## 2 Materials and Methods
### EAHX Performance Assessment
Room upper and lower setpoint temperatures delimiting office room thermal comfort also represented. Figure 3: Photograph of the EAHX while the buried pipes were being installed at an average depth of 5.5 m below soil surface. To assess the cooling performance of an EAHX, two main indices are used (monitoring data confirm negligible latent heat exchanges in the EAHX during the dry summer period; further details provided in Section 3.1):  
* EAHX outdoor air load removal, \[\dot{Q}_{\text{oa}}^{\text{EAHX}}=\dot{m}_{\text{a}}c_{\text{a}}\Delta T_{ \text{al,a0}};\] (1)
* EAHX room load removal, \[\dot{Q}_{\text{r}}^{\text{EAHX}}=\dot{m}_{\text{a}}c_{\text{a}}\Delta T_{ \text{al,rs}};\] (2) where the gradients \(\Delta T_{\text{al,a0}}\) and \(\Delta T_{\text{al,rs}}\) are defined as \[\Delta T_{\text{al,a0}}= \begin{cases}T_{\text{aL}}-T_{\text{a0}}&\text{ if }\ T_{\text{aL}}<T_{\text{a0}};\\ 0&\text{otherwise};\end{cases} \] (3) and \[\Delta T_{\text{al,rs}}= \begin{cases}T_{\text{aL}}-T_{\text{rs}}^{\text{U}}& \text{ if }\ T_{\text{aL}}<T_{\text{rs}}^{\text{U}};\\ 0&\text{otherwise}\;.\end{cases} \] (4)  
EAHX outdoor air load removal is a useful performance metric to assess EAHX \"total\" cooling capacity. However, when studying standalone EAHX cooling, EAHX room load removal is a much more appropriate performance metric, as it assesses EAHX \"effective\" _room_ cooling capacity. Divided by the (cooled) room floor area,  
\[\dot{q}_{\text{r}}^{\text{EAHX}}=\frac{\dot{Q}_{\text{r}}^{\text{EAHX}}}{A_{ \text{r}}}, \tag{5}\]  
with units W/m\({}^{2}\), the specific EAHX room load removal allows for a straightforward comparison to the room _design_ cooling demand, a fundamental parameter in HVAC design (in general, \(\dot{q}_{\text{i}}^{\text{EAHX}}=\dot{Q}_{\text{j}}^{\text{EAHX}}/A_{\text{r}}\), with \(j\in\{\text{a0,r}\}\)). Given the outdoor air and EAHX exit air temperatures' dynamic nature, to assist the detailed analysis of the EAHX performance indices, regions A, B, C and D--see Figure 4--were defined. These regions are characterized as follows:  
* **Region A**: Nighttime (from evening to the start of the working day) with outdoor air temperature lower than EAHX exit air temperature, \(T_{\text{a0}}<T_{\text{aL}}\). In this region, the EAHX heats the outdoor air, operating, therefore, in heating mode. Since this paper discusses cooling performance, Region A is excluded from the analysis. * **Region B**: From the start of the working day to noon with EAHX exit air temperature lower than outdoor air temperature and both of these lower than the upper room setpoint temperature, \(T_{\text{aL}}<T_{\text{a0}}<T_{\text{rs}}^{\text{U}}\). In this region, the EAHX cools the outdoor air, operating, therefore, in cooling mode. Since the outdoor air temperature is lower than the room upper setpoint temperature, EAHX room load removal has two components, \[\dot{Q}_{\text{r}}^{\text{EAHX}}=\dot{Q}_{\text{oa}}^{\text{EAHX}}+\dot{Q}_{ \text{r}}^{\text{OA}}=\dot{m}_{\text{a}}c_{\text{a}}\Delta T_{\text{aL,a0}}+ \dot{m}_{\text{a}}c_{\text{a}}\Delta T_{\text{a0,rs}},\] (6) namely, the EAHX outdoor air load removal component, \(\dot{Q}_{\text{oa}}^{\text{EAHX}}\); and the outdoor air room free-cooling component, \(\dot{Q}_{\text{r}}^{\text{OA}}\) (actually, this latter component is independent of the EAHX; however, because the flow of outdoor air in large-diameter EAHXs has negligible added fan cost--negligible pressure losses--, \(\dot{Q}_{r}^{\rm OA}\) is absorbed into \(\dot{Q}_{r}^{\rm EAHX}\)). In Equation (6), the outdoor air to room upper setpoint temperature gradient, \(\Delta T_{\rm a0,rs}\), is defined as,  
\[\Delta T_{\rm a0,rs}= \begin{cases}T_{\rm a0}-T_{\rm rs}^{\rm U}&\text{ if }\ T_{\rm a0}<T_{\rm rs}^{\rm U};\\ 0&\text{otherwise }.\end{cases}  \tag{7}\]  
In region B, due to outdoor air free cooling, the following inequation applies: \(Q_{r}^{\rm EAHX}\geq Q_{\rmoa}^{\rm EAHX}\).