Biomedical Engineering Reference
In-Depth Information
Example 5-10. Nonisothermal PFR. The exothermic gas phase reaction:
k f
A
%
B
þ
C
r ¼ k f p A k b p B p C
k b
is carried out in a PFR operating at 50 bar with negligible pressure drop. The feed consists of
pure A and the required conversion is 70%. The rate data is given by
k f ¼ 0:435 exp
mol s 1
E f
RT
$m 3
$bar 1
;
E f ¼ 20 kJ
=
mol
k b ¼ 147 exp
mol s 1
E b
RT
$m 3
$bar 2
;
E b ¼ 60 kJ
=
mol
1. Find the optimum temperature progression in the reactor with the maximum allowed
temperature of 350 C.
2. What is the reactor space time required if the optimum temperature progression is taken?
3. What is the heat to be removed if C P z
0?
Solution. The stoichiometry:
A
%
B
þ
C
V ¼ 0
F A 0
0
0
V ¼ V
F A
F B
F C
þÞ ¼ F T
F A 0 1 f A
þ ¼ F A 0 1 þ f A
F A 0 f A
F A 0 f A
The partial pressures in the reaction mixture are given by
F A
F T P ¼
1 f A
1 þ f A P
p A ¼
(E5-10.1a)
F B
F T P ¼
f A
1 þ f A P ¼ p C
p B ¼
(E5-10.1b)
Thus, the reaction rate is given by
r ¼ k f P 1 f A
f A
1 þ f A 2
1 þ f A k b P 2
(E5-10.2)
1. The optimum temperature is the temperature that gives rise to the maximum reaction rate,
that is,
f A
1 þ f A 2
d T ¼ P 1 f A
d r
d k f
d k b
d T
d T P 2
0 ¼
(E5-10.3)
1 þ f A
Since the final pressures are not functions of temperature for the required conversion of A.
Since based on the rate law,
d k f
d T ¼ k f
E f
RT 2
d k b
d T ¼ k b E b
(E5-10.4)
RT 2
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