## 2 Methodology
### Model Initialization  
To obtain the model's initial pressure, temperature, and saturation steady-state conditions (Figure 3), we separately simulated three subdomains (GHBL, TPL, and FGL). We achieved consistent heat flux between the subdomains' contact surfaces by fine-tuning the geothermal gradient. Finally, we merged them to complete the initialization of the model [37; 38; 39; 40; 41; 42; 43]. The capillary pressure calculation adopted the van Genuchten model, where the maximum reference aqueous saturation \(S_{mxA}\) is 1, the irreducible aqueous saturation \(S_{irA}\) is 0.30, the porosity distribution index \(\lambda\) is 0.45, and the initial capillary pressure \(P_{0}\) is 1 \(\times\) 10\({}^{4}\) Pa [24; 44; 45; 46]. The capillary force varies with the change in aqueous saturation \(S_{A}\). The relative permeability calculation adopted the Stone model, where \(K_{rA}\) is the aqueous phase relative permeability and \(K_{rG}\) is the gas phase relative permeability. The irreducible aqueous saturation \(S_{irA}\) and irreducible gas saturation \(S_{irG}\) are 0.30 and 0.03, respectively, and the aqueous phase permeability reduction index \(nA\) and gas phase permeability reduction index \(nG\) are 3.5 and 2.5, respectively [24; 44; 45; 46]. \(K_{rA}\) varies with the change in aqueous saturation \(S_{A}\), while \(K_{rG}\) varies with the change in gas saturation \(S_{G}\). The above model parameter settings are based on previous research work ([PERSON] et al., 2018; [PERSON] et al., 2023; [PERSON] et al., 2019; [PERSON] et al., 2020) that verified the applicability of these models and parameters in this sea area [44; 45; 46]. During the simulation process, the wellbore grids were considered as  
Figure 2: Model schematic diagram. (**a**) Geological model and logging curve of the SHSC-4 well. (**b**) Model mesh.  
a \"pseudo porous medium\" and given a fixed production pressure difference of 4 MPa. The porosity of the wellbore grids is 1, and the permeability is 10,000 D, without considering capillary force, the relative permeability varies linearly with the saturation of each phase and has extremely low residual gas saturation [43]. The assumption was made that the OB and UB layers had a permeability of 2.0 mD and porosity of 0.3, respectively [44]. The detailed parameters of the model are summarized in Table 2.  
\begin{table}
\begin{tabular}{c c} \hline
**Parameter** & **Value and Unit** \\ \hline OB and UB thickness [35; 36] & 20 m \\ GHBL thickness [8; 44; 45; 46] & 35 m \\ TPL thickness [8; 44; 45; 46] & 15 m \\ FGL thickness [8; 44; 45; 46] & 27 m \\ OB and UB initial permeability & 2.0 mD \\ GHBL initial permeability [8; 44; 45; 46] & 2.9 mD \\ TPL initial permeability [8; 44; 45; 46; 44] & 1.5 mD \\ FGL initial permeability [8; 44; 45; 46] & 7.4 mD \\ Wellbore radius [44; 45; 46] & 0.1 m \\ Salinity [44; 45; 46] & 3.5\% \\ GHBL and TPL initial hydrate saturation [8; 44; 45; 46] & Extracted from logging curve (Figure 2a) \\ FGL initial free gas saturation [8; 44; 45; 46] & Extracted from logging curve (Figure 2a) \\ OB and UB porosity & 0.30 \\ GHBL porosity [8; 44; 45; 46] & 0.35 \\ \hline \end{tabular}
\end{table}
Table 2: Model parameters.  
Figure 3: Model’s initial pressure, temperature, hydrate saturation, and gas saturation.