High Temperature Catalysis - Max Planck Society3. High Temperature Catalytic Processes in Industry...

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

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 ==


Material 1

T

Material 2

T

Material 1

T

Material 1

T

T

)()( eb

cav qq =


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


KcmT ⋅⋅= 2884.0maxλWien‘s Displacement Law:


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=


4.3 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


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


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


example 3: literature results on CO oxidation on supported Pt catalysts

Can. J. Chem. Eng. 61 1983 194


example 4: elementary step kinetic model:

[ ]

⎟⎠⎞

⎜⎝⎛ −=

= ∏=

′

RTETAk

Xkq

ißii

K

kkii

i

ki

exp

1

ν


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


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

=⇒+

=

≡+

==

+=

−−==

+⎯⎯ →←+

⎯⎯ →←+

→+

−

−

∗

−

∗

∗∗−

∗

∗

∗

−

−


Limiting cases:

[ ][ ]

[ ][ ] [ ] 0for

for

)~(

1

12

1

12

12

→=

∞→=

=⇒+

=

−

−

Mk

Mkkk

Mkk

pMfkkMk

Mkkk

observed

observed

observed


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


5.2 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


5.3 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


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)


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

=


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( +

=

−

+−

+=⇒+= ∑∫


∑=

=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


Glowing Thanks For Your Attention !!!

High Temperature Catalysis - Max Planck Society3. High Temperature Catalytic Processes in Industry...

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