66
4 Development of a Mathematical Model for an Aerobic Fixed-Bed …
L
Le
Fig. 4.2 Profile of substrate concentration in a hybrid bioreactor
Fig. 4.3 Divisions in substrate concentration profile within the biofilm
respectively. J 0 , the substrate flux corresponding to S min , is zero. Now, J, the substrate
flux, can be determined from the solution of mass balance equation of substrate in
biofilm, i.e.,
d
2 S f
dz 2 =
k X f S f
D f (K + S f )
(4.6)
Multiplying both sides of Eq. (4.6) by 2
dS f
dz
and integrating both sides, we get,
dS f
dz
2
= 2k X f
S f
D f (K + S f )
dS f
⇒
dS f
dz
2
=
2k X f
D f
1 −
K
(K + S f )
dS f
4 Development of a Mathematical Model for an Aerobic Fixed-Bed …
L
Le
Fig. 4.2 Profile of substrate concentration in a hybrid bioreactor
Fig. 4.3 Divisions in substrate concentration profile within the biofilm
respectively. J 0 , the substrate flux corresponding to S min , is zero. Now, J, the substrate
flux, can be determined from the solution of mass balance equation of substrate in
biofilm, i.e.,
d
2 S f
dz 2 =
k X f S f
D f (K + S f )
(4.6)
Multiplying both sides of Eq. (4.6) by 2
dS f
dz
and integrating both sides, we get,
dS f
dz
2
= 2k X f
S f
D f (K + S f )
dS f
⇒
dS f
dz
2
=
2k X f
D f
1 −
K
(K + S f )
dS f