I've been working some math, and it seems like maybe pipe length is the key factor not area or pipe diameter. Well at least if we are willing to do total swags.
dQ/dt = k * A * dT/dx (dQ/dt = heat over time, k is coefficient of conductivity, A is area, dT is temp gradiant across distance dx)
PEX k = 0.4W/mC
Soil k varies from 0.2W/mC to 1.1 W/mC
In my case, I'm going to assume 80F water thru 62F ground (10C delta). But the ground next to the pipe is going to warm up, reducing the temp gradient. But how far out does the warming go?
Thinking about it, I can ignore this by simply defining dx as far enough away to get 10C dT. In the case of a pipe, you can assume the pipe is the center of a cylinder of earth. So that cylinder of earth has surface area of length * (dx * 2 *pi).
dQ/dt = k * l * 2 * pi * dT
So for a 10C dT, I'm calculating anywhere from 12W/m to 60W/m of heat transfer. Picking a value that maches PEX conductivity gives me about 25W/m.
My tank maintains temp pretty well with all lights off. I have 3*250W halides and 2*110W VHO. So, I need about 1kW of heat transfer. So, I'm guessing 40m (~150') of PEX.
Really ground temp here is 55F and tank is 80F, so that's 14C dT and the ground is moist year round. So... I figure I'll buy 200' of PEX and that should do it. We'll see...
I'm not a geothermal engineer, not even close. So don't trust anything I say. Haven't even built my loop yet. I'm just sick of running a chiller every day of the year. If it only runs on days that I wish I had AC in the house, that will be a victory.
Yeah, I know more fans, less power, open hood, streams not closed loops, etc. but the looks and noise and closed doors on the cherry canopy are not negotiable with the local "decider"
My streams are out in the garage in a bucket, they didn't make the cut. And neither did the 70cfm orion fans, now it's strictly ultra-quiet 30cfm PC fans. Same with the iwaki pumps, now its dual massive sequence pumps - big, power hungry, heaters in the sealed cabinet, but quiet and invisible.