Aerobic heterotrophic conversion of organic matter
MWbiom and MW org are the molar weights for biomass and organic matter, respectively, and Y obs is the yield constant on a weight/ weight basis.
If, for example, Yobs = 0.5 kg biomass/kg of organic matter, Expression (3.12) is:
b·MWbiom 0.5
1· MWorg
(a orb can be randomly chosen when evaluating the expression; here a has been set at 1 ).
The molar weights for biomass (CsH7N02) and organic matter (C1sH1g()9N), respectively,.are in this example MWbiom= 113 g/mole, MWorg= 393 g/mole.
.
0.5 ·1. 393
b 1s found: b =
113
= 1.74
Hence the equation of reaction is:
C1sH1g()9N + 0.74 NH3 + 8.8 02---+
1.74 · CsH7N02 + 9.3 C02 + 4.52 H20
(3.13)
(it is seen that some nitrogen has to be added in the form of ammonia (or ammonium) as there is not sufficient nitrogen in the organic matter for assimilation in the
biomass).
Yield constants can be expressed in many different units. In Expression (3.13), Yobs
= 0.5 kg biomass/kg organic matter. If the COD unit is used, the biomass and the
organic matter can be converted into COD. As the conversion factor with the
assumed compositions of biomass and organic matter in both cases is 1.42 kg 02/kg
matter, Yobs = 0.50 kg COD(X)/kg COD(S). Expressed in terms of mole, the yield
constant in Expression (3.13), Yobs = 1.74 moles of biom./ mol organic matter.
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Example 3.2
The observed yield constant for aerobic oxidation of acetic acid (HAc) is 0.55 kg
COD/kg COD.
Evaluate the equation of reaction when the biomass is assumed to have the composition CsH1N02.
COD of acetic acid and biomass is calculated:
CH3COOH + 2 02 -> 2 C02 + 2 H20
CsH1N02 + 5 02 + W-> 5 C02 + 2 H20 + NH!
1 mole of acetic acid(= 12 + 3 · 1 + 12 + 16 + 16 + 1 = 60 g) corresponds to 2 moles
of oxygen (= 2 · 16 · 2 = 64 g), that is, 64 g COD/60 g HAc = 1.07 g COD/g HAc.
1 mole of biomass(= 5 · 12 + 7 · 1 + 14 + 2 · 16 = 113 g) corresponds to 5 moles of
oxygen (= 5 · 16 · 2 = 160 g), that is, 160 g COD/113 g biomass = 1.42 g COD/g biomass.