## 2 Experimental Methodology  
Figure 1 shows a comparison test with the existing open underground heat exchanger and cooling and heating operation used to evaluate the energy efficiency and performance coefficient of the system suitable for on-site testing using the test method of the water-water geothermal source heat pump unit. An automatic cross-operating control system was used to maintain the optimal supply of heat sources for the existing SCW and for balancing well underground heat exchangers. The balancing well cross-mixed heat exchange geothermal heat pump system consisted of a geothermal source heat pump  
and underground heat exchanger and includes the cross-operation controller among the mechanical piping and circulation pump and system control system. The test targets were a geothermal source heat pump for 30 RT-level cooling and heating and two underground heat exchangers with a typical SCW system installed with a diameter of 10 in (0.254 m) and depth of 300 m. The SCW underground heat exchanger had a natural water level of 4.7 m and a maximum quantity of 350 tons/day. The distance between the two wells was approximately 12 m.  
To verify that the experimental measurements were reasonable, as shown in Figure 1, a justifiable means of validation was required. The simplest expression of the heat balance equation is  
\[\dot{q_{in}}=\dot{m}\cdot C_{p}\cdot(T_{out}-T_{in}) \tag{1}\]  
where \(\dot{q_{in}}\) (W) represents the measured heat input to the water heater elements and pumps; \(\dot{m}\) (liter per minute, LPM) is the flow rate; \(C_{p}\) denotes the specific heat of water; and \(T_{in}\) and \(T_{out}\) represent the temperatures measured with a thermostat. After applying all the calibration equations to the measurement devices, the heat transfer rate predicted by the right-hand side of Equation (1) can be compared to the measured power input (left hand side of Equation (1)). The numbers summarised in Table 1 are the average values over the length of each test, and they were used to compare the instrumentation uncertainties and total heat input error. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Location**} & **Transducer** & \multirow{2}{*}{**Average q (W)**} & \multirow{2}{*}{**Difference (W)**} & \% of Average \\  & **Reading (W)** & & & **Power** \\ \hline A & 2506.6 & 2657.8 & 101.2 & 3.88 \\ B & 3207.2 & 3302.5 & 93.3 & 2.82 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Heat balance check. Figure 1: Schematic of the water-water geothermal heat pump system for operating standing column well (SCW) and balancing well geothermal heat exchanger system. LPM: liter per minute  
The uncertainties in the temperature measurement were \(\pm 0.01\)\({}^{\circ}\)C for the probes and \(\pm 0.04\)\({}^{\circ}\)C for the signal conditioner of the digital displays with the analog signal. The total uncertainty for the temperature measurements are expressed in quadratic form, as shown in Equation (2):  
\[\Delta\mathrm{T}=\sqrt{\left(\pm 0.01\right)_{\mathrm{in}}^{2}+\left(\pm 0.04 \right)_{\mathrm{in}}^{2}}+\sqrt{\left(\pm 0.01\right)_{\mathrm{out}}^{2}+ \left(\pm 0.04\right)_{\mathrm{out}}^{2}}\approx\pm 0.0825\text{ }^{\circ}\mathrm{C} \tag{2}\]  
Considering that \(\Delta\mathrm{T}\) for each test is approximately \(5\text{ }^{\circ}\mathrm{C}\), the uncertainty due to the temperature measurement becomes:  
\[\mathrm{Error}=\frac{\pm 0.0825\text{ }^{\circ}\mathrm{C}}{5\text{ }^{\circ}\mathrm{C}}\times 100\%=\approx\pm 1.65\% \tag{3}\]  
Using the highest error for the flowmeter taken from Table 2 of \(\pm 2.03\%\), the total uncertainty in the heat balance equation was computed as:  
\[\mathrm{Total\ Error}=\sqrt{\left(\pm 0.0165\right)^{2}+\left(\pm 0.0203 \right)^{2}}\approx 2.62\% \tag{4}\]  
As shown in Figure 2, the balancing well cross-mixed heat exchanger system is characterized by different operation methods in the two SCW-type geothermal heat exchangers with 100% pumping from each geothermal heat exchanger, while the recovery quantity is different.