An Introduction to Kinetics in Heterogeneous Catalysis

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 ([email protected]) Ruhr Universität Bochum Room NC 5/69 Universitätsstraße 150 D-44780 Bochum

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.

1 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

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.

2 Reactors: Different scale – different objectives 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. Laboratory: 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. 5

Reactor types Batch reactor Continuous stirred Plug flow (BR) tank reactor (CSTR) reactor (PFR)

3 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 8

4 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

Reactor Catalyst Catalyst Active bed particle site What?

Who? Engineers? Inorganic Industrial Physical /Theoretical chemistry? chemistry? chemistry? 10

5 Macroscopic definitions

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

n& e,0 − n& e converted educt Conversion Xe = n& e,0 supplied educt

n& p -ν e formed product Selectivity Sp = ⋅ n& e,0 − n& e ν p converted educt

n& p -ν e formed product Yield Yp = ⋅ n& e,0 ν p supplied educt

As selectivity and yield definitions contain stoichiometric coefficients, these numbers are in general only meaningful if the respective stoichiometric equations are given 11

Mind the thermodynamics

Endothermic synthesis Endothermic synthesis: Equilibrium conversion increases with T

Exothermic synthesis: Exothermic synthesis Equilibrium conversion decreases with T. Real conversion increases for kinetic reason and might be capped. 12

6 Is the knowledge of X, S, Y sufficient?

1.0 15 A C B D C D 0.8 k1

A + B C -1 10 k-1 0.6 mol s S -2 k 0.4 2 / 10 A + B D φ 5 k -2 0.2

0 0.0 0,0 0,2 0,4 0,6 0,8 1,0 0.0 0.2 0.4 0.6 0.8 1.0 z X(A)

• Never compare selectivity at different conversion levels • Judge a catalyst on yield basis is better, but the specific activity information in easily lost 13

Product formation: parallel or sequential

k-2 k1 k1 k2 D A + B C A + B C D k2 k-1 k-1 k-2 15 A 15 A B B C C D D -1 -1 10 10 mol s mol s -2 -2 / 10 / 10 φ 5 φ 5

0 0 0,0 0,2 0,4 0,6 0,8 1,0 0,0 0,2 0,4 0,6 0,8 1,0 z z • Identifying a maximum does not “reveal” a sequential mechanism • The profiles might mislead in case of equilibrium reactions

7 S versus X plot – parallel product formation

k1 1,0 A + B C C D k-1 -3 0,8 r1 = ρ k1 pA pB ρ = 10 mol m -9 -2 -1 k1 = 4 10 Pa s 0,6 r-1 = ρ k-1 pC k = 2 10-4 Pa-1 s-1 S -1 0,4 -9 -2 -1 k2 k = 1 10 Pa s A + B D 2 k -5 -1 -1 0,2 -2 k-2 = 4 10 Pa s r = ρ k p p 2 2 A B 0,0 0,0 0,2 0,4 0,6 0,8 1,0 r-2 = ρ k-2 pD X(A)

• Extrapolation of selectivity at zero conversion: finite values for parallel reactions • Selectivity ratio equals ratio of initial formation rates (not constants!) 15

S versus X plot – sequential product formation

k1 1,0 A + B C C D k-1 -3 0,8 r1 = ρ k1 pA pB ρ = 10 mol m -9 -2 -1 k1 = 4 10 Pa s 0,6 r-1 = ρ k-1 pC k = 2 10-4 Pa-1 s-1 S -1 0,4 -9 -2 -1 k2 k = 1 10 Pa s A + C D 2 k -5 -1 -1 0,2 -2 k-2 = 4 10 Pa s r = ρ k p p 2 2 A C 0,0 0,0 0,2 0,4 0,6 0,8 1,0 r-2 = ρ k-2 pD X(A)

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

8 What is the proper range to make extrapolations

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

k2 k-1 k-1 k-2 1,0 1,0 A A B B 0,8 0,8

0,6 0,6 X X

0,4 0,4

0,2 0,2

0,0 0,0 0,0 0,2 0,4 0,6 0,8 1,0 0,0 0,2 0,4 0,6 0,8 1,0 τ aka w/f τ aka w/f mod mod • Conversion increases under differential conditions linear with w/f • The origin must be precisely passed

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!

9 How to describe the reaction?

General term for the reaction rate

1 1 dni r = [mol s-1 m-3] V νi dt

Terms for the reaction rate in homogeneous catalysis

st -1 r = k(T ) cA 1 order: k [s ]

2 nd 3 -1 -1 r = k(T ) cA or r = k(T ) cA cB 2 order: k [m mol s ] k(T ) = k0exp(− EA / R T )

Concentrations are here only convenient as the reaction volume hardly changes 19

How to describe the reaction rate(s)?

Terms for the reaction rate in heterogeneous catalysis:

m1 m2 Formal kinetics: power law r = k(T ) p1 p2 “Well, one does not know much of the mechanism and fits parameters”

k(T ) pm1 pm2 r = 1 2 m3 Formal kinetics: hyperbolic form (1+ K1(T ) p1 + K2(T ) p2 ) “One knows the mechanism a bit and makes simplifications”

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

1 dnreac,i 1 r = = n&reac,i = ρ k0 exp()()− Ea / R T f px , Θx ν i ∆V dt ν i ∆V 20

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

k r = ρ k p θ r = ρ k θ ads,A ads,A ads,A A * des,A des,A A A + * A--* kdes,A

θ =1-θ * A

kads,A pA KA pA kads,A In fast equilibrium: θ A = = with KA = kdes,A + kads,A pA 1+ KA pA kdes,A 21

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

k r = ρ k p θ r = ρ k θ ads,M ads,M ads,M M * des,M des,M M M + * M--* kdes,M

θ =1-θ * M

kads,M pM KM pM kads,M In fast equilibrium: θM = = with KM = kdes,M + kads,M pM 1+ KM pM kdes,M 22

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

2 k r = ρ k p θ 2 r = ρ k θ ads,B ads,B ads,B B * des,B des,B B B2 + 2 * 2 B--* kdes,B

θ =1-θ * B

k p K p k In fast equilibrium: θ = ads,B B = B B with K = ads,B B B k kdes,B + kads,B pB 1+ KB pB des,B 23

Towards reaction – Co-adsorption

As soon as one thinks of reaction there shall be co- adsorption of reactants. Thus, two points are important to underline:

θ =1-θ θ =1-θ -θ * B might not hold anymore, but * A B

On the other hand, adsorption could also proceed on multiple sites

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

12 The micro-kinetic reaction on the surface (parallel product formation) Primary Educts Primary product 1 product 2

2 r1 = re→P1,ads = ρ k1 θ A θB r2 = re→P2,ads = ρ k2 θ A θB r-1 = rP1,ads→e = ρ k-1 θP1 r-2 = rP2,ads→e = ρ k-2 θP2 25

The micro-kinetic reaction on the surface (sequential product formation) Educts Primary Secondary product product

r1 = r→P1,ads = ρ k1 θ A θB r2 = r→P2,ads = ρ k2 θB θP1

r-1 = rP1,ads→ = ρ k-1 θP1 r-2 = rP2,ads→ = ρ k-2 θP2 26

13 Models assuming rate limiting steps (1)

Case 1: Eley-Rideal-mechanism

Component A1 is chemisorbed, component A2 is in gas-phase. The reaction proceeds slow between chemisorbed A1 and A2 from the gas- phase.

K1⋅p1 A1 + * A1--* θ1 = 1+ K1⋅p1

A1--* + A2 (g) products r=k⋅θ 12⋅ p

Kpp⋅ ⋅ r=k⋅ 112 1+K11⋅ p

Kp⋅ rkp≈ ⋅ 11large (>> 1):2 Order of A1 is 0

Kp11⋅ small (<< 1):rkKpp≈ ⋅ 112⋅ ⋅ Order of A1 is 1 27

Models assuming rate limiting steps (2)

Case 2: Langmuir-Hinshelwood-mechanism

Component A1 is chemisorbed, component A2 is chemisorbed. The reaction proceeds slow between chemisorbed A1 and A2 at the surface.

Kp11⋅ A + * A --* θ 1 = 1 1 1+K11⋅⋅ p +K 2 p 2

Kp22⋅ A2 + * A2--* θ 2 = 1+K11⋅⋅ p +K 2 p 2

A1--* + A2 --* products r=k⋅θ 12⋅θ

KpKp11⋅ ⋅ 2⋅ 2 r=k⋅ 2 ()1+K11⋅⋅ p +K 2 p 2

Kp22⋅ Kp11⋅ large (>> 1):rk≈⋅ Order of A1 is –1 Kp11⋅ KKp122⋅ ⋅ * Kp11⋅ small (<< 1):rk≈⋅ ⋅⋅p=kp1 1 Order of A is 1 1+K⋅ p 2 1 ()22 28

14 Extrapolation of formal kinetics…

…is simply not possible 29

Are models assuming a rate limiting step sufficient?

According to what one assumes as rate limiting step, one can derive a suitable kinetic expression! (refer to Hougen-Watson terms)

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

One should move to micro kinetics accounting for all steps

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

Educt Product

O2- O2-

2e- 2e-

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

} 5 parameters

} 13 parameters

16 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.

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

17 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 35

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. Analysis

vent PI Hot box Gas feed 1

PI Gas feed 2 vent

reactor 36

18 TPD experiment - molecular adsorption

5 30 -1 θ = 1.00 β = 0.05 K s θ0 = 1.00 0 25 -1 4 T = 527.00 K β = 0.40 K s θ0 = 0.80 max.

-1 -1 20 3 θ0 = 0.60 -1 Tmax. = 514.60 K β = 0.20 K s mol s mol s mol 15

-8 -8 2 θ0 = 0.40 / 10 / 10 10 -1 φ φ T = 503.30 K β = 0.10 K s max. -1 T = 495.55 K β = 0.05 K s 1 θ = 0.20 max. 0 5 -1 Tmax. = 485.66 K β = 0.03 K s θ = 0.10 -1 0 T = 471.23 K β = 0.01 K s 0 0 max. 200 300 400 500 600 700 800 100 200 300 400 500 600 700 800 T / K T / K

• Declining branches overlap for initial coverage variation • Rising branches overlap for heating ramp variation • Rapid decline of the signal after reaching the maximum 37

TPD experiment - dissociated adsorption

1,5 10 -1 β = 0.05 K s θ0 = 1.00 θ0 = 1.00 -1 β = 0.40 K s Tmax. = 497.60 K θ0 = 0.80 -1 1,0 -1 -1 θ0 = 0.60 Tmax. = 488.90 K β = 0.20 K s mol s mol s mol 5

-8 -8 θ = 0.40 / 10 0,5 0 / 10 -1 φ φ T = 480.50 K β = 0.10 K s max. -1 θ = 0.20 Tmax. = 474.52 K β = 0.05 K s 0 -1 T = 466.63 K β = 0.03 K s θ = 0.10 max. -1 0 T = 454.68 K β = 0.01 K s 0,0 0 max. 100 200 300 400 500 600 700 800 100 200 300 400 500 600 700 800 T / K T / K

• Declining branches overlap for initial coverage variation • Rising branches overlap for heating ramp variation • Slow decline of the signal after reaching the maximum 38

19 TPD experiment - readsorption

2 1,0 -1 -1 β = 0.05 K s with readsorption β = 0.05 K s θ = 1.00 3 -1 -1 θ = 1.00 0 k0,des = 1 10 s Pa 0 -1 Ea,des = 40 kJ mol -1 -1 without readsorption -1 13 -1 φ = 500 ml min mol s mol 1 k0,des = 1 10 s s mol 0,5 inert

-8 -8 -1 -1 φinert = 200 ml min Ea,des = 145 kJ mol -1 / 10 / 10 φ = 150 ml min

φ φ inert -1 φinert = 100 ml min -1 φinert = 50 ml min

0 0,0 100 200 300 400 500 600 700 800 100 200 300 400 500 600 700 800 T / K T / K

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

Energetics of ad- and desorption

• Non activated adsorption • Activated adsorption

0,2 0,2 2 X 2 X(g) (g) 0,1 0,1

X2 (g) X2 (g)

/ a.u. / 0,0 a.u. / 0,0

pot pot E E X2 (ads) X2 (ads) -0,1 -0,1

2 X -0,2 2 X(ads) -0,2 (ads)

0,0 0,2 0,4 0,6 0,8 1,0 1,2 0,0 0,2 0,4 0,6 0,8 1,0 1,2 d / a.u. d / a.u.

• Lennard-Jones potentials cross • The activation energy of adsorption increases also that of the desorption 40

20 TPA experiment – Study an activated adsorption

5 7,7 -1 -1 β = 0.05 K s β = 0.05 K s -1 Ea,ads = 50.0 kJ mol 4 7,6 E = 50.0 kJ mol-1 E = 60.0 kJ mol-1 a,ads a,ads E = 60.0 kJ mol-1 -1 -1 -1 a,ads Ea,ads = 70.0 kJ mol -1 3 7,5 Ea,ads = 70.0 kJ mol mol s mol s mol

-8 -7 2 7,4 / 10 / 10 φ φ 1 7,3

0 7,2 100 200 300 400 500 600 700 800 100 200 300 400 500 600 700 800 T / K T / K

• TPD responses for 60 and 70 kJ mol-1 similar • TPA traces are clearly distinguishable • Complementary TPA study required to complete the information pool 41

Catalytic fixed bed reactor – basics (1)

Oven • Catalyst sandwiched between inert beds Outlet Reactor Inlet • (Movable) thermocouple in the bed centre • Fixation by quartz wool plugs

Fixed Bed

quartz fibers catalyst quartz crystals

21 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.

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.

22 Catalytic fixed bed reactor – test for limitations

External mass transfer limitation: 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

Internal mass transfer limitation: 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

Mathematical description of the PFR

Reactants Products

How much? What? ∆∆VSz = . . ninf neff

∆zut= ∆ 46

23 Deriving the spatial derivative form

∆nacc,i = ∆ninf ,i + ∆nreac,i − ∆neff ,i

dn&i n&eff,i = n&inf,i + u ∆t dz 0

1 dnreac,j,i 1 rj = = n&j,i = ρ k0,j exp()− Ea,j / R T f j ()px , Θx ν j,i ∆V dt ν j,i ∆V

dn &acc,i dn&i = − u + S u ρ ∑ν j,i k0,j exp()− Ea,j / R T f ()px , Θx dt dz j