8. Heterogeneous reaction
• solid – fluid (liquid, gas)






Dissolution of solids (e.g. MgCO3(s) + HNO3(l))
Chemical Vapor Deposition (SiH4(g)  Si(s) + 2H2)
Sublimation (U(s) + 3 F2(g)  UF6(g))
Reduction of solid oxides (NiO(s) + H2(g)  Ni(s) + H2O(g))
Metals oxidation (Zn(s) + O2(g)  ZnO(s))
Catalytic reactions
• liquid – gas
 Dissolution with chemical reaction
Cl2(s) + 2NaOH(l)  NaOCl(l) + NaCl(l) + H2O(l)
3NO2(g) + H2O(l)  2HNO3(l) + NO(g)
• solid – solid
 CoO(s) + Al2O3(s)  CoAl2O4(s)
Heat and mass transfer phenomena affect global reaction rate.
Example
Si(s) + O2(g)  SiO2(s)
cO2
t
D
s
O2
 2 cO2
porous
SiO2
x 2
Si
Air (O2)
O2

cO2 ( x)
co
J O( D2 ) flux density of O2 in SiO2 layer (mol.m-2.s-1)
c1
Convection +
Diffusion
k cO2 coefficient of mass transfer of O (m.s-1)
2
rS  kc2
N O2  kcO2 [c1  co ]
2 -1
DOs 2 diffusion coefficient of O2 in SiO2 (m .s )
c2
rS
x
J
N O2 flux density of O2 in gas phase(mol.m-2.s-1)
diffusion
( D)
O2
 D
s
O2
dcO2
dx
 DOs 2
[c2  c1 ]

rate of chemical reaction (mol. m-2.s-1)
Steady state
NO2  J O( D2 )   O2 rs
kcO2 [c1  co ]  DOs 2
[c2  c1 ]

 kc2

DOs 2 
kcO2  k 





c1 
co
s
DO2
k .kcO2 
(kcO2  k )
c1 a c2 calculation :

DOs 2 
DOs 2

c2  kcO2 co
 kcO2 
 c1 
D


k



c 
c
D
k .k 
(k  k )

DOs 2
DOs 2 


c1   k 
 c2  0


 

SiO2 layer thickness and Si conversion :
s
O2
cO2
2
cO2
reaction rate
rs 
co
1  (t ) 1
 s 
kcO2 DO2 k
M SiO2 , M Si ,  SiO2 ,  Si
rS 
 SiO d
2
M SiO2 dt
o
s
O2
cO2
 1
M SiO2
1
1 2
  
 co
t

s
2 DO2
 SiO2
 kcO2 k 
 o M SiO2  Si
   o X Si
o=
2 M Si  SiO2
Molar weights and densities of SiO2 a Si
o
Initial thickness of Si slab
3 limiting cases
1. Rate determining step is the external mass transfer of oxygen towards interface (gas - SiO2)
1
kcO2


,
s
O2
D
1
kcO2

1
 rs  kcO2 co ,
k
  kcO co
2
M SiO2
SiO

cO2 ( x )
t
co
c1
2
c2
x
2. Rate determining step is the internal mass transfer of oxygen in porous SiO2 layer

s
O2
D

1
,

s
O2
kcO2 D
DOs 2
1
  rs 
co ,
k

  2D c
s
O2 o
M SiO2
cO2 ( x)
t
 SiO
co

c1
2
c2
x
3. Rate determining step is chemical reaction taking place on the interface (SiO2 - Si)
1
 1
1
 s , 
 rs  kco ,
k
DO2 k
kcO2
Discussion: rS = f(composition), rS = f(temperature)
  kco
M SiO2
SiO
cO2 ( x)
t
co

c1
2
c2
x
External heat and mass transfer
Combustion of the spherical carbon particle
Oxygen molar flux at steady state
Energy flux at steady state
Surface temperature and concentration of oxygen
S
Two balance equations for unknown c1 , TS
Multiple steady state solutions as
in the case of CSTR!
Example
Catalytic reactions
• homogeneous catalysis




Ozone decomposition in the presence of Cl
SO2 oxidation by NOx
Esterification catalyzed by acids or bases
Enzymatic catalysis
O3 + Cl  ClO + O2
ClO + O3  Cl + 2O2
2O3  3O2
• heterogeneous catalysis
 NH3, CH3OH production
 SO2 to SO3 oxidation
 HDS, HDN processes
 Fluid Catalytic Cracking
 Hydrogenation
 Polymerization (Ziegler-Natta catalysts, metallocens)
Catalytic cycle
Non catalytic x catalytic reaction
Activated
complex of non
catalytic reaction
Encat – energy of activation for non catalytic reaction
Ecat - energy of activation for catalytic reaction
Energy
Encat
ri
e

Ei
RT

Ecat
Reactants
Adsorbed
reactants
Products
Adsorbed
products
Reaction pathway
The multi-step catalytic reaction
can be faster than one-step
reaction
Homogeneous x Heterogeneous Catalysts
Homogeneous
Heterogeneous
All atoms
Low
No
50-200 oC
Limited
Surface atoms
High (variable)
Important
200-1000 oC
Large
Characterization Structure, composition
Modification
Temperature stability
Well defined
Easy
Low
No clear defintion
Difficult
High
Separation
Difficult
Easy
packed beds
Recycling
Feasible
Feasible
Active
sites
Concentration
Diffusion disguises
Reaction conditions
Application
Raw materials
(impurities, ..,)
Equilibrium
Operation
conditions (T, P,…)
Catalytic
reaction
Kinetics
Properties of Catalyst,
Preparation procedure
Reactors continuous, batch
Hydrodynamics
Heat and mass
transfer
Steps in a catalytic reaction
1)
2)
3)
4)
5)
6)
7)
Mass transfer of reactants to the external surface of catalyst
Mass transfer of reactants in porous structure of catalyst
Adsorption of reactants
Surface reaction (+ migration)
Desorption of products
Mass transfer of products in porous structure of catalyst
Mass transfer of reactants from the external surface of catalyst
The transport steps (1,2,6,7) depend on T, P, composition, flow rates, pore
size, ....
The chemical steps (3,4,5) are
dependent on T, P, composition.
Elementary steps of catalytic reaction
Fluid phase
Products
Reactants
Desorption
Adsorption
Surface
reaction
Dissociation
Migration
Mechanisms in heterogeneous catalysis
Langmuir-Hinshelwood
Rideal-Eley
Desorption
Adsorption
Migration
Surface
reaction
Adsorption x Chemisorption
2 A  2[*]
2 A*
A2  2[*]
2A*
Adsorption (physical
phenomenon)
Energy of biatomic molecule A2
Chemisorption
(chemical
phenomenon)
Distance from catalyst surface
Emc, Emp – activation energy of migration in adsorbed and chemisorbed state
ED – energy of dissociation of molecule A2
Ed – energy of desorption of A2
Ea – energy of activation of transition from adsorbrd to chemisorbed state
Adsorption x Chemisorption
Adsorption
Chemisorption
Principal
van der Waals forces
no electron transfer !
covalent or ionic bonds
electron transfer
Adsorbent
all solids
specific sites
Adsorbat
gases T < Tc
reactive components
Temperature
low
higher
Enthalpy
10-40 kJ/mol
80-600 kJ/mol
Rate
high
depends on T
Activation energy low
Occupancy
multilayer
high
monolayer
Reversibility
YES
YES but …
Use
BET method
pore size distribution
surface concentration
of active sites
Chemisorption of fluid phase molecule(adsorbat)
Surface occupancy(Θ)
Θi =
Number of sites occupied by i-th component
Total number of sites
0 <
Θi < 1
Associative x Dissociative chemisorption
Adsorption (chemisorption) isotherm – Surface occupancy as a function of
partial pressure of given component at constant temperature
Henry isotherm
Θi = Hi . pi
Irving Langmuir
1920
1932
-
adsorption isotherm
-
kinetics of catalytic reactions
on ideal surfaces
-
Nobel Prize
Langmuir adsorption isotherm
Brunauer-Emmett-Teller (BET) adsorption
isotherm
Associative adsorption
M(g) + *
ka
kd
M-*
* - active site, ka a kd – kinetic constants for adsorption and desorption
Adsorption rate = ka . p . (1 - Θ)
p = partial pressure of adsorbat
Desorption rate = kd . Θ
Equilibrium
ka . p . (1 - Θ) = kd . Θ
Langmuir adsorption isotherm
Θ = Ns / N = K . p / (1 + K . p)
(K = ka/kd)
Asociative chemisorption
Langmuir adsorption (chemisorption) isotherm
Multicomponent asociative chemisorption
A(g) + *
ka
kd
A-*
Occupancy of A
Occupancy of B
KA = ka / kd
Irreversible chemisorption
B(g) + *
kb
kd
KA.pA
ΘA 
1 KA.pA  KB.pB
KB.pB
ΘB 
1 KA.pA  KB.pB
KB = kb / kd
catalyst poisoning
B-*
Dissociative chemisorption
M2(g) + 2 *
ka
kd
Rate of chemisorption
=
Rate of desorption
k d . Θ2
=
ka . p . (1 - Θ)2 = kd . Θ2
Θ2
(1 - Θ)2
= K’ . p

2 M-*
ka . p . (1 - Θ)2
(K’ = ka/kd)
K'.p
Θ
1 K'.p
Isotherms
Langmuir
(chemisorption, adsorption,
monolayer, micropores)
 Θ  K.p
n*
1 K.p
n
ads
Henry
(chemisorption, adsorption, low occupancy)
n
ads
n*
Freundlich
(chemisorption, adsorption, non ideal)
 Θ H p
n
ads
n*
1
 Θ  K pn
Θ  Aln B p 
Temkin
(chemisorption, non ideal
p
 1  (C 1) p
(p p) nmC nmC p
Brunauer-Emmett-Teller (BET)
(adsorption, multilayer)
nads
Virial
(adsorption, multilayer )
p (1 a  a 2  ...)
R.T
0
0
1
2
Brunauer-Emmett-Teller (BET)
Extention of Langmuir model
Assumptions:
adsorption in multilayer s, 1st layer interaction between adsorbent
and adsorbat, in 2nd and further layers condensation-like interaction
nads
p
 1  (C 1) p
(p p) nmC nmC p
0
0
Mesoporous alumina
-1
a (mmol g )
15
10
5
0
0,0
0,2
0,4
0,6
0,8
1,0
p/po
Temperature od calcination : 3,3 nm (450 oC) - 4,5 nm (600 oC) 5,1 nm (800 oC)
Reaction rate per mass
1
1 d 1 1 dni
rM  r 

m
m dt m  i dt
rM ,k
1
1 dk
 rk 
m
m dt
Reaction rate per surface
1
1 d 1 1 dni
rS  r 

S
S dt S  i dt
rS ,k
mole.kg 1.s 1
1
1 d k
 rk 
S
S dt
mole.m2 .s 1
Reaction rate per active center (turnover number)
1
1 d
1 1 dni
rRS 
r

s 1
nRS
nRS dt nRS  i dt
rRS ,k
1
1 d k

rk 
nRS
nRS dt
Reaction rate of catalytic reactions
Langmuir-Hishelwood ideal surface
Rate of elementary steps
Rate determining step x steady state hypothesis
CO oxidation on Pt
o
Overall reaction ( Gr  0 )
2CO(g) + O2(g)  2CO2(g)
nebo
2CO(g) + O2(g)  2CO2(g)
Pt surface atoms
Elementary steps of catalytic CO oxidation on Pt
1. CO chemisorption
CO(g) + [*]  CO*
r1  k f ,1 PCO *  kb,1CO
2. O2 dissociative chemisorption
O2(g) + 2[*]  2O*
* - Pt surface atoms = Catalytic
active centre
r2  k f ,2 PO2 *2  kb,2O2
3. Surface reaction between CO* and O*
CO* + O*  *CO2 + *
r3  k f ,3CO O  kb ,3CO2 *
4. CO2 desorption into gas phase
*CO2  CO2(g) + *
r4  k f ,4 CO 2  kb ,4 PCO2 *
Pi – partial pressures of gaseous components [Pa]
 i - occupancy (coverage) of the i-th species [-]
k f , j , kb , j - reaction rate constants
rj – rate of the j-th elementary step [mol/kg katalyzátoru/s
mol/molPt/s= 1/s]
Rate determining step in steady state
ri  ri  ri
Forward reaction rate
Fast step
Backward reaction rate
ri  ri  step is close to the equilibrium
Slow step =
Rate determining step
Relation between overall reaction rate and the rate of i-th
elementary step determines the stoichiometric number  i
(do not confuse with stoichiometric coefficient !)
r
ri
i
i
CO(g) + [*]  CO*
2
O2(g) + 2[*]  2O*
1
CO* + O*  *CO2 + *
2
*CO2  CO2(g) + *
2
2CO(g) + O2(g)  2CO2(g)
Rate determining step: surface reaction
Reaction rate as a function of measurable variables
Example
C2H5OH(g) (A1)  CH3CHO(g) (A2) + H(g)
(A3)
catalysts: CuO, CoO a Cr2O3
(Franckaerts J., Froment G.F., Kinetic study of the
dehydrogenation of ethanol, Chem. Eng. Sci. 19 (1964)
807-818).
Kinetics
kK1  P1  P2 P3 / K eq 
rM 
2
1  K1P1  K 2 P2 
rM (mol.g-1.hod-1), Pi (bar), k (mol.g-1.hod-1), Keq (bar), Ki
(bar-1).
Task: to estimate on the basis of experimental data kinetic
and adsorption parameters k , K1 , K 2
EXPERIMENTAL SET-UP
Franckaerts J., Froment G.F., Kinetic study of the dehydrogenation of ethanol, Chem. Eng. Sci. 19
(1964) 807-818
EXPERIMENTAL DATA
W / F1o
y1o
y4o
y2o
[g.hod/mol]
P
[bar]
[ ]
[ ]
[ ]
1,60
0,80
0,40
1,0
1,0
0,40
1,0
0,40
1,60
0,80
0,40
1,0
1,0
0,60
0,80
0,60
1,60
0,80
0,40
1,0
1,0
0,20
0,40
0,40
7,0
4,0
3,0
1,0
1,0
1,0
1,0
10,0
7,0
4,0
3,0
1,0
1,0
1,0
1,0
10,0
7,0
4,0
3,0
1,0
1,0
1,0
10,0
1,0
0,865
0,865
0,865
0,865
0,750
0,865
0,732
0,865
0,865
0,865
0,865
0,865
0,672
0,865
0,672
0,865
0,865
0,865
0,865
0,865
0,672
0,865
0,865
0,865
0,135
0,135
0,135
0,135
0,130
0,135
0,167
0,135
0,135
0,135
0,135
0,135
0,145
0,135
0,145
0,135
0,135
0,135
0,135
0,135
0,145
0,135
0,135
0,135
0,0
0,0
0,0
0,0
0,119
0,0
0,101
0,0
0,0
0,0
0,0
0,0
0,183
0,0
0,183
0,0
0,0
0,0
0,0
0,0
0,183
0,0
0,0
0,0
T
X1
o
[ C]
[ ]
225,0
225,0
225,0
225,0
225,0
225,0
225,0
225,0
250,0
250,0
250,0
250,0
250,0
250,0
250,0
250,0
275,0
275,0
275,0
275,0
275,0
275,0
275,0
275,0
0,066
0,083
0,055
0,118
0,052
0,060
0,052
0,038
0,149
0,157
0,108
0,218
0,123
0,152
0,106
0,094
0,254
0,262
0,20
0,362
0,230
0,118
0,148
0,196
Solution:
Minimize the objective function:
(k , K1 , K 2 ) 
2
NEXP
  X
i 1
exp
1,i
X
mod
1,i
(k , K1 , K 2 ) 
X1,mod
i (k , K1 , K2 ) calculated from isothermal catalytic PFR
model:
dX1
 rM ( X1 )
o
d W / F1 
W / F1o  0, X 1  0
ATHENA Visual Studio.
225 oC
k1
KA1
KA2
250 oC
5.767986E-01 +- 4.112E-01
4.839934E-01 +- 3.591E-01
1.011693E+01 +- 7.376E+00
8.863130E-01 +- 1.668E-01
4.876108E-01 +- 9.443E-02
3.044445E+00 +- 9.054E-01
275 oC
1.675828E+00 +- 4.225E-01
3.803293E-01 +- 1.473E-01
2.812096E+00 +- 1.078E+00
2.5
2
ln(KA2) = f(1/T)
y = 7084.1x - 12.075
R² = 0.8181
1.5
1
ln(k1) = f(1/T)
0.5
0
1.80E-03
y = -5802.3x + 11.056
R² = 0.9807
1.85E-03
1.90E-03
1.95E-03
2.00E-03
2.05E-03
-0.5
-1
-1.5
y = 1293.1x - 3.2791
R² = 0.7019
ln(KA1) = f(1/T)
Models of catalytic reactors
Expanded views of a fixed bed reactor
Models of catalytic reactors
Model equations involve:
• Balance equations for components of reaction mixture in both gas phase
and porous catalytical particle
• Balance of energy (enthalpy)
• Balance of momentum
• Flux constitutive equations for component and energy fluxes
Pseudo homogeneous
Heterogeneous
1-D
• withou axial dispersion
(pure plug flow)
• with axial dispersion
Gradients of concentration
and temperature between
phases
2-D
Radial dispersion
1-D pseudo homogeneous model without axial dispersion
dp
f
us
K
effective diameter of catalytic particle
friction coefficient
mean fluid velocity
overall heat transfer coefficient
1-D pseudo homogeneous model with axial dispersion
Boundary conditions
Dimensionless form
2-D pseudo homogeneous model with axial and radial dispersion
Balance element of volume
Balance equations
Boundary and initial conditions
Fluidized bed catalytic reactor
Experimental determination of kinetics of
heterogeneous catalytic reactions
OVERVIEW
1. Steady state techniques
1.1 Reactors: Batch, CSTR, PFR
1.2 Transport Disguises at Particle Scale
1.3 Kinetic Analysis : Single Reaction, Complex Reactions, Estimation Methods
2. Transient methods
2.1 Dynamical Changes in catalysts: Reaction Sites, Structure and Morphology,
Surface Composition
2.2 Modes of Operation: Steps and Pulses, Cycled Feed, Self-sustained
Oscillations, TAP, SSITKA
2.3 Modelling and estimation: CO chemisorption on Pt,NO reduction by H2,
Electrocatalytic Ethylene Epoxidation, CO methanation
1.
Steady state techniques
1.1 Reactors: Batch, CSTR, PFR
Screening of catalysts – high throughput methods - most
promising formulation investigated in more detail – scale up of
the catalytic reaction towards the industrial application starts
from the knowledge of detailed reaction kinetics  rate
equation(s)
Batch reactor, CSTR, PFR
outlet
inlet
reactor
catalyst
silica wadding
furnace
700oC
Calculation of reaction rate r [mol/kg/s]
CSTR
PFR
+ direct evaluation of r.r.
BATCH
+simple setup
+simple setup
-outlet condition’s control
+variation of m/F
-real hydrodynamics
differentiation
-temperature and conc.gradients -
-isothermicity
-isothermicity
-differentiation in r.r. calculation
o
A
F XA
rM 
A m
FAo  FA
XA 
FAo
rM 
1
A
dX A
d m / FAo 
1 n oA dX A
rM 
 A m dt
1.2 Transport Disguises at Particle Scale
Ideality at reactor scale (plug flow or ideal mixing), it is not sufficient to obtain
accurate kinetic data
external transfer
internal transfer
kio L
Shi 
Dmi
determ. of mass and heat transfer coefficients
determ. of effectiveness factor
external transfer
Deska
Re L  10
5
Re L  105
Shi  0,66 Re
1/ 2
L
1/ 3
i
Sc
Shi  0,036 Re 0L,8 Sci1 / 3
Koule
Shi  2,0  0,4(Re1L/ 2  0,06 Re 2L/ 3 ) Sci0,4
Re L 
uL

Sci 
Dmi

Packed bed
k cio M 2 / 3
jD 
Sci
G
Sci 

Dim
m
G
So
Re
d pG

jD  f (Re)  C. Re n
jH 
Pr 
h
Pr 2 / 3
C pG
C pm  m
m
jH  f (Re)  C  Re n
ha(Ts  To )  (  H r ) rV  (  H r )k xAa ( x oA  x As )
Ts
k xA x oA
x As
 1  (  H r )
(1  o )
To
hTo
xA
rV
c As
 1
o
cA
k cAac oA
rV
x As
 1
o
xA
k xAax oA
ha(Ts  To )  (  H r ) rV  (  H r )k xAa ( x oA  x As )
Ts
k xA x oA
x As
 1  (  H r )
(1  o )
To
hTo
xA
Criteria for the absence of transport limitations (packed bed)
c As  c oA
c
o
A
 0,95
Ts  To
 0,02
To
Experimental tests
m / F  konst
o
A
XA
FAo
N i  k gi ( cio  cis )
ci
x
T
  s
x
J is   Di
J Hs
(  H r ) Di ci ( ro ) ci
ci
T

 i
T ( ro )
 i sT ( ro ) ci ( ro )
ci ( ro )
N H  h (To  Ts )
cis  ci ( ro )
 d 2 ci a dci 
   vi rV (T , ck )
Di  2 
dx
x
dx


 i  Prater number
Ts  T ( ro )
0
a= 1
2
 d 2T a dT 
  (  H r ) rV (T , ck )
s  2 
dx
x
dx


x=0
x = ro
dc
 Di i  k gi (cio - c si )
dci
dT
0
0
dx
dx
dx
dT
 s
 h (To  Ts )
dx
plate
cylinder
sphere
Experimental tests (supposing that external gradients are
negligible)
m / F  konst
o
A
XA
1/ d p
1.3 Kinetic Analysis : Single Reaction, Complex Reactions,
Estimation Methods
The differential or integral method of kinetic analysis
LHHW kinetics
XA
Linearizationlinear
regression
Non-linear modelsnonlinear regression
o
A
m/F
Example
Ethanol dehydrogenation (Franckaerts, Froment, 1964)
AR+S
C2H5OH(g) CH3CHO (g) + H2 (g)
r.d.s.
rM 
Adsorption of A
k A ( PA  PR PS / K )
KA
PR PS  K R PR  K S PS  K w Pw
K
kK A ( PA  PR PS / K )
rM 
1  K A PA  K R PR  K S PS  K w Pw 2
1
Surface reaction
Desorption of R
k R KK R ( PA / PS  PR / K )
rM 
1  K A PA  KK R PA / PS  K S PS  K w Pw

M


(  )   X i  f i (  )
i 1

2
Example
Air oxidation of o-xylene on V2O5 (Vanhove, Froment 1975)
o-xylene
r2
r1
tolulaldehyde
r3
phtalic anhydrid
CO, CO2
Estimation methods
y  f(x, β)
e j β   y j  f(x j , β)
j  1, NEXP
Moment matrix of residuals
M(β) 
NEXP
 e j βe j β
T
j 1
Gradient, GaussNewton
Objective functions
 (β)  TraceQM(β

 (β)  Trace V 1M(β
 (β)  detM(β

MarquardtLevenberg
Quadratic
expansion
2. Transient methods
Reaction sites - single crystal surfaces, ultra high vacuum
structure sensitive reaction rate (Dahl et al. 1999: rate of
dissociative adsorption of nitrogen on Ru (0001) surface
was reduced by more than nine orders.
Structure and Morphology – CO oxidation on the Pt(110)
surface. Ertl (1994) has shown by photo-emission electron
microscopy that surface concentrations of reacting species
vary with time and 2D-space.
Grunwaldt (2000) found that structure of Cu particles
depend on the reduction potential of gas mixture CO+H2.
Surface composition – surface composition of catalyst may
change with gas composition – redox systems (Mars,
Krevelen, 1953)