Design of Geothermal Boreholes: Calculation Methodology

nPro can be used to design and calculate geothermal borehole fields. This page explains which calculation approaches are used for the simulation in nPro. The detailed validation of the calculation with EED, GEO-HAND^light, a scientific comparison study, and VDI 4640 is documented on the page Validation of the Geothermal Borehole Calculation.

Validation of the Calculation

The geothermal calculation in nPro has been extensively validated. The results were compared with the standard software EED (Earth Energy Designer), with GEO-HAND^light by Prof. Koenigsdorff, with a scientific comparison study of 12 software tools, and with the reference values of VDI 4640 Part 2. All validation scenarios, input values, and results can be found on a separate page:

➜ Validation of the Geothermal Borehole Calculation in nPro

System Setup: Geothermal Boreholes with Heat Pumps

Various technologies such as heat pumps or heat exchangers can be used for the thermal utilization of the ground. These supply heating energy either to individual buildings or to entire districts via a heating network. Figure 1 shows the connection between the heat pump or heat exchanger and the borehole heat exchanger that extracts heat from the ground. The dimensions of the borehole play a decisive role in calculating the heat yield. The borehole length (H) defines the depth to which the borehole extends into the ground. The borehole spacing (B) specifies the horizontal distance between two boreholes and affects the efficiency of heat extraction. The borehole radius (r) is important because it affects the contact area between the ground and the borehole. These borehole parameters are central to the design of an effective and high-performance geothermal borehole system, as they significantly influence the extraction and transfer of geothermal energy.

Setup of the borehole system — Figure 1: Interconnection and setup of a geothermal borehole field with heat pump [1]

Fundamentals of the Borehole Calculation

The calculation basis for geothermal boreholes used in nPro is based on the work of Prof. Koenigsdorff of Biberach University of Applied Sciences on the simplified design of borehole heat exchanger fields. He uses models based on the work of the Swedish scientists Eskilson and Hellström, which take different load conditions into account: base load, periodic load, and peak load. The base load represents the average, continuous heat demand over the year, while the periodic load reflects the monthly fluctuations in heat demand due to seasonal temperature differences. The peak load, in turn, describes the maximum heat demand during extremely cold periods (the coldest hours of the year). A key element of the calculation is the determination of the fluid temperatures in the boreholes and their influence on the ground. These calculations are essential to avoid overloading the boreholes or causing undesirable temperature changes in the ground. Prof. Koenigsdorff developed the software GEO-HAND^light and validated the results of his calculation methodology against the well-known software Earth Energy Designer (EED) and the guideline VDI 4640. To determine the thermal resistance of the base load, the g-function introduced by Eskilson is used. It is a thermal step response to heat transfer and accounts for the interaction between the individual boreholes. Unlike Koenigsdorff’s calculation, nPro uses an open-source computational core for calculating the g-function, which was developed as part of the doctoral thesis of Massimo Cimmino (now a professor at Polytechnique Montréal in Canada). Detailed information on the calculation fundamentals can be found in the book “Oberflächennahe Geothermie für Gebäude” (Shallow Geothermal Energy for Buildings) by Prof. Koenigsdorff and in the user manual for the GEO-HAND^light program (version 5.0). The source code of Prof. Cimmino’s open-source computational core is available in the public pygfunction code repository on GitHub.

How Are Geothermal Boreholes Designed with nPro?

The geothermal module in nPro offers four main calculation functions:

Calculation of the number of boreholes depending on the borehole length, the heat pump outlet temperature, and the borehole spacing.
Calculation of the borehole length depending on the borehole configuration, the borehole spacing, and the heat pump outlet temperature.
Calculation of the heat pump outlet temperature depending on the borehole length, the borehole spacing, and the borehole configuration.
Calculation of the temperature profiles at the heat pump outlet depending on the borehole length, the borehole spacing, and the borehole configuration.

For the calculation, nPro uses the extraction profiles calculated in the operational simulation, the air temperature profile selected via the location, and an assumed peak load duration of 4 hours. A rectangular borehole configuration is also assumed for the calculation.

Methodology for Determining the Borehole Length

To determine the borehole length, it is assumed that all boreholes in the geothermal field have the same length and are hydraulically connected in parallel. The calculation uses an iterative approach, since the values of the base load borehole resistance and the temperature response in the formula for the borehole length in turn depend on the borehole length. The iteration continues until the difference between the newly calculated and the previously calculated length is less than 1 metre. The results of this calculation methodology were verified by a validation based on data according to VDI Guideline 4640 Part 2 in a study by Prof. Koenigsdorff. nPro uses the same calculation approach.

Calculation basis:

\begin{gathered} H_{\mathrm{length}}= \frac{Q_{\mathrm{base,net}} \cdot (R_{\mathrm{base}} + R_{B}) + Q_{per} \cdot (R_{per} + R_{B}) + Q_{peak} \cdot (R_{peak} + R_{B})}{\Delta T_{\mathrm{response}} \cdot N_{\mathrm{boreholes}}} \end{gathered}

As an extension of Koenigsdorff’s calculation method, nPro additionally offers the option of designing the boreholes for a dominant cooling load. If the cooling demand is decisive for the design compared with the heat demand due to high periodic and peak loads (or a low maximum borehole outlet temperature), the required borehole length is determined based on the cooling load. This prevents excessively high temperatures at the borehole outlet.

Calculation of the Heat Pump Outlet Temperature

The heat pump outlet temperature corresponds to the temperature of the heat transfer fluid at the borehole inlet. Together with the temperature difference, it describes the state of the fluid before and after it passes through the borehole. The higher the temperature at the borehole outlet, the higher the efficiency of a connected heat pump. The decisive factor for the design is the minimum heat pump outlet temperature, which occurs in the steady state and is only reached after several decades. This steady-state temperature can be determined using the calculation approach applied.

Calculation basis:

\begin{gathered} T_{\mathrm{HP,out}}= T_{\mathrm{ground,undisturbed}} + \Delta T_{\mathrm{base}} + \Delta T_{per} + \Delta T_{peak} - 0.5 \Delta T_{\mathrm{fluid}} \end{gathered}

Validated Value Ranges and Determination of Input Values

This section explains which guideline values can be used for the input parameters of the borehole field calculation and where suitable values can be obtained.

Table 1: Value ranges for which the calculation has been validated, and possible sources for determining suitable input values.

Parameter	Validated range	Data source
Borehole length	50 - 200 m	calculated
Borehole spacing	≥ 6 m	---
Borehole thermal resistance	Typical range: 0.05 - 0.15 (mK)/W	Thermal response test or from analyses, e.g. by geoenergie-konzept.de
Borehole radius	0.025 - 0.1 m	e.g. overview by geoenergie-konzept.de
Thermal conductivity	1 - 6 W/(mK)	Thermal response test or VDI Guideline 4640 Part 1
Geothermal heat flux	25 - 135 mW/m²	Geographical maps, e.g. the map on the website of the German Geothermal Association (Bundesverband Geothermie)

Determination of Borehole Thermal Resistance and Thermal Conductivity

Grouting materials for borehole heat exchangers can be divided into conventional and thermally enhanced materials. On average, conventional materials have a higher mean resistance of approximately 0.1 (mK)/W compared with thermally enhanced materials at approximately 0.08 (mK)/W. In addition, the thermal resistance increases with increasing borehole radius (see overview by geoenergie-konzept.de).

Table 2: Example values for the borehole thermal resistance (based on an overview by geoenergie-konzept.de).

	Lower limit	Upper limit
Conventional grouting	0.075 (mK)/W	0.141 (mK)/W

Table 3: Example values for the thermal conductivity and volumetric heat capacity depending on rock type according to VDI Guideline 4640 Parts 1 and 2.

Rock type	Thermal conductivity in W/(mK)	Volumetric heat capacity in MJ/(m³K)
Clay/silt, water-saturated	1.8	2.0 - 2.8

Sources

Koenigsdorff et al.: GEO-HAND^light (Version 5.0) and user manual, 2022: https://innosued.de/energie/geothermie-software-2/
Koenigsdorff et al.: “Oberflächennahe Geothermie für Gebäude: Grundlagen und Anwendungen zukunftsfähiger Heizung und Kühlung”. Fraunhofer IRB Verlag, 2011. ISBN-13: 978-3816782711.
VDI Guideline 4640 Parts 1 and 2.
pygfunction code repository by Massimo Cimmino
Analysis of borehole thermal resistances by www.geoenergie-konzept.de
Koenigsdorff et al.: “GEO-HANDlight - Handrechenverfahren zur überschlägigen Bemessung von Erdwärmesondenfeldern”. In: 7. Internationales Anwenderforum Oberflächennahe Geothermie, 25–26 April 2007, Freising. Regensburg: OTTI, 2007, pp. 97-101.
Koenigsdorff et al.: “Erweiterung des Handrechenverfahrens GEO-HANDlight zur überschlägigen Bemessung von Erdwärmesondenfeldern auf die kombinierte Heizung und Kühlung”. In: Der Geothermiekongress 2007, Bochum, 29–31 October 2007, pp. 82-84.