Biomedical Engineering Reference
In-Depth Information
Q
Feed
C
A0
,
C
P0
= 0,
T
0
T
c
T
c
Cooling luid out
Cooling luid in
Q
Eluent
C
A
,
C
P
,
T
FIGURE 16.9
A jacketed CSTR with a saturated vapor
e
liquid fluid coolant.
As we have learned, to solve a nonisothermal reactor problem, two equations are needed:
mass balance and energy balance. For a constant fluid level in the CSTR, the mole balance of
reactant A leads to [see also eqn (5.35)]
d
ð
VC
A
Þ
d
t
¼ V
d
C
A
QC
A0
QC
A
þ r
A
V ¼
(16.1)
d
t
Substituting the reaction rate and dividing the reactor volume V throughout Eqn
(16.1)
,we
obtain
d
C
A
d
t
DðC
A0
C
A
Þr ¼
(16.13)
where D is the dilution rate.
We next look at energy balance for the reaction mixture. Noting that the volume and pres-
sure in the reactor are constant, we obtain from the first law of thermodynamics [see eqn
(3.113)],
X
N
S
QC
j0
ðH
j
H
j0
ÞþVrDH
R
þ
X
N
S
d
T
d
t
¼ Q W
s
C
Pj
VC
j
(16.14)
j¼1
j¼1
W
s
0
. Heat transfer into the
The energy of stirring is dissipated into the reaction mixture,
reactor is accomplished by the jacket:
Q ¼ UA
H
ðT
c
TÞ
(16.15)
Assuming that the heat capacities are constant, we have
H
j
H
j 0
¼ C
Pj
ðT T
0
Þ
(16.16)
Letting
V
ðT T
C
ÞþðT T
0
ÞD
X
N
S
C
j0
C
Pj
W
s
V
UA
H
H
R
¼
j¼1
0
@
1
A
T T
0
D
X
(16.17)
V
þD
X
N
S
N
S
UA
H
T
c
W
s
V
UA
H
¼
C
j0
C
Pj
C
j0
C
Pj
j¼1
j¼1
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