On the other hand, considering the k value of the time interval [mathematical expression not reproducible] of the GHEX's surface (r* = 1),
As mentioned previously, the method using the g-function (Eskilson 1987) is among the conventional methods of calculating underground temperature around the GHEX by applying theoretical analysis.
Here, [r.sub.p-out]/[L.sub.p] is the ratio of the radius to the length of the GHEX, and Geometry is the variable representing the shape of the arrangement of GHEXs.
Comparing the underground temperature calculation method of the present tool (Equations 1,6, and 19-21) with the calculation method by g-function (Equation 23), the first point of difference between the two methods is that in the present tool the surface temperature of the GHEX is obtained by applying the analysis solution of the ICS.
The configuration of the GSHP system is shown in Figure 6 and is mainly composed of three parts: the indoor unit, the heat pump, and the GHEX. The calculation formulas used for each element during the simulation are shown below.
Although actual GHEXs are several meters (feet) long and have temperature distribution within, the heating medium in the GHEX in this case is regarded as a lumped parameter system, as shown in Figure 7, and the heat balance in the infinitesimal time dt is considered.
Here, [c.sub.p1f] and [[rho].sub.1f] are, respectively, the specific heat and density of the heating medium; [V.sub.f] and [T.sub.f] are, respectively, the volume and temperature of the heating medium inside the heat exchanger; and [G.sub.1f] is the circulation flow rate of the GHEX. [K.sub.p-out] in Equation 29 is the heat transmission coefficient based on the outer surface area from the GHEX to the brine, and [A.sub.p-out] is the outer surface area of the GHEX.
The water heat source VRF is connected with a 75 m (246 ft) x 8 borehole double-U tube type GHEX configuration, and the GHEXs are arranged at intervals of 2 m (6.56 ft), as shown in Figure 8.
In Sweden and the Netherlands, where underground heat is commonly used, the phenomenon of temperature decrease due to the interference of ground heat exchangers (GHEXs) installed in residential complexes has been observed, and the use of artificial heat injection to control this temperature reduction poses a problem (Witte 2016).
The g-function is a well-known and excellent underground temperature calculation method that can handle the heat injection of several underground GHEXs and perform high-speed calculations.
Figure 1 shows the concept diagram of multiple GHEXs buried in a random layout.
* The analytic solution of the ICS and the ILS showed that at points that are a few meters (feet) apart, as in the case of multiple underground GHEXs, the temperature response of the ICS can be regarded as that of the ILS.