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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 5/69Universitätsstraße 150

D-44780 Bochum

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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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Table of contents

• Introduction. • Reactor types and characteristics. • From conversion and selectivity to mechanistic information. • Rate expression and constants, kinetic formalisms. • Operating conditions and experimental setup. • Towards kinetic modeling of experiments

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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. ♦ Model discrimination.

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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.

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Reactor typesBatch reactor

(BR)Continuous stirred

tank reactor (CSTR)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

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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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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

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Areas of balancingReactor Catalyst

bedCatalystparticle

Activesite

Engineers? Inorganicchemistry?

Industrialchemistry?

Physical /Theoreticalchemistry?

What?

Who?

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Macroscopic definitions

e,0

ee,0e n

nn=X &

&& −eductsuppliedeductconverted

p

e

ee,0

pp

-nn

n=S ν

ν⋅

− &&

&

eductconvertedproductformed

p

e

e,0

pp

-nn

=Y νν

⋅&

&

eductsuppliedproductformed

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

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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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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-1A + B C

k2

k-2A + B D

0,0 0,2 0,4 0,6 0,8 1,00

5

10

15

φ / 1

0-2 m

ol s

-1

z

A B C D

0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

1.0

S

X(A)

C D

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0,0 0,2 0,4 0,6 0,8 1,00

5

10

15

φ / 1

0-2 m

ol s

-1

z

A B C D

0,0 0,2 0,4 0,6 0,8 1,00

5

10

15

φ / 1

0-2 m

ol 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-1A + B C

k-2

k2D

k2

k-2D

k1

k-1A + B C

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S versus X plot – parallel product formation

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

• Selectivity ratio equals ratio of initial formation rates (not constants!)

k1

k-1A + B C

k2

k-2A + B D

0,0 0,2 0,4 0,6 0,8 1,00,0

0,2

0,4

0,6

0,8

1,0

S

X(A)

C D

BA11 = ppkr ρ

C1-1- = pkr ρ

BA22 = ppkr ρ

D2-2- = pkr ρ

ρ = 10 mol m-3

k1 = 4 10-9 Pa-2 s-1

k-1 = 2 10-4 Pa-1 s-1

k2 = 1 10-9 Pa-2 s-1

k-2 = 4 10-5 Pa-1 s-1

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0,0 0,2 0,4 0,6 0,8 1,00,0

0,2

0,4

0,6

0,8

1,0

S

X(A)

C D

S versus X plot – sequential product formation

• Extrapolation of selectivity at zero conversion: Zero selectivity for secondary products

k1

k-1A + B C

k2

k-2A + C D

BA11 = ppkr ρ

C1-1- = pkr ρ

CA22 = ppkr ρ

D2-2- = pkr ρ

ρ = 10 mol m-3

k1 = 4 10-9 Pa-2 s-1

k-1 = 2 10-4 Pa-1 s-1

k2 = 1 10-9 Pa-2 s-1

k-2 = 4 10-5 Pa-1 s-1

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0,0 0,2 0,4 0,6 0,8 1,00,0

0,2

0,4

0,6

0,8

1,0

X

τmod aka w/f

A B

0,0 0,2 0,4 0,6 0,8 1,00,0

0,2

0,4

0,6

0,8

1,0

X

τmod 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-1A + B C

k-2

k2D

k2

k-2D

k1

k-1A + B C

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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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How to describe the reaction?

tn

Vr dd11= i

iν [mol s-1 m-3]

General term for the reaction rate

A)(= cTkrTerms for the reaction rate in homogeneous catalysis

or2A)(= cTkr BA)(= ccTkr

1st order: k [s-1]

2nd order: k [m3 mol-1 s-1]

)Rexp(=)( A0 TEkTk /−

Concentrations are here only convenient as the reaction volume hardly changes

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How to describe the reaction rate(s)?

( ) ( )xxai,reaci

ireac,

i

Rexp Θ−=∆

=∆

= ,/110 pfTEkn

Vdtdn

Vr ρ

νν&

Terms for the reaction rate in heterogeneous catalysis:21

21)(= mm ppTkr Formal kinetics: power law

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21

2211

21

)()(1)(= m

mm

pTKpTKppTkr

)( ++ 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”

“One knows the mechanism a bit and makes simplifications”

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Rate expressions of sorption processes(atom adsorption and successive desorption)

*= AAads,Aads, θρ pkr AAdes,Ades, = θρ kr

AA

AA

AAads,Ades,

AAads,A +1=+= pK

pKpkk

pkθ

A-=* θθ 1

Ades,

Aads,A = k

kKwith

kads,A

kdes,AA + * A--*

In fast equilibrium:

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Rate expressions of sorption processes(molecular adsorption and successive desorption)

*= MMads,Mads, θρ pkr MMdes,Mdes, = θρ kr

MM

MM

MMads,Mdes,

MMads,M +1=+= pK

pKpkk

pkθ

M-=* θθ 1

Mdes,

Mads,M = k

kKwith

kads,M

kdes,MM + * M--*

In fast equilibrium:

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Rate expressions of sorption processes(dissociated adsorption and successive desorption)

2BBads,Bads, *= θρ pkr 2

BBdes,Bdes, = θρ kr

B-=* θθ 1

BB

BB

BBads,Bdes,

BBads,B +1

=+

=pKpK

pkkpk

θ with

kads,B

kdes,BB2 + 2 * 2 B--*

In fast equilibrium:Bdes,

Bads,B = kk

K

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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-=* θθ 1 BA --=* θθθ 1might not hold anymore, but

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The micro-kinetic reaction on the surface

EductsPrimaryproduct 1

Primaryproduct 2

BA1adsP1,e1 == θθρ krr →

P11-eadsP1,1- == θρ krr →

2BA2adsP2,e2 == θθρ krr →

P22-eadsP2,2- == θρ krr →

(parallel product formation)

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The micro-kinetic reaction on the surface

Primaryproduct

Educts Secondaryproduct

BA1adsP1,1 == θθρ krr →

P11-adsP1,1- == θρ krr →

P1B2adsP2,2 == θθρ krr →

P22-adsP2,2- == θρ krr →

(sequential product formation)

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Models assuming rate limiting steps (1)

Case 1: Eley-Rideal-mechanismComponent A1 is chemisorbed, component A2 is in gas-phase. The reaction proceeds slow between chemisorbed A1 and A2 from the gas-phase.

A1 + * A1--*

A1--* + A2 (g) products r = k p1 2⋅ ⋅θ

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111 pK+1

pK=⋅

⋅θ

large (>> 1): Order of A1 is 0

small (<< 1): Order of A1 is 1

r k p2≈ ⋅

r k K p p1 1 2≈ ⋅ ⋅ ⋅

K p1 1⋅

K p1 1⋅

r = kK p p1 + K p

1 1 2

1 1⋅

⋅ ⋅⋅

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Models assuming rate limiting steps (2)Case 2: Langmuir-Hinshelwood-mechanismComponent A1 is chemisorbed, component A2 is chemisorbed. The reaction proceeds slow between chemisorbed A1 and A2 at the surface.

A1 + * A1--*

A2 + * A2--*

A1--* + A2 --* products r = k 1 2⋅ ⋅θ θ

θ 11 1

1 1 2 2=

K p1 + K p + K p

⋅⋅ ⋅

θ 22 2

1 1 2 2=

K p1 + K p + K p

⋅⋅ ⋅

( )r = k

K p K p

1 + K p + K p1 1 2 2

1 1 2 2

⋅⋅ ⋅ ⋅

⋅ ⋅ 2

large (>> 1): Order of A1 is –1

small (<< 1): Order of A1 is 1

K p1 1⋅

K p1 1⋅

r kK pK p

2 2

1 1≈ ⋅

⋅⋅

( )r k

K K p

1 + K pp = k p1 2 2

2 21

*1≈ ⋅

⋅ ⋅

⋅⋅ ⋅2

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Extrapolation of formal kinetics…

…is simply not possible

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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)

One should move to micro kinetics accounting for all steps

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Mars-van Krevelen mechanism(Two rate limiting steps!)

O2- O2-

2 e- 2 e-

ProductEduct

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Best to do only micro kinetics?In principle: yes! (but how to determine all those parameters?)

5 parameters}

13 parameters}

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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.

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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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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

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A catalytic test benchA 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 boxPI

PI

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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 8000

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 m

ol s

-1

T / K

β = 0.05 K s-1

100 200 300 400 500 600 700 8000

5

10

15

20

25

30

Tmax. = 471.23 KTmax. = 485.66 KTmax. = 495.55 KTmax. = 503.30 K

Tmax. = 514.60 K

Tmax. = 527.00 K

φ / 1

0-8 m

ol s

-1

T / K

θ0 = 1.00

β = 0.01 K s-1β = 0.03 K s-1β = 0.05 K s-1β = 0.10 K s-1

β = 0.20 K s-1

β = 0.40 K s-1

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TPD experiment - dissociated adsorption

100 200 300 400 500 600 700 8000

5

10

Tmax. = 454.68 KTmax. = 466.63 KTmax. = 474.52 KTmax. = 480.50 K

Tmax. = 488.90 K

Tmax. = 497.60 K

φ / 1

0-8 m

ol s

-1

T / K

θ0 = 1.00

β = 0.01 K s-1β = 0.03 K s-1β = 0.05 K s-1β = 0.10 K s-1

β = 0.20 K s-1

β = 0.40 K s-1

100 200 300 400 500 600 700 8000,0

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 / 1

0-8 m

ol 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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TPD experiment - readsorption

• Readsorption broadens TPD responses

• The impact of readsorption varies with the inert flow

100 200 300 400 500 600 700 8000

1

2with readsorptionk0,des = 1 103 s-1 Pa-1

Ea,des = 40 kJ mol-1

without readsorptionk0,des = 1 1013 s-1

Ea,des = 145 kJ mol-1

φ

/ 10-8

mol

s-1

T / K

β = 0.05 K s-1

θ0 = 1.00

100 200 300 400 500 600 700 8000,0

0,5

1,0

φinert = 500 ml min-1

φinert = 200 ml min-1

φinert = 150 ml min-1

φinert = 100 ml min-1

φinert = 50 ml min-1

φ / 1

0-8 m

ol s

-1

T / K

β = 0.05 K s-1

θ0 = 1.00

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Energetics of ad- and desorption

• Lennard-Jones potentials cross

• The activation energy of adsorption increases 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)

X2 (ads)

X2 (g)

2 X(g)

Epo

t / 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

X2 (ads)

2 X(ads)

X2 (g)

2 X(g)

Epo

t / a

.u.

d / a.u.

• Non activated adsorption • Activated adsorption

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TPA experiment – Study an activated adsorption

100 200 300 400 500 600 700 8000

1

2

3

4

5

Ea,ads = 70.0 kJ mol-1Ea,ads = 60.0 kJ mol-1Ea,ads = 50.0 kJ mol-1

φ / 1

0-8 m

ol s

-1

T / K

β = 0.05 K s-1

100 200 300 400 500 600 700 8007,2

7,3

7,4

7,5

7,6

7,7

Ea,ads = 70.0 kJ mol-1Ea,ads = 60.0 kJ mol-1

Ea,ads = 50.0 kJ mol-1

φ / 1

0-7 m

ol 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

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Catalytic fixed bed reactor – basics (1)

quartz fibers

ReactorReactor

OvenOven

InletInletOutletOutlet

Fixed BedFixed Bed

catalyst quartz crystalsquartz fibers

ReactorReactor

OvenOven

InletInletOutletOutlet

Fixed BedFixed Bed

catalyst quartz crystals

• Catalyst sandwiched between inert beds

• (Movable) thermocouple in the bed centre

• Fixation by quartz wool plugs

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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.

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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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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

External mass transfer limitation:

Internal mass transfer limitation:

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Mathematical description of the PFR

Reactants Products

How much?What?

S S

ninf. neff

.

∆ ∆z u t=

∆ ∆V S z =

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Deriving the spatial derivative form

( ) ( )∑ Θ−+−=j

xxja,j,ij,ii,acc R ,/exp0 pfTEkuSu

dznd

dtnd

νρ&&

i,effi,reaci,infi,acc nnnn ∆−∆+∆=∆

( ) ( )xxjja,j,i,jij,

ij,reac,

ij,j R Θ−=

∆=

∆= ,/exp11

0 pfTEknVdt

dnV

r ρνν

&

tudznd

nn ∆+=0

iiinf,ieff,

&&&

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