# Heat Transfer Performance and Operation Scheme of the Deeply Buried Pipe Energy Pile Group
## 3 Numerical Simulations: Thermal Behavior of DBP-EP
### Technical Features of the Used Software
#### 3.1.2 Boundary Condition  
Referencing experimental data from DBP-EP, the geometric parameters of the model are set at 10 m \(\times\) 10 m \(\times\) 120 m. The stratum material from top to bottom is set as a fill layer (0-10 m); a fine sand layer (10-17 m); a clay layer (17-25 m); a gravel layer (25-50 m); and a mudstone layer (50-120 m). Horizontal boundaries are positioned beneath the model surface at depths of 50 m, 75 m, and 100 m to delineate distinct mudstone layers, designated as mudstone layers 1, 2, and 3. Table 1 shows the physical parameters of formation materials. These layers are characterized by sequentially decreasing porosities of 0.25, 0.20, and 0.15, aiming to replicate the gradual compaction of actual stratigraphic formations with increasing depth. To enhance the fidelity of domain temperature simulation, an initial surface temperature of 17 \({}^{\circ}\)C is prescribed. With every meter descent from the surface, the temperature rises by 0.03 \({}^{\circ}\)C. Concurrently, the inlet water temperature is held constant at 30 \({}^{\circ}\)C. Due to the complex geological composition, to avoid interference from other factors on the pile's heat transfer behavior, the foundation of the modeling of the DBP-EP rests upon the following subsequent presumptions:  
1. The assumption of soil homogeneity is made; the thermophysical parameters of each layer of rock and soil are isotropic and remain unchanged, with no consideration given to the influence of internally generated steam on heat migration or the effects of thermal radiation within the soil on the thermal transfer processes of DBP-EPs.
2. The material used to backfill the pile is in complete contact with the surfaces of the heat exchange pipes, ensuring uniform thermal conductivity throughout the surrounding rock and soil layers. Any contact thermal resistance is considered negligible, and the system is assumed to conduct heat purely.
3. The potential impact of groundwater seepage on the heat exchange process of the pile was not accounted for in this analysis.  
To facilitate enhancement precision of subsequent heat transfer computations concerning the pile, a refinement of the mesh was implemented at the interface connecting the heat exchange pipes and the DBP-EP. Tetrahedral meshes were chosen to partition the model, resulting in 236,228 boundary elements within the model. This mesh configuration remained unaltered throughout subsequent calculations. Figure 5 illustrates the mesh division model of the DBP-EP.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Material**} & **Density** & **Thermal** & \\  & **(kg/m\({}^{3}\))** & **Conductivity** & **Porosity** \\  & & **(W/(m\({}^{\circ}\)C))** & \\ \hline Backfill (fine sand) & 1750 & 0.58 & 0.45 \\ Pile (concrete) & 2350 & 2.20 & 0 \\ Fine sand & 2350 & 2.50 & 0.45 \\ Clay & 2000 & 1.00 & 0.40 \\ Gravel & 2000 & 2.31 & 0.30 \\ Mudstone 1 & 2000 & 1.90 & 0.25 \\ Mudstone 2 & 2000 & 1.90 & 0.20 \\ Mudstone 3 & 2000 & 1.90 & 0.15 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Physical parameters of formation materials.