Page 195 - Materials Chemistry, Second Edition

Sustainability of (H 2 ? CH 4 ) by Anaerobic Digestion 183

3.2.3 Thermal Energy Loss
The difference between the working temperature of the digester T w and the per-
vading outdoor ambient temperature T a is responsible for the heat loss from the
fermenting broth. The amount of energy lost should be supplied from such a
temperature control system and it depends on the insulation of the fermenting
broth, the surface area exposed to the ambient and the duration of the batch run.
The energy loss per unit volume of reactor can be calculated as follows:
ð
E l ¼ð4:5 k=s DtT w Þ DT=DÞ =g ð6Þ
where
-1
k (Kcal h -1 m -1 °C ) is the thermal conductivity of the digester walls (e.g.,
material such as concrete or steel, coupled with an
insulator, polystyrene foam, is an example)
s is the thickness of the reactor/insulating walls
Dt (T w ) is the total duration of fermentation (h)
DT = T w - T a according to the season (°C)
D is the diameter of reactor

The resistance to heat transport is here only considered for the insulating
material (k/s). This assumption leads to an overestimation of the insulator thick-
ness for the same energy loss. Some explanations are given here about the above
assumption. The heat flux from the bioreactor crosses three heat resistances in
series. Therefore, the global thermal resistance U -1 is:

U 1 ¼ 1=h i þ s=k þ 1=h e ð7Þ
where h i and h e are the internal and external convective heat transfers. A very thick
insulator leads a higher resistance, due to a series of phenomena (Rohsenaw and
Hartnett 1973) and both the convective coefficients, h i and h e can be disregarded; the
situation graphically reported in Fig. 6 occurs, and hence, the controlling resistance
will be that of the insulator, in terms of thickness s and heat conductivity k.

Fig. 6 Assumption used for
the evaluation of heat loss T w
across bioreactor wall
h e

h i

T a

s