Geothermal GSHP Vertical Borehole Calculator

Principles of Vertical Borehole Ground Heat Exchanger (GHEX) Sizing

A Ground Source Heat Pump (GSHP) leverages the near-constant subterranean temperature of the earth as a heat source in winter and a heat sink in summer. Vertical boreholes (typically 150 to 500 feet deep, spaced 15 to 25 feet apart) contain high-density polyethylene (HDPE) U-tubes backfilled with specialized high-conductivity bentonite grout.

ASHRAE Design Equation for Borehole Length

According to the ASHRAE Handbook of HVAC Applications and Kavanaugh & Rafferty methodology, the required total ground loop linear length $L$ is calculated independently for peak cooling and peak heating:

Where:

• $q_{cond} = \text{Cooling Load} \times \left(1 + \frac{3.412}{\text{EER}}\right)$: Total heat rejected to ground including compressor heat.
• $q_{evap} = \text{Heating Load} \times \left(1 - \frac{1}{\text{COP}}\right)$: Net heat extracted from the earth (compressor power contributes to indoor heat).
• $R_b$: Borehole thermal resistance (resistance of HDPE pipe walls and grout annulus).
• $T_{ewt}$: Design Entering Water Temperature from the ground field to the heat pump.

Impact of Thermally Enhanced Grout

Standard bentonite grout has poor thermal conductivity ($k_g \approx 0.42\ \text{Btu/hr}\cdot\text{ft}\cdot^\circ\text{F}$), creating a thermal bottleneck inside the borehole. Adding silica sand or graphite elevates conductivity to $1.0 - 1.2\ \text{Btu/hr}\cdot\text{ft}\cdot^\circ\text{F}$, slashing $R_b$ by up to $35\%$ and reducing required drilling footage by $15\%$ to $25\%$, saving thousands of dollars in commercial drilling costs.