Geothermal Borehole Spacing Thermal Interference Calculator

Introduction

Ground-source heat pumps work because the Earth changes temperature much more slowly than outdoor air. A vertical borehole lets the circulating loop fluid give heat to the ground in summer and pull heat back out in winter. That simple idea becomes more complicated when a project uses many boreholes instead of one. Each hole develops a thermal plume in the surrounding soil or rock. If two plumes overlap too aggressively, the field no longer behaves like a collection of independent heat exchangers. Instead, neighboring boreholes start to warm one another in cooling season or cool one another in heating season. That interaction is called thermal interference, and it shows up as less favorable entering fluid temperatures at the heat pump.

This calculator is designed to make that tradeoff visible before a drilling plan is finalized. Enter the building loads, the annual equivalent run hours, the number and depth of boreholes, the center-to-center spacing, and a few thermal property assumptions. The tool then estimates the per-borehole line load, combines that load with a simplified resistance model, and predicts the minimum winter entering fluid temperature and the maximum summer entering fluid temperature. Those predicted temperatures are compared with the allowable operating window you specify. If the layout appears too tight, the calculator also iterates toward a larger recommended spacing.

The goal is not to replace a full g-function design package on a large commercial job. The goal is to give designers, installers, energy consultants, and curious building owners a transparent first-pass check. The inputs are all familiar quantities that usually exist early in design, and the outputs answer the question that matters most in conversation: will this borefield stay inside the heat pump's acceptable entering fluid temperature range, or do we need more spacing, more depth, or more boreholes?

How to use

Start with the two peak load fields. Peak heating extraction load is the rate at which the building will pull heat from the ground during the coldest design condition. Peak cooling rejection load is the rate at which the building will dump heat back into the ground at the hottest design condition. The calculator expects those values in kBTU per hour, then converts them internally to BTU per hour so the line-load math stays consistent with borehole depth and thermal resistance units.

The annual equivalent full-load heating and cooling hours tell the model how long those seasonal effects are allowed to accumulate. A field that sees a short, sharp peak behaves differently from a field that runs heavily for months. Longer equivalent hours increase the time-based ground resistance term because the soil has less opportunity to recover between periods of use. In plain language, more run hours give the thermal plume more time to build up, which is why similar peak loads can produce different loop temperatures from one project to the next.

Next, describe the physical layout. Borehole depth is the active drilled length of each vertical exchanger. Number of boreholes distributes the building load across the field, and center-to-center spacing is the average distance from one borehole to the next. Those three inputs work together. If depth increases, the same load is spread across more heat exchange length. If borehole count increases, each borehole handles less of the total load. If spacing increases, the plumes have more room to dissipate before they reach neighboring boreholes. The calculator is especially helpful for testing how much resilience you lose when a tight site forces spacing downward.

The material property inputs translate that geometry into heat transfer performance. Ground thermal conductivity represents how readily the native soil or rock moves heat. Higher conductivity usually means the field can absorb or release the same load with a smaller temperature penalty. Grout thermal conductivity reflects how easily heat moves from the pipe bundle to the borehole wall. Effective pipe thermal resistance captures the combined resistance of the pipe circuit, pipe configuration, and circulation conditions. These values do not need to be perfect to make the calculator useful, but better estimates will produce more credible temperature predictions.

Finally, enter the undisturbed ground temperature and the minimum and maximum allowable entering fluid temperatures from the heat pump documentation or design basis. After you click analyze, the results area reports the predicted minimum winter entering fluid temperature, the predicted maximum summer entering fluid temperature, an interference index, and a spacing recommendation. Read those results together. A winter temperature below the minimum limit suggests the field may overcool during sustained extraction. A summer temperature above the maximum suggests it may overheat during sustained rejection. The interference index offers a quick severity check by comparing the estimated temperature swing with the allowable swing around ground temperature.

If the output indicates a problem, use the calculator as a design conversation tool rather than as a single yes-or-no gate. Increase spacing to see how much land area buys you additional temperature margin. Increase borehole count to see how spreading the load changes the result. Increase depth to see whether longer holes solve the issue more efficiently than a wider field. Because the model is fast and transparent, it encourages that kind of tradeoff testing early enough to matter.

Formula

At the heart of the model is heat per unit length. The total building load is divided among the boreholes, and each borehole's share is divided by depth to produce a line load. That line load is then multiplied by a composite thermal resistance that represents the path from the fluid, through the pipe and grout, and into the surrounding ground. The simplified resistance chain below preserves the cylindrical conduction intuition used in more advanced geothermal design methods while keeping the calculation easy to audit.

In that expression, R_pipe is the user-entered effective pipe resistance, k_g is grout conductivity, k_soil is ground conductivity, s is spacing, r₀ is an internally approximated effective borehole radius, t_year is 8,760 hours, and t_load is the annual equivalent full-load heating or cooling time. The factor F stands in for spacing geometry effects that become more pronounced when boreholes are crowded. The logarithms matter because radial heat flow does not scale linearly with distance. Doubling spacing helps, but it does not cut resistance in half.

The calculator also reports an interference index. It is not a universal industry standard; it is a simple screening ratio that compares the estimated thermal swing against the usable temperature swing allowed by the heat pump. The closer that ratio gets to 1, the closer your design is to consuming all of its temperature margin.

Here, Q is the seasonal peak load, N is borehole count, L is borehole depth, and T_g is undisturbed ground temperature. When the index rises above 1, the estimated fluid temperature leaves the allowable window. Even values below 1 deserve interpretation. A result near 0.9 means the design may technically pass but has little reserve for colder winters, hotter summers, field imbalance, or uncertainty in conductivity assumptions. A result near 0.5 means the field has much more breathing room.

Example

Consider a 12-borehole residential field serving a roughly 9-ton heat pump. Each borehole is 220 feet deep and the array is laid out at 18 feet center to center. The peak heating extraction load is 110 kBTU per hour and the peak cooling rejection load is 120 kBTU per hour. Annual equivalent full-load hours are 1,900 in heating and 1,200 in cooling. Ground conductivity is 1.2 Btu/hr-ft-°F, grout conductivity is 0.8, effective pipe resistance is 0.12 °F-hr-ft/Btu, and the undisturbed ground temperature is 55°F. The heat pump manual says entering fluid temperature should remain between 30°F and 100°F.

With those values, the total seasonal loads are split across 12 boreholes, then divided by 220 feet to estimate line loads of about 41.7 Btu/hr-ft in heating and 45.5 Btu/hr-ft in cooling. Those line loads are combined with the composite resistance terms, producing a predicted winter entering fluid temperature in the low 40s and a predicted summer entering fluid temperature safely below the upper limit. The exact values depend on the conductivity and run-hour assumptions, but the important design conclusion is that the array stays inside the operating window with a usable safety margin. The interference index lands below 1, which tells you the field is not exhausting all of the temperature swing the heat pump can tolerate.

Now imagine that the site becomes constrained and spacing must drop from 18 feet to 12 feet to avoid a driveway, septic field, or property setback. The loads have not changed, but the thermal plumes are now much closer together. In the simplified model, that tighter spacing raises the resistance terms associated with grout geometry and ground interaction. The predicted winter temperature moves downward and the predicted summer temperature moves upward. In many cases the field may still pass, but it passes with less resilience. That is exactly why the recommended spacing output matters. If the interference index climbs close to 1, the calculator may suggest a wider spacing that restores the original buffer without requiring a complete redesign.

The worked example also highlights a practical point about communication. Homeowners often understand the result more quickly when it is framed as a temperature limit problem rather than as an abstract conductivity problem. Designers and drillers, on the other hand, often want to see the intermediate values so they can compare this transparent estimate with their rule-of-thumb tables or more detailed software. The CSV export supports that workflow by recording the main results and the key intermediate thermal terms in a format that is easy to paste into a proposal, submittal, or commissioning memo.

Limitations and assumptions

This is a simplified calculator, so its assumptions matter. It treats the ground as if conductivity were uniform around the borefield, yet real geology can be layered, fractured, or influenced by groundwater movement. Fast groundwater flow can carry heat away more effectively than a simple radial conduction model predicts. In other cases, dry soils or poorly consolidated materials can perform worse than the bulk conductivity suggests. For a small residential system, the approximation is often directionally useful. For a large campus or mission-critical facility, it should be treated as a screening step rather than a final design basis.

The model also assumes that the annual equivalent full-load hours capture the thermal history well enough to represent seasonal buildup. That works reasonably for first-pass analysis, but it is still a compression of a much richer load profile. Strong long-term imbalance can matter. A building that rejects much more heat in cooling season than it extracts in heating season can ratchet ground temperature upward over several years, even if a single-year snapshot looks acceptable. The reverse can happen in heating-dominated applications. A detailed borefield model with monthly or hourly loads is the right follow-up when the project size or the risk justifies more precision.

Another limitation is that the calculator focuses on loop temperature, not full system energy performance. Entering fluid temperature strongly affects compressor lift and efficiency, but the page does not explicitly model pumping energy, antifreeze concentration, Reynolds number, or detailed pipe arrangement. Those variables influence cost, pressure drop, and the shape of the true borehole resistance curve. In practice, a field that barely stays within allowable temperature limits may still produce unattractive operating cost if the temperatures are consistently close to the edge. Treat the results as a temperature feasibility screen, then continue into hydraulic and equipment optimization if the project moves forward.

The recommended spacing routine is intentionally simple too. It increases spacing in fixed steps until the predicted temperatures return inside the allowable band or the search window ends. That makes the recommendation easy to understand, but it is not the same as a global optimization across spacing, borehole count, depth, grout choice, and load management. If the recommendation becomes very large, that is a useful signal in itself. It usually means the site may need a different combination of more holes, deeper holes, better thermal properties, or supplemental design measures rather than just a few extra feet between boreholes.

Even with those caveats, this kind of transparent calculator is valuable early in design. It helps a team talk in concrete terms about why spacing is not just a surveying convenience. Wider spacing reduces thermal interference, which protects entering fluid temperature, which protects heat pump performance and operating stability. When paired with a thermal conductivity test, manufacturer temperature limits, and a realistic view of building load balance, the tool becomes a practical way to reduce surprises before drilling begins. Use it to compare alternatives, document assumptions, and explain the logic behind a geothermal layout long before a drill rig arrives on site.