Help With Heat Pump Size Please.

Hello. I am making a gas generation plant on my farm and I would be very pleased if you can help me with making a heat pump the correct size.

I have made a round concrete tank in the ground that is diameter 4m and height 3m that will be full of liquid food waste. I need to heat the contents to 40 degrees celsius by use of a heat pump with a heat exchanger in the tank. The decomposing of the waste is exothermic and will require very little heat input once the process is started but I require the heat pump to be capable of making the initial heating during start up.

The tank is constructed of 250mm thickness 25MPa concrete and the surrounding ground is sandy and quite waterlogged in winter especially. The ground temperature I measured today (after a cold weekend) at 1 meter deepth is 13 degrees C, last week the same measurement was 17 degrees C.

I need to be able to raise the contents of the tank (approx 30 cubic meters) to 40 C in around 24 hours. I can calculate how much heat would be required to do this but I do not have any reference material to give me figures on expected heat losses through the tank itself. Are there standard figures available to work with or accepted ways of assessing these losses?

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Is it too late to insulate the inside wall and then reline
the inside with concrete or sprayed fibreglass resin.

The insulation would keep the heat in, concrete has K values of

Concrete, lightweight........0.1 - 0.3
Concrete, medium............0.4 - 0.7
Concrete, dense...............1.0 - 1.8
Concrete, stone................1.7

The conduction of heat is quantified using the thermal conductivity
coefficient, or k-value (W/m.K), of the materials used in its construction.
This is the rate at which heat flows through a material between points at
different temperatures. The thermal resistance, or R-value (m2K/W), is
calculated by dividing the thickness of the material (in metres) by the k-value.
From this, the thermal transmittance, U-value (W/m2.K) of a building element,
is calculated as the inverse of the sum of the R-values of the component parts
and adjacent air layers.

The U-value is the measure of heat transmittance through a material and the lower
the U value the less heat is transmitted through a construction i.e. the better the insulation quality.

Regards

Rob

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Thank you Rob White for your kind assistance.

It would be quite expensive to insulat and resin line the tank. I already looked at fibreglass and resin lining the tank to make it gas tight but it was too much cost. The tank was already there for 20 years ago and I added an overflow sump on one side, installed the necessary pipes and a access hatch with a seal and I made the few small cement cracks repaired and used a painted treatment. I have already gas tested the tank at 2 psi for 24 hours and it is almost leak free.

I'm also not too sure if higher insulation would have an effect on the decomposition process which is exothermic. If the tank is too well insulated would the heat produced by the process kill the bacteria that makes the process happen? I'm not sure, I'm old but I'm new to all this and design information is not easily available. I've based my design on a system in Brazil that is up and working well and the gentleman there that made it gave me some information and figures.

So from the figures you have stated Rob, the concrete is fairly strong and would have been vibrated when it was made so it should be somewhere around the medium range.

If I assume a K-value of 0.5 with a thickness of 250mm that would give an R value of 0.25/0.5 = 0.5W/m2K and a U value of 2.0.

Tha area of the base of the tank is 12.57m² and the depth of the liquid in the tank will be about 2.5m and the circumference is 12.57 so the area of the side will be 31.43m². The total area losing heat will be around 44m².

So my quantity of heat requirement would be the temperature difference multiplied by the area multiplied by the U value. H = A U (ti - to) =44x2x(40-13) = 2376W. Is this correct? So how would I come to a suitable heat pump from that figure?

Thank you in advance.