Experimental Study of Biodegradation of Ethanol and Toluene Vapors

where r φ is the vector of flow into the system (=In – Out), and r is the vector of the
overall conversion rates.
If the well-known assumption (Roels, 1983) is made that no net accumulation of
NADH 2 and ATP takes place, except as an integral part of the biomass ( r = r 0 ), the
overall conversion rates of the key compounds can be obtained:
1
2
5 6
=
r = −1.27ν −ν
(5-14a)
e
r
x
=ν 1
(5-14b)
r = −0.5
(5-14c)
o
ν
2 3
r = 0.27ν +
(5-14d)
co2 1
ν
2
− α E
⋅ν
− .5⋅ν
+ δ ⋅ν
0
(5-14e)
1 1
0
2 3
=
.81⋅ν + 3ν
−ν
0
(5-14f)
1
1 2 3
=
From the above equations, it is possible to express the overall conversion rates
of ethanol, oxygen, and carbon dioxide in terms of
r x
(overall conversion rate of
biomass). For instance, coupling Equations (5-14a), (5-14b), (5-4) and (5-2) with
Equations (5-14e) and (5-14f), the overall conversion rate of ethanol becomes (See
Appendix D for detailed mathematical derivations):
−
− 0.635 + 2δ
+ K
ATP
r
e
= (
) rx
+ ( ) ⋅ C
x
= rx
+
max
3δ
− 0.5 3δ
− 0.5 Yex
m
1
m C
e
x
(5-15)
Equation (5-15) describes the amount of ethanol required for the production of biomass
and maintenance. The following equations relate the maximal yields and maintenance to
the metabolic model parameters (K,δ, m ATP ) based on Equation (5-15):
86