An efficient approach towards predictive kinetic models W. Hauptmann, M. Votsmeier, J. Gieshoff, D. G. Vlachos, A. Drochner, H. Vogel
Introduction - Literature Mechanisms - 1.0 0.8 0.6 0.4 0.2 heating Experiment Run1 Olsson 1999 Koop 2008 Olsson 2001 0.0 100 150 200 250 300 350 T / C, eq L. Olsson, B. Westerberg, H. Persson, E. Fridell, M. Skoglundh, B. Andersson, Journal of Physical Chemistry B 1999, 103, 10433-10439. J. Koop, Dissertation, Universität Karlsruhe 2008. L. Olsson, H. Persson, E. Fridell, M. Skoglundh, B. Andersson, Journal of Physical Chemistry B 2001, 105, 6895-6909. 2
Modeling Process - Process Steps - Model Model Development Experiments Simulation Model Model Analysis Optimization Predictive Model Model 3
Experiments Model Model Development Experiments Simulation Model Model Analysis Optimization Predictive Model Model 4
Experiments - Test Bench - Gas supply Analytics Monolith holder Oven 5
Experiments - Inverse Hysteresis - 1.0 0.8 0.6 0.4 heating cooling Experiment Run1 Experiment Run2,eq 400 T Ofen 0.2 0.0 T / C 300 200 100 Pre- Treatment Run1 Run2 100 150 200 250 300 350 T / C x x x+60 x x +74 x x +74 x x +74 x +74 t / min 0 (NO) = 430 vol.-ppm; 0 (O 2 ) = 6 vol.-%; balance N 2 ; = ±5 K min -1 ; 6
Model Development Model Model Development Experiments Simulation Model Model Analysis Optimization Predictive Model Model 7
Model Development - Mechanism - R1 R2 R3 R4 R5 R6 R7 R8 O 2 + 2 Pt 2 Pt-O NO + Pt Pt-NO NO 2 + Pt Pt-NO 2 Pt-NO + Pt-O Pt-NO 2 + Pt 2 Pt-O O 2 + 2 Pt Pt-NO NO + Pt Pt-NO 2 NO 2 + Pt Pt-NO 2 + Pt Pt-NO + Pt-O L. Olsson, H. Persson, E. Fridell, M. Skoglundh, B. Andersson, Journal of Physical Chemistry B 2001, 105, 6895-6909. W. Hauptmann, M. Votsmeier, J. Gieshoff, D. G. Vlachos, A. Drochner, H. Vogel, Topics in Catalysis 2009, doi: 10.1007/s11244-009-9369-z. 8
Model Development - Pre-exponential Factors - Collision Theory Theory Transition State State Theory Theory Adsorption Desorption Bimolecular Surface Reaction Sticking Coefficient A = 10 10 16 16 s -1-1 (DoF (DoF Transition State > DoF Transition State > DoF Adsorbates ) Adsorbates ) A = 10 10 11 11 s -1-1 (Mobile adsorbates (Mobile adsorbates without rotation) without rotation) J. A. Dumesic et. al., The Microkinetics of Heterogeneous Catalysis, American Chemical Society, Washington DC 1993. 9
Model Development - Activation Energy - Surface reaction (AB (AB A + B): B): Activation energy energy (forward reaction): Surf Ea f xab, TS H H H Surf Surf :: Dissociation Surf H Q D AB QAQB Q Q AB A Q A C B C Q B Adsorption: E a = a 0.0 0.0 kj kj mol mol -1-1 Desorption: E a = a Heat Heat of of adsorption UBI-QEP Bimolecular reaction H Surf Q C Q AB D AB D BC Q A Q BC Activation energy energy (back (back reaction): Surf Ea Ea H b f E. Shustorovich, H. Sellers, Surface Science Reports 1998, 31, 1-119. 10
Simulation Model Model Development Experiments Simulation Model Model Analysis Optimization Predictive Model Model 11
Simulation - Initial Mechanism - 1.0 0.8 0.6 0.4 0.2 heating Experiment Run1 Simulation Run1,eq 0.0 100 150 200 250 300 350 T / C 0 (NO) = 430 vol.-ppm; 0 (O 2 ) = 6 vol.-%; balance N 2 ; = ±5 K min -1 ; 12
Modeling Process - Process Steps - Model Model Development Experiments Simulation Model Model Analysis Optimization Predictive Model Model 13
Model Analysis - Sensitivity Analysis - Objective: Identification of of relevant parameters and/or and/or reactions. 14
Model Analysis - Sensitivity Analysis - Objective: Identification of of relevant parameters and/or and/or reactions. Procedure: Iterative variation of of each each parameter value. value. Calculation of of normalized sensitivity coefficients (NSC). (NSC). Calculation: Resi SCi, r Para NSC i, r r Para Res i r Res i Para r 15
Model Analysis - Sensitivity Analysis - Objective: Identification of of relevant parameters and/or and/or reactions. Reaction R7 R6 R5 R4 R3 R2 R1-0.6-0.4-0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 NSC A' = A Original / 10 Ea' = Ea Original +-20 kj mol -1 Ea' = Ea Original +-30 kj mol -1 Procedure: Iterative variation of of each each parameter value. value. Calculation of of normalized sensitivity coefficients (NSC). (NSC). Calculation: Resi SCi, r Para 16 NSC i, r r Para Res i r Res i Para Interpretation: NSC-value corresponds to to parameter impact. impact. Sign Sign (+/-) (+/-) shows shows proportionality. r
Model Analysis -Result - Pt-NO + Pt-O Pt-NO 2 + Pt Pt-NO 2 NO 2 + Pt NO 2 + Pt Pt-NO 2 Pt-NO NO + Pt NO + Pt Pt-NO 2 Pt-O O 2 + 2 Pt O 2 + 2 Pt 2 Pt-O A' = A Original / 10 Ea' = Ea Original +-20 kj mol -1 Ea' = Ea Original +-30 kj mol -1-0.6-0.4-0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 NSC 17
Optimization Model Model Development Experiments Simulation Model Model Analysis Optimization Predictive Model Model 18
Optimization - Iterative Process - Model Initial Guess DoE Use last Initial Guess. Reduce Size of Design. Use opt. Parameters as Initial Guess. Keep Size of Design. Fit Polynomial Reference Data No Res New < Res Old Yes Minimize Objective Function Res < SC No Yes Stop Optimization 19
Optimization - Optimization Results - 1.0 0.8 0.6 0.4 heating 0.2 Experiment Run1 Simulation Run1,eq 0.0 100 150 200 250 300 350 T / C 0 (NO) = 430 vol.-ppm; 0 (O 2 ) = 6 vol.-%; balance N 2 W. Hauptmann, M. Votsmeier, J. Gieshoff, D. G. Vlachos, A. Drochner, H. Vogel, Topics in Catalysis 2009, doi: 10.1007/s11244-009-9369-z. 20
Optimization - Model Assessment - 1.0 0.8 0.6 0.4 0.2 heating Experiment Run1 Simulation Run1,eq 0.0 100 150 200 250 300 350 T / C 0 (NO) = 280 vol.-ppm; 0 (O 2 ) = 6 vol.-%; balance N 2 W. Hauptmann, M. Votsmeier, J. Gieshoff, D. G. Vlachos, A. Drochner, H. Vogel, Topics in Catalysis 2009, doi: 10.1007/s11244-009-9369-z. 21
Optimization - Model Assessment Light-Off/Light-Out- 1.0 0.8 0.6 0.4 0.2 Mechanism can t can t describe inverse inverse hysteresis Experiment Run1 Simulation Run1,eq 0.0 100 150 200 250 300 350 T / C 0 (NO) = 430 vol.-ppm; 0 (O 2 ) = 6 vol.-%; balance N 2 22
Model Elaboration Model Model Development Experiments Simulation Model Model Analysis Optimization Predictive Model Model 23
Model Elaboration - Implementation of Catalyst Deactivation - R1 R2 R3 R4 R5 R6 R7 R8 R9 R10 O 2 + 2 Pt 2 Pt-O NO + Pt Pt-NO NO 2 + Pt Pt-NO 2 Pt-NO + Pt-O Pt-NO 2 + Pt Pt-NO 2 PtOx + NO 2 Pt-O O 2 + 2 Pt Pt-NO NO + Pt Pt-NO 2 NO 2 + Pt Pt-NO 2 + Pt Pt-NO + Pt-O PtOx + NO Pt-NO 2 W. Hauptmann, M. Votsmeier, J. Gieshoff, A. Drochner, H. Vogel, Applied Catalysis B: Environmental 2009, accepted. 24
Model Elaboration - Model Performance - 1.0 0.8 0.6 0.4 heating cooling Experiment Run1 Experiment Run2 Simulation Run1 0.2 Simulation Run2, eq 0.0 100 150 200 250 300 350 T / C 0 (NO) = 430 vol.-ppm; 0 (O 2 ) = 6 vol.-%; balance N 2 W. Hauptmann, M. Votsmeier, J. Gieshoff, A. Drochner, H. Vogel, Applied Catalysis B: Environmental 2009, accepted. 25
Model Elaboration - Model Assessment - 1.0 0.8 0.6 0.4 heating cooling Experiment Run1 Experiment Run2 0.2 Simulation Run1 Simulation Run2,eq 0.0 100 150 200 250 300 350 T / C 0 (NO) = 280 vol.-ppm; 0 (O 2 ) = 6 vol.-%; balance N 2 W. Hauptmann, M. Votsmeier, J. Gieshoff, A. Drochner, H. Vogel, Applied Catalysis B: Environmental 2009, accepted. 26
Model Elaboration - Model Assessment II- 1.0 0.8 0.6 0.4 0.2 heating cooling 100 0 2 4 6 8 t / h 0.0 50 100 150 200 250 300 350 400 200 T / C300 Exp. Part1 Exp. Part2 Exp. Part3 Sim. Part1 Sim. Part2 Sim. Part3,eq T 1.0 0.8 0.6 0.4 0.2 T Exp. Sim. 0.0 0 1 2 3 4 5 6 7 8 350 300 250 200 150 100 T / C T / C t / h 0 (NO) = 430 vol.-ppm; 0 (O 2 ) = 6 vol.-%; balance N 2 W. Hauptmann, M. Votsmeier, J. Gieshoff, A. Drochner, H. Vogel, Applied Catalysis B: Environmental 2009, accepted. 27
Summary Experiments: Experiments: The The NO NO oxidation oxidation on on Pt Pt shows shows an an inverse inverse hysteresis hysteresis Model Model Development: Development: Applied Applied theories theories are are appropriate appropriate to to parameterize parameterize kinetic kinetic models. models. Simulation: Simulation: Low Low temperature temperature activity activity of of the the initial initial mechanism mechanism is is to to high. high. Model Model Analysis: Analysis: Sensitivity Sensitivity analysis analysis and and Shainin Shainin analysis analysis are are able able to to determine determine the the active active parameters. parameters. Optimization: Optimization: Iterative Iterative process process is is appropriate appropriate for for parameter parameter estimation. estimation. Predictive Predictive Model: Model: Model Model without without catalyst catalyst deactivation deactivation is is able able to to describe describe the the light-off-behavior. light-off-behavior. Model Model including including catalyst catalyst deactivation deactivation is is able able to to describe describe the the light-off/light-out light-off/light-out behavior. behavior. 28
Special thanks go to Alfons Drochner Herbert Vogel Martin Votsmeier Jürgen Gieshoff Dion Vlachos 29
Thank you for your kind attention!