1. Generalized Kinetics of Fischer-Tropsch Synthesis on Supported Cobalt
Calvin H. Bartholomew and Uchenna Paul, Brigham Young University

2. Macro-Kinetic Models for FTS on Cobalt
Representative macro-kinetic models (i.e. rate expression) are needed for modeling/design of Fischer-Tropsch reactors and processes.
A dozen previous macrokinetic studies, each covering a relatively narrow range of conditions, provide a variety of rate expressions. It is unclear which is best.
Power law (PL) and Langmuir-Hinshelwood (LH) rate expressions reported in previous studies may not be statistically valid since too many parameters were fitted to too few data.
Accordingly, probably none of the previously reported rate models is reliable.

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

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

5. Rate Expression Derived from Original Carbide Mechanism
(Huber, 2000)
Model 1

6. Calculated and measured values are in reasonable agreement.
NSSE = 4-8 x 10-5 for several sets of data.
Rate calculated vs. rate measured in this study for rate expressions derived from carbide theory, power law.

7. Results of Nonlinear Regression
B = 1.0 ± 0.4
Conclusion: constants A and B in the rate equa-tion are highly correlated; one must be specified before the other can. B
Model 1 A
Correlation between A and B for Model 1 fitted to the data of this study at 473 K. Ellipse indicates 95 % confidence limit for each constant.

8. Very good fit of Model 1 to data
Very good fit of Model 1 to data. However, limited number of data, especially at the higher temper-ature, limits con-fidence in model.
Four-parameter fit to Model 1 for data at two temperatures, 473 and 493 K.

9. Solution to Dilemma? More data and models
Combine available, usable data from several studies with GH data, all referenced to standard conditions
Consider different models for CO dissociation (unassisted and H-assisted)
More sophisticated fitting of the data to obtain kinetic constants
Nonlinear regression with normalized errors
Reduce data scatter by throwing out obvious outliers
Specify kinetic constants from a micro-kinetic model (MKM)

10. Issues Addressed in This Talk
How can rate data from previous studies be combined to get a general rate expression?
How can we use a microkinetic model to improve the rate expression?
How good is such a model statistically in predicting rate data?

11. 4 studies, 128 data points

12. Kinetically relevant steps for Models 1 and 2

13. Kinetically relevant steps for Model 3
Model 3: H-assisted dissociation of CO as RDS based on MKM
H2 (g) + 2 S ↔
2 H–S
(1)
CO (g) + S
CO–S
(2)
CO–S + H–S →
C–S + OH–S
RDS
(3)

14. Rates Expressions for Models 1-3

16. Confidence Intervals Model 1a (High Eact)
Removing outliers reduces 95% CI and increases r2 to 0.95; moreover, parameters are not changed much.
Confidence interval is much better for the larger data set (107 vs. 27 data points). However, is model theoretically sound?

17. Microkinetic Model Formulation
Two previous models were based on data at 1 atm; parameters are not useful for predicting rates under commercial conditions.
Steps in developing the present model
1. Derive an LH rate expression from a plausible sequence of elementary steps.
2. Estimate C, H, O binding energies and incorporate them in UBI-QEP theory to estimate activation energies for the elementary steps. Calculate preexponential factors from Transition State Theory.
3. Calculate apparent activation energies and heats of adsorption from the activation energies for the elementary steps.
4. Calculate rates of CO conversion from the LH expression for the combined set of 128 points using the estimated apparent Eact and H’s.
5. Compare calculated rates with experimental rates and calculate errors.
6. Minimize the errors by changing the values of the C, H, O binding energies.
Theory informs experiment; experiment in turn informs theory.

18. Microkinetic Model for FTS on Co

19. What does the Microkinetic Model teach?
- Routes for CO dissociation and carbon hydrogen-ation on Co have equally high activation barriers; hence Model 1 in which carbon hydrogenation is postulated to be the rate-determining step is suspect The apparent activation for Model 2, calculated from the activation energies for the kinetically relevant steps is negative. Thus Model 2 is suspect Only the parameters for Model 3 are consistent with theory.

21. How well does Model 3 predict rates?
- Nonlinear correlation coefficient of is consistent with an excellent fit of the generalized data set—equally good compared to Models 1 and The confidence interval for Model 3 is as good as for those of Models 1 and It predicts TOF data for different conditions in excellent agreement with reported TOF data (as do Models 1 and 2).

23. Confidence Intervals: Model 3
Removing outliers reduces 95% CI and increases r2 from 0.85 to 0.93; moreover, parameters are not changed measurably.
Model 3 is theoretically sound, i.e. based on para-meters for elementary steps; confidence interval is close to model prediction

26. Kinetic parameters for CO Conversion on Supported Cobalt Catalysts and Prediction of TOF

28. Conclusions
Obtaining general macrokinetic model from several sets of data is possible.
Requires normalizing to common set of conditions.
Requires well-defined TOF; structure insensitivity
Models are improved by larger data set, discarding outliers and normalizing residuals.
Microkinetic model can be used effectively to sort out macrokinetic models and specify constants with greater statistical confidence.

29. Conclusions-continued
Model 3 is theoretically sound and recommended for modeling FTS on cobalt.
Possible to substantially reduce errors (con-fidence intervals) for fitting Model 3 to data.
Use D-optimal statistical and sequential design for a set of new kinetic experiments using a well-characterized cobalt catalyst.
Experiments should be performed in a CSTR slurry or Berty reactor using micron catalyst particles (in slurry) or a micron coating of catalyst on a monolith (in Berty). Need 50 data points at 3 different temperatures and 4-5 different values of PCO, PH2.
Accurately determine TOF rates using total H2 chemisorption at 100ºC; requires 4-5 repetitions.

30. BYU Catalysis Group Spring 2006

31. Thanks for listening