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CPE360 > Ideal & Semi-Batch Reactors, Multiple Reactions & Product Distribution > Flashcards

Ideal & Semi-Batch Reactors, Multiple Reactions & Product Distribution Flashcards

1
Q

What are the assumptions for a batch reactor

A
  • No flow in & out during reaction
  • Perfectly mixed
  • Generally has constant pressure OR volume
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2
Q

What are the assumptions for a CSTR

A
  • Steady state ie. no acc
  • Continuous flow in & out
  • Perfectly mixed
  • Product stream has the same concentrations as the vessel contents
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3
Q

What are the assumptions for a PFR

A
  • Steady state
  • Perfect radial mixing
  • No axial mixing
  • Continuous flow in & out
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4
Q

State the suitability, advantages & disadvantages of a batch reactor

A

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

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5
Q

State the suitability, advantages & disadvantages of a CSTR

A

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

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6
Q

State the suitability, advantages & disadvantages of a PFR

A

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

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7
Q

Derive the design equation for a batch reactor, starting with the mass balance

A –> R

A

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)

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8
Q

Derive the design equation for a CSTR, starting with the mass balance

A –> P

A

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)

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9
Q

Derive the design equation for a PFR, starting with the mass balance

A –> P

A

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)

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10
Q

Outline what can be deduced from the 1/rA plot (Levenspiel plot) for a:

  1. Batch reactor
  2. CSTR
  3. PFR
A
  1. 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
  2. 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
  3. 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

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11
Q

Define space time and write the equation

A

Def: The time to process one reactor volume of feed measured at specified conditions

Eqn: tao = V/v0

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12
Q

Define space velocity and write the equation

A

Def: The number of reactor volumes of feed at specified conditions which can be treated in unit time

Eqn: s = 1/tao

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13
Q

State the assumptions for a semi-batch/semi-PFR system

A
  • 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

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14
Q

Describe when a semi-batch reactor would be used and state the advantage

A
  • 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.

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15
Q

Describe the differences in the plotted graphs for the following semi-batch reactions when:

A + B –> R
R + B –> S

  1. A is added slowly into B
  2. B is added slowly into A
A
  1. 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.
  2. 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.
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16
Q

When would a semi-PFR be used? Why?

A

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.

17
Q

Define selectivity and instantaneous selectivity (with the equations)

A –> B

A –> C

A

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)

18
Q

Define yield and instantaneous yield (with the equations)

A –> B (desired)

A –> C

A

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)

19
Q

How do you use selectivity to optimise? ie. what are the rules?

A –> R (desired)
A –> S

A
  • 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

20
Q

How else can parallel reactions be optimised for the desired product?

A –> R (desired)
A –> S

A

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).
21
Q

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?

A

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
22
Q

What is this system of multiple reactions called?

A –> R
A –> T
R –> S
R –> U

A

Denbigh system

23
Q

Derive the design equations from mass balance for the following parallel reactions in a CSTR:

A –> B
A –> C

A

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)

24
Q

What is a series-parallel reaction? Give an example

A

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

25
Q

Derive the design equations from mass balance for the following series-parallel reactions in a CSTR:

A + B –> R
R + B –> S

A

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

26
Q

Why is calculating concentration different in a PFR? Why?

A

The concentration varies down the length of the PFR because there is no axial mixing

27
Q

How do you quantitatively determine the product distribution for parallel reactions in a PFR?

A –> B (desired)
A –> C

A

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

28
Q

How do you quantitatively determine the product distribution for parallel reactions in a CSTR?

A

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

CPE360 (5 decks)

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