## 2 Methods  
### Characterization of an EAHX for Standalone Room Cooling  
Figure 1 sketches a large-diameter EAHX for office building cooling. In the daytime, hot outdoor air enters the EAHX at temperature \(T_{\text{a0}}\) and flows along a horizontal pipe with length \(L\) buried at depth \(z\). Since the pipe is in contact with soil at temperature \(T_{\text{s0}}\) (undisturbed soil temperature), which is lower than outdoor air, cooled air at temperature \(T_{\text{aL}}\) leaves the EAHX at an air handling unit (AHU) before being delivered to the building (the AHU allows a bypass to the EAHX). Figure 1 also sketches the flow of air inside the building. Air from the EAHX enters the building and contacts buried structural elements with large thermal mass that are cooled during the nighttime [23], when outdoor air temperatures are lower; as a result, during the daytime, air is supplied to the room at a temperature \(T_{\text{aS}}\), which is lower than \(T_{\text{aL}}\). The room (air) setpoint temperature is depicted in Figure 1 as \(T_{\text{ar}}\). Using the classification scheme of [PERSON] et al. [4], Figure 1 sketches an open-loop horizontal single-pipe EAHX for cooling. Moreover, the coupling with building thermal mass (TM) and nighttime forced ventilation results in a hybrid EAHX-TM system operating in continuous mode. Figure 1: Sketch of a large-diameter EAHX for office building cooling. The above classification makes no distinction between EAHX for outdoor air load removal--for air pre-cooling--and EAHX for room load removal, i.e., for standalone room cooling. To clarify the meaning given in this paper to an EAHX capable of removing room loads, Figure 2 presents a sketch of the thermo-hygrometric processes with air from the instant air enters the EAHX \((T_{\mathrm{a0}},\ \omega_{\mathrm{a0}})\) until it leaves the office room \((T_{\mathrm{ar}},\ \omega_{\mathrm{ar}})\). Sensible cooling of outdoor air is depicted in Figure 2 by the horizontal line, from right to left, with constant specific humidity \(\omega_{\mathrm{a0}}=\omega_{\mathrm{as}}\), a reasonable approximation for EAHXs operating in hot and dry climates [17]. In fact, for these climates, the EAHX inner surface temperature remains larger than the air dew temperature, preventing condensations; moreover, indoor air quality constraints impose the choice of EAHX materials (or coatings) impervious to water, preventing moisture transfer from the soil to the air flowing inside the EAHX. The line from \(T_{\mathrm{a0}}\) to \(T_{\mathrm{as}}\) is divided into three subprocesses. The first subprocess occurs in the EAHX and is the sensible cooling of air from outdoor temperature \(T_{\mathrm{a0}}\) to temperature \(T_{\mathrm{ar}}\), which is equal to the room design setpoint temperature. This subprocess translates into outdoor air load extraction, \(\dot{Q}_{\mathrm{oa}}^{\mathrm{EAHX}}\). Still occurring inside the EAHX, the next subprocess corresponds to the sensible cooling from temperature \(T_{\mathrm{ar}}\) to the EAHX exit temperature, \(T_{\mathrm{aL}}\). This subprocess translates into the EAHX room (air) load extraction \(\dot{Q}_{\mathrm{rm}}^{\mathrm{EAHX}}\). The third subprocess depicted in Figure 2 results from heat transfer between the air and buried building structural elements that are cooled during the nighttime. This sensible cooling from \(T_{\mathrm{aL}}\) to supply air temperature \(T_{\mathrm{as}}\) also translates into a room (air) load extraction, but occurring in the building, not the EAHX. This building load removal is represented as \(\dot{Q}_{\mathrm{rm}}^{\mathrm{bldg}}\).