Transcript Rate equations Langmuir-Hinshelwood / Hougen-Watson

Chemical Reactor Analysis and Design
3th Edition
G.F. Froment, K.B. Bischoff†, J. De Wilde
Chapter 2
Kinetics of Heterogeneous Catalytic Reactions
Introduction
Principles homogeneous reaction kinetics: valid
r  k(T) CaA' C bB' ...
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 5
Chapter 3: other steps
Introduction
Potential energy
Principles of catalysis:
A╪
non-cat
• Reaction accelerated
Main reason: decrease Ea
• Reverse reaction similarly accelerated
(principle microscopic reversibility)
Al
Ea
cat
Ea
ΔH
B
A
Overall equilibrium not affected !
Progress of reaction
Example: homogeneous versus catalytic ethylene hydrogenation
[Boudart, 1958]
 43,000
r  1027 exp 
 pH2
RT 

 13,000
27
Catalytic (CuO/MgO): r  2.10 exp 
 pH2
RT 

Homogeneous:
At 600 K:
1.44•1011
times faster
Introduction
Types of catalysts:
Acid (silica/alumina, …):
• Can act as Lewis (electron acceptor) or Brønsted (proton donor) acids
• Form some sort of carbonium /carbenium ion from hydrocarbons
Metal (Pt, Pd, …):
• Primarily used in hydrogenations and dehydrogenations
Classical example: ethanol decomposition:
C 2 H 5 OH acid

 C2 H 4  H 2O
(dehydration)
C 2 H 5 OH metal

 C 2 H 4 O  H 2
(dehydrogenation)
catalyst
catalyst
With hydrocarbons: Acid catalyst: cracking or isomerization
Metal catalyst: (de)hydrogenations
Introduction
Types of catalysts:
Dual function or bifunctional:
single function
Certain intimacy of the
two catalysts required !
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 !
Introduction
Types of catalysts:
Dual function or bifunctional:
A
site
site
site
site
1
2
1
2
R
A
S
trivial polystep
R
S
non-trivial polystep
• as if steps were
successively performed
• Rl1 intermediate continuously
“bled off” => equilibrium shifted
toward higher overall conversion
Unique conversion or selectivity can be achieved !
Introduction
Types of catalysts:
Dual function or bifunctional:
Example: Industrially important isomerization of saturated hydrocarbons
(encountered in “catalytic reforming”):
saturate
−H2
iso-saturate
metal cat.
metal cat.
unsaturate
H2
iso-unsaturate
acid cat.
Introduction
Types of catalysts:
Dual function or bifunctional:
Example: Cumene cracking:
Acidic silica/alumina catalyst:
=> Intermediate: no role
Pt/Al2O3 catalyst:
=> Metal sites: permit alternative,
and then dominant, reaction
Presumed sequence:
Adsorption on solid catalysts
Physisorption
Chemisorption
Through van der Waals forces
Involves covalent chemical bonds
Multi-layer coverage possible
Only single layer coverage
Surface-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
Al
[kmol/kg cat. s]
Al
ra  k a C ACl
with:
ka  Aa e  Ea / RT
rd  k d C Al
with:
k d  Ad e  Ed / RT
Heat of
adsorption:
Qa  Ed  Ea
(more than 42 kJ/mol)
Unknown surface concentrations [kmol/kg cat.]
Adsorption on solid catalysts
Total concentration of sites:
Ct  Cl  C Al
If at equilibrium: adsorption isotherm:
k d C Al  k a C ACl

C Al
Ct K A C A

1  K AC A
with:
k a C A Ct  C Al 
ka
KA 
kd
C Al
K AC A

Alternate formulation: fractional coverage:  
Ct 1  K A C A
Langmuir
Multi-layer
physisorption
II with finite
porosity solid
Types of adsorption isotherm. After Brunauer et al. [1940].
Adsorption on solid catalysts
Extension of the Langmuir treatment:
Two species adsorbing on the same sites:
Al
Bl
Al
dCAl
 k aA C A Cl  k dA C Al
dt
Total concentration of sites:
Bl
dCBl
 k aB C B Cl  k dB C Bl
dt
Ct  Ct  C Al  CBl
Unknown surface species concentrations [kmol/kg cat.]
If at equilibrium: unknown surface concentrations can be eliminated:
C Al  K AC ACl
CBl  K B CB Cl
Ct  Cl  K AC ACl  K B CB Cl
Ct
Cl 
1  K AC A  K B C B
Ct K i Ci
Cil 
1  K AC A  K B C B
(i: A, B)
Adsorption on solid catalysts
Extension of the Langmuir treatment:
Molecule dissociating upon adsorption:
A2  2l
2 Al
If at equilibrium:
C Al2  K AC A2 Cl2
Ct  Cl  K AC A2 Cl
C Al 
Ct K A C A2
1  K A C A2
Adsorption on solid catalysts
More general isotherms for nonuniform surfaces:
Integrating over the individual sites:
 Aa / Ad exp[Qa  i  / RT ]C A
 
d i
1   Aa / Ad  exp[Qa  i  / RT ]C A
0
1
If Qa depends logarithmically on surface coverage:
 Qa 

  exp  
Qa  Qam ln
 Qam 
 Qa
1
d
exp 
and: d 
dQa
dθ  
Qam
dQa
 Qam
1 
exp Qa / Qam dQa
Then:  
Qam 0 1   Ad / Aa  C A1 exp Qa / RT 

As Qam >> RT
 Aa

C A 
θ  
 Ad


dQa


RT / Qam
,
Freundlich
m
Qam
aCRT
A
isotherm
(often used for liquids)
Adsorption on solid catalysts
More general isotherms for nonuniform surfaces:
If Qa depends linearly on surface coverage:
Qa  Qa0 1   
 RT
  
 Q a 0
  Aa

 ln  C A 
  Ad

Temkin
isotherm
(e.g. ammonia synthesis)
Application more general isotherms to multicomponent systems:
Focus on Langmuir treatment
Not yet possible !
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
3 steps: 1) chemisorption of A:
2) reaction:
3) desorption of R:
R
Al
Al
Rl
Al
Rl
Rl
K A K sr
Overall equilibrium constant: K 
KR
Total concentration of sites:

C Al
ra  k A  C ACl 
KA


C Rl 

rsr  k sr  C Al 
K sr 




with:

C R Cl
rd  k  C Rl 
Kd




or:
 CRl

rd  k R 
 CRCl 
 KR

with:
with:
Ct  Cl  C Al  CRl
'
R
May not always
be constant !
Rate equations
Langmuir-Hinshelwood / Hougen-Watson:
Single reaction:
Rigorous combination three consecutive rate steps
=> very complicated expression !
dCA
W

 rA
dt
V
dCAl
 rA  rsr
dt
dCRl
 rsr  rd
dt
dCR
W
 rd
dt
V
with:
W = mass of catalyst
V = volume of fluid
A) Steady-state approximation on surface species:
ra  rsr  rd  rA
rA 
C t C A  C R / K 
 1
 1
1  K sr 
1  K sr
1
1   1

  
 K A C A  




Kk R 
K sr k A
 K A k sr k A Kk R   K A k sr
 K A k sr

 K R C R

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:
If:
If:
.
.
.
k A , k R  k sr
reduces to
k R , k sr  k A
reduces to
K A k sr Ct C A  CR / K 
rA 
1  K AC A  K R C R
k ACt C A  CR / K 
rA 

1 
 K RCR
1  1 
 K sr 
• 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:
C Al
C A Cl 
0
KA
kA  ; But rA remains finite
Not true equilibrium
(then rA = 0)
kR  
Then:
But rR remains finite
Ct  Cl 1  K ACA  KRCR 
or:
C Al  K AC ACl
CRl  K r CR Cl
Ct
or: Cl 
1  K AC A  K RCR


K RCR 
C Rl 
C l
rA  k sr  K A C A 
and: rA = rsr  k sr  C Al 
K sr 
K sr 


K A k sr Ct C A  C R / K 
Ct often not measurable

=> Combine: k = kiCt
1  K AC A  K R C R
Rate equations
Langmuir-Hinshelwood / Hougen-Watson:
Different step rate-controlling => different rate expression
Example: Competitive hydrogenation p-xylene (A) and tetralin (B):
(liquid phase)
Experimental data [Wauquier and Jungers, 1957]:
Total
Composition of Mixture
Hydrogenation Rate
CA
CB
CA + CB
Exp.
Calc.
610
462
334
159
280
139
57
10
890
601
391
169
8.5
9.4
10.4
11.3
8.3
9.0
9.8
11.3
CA + CB ↑
r = rA + rB ↓
Negative order ?
Rate equations
Langmuir-Hinshelwood / Hougen-Watson:
Additional data:
Hydrogenation rate of A alone:
Hydrogenation rate of B alone:
rA 1  12.9
rB 2  6.7
(zero-order)
(zero-order)
B is more strongly adsorbed than A: K A K B  0.18
Consistent rate equation ? => Hougen-Watson description:
1) A → product with surface reaction rate controlling
Al
Al
CAl  K ACACl
Al  product
Al  product rA 1 kr1A' C1Al k1' C Al
product weakly adsorbed
Ct  Cl  C Al  Cl 1  K AC A 
rA 1
k1' Ct K AC A

1  K AC A
Liquids: KACA >> 1
rA 1  k1' Ct
 k1 = 12.9
Rate equations
Langmuir-Hinshelwood / Hougen-Watson:
2) B → product
Similar as for A:
rB 1
k 2' Ct K B C B

 k 2' Ct  k 2 = 6.7
1  K B CB
3) A and B react simultaneously:
Ct  Cl  C Al  CBl
(product weakly adsorbed)
 Cl K AC A  K B CB 
k1 K AC A
rA  k C Al 
K AC A  K B C B
'
1
Then:
r  rA  rB 
k1 K AC A  k 2 K B C B

K AC A  K B C B
Explains experimental data !
k 2 K B CB
and: rB  k CBl 
K AC A  K BCB
'
2
k1  K A C A  k 2 
K B CB
K A CA
1
K B CB
CA
 6.7
CB
CA
0.18
1
CB
12.90.18

Rate equations
Langmuir-Hinshelwood / Hougen-Watson:
Coupled reactions: e.g. dehydrogenation reactions: A
Assume: Adsorption A rate controlling: A  l
RS
Al

C Al 
with: r = rA  k 
 p ACl  K 
A 

C C
Al  l Rl  Sl K sr  Rl Sl
C AlCl
'
A
Reaction step:
Desorption steps: Rl
Rl
CRl  Cl KR pR
Sl
S l
CSl  Cl KS pS
Total concentration of sites:
Ct  Cl  C Al  CRl  CSl
 K

 Cl 1  A p R p S  K R p R  K S p S 
K


with:
K  K A Ksr / KR KS
Rate equations
Langmuir-Hinshelwood / Hougen-Watson:
rA 
k A  p A  pR pS / K 
KA
1
pR pS  K R pR  K S ps
K
Form kinetic equation different according to assumptions !
Kinetic equations for reactions catalyzed by solids:
(kineticfactor)(driving force group)
overall rate 
(adsorption group)
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:
A+B→R
Hougen-Watson:
A+l
Al
B+l
Bl
Al + Bl
Rl
Rl
R+l
Eley-Rideal: one adsorbed species reacts with
another species in the gas phase
A+l
Al
Al + B
Rl
Rl
R+l
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, (Pt sites, l)
(Al2O3 sites, σ)
2. isomerization,
(Pt sites, l)
3. hydrogenation,
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:
r
pH 2
p 

kK5 K D  p A  B 
K 

1
 K5 K D pA 
pB
K7 K H
Three rival models:
=> Model discrimination using regression and statistical tests
Rate equations
Langmuir-Hinshelwood / Hougen-Watson:
Complex catalytic reactions:
Petroleum refining
Petrochemical processes
Feedstock 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
(often based on physical properties, like boiling range)
Small number of reactions between pseudo-components
Rate coefficients depend upon the feed composition !
Costly experimentation required when feedstock changes
Rate equations
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 coefficients
to tractable level !
Rate equations
Elementary steps of cyclic and acyclic hydrocarbons and carbenium ions
Rate equations
Generation 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
Evans-Polanyi relationship:
Relationship between the activation energies of two elementary
steps belonging to the same type.