## 3 Numerical Solution Method and Model Validation
### Validation of the Model  
In light of the well drilling process in the shallow gas hydrate reservoir in deep water, the stability of the horizontal well was simulated, with the horizontal section of the well assumed to be 400 m long and all the physical parameters of the simulated reservoir assumed to be isotropic. The basic parameters used in the simulations are shown in Table 1. The two-dimensional model of the hydrate reservoir was established as a quarter circle with a radius of 4 m, where the horizontal well diameter is 0.1143 m.  
The model was divided by mapping grids, which included 6 vertex units, 160 boundary units, and 1050 domain units and had a minimum unit mass of 0.9833. In addition, the grids near the wellbore were properly refined by the distribution function. In the simulations by COMSOL Multiphysics, the boundary conditions were as follows:  
1. AD was the boundary of the drilling fluid invading the hydrate reservoir, the temperature and pressure of the drilling fluid invading the reservoir were set, the volume fraction of the liquid phase was set at 1, and the boundary load condition of the solid field was set as the drilling fluid invading pressure. 2. AB and CD were both set as symmetrical boundaries, the solid field was set as roller supporting, with the normal displacement of 0. 3. BC was the outer boundary, which was set as the outflow boundary condition in the porous medium phase transfer and the porous medium heat transfer modules, as the boundary with the constant pressure of the initial pressure of the hydrate reservoir in the Darcy law module, and as the boundary with the load condition of the initial pressure in the solid field. The proposed model was verified by using the drilling data of the SH2 vertical well in the hydrate reservoir of the Shenhu Sea area. In the layers at 200.1 m and 217.5 m below the mud line, the hydrate saturations calculated by the model are in good agreement with \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Parameter** & **Unit** & **Value** & **Parameter** & **Unit** & **Value** \\ \hline Depth & m & 1420–1464 & \begin{tabular}{c} Horizontal section \\ length \\ \end{tabular} & m & 400 \\ \hline Absolute porosity & - & 0.4 & Poisson’s ratio & - & 0.35 \\ \hline Initial hydrate & - & 0.33 & \begin{tabular}{c} Absolute \\ permeability \\ \end{tabular} & m\({}^{2}\) & \(4.935\times 10^{-14}\) \\ \hline Sea level & \({}^{\circ}\)C & 25 & Pore pressure & MPa & 14.508 \\ \hline Internal friction & \({}^{\circ}\) & 12 & \begin{tabular}{c} Initial temperature \\ of reservoir \\ \end{tabular} & \({}^{\circ}\)C & 13.373 \\ \hline Vertical depth & m & 1435.1 & \begin{tabular}{c} Minimum horizontal \\ principal stress \\ \end{tabular} & MPa & 15.47 \\ \hline Sea water depth & m & 1235 & \
\begin{tabular}{c} Ultimate horizontal \\ principal stress \\ \end{tabular} & MPa & 15.47 \\ \hline Elastic modulus & MPa & \(S_{\text{h}}=0.32\) & Vertical stress & MPa & 16.36 \\ \hline Cohesion & MPa & \(S_{\text{h}}=0.0.1\) &
\begin{tabular}{c} Temperature of \\ injected drilling fluid \\ \end{tabular} & \({}^{\circ}\)C & 25 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Basic drilling parameters. those from the field logging data, so these two reservoir layers were taken as the main research objects. The basic data are shown in Table 2.  
The effects of drilling fluid invasion in these two layers were simulated by COMSOL software. The basic data are shown in Table 3. The simulation results showed that the wellbore at these two layers expanded in some degrees, and the yield radii of the wellbore at these two layers after drilling fluid invasion were 0.00998 m and 0.01191 m, respectively, as shown in Figure 3. By comparing with the measured caliper data of the wellbore from logging, the errors at these two points were 9.78% and 5.99%, respectively, which verified the accuracy in simulating the horizontal well drilled in the hydrate reservoir at sea. Figure 4 shows the details. Figure 4: Comparison of well caliper data from logging and simulation.