Tutorial trk Solutions
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The exothermic reaction
A--->B + C
was carried out adiabatically and the following data recorded:
The entering molar flow rate of A was 300 mol/min.
(a) What are the PFR and CSTR volumes necessary to achieve 40 % conversion?
(b) Over what range of conversions would the CSTR and PFR reactor volumes be identical?
(c) What is the maximum conversion that can be achieved in a 105 dm3 CSTR?
(d) What conversion can be achieved if a 72 dm3 PFR is followed in series by a 24 dm3 CSTR?
(e) What conversion can be achieved if a 24 dm3 CSTR is followed in a series by a 72 dm3 PFR?
(f) Plot the conversion and rate of reaction as a function of PFR reactor volume up to a volume of 100 dm3.
QUESTIONS
X 0 0.2 0.4 0.45 0.5 0.6 0.8 0.9-rA
(mol/dm3.min
1.0 1.67 5.0 5.0 5.0 5.0 1.25 0.91
PART (A)
Recall Simpson One-Third Rule Formula:
PFR Volume:
Using Simpson One-Third Rule;
X
AAPFR r
dXFV
0
0
hXXXX
hwhere
XfXfXfh
dXXfX
X
0102
210
2
43
2
0Xh
2.02
04.0
,4.0,2.0,0 210 XXX
)4.0()2.0(4
)0(3000
Xr
F
Xr
F
Xr
FXV
A
A
A
A
A
APFR
What are the PFR and CSTR volumes necessary to achieve 40 % conversion?
0 0.2 0.4 0.6 0.8 10
100
200
300
400
X
FA
0/-
rA
PART (A)X 0 0.2 0.4 0.45 0.5 0.6 0.8 0.9-rA
(mol/dm3.min)
1.0 1.67 5.0 5.0 5.0 5.0 1.25 0.91
FA0/-rA
(dm3)300 180 60 60 60 60 240 330
)4.0()2.0(4
)0(3000
Xr
F
Xr
F
Xr
FXV
A
A
A
A
A
APFR
6018043003
2.0
372dm
Levelspiel Plot
VPFR
PART (A)
CSTR Volume:
Substituting the value of FA0/–rA at X=0.4;
A
ACSTR r
XFV
0
4.060 3dmVCSTR
324dm
0 0.2 0.4 0.6 0.8 10
100
200
300
400
X
FA
0/-
rA
VCSTR
Levelspiel Plot
PART (B) Over what range of conversions would the CSTR and PFR reactor volumes be identical?
A
A
A
A
r
FdX
r
F
4.06.006.0
4.0
0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
50
100
150
200
250
300
350
X
FA
0/-
rA
The volume of both
reactors are identical at X=0.4-0.6,
6.0
4.0
6.0
4.0 CSTRPFR VV
From Levelspiel Plot;
PART (B) Over what range of conversions would the CSTR and PFR reactor volumes be identical?
)6.0()5.0(4
)4.0(3000
Xr
F
Xr
F
Xr
FXV
A
A
A
A
A
APFR
Xh
1.02
4.06.02.0,1.0,0 210 XXX
31260604603
1.0dm
33
120120 122.060 dmdmXX
r
F
r
XXFV
exitA
A
exitA
ACSTR
Using Simpson One-Third Rule
Proving by calculation;
Volume of PFR
Volume of CSTR
By trial and error, calculate what is X that gives a CSTR volume of 105 dm3
Trial 1: X=0.6,
PART (C) What is the maximum conversion that can be achieved in a 105 dm3 CSTR?
330 366.060 dmdmr
XFV
A
ACSTR
Trial 2: X=0.8,
330 1928.0240 dmdmr
XFV
A
ACSTR
Trial 3: X=0.7,
330 1057.0150 dmdmr
XFV
A
ACSTR
0 0.2 0.4 0.6 0.8 10
100
200
300
400
XF
A0
/-rA
X=0.7
The max conversion can be achieved in 105 dm3 of CSTR is 0.7
By trial and error, calculate what is X2
that gives a CSTR volume of 24 dm3
Trial 1: X=0.6,
Trial 2: X=0.7,
PART (D) What conversion can be achieved if a 72 dm3 PFR is followed in series by a 24 dm3
CSTR?
33120 124.06.060 dmdmr
XXFV
exitA
ACSTR
X2=?
X1=0.4FA0=300 mol/dm3
VCSTR=24 dm3
VPFR=72 dm3
33120 454.07.0150 dmdmr
XXFV
exitA
ACSTR
Now, we know that the
conversion must be
between 0.6-0.7.
From part (a)
Trial 3: X=0.64,
PART (D) What conversion can be achieved if a 72 dm3 PFR is followed in series by a 24 dm3
CSTR?
exitA
ACSTR r
XXFV
120
X2=?
X1=0.4FA0=300 mol/dm3
VCSTR=24 dm3
VPFR=72 dm3
0 0.2 0.4 0.6 0.8 10
100
200
300
400
X
FA
0/-
rA X=0.64
33 244.064.0100 dmdm
X=0.64 can be achieved if a 72 dm3 PFR is followed in series by a 24 dm3 CSTR.
By trial and error, calculate what is X2 that gives a PFR volume of 72 dm3
Trial 1: X=0.8,
PART (E) What conversion can be achieved if a 24 dm3 CSTR is followed in a series by a 72 dm3 PFR?
X2=?
X1=0.4
FA0=300 mol/dm3
VCSTR=24 dm3
VPFR=72 dm3
)8.0()6.0(4
)4.0(3000
Xr
F
Xr
F
Xr
FXV
A
A
A
A
A
APFR
Xh
2.02
4.08.0 ,8.0,6.0,4.0 210 XXX
336240604603
2.0dm
From part (a)
By trial and error, calculate what is X2 that gives a PFR volume of 72 dm3
Trial 2: X=0.9,
PART (E) What conversion can be achieved if a 24 dm3 CSTR is followed in a series by a 72 dm3 PFR?
X2=?
X1=0.4
FA0=300 mol/dm3
VCSTR=24 dm3
VPFR=72 dm3
)9.0()65.0(4
)4.0(3000
Xr
F
Xr
F
Xr
FXV
A
A
A
A
A
APFR
Xh
25.02
4.09.0,9.0,65.0,4.0 210 XXX
317.683301074603
25.0dm
Trial 3: X=0.91,
PART (E) What conversion can be achieved if a 24 dm3 CSTR is followed in a series by a 72 dm3 PFR?
0 0.10.20.30.40.50.60.70.80.9 10
50
100
150
200
250
300
350
X
FA
0/-
rA
)91.0()655.0(4
)4.0(3000
Xr
F
Xr
F
Xr
FXV
A
A
A
A
A
APFR
Xh
255.02
4.091.0,91.0,655.0,4.0 210 XXX
391.713461104603
25.0dm
X=0.91 can be achieved if a 24 dm3 CSTR is followed in a series by a 72 dm3 PFR
PART (F) Plot the conversion and rate of reaction as a function of PFR reactor volume up to a volume of 100 dm3?
X 0 0.2 0.4 0.45 0.5 0.6 0.8 0.9-rA
(mol/dm3.min)
1.0 1.67 5.0 5.0 5.0 5.0 1.25 0.91
FA0/-rA
(dm3)300 180 60 60 60 60 240 330
VPFR (dm3) 0 48 72 76.5 80 84 104 130.5
PART (F) Plot the conversion and rate of reaction as a function of PFR reactor volume up to a volume of 100 dm3?
0 10 20 30 40 50 60 70 80 90 1000
0.1
0.2
0.3
0.4
0.5
0.6
0.7
VPFR (dm3)
X
0 10 20 30 40 50 60 70 80 90 1000.00
1.00
2.00
3.00
4.00
5.00
6.00
VPFR (dm3)
-rA
(m
ol/dm
3.m
in)
THANK YOU
