S. Floyd, K. Y. Choi, T. W. Taylor, and W. H. Ray, Polymerization of olefins through heterogeneous catalyst. III. Polymer particle modeling with an analysis of intraparticle heat and mass transfer effects, Journal of Applied Polymer Science, issue.1, pp.32-2935, 1986.

S. Floyd, K. Y. Choi, T. W. Taylor, and W. H. Ray, Polymerization of olefins through heterogeneous catalyst. IV. Modeling of heat and mass transfer resistance in the polymer particle boundary layer, Journal of Applied Polymer Science, issue.7, pp.31-2231, 1986.

T. F. Mckenna and J. B. Soares, Single particle modelling for olefin polymerization on supported catalysts: A review and proposals for future developments, Chemical Engineering Science, vol.56, issue.13, pp.56-3931, 2001.
DOI : 10.1016/S0009-2509(01)00069-0

R. A. Hutchison, C. M. Chen, and W. H. Ray, Polymerization of olefins through heterogeneous catalysis. X: Modeling of particle growth and morphology, Journal of Applied Polymer Science, issue.8, pp.44-1389, 1992.

K. B. Mcauley and J. F. Macgregor, On-line inference of polymer properties in an industrial polyethylene reactor, AIChE Journal, vol.37, issue.6, pp.37825-835, 1991.
DOI : 10.1002/aic.690370605

K. B. Mcauley, J. F. Macgregor, and A. E. Hamielec, A kinetic model for industrial gas-phase ethylene copolymerization, AIChE Journal, vol.36, issue.6, pp.36837-850, 1990.
DOI : 10.1002/aic.690360605

K. B. Mcauley, J. P. Talbot, and T. J. Harris, A comparison of two-phase and well-mixed models for fluidized-bed polyethylene reactors, Chemical Engineering Science, vol.49, issue.13, pp.49-2035, 1994.
DOI : 10.1016/0009-2509(94)E0030-T

K. Y. Choi and W. H. Ray, The dynamic behaviour of fluidized bed reactors for solid catalyzed gas phase olefin polymerization, Chemical Engineering Science, issue.12, pp.40-2261, 1985.

H. Hatzantonis, H. Yiannoulakis, A. Yiagopoulos, and C. Kiparissides, Recent developments in modeling gas-phase catalyzed olefin polymerization fluidized-bed reactors: The effect of bubble size variation on the reactor's performance, Chemical Engineering Science, vol.55, issue.16, pp.553237-3259, 2000.
DOI : 10.1016/S0009-2509(99)00565-5

F. A. Fernandes and L. M. Lona, Fluidized-bed reactor modeling for polyethylene production, Journal of Applied Polymer Science, vol.33, issue.2, pp.81321-332, 2001.
DOI : 10.1021/ie00027a001

A. Kiashemshaki, N. Mostoufi, R. S. Gharebagh, and S. Pounnahadian, Reactor Modeling of Gas-Phase Polymerization of Ethylene, Chemical Engineering & Technology, vol.91, issue.11, pp.27-1227, 2004.
DOI : 10.1002/ceat.200401964

A. Kiashemshaki, N. Mostoufi, and R. S. Gharebagh, Two-phase modeling of a gas phase polyethylene fluidized bed reactor, Chemical Engineering Science, vol.61, issue.12, pp.61-3997, 2006.
DOI : 10.1016/j.ces.2006.01.042

M. Alizadeh, N. Mostoufia, S. Pourmahdian, and R. S. Gharebagh, Modeling of fluidized bed reactor of ethylene polymerization, Chemical Engineering Journal, vol.97, issue.1, pp.27-35, 2004.
DOI : 10.1016/S1385-8947(03)00133-5

G. Dompazis, V. Kanellopoulos, and C. Kiparissides, A Multi-Scale Modeling Approach for the Prediction of Molecular and Morphological Properties in Multi-Site Catalyst, Olefin Polymerization Reactors, Macromolecular Materials and Engineering, vol.87, issue.6, pp.290-525, 2005.
DOI : 10.1016/S0009-2509(98)00122-5

B. Kou, K. B. Mcauley, C. C. Hsu, D. W. Bacon, and K. Z. Yao, Mathematical Model and Parameter Estimation for Gas-Phase Ethylene Homopolymerization with Supported Metallocene Catalyst, Industrial & Engineering Chemistry Research, vol.44, issue.8, pp.44-2428, 2005.
DOI : 10.1021/ie048957o

M. Ohshima and M. Tanigaki, Quality control of polymer production processes, Journal of Process Control, vol.10, issue.2-3, pp.135-148, 2000.
DOI : 10.1016/S0959-1524(99)00042-6

K. M. Moudgalya and S. Jaguste, A class of discontinuous dynamical systems II. An industrial slurry high density polyethylene reactor, Chemical Engineering Science, vol.56, issue.11, pp.56-3611, 2001.
DOI : 10.1016/S0009-2509(01)00044-6

C. P. Bokis, S. Ramanathan, J. Franjione, A. Buchelli, M. L. Call et al., Physical properties, reactor modeling, and polymerization kinetics in the low-density polyethylene tubular teactor process, Industrial Engineering Chemistry Research, issue.5, pp.411017-1030, 2002.

N. P. Khare, K. C. Seavey, Y. A. Liu, S. Ramanathan, S. Lingard et al., Steady-State and Dynamic Modeling of Commercial Slurry High-Density Polyethylene (HDPE) Processes, Industrial & Engineering Chemistry Research, vol.41, issue.23
DOI : 10.1021/ie020451n

M. Hinchliffe, G. Montagre, M. Willis, and A. Burke, Hybrid approach to modeling an industrial polyethylene process, AIChE Journal, vol.42, issue.12, pp.49-3127, 2003.
DOI : 10.1002/aic.690491213

R. Bindlish, J. B. Rawlings, and R. E. Yong, Parameter estimation for industrial polymerization processes, AIChE Journal, vol.36, issue.8, pp.49-2071, 2003.
DOI : 10.1137/1.9781611971217

A. Prasetya, L. Liu, J. Litster, F. Watanabe, K. Mitsutani et al., Dynamic model development for residence time distribution control in high-impact polypropylene copolymer process, Chemical Engineering Science, vol.54, issue.15-16, pp.54-3263, 1999.
DOI : 10.1016/S0009-2509(98)00410-2

N. M. Ghasem, Dynamic behavior of industrial gas phase fluidized bed polyethylene reactors under PI control. Chemical engineering technology, pp.133-140, 2000.

C. Sato, T. Ohtani, and H. Nishitani, Modeling, simulation and nonlinear control of a gas-phase polymerization process, Computers & Chemical Engineering, vol.24, issue.2-7, pp.945-951, 2000.
DOI : 10.1016/S0098-1354(00)00375-6

A. B. Gorbach, S. D. Naik, and W. H. Ray, Dynamics and stability analysis of solid catalyzed gas-phase polymerization of olefins in continuous stirred bed reactors, Chemical Engineering Science, vol.55, issue.20, pp.55-4461, 2000.
DOI : 10.1016/S0009-2509(00)00080-4

G. J. Wells, W. H. Ray, and J. Kosek, Effects of catalyst activity profiles on polyethylene reactor dynamics, AIChE Journal, vol.34, issue.12, pp.472768-2780, 2001.
DOI : 10.1021/cen-v078n006.p055

G. Dompazis, V. Kanellopoulos, V. Touloupides, and C. Kiparissides, Development of a multi-scale, multi-phase, multi-zone dynamic model for the prediction of particle segregation in catalytic olefin polymerization FBRs, Chemical Engineering Science, vol.63, issue.19, pp.63-4735, 2008.
DOI : 10.1016/j.ces.2007.08.069

J. A. Debling, G. C. Han, F. Kuijpers, J. Verburg, J. Zacca et al., Dynamic modeling of product grade transitions for olefin polymerization processes, AIChE Journal, vol.40, issue.3, pp.40-506, 1994.
DOI : 10.1002/aic.690400312

A. M. Cervantes, S. Tonelli, A. Brandolin, J. A. Bandoni, and L. T. Biegler, Large-scale dynamic optimization for grade transitions in a low density polyethylene plant, Computers & Chemical Engineering, vol.26, issue.2, pp.26-227, 2002.
DOI : 10.1016/S0098-1354(01)00743-8

H. S. Yi, J. H. Kim, C. Han, J. Lee, and S. S. Na, Plantwide Optimal Grade Transition for an Industrial High-Density Polyethylene Plant, Industrial & Engineering Chemistry Research, vol.42, issue.1, pp.42-91, 2003.
DOI : 10.1021/ie0202221

C. Chatzidoukas, J. D. Perkins, E. N. Pistikopoulos, and C. Kiparissides, Optimal grade transition and selection of closed-loop controllers in a gas-phase olefin polymerization fluidized bed reactor, Chemical Engineering Science, vol.58, issue.16, pp.58-3643, 2003.
DOI : 10.1016/S0009-2509(03)00223-9

D. Feather, D. Harrell, R. Lieberman, and F. J. Doyle, Hybrid approach to polymer grade transition control, AIChE Journal, vol.48, issue.10, pp.50-2502, 2004.
DOI : 10.1016/0009-2509(93)80218-F

M. R. Rahimpour, J. Fathikalajahi, B. Moghtaderi, and A. N. Farahani, A Grade Transition Strategy for the Prevention of Melting and Agglomeration of Particles in an Ethylene Polymerization Reactor, Chemical Engineering & Technology, vol.15, issue.12, pp.28-831, 2005.
DOI : 10.1002/ceat.200500055

D. P. Lo and W. H. Ray, Dynamic modeling of polyethylene grade transitions in fluidized bed reactors employing vickel-diimine catalysts, Industrial & Engineering Chemistry Research, issue.3, pp.45-993, 2006.

R. Rawatlal and I. Tincul, Development of an Unsteady-State Model for Control of Polymer Grade Transitions in Ziegler-Natta Catalyzed Reactor Systems, Macromolecular Symposia, vol.213, issue.1, pp.80-89, 2007.
DOI : 10.1080/10543414.1999.10744528

F. Rodriguez, Principes of Polymer Systems, p.167, 1970.

K. B. Mcauley, J. F. Macgregor, and A. E. Hamielec, A kinetic model for industrial gas-phase ethylene copolymerization, AIChE Journal, vol.36, issue.6, pp.36-837, 1990.
DOI : 10.1002/aic.690360605

M. Alizadeh, N. Mostoufia, S. Pourmahdian, and R. S. Gharebagh, Modeling of fluidized bed reactor of ethylene polymerization, Chemical Engineering Journal, vol.97, issue.1, pp.27-35, 2004.
DOI : 10.1016/S1385-8947(03)00133-5

A. Kiashemshaki, N. Mostoufi, R. S. Gharebagh, and S. Pounnahadian, Reactor Modeling of Gas-Phase Polymerization of Ethylene, Chemical Engineering & Technology, vol.91, issue.11, pp.27-1227, 2004.
DOI : 10.1002/ceat.200401964

A. G. Neto, M. F. Freitas, M. Nele, and J. C. Pinto, Modeling ethylene/1-butene copolymerizations in industrial slurry reactors, Industrial & Engineering Chemistry Research, issue.8, pp.44-2697, 2005.

H. M. Quackenbos, Practical use of intrinsic viscosity for polyethylenes, Journal of Applied Polymer Science, vol.13, issue.2, pp.341-351, 1969.
DOI : 10.1002/app.1969.070130207

C. P. Bokis, H. Orbey, and C. Chen, Properly model polymer processes, Chemical Engineering Progress, issue.4, pp.39-52, 1999.

I. C. Sanchez and R. H. Lacombe, Statistical Thermodynamics of Polymer Solutions, Macromolecules, vol.11, issue.6, pp.1145-1156, 1978.
DOI : 10.1021/ma60066a017

I. C. Sanchez and R. H. Lacombe, An elementary molecular theory of classical fluids. Pure fluids, The Journal of Physical Chemistry, vol.80, issue.21, pp.80-2352, 1976.
DOI : 10.1021/j100562a008

W. G. Chapman, G. Jackson, and K. E. Gubbins, Phase equilibria of associating fluids. Chain molecules with multiple bonding sites, Molecular Physics, issue.5, pp.65-1057, 1988.

W. G. Chapman, K. E. Gubbins, G. Jachson, and M. Radosz, New reference equation of state for associating liquids, Industrial & Engineering Chemistry Research, vol.29, issue.8, pp.29-1709, 1990.
DOI : 10.1021/ie00104a021

S. H. Huang and M. Radosz, Equation of state for small, large, polydisperse, and associating molecules, Industrial & Engineering Chemistry Research, vol.29, issue.11, pp.29-2284, 1990.
DOI : 10.1021/ie00107a014

J. Gross and G. Sadowski, Perturbed-Chain SAFT:?? An Equation of State Based on a Perturbation Theory for Chain Molecules, Industrial & Engineering Chemistry Research, vol.40, issue.4, pp.40-1244, 2001.
DOI : 10.1021/ie0003887

H. Orbey, C. P. Bokis, and C. C. Chen, Equation of State Modeling of Phase Equilibrium in the Low-Density Polyethylene Process:?? The Sanchez???Lacombe, Statistical Associating Fluid Theory, and Polymer-Soave???Redlich???Kwong Equations of State, Industrial & Engineering Chemistry Research, vol.37, issue.11, pp.37-4481, 1998.
DOI : 10.1021/ie980220+

N. P. Khare, K. C. Seavey, Y. A. Liu, S. Ramanathan, S. Lingard et al., Steady-State and Dynamic Modeling of Commercial Slurry High-Density Polyethylene (HDPE) Processes, Industrial & Engineering Chemistry Research, vol.41, issue.23
DOI : 10.1021/ie020451n

N. P. Khare, B. Lucas, K. C. Seavey, Y. A. Liu, A. Sirohi et al., Steady-State and Dynamic Modeling of Gas-Phase Polypropylene Processes Using Stirred-Bed Reactors, Industrial & Engineering Chemistry Research, vol.43, issue.4, pp.43-884, 2004.
DOI : 10.1021/ie030714t

H. Orbey, C. P. Bokis, and C. C. Chen, Equation of State Modeling of Phase Equilibrium in the Low-Density Polyethylene Process:?? The Sanchez???Lacombe, Statistical Associating Fluid Theory, and Polymer-Soave???Redlich???Kwong Equations of State, Industrial & Engineering Chemistry Research, vol.37, issue.11, pp.37-4481, 1998.
DOI : 10.1021/ie980220+

S. H. Huang and M. Radosz, Equation of state for small, large, polydisperse, and associating molecules, Industrial & Engineering Chemistry Research, vol.29, issue.11, pp.29-2284, 1990.
DOI : 10.1021/ie00107a014

N. P. Khare, B. Lucas, K. C. Seavey, Y. A. Liu, A. Sirohi et al., Steady-State and Dynamic Modeling of Gas-Phase Polypropylene Processes Using Stirred-Bed Reactors, Industrial & Engineering Chemistry Research, vol.43, issue.4, pp.43-884, 2004.
DOI : 10.1021/ie030714t

F. Tumakaka, J. Gross, and G. Sadowski, Modeling of polymer phase equilibria using Perturbed-Chain SAFT. Fluid Phase Equilibria, pp.194-197, 2002.

A. Ghosha, W. G. Chapmana, and R. N. French, Gas solubility in hydrocarbons: a SAFT-based approach. Fluid Phase Equilibria, pp.229-243, 2003.

F. Tumakaka, J. Gross, and G. Sadowski, Modeling of polymer phase equilibria using Perturbed-Chain SAFT. Fluid Phase Equilibria, pp.194-197, 2002.

A. Ghosha, W. G. Chapmana, and R. N. French, Gas solubility in hydrocarbons: a SAFT-based approach. Fluid Phase Equilibria, pp.229-243, 2003.

J. Gross and G. Sadowski, Modeling Polymer Systems Using the Perturbed-Chain Statistical Associating Fluid Theory Equation of State, Industrial & Engineering Chemistry Research, vol.41, issue.5, pp.41-1084, 2002.
DOI : 10.1021/ie010449g

O. Olabisi and R. Simha, Pressure-Volume-Temperature Studies of Amorphous and Crystallizable Polymers. I. Experimental, Macromolecules, vol.8, issue.2, pp.206-210, 1975.
DOI : 10.1021/ma60044a022

T. J. De-vries, P. J. Somers, T. W. De-loos, M. A. Vorstman, and J. T. Keurentjes, -propylene) in Ethylene and Carbon Dioxide:?? Experimental Results and Modeling with the Statistical Associating Fluid Theory Equation of State, Industrial & Engineering Chemistry Research, vol.39, issue.12
DOI : 10.1021/ie0001218

O. M. Goral, K. Blazej, A. Bok, A. Skezecz, and A. Maczynski, Vapor-liquid equilibria,Volume 7 Hydrocarbons Part3 Binary systems of C1 to C4 with C2 to C40 hydrocarbons, 1999.

W. Gao, R. L. Robinson, and K. A. Gasem, Solubilities of hydrogen in hexane and of carbon monoxide in cyclohexane at temperatures from 344.3 to 410.9K and pressures to 15Mpa, Journal of Chemical and Angineering Data, issue.3, pp.46-609, 2001.

R. B. Williams and D. L. Katz, Vapor-Liquid Equilibria in Binary Systems. Hydrogen with Ethylene, Ethane, Propylene, and Propane, Industrial & Engineering Chemistry, vol.46, issue.12, pp.46-2512, 1954.
DOI : 10.1021/ie50540a033

R. S. Poston and J. J. Mcketta, Vapor-liquid equilibrium in the n-hexane-nitrogen system, Journal of Chemical and Engineering Data, issue.3, pp.11-364, 1966.

H. Wen, H. S. Elbro, and P. Alessi, Polymer solution data collection, Part 1: Vapor-liquid equilibrium, pp.106-111, 1992.

H. A. Kennis, L. W. Th, and J. D. Arons, The influence of nitrogen on the liquid???liquid phase behaviour of the system n-hexane???polyethylene: experimental results and predictions with the mean-field lattice-gas model, Chemical Engineering Science, vol.45, issue.7, pp.45-1875, 1990.
DOI : 10.1016/0009-2509(90)87063-X

T. Xie, K. B. Mcauley, J. C. Hsu, and D. W. Bacon, Modeling molecular weight development of gas-phase ?-olefin copolymerization, AIChE J, issue.5, pp.41-1251, 1995.

J. B. Soares, Mathematical modeling of the microstructure of polyolefins made by coordination polymerization: a review, Chemical Engineering Science, issue.13, pp.56-4131, 2001.

A. G. Neto, M. F. Freitas, M. Nele, and J. C. Pinto, Modeling ethylene/1-butene copolymerizations in industrial slurry reactors, Industrial & Engineering Chemistry Research, issue.8, pp.44-2697, 2005.

G. C. Han-adebekun, M. Hamba, and W. H. Ray, Kinetic study of gas phase olefin polymerization with a TiCl 4 /MgCl 2 catalyst I. Effect of polymerization conditions, Journal of Polymer Science. Part A: Polymer Chemistry, issue.10, pp.35-2063, 1997.

I. L. Kim, J. H. Kim, and S. I. Woo, Kinetic study of ethylene polymerization by high-active silica supported TiCl 4 /MgCl 2 catalysts, Journal of Applied Polymer Science, issue.4, pp.39-837, 1990.

N. P. Khare, K. C. Seavey, Y. A. Liu, S. Ramanathan, S. Lingard et al., Steady-State and Dynamic Modeling of Commercial Slurry High-Density Polyethylene (HDPE) Processes, Industrial & Engineering Chemistry Research, vol.41, issue.23
DOI : 10.1021/ie020451n

J. H. Kim, I. Kim, and S. I. Woo, Computer simulation study of ethylene polymerization rate profile catalyzed over highly active Ziegler-Natta catalysts, Industrial & Engineering Chemistry Research, vol.30, issue.9, pp.30-2074, 1991.
DOI : 10.1021/ie00057a004

W. K. Shaffer and W. H. Ray, Polymerization of olefins through heterogeneous catalysis. XVIII. A kinetic explanantion for unusual effects, Journal of Applied Polymer Science, issue.6, pp.65-1053, 1997.

G. J. Wells, W. H. Ray, and J. Kosek, Effects of catalyst activity profiles on polyethylene reactor dynamics, AIChE Journal, vol.34, issue.12, pp.472768-2780, 2001.
DOI : 10.1021/cen-v078n006.p055

H. Hatzantonis, H. Yiannoulakis, A. Yiagopoulos, and C. Kiparissides, Recent developments in modeling gas-phase catalyzed olefin polymerization fluidized-bed reactors: The effect of bubble size variation on the reactor's performance, Chemical Engineering Science, vol.55, issue.16, pp.553237-3259, 2000.
DOI : 10.1016/S0009-2509(99)00565-5

F. A. Fernandes and L. M. Lona, Heterogeneous modeling of fluidized bed polymerization reactors. Influence of mass diffusion into the polymer particle, Computers & Chemical Engineering, vol.26, issue.6, pp.26-841, 2002.
DOI : 10.1016/S0098-1354(02)00010-8

K. B. Mcauley, J. F. Macgregor, and A. E. Hamielec, A kinetic model for industrial gas-phase ethylene copolymerization, AIChE Journal, vol.36, issue.6, pp.36837-850, 1990.
DOI : 10.1002/aic.690360605

C. Chatzidoukas, J. D. Perkins, E. N. Pistikopoulos, and C. Kiparissides, Optimal grade transition and selection of closed-loop controllers in a gas-phase olefin polymerization fluidized bed reactor, Chemical Engineering Science, vol.58, issue.16, pp.58-3643, 2003.
DOI : 10.1016/S0009-2509(03)00223-9

J. Y. Kim and K. Y. Choi, Modeling of particle segregation phenomena in a gas phase fluidized bed olefin polymerization reactor, Chemical Engineering Science, vol.56, issue.13, pp.56-4069, 2001.
DOI : 10.1016/S0009-2509(01)00078-1

J. A. Debling and W. H. Ray, Heat and Mass Transfer Effects in Multistage Polymerization Processes: Impact Polypropylene, Industrial & Engineering Chemistry Research, vol.34, issue.10, pp.34-3466, 1995.
DOI : 10.1021/ie00037a035

A. Yiagopoulos, H. Yiannoulakis, V. Dimos, and C. Kiparissides, Heat and mass transfer phenomena during the early growth of a catalyst particle in gas-phase olefin polymerization : the effect of prepolymerization temperature and time, Chemical Engineering Science, vol.56, issue.13, pp.56-3979, 2001.
DOI : 10.1016/S0009-2509(01)00071-9

G. C. Han-adebekun and W. H. Ray, Polymerization of olefins through heterogeneous catalysis. XVII. Experimental study and model interpretation of some aspects of olefin polymerization over a TiCl4/MgCl2 catalyst, Journal of Applied Polymer Science, vol.65, issue.6, pp.65-1037, 1997.
DOI : 10.1002/(SICI)1097-4628(19970808)65:6<1037::AID-APP1>3.0.CO;2-L

M. Hamba, G. C. Han-adebekun, and W. H. Ray, Kinetic study of gas phase olefin polymerization with a TiCl 4 /MgCl 2 catalyst. II. kinetic parameter estimation and model building, Journal of Polymer Science.Part A: Polymer Chemistry, issue.10, pp.31-2075, 1997.

E. J. Nagel, V. A. Kirllov, and W. H. Ray, Prediction of Molecular Weight Distributions for High-Density Polyolefins, Industrial & Engineering Chemistry Product Research and Development, vol.19, issue.3, pp.19-372, 1980.
DOI : 10.1021/i360075a016

Y. V. Kissin, R. I. Mink, and T. E. Nowlin, Ethylene polymerization reactions with Ziegler-Natta catalysts. I. Ethylene polymerization kinetics and kinetic mechanism, Journal of Polymer Science Part A: Polymer Chemistry, vol.27, issue.23, pp.374255-4272, 1999.
DOI : 10.1002/masy.19950890113

S. Floyd, R. A. Hutchinson, and W. H. Ray, Polymerization of olefins through heterogeneous catalysis???V. Gas-liquid mass transfer limitations in liquid slurry reactors, Journal of Applied Polymer Science, vol.32, issue.6, pp.32-5451, 1986.
DOI : 10.1002/app.1986.070320617

M. Seth, P. M. Margl, and T. Ziegler, A Density Functional Embedded Cluster Study of Proposed Active Sites in Heterogeneous Ziegler???Natta Catalysts, Macromolecules, vol.35, issue.20, pp.35-7815, 2002.
DOI : 10.1021/ma0204554