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# Geothermal energy in nPro

Note: Not all parts of the calculation logic shown correspond to the latest software version. However, most of the technical description is still applicable.

## Estimation of the length of geothermal probes

How much heat a borehole heat exchanger can extract from the ground depends on several factors. These include the thermal conductivity of the ground, the number of operating hours and, if applicable, the influence of neighboring probes. The higher the thermal conductivity of the soil, the more heat can flow to the probe from the surrounding area and the more heat can be extracted from the subsurface. In addition, groundwater flow can increase heat conduction in the ground. Ideally, the distance between two neighboring geothermal probes should not be less than 7 m (minimum: 5 m).

Table 1: Specific extraction rates of near-surface sediments per meter of borehole heat exchanger length according to the VDI guideline 4640 [3]
Gravel, sand, dry < 25 W/m < 20 W/m
Gravel, sand, water-bearing 65-80 W/m 55-65 W/m
Clay, loam, moist 35-50 W/m 30-40 W/m
Boulder clay 45 W/m 45 W/m

## Estimation of the area of the ground collector

Geothermal collectors are plastic pipes that are laid directly under the earth's surface and extract heat from the ground in the area. The collectors are laid below the frost line at a depth of approx. 1.2 to 1.5 m. Ground collectors indirectly use the solar radiation on the ground as well as heat from the ambient air, which penetrates through heat conduction or through precipitation into the ground. For optimal utilization, areas with geothermal collectors should not be built over, so that as much solar radiation as possible as well as precipitation hits the area. For residential buildings, about 1.5 to 2 times the living area to be heated is required for heating with a heat pump. For each kW of heating capacity, around 15 to 30 m² of collector area is required (depending on the soil conditions).

Table 1: Specific extraction powers according to the VDI guideline 4640 [3]
Dry, non-cohesive soil 10 W/m² 8 W/m²
Cohesive soil, moist 20-30 W/m² 16-24 W/m²
Water saturated sand/gravel 40 W/m² 32 W/m²

## Geothermal model for heating and cooling

The geothermal model can be used as both a heat source and heat sink (cooling source). The energy flows of the model are shown in Figure 1. In the upper figure, the energy flows are shown for the case when both a heat pump and a chiller are considered. This case is given, for example, when a temperature of 40 °C is required to meet heat demands and a temperature of 2 °C is required to meet cooling demands, but at the same time the temperature of the geothermal source is 8 °C. When using a heat pump and a chiller, the thermal extraction power determined in the design calculation results in $$Q_\mathrm{ground} = \max \left(\max(Q_\mathrm{HP,evap,t}), \max(Q_\mathrm{CH,cond,t})\right)$$ Here, $$Q_\mathrm{HP,evap,t}$$ is the annual heat profile at the evaporator of the heat pump and $$Q_\mathrm{CH,cond,t}$$ the annual heat profile at the condenser of the chiller. The heat flow at the evaporator of the heat pump is $$Q_\mathrm{HP,evap,t} = Q_\mathrm{HP,cond,t} \cdot (1-\frac{1}{COP_\mathrm{HP,t}})$$ and the heat flow at the condenser of the chiller is $$Q_\mathrm{CH,cond,t} = Q_\mathrm{CH,evap,t} \cdot (1+\frac{1}{COP_\mathrm{CH,t}})$$

Figure 1: Geothermal energy model in nPro
In the nPro tool, geothermal energy can be used for heating and cooling. In addition, heat pumps and chillers can be considered to raise or lower the temperature level.

## Can a seasonal storage operation be modeled in the geothermal model?

In the geothermal model, a further model boundary condition can be defined, which allows to represent a seasonal storage operation. This can be used, for example, for aquifer storages or to model ice storages. If heat and cold utilization is enabled in the model, the ratio of heat extracted annually from the ground to heat injected annually into the ground can be defined by the storage cycle efficiency $$\eta$$: $$\sum_t Q_\mathrm{HP,evap,t} = \eta \cdot \sum_t Q_\mathrm{CH,cond,t}$$ For aquifer storages, $$\eta$$ = 70% is a commonly used assumption.

## Sources

1. Planungshandbuch Wärmepumpen (Viessmann)
2. Leitfaden zur geothermischen Nutzung des oberflächennahen Untergrundes
3. Guideline VDI 4640: Thermische Nutzung des Untergrunds

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