4. Applications of the Design Equations for Continuous-Flow Reactor I
Feb/28 2011 Spring 1
o 1st order dependence
• k is specific constant, ftn of only Temp.
CA0, entering concentration - Rearrange
) 1
0
( X
kC kC
r
A
A
A
r
AkC
A1 X 1 1
1
0
0
rA
1
X
4. Applications of the Design Equations for Continuous-Flow Reactor II
Feb/28 2011 Spring 2
o Reactor size of CSTR and PFR - Raw data
- Manipulated
20 0.05
0.8
12.7 0.079
0.7
8.85 0.113
0.6
5.13 0.195
0.4
3.33 0.30
0.2
2.70 0.37 0.1
2.22 0.45 0.0
(1/-rA)(m3s/mol) -rA(mol/m3s)
X
20 12.7
8.85 5.13
3.33 2.70
2.22 (1/-rA)(m3s/mol)
8.0 5.06
3.54 2.05
1.33 1.08
0.89 [FA0/-rA](m3)
0.05 0.8 0.079
0.7 0.113
0.6 0.195
0.4 0.30
0.2 0.37
0.1 0.45
0.0 -rA(mol/m3s)
X
4. Applications of the Design Equations for Continuous-Flow Reactor II
Feb/28 2011 Spring 3
o Reactor sizing
0
Plots for sizing CSTR and PFR
r
AX
1
CSTR rA
1
X
PFR
X A
r dX
0
1
5. Reactors in Series I
Feb/28 2011 Spring 4
o Given -rA as a function of conversion, one can also design any sequence of reactors
Only valid if there are no side streams
o CSTRs in series 1
5. Reactors in Series II
Feb/28 2011 Spring 5
o CSTRs in series 2 - Reactor 1
• molar flow rate of A at point 1 is
- Reactor 2
• molar flow rate of A at point 2 is
0
0 Generaton
Out -
In
1 1 1
0
V r F
F
A A A1 0 0
1
F F X
F
A
A
A 1 0 1 11 X
F r V
A
A
0
0 Generaton
Out -
In
2 2 2
1
V r
F
F
A A A2 0
0
2
F F X
F
A
A
A5. Reactors in Series III
Feb/28 2011 Spring 6
o CSTRs in series 3
- Combining & rearranging
)
(
2 12 0
2
X X
r V F
A
A
2
2 0
0 1
0 0
2 2 1
2
) (
) (
A
A A
A A
A A A
r
X F
F X
F F
r F V F
5. Reactors in Series IV
Feb/28 2011 Spring 7
o CSTRs in series 4
- Large number of CSTRs in series
⇒ PFR approximation
5. Reactors in Series V
Feb/28 2011 Spring 8
o PFRs in series - By definition
2
0 1 0
12 0
0 0
X
X A
A X
A A
X
A
A
r
F dX r
F dX r
F dX
5. Reactors in Series VI
Feb/28 2011 Spring 9
o Consider a PFR between two CSTRs
5. Reactors in Series VII
Feb/28 2011 Spring 10
o Example 1
- For the irreversible gas-phase reaction: the following correlation was determined from laboratory data (the initial concentration of A is 0.2 g mol/L):
The volumetric flow rate is 5 m3/s.
a. Over what range of conversions are the plug-flow reactor and CSTR volumes identical?
5. Reactors in Series VIII
Feb/28 2011 Spring 11
o Example 1
b. What conversion will be achieved in a CSTR that has a volume of 90 L?
c. What plug-flow reactor volume is necessary to achieve 70% conversion?
d. What CSTR reactor volume is required if effluent from the plug-flow reactor in part (c) is fed to a CSTR to raise the conversion to 90%?
o Example 2
5. Reactors in Series IX
Feb/28 2011 Spring 12
o Example 2
- Pure A is fed at a volumetric flow rate of 1000 dm3 /h and at a concentration of 0.005 mol/dm3 to an
existing CSTR, which is connected in series to an existing tubular reactor.
VCSTR = 1200 dm3, Vtubular = 600 dm3,
X1, X2 = ? The reciprocal rate vs. conversion given
5. Reactors in Series X
Feb/28 2011 Spring 13
o Example 2
- The reciprocal rate vs. conversion given
