Ideal & Semi-Batch Reactors, Multiple Reactions & Product Distribution Flashcards
What are the assumptions for a batch reactor
- No flow in & out during reaction
- Perfectly mixed
- Generally has constant pressure OR volume
What are the assumptions for a CSTR
- Steady state ie. no acc
- Continuous flow in & out
- Perfectly mixed
- Product stream has the same concentrations as the vessel contents
What are the assumptions for a PFR
- Steady state
- Perfect radial mixing
- No axial mixing
- Continuous flow in & out
State the suitability, advantages & disadvantages of a batch reactor
Suitability: Producing small amounts of materials
AD: High conversion per unit volume, low instrument cost, flexibility of operation & easy to clean
DIS: High labour & handling costs, considerable shut down tome & poor quality of control
State the suitability, advantages & disadvantages of a CSTR
Suitability: Large scale, fast reactions & high temperatures
AD: High conversion per unit volume, low operating/labour costs, continuous operation & good heat transfer
DIS: Undesired thermal gradients, poor temp control & shutdown & cleaning can be expensive
State the suitability, advantages & disadvantages of a PFR
Suitability: Reactions that require agitation and/or use different concentrations
AD: Continuous operation, good temp control, easily adapts to two phase runs, good control, simple construction, low operating/labour costs & easy to clean
DIS: Lowest conversion per unit volume, by-passing & channelling issues due to poor agitation
Derive the design equation for a batch reactor, starting with the mass balance
A –> R
acc = in - out + prod. - cons.
dNA = 0 - 0 + 0 - (-rA)V dt
In terms of concentration (constant volume):
dNA/V = d(CAV)/V = - (-rA) dt
t = - dCA/(-rA)
In terms of conversion:
dCA = - CA0 dXA
t = CA0 dXA/(-rA)
Derive the design equation for a CSTR, starting with the mass balance
A –> P
acc = in - out + prod. - cons.
0 = CA0 v - CA v + 0 - (-rA)V
In terms of concentration:
V/v = (CA0 - CA)/(-rA)
In terms of conversion:
V/v = (CA0 XA)/(-rA)
V/FA0 = XA/(-rA)
Derive the design equation for a PFR, starting with the mass balance
A –> P
acc = in - out + prod. - cons.
0 = F - (F+dF) + 0 - (-rA)dV
0 = F - F - dF - (-rA)dV
- dF = (-rA) dV
FA0 dXA = (-rA) dV
V = FA0 dXA/(-rA)
V/FA0 = dXA/(-rA)
Remember: F = C v
V/(CA0 v) = dXA/(-rA)
Outline what can be deduced from the 1/rA plot (Levenspiel plot) for a:
- Batch reactor
- CSTR
- PFR
- Batch
For 1/rA vs. CA:
When CA is high (ie. close to CA0), 1/rA is low therefore, rA is high & the area under the curve = time
For 1/rA vs. XA
When XA is high (ie. further from X0), 1/rA is higher therefore, rA is small & the area under the curve = time/CA0 - CSTR
For a 1/rA vs. CA: When CA is high (ie. close to CA0), 1/rA is low therefore, rA is high & the area above the curve = V/v - PFR
For 1/rA vs. XA
When XA is high (ie. further from X0), 1/rA is higher therefore, rA is small & the area under the curve = V/F
NOTE: For both plots with conversion or concentration, the area above or below the curve is equal for each plot
Define space time and write the equation
Def: The time to process one reactor volume of feed measured at specified conditions
Eqn: tao = V/v0
Define space velocity and write the equation
Def: The number of reactor volumes of feed at specified conditions which can be treated in unit time
Eqn: s = 1/tao
State the assumptions for a semi-batch/semi-PFR system
- Perfectly mixed
- Reactor is filled during operation so the intial conc of A is at a maximum but B can be kept at relatively low conc
Describe when a semi-batch reactor would be used and state the advantage
- For highly exothermic reactions
- When 1 reagent is a gas
- A distillation where reagents are added all at t=0 but the product is removed continuously
AD: To increase the production of a desired product and limit the amount of by-products, which may be harmful or reduce yield.
Describe the differences in the plotted graphs for the following semi-batch reactions when:
A + B –> R
R + B –> S
- A is added slowly into B
- B is added slowly into A
- R is used as soon as it is produced so it doesn’t show on the curve. Because B is in low concentration, there will become less and less as A is added and A will take over.
- Because B is in low concentration & is being added in slowly it is not shown on the graph. The intermediate product, R will have an arching curve.
When would a semi-PFR be used? Why?
When you want to add a certain reagent at intervals. This allows the concentration of this component to remain relatively constant and the other declines.
Define selectivity and instantaneous selectivity (with the equations)
A –> B
A –> C
Selectivity:
A measure of success of using a particular reactor/operating conditions in producing a desired product compared to a by-product
S B/C = (Moles of B produced)/(Moles of C produced)
Instantaneous selectivity:
The production rate of one components per production rate of another component
S B/C = rB/rC = (k1 CA^a1)/(k2 CA^a2) = (k1/k2) CA^(a1 - a2)
Define yield and instantaneous yield (with the equations)
A –> B (desired)
A –> C
Yield:
The moles of a specific product formed per mole of reactant consumed
= (Moles A consumed to form B)/(Total moles of A consumed)
= CB/(CA0 - CA)
Instantaneous yield:
The rate of formation of a specific product as a fraction of the total rate of reactant consumed
= (Rate of consumption of A to form B)/(Total rate of consumption of A)
= rB/(rB + rC)
How do you use selectivity to optimise? ie. what are the rules?
A –> R (desired)
A –> S
- Small reactor size
- Maximisation of the desired product
- Minimise undesirable reactions
S R/S = rR/rS = (k1 CA^a1)/(k2 CA^a2) = (k1/k2) CA^(a1 - a2)
If:
a1 - a2 > 0 - High reactant concentration is desirable to increase the R/S ratio using a batch or PFR or minimise reactor size
a1 - a2 < 0 - Low reactant concentration is desirable using a CSTR
a1 - a2 = 0 - The product distribution is fixed by k1/k2 so it makes no difference what reactor is used
How else can parallel reactions be optimised for the desired product?
A –> R (desired)
A –> S
By changing k1/k2:
- If the activation energy is different for the 2 reactions the changing the temperature will change k1/k2
- If a catalyst is used, it can accelerate or depress any reaction (this is very effective).
For the following parallel reactions:
A + B –> R (desired)
A + B –> S
What can be done in terms of concentration to maximise the selectivity of the desired product, S?
rR = k1 CA^a CB^b
rS = k1 CA^c CB^d
If:
- a-c>0 and b-d>0, keep CA, CB high
- a-c<0 and b-d<0, keep CA, CB low
- a-c>0 and b-d<0, keep CA high, CB low
- a-c<0 and b-d<0, keep CA low, CB high
What is this system of multiple reactions called?
A –> R
A –> T
R –> S
R –> U
Denbigh system
Derive the design equations from mass balance for the following parallel reactions in a CSTR:
A –> B
A –> C
acc = in - out + prod. - cons.
- rA = k1 CA + k2 CA
rB = k1 CA
rC = k2 CA
0 = v CA0 - CA + 0 - (-rA)V
A: v CA0 - v CAf = (k1 + k2) CAf V
V/v = (CA0 - CAf)/(CAf (k1 + k2))
B: v CB0 - v CBf = - k1 CAf V
V/v = (CB0 - CBf)/(-k1 CAf)
C: v CC0 - v CCf = -k2 CAf V
V/v = (CC0 - CCf)/(-k2 CAf)
What is a series-parallel reaction? Give an example
A combination of series and parallel, where the reactions are assumed to be irreversible, elemental, bimolecular & constant density
A + B –> R
R + B –> S
S + B –> T
Derive the design equations from mass balance for the following series-parallel reactions in a CSTR:
A + B –> R
R + B –> S
acc = in - out + prod. - cons.
rA = - k1 CA CB rB = - k1 CA CB - k2 CR CB rR = k1 CA CB - k2 CR CB rS = k2 CR CB
0 = v CA0 - CA + 0 - (-rA)V
If B is not a solvent, use B to calculate volume.
If B is a solvent, it is in very high concentration so use A instead.
To calculate the final conversion of S you will first need R so do the mass balance about R first then sub in. Generally in this case, CA = CB
Why is calculating concentration different in a PFR? Why?
The concentration varies down the length of the PFR because there is no axial mixing
How do you quantitatively determine the product distribution for parallel reactions in a PFR?
A –> B (desired)
A –> C
First, calculate the instantaneous fractional yield (IFY) for the desired product (B) and simplify it.
= dCB/-dCA
= rB/(rB + rC)
Secondly, calculate the overall fractional yield (OFY) from the following equations (this should be a number):
= CBf/(CA0 - CAf)
= -1/(CA0 - CAf) [integral (IFY dCA)][CAf, CA0]
= 1/(CA0 - CAf) [integral (IFY dCA)][CA0, CAf]
Remember: CAf = CA0(1 - XA)
Thirdly, the concentration of the desired product will be:
CRf = OFY x CAf
Finally, the concentration of the undesired product will be:
CSf = (1 - OFY) x CAf
How do you quantitatively determine the product distribution for parallel reactions in a CSTR?
First, calculate the instantaneous fractional yield (IFY) for the desired product (B) and simplify it.
= dCB/-dCA
= rB/(rB + rC)
Remember: CAf = CA0(1 - XA)
Secondly, calculate the overall fractional yield (OFY), which is equal to the IFY at the exit (this should be a number):
= CBf/(CA0 - CAf)
= rB/(rB + rC)
Thirdly, the concentration of the desired product will be:
CRf = OFY x CAf
Finally, the concentration of the undesired product will be:
CSf = (1 - OFY) x CA
