Reactors in Series, Autocatalytic Reactions & Recycle Streams Flashcards
What are the general concepts for optimising reactor systems?
Choosing reactors with small size and adequate product distribution (ie. maximising desired product).
What is the general rule for optimising a single reaction?
- When the reaction order > 0, keep conc high
- When reaction order < 0, keep conc low
What is the general rule for optimising reactions in series when the intermediate product is desired?
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
What is the general rule for optimising reactions in parallel
- 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
True or false: Continuously operated reactors have an equivalent product distribution to reactors with a non-flow operation eg. batch reactor
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
What is the general rule for optimising reactions through temperature control?
High temps generally favour reactions with a higher activation energy
How do you calculate the total volume of 3 PFRs in series? Write the design equation
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)
Why are PFRs in series more efficient than CSTRs in series for reactions with order n>0
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
Explain, which equations, how to optimise CSTRs in series by minimising the size and calculating conversion
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
- V1/F0 = ( 1 / (-rA1) ) (X1 - 0)
- 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
On the Levenspiel plot, where is the optimal size ratio for 2 CSTRs in series?
When the slope of the tangent at the intercept = the diagonal of the rectangle above the curve.
In general, what are the optimum size ratios for 2 CSTRs in series when the reaction is:
- 1st order
- n > 1
- n < 1
- Equal size
- Small reactor first
- Large reactor first
Which combination has the smallest reactor volume?
- 2 PFRS
- 2 CSTRs
2 PFRs is smaller than 2 CSTRs
Which combination has the smallest reactor volume?
- PFR –> CSTR
- CSTR –> PFR
They are not equal so cannot be compared
How do you calculate the volume of reactors in series using the Levenspiel plot
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
How do you use the volume of a pilot scale reactor to achieve a given conversion to calculate the volume of a larger scale?
- Use the design equation to calculate the rate of reaction for the pilot scale volume & conversion.
- Use the rate law to calculate the rate constant, k
- Substitute this information back into the design equation to calculate the new volume
Describe the Levenspiel plot for an autocatalytic reaction
The concentration curve drops down and comes back up again so to maximise rate you need to minimise the area under the curve
What is an autocatalytic reaction?
A reaction in which one of the products of the reaction acts as a catalyst
Write the rate law for the elementary autocatalytic reaction
A + R –> R + R
- rA = - dCA/dt = k CA^a CR^b
Describe the rA vs. concentration plot for an autocatalytic reaction
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.
Compare the circumstances where a CSTR would be preferred over a PFR for an autocatalytic reaction (and vice versa)
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
Write the equation for the recycle ratio, R
R = volume of fluid returned to the reactor / volume leaving the system
Write the mass balance equations for an autocatalytic reactor at the points where the recycle is added
v1 = v0 + Rv2 v1 = v2 + Rv2
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
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)
For an autocatalytic reactor with a recycle stream, write the flow of component A at point 1 in terms of the recycle ratio
FA1 = RFA0 + FA0 FA1 = FA0 (R + 1)
What happens if the recycle ratio is too large?
The reactor volume becomes too large
