32
J. Oomes and A.S. Menawat
balance equation can be used to compute the product concentration provided
the observability condition holds. If the observability criterion is satisfied, an
equation for computing the cell mass concentration from the glucose and
spectinomycin concentrations can be derived. Following a step-by-step procedure [50-52], it is easy to determine that S and P measurements make the process
observable. The EDR for the cell mass concentration is given by
Sr S dV
#.
( Ke
S )
C= -- ,S + V
V d t +~-~-~-~ exp
CS
S
K i
+ ~1 ~
exp /
+ ~2
exp
vls
\
S
Kil
~P2S
Ke2
S )
S
Ki2
(2)
7.2 Air Flow Rate
The activation-reaction-inhibition model describes the mechanism of spectinomycin biosynthesis as shown in the previous section. Furthermore, the
simulated profiles of the model match the data accurately (Table 2). However,
the oxygen dynamics do not appear in the model (Eq. A.7) because the dissolved
oxygen is controlled at 50%. The air flow rate which varies to meet the oxygen
demand contains physiological information otherwise present in dissolved oxygen measurements. The following equation approximates the oxygen utilized
during the fermentation when dissolved oxygen is constant.
1 mexp(
0 UR = ~ca
S
K i
+~
el~e~exp
S
1(
+ ~
e2/~P~ exp
S
= kt,, (A* - A)
i~x) C-Ke P~)
S)C--KeP2)
Ki2
(3)
Where Yca, Yvla and YP2A are the yield coefficients for cell, product 1 and
product 2 respectively. The above equation can be implemented to estimate the
oxygen uptake rate (OUR) measurements of dissolved oxygen in the bioreactor
provided the value of the mass transfer coefficient kza is available for every data
point. Since the k~a is a function of the hydrodynamic conditions of the bioreactor it plays a significant role in its operation and control. In general k~, is
a function of the volumetric air flow rate v, the medium viscosity #, the medium
density p and the power to volume ratio P/V used by the bioreactor. Under
similar hydrodynamic conditions and agitation, a direct correlation exists between the air flow rate v and the mass transfer coefficient kt,. Physiologically,
J. Oomes and A.S. Menawat
balance equation can be used to compute the product concentration provided
the observability condition holds. If the observability criterion is satisfied, an
equation for computing the cell mass concentration from the glucose and
spectinomycin concentrations can be derived. Following a step-by-step procedure [50-52], it is easy to determine that S and P measurements make the process
observable. The EDR for the cell mass concentration is given by
Sr S dV
#.
( Ke
S )
C= -- ,S + V
V d t +~-~-~-~ exp
CS
S
K i
+ ~1 ~
exp /
+ ~2
exp
vls
\
S
Kil
~P2S
Ke2
S )
S
Ki2
(2)
7.2 Air Flow Rate
The activation-reaction-inhibition model describes the mechanism of spectinomycin biosynthesis as shown in the previous section. Furthermore, the
simulated profiles of the model match the data accurately (Table 2). However,
the oxygen dynamics do not appear in the model (Eq. A.7) because the dissolved
oxygen is controlled at 50%. The air flow rate which varies to meet the oxygen
demand contains physiological information otherwise present in dissolved oxygen measurements. The following equation approximates the oxygen utilized
during the fermentation when dissolved oxygen is constant.
1 mexp(
0 UR = ~ca
S
K i
+~
el~e~exp
S
1(
+ ~
e2/~P~ exp
S
= kt,, (A* - A)
i~x) C-Ke P~)
S)C--KeP2)
Ki2
(3)
Where Yca, Yvla and YP2A are the yield coefficients for cell, product 1 and
product 2 respectively. The above equation can be implemented to estimate the
oxygen uptake rate (OUR) measurements of dissolved oxygen in the bioreactor
provided the value of the mass transfer coefficient kza is available for every data
point. Since the k~a is a function of the hydrodynamic conditions of the bioreactor it plays a significant role in its operation and control. In general k~, is
a function of the volumetric air flow rate v, the medium viscosity #, the medium
density p and the power to volume ratio P/V used by the bioreactor. Under
similar hydrodynamic conditions and agitation, a direct correlation exists between the air flow rate v and the mass transfer coefficient kt,. Physiologically,