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L9-1
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign.
L9-1
XA AA0
A0dXt=N -r V
XA dXAV =FA0 -rA0
Review: Isothermal Reactor DesignV j
j0 j jdN
F F r dVdt
In Out- +Generation =Accumulation1. Set up mole balance for specific reactor
2. Derive design eq. in terms of XA for each reactor
Batch
A0 AA
F XV = -r
CSTR PFR
3. Put Cj is in terms of XA and plug into rA
j0 j A0 A 0 0j
A 0
C C X T ZPC1 X P T Z
n
A jr kC
nj0 j A0 A 0
AA 0
C C X TPr k1 X P T
4. Plug rA into design eq & solve for the time (batch) or V (flow) required for a specific XA or the XA obtained for given V , 0, time, etc
(We will always look conditions where Z0=Z)
Be able to rearrange equations & integrate for Q2
Reaction order needs to be determined.
L9-2
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign.
L9-2
Review: Analysis of Rate Data
• Constant-volume batch reactor for homogeneous reactions: make concentration vs time measurements during unsteady-state operation
• Differential reactor for solid-fluid reactions: monitor product concentration for different feed conditions during steady state operation
Goal: determine reaction order, a, and specific reaction rate constant, k
• Data collection is done in the lab so we can simplify BMB, stoichiometry, and fluid dynamic considerations
• Want ideal conditions → well-mixed (data is easiest to interpret)
Method of Excess Differential method Integral method Half-lives method Initial rate method Differential reactor More complex kinetics
L9-3
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign.
L9-3
Review: Method of ExcessA + B → products Suspect rate eq. -rA = kCA
aCBb
1.Run reaction with an excess of B so CB ≈ CB0
2.Rate equation simplifies to –rA = k’CAa where k’=kACB
b ≈ k’=kACB0b and a
can be determined
3.Repeat, but with an excess of A so that CA ≈ CA0
4.With excess A, rate simplifies to –rA = k’’CBb where k’’=kACA
a ≈ k’’=kACA0a
5.Determine kA by measuring –rA at known concentrations of A and B, where
13AA
A B
r 1k dm molsC C
a b
a b
L9-4
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign.
L9-4
Review: Differential Method
1. Plot DCA/Dt vs t
2. Determine dCA/dt from plot by graphical or numerical methodsa) Draw rectangles on the graph.
Then draw a curved line so that the area above the curve that is cut off of each rectangle approximately fills the unfilled area under the curve
b) -dCA/dt is read using the value where the curve crosses a specified time
3. Plot ln(-dCA/dt) vs ln CA
j0 j j jdF F r V Ndt
0 0
jj
dCr
dt Where –rA = kCA
a
alpha power
Average slope
AA l
dCl
tnkn
dlnCa
A
A
dC dtkC a
Curved line represents –dCA/dt
Slope of line = α
Insert α, –dCA,p/dt, & corresponding CA,p
L9-5
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign.
L9-5
Review: Integral Method
• A trial-and-error procedure to find reaction order• Guess the reaction order → integrate the differential
equation• Method is used most often when reaction order is known
and it is desired to evaluate the specific reaction rate constants (k) at different temps to determine the activation energy
• Looking for the appropriate function of concentration corresponding to a particular rate law that is linear with time
L9-6
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign.
For the reaction A products
For a first-order reaction - rA = k CAA
AdC kC
dt
A0
A
Cln kt
C
ln (CA0/CA)
t
2AA
dC kCdt
For a second-order reaction - rA = k CA2
A A0
1 1 ktC C
1/CA
t
For a zero-order reaction -rA = k AdC kdt
A A0C C kt
CA
t
AA
dC rdt
Plot of CA vs t is a straight
line
Plot of ln(CA0/CA) vs t is a straight
line
Plot of 1/CA vs t is a straight line
L9-7
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign.
L9-7
AA
dC kCdt
a A products
1 1A A0
1 1 1tk 1 C Ca aa
A A0 1 21C C at t = t2
1
1 2 1A0
2 1 1tk 1 C
a
aa
1
1 2 A02 1ln t ln 1 lnCk 1
aa
a
ln (t1/2)
ln CA0
Slope = 1- a
A Ar kC a
Plot ln(t1/2) vs ln CA0. Get a straight line with a slope of 1-α
Review: Method of Half-livesHalf-life of a reaction (t1/2): time it takes for the concentration of the reactant to drop to half of its initial value
L9-8
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign.
L9-8
Review: Method of Initial Rates• When the reaction is reversible, the method of initial rates
can be used to determine the reaction order and the specific rate constant
• Very little product is initially present, so rate of reverse reaction is negligible– A series of experiments is carried out at different initial
concentrations
– Initial rate of reaction is determined for each run
– Initial rate can be found by differentiating the data and extrapolating to zero time
– By various plotting or numerical analysis techniques relating -rA0 to CA0, we can obtain the appropriate rate law:
A0 A0r kC a
L9-9
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign.
L9-9
Conversion of reactants & change in reactant concentration in the bed is extremely small
Review: Differential Catalyst Bed
FA0
CpCA0
FAe
Fp
DW
DL
r’A: rate of reaction per unit mass of catalyst
flow in - flow out + rate of gen = rate of accum.
A0 Ae AF F r W 0 D
A0 Ae 0 A0 AeA
F F C Cr
W W
D D
When constant flow rate, 0 = :
0 p0 A0 AeA
CC Cr
W W
D D
Product concentration
The reaction rate is determined by measuring product concentration, Cp
L9-10
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign.
L9-10
L9: Reactor Design for Multiple Reactions
• Usually, more than one reaction occurs within a chemical reactor• Minimization of undesired side reactions that occur with the desired
reaction contributes to the economic success of a chemical plant• Goal: determine the reactor conditions and configuration that
maximizes product formation• Reactor design for multiple reactions
• Parallel reactions• Series reactions• Independent reactions• More complex reactions
• Use of selectivity factor to select the proper reactor that minimizes unwanted side reactions
L9-11
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign.
L9-11
Classification of Multiple Reactions
A B Ck1 k2
A
C
B
k2
k1
A Bk1 C Dk2
2) Series reactionsDesired product
3) Independent reactions Crude oil cracking
Desired product
4) Complex reactions k1A B C D k2A C E
1) Parallel or competing reactions
L9-12
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign.
L9-12
Parallel ReactionsPurpose: maximizing the desired product in parallel reactions
DkD
A+B
UkU
(desired)
(undesired)
1 1D AD Bkr C Ca b
2 2U AU Bkr C Ca b
Rate of disappearance of A: D UA rr r
Define the instantaneous rate selectivity, SD/U
Goal: Maximize SD/U to maximize production of the desired product
EDRT 1 1
D A B
EURT AUA
2 2BAA e C Cr e C C
a b a b
1 2 1 2 1 2 1 2D U A B D U A
E ED UD D RT
UB
U
k AS C C S e
kC C
Aa a b b a a b b
EDRT
AD1 1
D Br CA e Ca b
EURT
AU2 2
U Br CA e Ca b
E
RTk T Ae
DD U
U
rrate of formation of DSrate of formation of U r
D1 1
U2 2
ERT AU B
ERT
D A BD U
A e C C
A es
C C
a b
a b
L9-13
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign.
L9-13
Maximizing SD/U for Parallel Reactions: Temperature Control
E ED UD RT 1 2 1 2
D U A BU
AS e C CA
a a b b
What reactor conditions and configuration maximizes the selectivity?Start with temperature (affects k):
a) If ED > EU
E ED UD U RTE E
0 e 1RT
Specific rate of desired reaction kD increases more rapidly with increasing T
Use higher temperature to favor desired product formation
b) If ED < EU
E ED UD U RTE E
0 e 1RT
Specific rate of desired reaction kD increases less rapidly with increasing T
Use lower T to favor desired product formation (not so low that
the reaction rate is tiny)
L9-14
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign.
L9-14
Maximize SD/U for Parallel Reactions using Temperature
E ED UD RT 1 2
D U AU
AS e CA
a a
What reactor temperature maximizes the selectivity?ED = 20 kcal/mol, EU = 10 kcal/mol, T = 25 ◦C (298K) or 100 ◦C (373K)
SD/U is greater at 373K, higher temperature to favors desired product formation
cal cal20,000 10,000mol mol
cal1.987 298K8mol KD D1 2 1 2
D U A D U AU U
A AS e C S 4.6 10 CA A
a a a a
cal cal20,000 10,000mol mol
cal1.987 373K6mol KD D1 2 1 2
D U A D U AU U
A AS e C S 1.4 10 CA A
a a a a
A
U
D
kU
kD
kD/U
a) ED > EUT = 25 ◦C (298K):
T = 100 ◦C (373K):
L9-15
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign.
L9-15
Maximizing SD/U for Parallel Reactions: Concentration
1 2 1 2a) 0a a a a
E ED UD RT 1 2 1 2
D U A BU
AS e C CA
a a b b
What reactor conditions and configuration maximizes the selectivity?Now evaluate concentration:
→ Use large CA
1 2 1 2b) 0a a a a
→ Use small CA
1 2 1 2c) 0b b b b
→ Use large CB
1 2 1 2d) 0b b b b
→ Use small CB
How do these concentration requirements affect reactor selection?
DkD
A+B
UkU
1 2AC a a 1 2
AC a a
1 2BC b b 1 2
BC b b
L9-16
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign.
L9-16
Concentration Requirements & Reactor Selection
CA00
CB00
CA0
CB0
How do concentration requirements play into reactor selection?
CSTR: concentration is always at its lowest value (that at outlet)
PFR
PFR (or PBR): concentration is high at the inlet & progressively drops to the outlet concentration
CA(t)CB(t)
DkD
A+B
UkU
Batch: concentration is high at t=0 & progressively drops with increasing time
Semi-batch: concentration of one reactant (A as shown) is high at t=0 & progressively drops with increasing time, whereas concentration of B can be kept low at all times
CB0
CA
L9-17
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign.
DkD
A+BUkU
b1 b2
High CB favors
desired product
formation
b1 b2
High CB favors
undesired product
formation(keep CB
low)
a1 a2High CA favors desired
product formationa1 a2
High CA favors undesired product formation
(keep CA low)
PFR/PBR
Batch reactor
When CA & CB are low (end time or position), all rxns will be slow
High P for gas-phase rxn, do not add inert gas (dilutes reactants)
PFR/PBR w/ side streams feeding low CB CB
←High CA
Semi-batch reactor, slowly feed B to large amount of A
CB CB CBCSTRs in seriesB consumed before leaving CSTRn
CA00
CB00
CA0
CB0 CSTR
PFR/PBRPFR/PBR w/ high recycle
• Dilute feed with inerts that are easily separated from product
• Low P if gas phase
PFR/PBRSide streams feed low CA
←High CB
CASemi-batch reactor slowly feed A to large amt of B
CA CA CACSTRs in series
L9-18
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign.
L9-18
Different Types of Selectivityinstantaneous rate selectivity, SD/U
DD U
U
rrate of formation of DSrate of formation of U r
DD U
U
F molar flow rate of desired productSF molar flow rate of undesir
ExitE ed prx oductit
overall rate selectivity, D US
DD U
U
N moles of desired productSN moles of undes
Fiir
nalFi ed pr unal od ct
DD
A
rrate of formation of DYrate of consumption of A r
instantaneous yield, YD
(at any point or time in reactor)
overall yield, DY
DD
A0 A
FYF F
flowD
DA0 A
NYN N
batchEvaluated at outlet
Evaluated at tfinal
L9-19
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign.
L9-19
Series (Consecutive) Reactions
(desired) (undesired)A D U
k1 k2 Time is the key factor here!!!
Spacetime t for a flow reactor Real time t for a batch reactor
To maximize the production of D, use:
Batch
or PFR/PBR orn
CSTRs in series
and carefully select the time (batch) or spacetime (flow)
L9-20
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign.
L9-20
Concentrations in Series ReactionsA B C
k1 k2-rA = k1CA
rB,net = k1CA – k2CB
k1A A1 A
A00A 1
AdF dCdV dV
C C ek C k C t
How does CA depend on t?
How does CB depend on t?
1 AB
2 Bk CdF Cd
kV
k1A01
B2 B0 C ekdC
dk C
V t
kB 11 A0 2 B
dC k C e k Cd
tt
Substitute
kB 12 B 1 A0
dC k C k C ed
tt
Use integrating factor (reviewed
on Compass)
k2
B k k2 11 A0
d C ek C e
d
tt
t
k k1 2B 1 A0
2 1
e eC k Ck k
t t
0
V t
C A0 A BC C C C
L9-21
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign.
L9-21
The reactor V (for a given 0) and t that maximizes CB occurs when dCB/dt=0
k k1 A0B 1 21 2
2 1
k CdC k e k e 0d k k
t tt
1opt
1 2 2
k1 lnk k k
t
0
V t
so opt 0 optV t
AB
C
k1A A0C C e t
k k1 2B 1 A0
2 1
e eC k Ck k
t t
C A0 A BC C C C topt
Reactions in Series: Cj & Yield