# Optimization Design Study of Pipe Curtain Freezing Scheme for Sanya Estuary Submarine Channel
## 3 Three-Dimensional Numerical Modelling
### Selection of Relevant Parameters and Brine Cooling Programme
#### 3.5.2 Salt Water Cooling Program  
The cooling strategy for the brine in this project is executed according to a predefined schedule, prohibiting direct reduction of the brine temperature for recycling purposes. The model is analyzed using transient analysis, with the brine cooling plan implemented in COMSOL software through interpolating functions. The wall of the freezing tube serves as the thermal boundary condition, with the low-temperature brine inside the freezing tube acting as the temperature boundary condition. The technical parameters for the freezing tube are as follows: 1 The active freezing time cycle of the freezing tube is 40 days, with each analysis step lasting 24 h (1 day); 2 The initial temperature is 18 \({}^{\circ}\)C, which is reduced to \(-15\)\({}^{\circ}\)C by the 5 th day of the freezing process, and the temperature of the brine remains at \(-28\)\({}^{\circ}\)C from the 10 th to the 40 th day, ensuring that the brine temperature is sufficiently lowered to \(-28\)\({}^{\circ}\)C for smooth excavation of the submarine tunnel; 3 In the design, the average temperature of the permafrost curtain in the strong freezing zone is set at \(\leq-10\)\({}^{\circ}\)C, and the average temperature of the permafrost curtain in the weak freezing zone is \(\leq-8\)\({}^{\circ}\)C. If the temperature of the brine and the thickness of the permafrost curtain do not meet the pre-set design criteria, the duration of active freezing should be appropriately extended, with the brine cooling schedule shown in Table 2.  
Before excavation, probe holes must be opened in the frozen area to verify the temperature of the frozen soil and the thickness of the frozen wall, ensuring the normal operation of the freezing system. Based on the measured temperature data of the brine and the temperature of the measurement holes, it is determined whether there is any intersection of rings in the frozen curtain, ensuring that there is minimal pressure on the soil layer in the frozen curtain before formal excavation. Four different paths are established in the model solely to clearly indicate the cooling law of the temperature field and provide a reference for the next construction phase. For the accuracy of the numerical analysis of the temperature field of the freezing method, this group has compared the numerical analysis with many on-site measurements, with the relevant data obtained matching the expected values, proving the reliability of the current numerical simulation method. This reliability can be further supported by related literature [28; 29].  
\begin{table}
\begin{tabular}{c c} \hline
**Parameter Name** & **Parameter Value** \\ \hline Soil density (kg/m\({}^{3}\)) & Unfrozen ground 1920 \\  & Tundra 1880 \\ Soil thermal conductivity (W/(m\(\cdot\)K)) & Unfrozen ground 1.18 \\  & Tundra 1.79 \\ Specific heat of soil (J/(kg\(\cdot\)K)) & Unfrozen ground 1.53 \\ Soil permeability coefficient(m/s) & Tundra 1.61 \\ Soil porosity & Unfrozen ground 0.56 \(\times\) 10\({}^{-4}\) \\ Density of ice (kg/m\({}^{3}\)) & Tundra 1.91 \(\times\) 10\({}^{-30}\) \\ Thermal conductivity of water (W/(m\(\cdot\)K)) & 0.4 \\ Thermal conductivity of ice (W/(m\(\cdot\)K)) & 920 \\ Specific heat of water (J/(kg\(\cdot\)K)) & 0.55 \\ Specific heat of ice (J/(kg\(\cdot\)K)) & 2.14 \\ \multicolumn{2}{c}{Specific heat of water (J/(kg\(\cdot\)K))} & 4180 \\ \multicolumn{2}{c}{Specific heat of ice (J/(kg\(\cdot\)K))} & 2100 \\ Latent heat of phase transition of water ice (KJ/(kg\(\cdot\)K)) & 334 \\ \hline \end{tabular}
\end{table}
Table 1: List of relevant material parameters.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline Time/d & 0 & 5 & 15 & 20 & 30 & 40 \\ \hline Temperature/\({}^{\circ}\)C & 18 & \(-15\) & \(-28\) & \(-28\) & \(-28\) & \(-28\) \\ \hline \end{tabular}
\end{table}
Table 2: Saltwater cooling program.