A.C. van Veen Ruhr Universität Bochum Room NC 5/69 Universitätsstraße 150 D Bochum. References

(1)

An introduction to kinetics in

heterogeneous catalysis

-How to measure properly activity and selectivity,

what are underlying fundamentals, how looks like

the mathematical description

A.C. van Veen

(andre.vanveen@rub.de)

Ruhr Universität Bochum

Room NC 5/69

Universitätsstraße 150

D-44780 Bochum

2

References

• O. Levenspiel, “Chemical reaction engineering”, 3rd edition, Wiley (1999), ISBN 0-471-25424-X.

• M. Baerns, H. Hofmann, A. Renken, “Chemische Reaktionstechnik”, 2nd edition, Thieme (1992), ISBN 3-13-687502-8.

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3

Introduction

Objectives of the lecture:

• Macro / microscopic meaning of activity and selectivity.

• The 1-dimensional pseudo homogeneous model without dispersion

• Good experimental design to achieve intrinsic information Beyond the scope of the lecture are:

1. More complex reactor models (radial dimension) 2. Calculations accounting for transfer limitations

3. Details on parameter estimation in heterogeneous catalysis 4. Statistical treatment of results:

♦ Error propagation.

♦ Confidence intervals.

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5

Reactors: Different scale – different objectives

Obtain as much information on a reaction network as possible: • Operate with partial conversion: Nothing says less than a “full reactant

conversion” case!

• Have the possible product spectrum represented: Intermediates formation bares valuable information on the mechanism.

• Vary the reactant composition and add products: Stoichiometric decoupling is compulsory for uncorrelated parameter estimation • Use a simple describable reactor: Isothermal conditions, plug flow or

CSTR but no mixed situations.

Laboratory:

Industry:

Produce a chemical so that costs of the process are minimal:

• Obtain high conversions: Recycle streams are costly and require a purge! • Restrict the product spectrum: The reactor is only a part of a process. • Use one optimum reactant composition: Process integration and capacity

limits of downstream units require steady operation.

6

Reactor types

Batch reactor

(BR)

tank reactor (CSTR)

Continuous stirred

Plug flow

reactor (PFR)

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7

Batch reactor

• Closed system

• Performance data as a function

of time

• Reaction over the reactor at the

same concentration level

• Might also originate from a

tubular reactor with closed

(fast) recycle loop

⇒

Data analysis over time, i.e.

c(p) vs. t, high conversions

straight forward, but mind

adsorption and inert purge

8

Continuous stirred tank reactor

• Open system

• Performance data as a function

of flow rate

• Reaction over the reactor

(catalyst) at the same

concentration (partial pressure)

• Might also originate from a

tubular reactor with injection,

(fast) recycle loop and purge

⇒

Data analysis over residence

time, i.e. c (p) vs.

τ

, differential

conversions straight forward,

but mind adsorption and inert

purge

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9

Plug flow reactor

• Open system

• Performance data as a function

of flow rate

• Reaction over the reactor at

varying concentration level

• Fluid segments cross the

reactor individually

• Reaction time scales to the

positions in the reactor

⇒

Data analysis over residence

time, i.e. c (p) vs.

τ

, mind high

conversions without integration

over the reactor

10

Areas of balancing

Reactor Catalyst bed Catalyst particle Active site Engineers? Inorganic chemistry? Industrial chemistry? Physical /Theoretical chemistry? What? Who?

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11

Macroscopic definitions

e,0 e e,0 e

_n

n

=

X

&

−

educt

supplied

educt

converted

p e e e,0 p p

-n

n

=

S

₋

⋅

_ν

ν

&

educt

converted

product

formed

p e e,0 p p

-n

n

=

Y

⋅

_ν

ν

&

educt

supplied

product

formed

Conversion, selectivity and yield are dimensionless numbers ranging from 0 to 1 or 0 to 100%

Conversion

Selectivity

Yield

As selectivity and yield definitions contain stoichiometric coefficients, these numbers are in general only meaningful if the respective

stoichiometric equations are given

12

Mind the thermodynamics

Endothermic synthesis: Equilibrium conversion increases with T Exothermic synthesis: Equilibrium conversion decreases with T. Real conversion increases for kinetic reason and might be capped.

Exothermic synthesis

Endothermic synthesis

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13

Is the knowledge of X, S, Y sufficient?

• Never compare selectivity at different conversion levels • Judge a catalyst on yield basis is better, but the specific activity

information in easily lost

k₁ k-1 A + B C k₂ k_-2 A + B D 0,0 0,2 0,4 0,6 0,8 1,0 0 5 10 15 φ / 10 -2 mo l s -1 z A B C D 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 S X(A) C D 14 0,0 0,2 0,4 0,6 0,8 1,0 0 5 10 15 φ / 10 -2 mo l s -1 z A B C D 0,0 0,2 0,4 0,6 0,8 1,0 0 5 10 15 φ / 10 -2 mo l s -1 z A B C D

Product formation: parallel or sequential

• Identifying a maximum does not “reveal” a sequential mechanism • The profiles might mislead in case of equilibrium reactions

k₁ k-1 A + B C k-2 k₂ D k2 k_-2 D k₁ k-1 A + B C

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15

S versus X plot – parallel product formation

• Extrapolation of selectivity at zero conversion: finite values for parallel reactions

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17 0,0 0,2 0,4 0,6 0,8 1,0 0,0 0,2 0,4 0,6 0,8 1,0 X τ_mod aka w/f A B 0,0 0,2 0,4 0,6 0,8 1,0 0,0 0,2 0,4 0,6 0,8 1,0 X τ_mod aka w/f A B

What is the proper range to make extrapolations

• Conversion increases under differential conditions linear with w/f • The origin must be precisely passed

k₁ k-1 A + B C k_-2 k₂ D k2 k_-2 D k₁ k-1 A + B C 18

What is catalytic activity?

What is catalytic selectivity?

Catalytic activity relates to the density of sites

ρ

and their

individual activity related to

k

in the surface reaction step.

However, adsorption and desorption interplay as well!

Catalytic selectivity (at molecular level) relates to ratio of

reaction rates

in selective and unselective reaction paths.

However, adsorption and desorption interplay as well!

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19

How to describe the reaction?

t

n

V

r

d

1

1 =

i i

ν

[mol s

-1

m

-3

]

General term for the reaction rate

A

)

(

=

k

T

c

r

Terms for the reaction rate in homogeneous catalysis

or 2 A

)

(

=

k

T

c

r

=

k

(

T

)

c

_A

c

_B 1st_order:_k_[s-1_] 2nd_order:_k_[m3_mol-1_s-1_]

)

R

exp(

=

)

(

T

k

₀

E

_A

T

k

−

/

Concentrations are here only convenient as the reaction volume hardly changes

20

How to describe the reaction rate(s)?

(

a

) (

x x

)

i, reac i i reac, i

R

exp

−

Θ

=

∆

=

∆

=

1

1 n

k

₀

E

/

T

f

p

,

V

dt

dn

V

r

ρ

ν

&

Terms for the reaction rate in heterogeneous catalysis:

2 1 2 1

)

(

=

_k

_T

_p

m

_p

m

r

Formal kinetics: power law

3 2 1 2 2 1 1 2 1

)

(

)

(

1 )

(

=

m m _m

p

T

K

p

T

K

p

T

k

r

)

(

+

Formal kinetics: hyperbolic form

Micro kinetics: Set of many parallel equations for adsorption and desorption, reaction

“Well, one does not know much of the mechanism and fits parameters”

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21

Rate expressions of sorption processes

(atom adsorption and successive desorption)

*

=

_ads,_A _A A ads,

ρ

k

p

θ

r

_des,_A

=

ρ

k

_des,_A

des,M

=

ρ

k

des,M

θ

M M M M M M M ads, M des, M M ads, M= ₊ =₁₊_K _p p K p k k p k

θ

M

-=

*

θ

1

M des, M ads, M=_k k K

with

k_ads,M k_des,M M + * M--* In fast equilibrium:

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23

Rate expressions of sorption processes

(dissociated adsorption and successive desorption) 2 B B ads, B ads,

=

ρ

k

p

θ

_*

r

2 B B des, B des,

=

ρ

k

θ

r

B

-=

*

θ

1

B B B B B B ads, B des, B B ads, B + 1 = + = p K p K p k k p k

θ

with

k_ads,B k_des,B B₂+ 2 * 2 B--* In fast equilibrium: B des, B ads, B=_k k K 24

Towards reaction – Co-adsorption

• Knowing the adsorption of reactants is not trivial information • There might be cooperation of different sites

As soon as one thinks of reaction there shall be

co-adsorption of reactants. Thus, two points are important to

underline:

On the other hand, adsorption could also proceed on

multiple sites

B

-=

*

θ

(13)

θ

r

_→

(parallel product formation)

θ

r

_→

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27

Models assuming rate limiting steps (1)

Case 1:Eley-Rideal-mechanism

Component A₁is chemisorbed, component A₂is in gas-phase. The reaction proceeds slowbetween chemisorbed A₁and A₂from the gas-phase. A₁+ * A₁--* A₁--* + A_{2 (g)} products r = k⋅θ1⋅p2 1 1 1 1 1 ₁₊_K _p p K = ⋅ _⋅ θ large (>> 1): Order of A₁is 0 small (<< 1): Order of A₁is 1 r≈ ⋅k p2 r≈ ⋅k K p p1⋅ ⋅1 2 K p1⋅ 1 K p1⋅ 1 r = k K p p 1 + K p1 11 21 ⋅ ⋅ ⋅_⋅ 28

Models assuming rate limiting steps (2)

Case 2: Langmuir-Hinshelwood-mechanism

Component A₁is chemisorbed, component A₂is chemisorbed. The reaction proceeds slowbetween chemisorbed A₁and A₂at the surface.

A₁+ * A₁--* A₂+ * A₂--* A₁--* + A₂--* products r = k⋅θ θ1⋅ 2 θ1 1 1 1 1 2 2 = K p 1 + K p + K p ⋅ ⋅ ⋅ θ₂ 2 2 1 1 2 2 =_{1 + K p + K p}K p_⋅ ⋅ _⋅

(

)

r = k K p K p 1 + K p + K p 1 1 2 2 1 1 2 2 ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ 2 large (>> 1): Order of A₁is –1 small (<< 1): Order of A₁is 1 K p1⋅ 1 K p1⋅ 1 r k K p K p21 21 ≈ ⋅ ⋅_⋅

(

)

r k K K p 1 + K p p = k p 1 2 2 2 2 1 * 1 ≈ ⋅ ⋅ ⋅ ⋅ 2⋅ ⋅

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29

Extrapolation of formal kinetics…

…is simply not possible

30

Are models assuming a rate limiting step sufficient?

• The rate limiting step might change with temperature • There might be coupling between steps

According to what one assumes as rate limiting step, one

can derive a suitable kinetic expression!

(refer to Hougen-Watson terms)

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31

Mars-van Krevelen mechanism

(Two rate limiting steps!)

O2- O

2-2 e- 2 e

-Product

Educt

32

Best to do only micro kinetics?

In principle: yes! (but how to determine all those parameters?)

5 parameters

}

13 parameters

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33

Towards transient experiments

Why are transient kinetic experiments very useful? • Separation of elementary steps

(information on individual rate constants or the site density) • High information density

• Rapid data acquisition

Why are transient kinetic experiments not the only used ones? 1. Data interpretation is usually more complicated

(A suitable/uncomplicated mathematical description is required) 2. The experimental effort is usually much higher

♦ The influence of the apparatus on the signal (dead volumes, adsorption) must be minimized.

♦ Heating ramps have to be perfectly linear.

♦ A very sensitive on-line analysis is required.

34

Thermal desorption analysis - Principle

Thermal desorption analysis uses desorption rate / uniform surface temperature data from linear ramped sample heating starting from a

know initial coverage. Available information includes:

• Type of adsorption (molecular / atomic = dissociated)

• Desorption kinetics (frequency factor and activation energy)

• Interaction of adsorbed species Prerequisites:

1. The apparatus does not influence the signal shape (Immediate flushing of desorbed species)

2. Heating rate variation is possible over a wide range

(typically a variation of almost 2 orders of magnitude desired) 3. The adsorption must be controlled to establish coverage data

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35

TPD reactor

• Isothermal fixed bed located in a “pocket oven” (ramps 0.5 – 25 K min-1₎

• Detection of the desorbed quantity diluted in the inert carrier

36

A catalytic test bench

A catalytic test bench for continuous reactors has typically 3 sections: • Gas feed section: Provide a constant flow where reactant ratios may be

varied as well as the overall feed rate. Systems often include a second line for pretreatment or purging of catalysis in bypass.

• Reactor / bypass section: Often housed in a hot box to avoid condensation of reactants / products.

• Analysis section: Typically online detection for quantitative analysis, usually exploitation along with an inert tracer in small concentration.

reactor Analysis vent vent Gas feed 1 Gas feed 2 Hot box PI PI

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37

TPD experiment - molecular adsorption

• Declining branches overlap for initial coverage variation • Rising branches overlap for heating ramp variation • Rapid decline of the signal after reaching the maximum

200 300 400 500 600 700 800 0 1 2 3 4 5 θ₀ = 0.10 θ₀ = 0.20 θ₀ = 0.40 θ₀ = 0.60 θ₀ = 0.80 θ₀ = 1.00 φ / 1 0 -8 mo l s -1 T / K β = 0.05 K s-1 100 200 300 400 500 600 700 800 0 5 10 15 20 25 30 T_max. = 471.23 K T_max. = 485.66 K T_max. = 495.55 K T_max. = 503.30 K T_max. = 514.60 K T_max. = 527.00 K φ / 1 0 -8 mo l s -1 T / K θ₀ = 1.00 β = 0.01 K s-1 β = 0.03 K s-1 β = 0.05 K s-1 β = 0.10 K s-1 β = 0.20 K s-1 β = 0.40 K s-1 38

TPD experiment - dissociated adsorption

100 200 300 400 500 600 700 800 0 5 10 T_max. = 454.68 K T_max. = 466.63 K T_max. = 474.52 K T_max. = 480.50 K T_max. = 488.90 K T_max. = 497.60 K φ / 10 -8 mo l s -1 T / K θ₀ = 1.00 β = 0.01 K s-1 β = 0.03 K s-1 β = 0.05 K s-1 β = 0.10 K s-1 β = 0.20 K s-1 β = 0.40 K s-1 100 200 300 400 500 600 700 800 0,0 0,5 1,0 1,5 θ₀ = 0.10 θ₀ = 0.20 θ₀ = 0.40 θ₀ = 0.60 θ₀ = 0.80 θ₀ = 1.00 φ / 10 -8 mo l s -1 T / K β = 0.05 K s-1

• Declining branches overlap for initial coverage variation • Rising branches overlap for heating ramp variation • Slow decline of the signal after reaching the maximum

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39

TPD experiment - readsorption

• Readsorption broadens TPD responses • The impact of readsorption varies with the inert flow

100 200 300 400 500 600 700 800 0 1 2 with readsorption k_0,des = 1 103 s-1 Pa-1 E_a,des = 40 kJ mol-1 without readsorption k_0,des = 1 1013 s-1 E_a,des = 145 kJ mol-1 φ / 1 0 -8 mo l s -1 T / K β = 0.05 K s-1 θ₀ = 1.00 100 200 300 400 500 600 700 800 0,0 0,5 1,0 φ_inert = 500 ml min-1 φ_inert = 200 ml min-1 φ_inert = 150 ml min-1 φ_inert = 100 ml min-1 φ_inert = 50 ml min-1 φ / 1 0 -8 mo l s -1 T / K β = 0.05 K s-1 θ₀ = 1.00 40

Energetics of ad- and desorption

• Lennard-Jones potentials cross

• The activation energy of adsorptionincreases also that of the desorption

0,0 0,2 0,4 0,6 0,8 1,0 1,2 -0,2 -0,1 0,0 0,1 0,2 2 X_(ads) X_{2 (ads)} X_{2 (g)} 2 X_(g) Epot / a.u. d / a.u. 0,0 0,2 0,4 0,6 0,8 1,0 1,2 -0,2 -0,1 0,0 0,1 0,2 X_{2 (ads)} 2 X_(ads) X_{2 (g)} 2 X_(g) Epot / a.u. d / a.u.

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41

TPA experiment – Study an activated adsorption

100 200 300 400 500 600 700 800 0 1 2 3 4 5 E_a,ads = 70.0 kJ mol-1 E_a,ads = 60.0 kJ mol-1 E_a,ads = 50.0 kJ mol-1 φ / 1 0 -8 mo l s -1 T / K β = 0.05 K s-1 100 200 300 400 500 600 700 800 7,2 7,3 7,4 7,5 7,6 7,7 E_a,ads = 70.0 kJ mol-1 E_a,ads = 60.0 kJ mol-1 E_a,ads = 50.0 kJ mol-1 φ / 1 0 -7 mo l s -1 T / K β = 0.05 K s-1

• TPD responses for 60 and 70 kJ mol-1_similar

• TPA traces are clearly distinguishable

• Complementary TPA study required to complete the information pool

42

Catalytic fixed bed reactor – basics (1)

quartz fibers Reactor Reactor Oven Oven Inlet Inlet Outlet Outlet Fixed Bed Fixed Bed

catalyst quartz crystals quartz fibers Reactor Reactor Oven Oven Inlet Inlet Outlet Outlet Fixed Bed Fixed Bed

catalyst quartz crystals

• Catalyst sandwiched between inert beds • (Movable) thermocouple

in the bed centre • Fixation by quartz wool

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43

Catalytic fixed bed reactor – basics (2)

Reactant flow rates should be high enough

• Upper flow limit: Pressure drop over the catalyst bed

• Upper flow limit: Sufficient conversion for reasonable analysis • Lower flow limit: Strong dispersion

• Lower flow limit: Use of a too shallow catalyst bed

The minimum bed length should be equal to the inner tube diameter • Lower flow limit: “External” mass transfer limitation:

The stagnant film thickness increases with decreasing flow and the concentration at the catalyst particle differs from the fluid bulk.

⇒Reaction at lower concentration level, thus underestimation of the specific activity.

44

Catalytic fixed bed reactor – basics (3)

Catalyst particles should have a well defined size (sieve fraction) • Defined sieve fraction: Achieve homogeneous radial gas distribution • Lower size limit: Increasing pressure drop with decreasing size • Upper size limit: Channeling or bypassing

The maximum particle size should be 1/10th_{of the inner tube diameter}

• Upper size limit: “Internal” mass transfer limitation:

Pores in particles are too long and compounds react before reaching the end of the pore.

⇒Only part of the active sites (towards the pore mouth) react, thus underestimation of the specific activity.

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45

Catalytic fixed bed reactor – test for limitations

Lab-Test: Probing if the specific catalyst activity is the same as for smaller particles (at comparable pressure drop) (Dilution in bigger inert particles

Numerical criterion: Estimation of the degree of pore usage from the

(modified) Thiele (Φ) or Weisz (Ψ’) modulus, ideally < 0.3

Lab-Test: Probing the specific catalyst activity at different flow rate, i.e. identical conversion at identical w/f (at comparable pressure drop) (Dilution in bigger inert particles)

Numerical criterion: Estimation of the external degree of catalyst usage from the Damköhler number II (DaII), ideally < 0.1

A.C. van Veen Ruhr Universität Bochum Room NC 5/69 Universitätsstraße 150 D Bochum. References

An introduction to kinetics in

heterogeneous catalysis

-How to measure properly activity and selectivity,

what are underlying fundamentals, how looks like

the mathematical description

A.C. van Veen

(andre.vanveen@rub.de)

Ruhr Universität Bochum

Room NC 5/69

Universitätsstraße 150

D-44780 Bochum

References

Table of contents

Introduction

Reactors: Different scale – different objectives

Laboratory:

Industry:

Reactor types

Batch reactor

(BR)

tank reactor (CSTR)

Continuous stirred

Plug flow

reactor (PFR)

Batch reactor

• Closed system

• Performance data as a function

of time

• Reaction over the reactor at the

same concentration level

• Might also originate from a

tubular reactor with closed

(fast) recycle loop

⇒

Data analysis over time, i.e.

c(p) vs. t, high conversions

straight forward, but mind

adsorption and inert purge

Continuous stirred tank reactor

• Open system

• Performance data as a function

of flow rate

• Reaction over the reactor

(catalyst) at the same

concentration (partial pressure)

• Might also originate from a

tubular reactor with injection,

(fast) recycle loop and purge

⇒

Data analysis over residence

time, i.e. c (p) vs.

τ

, differential

conversions straight forward,

but mind adsorption and inert

purge

Plug flow reactor

• Open system

• Performance data as a function

of flow rate

• Reaction over the reactor at

varying concentration level

• Fluid segments cross the

reactor individually

• Reaction time scales to the

positions in the reactor

⇒

Data analysis over residence

time, i.e. c (p) vs.

τ

, mind high

conversions without integration

over the reactor

Areas of balancing

Macroscopic definitions

n

n

n

=

_n

₋

_ν

_ν