temporal analysis of products(tap)- approach: theory and ...temporal analysis of...

Temporal Analysis of Products(TAP)-Approach: Theory and Application

Gregory Yablonsky,

Parks College of Engineering, Aviation and Technology,

Department of Chemistry, Saint Louis University

(Missouri, USA)

or Chemical Calculus

Gregory YablonskyParks College, Department of Chemistry, Saint Louis University

OUTLINE

• Concepts and history• Experimental devices of chemical kinetics• TAP-apparatus: principle• Qualitative analysis of data• Quantitative analysis of data(a) Fitting(b) Moments(c) Kinetically mode-free analysis ( Y-procedure)• Future: Rate-Reactivity Model• Back to History and Conclusions

• Experimental Devices of Chemical Kinetics

temporal change of transport change due to

amount of component change reaction

Typical Requirements to Kinetic Experiments:

• Isothermicity

• Intensive heat exchange with surroundings

• Dilution of reactive medium

• Rapid recirculation

• Uniformity of the chemical composition

• Intensive mixing

G.B. Marin & G.S. Yablonsky (2011). Kinetics of Chemical Reactions. Decoding

Complexity 7

Reactors for Kinetic Experiments

feed product feed product

recycle

catalyst zone

Batch reactor CSTR Continuous-flow reactor with

recirculation

PFR Differential PFR

Complexity 8

Reactors for Kinetic Experiments

catalyst zone

Convectional pulse

reactor

Diffusional pulse

reactor / TAP

reactor

Thin-zone TAP

reactor

What are we measuring as a rate in Chemical Kinetics?

CHANGE IN SPACE OR IN TIME- Algebraic difference of inlet and outlet

concentrations (CSTR)

- First time derivative of the concentration dependence (batch reactor)

- First time derivative of the outlet concentration dependence

on the residence time (plug-flow reactor, PFR)

- First longitudinal derivative of the concentration dependence

(some plug-flow reactors)

- Second longitudinal derivative of the concentration dependence

(Temporal Analysis of products, TAP)

G.B. Marin & G.S. Yablonsky (2011). Kinetics of Chemical

Reactions. Decoding Complexity

Types of Temporal Evolution Relaxation

slowintermediate

Simple exponential relaxation Relaxation with induction period

Relaxation of different components at different time scales

Relaxation with “overshoots” (1) & (3) and start in “wrong” direction

Relaxation with different steady states

Damped oscillations

Belousov-Zhabotinsky reaction

Regular oscillations around a

steady state

Chaotic oscillations

Anatoly Zhabotinsky (1938 – 2008)

Gerhard Ertl (1936 - )

Progress in time resolutionfor 150 years

• From second to femptoseconds (10 -15 sec)

Complexity 18

Non-Steady-State Models

describes the temporal evolution of a chemical reaction mixture from an initial state

to a final state

• closed system: equilibrium

• open system: steady state

Three methods for studying non-steady-state behavior:

• change in time t: change in dynamic space (c,t)

• change of parameters k: change in parametric space (c,k)

• change of a concentration with respect to others: change in phase space

Rutherford Aris (1929 – 2005)

Calculus’ foundation: Cavalieri is a precursor of infinitesimal calculus

In Europe, the foundational work was a treatise due to Bonaventura Cavalieri, who argued that volumes and areas should be computed as the sums of the volumes and areas of infinitesimal thin cross-sections

Founders of infinitesimal calculus: Newton and Leibnitz

Isaac Newton (1743-1727)

Gottfried Wilhelm Leibnitz (1646-1716)

‘Drop-by-drop’: titration,determination of the equivalent point

The origins of volumetric analysis are in late-18th-century French chemistry. Francois Antoine Henri Descroizilles developed the first burette (which looked more like a graduated cylinder) in 1791. Joseph Louis Gay-Lussac developed an improved version of the burette that included a side arm, and coined the terms "pipette" and "burette" in an 1824 paper on the standardization of indigo solutions

Manfred Eigen (1927): Chemical relaxation, but not calculus

Experimental calculus in chemistry: John T. Gleaves

• Temporal Analysis of Products (TAP),

a vacuum transient response experiment performed by injecting a small number of gas molecules into an evacuated reactor containing a solid sample, which provides precise kinetic characterization of gas- solid interactions with submillisecond time resolution (developed by J.T. Gleaves in 1988)

Pulse valve

Microreactor

Mass spectrometer

Catalyst

Vacuum (10-8 torr)

Reactantmixture

0.0 time (s) 0.5

Reactant

Product

Continuous flow valve

TAP Reactor System-Overview

TAP-3 System

IR Probe

Reactor

New Developments in TAP Instrumentation

Aiming

towards

‘kinetically

appropriate’

operando

reactors

Measuring Intrinsic Kinetic Characteristicswith Probe Molecules

Pulse valve

Mass spectrometer

Molecular beam

Scattered beam

P ≈ 10-9 Pa

Target

Differentially pumped

vacuum system

Molecular Beam Scattering – MBS experiment – Inspiration for TAP

Sticking probability of H2 on different

surfaces. Data of Rendulic and Winkler , Int. J. Mod.

Phys. B 3, 941, 1989.

Pulse valve

Mass spectrometer

Molecular beam

Scattered beam

P ≈ 10-9 Pa

Target

vacuum system

Molecular Beam Scattering – MBS experiment – Inspiration for TAP

Multi-component

Polycrystalline

Multiphasic

Heterogeneous Surface

Defects

Changes with Reaction

Practical Catalyst

(Complex Particles)

Pulse valve

Mass spectrometer

Molecular beam

Scattered beam

P ≈ 10-9 Pa

Target

vacuum system

Pulse valve

spectrometer

Reaction zone

Catalyst sampleExit flow

P ≈ 10-7 Pa

Input pulse

Molecular Beam Scattering – MBS experiment

Temporal Analysis of Products - TAP experiment

Insignificant change

Small number of pulses1 32 4

Key Features of TAP Pulsing

Significant change

1 50002500 7500Large number of pulses

Key Advantages:Small pulse size

Low adiabatic temperature rise

Isothermal experiments

Minimal surface reconstruction

No mass transfer limitations

Millisecond time resolution

Oxidation state can be

manipulated

Inert Reactant ProductInert Reactant Product

Small number of pulses

State-defining Experiment

State-Defining & State-Altering Experiment

Inert Reactant Product

Large number of pulses0.0

State-altering Experiment

TAP Multipulse Experiment Combines

TAP-results

• About 20 machines working in the world• About 10 research groups

US-St. Louis, HoustonEurope – Belgium, Ghent; Netherlands, Delft ; N.Ireland, UK, Belfast; Germany – Ulm, Rostock, Bohum; France –Lyon; Spain; Switzerland –Zuerich;Asia- Japan – Tokyo, Toyota City;Thailand – Bangkok.Many catalytic reactions: oxidation of simple molecules, many reactions of complete and selective oxidation of hydrocarbons

• Interrogative kinetics, a systematic approach combining small stepwise changes in catalyst surface composition with precise kinetic characterization after each change to elucidate the evolution of catalyst properties and provide information on the relationship between surface composition and kinetic properties. (developed by J.T. Gleaves and G. Yablonsky in 1997)

The main idea is to combine two types of experiments:

Was firstly introduced in the paper:Gleaves, J.T., Yablonskii, G.S., Phanawadee, Ph., Schuurman, Y.

“TAP-2: An Interrogative Kinetics Approach” Appl. Catal., A: General, 160 (1997) 55.

A state-defining experiment in which the catalyst composition

and structure change insignificantly during a kinetic test

A state-altering experiment in which the catalyst composition

is changed in a controlled manner

Interrogative Kinetics (IK) Approach

Principles of the TAP-experiment

• 3 principles:

• (1) Insignificant change of catalyst composition during the single pulse

• (2) Controlled change of catalyst composition during the series of pulses

• (3) Uniformity of the active zone regarding the composition

=========

And… Transport is well-defined: Knudsen diffusion

Thin Zone TAP experiments

Thin-zone and Single Particle Reactor Configurations

Thin-zone

Single-particle

QUALITATIVE ANALYSIS

ÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉ

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0.0 0.1 0.2 0.3 0.4 0.50.5time(s)

Butane Response after Reaction

Experimental and Predicted ResponsesArgon and Butane Pulsed over VPO

0.5time(s)

Experimental and Predicted Responses Argon Pulsed over Quartz Particles

440400

360320

Temp.time (s)

Non-uniformity along the catalyst bed was produced in multi-pulse experiment

porosity

z2 ka CA*

Transport + Irreversible Adsorption

Standard Diffusion Curve

diffusivity

Experimental and predicted responsesButane pulsed over oxygen treated VPO

TAP-data qualitative analysis

• Distinguishing irreversible and reversible adsorption and interaction processes.

• Different “pump-probe” experiments• Testing of the temperature influence• Testing of the catalyst pretreatment• Change of pulse parameters (pulse intensity, time

interval between pulses etc)

Preliminary result: some hypotheses about thedetailed mechanism (types of adsorption and interactions, diffusion into the catalyst bulk etc)

Probe Molecules:TAP as a Surface Sensitive Materials Characterization Tool

Spectroscopic

TechniquesXPS, TEM, LEIS, etc.

Photons, electrons, ions

Near surface layers

Signal is proportional to

surface concentration

Well-defined (model)

materials

TAPProbe molecule pulsing

Reactants, products,

intermediates, bases, etc.

Exclusive to the surface

Signal follows exponential

kinetic dependence –

ultrasparse concentrations can

be detected

Real materials

Can distinguish active/inert

Wavelength time (s)

Vacuum Transformation of

Oxygen-treated (VO)2P2O7

Probe Molecules Indicate Kinetic Effects of

Structural Change

Activity-Structure Relationship for Complex Catalysts

Intrinsic kinetic

measurements

Techniques for Intraparticle Transport

• PFG NMR

• Quasi-elastic Neutron Scattering

• Single crystal membranes

• Zero Length Chromatography

• Frequency Response

• TAP

• PFG NMR

• Quasi-elastic Neutron Scattering

• Single crystal membranes

• Zero Length Chromatography

• Frequency Response

• TAP

Diffusing species

must be in contact

with the

microporous

material for and

extended time.

Microscopic Methods• PFG NMR• Quasi-elastic Neutron Scattering

Macroscopic Methods• Single crystal membranes• Zero Length Chromatography• Frequency Response• TAP

Diffusivity

measurements

polarized by two

orders of

magnitude.

TAP for Intraparticle Transport

• Millisecond time resolution

• Small quantity of sorbent, measurement at low pore occupancy

• No carrier gas which may influence mass transfer

• Knudsen regime, no external mass transport limitations

TAP for Intraparticle Transport

• Kinetic Processes • In the Porous Channel

– Adsorption/desorption into/from pore mouth

– Residence time in pores

– Diffusivity in microporous channel

• External Surface

• Activation energy 1/pore radius• Optimum pore size

• Catalyst coking studies• External plane vs. microporous channel

Unique Experiments with TAP

• Pump/Probe format

• Intraparticle transport at low pore occupancy

Pump/Probe FormatSeparation of 2 Reactants

Reactant A (e.g.

Reactant B (e.g. H2O)

Pulse response of

product at reactor

exit (e.g. N2O or N2)

How does H2O hinder the storage of NOx or facilitate its reduction?

New Pump/Probe Experiments for Multicomponent (Competitive)

Intraparticle TransportReactant A (e.g. CH4) Reactant B (e.g. CO)

Pulse response

of gas B at

reactor exit

Pulse response of

gas A at reactor exit

TAP-DATA QUANTITATIVE ANALYSIS

Inert zone Catalyst zone

Thin-Zone TAP -Reactor (TZTR) Idea

Dimensionless Axial Coordinate

0.0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.00.00

Vacuum

Thin-Zone TAP- Reactor (TZTR)

CI(x,t)xLTZ

CII (x,t)xLTZ

CTZ(t)

For concentrations

DCI (x,t)

x xLTZ

DCII (x,t)

x xL TZ

FluxI (x,t)xLTZ

Flux II (x,t)xLTZ

LcatRTZ(CS,CTZ ,TZ )

For flows

TZTR vs CSTR

CSTR: SRVCVC 0 Uniformity is achieved by convective

mixing

X kappres, cat

1 kappres, cat

diffConversion

Apparent rate constant

Diffusional residence time in catalyst zone

In TZTR uniformity is insured by diffusion

),(),(TZTR:

TZTR vs Differential PFR

TZTRDifferential PFR:

Conversion vs Non-Uniformity

TAP: Diffusion SRx

PFR: Convection SRx

Provides Uniformity at X ≤ 20% Provides Uniformity

at X ≤ 80%

Convectional Flow = Diffusional Flow = gVC

Cg 2Lc

1 (1 X)LrLc

Shekhtman S.O., Yablonsky G.S. Ind. Eng. Chem. Res. 44 (2005) 6518-6522.

2) Moment analysis

1) Curve fitting

× Loss of transient information Robust

3) ‘State-of-the-art’: Y-Procedure

× What about fast processes within the pulse?

Thin Zone TAP data analysis: Quantitative Analysis

× Relies on an a priori assumed mechanism

× Relies on an a priori assumed mechanism (ambiguous)

Curve Fitting

A drawback is that it relies on the

a priori assumed mechanism

MOMENT ANALYSIS

time(s)

PulseNumber

M0 Fexit (t )dt

Zeroth Moment

Kinetic Characteristics from Pulse Response Moments

• Conversion (number of surfaceoxygen atoms and hydrocarbon)

• Selectivity• Product Yield• Residence time• Apparent rate constants• Apparent time delay

Quantities calculated from 0th, 1st, and

2nd moments

Shekhtman, S. Interrogative Kinetics A New Methodology or Catalyst Characterization. Doctoral Thesis, Washington University, 2003.

“State-by- state” kinetic catalyst screening:

“Show me state”Step 1 Introducing catalyst scale

Presenting conversions/yields vs amounts of consumed

/released reactants/removed oxygen/

via dimensionless scales (catalyst alteration degree; catalyst

oxidation/reduction degree

Step 2 Presenting catalyst state

Presenting kinetic characteristics(apparent kinetic constants and

time delays) as functions of catalyst scale (catalyst alteration degree, catalyst

oxidation/reduction degree)

Step 3 Revealing mechanism

Revealing mechanism of the complex reaction by comparison of different

kinetic characteristics (apparent kinetic constants, time delays)

Considerations for mechanism revealing

1) Routes:

Difference between apparent kinetic

constants of gas reactants is a fingerprint of

different reaction routes

2) Catalyst intermediates

Apparent time delay of gas reactant is a

fingerprint of the surface intermediate presence

==============================These characteristics depend on the catalyst state

Apparent Kinetic Constants and TOF

for Furan Oxidation as a Function of Oxidation State

00.20.40.60.81

Catalyst Oxidation Degree

r0 , (

00.20.40.60.81

Catalyst Oxidation DegreeN

Non-steady-state TOF defined as the apparent

constant divided by the oxidation degree, for

furan and products (MA, CO2 and AC),

versus the catalyst oxidation degree.

All apparent kinetic constants are different

Apparent Time Delays

00.20.40.60.81

Catalyst Oxidation Degree

Appare

For all reactants, apparent time delays are different.

At least four intermediates can be involved

Detailed Mechanism of Furan Oxidation Over VPO

At least three independent routes

At least four specific intermediates

1) O2 + 2Z 2ZO;

2) Fr + ZO X;

3) Fr + ZO Y;

4) Fr + ZO U;

5) X MA+ Z + H2O;

6) YAC + Z + CO2 + H2O;

7) UZ + CO2+ H2O;

8) ZO + L LO + Z;

9) CO2 + Z1 Z1CO2.

where X, Y, U, Z1CO2 are different

surface intermediates, ZO and LO

– surface and lattice oxygen

respectively, Z and Z1 are different

catalyst active sites.Stoichiometric

coefficients of surface substances

will be specified in the course of

reaction. Steps 2-4 are supposed

to differ kinetically.

A drawback of the moment analysis

The moment analysis uses the

information which is averaged

within the pulse

Kinetically model-free analysis

Y-PROCEDURE

Kinetic Model-Free Analysis

Reactor Model:

Accumulation - Transport Term = Reaction Rate

Batch Reactor: Non SRdt

CSTR: Convection SRCCVdt

dCVg )( 0

TAP: Diffusion SRx

PFR: Convection SRx

The biggest methodologicaldifficulty in non-steady-state studies:

comparison with the steady-state experiment

1. CSTR-data provides the steady-state

reaction rate without assumptions on the

kinetic model (kinetic model – free data):

2. Presently all kinetic methods (CSTR,

PFR, TAP) do not provide data on the non-steady

state reaction rate in a kinetic model –free manner

• TWO IDEAS:

• I. Experimental idea: Thin-Zone TAP-Reactor (TZTR)

• 2. Theoretical Idea: Extracting the non-steady reaction rate in model-free manner

• (Y-procedure)

75AIChE Annual Meeting,

October 2012, Danckwerts Memorial Lecture

0=xδ=C(x,0) 0=t)(0,x

0=t)C(L,t)(L,x

Initial Pulse(Dirac delta)

Boundary Conditions

Closed valve

Vacuum

Observation(molecular flux)

Transport equation(Knudsen diffusion)

One zone: the diffusion equation requires an initial condition and two boundary conditions (as a second order PDE)

II)NR(C,=

C=C=C III

)NR(C,=dt

0=xδ=C(x,0) 0=t)(0,x

0=t)C(L,t)(L,x

Initial Pulse(Dirac delta)

Boundary Conditions

Closed valve

Concentration continuity

TZ gas phasebalance

TZ surfacebalance

Vacuum

Observation(molecular flux)

Transport equation(Knudsen diffusion)

G. S. Yablonsky, D. Constales, et. al., Chem. Eng. Sci., 62, 6754 (2007)

Two zones: each zone requires two boundary conditions

Calculating surface concentrations (instantaneous storages)as a transient difference between total uptake and release

Uptake Release

dτ(τRνRelease(t)Uptake(t)(t)C

Mathematical foundation of the Y-procedure:3 steps

• 1. exact solution in the Laplace domain;• 2. switching to the Fourier domain to allow sufficient

computation;• 3. introduction to discretization and filtering in the Fourier

domain to deal with the real data (in the time domain) subject to noise.Transposition to the Fourier domain combined with time discretization and filtering of the high-frequency noise leads to an efficient practical method for the reconstruction of gas-phase concentrations in a non-steady-state regime without any presuppositions about the kinetic dependence, that is, it is a model-free procedure.

The Y-Procedure analysis provides us with:

• 'Model free' transient kinetics

• For complex multicomponent catalysts

• At the upper limit of the surface science range (10-6

torr)• Keeping high spacial uniformity for conversions up to 80% [1]

How do we deal with this information?

[1] - S. Shekhtman, et. al., Chem. Eng. Sci., 59, 5493 (2004)

Numerical solution(Method of Lines)

Y-Procedure(FFT)

Model mechanisms(set in advance)

Transient intrinsickinetics

(reconstructed)

Developing the Y-Procedure methodology: Numerical experiments

Simulateddata

• How do we extract a complex catalytic mechanism from corresponding transient kinetics?

• Which parameters we can extract from these data and how?

Irreversible adsorption: Simulation

A + Z → AZ k

AAZtotZ,A )CCk(C=R

k = 1000 m3/mol/s

CZ,tot = 5 nmol/m2

Np = 10-11 – 10-8 mol/pulse

lation

ctionExample (Np = 5·10-10 mol/pulse)

Irreversible adsorption: Trajectories in the rate/composition space,i.e R(t) vs. CA(t) vs. CZA(t), for different pulse intensities

Characteristic surface defined by R(Cg,CS)

Reaction rate

Surface concentration

Gas concentration

Irreversible adsorption: State-defining experiment (small pulse)

Np = 1·10-10 mol/pulse

totZ,app kC=k

AtotZ,A CkCR

Irreversible adsorption: State-altering experiment (big pulse)

AAZtotZ,A )CCk(C=R

Irreversible adsorption: State-altering experiment (big pulse)

totZ,C

AZtotZ,

A kCkC=C

Irreversible adsorption: Multi-pulse experiment (series of small pulses)

AappA CkR

ZAtotZ,app kCkCk

Irreversible adsorption: Multi-pulse experiment (series of small pulses)

AappA CkR

ZAtotZ,app kCkCk

Reversible adsorption: Simulation

A + Z AZ k+

AZAAZtotZ,

A Ck)CC(Ck=R

→←k-

k = 10 1/s

CZ,tot = 0.5 nmol/m2

Np = 10-11 – 10-8 mol/pulse

k = 1000 m3/mol/s

lation

Example (Np = 5·10-10 mol/pulse)

Reversible adsorption: Trajectories for different pulse intensities

Surface defined by R(Cg,CS)=0

Gas rate

Surface concentration

Gas concentration

Reversible adsorption: State-defining experiment (small pulse)

Plane trajectory:

totZ,Ck

AZtotZ,

Reversible adsorption: State-altering experiment (big pulse)

totZ,C

Non-plane trajectory:

AZA CkCk=C

Reversible adsorption: Transient Equilibrium

Isotherm (Rads = Rdes)

eqeqA,

eqA,totZ,

eqAZ,1/K+C

The ‘menu’ of TAP experiments

How does pulse intensity affects the catalyst state for irreversible/reversible reactions?

Pulse Intensity

Irreversible

Reaction

Reversible

Reaction

Change within each pulse

Change from pulse to pulse

Change within each pulse

Change from pulse to pulse

Small pulse small controlled small Small

Big pulse big big big non

What parameters can we extract?

ExperimentIrreversible

Reaction

Reversible

Reaction

State-defining kapp = kCZ,tot k+app = k+CZ,tot and k-

State-alteringk and CZ,tot k+ and CZ,tot if k- is

CO + Z CO

ZCOCOZCOtotZ,

CO Ck)CC(Ck=R

→←k-

Application to CO adsorption on Pd: Experimental results for a reversible adsorption

Np = 5·10-9 - 1·10-7 mol/pulse

Example (Np = 1·10-7 mol/pulse)

CO + Z COk+

→←k-

Application to CO adsorption on Pd: Experimental results for a reversible adsorption

3totZ,m

Isotherm fitting:

Decoding complex mechanisms:

Classical problem – Langmuir-Hinshelwood or Eley-Rideal?

For any combination of elementary steps, surface uptakes of CO and oxygen can be calculated as:

)dτ(τR(τ(R(t)C

COCOZCO 2))

COOZO dτ(τR(τ(2R(t)C22

Step 1: Directly comparing rates in a state-defining experiment

Step 2: Testing coherency of the entire data set (time invariant parameters)

Apparent kinetic parameters:

ER+OAP

Step 2: Decision tree for oxygen pre-covered surface

Testing rates

Legend:

ER - Eley-Rideal LH - Langmuir-Hinshelwood OAP -Oxygen Additional ProcessBuffer - spectator CO

Testing parameters

TAP: New Results

• I. MOMENTARY EQUILIBRIUM:PULSE AND DIFFUSION (Ind. Eng. Chem. Res., 52 (44), 15417–15427 (2013) )

101AIChE Annual Meeting,

October 2012, Danckwerts Memorial Lecture

Thin-zone and Single Particle Reactor Configurations

Thin-zone

Single-particle

Thin-Zone TAP -Reactor (TZTR) Idea

Dimensionless Axial Coordinate

0.0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.00.00

Vacuum

The Y-Procedure analysis provides us with:

• 'Model free' transient kinetics

Momentary equilibrium

105NASCRE-3, Houston, TX,

20/03/2013

• Adsorption equilibrium is an essential step of catalytic processes,

which is often used to measure the total concentration of catalytic sites.

• The total concentration of sites

is typically determined by:

- Very sensitive pressure and microbalance

measurements in equilibrated closed system.

- Chemisorption of irreversibly adsorbing molecules.

- Chemisorption of reversibly adsorbing molecules

at low temperatures (much less than operating).

Introduction

20/03/2013

• Adsorption equilibrium is an essential step of catalytic processes,

which is often used to measure the total concentration of catalytic sites.

• The total concentration of sites

is typically determined by:

- Very sensitive pressure and microbalance

measurements in equilibrated closed system.

- Chemisorption of irreversibly adsorbing molecules.

- Chemisorption of reversibly adsorbing molecules

at low temperatures (much less than operating).

• Measuring the concentration of adsorption sites by

reversible chemisorption under realistic operating temperatures and

non-steady-state conditions presents a significant challenge.

Outline

20/03/2013

• TAP experiments and data analysis

• Momentary Equilibrium

• Pulse-Intensity Modulation

• Experimental example

• Conclusions

Outline

20/03/2013

• Introduction

• Conclusions

Outline

20/03/2013

• Introduction

• Conclusions

Thin-Zone (TZ) Temporal Analysis of Products (TAP)

20/03/2013

timeQMStime

Inlet pulse Exit flow

pulse valve

catalyst

thermocouple

Fexit(t)Finlet(t)

J. T. Gleaves et al. (2010)

Thin-Zone (TZ) Temporal Analysis of Products (TAP)

20/03/2013 111

timeQMStime

Inlet pulse Exit flow

pulse valve

catalyst

thermocouple

Fexit(t)Finlet(t)

Gas concentrationR(t)

Reaction rateCs(t)

Surface storage+

Y-Proc.

Kinetically “model-free” characteristics in the catalyst zone

stoichiometric

assumptions

G. S. Yablonsky et al. (2007)

Outline

20/03/2013

• Introduction

• Conclusions

Case study

20/03/2013

CO + Z ZCOk+

𝐾𝑒𝑞 =𝑘+

𝑘−

Single-site CO adsorption:

Case study

20/03/2013

CO + Z ZCOk+

𝐾𝑒𝑞 =𝑘+

𝑘−

𝑅𝐶𝑂 = −𝑑𝐶𝐶𝑂𝑑𝑡= 𝑘+𝐶𝑍𝐶𝐶𝑂 − 𝑘

−𝐶𝑍𝐶𝑂 =

= 𝑘+(𝐶𝑍,𝑡𝑜𝑡−𝐶𝑍𝐶𝑂)𝐶𝐶𝑂 − 𝑘−𝐶𝑍𝐶𝑂

• Kinetics is governed by

Case study

20/03/2013

CO + Z ZCOk+

𝐾𝑒𝑞 =𝑘+

𝑘−

We used numerical TZ TAP experiments with realistic noise model

to elucidate kinetic behavior during CO adsorption in TAP.

𝑅𝐶𝑂 = −𝑑𝐶𝐶𝑂𝑑𝑡= 𝑘+𝐶𝑍𝐶𝐶𝑂 − 𝑘

−𝐶𝑍𝐶𝑂 =

= 𝑘+(𝐶𝑍,𝑡𝑜𝑡−𝐶𝑍𝐶𝑂)𝐶𝐶𝑂 − 𝑘−𝐶𝑍𝐶𝑂

• Kinetics is governed by

• Surface CO uptake can be obtained as

𝐶𝑍𝐶𝑂(𝑡) = 0

𝑅𝐶𝑂 𝑡′ 𝑑𝑡′

Intra-pulse kinetic characteristics

20/03/2013

Pulse-response experiment

in TZ TAP microreactor

t, (s)

CZCO…

Momentary Equilibrium (ME)

20/03/2013

Pulse-response experiment

in TZ TAP microreactor

t, (s)

CZCO…

𝑅𝐶𝑂 𝑡 = 0 → 𝑟+ = 𝑟−

Momentary Equilibrium (ME)

20/03/2013

How do we use ME to obtain isotherms and

estimate the total concentration of sites?

Are the surface and gas concentrations in ME related

via the equilibrium constant?

Outline

20/03/2013

• Introduction

• Conclusions

Pulse-Intensity Modulation

20/03/2013

𝐶𝑍𝐶𝑂,𝑀𝐸 =𝐾𝑒𝑞𝐶𝑍,𝑡𝑜𝑡𝐶𝐶𝑂,𝑀𝐸

1 + 𝐾𝑒𝑞𝐶𝐶𝑂,𝑀𝐸

Langmuir isotherm:

Pulse-Intensity Modulation

20/03/2013

𝐶𝑍𝐶𝑂,𝑀𝐸 =𝐾𝑒𝑞𝐶𝑍,𝑡𝑜𝑡𝐶𝐶𝑂,𝑀𝐸

1 + 𝐾𝑒𝑞𝐶𝐶𝑂,𝑀𝐸

Langmuir isotherm:

Fexit(t)

t, (s)

Outline

20/03/2013

• Introduction

• Conclusions

Experimental example

20/03/2013

CO adsorption on Pt/Mg(Al)Ox (1 wt. % Pt)

Pulse-intensity range: Np,CO = 1 – 14.5nmolCO

Temperature range: T = 50 – 140 °C

20/03/2013

Estimated concentration of adsorption sites: CZ,tot = 0.3-0.55 (mmol/kgcat)

Estimated heat of CO adsorption: ΔHads= - 17.9 (kJ/molCO)

Rate-concentration trajectories

20/03/2013

t, (s)

State-defining trajectory

20/03/2013

𝑅𝐶𝑂 = 𝑘+𝐶𝑍𝐶𝐶𝑂 − 𝑘

−𝐶𝑍𝐶𝑂

𝑅𝐶𝑂𝐶𝐶𝑂≈ 𝑘+𝐶𝑍,𝑡𝑜𝑡 − 𝑘

−𝐶𝑍𝐶𝑂𝐶𝐶𝑂

State-altering trajectory

20/03/2013

𝑅𝐶𝑂 = 𝑘+𝐶𝑍𝐶𝐶𝑂 − 𝑘

−𝐶𝑍𝐶𝑂

𝑅𝐶𝑂 + 𝑘−𝐶𝑍𝐶𝑂𝐶𝐶𝑂

= 𝑘+𝐶𝑍,𝑡𝑜𝑡 − 𝑘+𝐶𝑍𝐶𝑂

Parameter estimation

20/03/2013

ME State-defining State-altering

N/A k+ k+

N/A k- k-

Keq Keq Keq

CZ,tot CZ,tot CZ,tot

Numerical example

20/03/2013

CO adsorption on Pt/Mg(Al)Ox (1 wt. % Pt)

Pulse-intensity range: Np,CO = 1 – 14.5nmolCO

Temperature range: T = 50 – 140 °C

20/03/2013

Estimated concentration of adsorption sites: CZ,tot = 0.3-0.55 (mmol/kgcat)

Estimated heat of CO adsorption: ΔHads= - 17.9 (kJ/molCO)

20/03/2013

TAP: New Results

• II. Independence of the final catalyst activity profile on the pulse procedure (AICHEJ, 2015,61,1, 31-35)

• The activity profile of a prepared catalytic system depends on the total amount of admitted substance. It does not depend on the pulse procedure whether it is a number of small pulses or one big pulse.

Uniqueness of the profile. It is based on two principles of uniqueness

• (I) At any position (longitudinal or radial) of the catalytic unit,

the final catalyst composition is uniquely defined by the

integral amount of gas substance concentrations related to the

given position.

This statement reflects a chemical feature. It is completely

independent of the fluid dynamics.

• (II) The integral amount of gas substance concentrations

related to the given position is uniquely defined by the total

amount of molecules admitted to the chemical reactor.

This statements reflects a specific hydrodynamic feature of our

device, viz the type of transport, boundary conditions etc

Computational and theoretical result

It was proven for different cases

• Longitudinal and radial profiles

• Non-porous and porous catalysts

• Mono-and bimolecular adsorption

• Different TAP-reactor configurations

(one zone; three-zone; thin-zone)

TAP: New Results on reaction-diffusion systems

(III) Optimal configuration of catalytic units

(Wallace, Feres, Yablonsky, 2015, submitted)

A. When catalytic activity (k) is sufficiently small, conversion is maximized by having all the catalytic particles (units) together right at the point of gas injection.

B. When k is very large, the optimal configuration for conversion approaches that in which the catalyst particles are equally spaced along the line of the reactor.

FUTURE

RATE–REACTIVITY MODEL

(Yablonsky, Redekop et al, submitted)

Rate-Reactivity Model (RRM):

a new basis for non-steady-state characterization of

heterogeneous catalysts

Catalysis is a complex phenomenon

• Multiple crystallographic phases

• Catalyst modifications by the reaction (phase transitions, coking, etc.)

• Emergent “true” active sites

• Hierarchy of meso- and nano-porous diffusions

The kinetic model must deal with two intersecting complexities:

Complexity of the material

Complexity of the reaction

• Multiple reaction pathways consisting of many reaction steps

• Energetically heterogeneous population of active sites

• Lateral interactions between adsorbed species

• Elemental transport at the molecular scale (spillover, surface/bulk exchange, etc.)

These interacting phenomena may not follow the “mass action law”

Catalytic kinetics: why?

mechanism

elucidation

materials

characterization

Kinetic data

kinetic

modeling

J. Hagens

G. B. Marin & G. S. Yablonsky

I. Chorkendorff & J.W. Niemantsverdriet

Edit. M. Che & J. C. Vedrine

Catalytic kinetics: how?

• Combinatorial screening

• High-throughput steady-state kinetics

• Non-steady-state (transient) kinetics

D. Farrusseng, Surface Science Reports 63 (2008) 487-513

M. Kramer, et al., Journal of Catalysis 251 (2007) 410

S. Senkan, Angewandte Chemie 40 (2001) 312-329

J.A. Moulijn, et al., Catalysis Today 81 (2003) 457-471

K. Metaxas, et al., Topics in Catalysis 53 (2010) 64-76

V. Prasad, et al., Chemical Engineering Science 65 (2010) 240-246

A.C. van Veen, et al., Journal of Catalysis 216 (2003) 135-143

R.J. Berger, et al., Applied Catalysis A: General 342 (2008) 3-28

G. Marin and G. Yablonsky, Kinetics of Chemical Reactions (2011) Wiley

Kinetic devices and the information they provide

recycle

feed product

(a) (b) (c) (d)

feed product(e)

catalyst zone

(f) (g) (h)

catalyst zone

recycle

feed product

recycle

feed product

(a) (b) (c) (d)

feed productfeed product(e)

catalyst zonecatalyst zone

(f) (g) (h)

catalyst zone

• Transport regimes:

Convection vs. diffusion

Well-defined vs. ill-defined

Achievable time resolution

Spatially uniform vs. non-uniform

Steady-state vs. non-steady-state

𝑗 = 𝑣𝐶

𝑗 = −𝐷𝛻𝐶

recycle

feed product

(a) (b) (c) (d)

feed product(e)

catalyst zone

(f) (g) (h)

catalyst zone

recycle

feed product

recycle

feed product

(a) (b) (c) (d)

(f) (g) (h)

catalyst zone

• Observable characteristics:

Transformation rates (CSTR, TZ TAP via Y-Procedure)

Surface concentrations (SSITKA, operando surface spectroscopies, e.g. IR)

Gas concentrations (most devices)

Bulk material properties (operando bulk spectroscopies, e.g. XAS)

rarely

accessible

commonly used

recycle

feed product

(a) (b) (c) (d)

feed product(e)

catalyst zone

(f) (g) (h)

catalyst zone

recycle

feed product

recycle

feed product

(a) (b) (c) (d)

(f) (g) (h)

catalyst zone

• Observable vs. non-observable surface characteristics:

Typically, many hypothetical intermediates are assumed (validity is questionable)

If non-steady-state rates are available, total surface uptakes can be computed

Chemical Kinetics.Textbook Knowledge

• Detailed mechanism is a set of elementary reactions. Typically, the mass-action-law is assumed.

• An example:Hydrogen Oxidation 2H2 +O2 = 2H2O

• 1)H2 + O2 = 2 OH ; 2) OH + H2= H2O + H ; 3) H + O2 = OH + O;

• 4) O + H2 = OH + H ; 5)O + H2O=2OH; 6) 2H + M = H2 + M ;7) 2O + M = O2 + M;

• 8)H + OH + M = H2O + M; 9) 2 OH + M = H2O2 + M;10) OH + O + M = HO2 + M;

• 11) H + O2 + M = HO2 + M; 12) HO2 + H2 = H2O2 + H;13)HO2 +H2 = H2O +OH;

Typical mechanism of the heterogeneous reaction

• Adsorbed mechanism (Langmuir’s mechanism)

• 1) 2 K + O2 2 KO

• 2) K + B KB

• 3) KO + KB 2 K + BO

• Overall reaction 2B+O2 KB (B is CO)

• Particular cases of this mechanisms are

Calculation of surface uptakes

• Instantaneous uptakes can be calculated from

the transient mass-balance of the catalyst surface

𝑼𝑿 𝒕 = 𝟎

𝑹𝑿+ 𝝉 𝒅𝝉 −

𝑹𝑿− 𝝉 𝒅𝝉

• Uptakes are history-dependent and characterize the catalyst state

• «Observable» uptakes vs. hypothetical surface

intermediates

Calculation of surface uptakes (best case scenario)

CO + ½ O2 = CO2

Impact mechanism(a.k.a. Eley-Rideal)

Adsorption mechanism(a.k.a. Langmuir-Hinshelwood)

• Generally, it is not possible to express individual surface concentrations

through gaseous rates (uptake ≠ intermediate).

• But when all elementary steps:1) Exchange molecules with the gas phase

2) Certain connectivity condition are fulfilled

It is possible to express surface concentrations

through a linear combination of gaseous reaction rates (uptake =

intermediate):

Temporal Analysis of Products (TAP):

Experiments and

Data Analysis

time, s

norm. exit flow,mol/s

reversible

irreversible

1. Primary information from moments:

𝑀𝑛 =

𝜏𝑒𝑛𝑑

𝐹𝑒𝑥𝑖𝑡 𝑡 ∙ 𝑡𝑛𝑑𝜏

• Conversion• Selectivity• Mean residence time• Apparent rate coefficients

3. Model-free analysis via the Y-Procedure:

2. Model regression:

• Parameter estimation for microkinetic models

Yablonsky, et al (2007), Redekop, et al (2011)

Balcaen, et al (2011)

Gleaves, et al (1997)

U(t)Surface uptake

Rate Reactivity Model (RRM)

Main idea

𝑹 𝒕 = 𝝍𝑪𝑪 𝒕 + 𝝍𝑼𝑼 𝒕 + 𝝍𝑪𝑼𝑪 𝒕 𝑼(𝒕)

• Phenomenological model relates rates, gas concentrations, and surface uptakes

• For one gas interacting with the catalyst:

gas-to-surface

«impact» interactions

surface-to-gas

«release» interactions(can have n>1 for uptake)

gas-to-surface

«complex» interactions

«Slow» or insignificant compositional changes are lumped into the reactivities 𝝍(slow intermediates, concentrations of active sites, other structural parameters)

«Fast» compositional changes are reflected for by the uptake terms

(short-lived and/or fast-accumulating intermediates)

Model properties

ALWAYS linear in parameters (i.e. empirical reactivities 𝝍)

Does not relay on detailed mechanism, but rather on general knowledge

(only monomolecular gas-to-surface steps, gas release from the surface)

Drastically simplified when the catalyst state is not changed

by the measurement (state-defining experiment)

The same (standard) form for all reactions

Shifts the focus from the process to material characterization

gas-to-surface

«impact» interactions

surface-to-gas

«release» interactions(can have n>1 for uptake)

gas-to-surface

«complex» interactions

efficient parameter estimation using linear methods

Estimation of reactivities

𝑹 (𝒕𝟏)𝑹 (𝒕𝟐)⋮𝑵𝒕×𝟏

=𝑪(𝒕𝟏) 𝑼(𝒕𝟏) 𝑪 𝒕𝟏 𝑼(𝒕𝟏)

𝑪(𝒕𝟐) 𝑼(𝒕𝟐) 𝑪 𝒕𝟐 𝑼(𝒕𝟐)⋮ ⋮ ⋮

𝑵𝒕×𝟑

𝝍𝑪

𝝍𝑼

𝝍𝑪𝑼

𝟑×𝟏

𝑹 = 𝑨𝚿

SVD(A)

𝑹 = 𝑼𝚺𝑽𝑻𝚿 𝚿 = 𝑽𝚺−𝟏𝑼𝑻𝑹

• Matrix notation

• Linear estimation based on Singular Value Decomposition (SVD)

• Only the most important SVD components can be preserved for filtering out noise

time, s0.1 0.2 0.3 0.4 0.5

RRM example (state-defining)

Np, mol/pulse 1e-8

Ns, mol/kg 1e-3

kads, 100

kads*Ns, 0.1

kdes, 1/s 10

simulatio

• Kinetics: 𝑅𝐴 = 𝑘𝑎𝑑𝑠 𝑁𝑆 − 𝐶𝐴𝑍 𝐶𝐴 − 𝑘𝑑𝑒𝑠𝐶𝐴𝑍

• Single-site reversible adsorption: A + Z = AZ

• For small CAZ (state-defining): 𝑅𝐴 ≈ 𝑘𝑎𝑑𝑠𝑁𝑆𝐶𝐴 − 𝑘𝑑𝑒𝑠𝐶𝐴𝑍

time, s0.1 0.2 0.3 0.4 0.5

RRM example (state-defining)

Np, mol/pulse 1e-8

Ns, mol/kg 1e-3

kads, 100

kads*Ns, 0.1

kdes, 1/s 10

ψ0 2.3e-6

ψc 0.094

ψu -10.5

simulatio

estimated RRM

coeffs.

• Kinetics: 𝑅𝐴 = 𝑘𝑎𝑑𝑠 𝑁𝑆 − 𝐶𝐴𝑍 𝐶𝐴 − 𝑘𝑑𝑒𝑠𝐶𝐴𝑍

• Single-site reversible adsorption: A + Z = AZ

• For small CAZ (state-defining): 𝑅𝐴 ≈ 𝑘𝑎𝑑𝑠𝑁𝑆𝐶𝐴 − 𝑘𝑑𝑒𝑠𝐶𝐴𝑍

or in the RRM form 𝑅𝐴 ≈ 𝜓𝐶𝐶𝐴 + 𝜓

𝑈𝑈𝐴

𝑭𝑨 (𝒕)

𝑪𝑨 𝒕 ,

𝑹𝑨 (𝒕)

𝑼𝑨(𝒕)

Quantity

• For small perturbations,

only two RRM terms are required! 𝑅𝐴𝑑𝑡

Operation

𝑅𝑅𝑀

Generalization

𝑹𝒊 𝒕 =

𝒌=𝟏

𝝍𝒊,𝒌𝑪 𝑪𝒌 𝒕 +

𝒋=𝟏

𝝍𝒊,𝒋𝑼𝑼𝒋 𝒕 +

𝒌=𝟏

𝒋=𝟏

𝝍𝒊,𝒌,𝒋𝑪𝑼 𝑪𝒌 𝒕 𝑼𝒋 𝒕

• For many gases interacting with the catalyst:

The rate for every gas may depend on concentrations and uptakes of all

other gases Is it rigorously equivalent to microkinetics for (pseudo)monomolecular

mechanisms?

RRM example (complex)

Further generalization

𝑹𝒊 𝒕 =

𝒌=𝟏

𝝍𝒊,𝒌𝑪 𝑪𝒌 𝒕 +

𝒋=𝟏

𝝍𝒊,𝒋𝑼𝑼𝒋 𝒕 +

𝒌=𝟏

𝒋=𝟏

𝝍𝒊,𝒌,𝒋𝑪𝑼 𝑪𝒌 𝒕 𝑼𝒋 𝒕 +

𝒍=𝟏

𝒋=𝟏

𝝍𝒊,𝒍,𝒋𝑼𝑼𝑼𝒍 𝒕 𝑼𝒋 𝒕 + 𝝍𝒊,𝟎

surface-surface

interactions

zeroth term

constant emmision of the gas

(e.g. catalyst decomposition)

General strategy for systematic characterization

1. Individual reactants and products

2. Multiple reactants and reactants/products together

• Simultaneous pulsing of multiple gases

• Controlled time delay (pump-probe)

• Isotopic labeling

• State-defining experiments

• Titration and state-altering experiments (e.g. Momentary Equilibrium)

• Variable pulsing frequency (exchange with the bulk? spillover?)

• The influence of pretreatments

• Establish the scale of catalyst states (oxidation degree, coking, etc.)

3. Incremental characterization and mechanism refinement

• Coherency between different characteristics

• Decision trees to guide further experiments

• Classical parameter estimation and model discrimination

Conclusions

1. A novel phenomenological form of kinetic models is suggested

for systematic non-steady-state catalyst characterization

2. This Rate-Reactivity-Model (RRM) is always linear in parameters

3. The focus is on the material characterization,

one well-defined catalyst state at the time

4. The model is drastically simplified for state-defining experiments

5. Numerical examples are given for reversible adsorption

Strategies of Catalyst Kinetic Characterization

PropertiesApplied Kinetics

Surface Science

TAP State-by-State

Transient

ScreeningCSTR PFR

Domain of

working

conditions

Normal Conditions

High and ultra-

high vacuum

conditions

The top of the

surface science

domain

(10-1-10-2 Pa)

Information

about multi-

component

industrial

catalysts

provides provides does not provide provides

Observation

Regimesteady-state

steady-state and

unsteady-state

steady-state and

unsteady-stateunsteady-state

Separation of

the chemical

reaction and

transport

Well-defined

convection and

perfect mixing are

assumed (the validity

domains are

discussed)

Well-defined

convection

Direct

measurements of

the chemical

reaction rate

(convective

transport is

eliminated)

Well-defined

diffusion

Knudsen diffusion

regime

(convection is

eliminated)

Surface Science

TAP State-by-State

Transient

ScreeningCSTR PFR

Catal. Compo-

sition in a sin-

gle unsteady-

state exp.

The catalyst composition does change, but

this change is not measured

The change of

catalyst com-

position is directly

observed

of the catalyst

composition

Uniformity of

the catalyst

composition

within the

reaction zone

Uniformity is

assumed under

steady-state

conditions

There is axial non-

uniformity

(radial non-

uniformity is

neglected)

Surface

concentration

profiles can be

directly

characterized

The catalyst

composition is

uniform

Amount of gas

reactants stored

or released by

the catalyst

Are measured by

SSITKA-method

(typically, not

reliable)

Are measured by

SSITKA-method

(reliable for the

steady-state)

Directly measured

Directly measured in

a multi-pulse TAP

experiment

Model-free

analysis (no

assumption

about detailed

kinetic model)

Steady-state data can be analyzed in a

model-free manner, but

nonsteady-state data cannot be

For different

techniques, the

analysis can be

either model-free

or not

Model-free analysis

is possible

continued

CONCLUSIONS

A BRIDGE ACROSS THE “PRESSURE-GAP”:

TAP is waiting for you at this BRIDGE !

• BACK TO HISTORY…

• BACK TO CELEBRITIES…

Isaac Newton (1743-1727)

Gottfried Wilhelm Leibnitz (1646-1716)

‘Drop-by-drop’: titration,determination of the equivalent point

The origins of volumetric analysis are in late-18th-century French chemistry. Francois Antoine Henri Descroizilles developed the first burette (which looked more like a graduated cylinder) in 1791. Joseph Louis Gay-Lussac developed an improved version of the burette that included a side arm, and coined the terms "pipette" and "burette" in an 1824 paper on the standardization of indigo solutions

Manfred Eigen (1927): Chemical relaxation, but not calculus

Experimental calculus in chemistry: John T. Gleaves

Gregory S. Yablonsky

“It has seen further it is by standing on the

shoulders of giants”

(Isaac Newton,

Letter to Robert Hook, February 1676)

Acknowledgements

John Gleaves

Denis Constales

Guy Marin

THANK YOU

FOR YOUR ATTENTIVE PATIENCE !

Questions & Answers

Cg = 0

Fexit (t)

Finlet(t)

CgTZ(ω)RTZ(ω)

Thin catalytic zone

Inert zone Inert zone

CgTZ(t)RTZ(t)

F F T F F T F F T

I F FT I F FT

Solving inverse diffusion problemin two inert zones

Reconstructed kinetically model-freecharacteristics in the time domain

4 linear eqns. (2 for each zone)7 vector-variables (4 unknowns)

Yablonsky et al. Chem. Eng. Sci., 2007, 62, 6754-6767

Phenomenological representation of the transformation rate

The ‘Rate-Reactivity’Model (RRM)Rgi = ∑Rj (CM, , CMOx, Cad, NS, T) Cgj

+ Roj (CM, CMOx, Cad, NS, T) Ri, Roj are catalyst reactivities.Catalyst reactivities Ri and Roi are functions of intermediate concentrations. The last ones can be estimated as (Integral uptake ofreactants – Integral release of products)

Surface Science

TAP State-by-State

Transient

ScreeningCSTR PFR

Domain of

working

conditions

Normal Conditions

High and ultra-

high vacuum

conditions

The top of the

surface science

domain

(10-1-10-2 Pa)

Information

about multi-

component

industrial

catalysts

provides provides does not provide provides

Observation

Regimesteady-state

steady-state and

unsteady-state

steady-state and

unsteady-stateunsteady-state

Separation of

the chemical

reaction and

transport

Well-defined

convection and

perfect mixing are

assumed (the validity

domains are

discussed)

Well-defined

convection

Direct

measurements of

the chemical

reaction rate

(convective

transport is

eliminated)

Well-defined

diffusion

Knudsen diffusion

regime

(convection is

eliminated)

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