Optimization of Reaction Rate Parameters in Modeling of Heavy Paraffins Dehydrogenation
In the present study, a procedure was developed to
determine the optimum reaction rate constants in generalized
Arrhenius form and optimized through the Nelder-Mead method. For
this purpose, a comprehensive mathematical model of a fixed bed
reactor for dehydrogenation of heavy paraffins over Pt–Sn/Al2O3
catalyst was developed. Utilizing appropriate kinetic rate expressions
for the main dehydrogenation reaction as well as side reactions and
catalyst deactivation, a detailed model for the radial flow reactor was
obtained. The reactor model composed of a set of partial differential
equations (PDE), ordinary differential equations (ODE) as well as
algebraic equations all of which were solved numerically to
determine variations in components- concentrations in term of mole
percents as a function of time and reactor radius. It was demonstrated
that most significant variations observed at the entrance of the bed
and the initial olefin production obtained was rather high. The
aforementioned method utilized a direct-search optimization
algorithm along with the numerical solution of the governing
differential equations. The usefulness and validity of the method was
demonstrated by comparing the predicted values of the kinetic
constants using the proposed method with a series of experimental
values reported in the literature for different systems.
[1] George A. Olah, Hydrocarbon Chemistry, John Wiley, New York, 2002.
[2] N. A. Gaidai, S. L. Kiperman, Kinetic Models of Catalyst Deactivation
in Paraffin Dehydrogenation, Kinetics and Catalysis 42 (2001) 527-532.
[3] Maryam Saeedizad, Saeed Sahebdelfar, Zahra Mansourpour,
Deactivation kinetics of platinum-based catalysts in dehydrogenation of
higher alkanes, Chemical Engineering Journal 154 (2009) 76-81.
[4] Victor K. Shum, John B. Butt, Wolfgang M. H. Sachtler, The effects of
rhenium and sulfur on the activity maintenance and selectivity of
platinum/alumina hydrocarbon conversion catalysts, Journal of Catalysis
96 (1985) 371-380.
[5] Robert W. Coughlin, Koei Kwakami, Akram Hasan, Activity, yield
patterns, and coking behavior of Pt and PtRe catalysts during
dehydrogenation of methylcyclohexane: I. In the absence of sulfur,
Journal of Catalysis 88 (1984) 150-62.
[6] M. J. Dees, V. Ponec, On the influence of sulfur on the platinum/iridium
bimetallic catalysts in n-hexane/hydrogen reactions, Journal of Catalysis
115 (1989) 347-355.
[7] J. Barbier, P. Marecol, Effect of presulfurization on the formation of
coke on supported metal catalysts, Journal of Catalysis 102 (1986) 21-
28.
[8] M.J. Dess, V. Ponec, The influence of sulfur and carbonaceous deposits
on the selectivity and activity of Pt/Co catalysts in hydrocarbon
reactions, Journal of Catalysis 119 (1990) 376-387.
[9] G. Padmavathi, K. K. Chaudhuri,, D. Rajeshwer, G. Sreenivasa Rao,
K.R. Krishnamurthy, P.C. Trivedi, K. K. Hathi, N. Subramanyam,
Kinetics of n-dodecane dehydrogenation on promoted platinum catalyst,
Chemical Engineering Science 60 (2005) 4119-4129.
[10] M. M. Bhasin, J.H. McCain, B.V. Vora, T. Imai, P.R. Pujado,
Dehydrogenation and oxydehydrogenation of paraffins to olefins,
Applied Catalysis A: General 221 (2001) 397-419.
[11] Joseph A. Kocal, Bipin V. Vora, Tamotsu Imai, Production of linear
alkylbenzenes, Applied Catalysis A: General 221 (2001) 295-301.
[12] S. D. Harris, L. Elliott, D. B. Ingham, M. Pourkashanian, C. W. Wilson,
The optimisation of reaction rate parameters for chemical kinetic
modelling of combustion using genetic algorithms, Computer Methods
in Applied Mechanics and Engineering 190 (2000) 1065-1090
[13] André Bardow, Wolfgang Marquardt, Incremental and simultaneous
identification of reaction kinetics: methods and comparison, Chemical
Engineering Science 59 (2004) 2673-2684
[14] G. S. G. Beveridge, R. S. Schechter, Optimization: Theory and Practice,
New York: McGraw-Hill, 1970.
[15] H. Rabitz, M. Kramer, D. Dacol, Sensitivity Analysis in Chemical
Kinetics, Annual Review of Physical Chemistry 34 (1983) 419-461.
[16] Herschel Rabitz, Chemical sensitivity analysis theory with applications
to molecular dynamics and kinetics, Computers & Chemistry 5 (1981)
167-180.
[17] Robert Michael Lewis, Virginia Torczon, Michael W. Trosset, Direct
search methods: then and now, Journal of Computational and Applied
Mathematics 124 (2000) 191-207.
[18] Erwie Zahara, Yi-Tung Kao, Hybrid Nelder-Mead simplex search and
particle swarm optimization for constrained engineering design
problems, Expert Systems with Applications 36 (2009) 3880-3886.
[19] Rachid Chelouah, Patrick Siarry, Genetic and Nelder-Mead algorithms
hybridized for a more accurate global optimization of continuous
multiminima functions, European Journal of Operational Research 148
(2003) 335-348.
[20] C. J. Price, I. D. Coope, D. Byatt, A Convergent Variant of the Nelder-
Mead Algorithm, Journal of optimization theory and applications 113
(2002) 5-19.
[21] R. Nakamura, M. Shimoji, H. Niiyama, Strategies for using a computeroperated
reaction system for the evaluation of catalyst activity by
optimization of product yield, Catalysis Today 10 (1991) 119-129.
[22] Jeffrey C. Lagarias, James A. Reeds, Margaret H. Wright, Paul E.
Wright, Convergence properties of the Nelder-Mead simplex method in
low dimensions, SIAM Journal of Optimization 9 (1998) 112-147.
[23] Marco A. Luersen, Rodolphe Le Riche, Globalized Nelder-Mead
method for engineering optimization, Computers and Structures 82
(2004) 2251-2260.
[24] Julian Martinez, J.M. Martinez, Fitting the Sovova-s supercritical fluid
extraction model by means of a global optimization tool, Computers and
Chemical Engineering 32 (2008) 1735-1745.
[25] Maryam Mohagheghi, Gholamreza Bakeri, Maryam Saeedizad, Study of
the Effects of External and Internal Diffusion on the Propane
Dehydrogenation Reaction over Pt-Sn/Al2O3 Catalyst, Chemical
Engineering & Technology 30 (2007) 1721-1725.
[26] R.B. Bird, W.E. Stewart, E.N. Lightfoot, Transport Phenomena, second
edition, John Wily, New York, 2002.
[27] N. George, B.V. Kamath, A.G. Basrur, K.R. Krishnamurthy, Lithium
Promoted Pt-Sn/Al2O3 catalysts for dehydrogenation of n-decane:
Influence of Lithium metal precursors, Reaction Kinetics and Catalysis
Letters 59 (1996) 315-323.
[28] Jose O. Valderrama, The State of the Cubic Equations of State,
Industrial & Engineering Chemistry Research 42 (2003) 1603-1618.
[29] G. Zahedi, H. Yaqubi, M. Ba-Shammakh, Dynamic modeling and
simulation of heavy paraffin dehydrogenation reactor for selective olefin
production in linear alkyl benzene production plant, Applied Catalysis
A: General 358 (2009) 1-6.
[30] Curtis F. Gerald, Patrick O. Wheatley, Applied Numerical Analysis, 6th
Edition, Addison Wesley, 1999.
[1] George A. Olah, Hydrocarbon Chemistry, John Wiley, New York, 2002.
[2] N. A. Gaidai, S. L. Kiperman, Kinetic Models of Catalyst Deactivation
in Paraffin Dehydrogenation, Kinetics and Catalysis 42 (2001) 527-532.
[3] Maryam Saeedizad, Saeed Sahebdelfar, Zahra Mansourpour,
Deactivation kinetics of platinum-based catalysts in dehydrogenation of
higher alkanes, Chemical Engineering Journal 154 (2009) 76-81.
[4] Victor K. Shum, John B. Butt, Wolfgang M. H. Sachtler, The effects of
rhenium and sulfur on the activity maintenance and selectivity of
platinum/alumina hydrocarbon conversion catalysts, Journal of Catalysis
96 (1985) 371-380.
[5] Robert W. Coughlin, Koei Kwakami, Akram Hasan, Activity, yield
patterns, and coking behavior of Pt and PtRe catalysts during
dehydrogenation of methylcyclohexane: I. In the absence of sulfur,
Journal of Catalysis 88 (1984) 150-62.
[6] M. J. Dees, V. Ponec, On the influence of sulfur on the platinum/iridium
bimetallic catalysts in n-hexane/hydrogen reactions, Journal of Catalysis
115 (1989) 347-355.
[7] J. Barbier, P. Marecol, Effect of presulfurization on the formation of
coke on supported metal catalysts, Journal of Catalysis 102 (1986) 21-
28.
[8] M.J. Dess, V. Ponec, The influence of sulfur and carbonaceous deposits
on the selectivity and activity of Pt/Co catalysts in hydrocarbon
reactions, Journal of Catalysis 119 (1990) 376-387.
[9] G. Padmavathi, K. K. Chaudhuri,, D. Rajeshwer, G. Sreenivasa Rao,
K.R. Krishnamurthy, P.C. Trivedi, K. K. Hathi, N. Subramanyam,
Kinetics of n-dodecane dehydrogenation on promoted platinum catalyst,
Chemical Engineering Science 60 (2005) 4119-4129.
[10] M. M. Bhasin, J.H. McCain, B.V. Vora, T. Imai, P.R. Pujado,
Dehydrogenation and oxydehydrogenation of paraffins to olefins,
Applied Catalysis A: General 221 (2001) 397-419.
[11] Joseph A. Kocal, Bipin V. Vora, Tamotsu Imai, Production of linear
alkylbenzenes, Applied Catalysis A: General 221 (2001) 295-301.
[12] S. D. Harris, L. Elliott, D. B. Ingham, M. Pourkashanian, C. W. Wilson,
The optimisation of reaction rate parameters for chemical kinetic
modelling of combustion using genetic algorithms, Computer Methods
in Applied Mechanics and Engineering 190 (2000) 1065-1090
[13] André Bardow, Wolfgang Marquardt, Incremental and simultaneous
identification of reaction kinetics: methods and comparison, Chemical
Engineering Science 59 (2004) 2673-2684
[14] G. S. G. Beveridge, R. S. Schechter, Optimization: Theory and Practice,
New York: McGraw-Hill, 1970.
[15] H. Rabitz, M. Kramer, D. Dacol, Sensitivity Analysis in Chemical
Kinetics, Annual Review of Physical Chemistry 34 (1983) 419-461.
[16] Herschel Rabitz, Chemical sensitivity analysis theory with applications
to molecular dynamics and kinetics, Computers & Chemistry 5 (1981)
167-180.
[17] Robert Michael Lewis, Virginia Torczon, Michael W. Trosset, Direct
search methods: then and now, Journal of Computational and Applied
Mathematics 124 (2000) 191-207.
[18] Erwie Zahara, Yi-Tung Kao, Hybrid Nelder-Mead simplex search and
particle swarm optimization for constrained engineering design
problems, Expert Systems with Applications 36 (2009) 3880-3886.
[19] Rachid Chelouah, Patrick Siarry, Genetic and Nelder-Mead algorithms
hybridized for a more accurate global optimization of continuous
multiminima functions, European Journal of Operational Research 148
(2003) 335-348.
[20] C. J. Price, I. D. Coope, D. Byatt, A Convergent Variant of the Nelder-
Mead Algorithm, Journal of optimization theory and applications 113
(2002) 5-19.
[21] R. Nakamura, M. Shimoji, H. Niiyama, Strategies for using a computeroperated
reaction system for the evaluation of catalyst activity by
optimization of product yield, Catalysis Today 10 (1991) 119-129.
[22] Jeffrey C. Lagarias, James A. Reeds, Margaret H. Wright, Paul E.
Wright, Convergence properties of the Nelder-Mead simplex method in
low dimensions, SIAM Journal of Optimization 9 (1998) 112-147.
[23] Marco A. Luersen, Rodolphe Le Riche, Globalized Nelder-Mead
method for engineering optimization, Computers and Structures 82
(2004) 2251-2260.
[24] Julian Martinez, J.M. Martinez, Fitting the Sovova-s supercritical fluid
extraction model by means of a global optimization tool, Computers and
Chemical Engineering 32 (2008) 1735-1745.
[25] Maryam Mohagheghi, Gholamreza Bakeri, Maryam Saeedizad, Study of
the Effects of External and Internal Diffusion on the Propane
Dehydrogenation Reaction over Pt-Sn/Al2O3 Catalyst, Chemical
Engineering & Technology 30 (2007) 1721-1725.
[26] R.B. Bird, W.E. Stewart, E.N. Lightfoot, Transport Phenomena, second
edition, John Wily, New York, 2002.
[27] N. George, B.V. Kamath, A.G. Basrur, K.R. Krishnamurthy, Lithium
Promoted Pt-Sn/Al2O3 catalysts for dehydrogenation of n-decane:
Influence of Lithium metal precursors, Reaction Kinetics and Catalysis
Letters 59 (1996) 315-323.
[28] Jose O. Valderrama, The State of the Cubic Equations of State,
Industrial & Engineering Chemistry Research 42 (2003) 1603-1618.
[29] G. Zahedi, H. Yaqubi, M. Ba-Shammakh, Dynamic modeling and
simulation of heavy paraffin dehydrogenation reactor for selective olefin
production in linear alkyl benzene production plant, Applied Catalysis
A: General 358 (2009) 1-6.
[30] Curtis F. Gerald, Patrick O. Wheatley, Applied Numerical Analysis, 6th
Edition, Addison Wesley, 1999.
@article{"International Journal of Chemical, Materials and Biomolecular Sciences:53014", author = "Leila Vafajoo and Farhad Khorasheh and Mehrnoosh Hamzezadeh Nakhjavani and Moslem Fattahi", title = "Optimization of Reaction Rate Parameters in Modeling of Heavy Paraffins Dehydrogenation", abstract = "In the present study, a procedure was developed to
determine the optimum reaction rate constants in generalized
Arrhenius form and optimized through the Nelder-Mead method. For
this purpose, a comprehensive mathematical model of a fixed bed
reactor for dehydrogenation of heavy paraffins over Pt–Sn/Al2O3
catalyst was developed. Utilizing appropriate kinetic rate expressions
for the main dehydrogenation reaction as well as side reactions and
catalyst deactivation, a detailed model for the radial flow reactor was
obtained. The reactor model composed of a set of partial differential
equations (PDE), ordinary differential equations (ODE) as well as
algebraic equations all of which were solved numerically to
determine variations in components- concentrations in term of mole
percents as a function of time and reactor radius. It was demonstrated
that most significant variations observed at the entrance of the bed
and the initial olefin production obtained was rather high. The
aforementioned method utilized a direct-search optimization
algorithm along with the numerical solution of the governing
differential equations. The usefulness and validity of the method was
demonstrated by comparing the predicted values of the kinetic
constants using the proposed method with a series of experimental
values reported in the literature for different systems.", keywords = "Dehydrogenation, Pt-Sn/Al2O3 Catalyst, Modeling,Nelder-Mead, Optimization", volume = "5", number = "7", pages = "547-5", }
