Ideal Flow Reactors - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 212

F TUAi = F TUA0 + RF TTUAe = (1+R) F TUA0

(a)

f A0 + Rf Ae

1 + R

( 1+R ) F TUA0 -F A0 -R F Ae
(

f Ai =

=

1+R ) F TUA0

F A0
F TUA0

R F Ae
R F TUAe

F AE = (1+ R ) F Ae

F TUAE = (1 + R ) F TUAe

f AE

F Ae
F TUAe = F TUA0
f Ae = f AE

(b)

F TUAi = F TUA0 + RF TUAe = (1+R) F TUA0

F TUAE = (1 + R ) F TUAe

f A0 + Rf Ae
1 + R

( 1+R ) F TUA0 -F A0 -R F Ae

(

= f Ai =

1+R ) F TUA0

F AE = (1+ R ) F Ae

F A0
F TUA0

F Ae

F TUAe = F TUA0
f Ae = f AE

f AE

R F Ae
R F TUAe

FIGURE 5.15 A schematic of a recycle reactor system. The reactor outlet is split into two fractions, with one
fraction returned to the reactor inlet. (a) Recycle CSTR; (b) Recycle PFR.

Because the splitter does not alter the compositions of the streams in this case, the fractional
conversion at the reactor outlet is the same as that at the reactor system outlet.

f AE ¼ f Ae (5.71)

and the total molar flow rate at the reactor outlet is given by

F TUAE ¼ð1 þ RÞF TUAe ¼ð1 þ RÞF TUA 0 (5.72)

F AE ¼ð1 þ RÞF Ae (5.73)

The reactor inlet stream is a combined stream of two, one from the reactor system inlet and
the other is the recycle stream. Thus, molar balance leads to

F TUAi ¼ F TUA0 þ RF TUAe ¼ð1 þ RÞF TUA0 (5.74)

F Ai ¼ F A 0 þ RF Ae (5.75)

and the fractional conversion of A at the reactor inlet is given by

F TUAi F Ai
F TUAi

¼ ð 1 þ R Þ F TUA0 F A 0 RF A e
ð1 þ RÞF TUA0

1 f A 0

1 þ R R 1 f Ae

f Ai ¼ ¼ 1

1 þ R

(5.76)

f A 0 þ Rf Ae
1 þ R

¼