1. Mathematical modeling of a polymerization reactor for kinetic parameter estimation Adriano G Fisch 14/10/2015

2. 01 Introduction Catalyst development (1)Plant and material availability; (2)Many on- and off-specification material for disposal; (3)Plant operation variability (4)Response time of the quality control laboratory (e.g., density analysis) Tests are time and cost consuming Synthesis and tests at lab scale Tests at pilot scale Industrial runs

3. 01 Introduction Catalyst development Catalyst performance evaluation using a mathematical model Synthesis and tests at lab scale Process modeling Tests at pilot scale Industrial runs Runs in pilot scale for validation of the model predictions

4. 01 Introduction Model development for polymerization reactor (1)Mass transfer; (2)Heat transfer; (3)Thermodynamic equilibrium (e.g., VLE for slurry polymerization); (4)Kinetic of polymerization reaction; (5)Polymer properties; Experiments for the estimation of the kinetic constants of the catalyst and a proper mathematical model

5. 01 Introduction Objective The goal is to develop a mathematical model of ethylene copolymerization for kinetic parameter estimations

6. 01 Modeling (1)Bench scale reactor (ca. 300 mL); (2)Slurry ethylene copolymerization (focus on HDPE) (3)Semi-batch operation total pressure controled by ethylene feed; hydrogen and comonomer added in batchwise fashion Reactor: (1)Pseudo-homogeneous reaction medium; (2)Well-mixed reaction medium; Considerations:

7. 01 Modeling Population balance for volatile reactants: (1) (2) (3) Balance of j in liquid phase (L) Balance of j in vapor phase (V) Balance of j in reactor (4)Mass transfer of j between V-L phases

8. 01 Modeling Vapor-liquid equilibrium: (1)  -  method; (2)NRTL for liquid phase; (3)Redlich-kwong for vapor phase; (4)Hydrogen was considered to follow Henry law. Population balance for polymer chains: (5)Moments of distribution

9. 01 Modeling Kinetic of copolymerization with LCB formation: (1)Typical Ziegler-Natta catalyst 5 active sites; (2)LCB formation generation of macromonomer by in situ mechanism insertion of macromonomer by same site of its generation; (3)Insertion of co- and macromoner is not dependent on last unit inserted

10. 01 Modeling Catalyst performance: (6)Catalyst activity (7) Catalyst productivity (8)Polymerization reaction rate

11. 01 Modeling Polymer architecture: (9)Number-average molar mass (10) Weight-average molar mass (11)Z-average molar mass (12)Polydispersitiesand

12. 01 Modeling Polymer architecture: (13)Mass fraction of comonomer (14) Mass fraction of LCB (15) Weight-average molar mass of LCB

13. 01 Modeling Polymer architecture: (16)Frequency of comonomer (by 1000 C b ) (17) Frequency of LCB (by 1000 C b )

14. 01 Simulation Evaluation of the model capabilities (1) catalyst performance (2) polymer architecture molar weight distribution (MMD) chemical composition distribution (CCD) (1)Slurry copolymerization of ethylene and butene; (2)Kinetic constant from literature.

15. 01 Simulation Catalyst performance Figure 1. Effect of temperature on catalyst productivity. Figure 2. Effect of ethylene partical pressure on catalyst productivity.

16. 01 Simulation Polymer architecture - MMD Figure 3. Molar mass distribution. Reaction temperature of 70 °C. Figure 4. Molar mass distribution. Reaction temperature of 90 °C.

17. 01 Simulation Polymer architecture - CCD Figure 5. Comonomer incorporation in the polymer for each site (1-5) as a function of the reaction temperature. Time= 3600 s. Figure 6. Comonomer incorporation in the polymer for each site (1-5) as a function of the partial pressure of comonomer. Time= 3600 s.

18. 01 Simulation Polymer architecture - CCD Figure 7. Long chain branch incorporation and the average molar mass of the side chain for each site (1-5). Time= 3600 s.

19. 01 Conclusion The model is able to predict remarkable behavior of ethylene copolymerization, including LCB formation. It is possible to evaluate: (1) catalyst performance (global and by site) (2) polymer architecture (global and by site) molar weight distribution chemical composition distribution

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