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

[AJH]

On Mon, 17 Sep 2007 14:43:24 -0400, Crispin Pemberton-Pigott wrote:

>http://ehs.sph.berkeley.edu/hem/hem/protocols/WBT_data-calculation_sheet.xls
>
I haven't taken the time to look at this site yet.

>
>Specifically, the formula for calculation of the heat energy available from
>a sample of wood is in the Test-1 to Test-4 sheets in cell E22 which is
>titled "Effective calorific value (accounting for moisture in the wood)"

I suppose this is really a form of lower heating value as it assumes
all the latent heat is carried away, the thing that strikes me is that
it shows it as being discarded at the local boiling point, when in
fact it is discarded at the exit temperature above the pot. As a rule
of thumb I use a figure of 2.7MJ/kg for wood moisture discarded rather
than the 2.26MJ/kg used here, it's only about 800kJ per kg of wood
burned difference if the wood is 50%mc wwb.
>
>E22 contains the formula
>
>=(E20-(E21*((N22-E17)*4.2/1000+2.26)))/(1+E21)

OK I'll split this down on the fly but any M$ lemmings will need to
view in fixed pitch fonts:

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

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)

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

So (N22-E17)*4.2+2260 is the heat needed to raise 1kg of water to
steam in KJoules

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:

mc  heat needed
10% 257.5 kJ
20% 515   kJ
30% 772.5 kJ
40% 1030  kJ
50% 1287.5kJ

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.

All this heat has to be provided by the wood burning but as the oven
dry proportion of wood varies as moisture content increase the dry
portion of wood is given by 1-mc divided giving a heating value
corresponding to mc of:

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%

Ok so my figures better match yours but see the caveat that steam is
rejected at flue gas temperature not local boiling point to the effect
of moisture is worse than you predict, 10% in the case of 50% mc wood.

AJH