Chemical Reactor Analysis and Design

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)


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


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)


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


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)


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


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


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


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


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


Rate equations


Rate equations


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:

Documents

Chemical Reactor Analysis and Design