Design of Kinetic Experiments for Fischer-Tropsch Synthesis on Supported Fe Catalysts

1. Design of Kinetic Experiments for Fischer-Tropsch Synthesis on Supported Fe Catalysts Chemical Engineering and Statistics Brigham Young University Provo, Utah Brian Critchfield Uchenna Paul Prof. Calvin Bartholomew Prof. Dennis Tolley

2. Introduction • Langmuir-Hinshelwood models derived from mechanisms are generally found to fit rate data well for a number of catalytic reactions, e.g., for Fischer-Tropsch synthesis: • This model is nonlinear and, as a result, there is typically a high correlation between kinetic parameters.

3. Challenges in Collecting/Fitting Rate Data • Collecting enough data to regress the model parameters can betime consuming. • Without an appropriate experimental plan,parameter estimates may be poor; parameters may be highly correlated. • Due to the nonlinear nature of the model, thebest experimental design is not apparent.

4. Sequential/D-optimal Experimental DesignCan Be Very Helpful

5. D-Optimal Design (DOD) • a form of response surface design – using optimization methods (Other forms include: A-Optimal, E-Optimal, G-Optimal, and V-Optimal). • a proven tool for obtaining the most precise estimates of model parameters in the least number of experiments. • enables selection of conditions that minimize theoverall variances of the estimated parameters by spreading outdesign variables over available variable space. • reduces the volume of the confidence region for estimated parameters. • substantially reduces correlation among parameters.

6. How Does DOD Work? • A rate function is specified, yi = f(xi,q) where xi are the set of design parameter inputs and q is the set of kinetic coefficients. • Calculus and matrix algebra are used to maximize the following determinant: where F is the Jacobian matrix and F T is the transpose of the Jacobian matrix, where …..

7. The Jacobian the Jacobian of the rate function rFT is: where fN,p is the set of partial derivatives of rFT with respect to the pth parameter at the Nth set of experimental conditions; the N+1 set is the new experimental conditions. For example, f1,1 = ∂rFT/∂A where A = the preexponential factor

8. Obtain preliminary rate functions from literature Initial points Define D - Optimal criteria (Estimates of parameters) Determine D - Optimal experim ental design conditional upon experiments completed to date Response - Yes (linear) No (nonlinear) surface Select fractional factorial Select conditional D - linear? Optimal design set of runs Perform experiment based on selected design Experimental data Non - linear least squares fit of parameters Fitted parameters, s td. dev., confidence intervals Determine range of i ndependent variables Estimate refinement Yes (optimum value far from data input)? No Conclude Optimal Settings Sequential Design using DOD

9. Response surface (i.e., value of the determinant D as a function of PH2and PCO indices) for D-optimal design of rate expression for C2+hydrocarbons

10. Sequential Design Summary • Obtain initial estimates of parameters • Determine process condition that maximize D, i.e., minimize | FTF|-1/2 • Run experiment at calculated optimal conditions • Nonlinear regression to estimate parameters • Repeat until |FTF|-1/2 reaches asymptotic value

11. Thus, statistical methods provide a mapof the experiments, while optimization serves as a compass.

12. Overall Research Approach Detailed Kinetics Activity, Selectivity, Stability DFT Electronic structure of stable species, intermediates and transition states IR Surface species Microkinetic Model Microscopy Surface morphology and composition XPS, XRD, Mössbauer Alloy formation, oxidation states, surface composition Adsorption/Desorption TPD/TPH Heats, Coverages

13. FTS Reaction Kinetics on Fe • Collaboration with Manos Mavrikakis and Jim Dumesic • Objective: develop data for validation of microkinetic and LH models • More than a dozen previous kinetic studies • Most did not meet basic criteria of Ribeiro et al. (1997) for absence of heat/mass transfer effects, deactivation, etc. • None used optimal statistical design of experiments. • Data were fitted to power law and Eley-Rideal expressions mostly covering narrow ranges of operating conditions. • Few reported TORs, thus preventing valid comparisons. • Thus, much of previous work is unreliable or unusable

14. Our Approach to Kinetic Study • Derive LH and ER rate forms from a logical mechanism. • Use D-optimal/sequential design to optimize experimental conditions, minimize errors in rate parameters, and minimize number of experiments • Collect intrinsic rate data on a stable Fe-Pt/Al2O3catalyst in a Berty CSTR reactor over a wide range of commercially relevant conditions. • Pt-promoter and La-stabilized alumina support facilitate Fe reduction and hydrothermal stability. • Catalyst washcoated on monolith ensures high effectiveness, enabling operation over wide range of temperature. • Use nonlinear regression methods to fit rate data to best mechanisms.

15. Application of DOD to FTS on Fe 1. Select a reasonable mechanism.

16. (Application of DOD to FTS on Fe) 2. Derive LH rate expression from reasonable mechanism. 3. Choose independent variables: temperature, PCO, and PH2 and model parameters: A, Eact, Aads, and DHads.

17. (Application of DOD to FTS on Fe) 4. Conduct scoping runs to obtain preliminary values of model parameters. Catalyst is quite stable over > 150 h Run 11 Data are correlated well by the model.

18. (Application of DOD to FTS on Fe) 5. Set up Jacobian matrix with scoping runs and maximize determinant to obtain response surface for experimental parameters (i.e., PCO, and PH2 at a specified T) for the next set of experiments. Run 5 Steep gradient and maximum for D (snow-capped peak) is observed around PCO = 0.75 and PH2 = 10. Our next experiment should be in that region. PCO PH2

19. Values of |FTF|-1/2 with respect to the number of runs at 239°C.

20. K k Values of k and K with respect to the number of runs at 239°C.

21. Experimental rates versus model predicted rates for sequentially designed experiments at 239°C.

22. Joint 95% likelihood confidence regions for k, and K at 239°C at different stages of the sequential design procedure

23. Variation in parameters less than 5-10%

24. Conclusions • A stable, well-dispersed 15% FePt/Al2O3-La2O3 wash-coated monolith catalyst in combination with a CSTR facilitates obtaining intrinsic FTS rates under commer-cially-relevant conditions. • An LH rate expression based on C+H and OH + OH as RDSs provides the best fit to the data. • A sequential design procedure using DOD resulted in precise parameter estimates in a minimal number of (10-15) experiments at each of two temperatures. • Three data sets at three temperatures (37 total runs) could be combined to obtain a rate law fitting C2+ production rate data well over a wide range of T and partial pressures of CO and H2.

25. Acknowledgments • Collaboration with Professors James Dumesic and Manos Mavrikakis of U. Wisconsin • Funding from DOE/NETL

26. Brian Critchfield and Uchenna Paul

27. Professor James A. DumesicACS Somorjai Award Recipient • Friend, colleague, and collaborator for 34 years • Pioneer and leader in catalysis research • Bright, whimsical, youthful, creative, and modest Congratulations!