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9/9/2015
1
Basic Kinetics and Reactors
1. Rate Laws2. Basic Ideal Reactors3. Performance and Combinations4. Lab Reactors5. Laboratory Experiments
Basic Equations in CRE
n+1 Equations:
n Mass BalancesEnergy BalanceMomentum Balance
LHS = RHS
rate intrinsic
factoration ess/utilizeffectivencatalyst
indexn eactivatioactivity/dcatalyst
RHS
Mixing Reflects Type,Reactor LHS
r
r
9/9/2015
2
Rate Laws at the Core of Reaction Engineering
Chemistry Process...) cat, , P, T, ,C ,f(Crtion Interpreta Mechanism BAA
Examples
2
2/3
2
)1(
1
BBAA
BAA
AA
A
AA
CKCK
CkCr
kC
kCr
kCr
kCr
A
A
836 835
A Biochemical Example
(P) Products (S) Substrate (E) Enzyme
Rate
CS
Pkk
SK
KPSEkrate
ESEE
EPESES
m
o
o
1
4
3
4,32,1
)/(
:Analysis
9/9/2015
3
Amorphous Silicon Fabrication
Rate
H2
221
421 :Law RatekHk
SiHkkr
22
2
221
4
:Mechanism
HSiSiH
HSiHSiH
212
42122
212
412
2221412 )(0)(
:Analysis
Hkk
SiHkkSiHkr
Hkk
SiHkSiH
SiHkHkSiHkdt
SiHd
Hydrolysis in Supercritical Water
k
CH2O
HLOHRLROH k 2 :Mechanism
RLOHRLOH
o CCfkr 2),,(12
2
1.1rT
Increases in CH2O increases density which increases
9/9/2015
4
Epoxy‐Amine Kinetics
Rate
Conversion
EORCOOHCHNHRNHEOREONHRNH '' 2222
groups OHproduct by sisAutocataly
)"1()'1( OHkkAExkkAEr
1.1rT
Catalytic HDN
lnRN/RNo
time
)(1
)/( :Law Rate
3
3
NHRNK
KNHRHRNkKr
3k
2
1st
2 :Mechanism NHRHH RN
Increasing RNo
Strong competitive adsorption
9/9/2015
5
Thermal Cracking
logk1st
2/12
2/32/3
)21(1 :Law Rate
KAKA
kA
KA
kAr
CBAstk
1
TP
TP
TP
C
BA
A
2
2
2
Mechanism Underlying
logAo
2/1n 2/1n0n
Zero‐Order Kinetics
ktAA
kdtdA
o /
A/Ao
t
1.0
0
)1/(/ KAkAdtdA
9/9/2015
6
First‐Order Kinetics
ktAA
kAdtdA
o )/ln(
/
ln(A/Ao)
t
1.0
0
B/AAkkBAr
or
AKAkAr
A
A
high at '
lowat )1/(
Second‐Order Kinetics
ktAA
kAr
o
A
11
2
t
0
okAt
12/1
A
1
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7
Reversible Reactions
AABB
KBAkdtdA
BA
oo
)/(/
ln[(A-Ae)/(Ao-Ae)]
t
1.0
0))((/)(
)()(/
)1()(/
)()(/
)(/1
/)(/
21
2121
221
221
2121
ee
e
e
oo
oo
ooe
eeooee
AAkkdtAAd
AkkAkkdtdA
AKkAkkdtdA
ABkAkkdtdA
AABkAkBkAkdtdAK
BAA
AAABABK
Simultaneous Reactions
)(
)/(
22
11
21212
2
11
2
1
nnA
nnn
n
AkAkr
AkkAk
AkS
CA
BA
9/9/2015
8
Series Reactions
)exp()]exp()[exp(/
)exp(/
22112
1
1
21
tkA
Btktk
kk
kAB
tkAA
CBA
o
oo
o
12
2
2
1max
12
12max,
)0(
)/ln()0(
kk
k
oo
oB
k
kABB
kk
kkBt
Figure 2-4 JJC
Van de Vusse Network
DAA
CBA
3
21
•B is the desired product•High A favors D•Backmixing favors C•CSTR-PFR predicament
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9
Laboratory and Plant Reactors
A. LaboratoryA. Goal is information, not profitB. Run experiments at well-defined, intrinsic conditions
A. Direct measure of rate? = 1C. IsothermalD. No deactivation
B. PlantA. Use information for profitB. Run reactor at optimal conditions
A. May be integral (likely)B. May be diffusion limitedC. May be adiabaticD. Catalyst may/will deactivate
Basic Ideal ReactorsDifferential Integral
CA0
CA
CA
CSTR
Spatially Uniform
CA 0
CA
PFR
Low Per-Pass Conversion
CA 0
CA
PFR
Reaction Varies Concentration
A
Ao
C
C
AA
AA
AA
AA
AzzAzA
rdC
with
rddC
Q
rdVdF
rdzQCd
zrQCQC
/
/
constant at
/
/)(
0||
kC
C
kCr
CCr
QV
VrQCQC
Ao
A
AA
AAoA
AAoA
1
1
for or,
/
0
AAoA
AA
A
AA
CCr
or
rC
C
rddC
constant ely approximatat
/
9/9/2015
10
Comparison of PFR and CSTR Flow Patterns
Comparison of PFR and CSTR Performance
Inlet Outlet
A/Ao
PFR approaches outlet conditions
CSTR uniformly at outlet conditions
Driving Force
T/To
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11
Comparison of PFR and CSTR Performance
Normal Kinetics Autocatalytic Kinetics
A
Ao
C
C
AA rdC /
Comparison of PFR and CSTR Performance
PC /
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12
Comparison of PFR and CSTR Performance
oAQ /
n CSTR’s Approach PFR
Inlet Outlet
A/Ao
PFR approaches outlet conditions
CSTR uniformly at outlet conditions
9/9/2015
13
n CSTR’s Approach PFR
nT
non
oo
o
nkkAA
n
kAA
kAA
kAA
kAA
)/1(
1
)1(
1/
reactors For
)1(
1/ ;
1
1/ ;
1
1/
Q V, equal of reactors For two1
1/
kineticsorder -firstfor Equation CSTR Basic
22121
n An/Ao
1 0.250
2 0.160
3 0.125
4 0.107
5 0.095
10 0.073
15 0.065
20 0.061
25 0.059
50 0.054
PFR 0.050
k = 3
0.0000.0500.1000.1500.2000.2500.300
0 10 20 30 40 50 60
A/A
o
Number of CSTR's n
Subdivision of CSTR V
n CSTR’s Approach PFR
02468101214161820
0 20 40 60
Total Tau
(blue), Total Tau divided by n
(red) and Cost (green)
Number of CSTR's n
Subdivision at Constant Conversion
ktT
ktT/n
n(ktT/n)^0.6
n kT A/Ao kT/n n(kT/n)^0.61 95 0.010 95 15.3685949
2 17.76612 0.010 8.883061 7.415963569
3 10.82932 0.010 3.609772 6.480508818
4 8.524191 0.010 2.131048 6.298192158
5 7.520166 0.010 1.504033 6.387405228
10 5.813795 0.010 0.581379 7.222304882
15 5.4 0.010 0.36 8.125924063
20 5.2 0.010 0.26 8.912796783
25 5 0.010 0.2 9.518269694
50 4.8 0.010 0.096 12.25554825
PFR 4.605
A/Ao = 0.01
9/9/2015
14
n CSTR’s Approach a PFR
nx
x
n
comparingk
x
and
nk
xn
nC
P
P
nCC
T
1)1(
)1ln(
)1ln(
1)1(
/1
/1
0
0.2
0.4
0.6
0.8
1
1.2
0 20 40 60
TauP/TTauC
Number of CSTR's n
n CSTR's Approach PFR
tP/tCT @ xA = 0.5
tP/tCT @ xA = 0.9
tP/tCT @ xA = 0.95
tP/tCT @ xA = 0.99
n CSTR's tP/tCT @ xA = 0.5 tP/tCT @ xA = 0.9 tP/tCT @ xA = 0.95 tP/tCT @ xA = 0.99
1 0.693147181 0.255842788 0.15767012 0.046516871
2 0.836702662 0.532444361 0.431396165 0.255842788
3 0.888920156 0.664852131 0.582458682 0.421534885
4 0.91585771 0.739639602 0.671843991 0.532444361
5 0.932286279 0.787352331 0.730164017 0.609195253
10 0.965742986 0.889285095 0.857680901 0.787352331
15 0.977073033 0.925210059 0.903463906 0.854336679
20 0.982771413 0.943539691 0.926975664 0.889285095
50 0.993084543 0.977150873 0.970341806 0.954655118
The Recycle Reactor
PFR
Pump
Q
C0
F ,C11 F = Q + q
q,c
Q
CRecycle reactor model:
"large" can depend on conversion
ratio recycle/ ;/ ;/
Define
QqRFVQV
C
C C
dC
kF
dV
FdVd
kCddC
1
1
/
/
PFR For the
1
)1(lnln
/ with and1
and
:balance materialBy
1
1
1
Rf
Rf
C
Ck
CCfR
CRCC
qCQCFC
o
o
o
limit CSTR the1
1
then
1/1
/
since
)1(1
1
or
)1(
1
:)derivationfor JJC(seeRlargeFor
kf
RQq
QV
V
F
V
kRf
Rf
fk
9/9/2015
15
Models for Intermediate Levels of Mixing
Performance at Intermediate Levels of Mixing
A -> B -> C2A -> C
9/9/2015
16
Laboratory Reaction Engineering
Overview
Basic Goal: Estimation of intrinsic rate parameters from experimental data. Premise: Rate and adsorption constants, and not conversion or selectivity, per se, can be related to catalyst structure and composition. We can use kinetics as one of many tools for the evaluation of catalysts.
Laboratory Reactors for Evaluation of Catalysts
Mathematically convenient to acquire direct measure of rate. Practical realities often require integral data acquisition; iterative parameter estimation or differentiation of data follows.
1.
2.
9/9/2015
17
Basic Ideal ReactorsDifferential Integral
CA0
CA
CA
CSTR
Spatially Uniform
CA 0
CA
PFR
Low Per-Pass Conversion
CA 0
CA
PFR
Reaction Varies Concentration
A
Ao
C
C
AA
AA
AA
AA
AzzAzA
rdC
with
rddC
Q
rdVdF
rdzQCd
zrQCQC
/
/
constant at
/
/)(
0||
kC
C
kCr
CCr
QV
VrQCQC
Ao
A
AA
AAoA
AAoA
1
1
for or,
/
0
AAoA
AA
A
AA
CCr
or
rC
C
rddC
constant ely approximatat
/
(Differential analysis)(Integral analysis)
Analysis of Kinetics Data from Ideal ReactorsIntegral PFR Differential PFR CSTR
Integral Method Differential Method
C vs r vs CAAA
r vs C AA
C
A Aln r
Aln C
n
Rate Equation r = r (n, C, k)A A
Integration and Iteration Direct
9/9/2015
18
Real Reactors
Weekman (AIChE J. 20:833(1974)) summarizes the issues:
1. Sampling and Product Analysis 2. Isothermality 3. RTD and its measurement 4. Selectivity Disguise 5. Construction difficulty and cost 6. Availability, size, phase of reactants
Reactor Ideal Governing Equation Advantages Cautions
Sampling and Analysis of
Product Composition Isothermality
Residence Time
Control
Time Averaging Disquise
ConstructionDifficulty and
Cost
1.0
Fixed Bed Reactor (PFR)
Inexpensive; Common; Strong experience base. Separates contact time from time on stream (tos). High conversion facilitates analytical chemistry
Lab-scale fixed bed reactors can have significant backmixing, complicating data analysis
Good, normal sorts of problems
Poor-Fair, very difficult to achieve uniform temperature
Fair, channeling and vapor-liquid distribution issues
Poor due to transient behavior
Good, fairly straightforward
1.1
Axial Dispersion Reactor (ADR) None
Approximate Pe ~ 2(L/dp) to determine the extent of backmixing
Good, normal sorts of problems
Poor-Fair, very difficult to achieve uniform temperature
Fair, channeling and vapor-liquid distribution issues
Poor due to transient behavior
Good, fairly straightforward
1.2
Differential Fixed Bed Reactor (DPFR)
Low per-pass conversion provides rate vs. concentration data
Analytical chemistry can be challenging at low per-pass conversions
Poor-Fair, can be difficult at low conversions
Fair-Good, low heat release
Fair, channeling and vapor-liquid distribution issues
Poor due to transient behavior
Good, one of the simplest
1.3
Fixed Bed Reactor with Recycle (RPFR)
This is a PFR model with inlet and overall outlet flow rate Q. In the PFR, the flow rate is F = Q + q, where q is the recycle stream. The recycle ratio R = q/Q controls the mixing behavior of the reactor. At R = 0, the RPFR is a PFR. At R -> infinity, CSTR behavior is achieved. Please see Lab Reactor Summary, page 13, for more details
At "high" recycle ratio CSTR behavior is achieved, providing rate vs. concentration data.
The value of R needed for CSTR behavior depends on the conversion level
Fair-Good, rapid catalyst-reactant separation esential Good, well mixed
Good, well mixed at high circulation velocities
Poor, steady state operation
Fair-Poor, requiresrecirculating pumpor jets
2.1
CSTR/Internal Recycle Reactor (IRR)
Provides spatial uniformity in concentration and temperature at the outlet values. Provides rate vs concentration/temperature data. Separates contact time = V/Q from tos. Common realizations include Berty and Robinson-Mahoney reactors
The value of R needed for CSTR behavior depends on the conversion level
Good, normal sorts of problems Good, well mixed
Fair-Good, Solid acccurately known and gas-vapor known if good mixing
Poor, transient behavior
Fair-Good, more complex than batcor fixed bed
3.0
Batch Reactor (BR) Simple; Easy to use
Contact time and time on stream (tos) not separated
Fair, difficult on-line analysis problems Good, well mixed
Good, accurate residence time if rapid quenching
Poor, transient behavior
Good, fairly straightforward
Table 1. Laboratory Reactors for Kinetics Studies: Pros and Cons
)/()/(
)/(
)/(
)/(12
2
uCoLrLzd
CoCd
Lzd
CoCd
Pe i
jji
i rV
F
j
jii r
dV
dF
j
iji r
d
dC
jji
i rV
F
9/9/2015
19
Real Reactors: The Fixed Bed Reactor
Gas-Liquid, Powdered Catalyst, Decaying Catalyst System
Problem Comments Rating
Sampling and Analysis of Product Composition Isothermality Residence-Contact Time Measurement Selectivity Time Averaging Disguise Construction Difficulty and Cost
Normal Problems Very Difficult to Achieve Uniform Temperatures Channeling or Liquid Distribution may be a Problem Transient Behavior Fairly Straight- Forward
Good Poor-Fair Fair Poor Good
Axial Dispersion ModelPFR: -u dC/dz = r
Superimpose a diffusive flux:
D d C/dz - u dC/dz = ra
2 2
Letting: Z = z/L f = C/C Pe = Lu/D = L/u
a
0
The balance equation reduces to:
d f/dZ - df/dZ = r/C2 2
01
Pe
9/9/2015
20
RTD for Various Values of Pe
= t/
Peclet Number for Axial Diffusion (Pellet)
5
1.0
.2
Re = dpG/
Pe = u d /Di p z
thumbof rule useful a is /Then
/2~)/)(/()/)(/(/
2~/
Suppose
P
PPPPPR
PP
dL
dLdLDudddDuLDuLPe
DudPe
9/9/2015
21
Influence of Axial Dispersion on First-Order Conversion
Conversion in PFR
PFR
n
x
x
1
1
PFRn
n
PPPP
P
xx
PedLdLPen
dLn
before, As
.2 when /2/
/ mixers CSTR ofnumber Define
seriesin sCSTR'n th analogy wi JJC
Real Reactors: The Differential Reactor
Gas-Liquid, Powdered Catalyst, Decaying Catalyst System
Problem Comments Rating
Sampling and Analysis of Product Composition Isothermality Residence-Contact Time Measurement Selectivity Time Averaging Disguise Construction Difficulty and Cost
Can be Difficult at Low Conversions Low Heat Release Channeling Fatal V-L Distribution Problem Transient Behavior One of Simplest
Poor-Fair Fair-Good Fair Poor Good
9/9/2015
22
Real Reactors: A Collection of Other Type Reactors
Gas-Liquid, Powdered Catalyst, Decaying Catalyst System
Problem Comments Rating
Sampling and Analysis of Product Composition Isothermality Residence-Contact Time Measurement Selectivity Time Averaging Disguise Construction Difficulty and Cost
Rapid Catalyst-Reactant Separation Essential Well Mixed Well Mixed at Highly Circulating Velocities Steady State Operation Requires Recirculating Pump or Jets
Fair-Good Good Good Poor Fair-Poor
The Recycle Reactor
PFR
Pump
Q
C0
F ,C11 F = Q + q
q,c
Q
CRecycle reactor model:
"large" can depend on conversion
ratio recycle/ ;/ ;/
Define
QqRFVQV
C
C C
dC
kF
dV
FdVd
kCddC
1
1
/
/
PFR For the
1
)1(lnln
/ with and1
and
:balance materialBy
1
1
1
Rf
Rf
C
Ck
CCfR
CRCC
qCQCFC
o
o
o
limit CSTR the1
1
then
1/1
/
since
)1(1
1
or
)1(
1
:)derivationfor JJC(seeRlargeFor
kf
RQq
QV
V
F
V
kRf
Rf
fk
9/9/2015
23
Real Reactors: The Carberry, Robinson-Mahoney, Berty Type Reactors
Gas-Liquid, Powdered Catalyst, Decaying Catalyst System
Problem Comments Rating
Sampling and Analysis of Product Composition Isothermality Residence-Contact Time Measurement Selectivity Time Averaging Disguise Construction Difficulty and Cost
Normal Problems Well Mixed Solid Accurately Known; Gas-Vapor Known if Good Mixing Transient Behavior More Complex Than Batch or Fixed Bed
Good Good Fair-Good Poor Fair-Good
Real Reactors: The Stirred Batch Reactor
Gas-Liquid, Powdered Catalyst, Decaying Catalyst System
Problem Comments Rating
Sampling and Analysis of Product Composition Isothermality Residence-Contact Time Measurement Selectivity Time Averaging Disguise Construction Difficult and Cost
Difficult On-Line Analysis Problems Well Mixed Accurate Residence Time if Rapid Quenching Transient Behavior Fairly Straight Forward
Fair Good Good Poor Good