Page 71 - Elements of Chemical Reaction Engineering 3rd Edition

Sec. 2.3 Applications of the Design Equations for Continuous-Flow Reactors 43

(a) Equation (2-13) gives the volume of a CSTR as a function of FAo, X, and --rA:
Design
& (2.-13)
In a CSTR, the composition, temperature, and conversion of the effluent stream are
identical to that of the fluid within the reactor, since perfect mixing i’s assumed.
equation
Therefore, we need to find the value of -rA (or reciprocal thereof) at X = 0.8. From
either Table 2-2 or Figure 2-1 we see that when X = 0.8, then
dm3. s
I/-rA = 800 -
mol
Substitution into Equation (2- 13) gives

V = 0.867 -
S (E2-.2.1)
= 554.9 dm3 = 554.9 L
(b) Shade the area in Figure 2-1 which when multiplied by FA, yields the CSTR
volume. Rearranging Equation (2- 13) gives

(2-13)

(E2-:2.2)

Plots of ll-rA vs. X
are sometimes
referred to as
Levenspiel plots
(after Octave
L.evenspie1)

Conversion, X
Figure E2-2.1 Levenspiel CSTR plot.

In Figure E2-2.1 the value of VIF,, is equal to the area of a rectangle with a heLght
ll-rA = 800 d1n3.s/mol and a base X = 0.8. This rectangle is shaded in the figure.
To calculate the reactor volume, we multiply the area of the rectangle by FAO.