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What is a multiple reaction ?
• Require rate w.r.t. more than one species
• Require more than one stoichiometric equation and equilibrium expression
Classification: • Series (consecutive) reactions
A R S• Parallel (competing) reactions
A R A S
• Series – Parallel reactions 3
Criteria for selecting the reactor:• Good product distribution • Size of the reactor
Good product distribution could be the dominant criteria in many cases.
The above two criteria are contradictory to each other. Good design w.r.t one requirement may be poor w.r.t. the other.
An economic analysis will give the best compromise.
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Selectivity: A R (desired reaction)A S (undesired reaction)
Selectivity = rdesired/rundesired
The selectivity should be maximum for the chosen reactor.
Yield = rdesired /-rA
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Parallel reactions
A R (desired reaction)A S (undesired reaction)
A
RR Ck
dt
dCr 1
AS
S Ckdt
dCr 2
k1, k2, , are all constant for a specific system at a given temperature.
How to maximize S ??
AS
R Ck
k
dC
dCS
2
1
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AS
R Ck
k
dC
dCS
2
1
How to decide the concentration level??
Case – 1: > , ndesired > nundesired
High concentration is desirable as it maximizes the selectivity.
Case – 2: < , ndesired < nundesired
Low concentration is desirable as it maximizes the selectivity.
Case – 3: = , ndesired = nundesired
Concentration level does not affect the selectivity.
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Concentration can be maintained low:• Using a CSTR• Designing for high conversions• Increasing inerts in the feed• Decreasing pressure in gas phase
reactions
Concentration can be maintained high:• Using a PFR• Designing for low conversions• Decreasing inerts in the feed• Increasing pressure in gas phase reactions
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How to decide the temperature level??
Case – 1: ED > EU
High temperature is desirable as it maximizes the selectivity.
Case – 2: ED < EU
Low temperature is desirable as it maximizes the selectivity.
Case – 3: ED = EU
Temperature level does not affect the selectivity.
S is maximized at higher k1/k2
AS
R Ck
k
dC
dCS
2
1
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Example: A + B R (desired reaction)A + B S (undesired reaction)
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2
1 BAS
R CCk
k
dC
dCS
Case – 1: 1 > 1 and 2 > 2 Maintain both CA and CB high.
Case – 2: 1 < 1 and 2 < 2 Maintain both CA and CB low.
Case – 3: 1 = 1 and 2 = 2 CA and CB levels will not affect S.
Temperature levels can be decided based on the activation energies 12
•For parallel reactions, the concentration level of the reactants is the key to control product distribution.
•High reactant concentration favors the higher order reaction
•Low reactant concentration favors the lower order reaction
•Similarly high temperature favors the reaction with high activation energy
•Low temperature favors the reaction with low activation energy
Conclusions:
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Series reactions:A R S (I order at constant density)
meanopt kkk
kkt
log
12
12 /1)/ln( )(
2
1
0
max,12
2kk
k
A
R
k
k
C
C
Batch Reactor:
meanopt kkk
kk
log
12
12 /1)/ln(
)(
2
1
0
max,12
2kk
k
A
R
k
k
C
C
Plug Flow Reactor:
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CSTR:
A
AA
A
AA
Ck
CC
r
CC
1
00
10
1 kC
C
A
A
Material balance for species R: vCR0 = vCR + (-rR)V
0 = vCR + (-k1CA+ k2CR)V 0 = CR + (-k1CA + k2CR) CR(1 + k2) = k1CA
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)1)(1(1 21
01
2
1
kk
Ck
k
CkC AAR
For maximum concentration of R: dCR/d = 0
2120
max,
1/
1
kkC
C
A
R
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1
kkopt
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•For series reactions, the time of reaction / space time is the key for obtaining the maximum concentration of the desired product.
•For higher order reactions and series-parallel reactions, such analytical derivations for optimum space time would be tedious.
•In such cases, optimization methods can be used to find the optimum space time and the corresponding maximum concentration of the desired product.
Conclusions:
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Assignment:1. Find expressions for optimum space time
and maximum concentration of R for the following series reaction, if k1 = k2 in both CSTR and PFRA R S (I order at constant density)
2. Find expressions for optimum space time and maximum concentration of R for the following series reaction, if k1 = 2k2 in both CSTR and PFRA R S (I order at constant density)
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