Development of Reliable, Simple Rate Expressions from a Microkinetic Model

of FTS on CobaltCalvin H. Bartholomew, George Huber, and Hu Zou

Brigham Young UniversityAnd

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 10-20 fold, H2/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 ReactionSchemes and Kinetic

Models

Adsorption And Microcalorimetry

Heats, Coverages

Isotopic StudiesSSITKA and kinetics of

elementary steps

Detailed KineticsActivity, Selectivity,

Stability

XPS, XRD, MössbauerAlloy formation, oxidation

states, surface composition

IRSurface species

MicroscopySurface morphologyand composition

DFTElectronic structure of stable species, intermediates andtransition 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)

Rctn No. Reaction H eqK fA fE revA revE

1 H2+2*-->2H* -95.73 4.70E+02 1.0E+07 0.00

2 CO+*-->CO* -106.12 1.28E+01 1.0E+07 0.00

3 (rds) CO*+*-->C*+O* 36.47 9.24E-05 1.0E+13 90.52

4 C*+H*-->CH* + * -38.42 2.34E+04 1.0E+13 66.56

5 H* + O* --> OH* + * 43.82 1.30E-04 1.0E+13 106.12

6 OH* + H* --> H2O+ 2* 73.35 7.91E+01 1.0E+07 87.02

7 CH* + H* --> CH2* + * 13.21 8.29E-02 1.0E+13 42.45

8 CH2* + H* --> CH3* + * 44.56 3.73E-05 1.0E+13 53.06

9 CH3* + H* --> CH4 + 2* 3.78 3.85E+08 1.0E+07 123.34

10 CH2* + CH2* --> C2H4* + * 28.14 4.06E-04 1.0E+13 53.06

11 C2H4* + H* --> C2H5* + * 40.46 3.76E-04 1.0E+13 53.06

12 C2H5* + H* --> C2H6 + 2* 0.54 1.19E+10 1.0E+07 48.24

13 C2H4* + CH2* --> C3H6* + * -30.22 9.28E+02 1.0E+13 53.06

14 C3H6* + H* --> C3H7* + * 54.29 1.17E-05 1.0E+13 53.06

15 C3H7* + H* --> C3H8 + 2* 27.57 5.82E+08 1.0E+07 48.24

16 C2H4* --> C2H4+* 85.86 3.93E+01

17 C3H6* --> C3H6+* 114.80 1.95E+00 On Wisconsin

UWM

Preferred Adsorption Sites and Binding Energies for Intermediates in CH4 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 200C, Pressure Total = 20 atm.)

250.025.0

50.075.0

)1(2

2

COH

COH

PPb

PPar

Rate Expression Derived from Original Carbide Mechanism

(Huber, 2000)

0

10

20

30

40

50

60

70

80

0 10 20 30 40 50 60 70 80

Rate Measured (mole CO/h kg Co)

Ra

te C

alc

ula

ted

(m

ole

CO

/h k

g C

o) Model 1 Carbide

Model 2 Carbide

Power Law

Model Yates

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 10-5 for several sets of data.

-20

-15

-10

-5

0

5

10

15

20

0 5 10 15 20 25

Run #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)

Rctn No. Reaction H eqK fA fE revA revE

1 H2+2*-->2H* -95.73 4.70E+02 1.0E+07 0.00

2 CO+*-->CO* -106.12 1.28E+01 1.0E+07 0.00

3 (rds) CO*+*-->C*+O* 36.47 9.24E-05 1.0E+13 90.52

4 C*+H*-->CH* + * -38.42 2.34E+04 1.0E+13 66.56

5 H* + O* --> OH* + * 43.82 1.30E-04 1.0E+13 106.12

6 OH* + H* --> H2O+ 2* 73.35 7.91E+01 1.0E+07 87.02

7 CH* + H* --> CH2* + * 13.21 8.29E-02 1.0E+13 42.45

8 CH2* + H* --> CH3* + * 44.56 3.73E-05 1.0E+13 53.06

9 CH3* + H* --> CH4 + 2* 3.78 3.85E+08 1.0E+07 123.34

10 CH2* + CH2* --> C2H4* + * 28.14 4.06E-04 1.0E+13 53.06

11 C2H4* + H* --> C2H5* + * 40.46 3.76E-04 1.0E+13 53.06

12 C2H5* + H* --> C2H6 + 2* 0.54 1.19E+10 1.0E+07 48.24

13 C2H4* + CH2* --> C3H6* + * -30.22 9.28E+02 1.0E+13 53.06

14 C3H6* + H* --> C3H7* + * 54.29 1.17E-05 1.0E+13 53.06

15 C3H7* + H* --> C3H8 + 2* 27.57 5.82E+08 1.0E+07 48.24

16 C2H4* --> C2H4+* 85.86 3.93E+01

17 C3H6* --> C3H6+* 114.80 1.95E+00 On Wisconsin

UWM

2

50.075.0

)1(2

CO

COH

Pb

PPar

Approach

0.0

10.0

20.0

30.0

40.0

50.0

0.00 10.00 20.00 30.00 40.00 50.00

Measured Rate

Fit

Dat

a

Data points: 11Chi-squared: 0.20Chi-distr.prob. = 1.00

Huber and Bartholomew

r = a PH2^0.75 PCO^0.5 / (1 + b PCO)^2

0.0

5.0

10.0

15.0

20.0

25.0

30.0

0.0 5.0 10.0 15.0 20.0 25.0 30.0

Experimental TOF

Cal

cula

ted

TO

F

Zennaro et al.

Data points: 9Chi-squared: 0.15Chi-distr.prob. = 1.00

r = a PH2 0̂.75 PCO 0̂.5 / (1 + b PCO) 2̂

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.

Kinetic expression Mechanistic Implications References

Cobalt Catalysts

C1 2

-0.2 0.7CO CO Hr a P P

CO inhibits reaction; CO strongly adsorbed; high CO

Ribiero et al., 1997; Zennaro et al., 2000

C2 2CO H

COCO

21

a P Pr

bP

high CO; enolic mechanism;

hydrogenation of HCOH (rds) Yates and Satterfield, 1991; Zennaro et al., 2000

C3 CO H2

COCO1

m na P Pr

bP

,

m = 0.5 – 0.6, n = 0.6 – 0.9

moderate CO; Eley-Rideal; stepwise hydrogenation of Cs

Iglesia et al., 1993b.; Peluso et al., 2001

C4 2

0.5 0.5CO H

CO0.5

CO

21

a P Pr

b P

high CO; Cs + Hs and

Os + Hs are rds’s

Sarup, 1989; Keyser et al., 2000; Huber, 2000; Huber and Bartholomew 2005

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