Chemistry Reference
In-Depth Information
dS
b
dt
¼
Q
V
B
Þ
ð
1
e
Þ
r
p
@
q
B
B
ð
S
0
S
b
e
e
@
t
B
2
4
3
5
ð
(6.41)
R
p
þ
L
f
Z
k
max
S
f
K
s
1
eÞ
1
e
k
b
S
b
K
s
r
2
dr
S
f
X
f
4
p
B
V
p
S
b
X
susp
þ
e
þ
B
R
p
It is also possible to adapt Eq. (6.38) to the case of complete mixing:
2
@
ð
e
Þ
ð
R
p
þ
L
f
Þ
S
b
@
Q
V
B
3
1
B
t
¼
B
ð
S
0
S
b
Þ
k
fc
ð
S
b
S
s
Þ
(6.42)
e
e
R
p
B
6.1.4.1.2 Biomass Balance in the Reactor
Bacterial growth with time in a GAC
filter is inevitable if the influent contains dissolved organics that are biodegradable.
The change in biomass amount inside an adsorber alters the void ratio in the carbon
bed and thus the interstitial velocity. As in the case of substrate, a mass balance
equation can be constructed for the biomass present in the infinitesimal slice
z.
The biofilm growth and decay have been incorporated into a number of models
[1, 16, 17]. The change in biofilm thickness may be expressed as a function of both
time and the distance along the length of a reactor, as shown for the case of a
fluidized-bed biofilm reactor [16]:
D
@
L
f
ð
z
;
t
Þ
k
max
S
f
ð
z
;
t
Þ
L
f
ð
z
;
t
Þ
¼
K
d
L
f
ð
z
;
t
Þ
(6.43)
@
t
K
s
þ
S
f
ð
z
;
t
Þ
where
S
f
: average substrate concentration inside the biofilm (M
s
/L
3
),
K
d
: overall biofilm loss coefficient (1/T).
Only a few models also consider the change in suspended biomass [1]. In the
following model, shown in Eq. (6.44), the first three terms on the right-hand side
represent the variation of suspended biomass due to the substrate consumption,
the decay, and the loss with the effluent stream, respectively. The last term indi-
cates the increase in suspended biomass due to shear of attached biomass from the
carbon surface [1]:
X
susp
dX
susp
dt
Yk
max
S
b
K
s
Q
V
B
3 X
w
b
s
V
B
¼
S
b
b
þ
p
R
p
L
f
X
f
(6.44)
þ
e
e
r
B
B
where
X
w
: total mass of carbon in the reactor, (M
c
).
6.1.4.2
Characterization of BAC Reactors by Dimensionless Numbers
In GAC/BAC reactors, dimensionless analysis of the system helps in modeling
and serves as a guide in experimental work. The relative importance of each mass
Search WWH ::
Custom Search