Amalia Lekić Brettschneider, mag.ing.petrol., Assoc. Prof. Luka Perković, PhD Sc. ing.
Decarbonization of heating and cooling systems represents a special challenge in densely populated areas due to the increased concentration of heating and cooling energy consumption. One of the possibilities is the use of shallow geothermal systems, and the dimensioning it in the way that should anticipate and maximally avoid the unwanted effect of undercooling and overheating of the reservoir with the aim of meeting energy-efficient heating and cooling needs in the long term. The intensity of unwanted effects depends on numerous physical parameters of the reservoir and the flow of underground water, as well as the dynamics of the demand for heating and cooling of facilities on the surface.
The direct use of geothermal energy most often refers to geothermal heat pumps, whereby the system is used for heating and cooling spaces of various purposes (Lebbihiat et al., 2021). The possibilities of using heat pumps depend on the soil properties (thermal conductivity, thermal gradient, hydraulic conductivity, slope), dimensions and properties of borehole heat exchangers (BHE), as well as external factors such as external temperature and amount of precipitation. The properties of BHE are: length, diameter, wall thickness and cement properties. Vertical systems are more efficient and require a smaller space for their installation (Chen et al., 2022). Vertical closed systems have been shown to be more efficient than open systems, e.g. for heating greenhouses (Benli, 2013). Soil thermal conductivity values are influenced by lithological and physical properties, such as porosity, texture, water saturation, hydraulic and thermal conductivity, etc. (Luo et al., 2016).
A computer simulation of one such system was carried out in the area of the city of Zagreb. The simulation was carried out on a square model with a size of 100x100 m and a depth of 120 m. The borehole heat exchangers are located at a depth of 100 m. 3 cases of different lithology were considered: case A (clay, gravel, sand), case B (clay and gravel) and case C (clay and sand), shown in Figure 1.
Figure 1. Lithology of the 3 considered cases
Each individual case was tested with 4 types of borehole heat exchanger configurations (16 BHE, 10 BHE, 6 BHE and 3 BHE) arranged in the rectangular grid shown in Figure 2. This resulted in 12 considered scenarios.
Figure 2. Configurations of borehole heat exchangers
The reservoir model (Figure 3) contains initial and boundary conditions. The boundary conditions are hydraulic head on the north and south side, fixed temperature profile on the north side, fixed temperature on the top and bottom side, and zero-gradient boundary condition on the lateral east and west sides for both fluid flow and heat transport. Initial conditions are set for temperature and hydraulic gradient. For the initial conditions and the northern side of the border, a linear temperature increase with depth is applied.
Figure 3. Schematic view of boundary and initial conditions (a) and mesh around BHE (b)
The simulation of each of the 12 scenarios is carried out on an annual basis with hourly values and, considering the amount of data, the results of the C-03-BHE scenario will be presented (Figure 4). The balance for the whole year and two selected weeks, the 1st and 26th week of the year, are shown, representing heating demand in the winter and cooling demand in the summer.
Figure 4. Power and heat balance for scenario C-03-BHE for all year and two selected weeks: week #01 (winter) and week #26 (summer)
Temperature distribution show that scenario with high permeability, B-16-BHE results in lower temperature changes in the reservoir, while scenario C-03-BHE affects temperature field significantly, especially in the vicinity of BHE. Overheating and subcooling of the reservoir is negligible for B-16-BHE due to convective heat transfer but are significant for C-03-BHE. More precisely, for C-03-BHE, in the vicinity of the BHE the reservoir temperature can go up to 40 °C during the cooling and drop to 4 °C during the heating season. Overheating and subcooling of the reservoir reduces the coefficient of performance of the heat pump.
Figure 5. Temperature distribution between B-16-BHE (high hydraulic permeability) and C-03-BHE (low hydraulic permeability)
During the working life of the heat pump, the reservoir goes through phases of undercooling and overheating. Subcooling occurs in winter, when the heat accumulated in the reservoir is used to heat the space, and the temperature of the reservoir decreases. Overheating occurs in the summer. By cooling the space, the accumulated heat is pushed back into the reservoir. In this way, the reservoir is partially regenerated, which extends the working life of the heat pump.
Figure 6. Average reservoir temperatures during one year period for all 12 scenarios
Figure 6 shows the average reservoir temperatures within one year for all 12 scenarios. Lithological properties of case C shows the greatest oscillations of the reservoir temperature, while lithological properties of case B is the most constant.
During the heating season, the main indicator of efficiency of heat pump is coefficient of performance (COP). COP is a measure used to evaluate the efficiency of a heat pump system. It represents the ratio of the desired output (cooling or heating) to the required input (usually in the form of electrical energy). The larger the COP, the better the efficiency of the heat pump. In Figure 12 are presented relations between COP and probability density function (PDF) for all 12 scenarios during heating season. For all three lithological cases, the COP is oriented to the right, and it moves to the left (decreases) by decreasing the number of BHE’s due to the need for more energy to obtain the desired amount of heat from a smaller number of BHE. Lithological properties of case B proved to be the best.
Figure 7. COP histogram during heating season for all 12 scenarios
Results show that lithological conditions have a substantial impact on heat pump performance and can be a decisive factor in determining the structure of the surface equipment, mainly number of BHE and required capacity of heat pump and auxiliary heating device. Heat transfer between reservoir and BHE is substantially influenced by the convection of groundwater and this convection depends on the hydraulic conductivity of underlying layers. The movement of the average reservoir temperature depends on the lithology and the number of borehole heat exchangers. The COP decreases with decreasing the number of BHE’s.
NOMENCLATURE
e energy kWh
P power kW
ϕ heat flow rate kW
SUBSCRIPTS
B battery
BHE borehole heat exchanger
curt curtailment
dem demand
exp export
HE heater
HP heat pump
imp import
PV photovolatics
REFERENCES
- Lebbihiat, N., Atia, A., Arıcı, M., Meneceur, N., Geothermal energy use in Algeria: A review on the current status compared to the worldwide, utilization opportunities and countermeasures, Journal of Cleaner Production, 302, 126950, 2021.
- Chen, K., Zheng, J., Li, J., Shao, J., Zhang, Q., 2022. Numerical study on the heat performance of enhanced coaxial borehole heat exchanger and double U borehole heat exchanger, Applied Thermal Engineering, 203, 117916.
- Benli, H., 2013. A performance comparison between a horizontal source and a vertical source heat pump systems for a greenhouse heating in the mild climate Elaziğ, Turkey, Applied Thermal Engineering, 50, 197-206.
- Luo, J., Rohn, J., Xiang, W., Bertermann, D., Blum, P., 2016. A review of ground investigations for ground source heat pump (GSHP) systems, Energy & Buildings, 117, 160-175.
Amalia Lekić Brettschneider, mag. ing. petrol. is an assistant at the Department of Petroleum and Gas Engineering and Energy at the Faculty of Mining, Geology and Petroleum Engineering, University of Zagreb.
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Luka Perković, PhD Sc. ing. is an associate professor at the Department of Petroleum and Gas Engineering and Energy at the Faculty of Mining, Geology and Petroleum Engineering, University of Zagreb.
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