High Temperature CatalysisHigh Temperature Catalysis
RaimundRaimund HornHorn
Lecture Series Lecture Series ““Modern Methods in Heterogeneous CatalysisModern Methods in Heterogeneous Catalysis”” 30.10.200930.10.2009
FritzFritz--HaberHaber--Institute, MaxInstitute, Max--PlanckPlanck--Society,Society,Inorganic Chemistry DepartmentInorganic Chemistry Department
1. What is “High Temperature Catalysis”
2. Why can solid bodies glow and how can I measure their temperature?
3. High Temperature Catalytic Processes in Industry and Research
4. Surface and Gas Phase Reaction Kinetics
5. Physical Transport Processes of Momentum, Heat and Mass
6. Interaction of Chemistry and Transport
7. Numerical Simulation of High Temperature Catalytic Reactions
8. Research Example: Autothermal Methane Oxidation on Rh and Pt
OutlineOutline
goRTG
rrer >∝Δ
−
#
1. What is 1. What is „„High Temperature CatalysisHigh Temperature Catalysis““
High Temperature Catalysis = Catalysis on Glowing Catalysts
550°C ≤
T ≤
1300°C
High Temperature Catalysis = Catalysis on Glowing Catalysts
550°C ≤
T ≤
1300°C
1. What is 1. What is „„High Temperature CatalysisHigh Temperature Catalysis““
o when a solid body is heated its surface emits radiation of wavelengths in the range 0.1-10µm called thermal radiation
o heating raises some of the atoms and molecules of which the solid body consists of to higher energy levels from which they return spontaneously to lower energy states emitting electromagnetic radiation
o electromagnetic radiation can be either thought off as waves with a wavelength λ=c/ν
or as a bunch of photons with an energy ε=hν
o absorptivity and emissivity of an (opaque) body are defined as follows:
2. Why can solid bodies glow ?2. Why can solid bodies glow ?
)(
)(
)(
)(
ib
e
i
a
qqe
qqa
ν
νν
ν
νν ==
o qν(a)dν
and qν(i)dν
are the absorbed and incident radiation energy per unit area per unit time in the frequency range ν
to ν+dν
Some comments on that:
o for any real body, aν
will be less than unity and will vary considerably with ν
and temperature
o a hypothetical body for which aν
will be less than unity but independent of ν
and temperature is called a gray body
o the limiting case of a gray body with aν
=1 defines a black body
o the emissivity eν
is also a quantity less than unity for real, non- fluorescing surfaces and is equal to unity for black bodies
)(
)(
)(
)(
ib
e
i
a
qqe
qqa
ν
νν
ν
νν ==
2. Why can solid bodies glow ?2. Why can solid bodies glow ?
Material 1
T
Material 2
T
Material 1
T
Material 1
T
T
)()( eb
cav qq =
2. Why can solid bodies glow ?2. Why can solid bodies glow ?
Material 1
T
T
)()( eb
cav qq =
3
2
3
3 813
8)(nn cd
dNV
pVc
N πνν
πνν ν ==⇒=
number of modes inside a cavity of volume V
( )[ ]
( )[ ]kT
dEkTE
dEkTEEE =
−
−⋅=
∫
∫∞
∞
0
0
/exp
/exp
( )[ ]
( )[ ] ( ) 1/exp/exp
/exp
0
0
−=
−
−⋅=
∑
∑∞
=
∞
=
kThh
kTnh
kTnhnhE
n
n
νν
ν
νν
Traditional Physics(Rayleigh-Jeans 1905)
Quantum PhysicsMax Planck 1900
kTcd
dNV
Epn3
281 πνν
ρ νν ===
1)/exp(81
3
2
−===
kThh
cddN
VEp
n ννπν
νρ νν
Ultraviolet-Catastrophe
2. Why can solid bodies glow ?2. Why can solid bodies glow ?
KcmT ⋅⋅= 2884.0maxλWien‘s Displacement Law:
2. Why can solid bodies glow ?2. Why can solid bodies glow ?
Stefan-Boltzmann Law: 442
84)( 1067.5 TKm
WATAq eb ⋅⋅⋅⋅=⋅⋅= −σ
emissivities of different materials
Material 1
T
T
)()( eb
cav qq =
Material 1
T
T
eqqaqaq e
b
eecav ==⇒= )(
)()()(
2. Temperature Measurement by Pyrometrie2. Temperature Measurement by Pyrometrie
carbon calibration body @ 1060 °C
4)( TATP ⋅⋅= σRadiance of a black body
Radiance of a real body4)()( TATP ⋅⋅⋅= σλε
42
41
2
1
)()(
TATA
PP
⋅⋅⋅⋅⋅⋅
=σλεσλε
Two‐color pyrometer
)()(
2
1
λελε
=k
P ... total power of energy radiated from
P an object
ε
... emissivityσ
... Stefan‐Boltzmann constantA ... surface area observedT ... absolute temperature
cylindrical
graphite
body
(cavity)
yielding
homogeneous
temperature
distribution
(black body)
2. Temperature Measurement by Pyrometrie2. Temperature Measurement by Pyrometrie
2. Temperature Measurment by Pyrometrie2. Temperature Measurment by Pyrometrie
high temperature catalysis plays an important role in industry
industrial high temperature processes
4NH3 + 5O2 → 4NO + 6H2 O (900°C, Pt/Rh)
NH3 + CH4 + 1.5O2 → HCN + 3H2 O (1200°C, Pt/Rh)
NH3 + CH4 → HCN + 3H2 (1200°C, Pt/Rh)
CH4 + H2 O → CO + 3H2 (700-1100°C, Ni)
CH3 OH + ½ O2 → HCHO + H2 O (600-720°C, Ag)
catalytic combustion (noble metals)
fuel reforming (noble metals)
solid oxide fuel cells (800-1000°C, Ni cermet / YSZ / (La,Sr)MnO3 )
3. 3. High Temperature Catalytic High Temperature Catalytic Processes in Industry and ResearchProcesses in Industry and Research
high temperature processes at the research stage
CH4 + ½ O2 → CO + 2H2 (>1000°C, e.g. Rh)
2CH4 + O2 → C2 H4 + 2H2 O (600-800°C, e.g. Li/MgO)
CH4 + ½ O2 → HCHO + H2 O (>600°C, e.g. VOx )
C2 H6 + ½ O2 → C2 H4 + H2 O (700-1100°C, e.g. Pt/Sn)
C2 H6 + ½ O2 → CH3 CHO + H2 O (>500°C, VOx )
3. 3. High Temperature Catalytic High Temperature Catalytic Processes in Industry and ResearchProcesses in Industry and Research
3.1 „Bookkeeping“
domains: e.g. gaseous domain (3D), bulk domain (3D), interphase domain (2D)
phases:o gas phase (usually 1 per domain)o surface phase (1 or more per domain e.g. steps, terraces…)o bulk phase (1 or more per domain, e.g. CuO, Cu2 S )
species:o gas species Kg
f - Kgl, surface species Ks
f(n)-Ksl(n), bulk
species Kbf(n)-Kb
l(n)
example: corrosion of copper
4. 4. Surface and Gas Phase Reaction Surface and Gas Phase Reaction KineticsKinetics
4.2 Concentration within phases important for catalysis:
o for gas phase species (3D domain) the molar concentration is written
3 in ),...( ][mmolKKk
WYX l
gf
gk
kk ==
ρ
o the composition of surface phases is usually specified in terms of site fractions
),...,( 1)()(
)(
ls
fs
nK
nKkk NNnnZ
ls
fs
==∑=
o for kinetics we need the surface molar concentration of a species 2 in
)()(][
mmol
nnZX
k
nkk σ
Γ=
4. 4. Surface and Gas Phase Reaction Surface and Gas Phase Reaction KineticsKinetics
4.3 Surface reaction kinetics:
o classic expressions for adsorption (Langmuir adsorption, competitive adsorption, dissociative adsorption) and surface reaction rates (Langmuir Hinshelwood Hougen Watson) can be used to describe surface kinetics in high temperature catalytic reactions
o these type of rate expressions are comparably ease to determine experimentally but every catalyst will have a unique rate expression
o for example, Pt on alumina catalysts for CO oxidation may have a similar general form of the rate expression by the numerical values of the constants will vary among formulations. Even catalysts with the same composition may have different rate expressions due to differences in the manufacturing method
o if the mechanism changes with experimental conditions, e.g. change of rate limiting step at changing temperatures, the general form of the rate law might change
o elementary step mechanisms do not have these drawbacks but are difficult to determine
4. 4. Surface and Gas Phase Reaction KineticsSurface and Gas Phase Reaction Kinetics
example 1: Langmuir adsorption isotherm for a single component A
o the usual form of the Langmuir adsorption isotherm is
[ ]
)/(1)/(
)/()/(1)/()/(
][1][
])[(][)]([
)](])[[(][)]([)]([
)]([)](][[0)()()(
0
0
10
10
11
1
111
11
, 11
ppKppK
RTpRTpKRTpRTpK
AKAK
AkkAksA
sAAkkAksAsO
sAksOAkdt
sAdsAsOA
Ap
Ap
ap
apA
c
cA
kk
+=
⋅+
⋅=
+=
+=
Γ=
+=Γ−Γ=
−==
⎯⎯ →←+
−
−
−
−
−
−
θ
θ
A
AA bp
bp+
=1
θ
o this general form is readily derived from an elementary step mechanism applying mass action kinetics
4. 4. Surface and Gas Phase Reaction Surface and Gas Phase Reaction KineticsKinetics
example 2: competitive adsorption of two species A and B
o empirical expression
)/()/(1)/(
][][1][
)/()/(1)/(
][][1][
)()(
)()(
02,
01,
02,
2,1,
2,
02,
01,
01,
2,1,
1,
,
,
22
11
ppKppKppK
BKAKBK
ppKppKppK
BKAKAK
sBsOB
sAsOA
BpAp
Bp
cc
cB
BpAp
Ap
cc
cA
kk
kk
++=
++=
++=
++=
⎯⎯ →←+
⎯⎯ →←+−
−
θ
θ
BBAA
BBB
BBAA
AAA pKpK
pKpKpK
pK++
=++
=1
1
θθ
o an analogues treatment of the following elementary step mechanism using mass action kinetics as for the Langmuir adsorption leads to
4. 4. Surface and Gas Phase Reaction Surface and Gas Phase Reaction KineticsKinetics
example 3: Langmuir-Hinshelwood Rate Expressions
o Langmuir-Hinshelwood (Hougen Watson) rate expressions are often used to describe surface reactions such as e.g. A(s)+B(s)→C(s)o in this mechanism it is assumed that A and B adsorb competitively onto the surface and undergo a bimolecular surface reaction to C
[ ] [ ][ ] [ ]
[ ] [ ][ ] [ ]
[ ][ ][ ] [ ]( )22,1,
22,1,
2,1,
2,
2,1,
1,
,
,
1)]()][([][
1)(
1)(
)(2)()(
)()(
)()(22
11
BKAKBAKKk
sBsAkdtCd
BKAKBK
sB
BKAKAK
sA
sOCsBsA
sBsOB
sAsOA
cc
ccrxnrxn
cc
cB
cc
cA
k
kk
kk
rxn
++
Γ==
++Γ
=Γ⋅=
++Γ
=Γ⋅=
+⎯→⎯+
⎯⎯ →←+
⎯⎯ →←+−
−
θ
θ
4. 4. Surface and Gas Phase Reaction Surface and Gas Phase Reaction KineticsKinetics
example 3: literature results on CO oxidation on supported Pt catalysts
Can. J. Chem. Eng. 61 1983 194
4. 4. Surface and Gas Phase Reaction Surface and Gas Phase Reaction KineticsKinetics
example 4: elementary step kinetic model:
[ ]
⎟⎠⎞
⎜⎝⎛ −=
= ∏=
′
RTETAk
Xkq
ißii
K
kkii
i
ki
exp
1
ν
4. 4. Surface and Gas Phase Reaction Surface and Gas Phase Reaction KineticsKinetics
4.4 Gas phase reaction kinetics:o gas phase reactions proceed via radicals, often in chain reactionso radical chain reactions consist of initiation, branching and termination reactionso gas phase reactions are typically strongly pressure dependent and the kinetics are highly nonliner
example: H2 + O2 → H2 O
Initiation Branching Termination
⋅+⋅↔+ 222 HOHOH
⋅+↔+⋅⋅+⋅↔+⋅
⋅+⋅↔+⋅
⋅+⋅↔+⋅
HOHHOHOHOHOHO
OHHHOOHOOH
22
2
2
2
inertHOOHOH
OOHHOHOOOHOHHO
MHOMOH
wall⎯⎯→⎯⋅⋅⋅⋅
+↔⋅+⋅
+↔⋅+⋅+⋅↔++⋅
2
22222
222
22
,,,
o gas phase reactions are typically strongly pressure dependent and the kinetics are highly nonliner
PropagationMHOMOH +⋅↔++⋅ 22
4. 4. Surface and Gas Phase Reaction Surface and Gas Phase Reaction KineticsKinetics
Pressure dependence of gas phase reactions:o for surface reactions k is a function of To for gas phase reactions, k can be a function of T and po a simple explaination follows from the Lindemann mechanism (Frederick Lindemann 1921)
[ ] [ ][ ] [ ] [ ][ ]
[ ] [ ][ ][ ]
[ ] [ ][ ] [ ][ ][ ][ ] [ ][ ]
[ ][ ] )~(
0
12
12
12
122
12
1
211
,
,
22
11
pMfkkMk
Mkkk
BAkkMk
MBAkkMCkdtCd
kMkBAkC
MCkCkBAkdtCd
MCMC
CBA
CBA
observed
observed
kk
kk
=⇒+
=
≡+
==
+=
−−==
+⎯⎯ →←+
⎯⎯ →←+
→+
−
−
∗
−
∗
∗∗−
∗
∗
∗
−
−
4. 4. Surface and Gas Phase Reaction Surface and Gas Phase Reaction KineticsKinetics
Limiting cases:
[ ][ ]
[ ][ ] [ ] 0for
for
)~(
1
12
1
12
12
→=
∞→=
=⇒+
=
−
−
Mk
Mkkk
Mkk
pMfkkMk
Mkkk
observed
observed
observed
4. 4. Surface and Gas Phase Reaction Surface and Gas Phase Reaction KineticsKinetics
Example: rate constant for the association reaction
CCl3 +O2 →CCl2 O2
4. 4. Surface and Gas Phase Reaction KineticsSurface and Gas Phase Reaction Kinetics
example for non-linear behaviour and pressure dependence of gas phase reactions
explosion diagram for H2 /O2 system
inertHOOHOH wall⎯⎯→⎯⋅⋅⋅⋅ 2,,,
MHOMOHOHOOH
+⋅→++⋅⋅+⋅→+⋅
22
2
⋅+→+⋅ HOHHHO 2222
5. 5. Physical Transport Processes of Physical Transport Processes of Momentum, Heat and MassMomentum, Heat and Mass
5.1 Momentum transporto pair of parralel plates in rest with area A separated by distance Yo t=0 lower plate is set in motion in positive x direction with V=constant
dydv
AF
AYVF
xyx μτ
μ
−==
=
τyx =flux of x momentum in y direction in (kg⋅m/s)/m2/s=N/m2
o the x-momentum flows from a region of high momentum to a region of low momentum (similar to heat and mass)o the proportionality constant µ is called the (dynamic) viscosity, has the unit Pa⋅s=kg/m/s and is material specific (air 1.8E-5 Pa⋅s, glycerol 1 Pa⋅s)
Newton‘s law of viscosity
5. 5. Physical Transport Processes of Physical Transport Processes of Momentum, Heat and MassMomentum, Heat and Mass
5.2 Heat transport:
o q=heat flux in z direction in J/m2/so heat flows from a region of high temperature to low temperatureo the proportionality constant λ
is called the thermal conductivity, has the unit W/m/s and is material specific (air=0.025, stainless steel=16, Al=250)
Fourier‘s law of heat conduction
5. 5. Physical Transport Processes of Physical Transport Processes of Momentum, Heat and MassMomentum, Heat and Mass
5.3 Mass transport:
o J=molar flux in z direction in mol/m2/so mass (atoms, molecules) flow from a region with high concentration to
a region with low concentrationo the proportionality constant D is called the diffusion coefficient, has
the unit m2/s and is material specific (H2 in N2 =7.79E-5)
Fick‘s law of diffusion
6. 6. Interaction of Chemistry and TransportInteraction of Chemistry and Transport
Example: instantaneous reaction 2A → B (e.g. dimerization)o catalyst surrounded by a stagnant film through which A has to diffuse to reach the catalyst surfaceo at the surface, 2A → B react instanteneously
( )
( )
⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜
⎝
⎛
−==⇒⎟
⎠⎞
⎜⎝⎛ −=⎟
⎠⎞
⎜⎝⎛ −⇒
==
==
−−=+=⎟⎠⎞
⎜⎝⎛ −−⇒=
⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜
⎝
⎛
−⇒
=
⎟⎠⎞
⎜⎝⎛ −
−=
−=
++−==
−
0
/1
0
0
2121
211
1ln22
211
211
0at :2 condition boundary0at :1 condition boundary
ln2ln2211ln20
211
1
0:gives slab thin aover Aon balance mass
211
N :givesflux molar combined the into inserting
21 :require trystoichiome and state steady
2 :fluxmolar combined
A
ABAz
z
AA
A
AA
AA
a
Az
A
A
ABAz
AzBz
BzAzAA
ABAz
x
cDrNxx
x zx x z
KzKCzCxdz
dx
xdzd
dzdN
dzdx
x
cD
NN
NNxdz
dxcDrN
δ
δ
δ
6. 6. Interaction of Chemistry and TransportInteraction of Chemistry and Transport
Gas (Surface) Species Thermodynamics
Kinetic Model of Surface Chemistry
Kinetic Model of Gas Phase Chemistry
Gas Species Transport Data
Mathematical Model of Momentum, Heat and Mass Transport (Reactor Model)
ci
firi K
kk =
7. 7. Numerical Simulation of High Numerical Simulation of High Temperature Catalytic ReactionsTemperature Catalytic Reactions
Example: Plug Flow Model – Species Balance
Example: Plug Flow Model – Energy Balance
kkkkck
c WsPWAdz
dYuA && ′+= ωρ
( )TTPhhWsPhWAdzdTcuA wkk
K
kkkk
K
kkcpc
gg
−+′−−= ∑∑==
ˆ11
&&ωρ
0=ks&
system of coupled differential – algebraic equations since in catalysis
and 11
=∑=
sK
kkZ
7. 7. Numerical Simulation of High Numerical Simulation of High Temperature Catalytic ReactionsTemperature Catalytic Reactions
o gas-phase and surface chemical rate expressions:
[ ] [ ]∏∏∑=
′′
=
′
=
−==K
k
νkri
K
k
νkfii
I
iikik
kiki XkXkqq111
νω&
∑∑==
=′′⇔′K
kkki
K
kkki
11I)1,...,(i χνχν
kikiki ννν ′−′′=
[ ] [ ]∏∏∑=
′′
=
′
=
−==K
k
νkri
K
k
νkfii
I
iikik
kiki XkXkqqs111
ν&
gas concentration (mol/m3)
surface concentration (mol/m2)
7. 7. Numerical Simulation of High Numerical Simulation of High Temperature Catalytic ReactionsTemperature Catalytic Reactions
o typical Arrhenius expression for the forward rate constant:
⎟⎠⎞
⎜⎝⎛ −=
RTETAk iβ
ifii exp
o modification for coverage dependent rate constants possible
( )kiβ
ifi fRT
ETAk i θθθ ....,exp 21⋅⎟⎠⎞
⎜⎝⎛ −=
o rate constants for adsorption reactions are calculated from sticking coefficients
( ) km
tot
ifi W
RTkπ
γ2Γ
=
7. 7. Numerical Simulation of High Numerical Simulation of High Temperature Catalytic ReactionsTemperature Catalytic Reactions
o in first approximation thermodynamic properties of species (regardless of phase) are functions of temperature only
o thermodynamic data are neeeded to calculate the reverse rate constant for gas phase reactions even if no energy balance is solved
∑=
−=M
m
mkmkpk TaC
1
)1(0
k
kMM
m
mkmk
k
kT
kpkk Ta
mTa
RTHHdTCH
k,1
1
)1(0
0
000 )0( +
=
−
+=⇒+= ∑∫
kM
M
m
mkmk
kkk
T
kpk
k amTaTa
RSSdT
TC
Sk
,22
)1(
1
0
298
00
0
)1(ln)0( +
=
−
+−
+=⇒+= ∑∫
7. 7. Numerical Simulation of High Numerical Simulation of High Temperature Catalytic ReactionsTemperature Catalytic Reactions
∑=
=Δ K
k
kki
i
RS
RS
1
00
ν ∑=
=Δ K
k
kki
i
RTH
RTH
1
00
ν
⎟⎟⎠
⎞⎜⎜⎝
⎛ Δ−
Δ=
RTH
RSK ii
pi
00
exp
∑⎟⎠⎞
⎜⎝⎛= =
K
kki
RTpKK atm
pici1
ν
ci
firi K
kk =
calculation of the reverse rate constant from the forward rate constant and the equilibrium constant
if thermodynamic information for surface species are not available (which is usually the case), reverse rate parameters have to be specified
7. 7. Numerical Simulation of High Numerical Simulation of High Temperature Catalytic ReactionsTemperature Catalytic Reactions
Glowing Thanks For Your Attention !!!