SME
Chemical Reaction Engineering · Problem type
Levenspiel plot: which reactor is smaller
Use this for “20 mol/min of A at 2 mol/L reacts first order, k = 0.2 per min. Which needs less volume for 80% conversion? Read the CSTR as the rectangle and the PFR as the area under FA0 ÷ (−rA).”
Chart
CSTR: the rectangle 0 to X under the height at X, V = 200; PFR: the area under the curve, V = 80.47
This is an example. Type your own values to start a new problem.
FA0
Feed rate of A
example · mol/min
k
Rate constant
example · min⁻¹
CA0
Feed concentration
example · mol/L
X
Conversion
example
VCSTR
CSTR volume
calculated · L
VPFR
PFR volume
calculated · L
Formulas
VCSTR
=
FA0
×
X
k
× CA0 × (1 −
X
)
200
=
20
×
0.8
0.2 × 2 × (1 − 0.8)
VPFR
=
(
FA0
k
× CA0
)
×
(−ln(1
−
X
))
80.47
=
(
20
0.2 × 2
)
×
(−ln(1
−
0.8))
Assumptions
•
First order, isothermal, liquid phase (constant density): −rA = kCA0(1 − X).
•
The CSTR runs at the exit rate: its volume is the rectangle under the curve’s height at X.
•
The PFR passes through every rate on the way: its volume is the area under the curve.
Step-by-step
WE KNOW
FA0 = 20 mol/min, k = 0.2 min⁻¹, CA0 = 2 mol/L, X = 0.8
FIND
CSTR volume (VCSTR), PFR volume (VPFR)
Step 1 · Find CSTR volume (VCSTR)
Use VCSTR = FA0 × X ÷ (k × CA0 × (1 − X))
The
CSTR
balance
FA0X
=
(−rA)V
at
the
exit
rate:
X
wide,
FA0
−rA
at
X
high.
VCSTR
=
20
×
0.8
0.2 × 2 × (1 − 0.8)
VCSTR
=
20
×
0.8
0.2 × 2 × 0.2
VCSTR
=
20
×
0.8
0.4 × 0.2
VCSTR
=
20
×
0.8
0.08
VCSTR
=
16
0.08
VCSTR = 200 L
Step 2 · Find PFR volume (VPFR)
Use VPFR = (FA0 ÷ (k × CA0)) × (−ln(1 − X))
The
area
∫FA0
dX
kCA0(1 −
X
)
from
0
to
X
comes
to
(
FA0
kCA0
)(−ln(1
−
X
)).
VPFR
=
(
20
0.2 × 2
)
×
(−ln(1
−
0.8))
VPFR
=
20
0.4
×
(−ln(0.2))
VPFR
=
20
0.4
×
(−(−1.6094))
VPFR
=
20
0.4
×
1.6094
VPFR = 50 × 1.6094
VPFR = 80.47 L
Check
Put the numbers back in. Both sides should match.
200
=
20
×
0.8
0.2 × 2 × (1 − 0.8)
✓
80.47
=
(
20
0.2 × 2
)
×
(−ln(1
−
0.8))
✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
Related lessons
Batch, CSTR and PFR design
Main lesson
Second-order reaction in each reactor
Use this for “A second-order liquid reaction, k = 0.5 L/(mol·min), is fed at 2 mol/L. What space times reach 80% conversion in a CSTR and in a PFR?”
Batch time for a conversion
Use this for “A first-order reaction with k = 0.2 per min runs in a batch reactor. How long until 90% of A has reacted?”
CSTRs in series
Use this for “Two CSTRs, each with 5 min space time, run a first-order reaction with k = 0.2 per min. What conversion leaves the second tank?”