Experimental Study of Biodegradation of Ethanol and Toluene Vapors

Appendix F. Prediction Results at Unsteady State
If the dissolved oxygen (DO) is less than the critical value (C cr ), the system
would no longer be operated at steady state, and Equations (5-65) or (5-66) will no
longer be valid. Instead, the unsteady state equation has to be considered, thus Equation
(5-61) becomes:
dC
dt
x
= (μ − D)
⋅C
(F-1)
x
At this condition, bacteria are no longer growing, i.e., μ = 0
dC
C
x
x
= −D
⋅ dt
(F-2)
Integrated solution of Equation (F-1) is:
C
x
= C ⋅ exp( −D
⋅ )
(F-3)
x0 t
The results of prediction from Equation (F-3) is given in Figure F-1. This proves that
the model developed in this study can predict the transient process.
For ethanol balance:
dC
dt
e
= −r
+ φ
(F-4)
e
e
where
− r
e
1
=
Y
ex
⋅ r
x
1
+
Y
ep
⋅ r
p
+ m
e
⋅C
x
r
= μ ⋅ =0, formation rate of biomass.
x
C x
r
p
= k ⋅C
⋅C
, formation rate of by-product (acetic acid).
p
e
x
192