Numerical and experimental aspects of Temporal Analysis of Products: a tool for understanding and designing heterogeneous catalysts

Transcription

1 Numerical and experimental aspects of Temporal Analysis of Products: a tool for understanding and designing heterogeneous catalysts Guy B. Marin Laboratory for Chemical Technology, Ghent University NEXTLAB 2014 Rueil-Malmaison April

2 Introduction Case: total oxidation of volatile organic components Mathematical analysis Statistical analysis Best practices Conclusions Overview 2

3 Steady-state versus transient steady-state experiment transient ex A B C D A B Tamaru K (1964), Adv. Catal., 15, only rate-determining step manifested 3

4 Relaxation methods in heterogeneous catalysis Stimulus Reactor Response A B Pulse or step in carrier gas flow A A,B Pulse response TAP No carrier gas flow A Rob J. Berger et al., Appl. Catal. A: General, 342 (2008) 3 4

5 Temporal Analysis of Product (TAP) Pulse Response Experiment Pulse valve Exit flow (F A ) Inert 0.0 time (s) 0.5 Microreactor Catalyst Reactant mixture Reactant TC Product Vacuum (10-8 torr) Mass spectrometer 5

6 Temporal Analysis Types of Products of experiments (TAP) Single pulse experiment C 7 H 8 C7 H 8 Size ~ molecules CO 2 t/s Multi pulse experiment Size > molecules/pulse C 7 H 8 CO 2 t/s Knudsen diffusion regime No change in the state of the catalyst Molecular diffusion regime Deliberate change in the state of the catalyst O 2 t t/s Alternating pulse experiment C 7 H 8 t/s O 2 C 7 H 8 CO 2 CO 2 t/s t/s Two pulses of different gases By varying the time delay of the pulses, lifetime of active surface species can be determined 6

7 Temporal Analysis Pump-Probe of Products experiment (TAP) Alternating pulse experiment O 2 C 7 H 8 t t/s Two pulses of different gases By varying the time delay of the pulses, lifetime of active surface species can be determined 7

8 Temporal Resolution of TAP Pulse response A B Reactor bed A A L I L II L III B Inert zone I Inert zone II Catalyst zone 2 Cg C ε cat = Dcat 2 t x k + If reactant pulses small enough: Knudsen diffusion g a C g θ t j k j = θ j R j 88

9 Temporal Analysis of Products (TAP) setup TAP-1 TAP-2 TAP-3E J.T. Gleaves, et al. Studies in Surface Science and Catalysis, 38 (1988) John T. Gleaves, et al. Appl.Cat. A: General, 160 (1997) John T. Gleaves, et al. J. Mol. Cat. A: Chem, 315(2010)

10 TAP-3E Mass spectrometer chamber Manifold, Reactor Extractor Set of pneumatic cylinders: - Vacuum/Pressure experiments (By slide valve) - Heating system Main gate valve Main chamber Diffusion pump 10

11 TAP-3E The TAP-3E menu of experiments includes: Multireactors system (carousel). Reactor can be easily and rapidly removed from the system without venting the vacuum chambers. Easily switching between 6 reactors (in situ) within 1 minute. Vacuum pulse-responses. The four pulse valves can be triggered simultaneously or in a programmed alternating sequence Atmospheric pressure steady-state, step-transient, and SSITKA experiments, temperature programmed desorption (TPD), and temperature programmed reaction (TPR) experiments; Highly automated instrument that can be operated either locally or remotely via the Internet (with limited intervention on site for the initial experiment configuration) John T. Gleaves, et al., J. Mol. Catal. A: Chemical 315 (2010)

12 TAP-3E Reactor extractor Reactor carousel (6 reactors) Reactor 12

13 Reactor carousel and reactor extractor Turbo pump (Attached to Mass spectrometer chamber) Carousel 13

14 Manifold 14

15 TAP-3E The TAP-3E menu of experiments includes: Multireactors system (carousel). Reactor can be easily and rapidly removed from the system without venting the vacuum chambers. Easily switching between 6 reactors (in situ) within 1 minute. Vacuum pulse-responses. The four pulse valves can be triggered simultaneously or in a programmed alternating sequence Atmospheric pressure steady-state, step-transient, and SSITKA experiments, temperature programmed desorption (TPD), and temperature programmed reaction (TPR) experiments; Highly automated instrument that can be operated either locally or remotely via the Internet (with limited intervention on site for the initial experiment configuration) John T. Gleaves, et al., J. Mol. Catal. A: Chemical 315 (2010)

16 TAP-3E TAP-3E TAP-1 one pulse TAP-3 EXTREL QMS with conical aperture for increased signal-to-noise ratio 16

17 Experimental data and Knudsen model Experimental ( ) and simulated ( ) responses D = 1.75 x 10-3 m 2 /s D = 5.02 x 10-3 m 2 /s Ar He 298 K 298 K 17

18 Intracrystalline diffusion T=298K Ar quartz ( ) H-ZSM 5 ( ) 18

19 TAP-3: Atmospheric pressure experiments The TAP-3E menu of experiments includes: Multireactors system (carousel). Reactor can be easily and rapidly removed from the system without venting the vacuum chambers. Easily switching between 6 reactors (in situ) within 1 minute. Vacuum pulse-responses. The four pulse valves can be triggered simultaneously or in a programmed alternating sequence Atmospheric pressure steady-state, step-transient, and SSITKA experiments, temperature programmed desorption (TPD), and temperature programmed reaction (TPR) experiments; Highly automated instrument that can be operated either locally or remotely via the Internet (with limited intervention on site for the initial experiment configuration) John T. Gleaves, et al., J. Mol. Catal. A: Chemical 315 (2010)

20 TAP-3E: Atmospheric pressure experiments Slide valve (Atmospheric pressure experiments) Reactor Reactor carousel 20

21 Introduction Case: total oxidation of volatile organic components Mathematical analysis Statistical analysis Best practices Conclusions Overview 21

22 Mars-van Krevelen (Redox) cycle O 2 C 3 H 8 CuO-CeO 2 /γ-al 2 O 3 re-oxidation reduction O CO 2 O CuO or CeO 2 Al 2 O 3 V. Balcaen, et al., Catalysis Today, 157 (2010)

23 Reaction mechanism Elementary steps + Active sites CO 2 O 2 C 3 H 8 O *,s O ads CO 2 CO 2 O *,b CuO or CeO 2 Al 2 O 3 23

24 C 3 H 8? r 7 = k 7 C C3 H 8 C² O *,s r 5 = k 5 C C3 H 8 C O *,s? r 6 = k 6 C C3 H 8 O *,s C 3 H 8 O *,s NEXTLAB, IFPEN / Rueil-Malmaison April 2014 Kinetic modeling C 2 H 4 O *,s CH 3 Rates of elementary steps Kinetic model CO 2 *,s? CO *,s Optimal description of experimental data? CO 2 24

25 Calculated Experimental NEXTLAB, IFPEN / Rueil-Malmaison April 2014 Propane responses 623 K 673 K 723 K 773 K 823 K 873 K 25

26 Toluene: Oxygen labeling experiment Only 10% of water formed contained H 2 18 O Mainly lattice oxygen participates in reaction Unmesh Menon et al., J. Catal. 283 (2011) 1 26

27 Toluene: Oxygen labeling experiment + 18 O 2 18 O L + 18 O s 18 O s + 18 O L + 16 O L b 16 O L + b 18 O in CO 2 more than in H 2 O but still mainly 16 O in CO 2 Di-Oxygen is mainly required for re-oxidation of the reduced surface metal centers Unmesh Menon et al., J. Catal. 283 (2011) 1 27

28 Toluene: Carbon labeling experiment 12 C 6 H 5-13 CH 3 12 CO 2 13 CO 2 Activation of C-C bonds 13 CO 2 is formed before 12 CO 2 Unmesh Menon et al., J. Catal. 283 (2011) 1 Abstraction of methyl carbon atom followed by destruction of aromatic ring 28

29 Toluene: Hydrogen labeling experiment C 6 H 5 -CD 3 H 2 O, HDO, D 2 O Activation of C-H bonds Peaks of H 2 O, HDO, D 2 O very close to each other Unmesh Menon et al., J. Catal. 283 (2011) 1 Simultaneous abstraction of hydrogen from methyl and aromatic ring or scrambling of hydroxyl groups on the surface 29

30 Total oxidation mechanism: summary H 2 O H 2 O 2 1 O 2 3 CO 2 4 O - Cu 2+ O 2- V o 5 O 2 CO 2 Unmesh Menon et al., J. Catal. 283 (2011) 1 30

31 Introduction Case: total oxidation of volatile organic components Mathematical analysis Statistical analysis Best practices Conclusions Overview 31

32 TAP, designed for simple math gas inert catalyst inert 2 C C ε = D K C 2 CC t x Θ = KΘ CC KΘΘΘ t + K CΘ Θ Knudsen diffusion: constant diffusivity Tiny inlet pulse: essentially linear kinetics Long cylinder: 1D model suffices Linear equations in each zone 32

33 Laplace transform Laplace transform: + st = e F( t) 0 LF( s) dt Derivatives to algebra: LF' ( s) = slf( s) F(0) Initial conditions and C = 0 Θ = 0 Determine coverages from equation: L Θ = ( s + Transformed equations in each zone: K ΘΘ ) 1 K L ΘC 2 LC ε slc = D K( s) LC, i.e. 2 x LC 1 LF = D LF and = ( ε s + K( s)) LC x x D. Constales et al., Chem. Eng. Sci., 56 (2001) 133. C 33

34 3D effects justifiably neglected In 2D or 3D, additional terms in Laplacian Simple math, separation of variables is possible. Transversally nonuniform components exhibit 2 diffusional decay (pseudo-reaction ) At current aspect ratios, justifiably negligible: extinct in less than 1/15 th of peak time k = Dλ / r D. Constales et al., Chem. Eng. Sci., 56 (2001) 133 and 56 (2001)

35 Other boundary conditions Inlet can have premixing chamber. Outlet condition can be finite Order 1 effect similar to zone length uncertainty Order 2 effect similar to tiny time shift Justifiably neglected in current reactor setups out out F = vc v mv R B Zone length B G Time shift D. Constales et al. Chem. Eng. Sci., 61(2006)1878 ms 35

36 Fourier transform Fourier transform: (FF)( ω) + iωt = e F( t) dt System is empty for past eternity t < 0 So + = 0 + and hence FF ) out ω = LF ( i ω ) out ( = s Inversion, from Fourier back to time: (F -1 f )( t) 1 = + iωt e f ( ω) dω 2π Example response one-zone inert: real imaginary 36

37 Noise signal (mv) Di-oxygen pulse response modulus (mv) no meaningful information sample time (ms) frequency (Hz) 37

38 Thin-zone TAP-reactor: Uniformity C inlet = C outlet = C TZ g F inlet F outlet = S cat R TZ (C g,c s ) For not-too-fast reactions, narrow zone ( L cat /L < 1/20) minimizes spatial concentration and temperature non-uniformities. Observed kinetics can be related to a uniform catalyst composition. A Fourier-domain algorithm (the Y-Procedure) can be used to translate exit flow rates into otherwise non-observable gas concentrations C TZ g and rates R TZ within the uniform catalytic zone. The Y-Procedure is kinetically model-free, i.e. it does not require a priori assumptions about the mechanism and kinetic model of catalytic reactions. Shekhtman et al. Chem. Eng. Sci., 2004, 59, Yablonsky et al. Chem. Eng. Sci., 2007, 62,

39 Thin-zone TAP-reactor: Info on intermediates Information flow: Intermediates Coverage Uptake Release Redekop et al. Chem. Eng. Sci., 2011, 66,

40 Thin-zone TAP-reactor: use of Y-procedure Simulation results: CO oxidation via different mechanisms O 2 + 2CO 2 CO 2 Possible elementary steps: (1) O 2 + 2* 2O* (2) CO + * CO* Analysis of rate-concentration dependencies allows for model discrimination ER, ER+CO ads. LH, ER+LH (3) CO + O* * + CO 2 (4) CO* + O* 2* + CO 2 Possible mechanisms (combinations of steps): Eley-Rideal (ER): steps 1 and 3 Langmuir-Hinshelwood (LH): steps 1,2, and 4 ER + LH: steps 1-4 R CO2, (mmol/kg cat /s) time ER + CO ads.: steps 1,2, and 3 C CO C O*, (mol/m 3 )(mmol/kg cat ) Redekop et al. Chem. Eng. Sci., In Press 40

41 Introduction Case: total oxidation of volatile organic components Mathematical analysis Statistical analysis Best practices Conclusions Overview 41

42 Experimental data: time series 42

43 Conditions for maximum-likelihood estimates The independent variables contain no experimental errors The model is adequate The mean experimental error is zero All errors are normally distributed The errors are homoskedastic The errors are uncorrelated NEXTLAB, IFPEN / Rueil-Malmaison April

44 Heteroskedasticity of TAP noise More noise near peak than in tail 44

45 Autocorrelation of TAP noise F ε 2 ε 1 t ε 2 [1] ε 1 R. Roelant et al. Catal. Today 2007, 121,

46 Autocorrelation of TAP-noise F ε 1 ε 2 t ε 2 ε

47 G(aussian) H(omoskedastic) U(ncorrelated) Second-order statistical regression average experimental time series NLSQ model-calculated time series linear transform G H U transformed average expt. time series NLSQ transformed calculated time series R. Roelant, D. Constales, R. Van Keer, G.B. Marin, Chem. Eng. Sci. 2008, 63,

48 Principal Component Analysis and rescaling ε 2 ε 1 Rescaling of the principal component axes Projection on the Principal Component Axes 48 48

49 Estimation of diffusion coefficient Second Order Statistical Regression (SOSR): realistic confidence intervals 49

50 Introduction Case: total oxidation of volatile organic components Mathematical analysis Statistical analysis Best practices Conclusions Overview 50

51 Regression of TAP-Data: Best Practices The Ten Commandments: I. Thou shalt verify Knudsen II. Correct thy baseline III. Waste nor scrimp collection time IV. Beware spectrally localized noise V. Be neither finicky nor coarse in sampling 51

52 Regression of TAP-Data: Best Practices The Ten Commandments (cont d): VI. Count thy replicates VII. Thy pulse size will stray VIII. Thy kinetics be linear: pulse modestly IX. Rightfully regress X. Spare thy fancy weaving the network 52

53 I. Knudsen diffusion regime A Reactor bed inert zone inert zone A C ε t catalyst zone C 2 j j = D kc 2 a + ki i x θ D j = 4rε 2RT 3τ πm j D = D j ref T T ref M M ref j 53

54 IV. Spectrally localized noise standard deviation (mv) standard deviation (mv) 0 Hz 50 Hz 150 Hz 250 Hz regression sample time (ms) frequency (Hz) 54

55 ρ( t) V. Do not sample too much = exp( t ) θ Gauss-Markov stochastic process Correlation coefficient neighboring samples Correlation coefficient neighboring samples sample time (ms) sample time (ms) 55

56 VIII. Ensure state-defining conditions Catalyst State Rate = ka(...) Cg + k j(...) θ j Rate Coefficients that include catalyst state in the catalyst zones in the inert zones 2 Cg C ε cat = Dcat 2 t x g k a C g + k j θ j ε in C g t = D in 2 C g x 2 56

57 IX. Second-Order Statistical Regression noise needs to be whitened rendered homoskedastic t (s) 57

58 X. Parcimonious network selection Bode analysis helps bound network complexity In line with the experimental window on reality Example: NEXTLAB, IFPEN / Rueil-Malmaison April 2014! 58 58

59 XI: Be lazy, use TAPFIT code Purpose Solve the direct problem: calculate TAP pulse responses from a general 1D reactor model Solve inverse problems: regress TAP experimental data and estimate various physical and kinetic parameters Features Regresses the raw pulse responses (in volts) directly Regression NLSQ (classical non-linear least square regression) SOSR (second order statistical regression) Uses the Levenberg-Marquardt method for optimization Integration can be performed in time domain frequency domain (Fourier transformation, for linear kinetics) 59

60 Introduction Case: total oxidation of volatile organic components Mathematical analysis Statistical analysis Best practices Conclusions Overview 60

61 TAP offers a unique mix of opportunities: data acquisition near millisecond resolution insignificant perturbation of catalyst state robust math modeling both intuitive qualitative interpretation and advanced model-free analysis techniques challenges for catalytic, engineering and mathematical research Conclusions 61

62 This work was supported by Acknowledgments The Long Term Structural Methusalem Funding by the Flemish Government Advanced Grant of the European Research Council (N ) Marie Curie International Incoming Fellowship (N ) Profs. D. Constales and G.S.Yablonsky Dr. Vladimir Galvita Dr. Evgeniy Redekop Rakesh Batchu Dr. Veerle Balcaen Dr. Raf Roelant Dr. Unmesh Menon 62

63 Glossary For a linear, time-invariant system.. Transfer function HH(2ππππππ) is a mathematical representation in terms of temporal frequency υυ of the relation between the input X(2ππππππ) and output Y(2ππππππ) with zero initial conditions and zero-point equilibrium such that Y(2ππππππ)=H(2ππππππ) X(2ππππππ) Bode plot is a graph of the transfer function versus frequency, typically plotted with a log-frequency axis. Often it is a combination of magnitude plot HH(2ππππππ) and phase plot arg(hh(2ππππππ)). Poles of the transfer function show up on Bode plots as breakpoints at which the slope decreases. Zeros of the transfer function show up on Bode plots as breakpoints at which the slope increases. 63