Ideal Flow Reactors - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 217

(a)

F A0
Q A C A0 Q

Q , f Ae

C B0

C Ae , C Be

F B0 Q B

(b)

F B0
Q B

C B0 Q 0

Q , f Ae

C A

C Be , C A

A0

Q A

(c)

F A0
Q A C A0 Q 0

Q , f Ae

C B

C Ae , C B

B0

Q B

FIGURE 5.16 Selected feed schemes for a two reactant systems in PFR. (a) Feeding both A and B at the beginning.
(b) Feeding B at the beginning, while maintaining C A constant by adjusting the feed distributed along the reactor.
(c) Feeding A at the beginning, while maintaining C B constant by adjusting the feed distributed along the reactor.

For 90% conversion of A, find the concentration of R in the product stream as a function
of the reaction rate constants. Equal volumetric flow rates of the A and of the B streams
are fed to the reactor, and each stream has a concentration of 20 mol/L of the said reactant.
Therateparametersare: k 1 ¼ 0.1 mol 1/2 $ L 1/2 $ min 1 ; k 2 ¼ 0.2 min 1 ; K A ¼ 10 mol 1

$ L;

5mol 1/2 $ L 1/2 . The flow in the reactor follows: and K B ¼

1. PFR;
2. CSTR;
3. The best of the three PFR contacting (feeding) schemes in Fig. 5.16 .

Solution. As a warning, be careful to get the concentrations and flow rates right when you
mix the streams. To begin with, we find the differential selectivity of the desired product

d F A j due to the formation of R
d F A j total

r 1 A k 1 C A

k 1 C A þ k 2 C 1=2

s R = A ¼ ¼

r 1 A þ r 2 A ¼

(E5-7.3)

B

One can solve the problem by performing mole balances on each species and solve the differ-
ential equations using an automatic integrator. We can also do it more illustrative by using the
differential selectivity as defined by Eqn (E5-7.3) . This is the approach we will be taking here.

1. PFR. Referring to Fig. 5.16 a, noting that the starting concentration of each reactant in
the combined feed is C A0 ¼ C B0 ¼ 20 mol/L O 2 ¼ 10 mol/L. Based on the stoichiometry,