## 3 Methodology and Model Parameters  
### Numerical Simulation Scheme  
According to the real-life scenario of cracks and solution cavities characteristics in the carbonate formation of the Gaoshiti-Moxi area of the Sichuan Basin (Figure 3), three factors are considered for evaluating the influence of cracks and solution cavities on the wellbore stability, including cracks characteristics, solution cavities characteristics and connectivity between cracks and solution cavities. Based on the formation reality stated in Section 3.1, the parameters setting of these factors in the numerical simulation is simplified through an arithmetic progression to obtain the favorable rules regarding the influence of cracks and solution cavities characteristics on the wellbore stability, as shown in Table 2. The  
Figure 3: Distribution of cracks and solution cavities in the 5182–5187 m section of Well GS10 in the Gaoshiti–Moxi area of the Sichuan Basin: (**a**) 5182–5185 m section; (**b**) 5184.5–5187.5 m section.  
total stresses are employed to determine the stability of the wellbore. This is because the rock strength parameters, which are used for the numerical simulation, are calculated by using logging data. Additionally, there is another reason for using total stress. Considering the actual situation where a properly formed mud cake exists on the borehole wall, it is assumed that the gas in the formation does not flow. The equivalent drilling fluid density of collapse pressure (\(\rho_{c}\)) is calculated for these different conditions to analyze these factors affecting the wellbore stability. The model designs of the angle of the crack strike and the maximum horizontal principal stress direction (\(\beta\)), the dip angle of the crack (\(\theta\)), the solution cavity diameter (\(D\)), and the solution cavities quantity (\(N\)) are shown in Figures 4-7, respectively.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Factor** & **Parameter** & **Parameters Setting** & **Other Parameters** \\ \hline \multirow{4}{*}{Cracks characteristics} & \(\beta\) & \(0^{\circ}\), \(15^{\circ}\), \(30^{\circ}\), \(45^{\circ}\), \(60^{\circ}\), \(75^{\circ}\), \(90^{\circ}\) & \(L_{t}=10\) mm, \(\theta=90^{\circ}\) \\  & \(\theta\) & \(0^{\circ}\), \(15^{\circ}\), \(30^{\circ}\), \(45^{\circ}\), \(60^{\circ}\), \(75^{\circ}\), \(90^{\circ}\) & \(L_{t}=10\) mm, \(\beta=90^{\circ}\) \\  & \(L_{t}\) & 8 mm, 12 mm, 16 mm, 25 mm, 30 mm & \(\beta=90^{\circ}\), \(\beta=90^{\circ}\) \\ \hline \multirow{4}{*}{Solution cavities characteristics} & \(D\) & 152 mm, 304 mm, 457 mm, 609 mm, 762 mm, 914 mm & \(L=300\) mm \\  & & 1 (Unilateral distribution), 2 (Symmetrical distribution), 4 (Symmetrical distribution around the circumference), 8 (Symmetrical distribution around the circumference with two groups), 16 (Symmetrical distribution around the circumference with four groups) & \(L=300\) mm, \(D=152\) mm \\ \hline \multirow{4}{*}{Connectivity between cracks and solution cavities} & \multirow{4}{*}{Connectivity} & \multirow{4}{*}{Situation I: The cracks are not connected to the four solution cavities.} & \multirow{4}{*}{\(L_{t}=10\) mm, \(D=\)152 mm} \\  & & & \\ \cline{1-1} \cline{4-4}  & & & \\ \cline{1-1} \cline{4-4}  & & & \\ \cline{1-1} \cline{4-4}  & & & \\ \hline \hline \end{tabular} \(\beta\) is the angle of the crack strike and the maximum horizontal principal stress direction, \({}^{\circ}\); \(\theta\) is the dip angle of the crack, \({}^{\circ}\); \(L_{t}\) is the crack width, mm; \(D\) is the solution cavities diameter, mm; \(N\) is the solution cavities quantity, Integer; \(L\) is the distance from the solution cavities to the wellbore wall, mm.  
\end{table}
Table 2: Parameters setting of the analytical factors for the numerical simulation.  
Figure 6: Model design of the solution cavity diameter (\(D\)): (**a**) \(D=152\) mm; (**b**) \(D=304\) mm; (**c**) \(D=457\) mm; (**d**) \(D=609\) mm; (**e**) \(D=762\) mm; (**f**) \(D=914\) mm.