is based on the numerical simulation conditions and parameter settings, as shown in Section 3.2, which is in line with the real-life scenario of cracks and solution cavities characteristics in the carbonate formation in the Gaoshiti-Moxi area of the Sichuan Basin. The results of the sensitivity analysis may be different if other formations or geological conditions are studied.  
Figure 27: Displacement nephogram around the wellbore for (**a**) disconnected cracks and solution cavities; (**b**) connected cracks and solution cavities.  
Figure 26: Stress nephogram around the wellbore for (**a**) disconnected cracks and solution cavities; (**b**) connected cracks and solution cavities.  
As previously discussed, the presence of cracks and solution cavities in carbonate formation significantly diminishes the wellbore stability. In the case of vertical wells, cracks oriented closer to the direction of maximum horizontal stress can lead to reduced wellbore stability. Furthermore, the increased dip angle and width of cracks, along with the greater quantity and size of solution cavities, including connected cracks and solution cavities, all contribute to wellbore instability in carbonate formation. Consequently, a meticulous survey of cracks and solution cavities is essential during the drilling design phase for carbonate formation. This survey should encompass the relationship between cracks and in situ stress, crack dip angle and width, solution cavity diameters and quantity, as well as the connectivity of cracks and solution cavities. A comprehensive analysis of the characteristics of cracks and solution cavities should then be integrated to evaluate the wellbore stability. Ultimately, this approach enables the development of a reliable drilling design that incorporates appropriate drilling fluid densities and excellent drilling fluid properties. Such a design is crucial for ensuring the safety of drilling operations in carbonate formation.