Experimental Study of Biodegradation of Ethanol and Toluene Vapors

x
=ν 1
(5-28b)
Again, 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 biomass, Equations (5-28c)
and (5-28d) can be obtained:
− α b
⋅ν
+ δ ⋅ν
0
(5-28c)
1 1 3
=
13
.084 ⋅ν 1
+ ν
2
−ν
= 0
(5-28d)
7
1
3
Coupling Equations (5-28a) to (5-28d), the overall equation for the conversion of
benzyl alcohol becomes (see Appendix D-2 for detailed mathematical derivations):
r
( K + 1.274δ
)
r
(13/ 7) δ
m
⋅C
(13/ 7) δ
ATP
−
b
=
x
+ [ ]
x
(5-29)
If Equation (5-29) is re-written by introducing the defined maximal yields and
maintenance terms, Equation (5-30) can be formed:
1
− r
b
= rx
+ mbC
Y
max
bx
x
(5-30)
Equation (5-30) describes the amount of benzyl alcohol required for the production of
biomass and maintenance. By coupling Equations (5-29) and (5-30), the following
relations for the defined maximal yields and maintenance, and the metabolic model
parameters (K,δ, m ATP ) can be obtained:
1
max
Y bx
( 1.274δ
)
= K +
(13/ 7) δ
(5-30a)
matp
m
b
= (5-30b)
(13/ 7)δ
For continuous operation, at steady state, r = 0 , thus the following equations
can be obtained from Equation (5-28):
92