Environmental Engineering Reference
In-Depth Information
For continuous-flow reactors, in which there is a flow of reactants/products, it is
common to express the conversion as a function of the space time
, which is defined
as the time needed to process a volume V of reactants up to a given conversion:
τ
=
V
φ
V
0
=
c
A0
V
φ
n
,
A
0
=
c
A0
X
Af
−
τ
for any
ε
A
ð
Eq
:
6
:
20
Þ
R
ð Þ
f
If the density is constant (
ε
A
=
0), which holds for practically all liquid-phase and
some gas-phase reactions,
τ
can be expressed as
=
V
φ
V
0
=
c
A0
X
Af
−
=
c
A0
−
c
A
τ
for
ε
A
=0
ð
Eq
:
6
:
21
Þ
R
ð Þ
f
R
ð Þ
f
−
The reader should be aware that most engineers refer to
τ
as the
residence time
(see,
for instance, Chapter 3). Strictly speaking,
τ
is not the residence time and the reason
for this is detailed in Section 6.5.
Example 6.2 Solution of the molar balance for a CSTR
Consider the first-order irreversible reaction with constant volume (
ε
A
=0)
A
!
b
B+
c
C+
−
R
A
=kc
A
Then
=
1
k
X
A
X
A
=
c
A0
−
c
A
kc
A
τ
ð
Eq
:
6
:
22
Þ
1
−
Solutions of molar balances for CSTRs and different reaction types and orders can
be found in Levenspiel (1998, 2002). Note that there are no integrals in the expres-
sions relating
τ
with the conversion.
6.4 STEADY-STATE PLUG FLOW REACTORS (PFRs)
6.4.1
Isothermal PFR
In plug flow reactors (PFRs), the reactants are fed at one side of the reactor and then
flow parallel to the length of the reactor, leaving the reactor at the other side. The PFR
model assumes that the composition does not vary with the radius and there is no axial
mixing of the species in the reactor.
Contrary to the BR and CSTR, in the PFR, the composition is not the same
everywhere in the reactor but varies as a function of the axial position. At the
entrance of the reactor, there is a higher concentration of reactants than at the exit
of the reactor, resulting in a profile of concentrations along the flow path. If the
operation takes place in steady state, this profile does not vary in time. To address
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