[Stoves] RE Error in the recommended Shell Foundation HEH Project Water Boiling Test http://ehs.sph.berkeley.edu/hem/hem/protocols/WBT_data-calculation_sheet.xls

[Crispin Pemberton-Pigott]

Dear Andrew

Thanks for taking the time to look through this.

Nigel and I agree with your method.

>I suppose this is really a form of lower heating value as it assumes
>all the latent heat is carried away

Yes. I won't quibble about the discard temperature!

>>E22 contains the formula
>>=(E20-(E21*((N22-E17)*4.2/1000+2.26)))/(1+E21)

>First term  E20 is the cv of 1kg of bone dry wood given in kJoules

Yes. It is in this case 'average hard wood' and the LHV.

>The N22-E17 term is the temperature through which the water in the
>wood has to be raised before it boils off, let's illustrate this with
>an ambient temperature of 25C and normal pressure, hence the water
>boils at 100C. So we raise the water through 75 degrees C. This is
>then multiplied by the specific heat of water 
>(4.2  kJoule/kg per degC but it does vary with temperature)

Yes.

>I don't see why this term has been divided by 1000?
>The 2.26 figure is the latent heat of vapourisation but it's in MJ/kg
>so should be 2260kJ

Actually we had a good look at that and the method used is that the part in
the centre between the brackets:

((N22-E17)*4.2/1000+2.26)))

is the total heat required to get rid of one gm of water, in KiloJoules so
the 1000 is needed.  The entire calculation is done in KJ. The plan
apparently was to start with an energy requirement per gm and then multiply
it by the number of grams of moisture, and subtract that energy from that
available from the portion of the kg that was not water.  The formula starts
off OK but ends badly.

>In our sample of a 75 degree rise to boiling we're looking at:
>75*4.2+2260=2575kJ/kg but we only have the fraction of water in the
>wood sample to evaporate and this is directly proportional to the
>moisture content on a wet basis, giving the heat needed as the
>moisture content rises:

Agreed

[snip]

>Their equation seems to be (heat value of 1kg dry wood) minus (wrongly
>calculated heat rejected as steam) all divided by  (1 plus moisture
>content), I cannot figure that.

Therein lies the problem.

In an effort to find out how much of the kg is not water, the end figure
divides the energy remaining in the wood by dividing by (1+% moisture).
This does not give the same result as multiplying by (1-% moisture). The old
% discount v.s. % add-on problem.  In addition, it should not happen at the
end after the water heat is subtracted, but immediately after the LHValue.
That is why I said there were two errors.

>mc   dry wood   heat value  less steam available heat
>10%  90%        16572.6       257.5      16315.1
>20%  80%        14731.2       515         14216.2
>30%  70%        12889.8       772.5      12117.3
>40%  60%        11048.4     1030         10018.4
>50%  50%          9207        1287.5        7919.5

>>Moisture   Original    Corrected  Difference
>>  0%        18414        18414        +0.00%
>>10%        16749        16313        +2.61%
>>20%        15345        14212        +7.96%
>>30%        14164        12112        +16.94%
>>40%        13152        10011        +31.37%
>>50%        12275          7911        +55.17%

Looks right.  We agree within a few watts.

The reason I found out: I was doing a manual calculation for multiple %
moistures and I checked with that spreadsheet and couldn't get the numbers
to match(the story of my life). If you use the sheet and choose 'average
hardwood' (at the top) and then enter moisture levels you will see the
result of the different formula.

I am pleased to see the use of the LHValue for the evaluation.  This speaks
to the discussion I was having with Prof Lloyd about the heat content in
ethanol.

Regards
Crispin

(Nigel has given up on my simple concerns and gone back to composing emails
in Mandarin)