Reactors in Series, Autocatalytic Reactions & Recycle Streams

Question 1

What are the general concepts for optimising reactor systems?

Answer 1

Choosing reactors with small size and adequate product distribution (ie. maximising desired product).

Question 2

What is the general rule for optimising a single reaction?

Answer 2

• When the reaction order > 0, keep conc high

- When reaction order < 0, keep conc low

Question 3

What is the general rule for optimising reactions in series when the intermediate product is desired?

Answer 3

Do not intermix fluids (no recycle) that have different active ingredients ie. reactants or intermediates as this can depress the formation of the desired product

Question 4

What is the general rule for optimising reactions in parallel

Answer 4

• High conc favours the highest order reaction = PFR
• Low conc favours the lowest order reaction = CSTR
• When the reaction orders are the same the concentration has no effect on favourability

Question 5

True or false: Continuously operated reactors have an equivalent product distribution to reactors with a non-flow operation eg. batch reactor

Answer 5

True

A flow reactor with no recycle is the same as a batch reactor and a flow reactor with a recycle is the same as a semi-batch reactor

Question 6

What is the general rule for optimising reactions through temperature control?

Answer 6

High temps generally favour reactions with a higher activation energy

Question 7

How do you calculate the total volume of 3 PFRs in series? Write the design equation

Answer 7

V/F0 = integral [ 1 / (-rA) ] (X1, 0) + integral [ 1 / (-rA) ] (X2, 0) + integral [ 1 / (-rA) ] (X3, 0)

The total volume is equal to the sum of each integral, which is equal to the integral over the entire system as if it was 1 large PFR

V/F0 = integral [ 1 / (-rA) ] (Xfinal, 0)

Question 8

Why are PFRs in series more efficient than CSTRs in series for reactions with order n>0

Answer 8

Because the concentration in a CSTR immediately drops to a low value so a PFR is more efficient as it fits the Levenspiel plot better

Question 9

Explain, which equations, how to optimise CSTRs in series by minimising the size and calculating conversion

Answer 9

Looking at the Levenspiel plot, the aim is to maximise the size of the rectangle above the curve.

The design equation is:
V/F0 = ( 1 / (-rA) ) X

So for 2 CSTRs

1. V1/F0 = ( 1 / (-rA1) ) (X1 - 0)
2. V2/F0 = ( 1 / (-rA2) ) (X2 - X1)

The general solution is:
f’(x) = - [(f(x) - y0)/(x - x0)]

Where f’(x) is the tangent to the curve at the point of intersection with the rectangle.

To solve we find the value of f’ (x) and make this equal to the LHS of the general solution.

• For a first order reaction:
  V/F0 = ( 1 / k CA0 (1 - X) ) X
  f (x) = 1/(1 - X)
  f’ (x) = 1/(1 - X)^2
• For a n>0 order reaction
  V/F0 = ( 1 / k CA0^2 (1 - X)^2 ) X
  f (x) = 1/(1 - X)^2
  f’ (x) = 2/(1 - X)^3
• For a n<0 order reaction (eg. n=0.2)
  V/F0 = ( 1 / k CA0^0.2 (1 - X)^0.2 ) X
  f (x) = 1/(1 - X)^0.2
  f’ (x) = 0.2/(1 - X)^1.2

Now solve to find X

Question 10

On the Levenspiel plot, where is the optimal size ratio for 2 CSTRs in series?

Answer 10

When the slope of the tangent at the intercept = the diagonal of the rectangle above the curve.

Question 11

In general, what are the optimum size ratios for 2 CSTRs in series when the reaction is:

1. 1st order
2. n > 1
3. n < 1

Answer 11

1. Equal size
2. Small reactor first
3. Large reactor first

Question 12

Which combination has the smallest reactor volume?

1. 2 PFRS
2. 2 CSTRs

Answer 12

2 PFRs is smaller than 2 CSTRs

Question 13

Which combination has the smallest reactor volume?

1. PFR –> CSTR
2. CSTR –> PFR

Answer 13

They are not equal so cannot be compared

Question 14

How do you calculate the volume of reactors in series using the Levenspiel plot

Answer 14

If a CSTR is first use the design equation:
V = [ F0/(-rA) ] X

If a CSTR is second use the design equation but use the interval of the conversion:
V = [ F0/(-rA) ] (X2 - X1)

For a PFR, use Simpsons rule:
V = integral [ F0 / (-rA) ] dX (b, a)

V = [ (b - a)/3n ] [ f(x0) + 4 f(x1) + 2 f(x2) + 4 f(x3) + f(x4) ]

where f (x) = F0/(-rA) at a given conversion

Question 15

How do you use the volume of a pilot scale reactor to achieve a given conversion to calculate the volume of a larger scale?

Answer 15

1. Use the design equation to calculate the rate of reaction for the pilot scale volume & conversion.
2. Use the rate law to calculate the rate constant, k
3. Substitute this information back into the design equation to calculate the new volume

Question 16

Describe the Levenspiel plot for an autocatalytic reaction

Answer 16

The concentration curve drops down and comes back up again so to maximise rate you need to minimise the area under the curve

Question 17

What is an autocatalytic reaction?

Answer 17

A reaction in which one of the products of the reaction acts as a catalyst

Question 18

Write the rate law for the elementary autocatalytic reaction

A + R –> R + R

Answer 18

• rA = - dCA/dt = k CA^a CR^b

Question 19

Describe the rA vs. concentration plot for an autocatalytic reaction

Answer 19

At the start, rate is slow and there is very little product but as product forms the rate progressively increases and reaches a maximum. The curve then decreases as all of A is consumed.

Question 20

Compare the circumstances where a CSTR would be preferred over a PFR for an autocatalytic reaction (and vice versa)

Answer 20

At low conversions, CSTR is preferred to plug flow as it will provide a smaller volume and maximises rate (minimising area under the curve)

At high conversions, PFR is preferred

Question 21

Write the equation for the recycle ratio, R

Answer 21

R = volume of fluid returned to the reactor / volume leaving the system

Question 22

Write the mass balance equations for an autocatalytic reactor at the points where the recycle is added

Answer 22

v1 = v0 + Rv2
v1 = v2 + Rv2

Question 23

For an autocatalytic reactor with a recycle stream, write the concentration of component A at point 1 and point 2 in terms of conversion and recycle ratio

Answer 23

X1 = (CA0 - CA1)/CA0
CA1 = CA0 (1 - X1)

CA1 = (CA0 + CA2R)/(R+1)
CA1 = (CA0 +CA0(1-X2)R)/(R + 1)

Make the 2 eqns equal

CA0 (1 - X1) = (CA0 +CA0(1-X2)R)/(R + 1)

(1 - X1) = (1 + (1-X2)R)/(R + 1)

X1 = RX2/(R + 1)

Question 24

For an autocatalytic reactor with a recycle stream, write the flow of component A at point 1 in terms of the recycle ratio

Answer 24

FA1 = RFA0 + FA0 
FA1 = FA0 (R + 1)

Question 25

What happens if the recycle ratio is too large?

Answer 25

The reactor volume becomes too large