1. Progress in Development of Activity Models of FT Synthesis on Cobalt
Prof. Calvin H. Bartholomew
BYU Catalysis Laboratory
Department of Chemical Engineering
Brigham Young University

2. Outline
Simplify

3. Macro-Kinetic Models for FTS on Cobalt
Definition: Rate expression in the form of a power law or Langmuir-Hinshelwood expression:
r = k(T) f(XCO,PCO,PH2).
Application: Modeling/design of reactors and processes.
Previous Work: 15+ studies, provide a variety of rate expressions. Data vary in quality and ability to predict rates.

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

5. Limitations of Reported Kinetic Studies & Rate Expressions
Each study covers a relatively narrow range of conditions; too few data were collected.
Rate equations are probably not statistically representative, since too many parameters were fitted to too few data.
Some of the data is of poor quality due to use of a poorly designed catalyst or questionable reaction conditions, e.g. involving heat & mass transfer disguises and or deactivation, i.e. fails to meet minimum guidelines for collection rate data [Ribeiro et al., Catal. Rev.-Sci. Eng. 39, (1997)].
Data fitted to a rate expression having no physical basis or tied to a questionable mechanism.
Accordingly, roughly about 10 of the previously reported data sets is judged to be reliable; it is doubtful if any of the reported rate expressions is adequately predictive.

6. Predictions from “Best” Rate Equations and/or Rate Data
(Normalized to H2/CO = 2, Ptot = 20 atm, XCO = 0.50)
Three-fold difference in rate at given T

7. Typical Problems in an Almost Well-Designed Study
Positives:
− Good statistical design.
− Very good fit of Model 1 to data.
r2 = 0.929
Negatives:
− Few data, esp. at the higher T, limits confi-dence in model.
− A & B are highly correlated.
Four-parameter fit to Model 1 for data at two temperatures, 473 and 493 K. [Huber and Bartholomew, ACS Meeting, 4/08].

8. 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 [Huber and Bartholomew, ACS Meeting, 4/08].

9. Summary: Macro Kinetic Models for FT on Co
The “best” of previously reported rate expressions predict rates at fixed conditions that vary 3-fold. None are adequate for quantitative reactor design.
The “most reliable” rate data sets (about 10) cover different ranges of conditions; also predict different rates for a fixed set of conditions.
So the research and engineering communities have a problem!

10. What if…………….
1. Available data from the best studies could be normalized and combined to make one large data set?
− More data would mean smaller errors in fitted constants in rate expression.
− Resulting rate expression would more accurately represent reality.
2. Rate expression could be derived from a representative mechanism and some of the MacKM constants could be established from a MicKM?
− Rate expression will correctly predict rates over a wider range of conditions than presently possible.
− Correlation between MacKM constants would be largely eliminated; confidence intervals would be very small.

11. Key to Combining Rate Data
Define common known TOF at a fixed condition. Normalize other rates by the ratio of TOFstd/rate.
[Huber and Bartholomew, ACS Meeting, 4/08]
Common TOF
Several key studies confirm that TOF is a well-known value at fixed conditions for well reduced catalyst where dispersion D < 15%

12. TOF's From 5 different studies [Morselli, Ch. 4, Table 6]
a. 473 K, Ptot = 20 atm; H2/CO = 2

13. Effects of Dispersion mole/gCo-s
Rates in mole/gCo-s are linear with dispersion. [Iglesia et al., 1992]
Specific activity independent of dispersion for well-reduced catalysts! [Johnson et al., 1991]
Specific activity independent of dispersion for crystallite diameters larger than 6 nm.
[J.P. den Breejen,JACS, 2009.]

14. OBJECTIVES of this Study
Develop a macrokinetic model (MaKM) based on mechanisms and rate constants from a microkinetic model (MiKM)
validated with steady-state rate data.
2. Obtain a large set of representative rate data by combining available data based on a standard turnover frequency (TOF) at fixed conditions.
More data smaller errors in fitted constants in rate expression.

15. Method of Formulating Models

16. Criteria for Selecting and Combining Available Rate Data
A. Criteria for Selection
Data set largely meets basic criteria for obtaining quality rate data, i.e. absence of transports disguises or deactivation [Ribeiro et al., Catal. Rev.-Sci. Eng. 39, (1997)].
Publication provides sufficient information for independent calculation of rate.
B. Criteria for Combining Data
Assume that TOF rate from different data sets will be identical at fixed condition.
Use method of Huber et al. [2008] to normalize the rates.

17. Rate Data Recently Combined
Data cover wide ranges of data space:
PH2: 0.5 – 14 atm
PCO: 0.5 – 7 atm
XCO: 0.02 – 0.82
Next we need a MaKM.
We can derive from MiKM based on plausible mechanism.

18. Micro-Kinetic Models for FTS on Cobalt
Definition: Molecular scale model consisting of elementary steps and kinetic constants (Eact and Apre-expntl) for each elementary step.
Application: Accurate modeling/design of reactors and processes over a wide range of conditions.
Previous Work: One MiKM validated for methanation on Co [Storsaeter et al., 2006]. Van den Berg and van Helden, Paper O07 (Sasol).
This Work: Considered two mechanisms, direct and H- assisted CO dissociation; validated with comprehensive set of SS data.
We focus today on direct CO dissociation.

19. Mechanism 2: Direct CO Dissociation
Discussion today focuses especially on Steps 1-5, the kinetically relevant steps to form CH2.

20. Mechanism 2: Direct Dissociation
Issues to address
Is Step 3, direct CO dissociation, energetically and kinetically favorable on real Co catalysts ?
Which of the above steps are rate-determining. Which are in quasi-equilibrium? Which surface species are most abundant?

21. Optimized steady-state kinetic parameters at 473 K, 20 atm, H2/CO = 2
Optimized steady-state kinetic parameters at 473 K, 20 atm, H2/CO = 2.09 from NL Least Sqrs, with TOF Constraint
Step Ef Er
DHrxn Af Ar rf rr r
(kJ/mol)
bar-n s-1
bar-ns-1
rf – rr 1
20.0
89.0
-69.0
3.9E+04
2.9E+12
97.23
97.20
0.026 2
15.5
82.0
-66.5
1.3E+04
3.5E+11
18.22
18.20 3
120.5
162.4
-41.9
2.8E+13
9.1E+14
3.9E-05 4
120.4
70.0
50.4
4.8E+12
3.9E+08
2.5E-08 5
47.7
135.0
-87.3
4.9E+11
4.1E+10
3.4E-08
Values of Ef for Steps 3 and 4 are close to those predicted from UBI-QEP, much smaller than DFT values, close to experimental values from TPD and TPH.
Results indicate that direct dissociation is kinetically and energetically favorable and consistent with experimental observations.

22. CO, H2, and C coverages are consistent with experimental observations
Fixed values of Pi and optimized steady-state surface coverages at 473 K, 20 atm, H2/CO = 2.09 from NL Least Sqrs
[with TOF = s-1 and sum of qi = 1.00]
Species, i Pi qi CO
4.79
0.23 H2
10.50
0.24 C
0.44 CH
4.1E-08
CH2
7.9E-03
CH3
2.4E-04
CH4 C2
3.8E-03 O
1.3E-05 OH
5.9E-17
H2O
3.2E-09 V
0.085
Total
20.0
1.002
CO, H2, and C coverages are consistent with experimental observations
[e.g. qC ≈ 0.5 after rxn; Johnson et al., Surf.Sci, 1991].

23. Rate Expression Derived from Steps 1-5 [Except for SSA no assumptions were made]

24. MaKM and Initial Kinetic Constants from MiKM

27. Analysis of Data Uniformity and Fitting Platform
Rates vary 10-20% for combined and partial data sets and about 25% for different numerical platforms. Validation data predict rate within 15%.

28. Error Analysis
Errors in temperature is likely around 15%; other errors inherent in data measurements and numerical fitting may be 20-25%.

29. Most of the rate data fall within ±15%; hence a 95% confidence interval.
Thus, rate equation predicts experimental rates within a 95% CI!

30. EA = E3 + DH1+DH2/2 = 16.0 E3 = EA − DH1 − DH2/2 = 117.8
MaKM and Initial Kinetic Constants from MiKM and Final Values from Data Fit
EA = E3 + DH1+DH2/2 = 16.0
E3 = EA − DH1 − DH2/2 =
The apparent EA is only 16 kJ/mol, since it includes DHad for CO and H2.
Overall T dependence is consistent with 100 kJ/mol.
DHad values for CO and H2 are very close to experimental values.

31. Conclusions
Objectives have been met; micro and macro-kinetic models for direct dissociation of CO have been validated against a known TOF rate at a standard set of reaction conditions and against a large data set.
Direct CO dissociation is kinetically a feasible route for production of hydrocarbons in FTS.
It is possible to combine rate data from different kinetic studies into a large data set based on the principle of a common TOF at a standard condition.
A large data set consisting of 186 data points and spanning a wide range of reaction conditions was produced by combining data from over 10 studies. 166 data points lie within a 95% confidence interval.

32. Conclusions (cont)
A rate expression (MaKM) consisting of 8 kinetic parameters, validated against the large data set and consistent with the MiKM predicts FT rates within a confidence interval of 95%.
MaKM can be created from MiKM; MaKM can be used to validate MiKM.
Take home message: Present theoretical approaches (DFT, UBI-QEP, TST) are inadequate for predicting Eact and A values well enough for quantitative modeling of FTS. Principal problem is that present theoretical models of catalyst properties fall substantially short of reality. Theory needs to be validated against real data!
WE NEED MORE EXPERIMENTAL DATA!!

33. Acknowledgements DOE BYU catalysis group:
Especially Dr. Hu Zou and Dr. Uchenna Paul.

34. Guidelines for Collection of High Quality Intrinsic Rate Data
[Ribeiro et al. “Reproducibility of Turnover Rates in Heterogeneous Metal Catalysis: Compilation of Data and Guidelines for Data Analysis,” Catal. Rev.-Sci. Eng. 39, (1997).]
Without such data how can we model CO adsorption on real catalysts?

35. Nonlinear Least Squares Regression