Ideal Flow Reactors - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 227

Common analogy to CSTR includes stirred-tank reactor and fluidized bed reactors (solid e
liquid, solid e gas, solid e liquid e gas), while tubular reactor and packed-bed reactors are
more close to a PFR. There are other types of reactors that taking into mass transfer effects.
For example, counter-current flow reactor is a good choice for gas e solid and liquid e solid
systems where the aim is to reacting away part of the contents in the solid. This is commonly
seen in ore leaching, pulp, and paper, etc. The counter-current flow is achieved by flowing
gas (or liquid) up in a vertical reactor, while letting the solid moving down by gravity.

Example 5-8. Consider a simple elementary series reaction system

k 2 C
with a feed stream containing C A0 mol/L of A. If the intermediate product B is the desired
product, determine the optimum type of ideal isothermal flow reactor and contact time
required.
Solution. There are two types of ideal flow reactors applicable to this example: 1. PFR and
2. CSTR.

k 1

A / B /

V V+dV

F Ae
F Be
F Ce

A B C

F A0

dV

FIGURE E5-8.1 A schematic diagram of the PFR showing a differential control volume ( V , V þ d V ).

1. PFR. Figure E5-8.1 shows a sketch of the PFR system. Mole balances for species A and B
lead to

d F A þ r A d V ¼ 0 (E5-8.1)

d F B þ r B d V ¼ 0 (E5-8.2)

Since F A ¼ V / Q and the reaction mixture is of constant density, Eqns

(E5-8.1) and (E5-8.2) are rearranged to give

C A Q , F B ¼ C B Q ,

s ¼

d C A
d

¼ r A ¼r 1 ¼k 1 C A (E5-8.3)

s

d C B
d

¼ r B ¼ r 1 r 2 ¼ k 1 C A k 2 C B (E5-8.4)

s

Equations (E5-8.3) and (E5-8.4) can be solved together with the initial conditions
C A (

s ¼

0) ¼ C A0 and C B (

s ¼

0) ¼ 0 (see example 4-3) to give

C A ¼ C A 0 expðk 1 s Þ (E5-8.5)

k 1
k 2 k 1

e k 1 s e k 2 s

C B ¼ C A 0 ½ (E5-8.6)