Experimental Study of Biodegradation of Ethanol and Toluene Vapors

where ν 1 , ν 2 , ν 3, ν 4 are the rates of reactions according to Equations (5-3), (5-10),
(5-11), and (5-44) respectively. The following set of seven linear relations is obtained,
by writing out the compound balances for each of the seven compounds (ethanol,
toluene, biomass, oxygen, carbon dioxide, ATP and NADH 2 ):
r r
r θ ⋅ν
+ φ
(5-14)
= et
where φ r is the vector of flows, and r r is the vector of the overall conversion rates.
For continuous operation at steady state, r = 0 , the following equations can be
obtained from Equation (5-14):
r r
φ = −θ
et
⋅ν
(5-47)
Again, if the well-known assumption (Roels, 1983) is made that no net accumulation of
NADH 2 and ATP takes place, i.e., Equations (5-47a) and (5-47b) are obtained:
− α b
⋅ν
− .5ν
+ δ ⋅ν
0
(5-47a)
1 1
0
2 3
=
12
.81⋅ν 1
+ 3ν
2
−ν
3
+ ν = 0
(5-47b)
7
1
4
The following equations can be obtained from Equations 5-47:
φ +
e
= 1.27ν
1
ν
2
(5-47c)
φ
T
=ν 4
(5-47d)
φx = −ν 1
(5-47e)
where φ
e
, φT
and φx
represent the flow of ethanol, toluene, and biomass into the system
(C-mol/L h), respectively. Therefore, by coupling Equations (5-47c) to (5-47e) with
Equations (5-47a) and (5-47b), the relation between the flows of ethanol, toluene and
biomass with steady state, continuous mode operation can be expressed by:
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