The parameters of BHE design dictate the internal thermal resistance, as well as the pressure loss. This section briefly introduces the relevant design parameters of a coaxial BHE. Practical concerns about mechanical endurance etc. are largely omitted here.
Flow direction
In CBHE’s the downward and upward flow paths in a coaxial tube have different geometry;
therefore the thermal performance is different depending on flow direction. According to many studies of deep CBHEs, for maximum heat transfer in heat extraction mode (heating application) heat carrier should enter from the annulus tube; this way the heat carrier fluid loses minimum amount of heat on the way up and retains as high a temperature as possible. For injection mode (cooling application) the opposite direction is recommended. (Holmberg et al, 2016, p. 75).
Figure 12. Heat carrier temperature profile shapes with inlet from inner tube and annulus.
Flow rate
Flow rate dictates heat carrier residence time in the CBHE, and therefore also the temperature change that the heat carrier experiences between the inlet and outlet; ideally (with an adiabatic inner tube) by increasing the residence time the heat carrier would exit the CBHE in higher temperature, assuming that the temperature difference between the heat carrier and the ground is high enough. Heat pumps benefit from higher evaporator inlet temperatures, and therefore in this perspective low flow rate would be desirable. However, lowering the flow rate also has adverse effects: firstly the flow velocity in annulus should remain at turbulent region, or convective heat transfer will be severely weakened. Secondly, the total heat extractable from the heat carrier is dependent on flow rate, as seen in eq. 8. Therefore, even if heat pump COP could be improved by the increase in outlet temperature, the total heat flow may decrease. Since the drilling of deep boreholes is expensive, the heat output per borehole will need to be high enough to be economical. Thirdly, at lower flow rates the ratio of shunt heat transfer to useful heat transfer (output heat) tends to get higher, as shown e.g. by (Mazzotti et al, 2018). On the other hand, at higher values the increase of flow rate is countered by flow pressure loss, which, as shown previously in eq. 15, will increase very rapidly with increasing flow rate. It can be concluded that flow rate is an important subject of optimization in CBHE’s.
Tube materials
The most common material for u-tube collectors is high density polyethylene (HDPE). It has heat conductivity of 0.46 W/mK, and it is relatively cheap and durable (Mendrinos et al, 2016, p. 1). Although it is not optimal as either heat conductant (for outer tube) or insulator (for inner tube), its performance is reasonably good for shallow applications. Alternative solutions have
been suggested for both the outer and inner tubes. The optimal tube solution usually depends on borehole depth: deeper boreholes entail higher ground temperature, which makes investments in improved tube materials more profitable.
In an implementation described in e.g. (Holmberg et al, 2016, p. 68), the outer tube wall is a flexible liner situated very close or partially in contact with the borehole wall. This has the effect of maximizing cross-sectional flow area, as well as minimizing the thickness of the groundwater layer (and therefore thermal resistance) between tube wall and borehole wall. The outer tube can also be completely omitted, resulting in an open loop. This kind of implementation is the most optimal from the perspective of heat transfer, as the heat carrier will be in direct contact with borehole wall. On the flipside anti-freeze fluids cannot be used, possibly restricting heat extraction rates, and possible heat transfer surface fouling needs to be addressed.
Contrary to the outer tube wall, the inner tube should be designed to have maximum resistance to heat transfer; ideally it would be adiabatic. The inner tube wall is especially critical for deep boreholes, where the temperature difference between downward and upward flows is high. As an extremely performant option for high-temperature BHEs a vacuum-insulated steel wall has also been proposed for the inner tube (e.g. Lund, 2019, p. 19).
Tube diameters
Tube diameters need to be considered both in fluid mechanical and heat transfer point of view.
For a given flow rate, tube diameters dictate flow velocity, which in turn affects convective heat transfer coefficient as well as pressure loss. The outer tube diameter also dictates the heat transfer area between fluid flows and the ground.
Holmberg et al (2016, p. 69) note that in theory achieving turbulent flow in the annulus and laminar flow in the inner tube would be an optimal solution from the perspective of heat transfer, but that it is difficult to achieve, as usually annulus tube flow area is much larger than that of the inner tube. By increasing inner tube diameter, Reynolds number of inner tube flow would decrease. However, simultaneously heat transfer area between the inner tube and annulus is increased. Results by Pan et al (2020, p. 12) indicate that when inner tube flow is in turbulent region, shunt heat transfer area is more significant than inner tube flow convection coefficient. This in turn promotes large outer tube and small inner tube diameters. However, in hopes of minimizing shunt heat transfer area the inner tube diameter cannot be made arbitrarily small either, since at smaller diameters the pressure loss will be increased.
Aside from the technical aspects, the design needs to be economically optimized: wider boreholes are more expensive to drill. Borehole diameters in Finland typically range from 100 to 150 mm, with 115 mm being the most common diameter (JH-Lämpö). Optimally there should be minimal space between annulus outer wall and borehole wall to minimize the resistance of the groundwater/grouting layer, but having some clearance is required for the installation of the BHE.
5 BUILDING LOAD PROFILE
This subsection will cover the used building model, inputs and resulting load profile. The generated load profile will be used as input for the GSHP system model in section 7.