temporal analysis of products(tap)- approach: theory and ...temporal analysis of...
TRANSCRIPT
![Page 1: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/1.jpg)
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)
![Page 2: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/2.jpg)
or Chemical Calculus
Gregory YablonskyParks College, Department of Chemistry, Saint Louis University
![Page 3: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/3.jpg)
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
![Page 4: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/4.jpg)
• Experimental Devices of Chemical Kinetics
![Page 5: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/5.jpg)
temporal change of transport change due to
amount of component change reaction
![Page 6: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/6.jpg)
Typical Requirements to Kinetic Experiments:
• Isothermicity
• Intensive heat exchange with surroundings
• Dilution of reactive medium
• Rapid recirculation
• Uniformity of the chemical composition
• Intensive mixing
![Page 7: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/7.jpg)
G.B. Marin & G.S. Yablonsky (2011). Kinetics of Chemical Reactions. Decoding
Complexity 7
Reactors for Kinetic Experiments
feed product feed product
recycle
feed product feed product
catalyst zone
Batch reactor CSTR Continuous-flow reactor with
recirculation
PFR Differential PFR
![Page 8: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/8.jpg)
G.B. Marin & G.S. Yablonsky (2011). Kinetics of Chemical Reactions. Decoding
Complexity 8
Reactors for Kinetic Experiments
catalyst zone
inert
zone
Convectional pulse
reactor
Diffusional pulse
reactor / TAP
reactor
Thin-zone TAP
reactor
![Page 9: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/9.jpg)
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)
![Page 10: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/10.jpg)
10
G.B. Marin & G.S. Yablonsky (2011). Kinetics of Chemical
Reactions. Decoding Complexity
Types of Temporal Evolution Relaxation
c
t
c
t
c
t
slowintermediate
fast
Simple exponential relaxation Relaxation with induction period
Relaxation of different components at different time scales
![Page 11: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/11.jpg)
11
G.B. Marin & G.S. Yablonsky (2011). Kinetics of Chemical
Reactions. Decoding Complexity
Types of Temporal Evolution Relaxation
c
t
3
2
1
Relaxation with “overshoots” (1) & (3) and start in “wrong” direction
(2)
![Page 12: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/12.jpg)
12
G.B. Marin & G.S. Yablonsky (2011). Kinetics of Chemical
Reactions. Decoding Complexity
Types of Temporal Evolution Relaxation
c
t
I
II
c
t
Relaxation with different steady states
Damped oscillations
![Page 13: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/13.jpg)
Belousov-Zhabotinsky reaction
![Page 14: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/14.jpg)
14
G.B. Marin & G.S. Yablonsky (2011). Kinetics of Chemical
Reactions. Decoding Complexity
Types of Temporal Evolution Relaxation
c
t
c
t
Regular oscillations around a
steady state
Chaotic oscillations
![Page 15: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/15.jpg)
Anatoly Zhabotinsky (1938 – 2008)
![Page 16: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/16.jpg)
Gerhard Ertl (1936 - )
![Page 17: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/17.jpg)
Progress in time resolutionfor 150 years
• From second to femptoseconds (10 -15 sec)
![Page 18: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/18.jpg)
G.B. Marin & G.S. Yablonsky (2011). Kinetics of Chemical Reactions. Decoding
Complexity 18
Non-Steady-State Models
,d
fdt
c
c k
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
![Page 19: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/19.jpg)
Rutherford Aris (1929 – 2005)
![Page 20: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/20.jpg)
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
![Page 21: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/21.jpg)
Founders of infinitesimal calculus: Newton and Leibnitz
![Page 22: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/22.jpg)
Isaac Newton (1743-1727)
![Page 23: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/23.jpg)
Gottfried Wilhelm Leibnitz (1646-1716)
![Page 24: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/24.jpg)
‘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
![Page 25: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/25.jpg)
Manfred Eigen (1927): Chemical relaxation, but not calculus
![Page 26: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/26.jpg)
Experimental calculus in chemistry: John T. Gleaves
![Page 27: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/27.jpg)
• 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)
![Page 28: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/28.jpg)
TC
Pulse valve
Microreactor
Mass spectrometer
Catalyst
Vacuum (10-8 torr)
Reactantmixture
0.0 time (s) 0.5
Exit
flo
w (
F A)
Inert
Reactant
Product
Continuous flow valve
TAP Reactor System-Overview
![Page 29: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/29.jpg)
TAP-3 System
![Page 30: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/30.jpg)
IR Probe
and
Reactor
New Developments in TAP Instrumentation
Aiming
towards
‘kinetically
appropriate’
operando
reactors
![Page 31: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/31.jpg)
Measuring Intrinsic Kinetic Characteristicswith Probe Molecules
Pulse valve
Mass spectrometer
Molecular beam
Scattered beam
P ≈ 10-9 Pa
Target
(a)
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.
![Page 32: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/32.jpg)
Measuring Intrinsic Kinetic Characteristicswith Probe Molecules
Pulse valve
Mass spectrometer
Molecular beam
Scattered beam
P ≈ 10-9 Pa
Target
(a)
Differentially pumped
vacuum system
Molecular Beam Scattering – MBS experiment – Inspiration for TAP
Multi-component
Polycrystalline
Multiphasic
Heterogeneous Surface
Defects
Changes with Reaction
Practical Catalyst
(Complex Particles)
![Page 33: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/33.jpg)
Measuring Intrinsic Kinetic Characteristicswith Probe Molecules
Pulse valve
Mass spectrometer
Molecular beam
Scattered beam
P ≈ 10-9 Pa
Target
(a)
Differentially pumped
vacuum system
Pulse valve
Mass
spectrometer
Reaction zone
Catalyst sampleExit flow
P ≈ 10-7 Pa
(b)
Input pulse
Molecular Beam Scattering – MBS experiment
Temporal Analysis of Products - TAP experiment
![Page 34: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/34.jpg)
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
![Page 35: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/35.jpg)
Small number of pulses
Insignificant change
0.0
State-defining Experiment
State-Defining & State-Altering Experiment
Inert Reactant Product
Large number of pulses0.0
State-altering Experiment
TAP Multipulse Experiment Combines
![Page 36: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/36.jpg)
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
![Page 37: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/37.jpg)
• 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)
![Page 38: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/38.jpg)
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
![Page 39: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/39.jpg)
![Page 40: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/40.jpg)
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
![Page 41: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/41.jpg)
Thin Zone TAP experiments
![Page 42: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/42.jpg)
Thin-zone and Single Particle Reactor Configurations
Thin-zone
Single-particle
![Page 43: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/43.jpg)
QUALITATIVE ANALYSIS
![Page 44: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/44.jpg)
ÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉ
ÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉ
ÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉ
ÉÉÉÉÉÉÉÉÉÉÉÉÉ
ÉÉÉÉÉÉÉÉÉÉÉ
ÉÉÉÉÉÉÉÉÉ
ÉÉÉÉÉÉÉÉÉÉÉ
ÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉ
ÉÉ
É
É
É
É
É
É
É
É
É
É
É
ÉÉÉÉ ÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉ
ÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉ
ÉÉÉÉÉÉÉÉÉÉÉ
ÉÉÉÉÉÉÉÉÉ
ÉÉÉÉÉÉÉÉÉ
ÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉ
ÉÉÉÉ
É
É
É
É
É
ÉÉÉÉÉÉÉ
-0.1
0.1
0.3
0.5
0.7
0.9
1.1
0.0 0.1 0.2 0.3 0.4 0.50.5time(s)
Argon
Butane Response after Reaction
Rel
ativ
e Fl
ow
Experimental and Predicted ResponsesArgon and Butane Pulsed over VPO
0.5time(s)
No
rmal
ized
Flo
w
Experimental and Predicted Responses Argon Pulsed over Quartz Particles
440400
360320
280
Temp.time (s)
1.0
Rel
ativ
e In
ten
s.
0.0
0.1
Non-uniformity along the catalyst bed was produced in multi-pulse experiment
porosity
bCA
t DeA
2CA
z2 ka CA*
Transport + Irreversible Adsorption
Standard Diffusion Curve
diffusivity
Experimental and predicted responsesButane pulsed over oxygen treated VPO
![Page 45: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/45.jpg)
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)
![Page 46: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/46.jpg)
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
![Page 47: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/47.jpg)
Wavelength time (s)
Vacuum Transformation of
Oxygen-treated (VO)2P2O7
Probe Molecules Indicate Kinetic Effects of
Structural Change
![Page 48: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/48.jpg)
Activity-Structure Relationship for Complex Catalysts
Intrinsic kinetic
measurements
![Page 49: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/49.jpg)
Techniques for Intraparticle Transport
• PFG NMR
• Quasi-elastic Neutron Scattering
• Single crystal membranes
• Zero Length Chromatography
• Frequency Response
• TAP
![Page 50: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/50.jpg)
Techniques for Intraparticle Transport
• 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.
![Page 51: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/51.jpg)
Techniques for Intraparticle Transport
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.
![Page 52: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/52.jpg)
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
![Page 53: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/53.jpg)
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
![Page 54: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/54.jpg)
Unique Experiments with TAP
• Pump/Probe format
• Intraparticle transport at low pore occupancy
![Page 55: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/55.jpg)
Pump/Probe FormatSeparation of 2 Reactants
Reactant A (e.g.
NO)
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?
![Page 56: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/56.jpg)
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
![Page 57: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/57.jpg)
TAP-DATA QUANTITATIVE ANALYSIS
![Page 58: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/58.jpg)
Inert zone Catalyst zone
Thin-Zone TAP -Reactor (TZTR) Idea
Dimensionless Axial Coordinate
Dim
en
sion
less
Gas
Con
cen
trati
on
0.0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.00.00
.25
.50
.75
1.00
1.25
1.50
1.75
2.00
Vacuum
![Page 59: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/59.jpg)
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
Inert zone Catalyst zone
![Page 60: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/60.jpg)
TZTR vs CSTR
CSTR: SRVCVC 0 Uniformity is achieved by convective
mixing
X kappres, cat
diff
1 kappres, cat
diffConversion
Apparent rate constant
Diffusional residence time in catalyst zone
In TZTR uniformity is insured by diffusion
TZcat
Lx
II
Lx
I RLx
txCD
x
txCD
TZTZ
),(),(TZTR:
![Page 61: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/61.jpg)
TZTR vs Differential PFR
TZTRDifferential PFR:
Conversion vs Non-Uniformity
x
Cx
C
Xg
g
g
g
C
CX
TAP: Diffusion SRx
CDV
t
CV rg
2
2
PFR: Convection SRx
Cv
t
CVg
Provides Uniformity at X ≤ 20% Provides Uniformity
at X ≤ 80%
Convectional Flow = Diffusional Flow = gVC
x
CD
g
Cg
Cg 2Lc
Lr
X
1 (1 X)LrLc
Shekhtman S.O., Yablonsky G.S. Ind. Eng. Chem. Res. 44 (2005) 6518-6522.
![Page 62: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/62.jpg)
2) Moment analysis
1) Curve fitting
time
mol/s
× 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)
![Page 63: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/63.jpg)
Curve Fitting
A drawback is that it relies on the
a priori assumed mechanism
![Page 64: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/64.jpg)
MOMENT ANALYSIS
![Page 65: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/65.jpg)
1000
2000
3000
4000
5000
6000
10000
time(s)
PulseNumber
M0 Fexit (t )dt
0
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.
![Page 66: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/66.jpg)
“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)
![Page 67: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/67.jpg)
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
![Page 68: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/68.jpg)
Apparent Kinetic Constants and TOF
for Furan Oxidation as a Function of Oxidation State
0
200
400
600
800
1000
1200
1400
1600
00.20.40.60.81
Furan
MA
CO2
AC
Catalyst Oxidation Degree
Ap
pare
nt
Kin
eti
c C
on
sta
nt,
r0 , (
1/s
)
0
200
400
600
800
1000
1200
1400
1600
00.20.40.60.81
Furan
MA
CO2
AC
Catalyst Oxidation DegreeN
on
-Ste
ad
y-S
tate
TO
F,
Ap
pare
nt
Co
nsta
nt
/Ox
idati
on
De
gre
e,
(1/s
)
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
![Page 69: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/69.jpg)
Apparent Time Delays
0.0
0.5
1.0
1.5
2.0
2.5
00.20.40.60.81
Furan
MA
CO2
AC
Catalyst Oxidation Degree
Appare
nt
Tim
e D
ela
y, |r
2/r
1|,
(s)
For all reactants, apparent time delays are different.
At least four intermediates can be involved
![Page 70: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/70.jpg)
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.
![Page 71: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/71.jpg)
A drawback of the moment analysis
The moment analysis uses the
information which is averaged
within the pulse
![Page 72: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/72.jpg)
Kinetically model-free analysis
Y-PROCEDURE
![Page 73: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/73.jpg)
Kinetic Model-Free Analysis
Reactor Model:
Accumulation - Transport Term = Reaction Rate
Batch Reactor: Non SRdt
dCVg
CSTR: Convection SRCCVdt
dCVg )( 0
TAP: Diffusion SRx
CDV
t
CV rg
2
2
PFR: Convection SRx
Cv
t
CVg
![Page 74: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/74.jpg)
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
![Page 75: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/75.jpg)
• 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
![Page 76: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/76.jpg)
2
2
x
CD=
t
C
0=xδ=C(x,0) 0=t)(0,x
CD
0=t)C(L,t)(L,x
CD=F
0=x
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)
![Page 77: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/77.jpg)
2
2
x
CD=
t
C
I
II)NR(C,=
x
CD+
x
CD Z
III
C=C=C III
)NR(C,=dt
dNZ
Z
0=xδ=C(x,0) 0=t)(0,x
CD
0=t)C(L,t)(L,x
CD=F
0=x
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
![Page 78: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/78.jpg)
Calculating surface concentrations (instantaneous storages)as a transient difference between total uptake and release
Uptake Release
dτ(τRνRelease(t)Uptake(t)(t)C
t
0 i
iiS )
![Page 79: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/79.jpg)
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.
![Page 80: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/80.jpg)
The Y-Procedure analysis provides us with:
• 'Model free' transient kinetics
• Millisecond time resolution
• 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)
![Page 81: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/81.jpg)
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?
![Page 82: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/82.jpg)
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
Simu
lation
Reco
nstru
ctionExample (Np = 5·10-10 mol/pulse)
![Page 83: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/83.jpg)
Irreversible adsorption: Trajectories in the rate/composition space,i.e R(t) vs. CA(t) vs. CZA(t), for different pulse intensities
Np
↑
t
Characteristic surface defined by R(Cg,CS)
Reaction rate
Surface concentration
Gas concentration
![Page 84: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/84.jpg)
Np
↑
t
Characteristic surface defined by R(Cg,CS)
Irreversible adsorption: State-defining experiment (small pulse)
Np = 1·10-10 mol/pulse
totZ,app kC=k
AtotZ,A CkCR
![Page 85: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/85.jpg)
Np
↑
t
Characteristic surface defined by R(Cg,CS)
Irreversible adsorption: State-altering experiment (big pulse)
Np = 4·10-9 mol/pulse
AAZtotZ,A )CCk(C=R
![Page 86: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/86.jpg)
Np
↑
t
Characteristic surface defined by R(Cg,CS)
Irreversible adsorption: State-altering experiment (big pulse)
Np = 4·10-9 mol/pulse
k
totZ,C
AZtotZ,
A
A kCkC=C
R
![Page 87: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/87.jpg)
Np
↑
t
Characteristic surface defined by R(Cg,CS)
Irreversible adsorption: Multi-pulse experiment (series of small pulses)
Np = 1·10-10 mol/pulse
AappA CkR
ZAtotZ,app kCkCk
![Page 88: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/88.jpg)
Np
↑
t
Characteristic surface defined by R(Cg,CS)
Irreversible adsorption: Multi-pulse experiment (series of small pulses)
Np = 1·10-10 mol/pulse
AappA CkR
ZAtotZ,app kCkCk
![Page 89: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/89.jpg)
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
Simu
lation
Reco
nstru
ction
Example (Np = 5·10-10 mol/pulse)
![Page 90: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/90.jpg)
Reversible adsorption: Trajectories for different pulse intensities
Np
↑
t
Surface defined by R(Cg,CS)=0
Gas rate
Surface concentration
Gas concentration
![Page 91: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/91.jpg)
Reversible adsorption: State-defining experiment (small pulse)
Np
↑
t
Surface defined by R(Cg,CS)=0
Np = 1·10-10 mol/pulse
Plane trajectory:
totZ,Ck
k
A
AZtotZ,
+
A
A
C
CkCk
C
R
![Page 92: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/92.jpg)
Reversible adsorption: State-altering experiment (big pulse)
Np
↑
t
Surface defined by R(Cg,CS)=0
Np = 1·10-8 mol/pulse
k
totZ,C
Non-plane trajectory:
AZ
+
totZ,
+
A
AZA CkCk=C
CkR
![Page 93: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/93.jpg)
Reversible adsorption: Transient Equilibrium
Np
↑
t
Surface defined by R(Cg,CS)=0
Isotherm (Rads = Rdes)
eqeqA,
eqA,totZ,
eqAZ,1/K+C
CC=C
![Page 94: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/94.jpg)
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
known
![Page 95: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/95.jpg)
CO + Z CO
ZCOCOZCOtotZ,
+
CO Ck)CC(Ck=R
k+
→←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)
![Page 96: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/96.jpg)
CO + Z COk+
→←k-
Application to CO adsorption on Pd: Experimental results for a reversible adsorption
7101
8105
8101
9105
3totZ,m
mol5C
40Keq
Isotherm fitting:
![Page 97: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/97.jpg)
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
t
0
COCOZCO 2))
t
0
COOZO dτ(τR(τ(2R(t)C22
)))
![Page 98: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/98.jpg)
Step 1: Directly comparing rates in a state-defining experiment
![Page 99: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/99.jpg)
Step 2: Testing coherency of the entire data set (time invariant parameters)
Apparent kinetic parameters:
![Page 100: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/100.jpg)
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
![Page 101: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/101.jpg)
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
![Page 102: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/102.jpg)
Thin-zone and Single Particle Reactor Configurations
Thin-zone
Single-particle
![Page 103: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/103.jpg)
Inert zone Catalyst zone
Thin-Zone TAP -Reactor (TZTR) Idea
Dimensionless Axial Coordinate
Dim
en
sion
less
Gas
Con
cen
trati
on
0.0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.00.00
.25
.50
.75
1.00
1.25
1.50
1.75
2.00
Vacuum
![Page 104: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/104.jpg)
The Y-Procedure analysis provides us with:
• 'Model free' transient kinetics
• Millisecond time resolution
•
![Page 105: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/105.jpg)
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).
pi
Cs
![Page 106: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/106.jpg)
Introduction
106NASCRE-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).
• Measuring the concentration of adsorption sites by
reversible chemisorption under realistic operating temperatures and
non-steady-state conditions presents a significant challenge.
pi
Cs
![Page 107: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/107.jpg)
Outline
107NASCRE-3, Houston, TX,
20/03/2013
•
• TAP experiments and data analysis
• Momentary Equilibrium
• Pulse-Intensity Modulation
• Experimental example
• Conclusions
![Page 108: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/108.jpg)
Outline
108NASCRE-3, Houston, TX,
20/03/2013
• Introduction
• TAP experiments and data analysis
• Momentary Equilibrium
• Pulse-Intensity Modulation
• Experimental example
• Conclusions
![Page 109: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/109.jpg)
Outline
109NASCRE-3, Houston, TX,
20/03/2013
• Introduction
• TAP experiments and data analysis
• Momentary Equilibrium
• Pulse-Intensity Modulation
• Experimental example
• Conclusions
![Page 110: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/110.jpg)
Thin-Zone (TZ) Temporal Analysis of Products (TAP)
110NASCRE-3, Houston, TX,
20/03/2013
timeQMStime
Inlet pulse Exit flow
pulse valve
catalyst
inert
thermocouple
Fexit(t)Finlet(t)
J. T. Gleaves et al. (2010)
![Page 111: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/111.jpg)
Thin-Zone (TZ) Temporal Analysis of Products (TAP)
111NASCRE-3, Houston, TX,
20/03/2013 111
timeQMStime
Inlet pulse Exit flow
pulse valve
catalyst
inert
thermocouple
Fexit(t)Finlet(t)
Cg(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)
![Page 112: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/112.jpg)
Outline
112NASCRE-3, Houston, TX,
20/03/2013
• Introduction
• TAP experiments and data analysis
• Momentary Equilibrium
• Pulse-Intensity Modulation
• Experimental example
• Conclusions
![Page 113: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/113.jpg)
Case study
113NASCRE-3, Houston, TX,
20/03/2013
CO + Z ZCOk+
k-
𝐾𝑒𝑞 =𝑘+
𝑘−
Single-site CO adsorption:
![Page 114: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/114.jpg)
Case study
114NASCRE-3, Houston, TX,
20/03/2013
CO + Z ZCOk+
k-
𝐾𝑒𝑞 =𝑘+
𝑘−
𝑅𝐶𝑂 = −𝑑𝐶𝐶𝑂𝑑𝑡= 𝑘+𝐶𝑍𝐶𝐶𝑂 − 𝑘
−𝐶𝑍𝐶𝑂 =
= 𝑘+(𝐶𝑍,𝑡𝑜𝑡−𝐶𝑍𝐶𝑂)𝐶𝐶𝑂 − 𝑘−𝐶𝑍𝐶𝑂
Single-site CO adsorption:
• Kinetics is governed by
![Page 115: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/115.jpg)
Case study
115NASCRE-3, Houston, TX,
20/03/2013
CO + Z ZCOk+
k-
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
Single-site CO adsorption:
• Kinetics is governed by
• Surface CO uptake can be obtained as
𝐶𝑍𝐶𝑂(𝑡) = 0
𝑡
𝑅𝐶𝑂 𝑡′ 𝑑𝑡′
![Page 116: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/116.jpg)
Intra-pulse kinetic characteristics
116NASCRE-3, Houston, TX,
20/03/2013
Pulse-response experiment
in TZ TAP microreactor
RC
O,
(mm
ol/
kg
cat/s
)
CC
O,
(mm
ol/
m3)
CZ
CO,
(mm
ol/
kg
cat)
t, (s)
RCO
CZCO…
CCO
![Page 117: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/117.jpg)
Momentary Equilibrium (ME)
117NASCRE-3, Houston, TX,
20/03/2013
Pulse-response experiment
in TZ TAP microreactor
RC
O,
(mm
ol/
kg
cat/s
)
CC
O,
(mm
ol/
m3)
CZ
CO,
(mm
ol/
kg
cat)
ME
t, (s)
RCO
CZCO…
CCO
𝑅𝐶𝑂 𝑡 = 0 → 𝑟+ = 𝑟−
![Page 118: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/118.jpg)
Momentary Equilibrium (ME)
118NASCRE-3, Houston, TX,
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?
![Page 119: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/119.jpg)
Outline
119NASCRE-3, Houston, TX,
20/03/2013
• Introduction
• TAP experiments and data analysis
• Momentary Equilibrium
• Pulse-Intensity Modulation
• Experimental example
• Conclusions
![Page 120: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/120.jpg)
Pulse-Intensity Modulation
120NASCRE-3, Houston, TX,
20/03/2013
𝐶𝑍𝐶𝑂,𝑀𝐸 =𝐾𝑒𝑞𝐶𝑍,𝑡𝑜𝑡𝐶𝐶𝑂,𝑀𝐸
1 + 𝐾𝑒𝑞𝐶𝐶𝑂,𝑀𝐸
Langmuir isotherm:
![Page 121: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/121.jpg)
Pulse-Intensity Modulation
121NASCRE-3, Houston, TX,
20/03/2013
𝐶𝑍𝐶𝑂,𝑀𝐸 =𝐾𝑒𝑞𝐶𝑍,𝑡𝑜𝑡𝐶𝐶𝑂,𝑀𝐸
1 + 𝐾𝑒𝑞𝐶𝐶𝑂,𝑀𝐸
Langmuir isotherm:
Fexit(t)
t, (s)
Np,CO
![Page 122: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/122.jpg)
Outline
122NASCRE-3, Houston, TX,
20/03/2013
• Introduction
• TAP experiments and data analysis
• Momentary Equilibrium
• Pulse-Intensity Modulation
• Experimental example
• Conclusions
![Page 123: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/123.jpg)
Experimental example
123NASCRE-3, Houston, TX,
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
![Page 124: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/124.jpg)
Experimental example
124NASCRE-3, Houston, TX,
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)
![Page 125: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/125.jpg)
Rate-concentration trajectories
125NASCRE-3, Houston, TX,
20/03/2013
t, (s)
RCO
CZCO
CCO
![Page 126: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/126.jpg)
State-defining trajectory
126NASCRE-3, Houston, TX,
20/03/2013
𝑅𝐶𝑂 = 𝑘+𝐶𝑍𝐶𝐶𝑂 − 𝑘
−𝐶𝑍𝐶𝑂
𝑅𝐶𝑂𝐶𝐶𝑂≈ 𝑘+𝐶𝑍,𝑡𝑜𝑡 − 𝑘
−𝐶𝑍𝐶𝑂𝐶𝐶𝑂
![Page 127: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/127.jpg)
State-altering trajectory
127NASCRE-3, Houston, TX,
20/03/2013
𝑅𝐶𝑂 = 𝑘+𝐶𝑍𝐶𝐶𝑂 − 𝑘
−𝐶𝑍𝐶𝑂
𝑅𝐶𝑂 + 𝑘−𝐶𝑍𝐶𝑂𝐶𝐶𝑂
= 𝑘+𝐶𝑍,𝑡𝑜𝑡 − 𝑘+𝐶𝑍𝐶𝑂
![Page 128: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/128.jpg)
Parameter estimation
128NASCRE-3, Houston, TX,
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
![Page 129: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/129.jpg)
Numerical example
129NASCRE-3, Houston, TX,
20/03/2013
![Page 130: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/130.jpg)
Experimental example
130NASCRE-3, Houston, TX,
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
![Page 131: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/131.jpg)
Experimental example
131NASCRE-3, Houston, TX,
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)
![Page 132: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/132.jpg)
Q&A
132NASCRE-3, Houston, TX,
20/03/2013
![Page 133: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/133.jpg)
TAP: New Results
• II. Independence of the final catalyst activity profile on the pulse procedure (AICHEJ, 2015,61,1, 31-35)
![Page 134: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/134.jpg)
• 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.
![Page 135: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/135.jpg)
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
![Page 136: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/136.jpg)
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)
![Page 137: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/137.jpg)
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.
![Page 138: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/138.jpg)
FUTURE
RATE–REACTIVITY MODEL
(Yablonsky, Redekop et al, submitted)
![Page 139: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/139.jpg)
![Page 140: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/140.jpg)
Rate-Reactivity Model (RRM):
a new basis for non-steady-state characterization of
heterogeneous catalysts
![Page 141: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/141.jpg)
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”
![Page 142: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/142.jpg)
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
![Page 143: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/143.jpg)
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
![Page 144: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/144.jpg)
Kinetic devices and the information they provide
feed product feed product
recycle
feed product
(a) (b) (c) (d)
feed product(e)
catalyst zone
(f) (g) (h)
catalyst zone
inert
zone
feed product feed product
recycle
feed product
recycle
feed product
(a) (b) (c) (d)
feed productfeed product(e)
catalyst zonecatalyst zone
(f) (g) (h)
catalyst zone
inert
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
![Page 145: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/145.jpg)
Kinetic devices and the information they provide
feed product feed product
recycle
feed product
(a) (b) (c) (d)
feed product(e)
catalyst zone
(f) (g) (h)
catalyst zone
inert
zone
feed product feed product
recycle
feed product
recycle
feed product
(a) (b) (c) (d)
feed productfeed product(e)
catalyst zonecatalyst zone
(f) (g) (h)
catalyst zone
inert
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
![Page 146: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/146.jpg)
Kinetic devices and the information they provide
feed product feed product
recycle
feed product
(a) (b) (c) (d)
feed product(e)
catalyst zone
(f) (g) (h)
catalyst zone
inert
zone
feed product feed product
recycle
feed product
recycle
feed product
(a) (b) (c) (d)
feed productfeed product(e)
catalyst zonecatalyst zone
(f) (g) (h)
catalyst zone
inert
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
![Page 147: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/147.jpg)
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;
![Page 148: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/148.jpg)
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
![Page 149: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/149.jpg)
Calculation of surface uptakes
• Instantaneous uptakes can be calculated from
the transient mass-balance of the catalyst surface
𝑼𝑿 𝒕 = 𝟎
𝒕
𝑹𝑿+ 𝝉 𝒅𝝉 −
𝟎
𝒕
𝑹𝑿− 𝝉 𝒅𝝉
• Uptakes are history-dependent and characterize the catalyst state
• «Observable» uptakes vs. hypothetical surface
intermediates
![Page 150: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/150.jpg)
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):
![Page 151: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/151.jpg)
Temporal Analysis of Products (TAP):
Experiments and
Data Analysis
time, s
norm. exit flow,mol/s
inert
reversible
irreversible
1. Primary information from moments:
𝑀𝑛 =
0
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
![Page 152: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/152.jpg)
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)
![Page 153: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/153.jpg)
Rate Reactivity Model (RRM)
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
𝑹 𝒕 = 𝝍𝑪𝑪 𝒕 + 𝝍𝑼𝑼 𝒕 + 𝝍𝑪𝑼𝑪 𝒕 𝑼(𝒕)
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
![Page 154: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/154.jpg)
Rate Reactivity Model (RRM)
Estimation of reactivities
𝑹 𝒕 = 𝝍𝑪𝑪 𝒕 + 𝝍𝑼𝑼 𝒕 + 𝝍𝑪𝑼𝑪 𝒕 𝑼(𝒕)
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
![Page 155: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/155.jpg)
R, m
ol/
kg
ca
t/s
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
n
• Kinetics: 𝑅𝐴 = 𝑘𝑎𝑑𝑠 𝑁𝑆 − 𝐶𝐴𝑍 𝐶𝐴 − 𝑘𝑑𝑒𝑠𝐶𝐴𝑍
• Single-site reversible adsorption: A + Z = AZ
• For small CAZ (state-defining): 𝑅𝐴 ≈ 𝑘𝑎𝑑𝑠𝑁𝑆𝐶𝐴 − 𝑘𝑑𝑒𝑠𝐶𝐴𝑍
![Page 156: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/156.jpg)
R, m
ol/
kg
ca
t/s
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
n
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
𝑌
Operation
𝜳
𝑅𝑅𝑀
![Page 157: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/157.jpg)
Rate Reactivity Model (RRM)
Generalization
𝑹𝒊 𝒕 =
𝒌=𝟏
𝑵
𝝍𝒊,𝒌𝑪 𝑪𝒌 𝒕 +
𝒋=𝟏
𝑴
𝝍𝒊,𝒋𝑼𝑼𝒋 𝒕 +
𝒌=𝟏
𝑵
𝒋=𝟏
𝑴
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?
![Page 158: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/158.jpg)
RRM example (complex)
![Page 159: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/159.jpg)
Rate Reactivity Model (RRM)
Further generalization
𝑹𝒊 𝒕 =
𝒌=𝟏
𝑵
𝝍𝒊,𝒌𝑪 𝑪𝒌 𝒕 +
𝒋=𝟏
𝑴
𝝍𝒊,𝒋𝑼𝑼𝒋 𝒕 +
+
𝒌=𝟏
𝑵
𝒋=𝟏
𝑴
𝝍𝒊,𝒌,𝒋𝑪𝑼 𝑪𝒌 𝒕 𝑼𝒋 𝒕 +
𝒍=𝟏
𝑴
𝒋=𝟏
𝑴
𝝍𝒊,𝒍,𝒋𝑼𝑼𝑼𝒍 𝒕 𝑼𝒋 𝒕 + 𝝍𝒊,𝟎
surface-surface
interactions
zeroth term
constant emmision of the gas
(e.g. catalyst decomposition)
![Page 160: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/160.jpg)
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
![Page 161: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/161.jpg)
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
![Page 162: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/162.jpg)
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)
![Page 163: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/163.jpg)
PropertiesApplied Kinetics
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
Insignificant change
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
Strategies of Catalyst Kinetic Characterization
continued
![Page 164: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/164.jpg)
CONCLUSIONS
A BRIDGE ACROSS THE “PRESSURE-GAP”:
TAP is waiting for you at this BRIDGE !
![Page 165: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/165.jpg)
• BACK TO HISTORY…
• BACK TO CELEBRITIES…
![Page 166: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/166.jpg)
Isaac Newton (1743-1727)
![Page 167: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/167.jpg)
Gottfried Wilhelm Leibnitz (1646-1716)
![Page 168: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/168.jpg)
‘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
![Page 169: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/169.jpg)
Manfred Eigen (1927): Chemical relaxation, but not calculus
![Page 170: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/170.jpg)
Experimental calculus in chemistry: John T. Gleaves
![Page 171: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/171.jpg)
Gregory S. Yablonsky
![Page 172: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/172.jpg)
“It has seen further it is by standing on the
shoulders of giants”
(Isaac Newton,
Letter to Robert Hook, February 1676)
![Page 173: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/173.jpg)
Acknowledgements
John Gleaves
Denis Constales
Guy Marin
![Page 174: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/174.jpg)
THANK YOU
FOR YOUR ATTENTIVE PATIENCE !
![Page 175: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/175.jpg)
Questions & Answers
![Page 176: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/176.jpg)
![Page 177: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/177.jpg)
177
![Page 178: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/178.jpg)
178
Cg = 0
Fexit (t)
Finlet(t)
CgTZ(ω)RTZ(ω)
Fre
qu
en
cy d
om
ain
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
![Page 179: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/179.jpg)
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)
![Page 180: Temporal Analysis of Products(TAP)- Approach: Theory and ...Temporal Analysis of Products(TAP)-Approach: Theory and Application Gregory Yablonsky, Parks College of Engineering, Aviation](https://reader033.vdocuments.site/reader033/viewer/2022052015/602ca7d72512347ddc138a85/html5/thumbnails/180.jpg)
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)