Ideal Flow Reactors - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 243

There are two basic types of ideal flow reactors: PFR and CSTR. PFR represents a one-
dimensional flow reactor, like a piston. At steady state, the concentration of reactants as
well as products changes along the direction of flow in a PFR. The concentrations of
the reactants are the highest in a PFR presented to reaction. The analysis to a PFR is
similar to that for a batch reactor, the only difference being the independent variable:
rather than time t , it is the volume of reactor V . For PFR, it is the residence time or distance
along the reactor flow direction, whereas time is the independent variable for a batch
reactor.
Since the reaction mixture changes along the reactor, mole balance for PFR leads to

vt ¼ r j v QC j

v C j

(5.7)

vV

When steady state is reached, nothing in the reactor changes with time. Equation (5.7) is then
reduced to

d F j
d V

r j ¼ (5.11)

The reactor volume can be solved for a desired fractional conversion of f Ae ,

f Ae

V ¼ F A 0 Z

d f A
r A

(5.24)

0

Correspondingly, the space time (no side inlets or outlets) for a PFR is given by

f Ae

Q 0 ¼ C A 0 Z

V d f A

r A

s ¼

(5.25)

0

Tabl e 5. 2 shows a list of solutions for some single reactions with simple kinetics. For
steady nonisothermal PFR, one more equation needs to solved simultaneously with
Eqn (5.11) ,

X

N S

X

N R

F j0 C P j d T þ r i DH Ri d V ¼ UaðT c TÞ d V (5.100)

j¼1 i¼1

CSTR represents a reactor that is well mixed such that no concentration gradient exits.
CSTR is also termed chemostat. Mole balance for a given species j over the entire reactor
leads to

d n j
d t

F j0 F j þ r j V ¼ (5.33)

At steady state, only algebraic equations are resulted in CSTR analysis as the sole derivative
in the mole balance Eqn (5.33) is the rate change of moles with time t in the reactor. At steady