The city of Idaho Springs, Colorado, USA, is located about 50 km west of Denver in the foothills of the Rockies. The town was founded in 1859 by mining prospectors and flourished as a mining community throughout the 1860s. Today, the town has a population of about 1900 and attracts tourists to its historic downtown, hot spring, and the experimental Edgar Mine located just north of the town. Figure 1 shows the map of the city of Idaho Springs and the locations of the historic downtown, the hot spring, and the Edgar Mine.

The proposed heating/cooling geothermal heat pump system for the city of Idaho Springs can be visualized in Fig. 2. It was assumed that the rock mass temperature in the Edgar Mine would be relatively low since the mine was located at a shallow depth. Therefore, the authors envisioned that the collected cold groundwater would be stored in a closed section of the Edgar Mine in winter and used to cool down the condensers of heat pumps in summer as shown in Fig. 3a. In this way, the efficiency of heat pumps would be improved. In winter, geothermal hot spring water used for commercial bathing would be transported to the historic downtown and used to melt the snow on the pedestrian sidewalks. Furthermore, any residual heat from the hot spring water after snow melting could be used to heat the heat pump evaporators, which would improve the efficiency of the heat pumps (Fig. 3b).

As reviewed in the previous section, the use of a mine to improve heat pump efficiency is not a new idea. For example, Shiba (2008) also reported a case study in which hot spring water consumed in a public bathing facility was re-used to improve heat pump efficiency of buildings in Japan. However, to our best knowledge, we know of no case study in which a mine and hot spring are jointly utilized to assist in improving the efficiency of a geothermal heat pump system. The close proximity of a hot spring and available mine also makes the location of Idaho Springs and its potential distribution of a geothermal resource unique.

We also point out that there are acceptable flow and temperature range with heat pump source water. The extended range water–water heat pumps prefer a source and load flow rate of 2.5 to 3.0 gpm per nominal ton of capacity, i.e., 0.16 to 0.19 L s-1 per 3.5 kW. For most heat pumps (water–water or water–air) using R410a refrigerant for heating, 27 ∘C entering water temperature on the source side is the theoretical maximum for reliable operation to produce a leaving water temperature on the load side of 49 ∘C.

In order to assess the thermal capacity of the Edgar Mine, the temperature field inside the Mine was mapped. Temperature measurements were carried out on three different dates; 17 September, 24 October, and 25 November of 2013. Figure 4 shows the data for temperature, precipitation, and snowfall in Idaho Springs in 2013. The data were obtained from the website of AccuWeather.com. The ambient temperature decreased significantly during the measurement period. Measurements taken include the surface temperature of the rock mass, ambient temperature, and humidity at the 24 locations shown in Fig. 5. There are two main tunnels in the Edgar Mine. The eastern tunnel is called the Miami Tunnel, and the western tunnel the Army Tunnel. The height and width of the Miami Tunnel are about 2 and 2 m, and those of the Army Tunnel are about 4 and 5 m. An infrared thermometer (Fluke, Model: 62Max) was used to measure the rock surface temperature as shown in Photo 3. The temperature of groundwater accumulated at location 21 was also measured. The area between the entrance of the Army Tunnel (Location 24) and the location 19 was wet during this period.

The measured temperatures of the rock mass surface at the 24 locations are shown in Fig. 5. The temperature measured near the entrance of the two tunnels decreased during the three measurements due to the influence of the ambient temperature. On the other hand, the temperature inside the mine was stable. The highest surface temperature was always measured at location 9 (U.S. Geological Survey (USGS) classroom), and it was about 12.5 ∘C. The second highest temperature of 12 ∘C was measured at location 6.

Compared to the surface temperature of 27 ∘C of the rock mass that was reported in the paper by Rodriguez and Diaz (2009), the surface temperature of the rock mass in the Edgar Mine is much lower; however, this makes sense because the measured areas in the Edgar Mine has been excavated horizontally on just one level so that the typical temperature gradient (20–30 ∘C km-1) in depth is not expected.

Figure 6a and b show how the measured rock surface and the ambient temperatures change with the distance from the entrance. More specifically, the temperatures measured at locations 1, 2, 3, 4, 5, and 6 are shown in Fig. 6a, and the temperatures measured at locations 18, 19, 21, 23, and 24 are shown in Fig. 6b. Comparing the surface temperatures for locations near the entrance to each of the two tunnels, it is found that the surface temperature increases with the increasing distance from the entrance in the Miami Tunnel (Fig. 6a), and the surface temperatures at locations 4, 5, and 6 show no significant difference between the three measurement dates even though the ambient temperature decreases. Figure 6b, on the other hand, indicates that the surface temperature does not increase as the distance becomes greater in the Army Tunnel. Additionally, the surface temperatures shown in Fig. 6b are significantly different for each of the three measurements.

In order to understand the difference in the temperature profiles between the Miami Tunnel and the Army Tunnel, the relationship between the cover that is defined as the difference between the elevation of ground surface and that of the tunnel and the distance from the entrance is shown in Fig. 7. It can be seen that the cover above the Army Tunnel does not increase as much as that for the Miami Tunnel. The heat is transferred through the rock mass by conduction since no significant wind blows inside the underground mine. Therefore, as the cover becomes greater, the surface temperature of the rock mass is less influenced by the ambient temperature outside the Edgar Mine. The rock surface temperatures at locations 4, 5, and 6, with the cover greater than 150 m, is considered to be independent of the ambient temperature outside the mine. Figure 7 also shows the different topography above the Miami Tunnel and the Army Tunnel, which should explain why the Miami Tunnel is dry and the Army Tunnel is wetter. The thin and relatively flat cover above the Army Tunnel provide more opportunity for the surface water to permeate through to the tunnel.

In conclusion, it is found that the surface temperature of the rock mass in the Edgar Mine is relatively low due to its shallow depth. Therefore, the mine would be suitable for thermal energy storage in which cold groundwater would be stored in winter and used in summer as proposed in Fig. 2. Our recommendation is to utilize the groundwater that is naturally flowing in the mine in a designated storage area.

In order to understand the heat transfer between the flowing hot spring water and the ground, the ground temperature T (∘C) is first obtained following Kasuda and Achenbach (1965). T=Tmean-Tamp×exp-Dπ365α×cos2π365t-tshift-D2365πα, where Tmean, Tamp, D, α, t, tshift are the mean surface temperature, the amplitude of surface temperature, the depth below the surface, thermal diffusivity of the ground, time (day), and day of the year of the minimum surface temperature, respectively. We set Tmean to be 6.7 ∘C defined by the annual average air temperature; Tamp to be 23.7 ∘C defined as the average between the maximum, 29.9 ∘C, and the minimum, -17.5 ∘C, air temperature in July and January, respectively; D to be the depth in meters; α to be 1.19 × 10-2 m2 day-1 estimated value of thermal diffusivity of the ground; t to be the number of days for the present calculation; tshift to be 15 days in January defined by the number of days of the year with the minimum surface temperature.

Figure 8 shows the temperature profile in the ground at various depths and indicates that the ground temperature becomes more or less a constant value of 6.7 ∘C at the depth of approximately 6 m. Considering potentially significant excavation costs, we assume that the pipe is buried at the depth of 2 m, at which the ground temperature is not exactly constant but allows us to assume a constant temperature of 6.7 ∘C to simplify the calculation hereafter.

Figure 9 shows the schematic representation of the hot spring water flowing to the historic downtown. According to Repplier et al. (1982), the flow rate of the geothermal well used by the hot spring is 136 L min-1. Considering 25 % loss of the flow, the flow rate is assumed to be 100 L min-1. Under the conditions shown in the figure, the temperature loss was calculated as follows.

The Reynolds number of the internal flow through a pipe, ReD is ReD=ρumDiμ=995.0×0.212×0.17.69×10-4=27 430, where ρ, μ, um are density (kg m-3) and viscosity (N× s m-2) of the fluid, and internal flow rate (m s-1).

ReD is larger than 2300 indicating that the flow is turbulent. As the temperature of the fluid is higher than that of the surrounding ground temperature, the following equation can be applied to calculate the Nusselt number, NuD: NuD=0.023×Re0.8×Pr0.3=0.023×274300.8×5.20.3=134.0, where Pr is Prandtl number.

Convection heat transfer coefficient, h (W m-2× K) is h=NuD×kDi=134.0×0.620.1=830.8, where k is the thermal conductivity of the fluid (W m-2× K).

Total thermal resistance per unit length, Rtot (m × K W-1) is Rtot=Rconv+Rcond=1hπDi+lnDo/Di2πkp=1830.8×π×0.1+ln0.2/0.12×π×0.16=0.306, where kp is the thermal conductivity of a pipe (W m-1×  K). T∞-TxT∞-Tin=exp-xm˙cpRtotTx=6.7-exp-x1.66×4178×0.306×6.7-35, where Tx, T∞, Tin, m, cp are mean temperature at x=x (∘C), constant surface temperature (∘C), inlet temperature (∘C), mass flow rate (kg s-1), and specific heat of the fluid (J kg-1 × K).

Figure 10 shows the relationship between the mean temperature of the geothermal hot spring water and its traveled distance. It is found that the temperature would decrease from 35 to 28.6 ∘C while it is transported to the historic downtown over the distance of 540 m. In this calculation, the thickness of a pipe was assumed to be 5 cm. Figure 11 shows the result of a parametric study when the thickness of the pipe is varied from 1 to 9 cm. Figure 11 indicates that the outlet temperature monotonically increases with increasing thickness, but beyond the thickness of 5 cm, the increase of the temperature becomes very modest. Considering its high cost and the difficulties working with thick pipes, 5 cm thickness assumed in the calculation above is the most reasonable.

Figure 12 shows the design of the proposed snow melting system for the sidewalks of the historic downtown. The hot water transported from the hot spring source flows through the pipe system in the north and south pedestrian sidewalks. The depth, the spacing, and the size of buried pipes are appropriately adapted after having reviewed two previous case studies in which similar snow melting systems were installed. One case study covers the system in Klamath Falls, Oregon, reported by Lund (1999) and the other covers the system in Sapporo, Japan, reported by Sato and Sekioka (1979).

In order to calculate the heat supply from the hot spring water to the pedestrian sidewalks, the temperature decrease of the flow through the pipes buried in the sidewalks was calculated in the same way as the calculation of the temperature loss in Sect. 4. However, the buried depth of the pipes shown in Fig. 12 is only 8 cm, while that of the pipe in the previous section was assumed to be 2 m. Therefore, the geothermal hot water would significantly be influenced by cold ambient temperature. Thus, it is assumed that the flow is cooled down by the constant temperature, -7.7 ∘C, as shown in Fig. 13. The average temperature of the ground surface in 2013 was -7.7 ∘C between 1 November and 30 April, the average months of snowfall in Idaho Springs as shown in Fig. 4.

The outlet temperature Tout was found to be 3.1 ∘C. Therefore, the heat supply from the geothermal hot fluid to the surrounding ground q (W) is q=m˙cpTin-Tout=1.66×4184×28.6-3.1=177.108W= 177.1kW. According to Adlam (1950), 70 % of the heat is usefully consumed for snow melting, because approximately 8–10 % is emitted to the atmosphere and approximately 20–22 % is lost downwards to the ground. Therefore, the available heat for snow melting is qavailable=0.7×q=0.7×177.1=124.0kW. The outlet temperature of the geothermal fluid (3.1 ∘C) is so cold that it could not be used to heat up an evaporator of a heat pump. Therefore, the proposed system shown in Fig. 2b is not realistic and should be modified. The geothermal hot fluid flows 8 cm under the pedestrian sidewalks only on snowy days. Otherwise, it is transported to a heat pump of each building directly so that the heat can be used more effectively.

Chapman and Katunich (1956) estimated the required total heat flux for snow melting, q0 (W m-2) as follows: q0=qs+qm+Arqh+qe, where qs, qm, Ar, qh, qe are sensible heat flux (W m-2), latent heat flux (W m-2), snow-free area ratio, convective and radiative heat flux from snow-free surface (W m-2), and heat flux of evaporation (W m-2), respectively. According to Chapman and Katunich (1956), when Ar is 1.0, the system melts snow rapidly enough that no accumulation of snow occurs. However, this condition requires the maximum energy supply. When Ar is 0, the surface is covered with snow of sufficient thickness. This condition is not desirable but could be tolerable when time for snow clearance is not critical. Chapman and Katunich (1956) recommended that an intermediate value of Ar= 0.5 would be used for many non-critical situations. Thus, in this calculation, three required total heat fluxes for snow melting were calculated when Ar is 0, 0.5 and 1.0, and the required heat with Ar= 0.5 is considered to be the most important value in practice. The document prepared by ASHRAE (American Society of Heating, Refrigerating and Air-Conditioning Engineers) (2011) is used to calculate each heat flux as shown below.

Sensible heat flux, qs (W m-2) is qs=ρwaterscp,icets-ta+cp,watertf-ts/c1=1000×2.363.6×1062100×0+6.2+4290×0.56-0=10.1, where ρwater, s, cp,ice, cp,water, ta, tf, ts, c1 are density of water (kg m-3), snowfall rate water equivalent (mm h-1), specific heat of ice (J kg-1× K), specific heat of water (J kg-1× K), ambient temperature coincident with snowfall (∘C), liquid film temperature (∘C), melting temperature (∘C), and conversion factor. We find that it snowed in Idaho Springs for a total of 34 days in 2013. Therefore, the ambient temperature during the snowfall is assumed to be -6.2 ∘C, which is the average of ambient temperature of the 34 snowy days. Snowfall rate water equivalent is assumed 2.36 mm h-1 as the average snowfall rate per day is 56.6 mm day-1 in Idaho Springs.

Latent heat flux, qm (W m-2) is qm=ρwatershif/c1=1000×2.363.6×106×334000=219.0, where hif is heat of fusion of snow (J kg-1).

Convective and radiative heat flux from a snow-free surface, qh (W m-2), is qh=hcts-ta+σεsTf4-Ta4=12.3×0.56+6.2+5.67×10-80.9273.74-264.94=110.7, hc=0.037kairLReL0.8Pr13=0.037kairLVLνairc20.8Pr13=0.0370.02356.110.0×2.0×0.2781.3×10-50.80.713=12.3, where hc, Tf, TMR, σ, εs, kair, L, ReL, Pr, V, νair, c2 are convection heat transfer coefficient for turbulent flow (W m-2), liquid film temperature (K), mean radiant temperature of surroundings (K), Stefan–Boltzmann constant (= 5.67 × 10-8 W m-2× K4), emittance of surface (= 0.7 assumed), thermal conductivity of air at ta (W m-1 × K), characteristic length of slab in direction of wind (m), Reynolds number based on characteristic length L, and Prandtl number for air (= 0.7), design wind speed near slab surface (= 10 km h-1 assumed), kinematic viscosity of air (m2 s-1), and conversion factor (= 0.278), respectively.

Evaporation heat flux, qe (W m-2) is qe=ρdryairhmWf-Wahfg=1.33×0.0102×0.00393-0.00160×2499×103=79.2, hm=PrSc23hcρdryaircp,air=0.70.62312.31.33×1005=0.0102, where hm, Wa, Wf, hfg, ρdryair, Sc are mass transfer coefficient (m s-1), humidity ratio of ambient air, humidity ratio of saturated air at film surface temperature, heat of vaporization (J kg-1), density of dry air (kg m-3), and Schmidt number (= 0.6).

As a result, the required total heat flux for snow melting is 229.1, 324.0, and 418.9 W m-2 when Ar is 0, 0.5, and 1.0, respectively. The area of the pedestrian sidewalks is 1120 m2 (= 280 m × 2  m× 2); therefore, the required total heat is 256.6, 362.9, and 469.2 kW when Ar is 0, 0.5, and 1.0.

Comparing the heat supply from the geothermal hot fluid (124.0 kW) with the required total heat shown above, it is found that the heat supply would be insufficient to melt snow even when Ar is 0 for the entire section of sidewalks. As shown in Eq. (), the heat supply depends on mass flow rate and the difference between inlet and outlet temperature. As it is difficult to make the temperature difference larger, the required heat would be supplemented by drilling roughly two additional geothermal wells to satisfy the required total heat with Ar= 0.5, 362.9 kW. Or the snow melting area should be limited to approximately one-third of the total area of the pedestrian sidewalks.