2.5 Mathematical Modeling of Aerobic Fixed-Bed Hybrid Bioreactor
19
+ k h
X s / X B,H
K X + (X S / X B,H )
S O
K OH + S O
+η h
K O,H
K O,H + S O
S NO
K NO + S NO
X B,H
(2.3)
The rate of change of X s is given by
dX S
dt
= (1 − f p )(b H X B,H + b A X B,A ) − k h
X s / X B,H
K X + (X s / X B,H )
S O
K O,H + S O
+ η h
K O,H
K O,H + S O
S NO
K NO + S NO
X B,H
(2.4)
The rate of change of X p is given by
dX p
dt
= f p
b H X B,H + b A X B,A
(2.5)
The rate of change of X ND is given by
dX ND
dt
= (i XB − f p i XP )(b H X B,H + b A X B,A ) − k h
X ND / X B,H
K X + (X s / X B,H )
S O
K O,H + S O
+ η h
K O,H
K O,H + S O
S NO
K NO + S NO
X B,H
(2.6)
The rate of change of S ND is given by
dS ND
dt
= (−k a S ND + k h
X ND / X B,H
K X + (X s / X B,H )
S O
K O,H + S O
+ η h
K O,H
K O,H + S O
S NO
K NO + S NO
X B,H
(2.7)
The rate of change of S NH is given by
dS NH
dt
= [−i XB μ H
S s
K s + S s
S O
K O,H + S O
+ η g
K O,H
K O,H + S O
S NO
K NO + S NO
+ k a S ND ]X B,H − μ A
i XB +
1
Y A
S NH
K NH + S NH
S O
K O,A + S O
X B,A
(2.8)
The rate of change of S NO is given by
dS NO
dt
= −μ H η g
1 − Y H
2.86Y H
S S
K S + S S
K O,H
K O,H + S O
S NO
K NO + S NO
X B,H
+
μ A
Y A
S NH
K NH + S NH
S O
K O,A + S O
X B,A
(2.9)