Passive geothermal heat

I have an idea for using constant earth temperature to heat space without the use of a heat pump (which is why I describe it as passive geothermal heat, as opposed to the conventional technology of an earth-source heat pump). If it works the way I think it would work, then it could heat a room up to the same temperature as the deep earth (about 4 degrees Celsius or 40 degrees Fahrenheit in the Canadian Prairies) without any energy input.

First, you'd drill a borehole a few inches in diameter and 100+ feet deep. Then, you'd insert a 1/2" sealed copper tube to the bottom, and backfill with pea gravel and bentonite grout. You'd then attach a propane valve to the top of the tube (sticking out a few inches above the floor), and screw on a 1 lb propane tank upside down (the propane would then flow down to the bottom of the tube).

Someone please feel free to correct me if my assumptions about physics are wrong, but here is what I think would happen: the pipe and propane tank combined would become the new tank, so the bottom of the pipe would contain liquid propane and the top of the pipe plus the bulb (1lb tank at the top) would be filled with gas. The pipe would roughly equal the ground temperature (4 or 5 degrees Celsius, roughly 40 degrees Fahrenheit) so the pressure of the gas would be around 65 PSI. As the bulb cools down (due to the fact that the surface of the bulb is cooler than the interior) the propane gas inside would drop below the boiling point of propane at this pressure, would condense into liquid propane, and run down the insides of the bulb and down the sides of the pipe. As the pressure of the propane gas drops, some of the liquid at the bottom would evaporate to replace it. Thus, as long as the surface of the bulb is less than the ground temperature, the propane would flow up and down the pipe in an attempt to bring the heat from the ground to the bulb.

The cycle would stop when the air around the bulb is warmed up to the constant earth temperature (just above freezing) or the earth around the pipe has frozen because the bulb has been too greedy for heat (of course, heat from the surrounding earth would attempt to correct this). Juding from most rules-of-thumb about direct exchange geothermal heating, I expect that the unit could provide about 2000 watts (6800 btu/hr) for every 100' deep the pipe goes. So, you'd need enough of these units to meet the heat loss of the area they are sitting in.

I understand that commercially available propane (properly known as "liquefied petroleum gas") is only about 70% propane and contains several other chemicals, mostly methane. However, unless I am misquoting Dalton's law, the propane should continue to work independently of the other gasses.

In reality, you would probably need a bit of electricity to run a fan that blows the room air past the propane tank at the top of the pipe (encouraging heat transfer from inside the tank to the room air). There is probably not much use for this idea inside a home (most people like their homes more than a few degrees above freezing) but it would be a great way to heat garages, barns, crawl spaces, pump houses, etc. for free (or almost free).

Anyone care to rip my idea part?