How much pipe would I need in the ground to cool an outbuilding?

Question

I want to experiment with geothermal cooling, and have an r-10 insulated workshop which I'd like to cool during the worst of the summer heat this year. The workshop is about 400 square feet (37 m²), and 11' (3.3 m) ceilings, with a concrete floor.

To keep costs down, I'm not interested in investing in a heat pump. I'd like to try laying long horizontal loops of pipe in the nearby ground 4–6' down (1.2–1.8 m), run water through them, and then through a radiator in the shop I can blow air through.

The ground around here is the typical 55 °F (13 °C) average temperature, and in this area is mostly heavy dense clay. The water table will be many feet below the loops in the area I plan to lay them.

While I could do this experimentally, lay an arbitrary amount of pipe, and take measurements (inflow/outflow temp difference and flow rate), I'm wondering what equations and engineering knowledge I should be looking at to give me rough back-of-the-napkin numbers on how much pipe I'm looking at to produce a certain temperature differential in the shop.

Answer 1

The numerical answer depends a lot on the other numerical data that is missing.

1. What sort of a summer is this? I mean, length of days (geolocation of the house), solar radiation vs time (is it 1000KW per square meter?)
2. Are there already heat isolators in place? Is the building covered by a roof and is there air or space in between the ceiling and the roof-tiles? or is the roof cover just touching the internal air?
3. how much power could you invest into the pump? If it is infinite, than with enough mass flow rate, you could use a simple 2 meter pipe, and as long as you can heat the water in the pipes, you would be giving away the heat to the ground. Like trying to heat the Earth.
4. how much heat conduction is there, between the pipe and the soil? This could be best tested.
5. how much heat can you subtract from the radiator? You cannot heat the ground more than you can cool the air. So a generous radiator is a must (which is probably simpler than piping).

As the numbers would follow the above clarifications, experimentation is the only valid method for determining the required piping and the radiator.

Another point is, would you be trying to cool the workshop as a whole, or is it only the working point (one person standing) that you would like to cool. In the second case, using a spray-ventilator could work as well (if it is safe and no side-effects for the type of work you are doing). For the first case, cooling as a whole, isolating the sunrays from the building is the number 1 approach to take. A dark coated surface can rise to 80degrees Celcius under the sun, which essentially becomes a wonderful heater, and if you can put shadow-panels over your building, you would get rid of the sun's radiation and only deal with the hot air.

One last point: why not employ some solar panels, and use their power to power your cooling solution?