Wednesday, May 19, 2010

Joules, Watts, Kelvin, degree days and all

19 May : I have been trying to get to grips with some basic physics, to back up my ideas about Solar Geocharging.

The problem is that I haven't done it for a long time, and if you make one mistake (at one point you ask if something is watts, at another it is kW, or it is Seconds or Hours or Days we are talking about? Do we multiply or divide by 3600 or 24... ? and so on...)
I ought to get a fresh heatloss calculation done on the house to be sure of emissions, consumption etc. Let's start with the Borehole.

 As I see it, from my 3D model, there are 9700 cubic metres of Marl that our pipes can interact with. At density of 2200 kg / m3 that should be 20,000 metric tons (assuming that it is contained and not leaking.)
 If the thermal capacity of dense clay is 0.92 kJ/kg K then for ONE degree raise that should be:
Q (heat required in KJ) = 0.92 x 20,000 x 1000 x 1.... that would require 18,400,000 kJ

As Watts are Joules per second, we convert to hours by dividing by 3600, giving us 5,111 kWhrs !!
If our Sunboxes are putting down an average of 10-11 kWhr per day, that makes me think it would take 500 days to raise it by one degree, assuming no outward loss and no heat being pulled up? Seems like near infinity.... :(
If this is the case, then there is little hope of significant interseasonal storage from my humble little 4 sqm of sunbox, although it is already evident from what I observe that the heatpump is benefitting from Realtime and Diurnial warmth stored below in the clay immediately around the pipes. Can any of my readers help me here?

Like a Plugged in Laptop
It seems my earlier 'laptop' analogy fits here. You can run the laptop for a few hours, then you have to recharge. Like a laptop working with only its battery, the house draws energy from the ground all winter, and during the summer months, the ground is recharged by heat returning from the surrounding solar warmed earth.
But if you can work with your laptop plugged into the mains all the time on trickle, it will never overcharge the battery, but it will not run down either. Higher demand (e.g. in 3D rendering) drains the battery a bit, but continuous trickle charging brings it back up again.

Therefore it is becoming clearer:-
•••• Our ground is not likely to chill, but it will not get noticeably hotter. ••••
In the work by companies like ICAX, they use an entire playground or carpark for heat collecting, but we are using a humble 1.1 cu m of Sunbox, and 4.2 sq m of black collector, so can only expect 2kW at best.

Next task will be to do a heatloss calculation on the house...

PS Note that on 21 May, I have recalculated the 'Active Mass' of boreholes to have a radius of 3.6 metres, which gives a volume of 3,600 cu.m, a mass of 8,000 metric tons, and a Thermal capacity of 2,042 kWh/degree C, which would be a theoretical 200 days of charging to raise one degree.

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