ABSTRACT
Given the average residence time,
dXA (1 + εAXA) (−rA) (20.2)
t=−1 k
ln(1 −XA) (20.3)
The value of the rate constant can be calculated at 150◦C (reaction temperature), which is:
ln k=−5400 T
+ 12.5
where: k= 0.649 min−1 As t= 3 min XA = 0.857
To calculate the volume, one has the PFR equation:
τ = V v0
dXA ( − rA)
Substituting (−rA), we obtain the following solution:
τ =−1 k
[(1 + εA) ln (1 −XA) + εAXA] (20.4)
Calculating εA:
εA =−0.25 Substituting these values into Equation 20.4, we get:
τ = 2.58 min But
F0 = 100mol/min However:
FA0 + FB0 = 100 FA0 + 3FA0 = 100 FA0 = 25 mol/min
C0 = PRT = 2.88 × 10 −1mol/L
For v0:
v0 = F0C0 = 346 L/min
Therefore, the volume of PFR reactor is:
V = 0.89 m3
In the CSTR reactor, assuming the same conversion, we use the equation:
V v0
= τ =CA0 XA( − rA) Replacing the rate and substituting these values for the same conversion, we obtain:
τ = 4.71 min With the same input flow, we get:
V = 1.63 m3
This gives us a ratio of:
VCSTR VPFR
= 1.8
SE.2 The reaction A k−→R+ S is irreversible and first order. It is conducted in a PFR
with 50 tubes, each with “½’’ in diameter and 1.0 m of height. 200 kg/h of reactant A (MW = 80 g/gmol) with 30% inert is introduced at a pressure of 50 bar at 500◦C. The output conversion is 80%. Calculate the average residence time.
