10.37 Chemical and Biological Reaction Engineering, Spring 2007
Prof. K. Dane Wittrup
Lecture 9: Reactor Size Comparisons for PFR and CSTR
This lecture covers reactors in series and in parallel, and how the choice of reactor
affects selectivity versus conversion.
PFR vs. CSTR: Size and Selectivity
Material balance:
CSTR
V=
PFR
FAo
XA
−rA
V=∫
XA
0
FAo
dX A
−rA
“Levenspiel Plot”
• as X A increases, C A decreases
FAo
− rA
1st or 2nd
order
reaction
−rA decreases, for 1st and 2nd order,
F
so Ao increases
−rA
Figure 1. General Levenspiel Plot.
XA
PFR Volume
CSTR Volume
FAo
− rA
FAo
− rA
VCSTR
XA
VPFR
XA
Figure 2. Levenspiel plots for a CSTR and a PFR for positive order reactions.
So PFR is always a smaller reactor for a given conversion when kinetics are positive
order.
Cite as: K. Dane Wittrup, course materials for 10.37 Chemical and Biological Reaction Engineering, Spring
2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on
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Non-monotonically positive order kinetics arise:
• Autocatalytic reactions (e.g. cell growth)
• Adiabatic or non-isothermal exothermic reactions
• Product inhibited reactions (some enzymes)
Series of Reactors
Example: 2 CSTRs
FAo
v1
x1
FA1
v2
FA2
x2
Figure 3. Schematic of two CSTRs in series.
V1 =
FAo
X1
−rA1
0
2nd reactor:
In + Out + Prod = Acc
FA1 − FA2 + rA2 V2 = Steady state
10.37 Chemical and Biological Reaction Engineering, Spring 2007
Prof. K. Dane Wittrup
Lecture 9
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FA2 = FA0 − X 2 FA0
FAo
− rA
→
V2 =
FA0
−rA2
V1
( X 2 − X1 )
V2
X1
Figure 4. Reactor volumes for 2 CSTRs
in series.
X2
X
Multiple CSTRs begin to
approximate a single PFR
FAo
− rA
X
Figure 5. Reactor volumes for multiple CSTRs in series.
10.37 Chemical and Biological Reaction Engineering, Spring 2007
Prof. K. Dane Wittrup
Lecture 9
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2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on
[DD Month YYYY].
FAo
− rA
FAo
− rA
VPFR
VCSTR
VPFR
VCSTR
X
XA
Designed final
conversion
Final X
Figure 6. Levenspiel plots comparing CSTR and PFR volumes for changing kinetics.
Left: The CSTR has the smaller volume. Right: The PFR eventually has the smaller
volume.
Choice of PFR vs CSTR depends on conversion. Choose the reactor that has the
smallest volume Æreduce cost.
Reactors:
CSTR
FAo
−rA
VCSTR
VPFR
PFR
X
Final X
Figure 7. To achieve the desired conversion with smaller reactor volumes, use a
combination. In this case, use a CSTR then a PFR. By doing so, the reactor volume is
less than the area underneath the curve.
For competing parallel reactions, selectivity for desired product can dominate the
choice.
Example
A→ D
rD = kd C Aα1
A →U
α2
D = Desired, U = Undesired
rU = ku C A
10.37 Chemical and Biological Reaction Engineering, Spring 2007
Prof. K. Dane Wittrup
Lecture 9
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2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on
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SD /U =
Define “selectivity”
If
α1 > α 2 , as C A
rD kd (α1 −α 2 )
= CA
rU ku
increases, S D /U increases
-Favors PFR because C A starts at C Ao then drops whereas CSTR
concentrations are always at lower C A .
If
α1 < α 2 , as C A
increases, S D /U decreases
-CSTR favored
If
α1 = α 2
then
S D /U =
kd
, no dependence on C A
ku
-Therefore no CSTR/PFR preference.
Define a fractional yield
φ=
kd C αA1
dCD
=
− dC A kd C αA1 + ku C αA 2
Overall fractional yield
For a CSTR:
Φ=
Φ = φ Εxit C
All D produced
All A consumed
A
ΔC A = C A − C A
0
For a PFR:
If
Φ=
1
ΔC A
∫
C At
CA 0
f
φ dC A
α1 = α 2
φ
ΦΔC A
C Af
C A0
CA
Figure 8. Fractional yield versus concentration. Selectivity does not depend on CA.
10.37 Chemical and Biological Reaction Engineering, Spring 2007
Prof. K. Dane Wittrup
Lecture 9
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2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on
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If
α1 > α 2
φ
CA
Figure 9. Fractional yield versus concentration when α1 > α2.
CSTR
PFR
φ
φ
Φ PFR ΔC A
Φ CSTR ΔC A
C Af
C Af
C A0
CA
C A0
CA
Figure 10. Comparison of overall fractional yield for a CSTR and a PFR when α1 >
α2.
PFR is preferred because Φ PFR >Φ CSTR , therefore the yield of D per mol A consumed
is higher.
If
α1 < α 2
Φ CSTR ΔC A
φ
C Af
C A0
Φ PFR ΔC A
φ
C Af
CA
C A0 C A
CSTR
PFR
Figure 11. Comparsion of overall fractional yield for a CSTR and a PFR when α1 >
α2.
Φ PFR <Φ CSTR
10.37 Chemical and Biological Reaction Engineering, Spring 2007
Prof. K. Dane Wittrup
Lecture 9
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Cite as: K. Dane Wittrup, course materials for 10.37 Chemical and Biological Reaction Engineering, Spring
2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on
[DD Month YYYY].