Ideal Flow Reactors - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 242

this reaction rate is determined. The reaction rate to be used in Eqn (5.113) is the slope of the
tangent of the batch concentration curve at the reactor effluent concentration. Once the reac-
tion rate is determined, the reactor volume can be obtained by rearranging Eqn (5.113) ,

V ¼ Q C je C j 0
r je

(5.114)

If on the other hand, the reactor and throughput are known, the reactor effluent concen-
tration can be determined by combining Eqns (5.109) and (5.113) . Substituting Eqn (5.109)
into Eqn (5.113) , we obtain

Q C je C j 0
V

d C je
d t

¼ (5.115)

It is not convenient to use Eqn (5.115) to compute the concentration C je by inspecting the
batch concentration data as shown in Fig. 5.21 or Fig. 5.22 . Rearranging Eqn (5.115) , we can
obtain

d ln C je C j0
d t

Q
V ¼

(5.116)

Equation (5.116) indicates that the solution can be obtained by plotting the batch concen-
tration data (or rather the difference of batch concentration data) on a semilog scale plot. The
right-hand side of Eqn (5.116) is the slope of (the tangent to) the batch concentration (differ-
ence) data on a semilog plot, which must be equivalent to the dilution rate or space time, Q / V .
Figure 5.23 illustrates how to find the CSTR effluent concentration from the semilog plot of
the batch concentration difference data. The line with a slope of Q / V pinches the semilog
batch concentration difference data at exactly the effluent conditions. Therefore, the reactor
effluent concentration can be read (or computed) from the tangent point as indicated in
Fig. 5.23 .
Figure 5.23 can also be employed to find the reactor volume if the reactor effluent condi-
tions are known. In this case, draws the tangent to the batch concentration difference data
at the point corresponding to the reactor effluent conditions. The slope of the tangent is
then Q / V .

5.12. SUMMARY

, the reactor space time or its
inverse, D , the dilution rate. The space time is the time needed to feed a reactor full of reaction
mixture through the reactor. It is thus defined as the total volume of the reactor divided by the
inlet volumetric flow rate. That is,

There is one important parameter used for flow reactors, s

V
Q 0

s ¼

(5.3)

The dilution rate on the other hand is the frequency of how fast the reactor is filled:

Q 0
V

D ¼ (5.4)