Experimental Study of Biodegradation of Ethanol and Toluene Vapors

Appendix D: Mathematical Solutions and Derivations
Appendix D-1. Model for Ethanol Bioremediation
For ethanol bioremediation, the overall conversion rates of the key compounds
are given in Section 5.1.2 as:
r = −1.27ν −ν
(5-14a)
e
1
2
r
x
=ν 1
(5-14b)
r (5-14c)
o
= −0.5ν
2 3
co
= 0.27ν 2 1
+ ν
2
r (5-14d)
− 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).
Solving Equations (5-14f) and (5-14g) simultaneously, the reaction rates for the second
and third reactions, ν
2
andν 3
, can be expressed as a function of the biomass synthesis
rate (r x = ν 1
) as shown in Equation (D-1):
ν
2
( α1E
−1.81δ
)
=
⋅ν
1
(3δ
− 0.5)
(D-1)
Considering Equation (5-4): α
1 E
mATP
= K +
μ
ν
3
=
ν +
(3α
− 0.905)
ν =
⋅ν
(3δ
− 0.5)
1E
1.81
1
3
2
1
mATP
3( K + ) − 0.905
μ
= {
} ⋅ r
3δ
− 0.5
x
(D-2)
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