Environmental Engineering Reference
In-Depth Information
If the density is constant,
=c
A0
ð
X
Af
c
Af
ð
=
V
φ
V
0
d
X
A
−
dc
A
−
τ
=
−
for
ε
A
=0
ð
Eq
:
6
:
28
Þ
R
ð Þ
R
ð Þ
0
c
A0
Example 6.3 Solution of the molar balances for a PFR
Consider the first-order irreversible reaction with constant volume
ε
A
=0:
A
!
b
B+
c
C+
−
R
A
=kc
A
Then
=
1
1
=
1
k
ln
c
A0
τ
k
ln
ð
Eq
:
6
:
29
Þ
1
−
X
A
c
A
Solutions of molar balances for a PFR and different reaction types and orders can
be found in Levenspiel (1998, 2002).
6.4.2 Non-isothermal PFR
In a non-isothermal PFR, the temperature changes with the axial position (Figure 6.4).
If the non-isothermal PFR operates in the steady state, this temperature profile does
not vary in time. When the temperature varies along the reactor, an energy balance
must be solved in parallel with the molar balance.
A component
i
that enters any slice within the reactor introduces an enthalpy to the
slice
H
i
(T) (see Chapter 5):
H
i
T
ðÞ
=
H
i
T
re
ðÞ
+c
p
,
i
T
ð
−
T
ref
Þ
Δ
H
i
=c
p
,
i
T
ð
−
T
ref
Þ
ð
Eq
:
6
:
30
Þ
where T
ref
is a reference temperature,
c
p
,
i
is the molar heat capacity of the component
A, and
H
i
(T
R
) is the enthalpy at T
R
(unknown). The absolute enthalpy of a system
cannot be measured directly, so engineers usually work with enthalpy increments
Δ
H
is the enthalpy of a system minus the enthalpy of some reference sys-
tem, which can be chosen arbitrarily but is commonly chosen in a way that simplifies
the calculations.
H
instead.
Δ
d
Q
=
h
(T
f
-T)d
A
T
f
φ
n
,
Af
mol.s
-1
φ
n
,
A
0
mol.s
-1
Σ
φ
n
,
i
H
i
+d
Σ
φ
n
,
i
H
i
Σ
φ
n
,
i
H
i
T
T
f
(K)
T
0
(K)
dV (m
3
)
FIGURE 6.4
Non-isothermal PFR.
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