Reactors in Series

Question 1

What type of reactor cannot occur in series?

Answer 1

Batch

Question 2

What is the general purpose of putting reactors in series?

Answer 2

Maximise conversion or throughout.

Question 3

For 3 reactors in series, write the equations for the moles of A after each reactor for xA conversion.

Answer 3

nA1 = nA0 - xA1nA0
nA2 = nA0 - xA2nA0
nA3 = nA0 - xA3nA0

Question 4

What is the effect on residence time when putting CSTRs in series?

Answer 4

More molecules will have the same residence time at 1 given time, eventually forming a singular peak distribution.

Question 5

What is the effect on residence time when putting PFRs in series?

Answer 5

In a fixed infinitesimal volume, there is constant flow in and out of this volume to neighbouring fixed volumes - resembling a CSTR at steady state. A PFR is a infinite CSTR forming a singular peak distribution.

Question 6

How do you calculate the volume for a CSTR?

Answer 6

V/nA0 = 1/rA xA

Question 7

For a positive order reaction, does a small or large CSTR operate at a faster rate.

Answer 7

Smaller - higher concentration at exit conditions.

Question 8

Does a PFR operate at a faster or slower rate than a CSTR of the same size?

Answer 8

PFR operates at faster rate.

Question 9

Why is a reactor in series preferred over in parallel?

Answer 9

Higher overall conversion as conversion in reactor 1 is fed into reactor 2..

Question 10

If the same final conversion was achieved in a parallel and series reactor model then which would have the higher reaction rate?

Answer 10

They would have the same as a CSTR operates at exit conditions. However the first reactor in series would have a lower 1/rA therefore higher rate & throughput.

Question 11

How should the size be arranged for a series for a first order reaction in a CSTR to maximise conversion?

Answer 11

Conversion is independent of size order. Best results are 2 equal sized.

Question 12

How do you calculate conversion for a 1st order CSTR reactor in series?

Answer 12

xA = tk/(tk+1)
1-xA = 1/(tk+1) = CAi/CA(i-1)

Question 13

How should the size be arranged for a series for a zero order reaction in a CSTR to maximise conversion?

Answer 13

Rate is independent of concentration so size does not matter.

Question 14

How should the size be arranged for a series for a negative order reaction in a CSTR to maximise conversion?

Answer 14

Larger reactor should be placed first to keep conversion high & concentration low. Lower concentration = faster rate.

Question 15

How should the size be arranged for a series for a positive higher order reaction in a CSTR to maximise conversion?

Answer 15

Smaller reactor first to keep conversion low & concentration high. First reactor should have a high rate - smallest reactor.

Question 16

Generally, should a CSTR or PFR be put first in series?

Answer 16

PFR first as higher concentration & reaction time.

Question 17

For a zero order reaction, should a CSTR or PFR be placed first in series?

Answer 17

Rate is independent of concentration so order does not matter.

Question 18

For a higher order reaction, should a CSTR or PFR be placed first in series?

Answer 18

PFR first maximises rate & throughput.

Question 19

For a negative order reaction, should a CSTR or PFR be placed first in series?

Answer 19

CSTR first higher concentration has lower rate.

Question 20

For a first order reaction, should a CSTR or PFR be placed first in series?

Answer 20

Conversion independent of inlet concentration - order does not matter.

Question 21

How do you calculate conversion in a PFR?

Answer 21

xA = 1 - e(-kt)

Question 22

How do you connect a series of PFRs?

Answer 22

Becomes one large PFR. Change of shape only important for volume.

Question 23

How do you calculate the volume for a PFR?

Answer 23

V = [nA0/rA dxA] (xA,0)

Question 24

How do you calculate the number of CSTR reactors required in series for a given conversion xA?

Answer 24

V = nA0 xA/rA 
Vk/nA0u(t) = xA/(nA0(1-xA))^2 
Solve for xA
-> nA1 = nA0 - xAnA0
Substitute
Vk/nA1u(t) = xA/(nA0(1-xA))^2
Repeat until desired xA.

Question 25

How do you calculate the conversion after the 20th CSTR reactor in series?

Answer 25

CA20/CA0 = 1/(tk+1)^20 = 1 - xA

Question 26

How do you calculate the conversion after the 20th PFR in series?

Answer 26

Act as one big PFR.

CA/CA0 = e (-kt) = 1-xA

Question 27

How do you calculate the increased throughput in series compared to parallel for n reactors?

Answer 27

Parallel;
0 = nA0 - nA - rA nV
u(t) = nVk/(CA0/CA -1)
u(t) = nVk/(1/(1-xA) - 1)
Series;
0 = nA0 - nA - rA V
u(t) = Vk/(sqrt(CA0/CA2) - 1)
u(t) = Vk/(sqrt(1/(1-xA)) - 1)
COMPARE;
Series/Parallel = [Vk/(sqrt(1/(1-xA)) - 1)]/nVk/(1/(1-xA) - 1)