About Geothermal Borehole (GSHP) Sizing Calculator
The geothermal borehole calculator sizes the vertical ground heat exchanger of a ground-source heat pump (GSHP). It first finds the load that must be exchanged with the ground, which in heating is the building load minus the electrical compressor work, and in cooling is the building load plus the compressor work, then divides that ground load by the heat-transfer rate per metre of bore to obtain the required total borehole length.
Enter the building heating or cooling load, the heat-pump COP, the ground heat-transfer rate (directly in watts per metre or estimated from the ground thermal conductivity), and the maximum drilled depth per borehole. The tool reports the ground load in kW, the total bore length in metres, the number of whole boreholes, the depth of each, and the achieved extraction rate for a sanity check.
How It Works
- Choose heating or cooling mode and enter the building load (kW) and the heat-pump COP.
- The calculator finds the ground load: heating Q_ground = Q_load (1 - 1/COP) is extracted from the ground; cooling Q_ground = Q_load (1 + 1/COP) is rejected to the ground.
- Enter the ground heat-transfer rate directly in W/m, or estimate it from the ground thermal conductivity using q ~= 20 * lambda spanning the common VDI 4640 range.
- The total bore length is L = Q_ground / q. The number of boreholes is ceil(L / maxDepth) and each is L / N metres deep, with the achieved W/m reported as a check.
Worked Example
A house needs 10 kW of heating from a heat pump with a seasonal COP of 4. The compressor supplies 10 / 4 = 2.5 kW of work electrically, so the ground only has to provide Q_ground = 10 * (1 - 1/4) = 7.5 kW = 7500 W. With a ground heat-transfer rate of 50 W/m (moderately conductive, water-bearing ground), the required total bore length is L = 7500 / 50 = 150 m. If each borehole is limited to 100 m, then ceil(150 / 100) = 2 boreholes are needed, each 150 / 2 = 75 m deep, giving an achieved rate of 7500 / 150 = 50 W/m.
Formulas
- Ground load (heating)
Q_ground = Q_load * (1 - 1/COP)- Ground load (cooling)
Q_ground = Q_load * (1 + 1/COP)- Total borehole length
L = Q_ground[W] / q_per_metre[W/m]- Number and depth of boreholes
N = ceil(L / maxDepth) ; depth_each = L / N
Standards & References
- ASHRAE Handbook - HVAC Applications, geothermal energy
- IGSHPA closed-loop / ground heat exchanger design
- VDI 4640 thermal use of the underground
Frequently Asked Questions
Why is the ground load different from the building load?
A heat pump moves more heat than the electricity it consumes. In heating the ground supplies the building load minus the compressor work, Q_ground = Q_load (1 - 1/COP). In cooling the ground must absorb the building load plus the compressor work, Q_ground = Q_load (1 + 1/COP), so the cooling ground load is larger.
How is the heat-transfer rate per metre chosen?
Typical extraction rates run from about 20 W/m in dry, low-conductivity ground to 50 to 70 W/m in water-saturated rock. You can enter the rate directly, or let the tool estimate it from the ground thermal conductivity using a linear fit of roughly 20 W per metre per W/m.K.
How many boreholes do I need?
Divide the total required length by the maximum practical drilled depth and round up: N = ceil(L / maxDepth). The total length is then split evenly so each borehole is L / N metres deep. Multiple shorter boreholes also help avoid thermal interference between adjacent bores.
Is this a full ground heat exchanger design?
No. This is a rule-of-thumb sizing based on a representative W/m rate, suitable for feasibility and preliminary design. A detailed design uses borehole thermal resistance, undisturbed ground temperature, fluid temperatures, and multi-year load profiles, often via a thermal response test and g-function software.