## 2 Simulation Model and Calculation Method
### ATES System Model  
The ATES system model is as shown in Appendix B. The aquifer model was created based on the cylindrical model of [PERSON] et al. (2019) and the energy equation in FEFLOW (2019). Figure 2 shows a conceptual diagram of the cylindrical model. In this model, assuming that the upper and lower parts are horizontal aquifers under pressure and sandwiched between impermeable layers. The groundwater flow velocity between \begin{table}
\begin{tabular}{c c c} \hline Heat storage tank capacity [m\({}^{3}\)] & 1000 \\ \hline Number of layers [-] & 10 \\ \hline Inflow flow rate [L/min] & 833 \\ \hline Inflow temperature [\({}^{\circ}\)C] &
\begin{tabular}{c} Cooling: 7 \\ Heating: 45 \\ \end{tabular} \\ \hline \multicolumn{2}{c}{Initial temperature in the heat storage tank [\({}^{\circ}\)C]} & 15 \\ \hline \multirow{4}{*}{Cooling} & Heat storage operation & start & The 9 th layer is below 10 \({}^{\circ}\)C \\ \cline{2-3}  & & Stop & 8 th layer 8 \({}^{\circ}\)C or more \\ \cline{2-3}  & Heat utilization operation & start & The third layer is below 8 \({}^{\circ}\)C \\ \cline{2-3}  & & Stop & 8 th layer 11 \({}^{\circ}\)C or higher \\ \hline \multirow{4}{*}{Heating} & Heat storage operation & start & The 9 th layer is below 42 \({}^{\circ}\)C \\ \cline{2-3}  & Heat utilization operation & start & The third layer is below 41 \({}^{\circ}\)C \\ \cline{2-3}  & & Stop & 8 th layer 42 \({}^{\circ}\)C or higher \\ \hline \end{tabular}
\end{table} 
Table 1: The WTES system model settings. Figure 1: The stratum diagram of the heat storage well. GW_AC is flow rate from secondary side [m\({}^{3}\)/h], GW_MC is flow rate from water-cooled HP [m\({}^{3}\)/h], GW_ST is flow rate between layers [m\({}^{3}\)/h], T_AC is inflow temperature from secondary side [\({}^{\circ}\)C], T_MC is inflow temperature from heat source [\({}^{\circ}\)C], T_1 is temperature of layer 1 [\({}^{\circ}\)C], and T_N is temperature of layer N [\({}^{\circ}\)C]. layers is set to 0 m/s, and the heat transfer due to groundwater transfer is calculated. Then, consider the heat loss due to heat conduction include the inner and outer layers. The outer edge (boundary) of the cylinder of the aquifer is opened and flows out from the outer edge by water injection to lose heat. In the pumping operation, groundwater at underground temperature flows in from the outer edge. The parameters of the ATES system model were established using experimental data. The parameter was set by examining the thickness of the impermeable layer [39]. Figure 3 shows a geological map in which the ATES system was actually installed. The ATES system operates using three wells: a pumping well (6 m), a heat storage well (22 m-32 m), and a reduction well (80 m). The pumping and heat storage wells are sand gravel layers. The reduction wells are clay mixed sand and gravel layers. The excavation depth of the heat storage well is located between GL-22 m and GL-32 m. The ground of the heat storage well is a clay layer of the impermeable layer from GL-32 m, but the upper part of the heat storage well is a gravel layer in the water-permeable layer. The diameter of the well is 0.45 m, and the strainer position is GL-22 m to \(-\)30 m. The submersible pump is located at GL-22 m, and temperature sensors are installed at a total of five locations. The water pumped from the pumping well exchanges heat with the hot water sent from the heat pumps through a heat exchanger, and stores the heat in the heat storage well. The heat stored in the heat storage well is pumped up and sent to the air handling unit (AHU) installed in the building to perform heat utilization operation. It is a system that returns water to the reduction well after heat utilization operation. Figure 2: A conceptual diagram of the cylindrical model. The accuracy of the aquifer model was verified using the measured data. Figure 4 shows the results of verifying the accuracy of the aquifer model. The measured data in Figure 4 represents the data measured at 23 m in the aquifer.