Chemical Reactor Analysis and Design 3th Edition G.F. Froment, K.B. Bischoff † , J. De Wilde inetics of Heterogeneous Catalytic Reactions Chapter 2
Jan 16, 2016
Chemical Reactor Analysis and Design
3th Edition
G.F. Froment, K.B. Bischoff†, J. De Wilde
Kinetics of Heterogeneous Catalytic Reactions
Chapter 2
Introduction
Principles homogeneous reaction kinetics: valid
...CC)T(kr 'bB
'aA
But: information at locus of reaction required !
Solid surface of the catalyst (internal)
• Formation surface complex: Essential feature of reactions catalyzed by solids
Kinetic equation must account for this !
• Transport processes: May influence the overall rate
Introduction
1. Transport of reactants A, B, ... from the main stream to the catalyst pellet surface.
2. Transport of reactants in the catalyst pores.3. Adsorption of reactants on the catalytic site.4. Chemical reaction between adsorbed
atoms or molecules.5. Desorption of products R, S, ....6. Transport of the products in the catalyst
pores back to the particle surface.7. Transport of products from the particle
surface back to the main fluid stream.
Steps 1, 3, 4, 5, and 7: strictly consecutive processes Steps 2 and 6: cannot be entirely separated !
Chapter 2: considers steps 3, 4, and 5Chapter 3: other steps
Introduction
Principles of catalysis:
Progress of reaction
Pot
entia
l ene
rgy
A
A╪
Al
B
Eanon-cat
Eacat
ΔH
• Reaction accelerated Main reason: decrease Ea
• Reverse reaction similarly accelerated (principle microscopic reversibility)
Overall equilibrium not affected !
Example: homogeneous versus catalytic ethylene hydrogenation [Boudart, 1958]
Homogeneous:
Catalytic (CuO/MgO):
2
000,43exp1027
HpRTr
2
000,13exp10.2 27
HpRTr
At 600 K:1.44•1011 times faster
Introduction
Types of catalysts:
Acid (silica/alumina, …):
Metal (Pt, Pd, …):
• Can act as Lewis (electron acceptor) or Brønsted (proton donor) acids • Form some sort of carbonium /carbenium ion from hydrocarbons
• Primarily used in hydrogenations and dehydrogenations
Classical example: ethanol decomposition:
OHHCOHHCcatalyst
acid24252 (dehydration)
24252 HOHCOHHCcatalyst
metal (dehydrogenation)
With hydrocarbons: Acid catalyst: cracking or isomerizationMetal catalyst: (de)hydrogenations
Introduction
Types of catalysts:
Dual function or bifunctional:
single function dual function
True intermediate, R, must desorb, move through the fluid phase, and adsorb on the new site if any product S is to be formed !
Certain intimacy of the two catalysts required !
Introduction
Types of catalysts:
A R S
sitesite1 2
trivial polystepA R S
sitesite1 2
non-trivial polystep
Unique conversion or selectivity can be achieved !
• as if steps were successively performed
• Rl1 intermediate continuously “bled off” => equilibrium shifted toward higher overall conversion
Dual function or bifunctional:
Introduction
Types of catalysts:
Dual function or bifunctional:Example: Industrially important isomerization of saturated hydrocarbons (encountered in “catalytic reforming”):
saturate iso-saturate
unsaturate iso-unsaturateacid cat.
metal cat. metal cat.−H2 H2
Introduction
Types of catalysts:
Dual function or bifunctional:Example: Cumene cracking:
Acidic silica/alumina catalyst:
Pt/Al2O3 catalyst:
Presumed sequence:
=> Intermediate: no role
=> Metal sites: permit alternative, and then dominant, reaction
Adsorption on solid catalysts
Physisorption Chemisorption
Through van der Waals forces Involves covalent chemical bonds
Multi-layer coverage possible Only single layer coverageSurface-catalyzed reaction
Classical Langmuir theory: Hypotheses:• The adsorption sites are energetically uniform• Monolayer coverage• No interaction between adsorbed molecules• Heat of adsorption independent of surface coverage• Usual mass action laws can describe the individual steps
lA Al
lAaa CCkr RTEaaa eAk /
Aldd Ckr RTEddd eAk /with:
with:
[kmol/kg cat. s]
Unknown surface concentrations [kmol/kg cat.]
ada EEQ
Heat of adsorption:
(more than 42 kJ/mol)
Adsorption on solid catalysts
Allt CCC Total concentration of sites:
If at equilibrium: adsorption isotherm: lAaAld CCkCk
AltAa CCCk
AA
AAtAl CK
CKCC
1with:
d
aA k
kK
Alternate formulation: fractional coverage:AA
AA
t
Al
CK
CK
C
C
1
Types of adsorption isotherm. After Brunauer et al. [1940].
LangmuirMulti-layerphysisorption
II with finiteporosity solid
Adsorption on solid catalysts
Extension of the Langmuir treatment:Two species adsorbing on the same sites:
lA Al lB Bl
AldAlAaAAl CkCCkdt
dC BldBlBaB
Bl CkCCkdt
dC
BlAltt CCCC Total concentration of sites:
Unknown surface species concentrations [kmol/kg cat.]
If at equilibrium:
lAAAl CCKC lBBBl CCKC
lBBlAAlt CCKCCKCC
unknown surface concentrations can be eliminated:
BBAA
tl CKCK
CC
1 BBAA
iitil CKCK
CKCC
1(i: A, B)
Adsorption on solid catalysts
Extension of the Langmuir treatment:Molecule dissociating upon adsorption:
lA 22 Al2
If at equilibrium:22
2 lAAAl CCKC
lAAlt CCKCC2
2
2
1 AA
AAt
AlCK
CKCC
Adsorption on solid catalysts
More general isotherms for nonuniform surfaces:Integrating over the individual sites:
1
0 ]/exp[/1
]/exp[/i
Aiada
Aiada dCRTQAA
CRTQAA
If Qa depends logarithmically on surface coverage:
lnama QQ
am
a
Q
Qexp
aa
dQdQ
dd
and: aam
a
am
dQQ
Q
Q
exp
1dθ
0 1 /exp/1
/exp1
RTQCAA
dQQQ
Q aAad
aama
am
Then:
As Qam >> RT RTQCA
Aam
QRT
Ad
a
am
,
/
θ mAaC Freundlich
isotherm(often used for liquids)
Adsorption on solid catalysts
More general isotherms for nonuniform surfaces:If Qa depends linearly on surface coverage:
10aa QQ
A
d
a
a
CA
A
Q
RTln
0 Temkin
isotherm
(e.g. ammonia synthesis)
Application more general isotherms to multicomponent systems: Not yet possible ! Focus on Langmuir treatment
Rate equations
Langmuir-Hinshelwood / Hougen-Watson:Rate equation: substitute the concentrations and temperatures at the locus of reaction itself !
Expression required to relate the rate and amount of adsorption to the concentration of the component of the fluid in contact with the surface
Langmuir-Hinshelwood or Hougen-Watson rate equations
3. Adsorption of reactants on the catalytic site.4. Chemical reaction between adsorbed atoms
or molecules.5. Desorption of products R, S, ....
Rate equations
Langmuir-Hinshelwood / Hougen-Watson:Single reaction: A R
3 steps: 1) chemisorption of A: lA Al
A
AllAAa K
CCCkrwith:
2) reaction: Al Rl
sr
RlAlsrsr K
CCkrwith:
with:3) desorption of R: Rl lR
d
lRRlRd K
CCCkr '
lR
R
RlRd CCK
Ckror:
Overall equilibrium constant:R
srA
K
KKK
Total concentration of sites: RlAllt CCCC May not always be constant !
Rate equations
Langmuir-Hinshelwood / Hougen-Watson:Single reaction:
Rigorous combination three consecutive rate steps => very complicated expression !
V
Wr
dt
dCA
A srAAl rrdt
dC
dsrRl rrdt
dC
V
Wr
dt
dCd
R W = mass of catalystV = volume of fluid
with:
A) Steady-state approximation on surface species:
Adsra rrrr
RRAsr
sr
srAAA
R
sr
srARAsrA
RAt
A
CKkK
K
kKCK
Kk
K
kKKkkkK
KCCCr
1111111
/
Rate equations
Langmuir-Hinshelwood / Hougen-Watson:Single reaction:
A) Steady-state approximation on surface species (cont.):
• Rather complicated expression (single reaction)• 3 rate coefficients to be determined
B) Rate-determining step: Intrinsically much slower than the others:
B.1) Starting from the steady-state approximation expression:
srRA kkk ,If:
RRAA
RAtsrAA CKCK
KCCCkKr
1
/reduces to
AsrR kkk ,If:reduces to
RRsr
RAtAA
CKK
KCCCkr
1
11
/
.
.
.
• Much simpler expression• 1 rate coefficient to be determined
Rate equations
Langmuir-Hinshelwood / Hougen-Watson:Single reaction:
B.2) Direct application: e.g. surface reaction rate controlling:
But rA remains finite 0A
AllA K
CCC
or: lAAAl CCKC Not true equilibrium(then rA = 0)
lRrRl CCKC Rk But rR remains finite
Then: RRAAlt CKCKCC 1RRAA
tl CKCK
CC
1or:
sr
RlAlsrsr K
CCkrrA =and:
RRAA
RAtsrA
CKCK
KCCCkK
1
/Ct often not measurable=> Combine: k = kiCt
Rate equations
Langmuir-Hinshelwood / Hougen-Watson:
Example: Competitive hydrogenation
Different step rate-controlling => different rate expression
p-xylene (A) and tetralin (B): (liquid phase)
Composition of Mixture
Total Hydrogenation Rate
CA CB CA + CB Exp. Calc.
610 280 890 8.5 8.3 462 139 601 9.4 9.0 334 57 391 10.4 9.8 159 10 169 11.3 11.3
Experimental data [Wauquier and Jungers, 1957]:
CA + CB ↑ r = rA + rB ↓
Negative order ?
Rate equations
Langmuir-Hinshelwood / Hougen-Watson:
Hydrogenation rate of A alone: 9.121 Ar
7.62 BrHydrogenation rate of B alone:
(zero-order)
(zero-order)
Additional data:
B is more strongly adsorbed than A: 18.0BA KK
Consistent rate equation ? => Hougen-Watson description:
1) A → product with surface reaction rate controlling
lA lAAAl CCKCAl
AAlAllt CKCCCC 1
product weakly adsorbed
AA
AAtA CK
CKCkr
1
'1
1
Liquids: KACA >> 1
1'11 kCkr tA = 12.9
Rate equations
Langmuir-Hinshelwood / Hougen-Watson:2) B → product
Similar as for A: 2'2
'2
1 1kCk
CK
CKCkr t
BB
BBtB
= 6.7
3) A and B react simultaneously:
BlAllt CCCC (product weakly adsorbed)
BBAAl CKCKC
BBAA
AAAlA CKCK
CKkCkr
1'
1BBAA
BBBlB CKCK
CKkCkr
2'
2and:
Then:
BBAA
BBAABA CKCK
CKkCKkrrr
21
1
21
B
A
B
A
B
A
B
A
C
C
K
K
kC
C
K
Kk
118.0
7.618.09.12
B
A
B
A
C
CC
C
Explains experimental data !
Rate equations
Langmuir-Hinshelwood / Hougen-Watson:Coupled reactions: e.g. dehydrogenation reactions: A SR Assume: Adsorption A rate controlling: lA Al
A
AllAAA K
CCpkr '
with: r =
Reaction step: lAl lAl
SlRlsr CC
CCKSlRl
Desorption steps: Rl RRlRl pKCClR
Sl SSlSl pKCClS
Total concentration of sites: SlRlAllt CCCCC
SSRRSR
Al pKpKpp
K
KC 1
SRsrA KKKKK /with:
Rate equations
Langmuir-Hinshelwood / Hougen-Watson:
sSRRSRA
SRAAA
pKpKppK
KKpppk
r
1
/
Form kinetic equation different according to assumptions !
Kinetic equations for reactions catalyzed by solids:
group)n(adsorptio
group)force(drivingfactor)(kinetic overall rate
Summaries groups for various kinetic schemes: Tables 2.3.1-1[Yang and Hougen, 1950]
Rate equations
Langmuir-Hinshelwood / Hougen-Watson:GROUPS IN KINETIC EQUATIONS FOR REACTIONS ON SOLID CATALYSTS
Rate equations
Langmuir-Hinshelwood / Hougen-Watson:GROUPS IN KINETIC EQUATIONS FOR REACTIONS ON SOLID CATALYSTS
Rate equations
Langmuir-Hinshelwood / Hougen-Watson:GROUPS IN KINETIC EQUATIONS FOR REACTIONS ON SOLID CATALYSTS
Rate equations
Langmuir-Hinshelwood / Hougen-Watson:GROUPS IN KINETIC EQUATIONS FOR REACTIONS ON SOLID CATALYSTS
Rate equations
Hougen-Watson versus Eley-Rideal:
Hougen-Watson:
A + B → R
Eley-Rideal:
A + l Al
B + l Bl
Al + Bl Rl
Rl R + l
A + l Al
Al + B Rl
Rl R + l
one adsorbed species reacts with another species in the gas phase
Similar kinetic expressions !
Rate equations
Langmuir-Hinshelwood / Hougen-Watson:Coupled reactions:
Example: n-pentane isomerization on a dual function Pt/Al2O3 reforming catalyst [Hosten and Froment, 1971]
Three-step sequence:1. dehydrogenation,2. isomerization,3. hydrogenation,
(Pt sites, l)(Al2O3 sites, σ)(Pt sites, l)
Each step involves:• adsorption• surface reaction• desorption
Each of the steps can be rate determining ! Modeling and model discrimination
Rate equations
Langmuir-Hinshelwood / Hougen-Watson:Experimental observation: overall rate independent of total pressure
Neither of the steps of the dehydrogenation or hydrogenation reactions can be rate determining (involve change of number of moles)
One of the steps of the isomerization step is rate determining !
e.g., surface reaction proper in isomerization step rate determining:
BH
ADH
BAD
pKK
pKKp
K
ppKkK
r
75
5
12
Three rival models:=> Model discrimination using regression and statistical tests
Rate equations
Langmuir-Hinshelwood / Hougen-Watson:Complex catalytic reactions:
Petroleum refining
Petrochemical processesFeedstock very complex !(Paraffins, olefins, naphthenes, aromatics)
e.g. Vacuum Gas Oil (VGO) feedstock hydrocracker: C15 – C40
Conventional kinetic modeling: unrealistic number of rate coefficients !
Different options:
A) Consider pseudo-components, « lumps » of species
Small number of reactions between pseudo-components
(often based on physical properties, like boiling range)
Rate coefficients depend upon the feed composition !
Costly experimentation required when feedstock changes
B) Structure Oriented Lumping (SOL):
Accounts for typical structures of the various types of molecules
Lumping not completely eliminated
Rate parameters still depend upon feedstock composition
C) Single event concept + Evans-Polanyi relationship:• Full detail of the reaction pathways• Expressed in terms of elementary steps• Step involves moieties of the molecule => Can occur at various positions of the same molecule• Number of types of elementary steps
<<< Number of molecules in the mixture
Reduction of number of rate coefficientsto tractable level !
Rate equations
Rate equations
Elementary steps of cyclic and acyclic hydrocarbons and carbenium ions
Rate equationsGeneration of the network of elementary steps:
Matrix and vector representation of 2 Me-hexane and its isomer 3-Me-hexane [Froment, 1999].
Rate equations
Number of elementary steps of some classes of the hydrocarbon families in hydrocracking: paraffins, P; mononaphthenes, MNAP; dinaphthenes, DNAP; monoaromatics, MARO. From Kumar and Froment [2007].
Rate equations
Relationship between the activation energies of two elementary steps belonging to the same type.
Evans-Polanyi relationship: