Development of Reliable, Simple Rate Expressions from a Microkinetic Model of FTS on Cobalt Calvin H. Bartholomew, George Huber, and Hu Zou Brigham Young University And George Huber, Rahul Nabar, Peter Ferrin, Manos Mavrikakis, and James Dumesic University of Wisconsin, Madison

Background  Fischer-Tropsch Synthesis (FTS), is a key step in processes being developed and commercialized in the new GTL industry.  Improvements to GTL and FTS processes are facilitated by development of accurate, comprehensive reactor and kinetic models.  Rates and reactant/product compositions in a commercial FTS SBCR cover wide ranges; rates may vary fold, H 2 /CO ratios 2 to 100.  Microkinetic models (MKMs) and/or Langmuir-Hinshelwood models (LHMs) are needed for reliable prediction of rates over the full range of conditions.  While MKMs are the most powerful predictors, given large computational requirements of a comprehensive FTS reactor model, a reliable LHM may be the best compromise.

Kinetic Models for FTS on Cobalt  A dozen previous macrokinetic studies; each covers a narrow range of conditions.  Power law (PL) and LH rate expressions reported in previous studies may not be statistically valid since too many parameters were fitted to too few data.  Two microkinetic models for FTS on cobalt have been previously published. They have limited utility and have not been validated with a representative set of data.  Use of kinetic/thermo parameters from MCMs in building rate laws has been limited—hasn’t been done with Co FTS.

Issues Addressed in This Talk  What is a viable approach to microkinetic model and rate-law development?  How can we use microkinetic models to develop better rate laws?  What factors limit the validity of previously reported rate laws and how might they be overcome?

Surface Reaction Schemes and Kinetic Models Adsorption And Microcalorimetry Heats, Coverages Isotopic Studies SSITKA and kinetics of elementary steps Detailed Kinetics Activity, Selectivity, Stability XPS, XRD, Mössbauer Alloy formation, oxidation states, surface composition IR Surface species Microscopy Surface morphology and composition DFT Electronic structure of stable species, intermediates and transition states Microkinetic Model Development

Information from MKM  Kinetic parameters for each elementary step  Site requirements  Predictions of rate over a wide range of conditions from solution of the differential equations

Microkinetic Model for Fischer Tropsch Synthesis on Co(0001) On Wisconsin UWM

Preferred Adsorption Sites and Binding Energies for Intermediates in CH 4 Formation on Fe(110) and Co(0001) (Gokhale and Mavrikakis, 2005; courtesy of the American Chemical Society)

Kinetic Study: Statistical Design (H&B, BYU; Temperature 200C, Pressure Total = 20 atm.)

Rate Expression Derived from Original Carbide Mechanism (Huber, 2000)

Rate calculated vs. rate measured in this study for rate expressions derived from Carbide Theory, Power Law and rate expressions proposed by Yates and Satterfield. Calculated and measured values are in reasonable agreement. NSSE = 4-8 x for several sets of data.

Normalized deviation from average value (%) versus run number. (Normalized deviation from average value = (value – average value) /average value x 100) [Huber and Bartholomew, 2005]. Deviations are within + or – 5%.

Correlation between A and B for Model 1 derived from Carbide Theory. Ellipse indicates 95 % confidence limit for each constant. Results of Nonlinear Regression Conclusion: A and B (a and b) in rate equation cannot be specified! a = 81.1 ± 43 b = 1.0 ± 0.4

This is a Can of Worms!

Solution to Dilemma?  Use MKM to specify all variables except one  Use nonlinear regression to determine the unspecified parameter

Microkinetic Model for Fischer Tropsch Synthesis on Co(0001) On Wisconsin UWM

Approach

Conclusions  Dilemma: Typical approach to fitting kinetic data to LHE may lead to highly correlated constants; standard errors are large and constants are unspecified.  Solution: use constants from theory or MKM to specify all but one constant, which can be fitted by nonlinear regression.  For Co(0001) CO dissociation is rds and CO is masi. On stepped sites C + H could be rds.

BYU Catalysis Group Spring 2005

Thanks for listening.

Representative Simple Reaction Rate Equations for CO Consumption in FTS on Co Catalysts