» Download Article

Authors
Krallis Apostolos, Kiparissides Costas

Identifier
None

Index Terms
computing elements,distributions,mathematical model,numerical algorithms,polymerization

Abstract
In the present study a population balance approach is described to follow the time evolution of molecular polymer properties in free-radical polymerizations. The model formulation is based on the fixed pivot technique (FPT) which was properly adapted to calculate the combined molecular weight - long chain branching distribution. At first the predictive capabilities of the proposed model were tested against experimental measurements and simulation results taken from the open literature, on molecular weight distribution (MWD) of branched polymers. Then the MWD calculated by the FPT was compared with the MWD calculated by the method of classes. However the FPT proved to be a faster method for the calculation of the MWD.

References

[1] Baltsas, A., A.D. Achilias and C. Kiparissides
    (1996). A theoretical investigation of the
    production of branched copolymers in continuous
    stirred tank reactors. Macromolecular Theory and
    Simulation. 5, 477-497.
[2] Canu, P., and W.H. Ray (1991). Discrete weighted
    residual methods applied to polymerization
    reactions. Comput. Chem. Engin. 15, 549-558.
[3] Hamer, J.W. and W.H. Ray (1986). Continuous
    tubular polymerization reactors - I. A detailed
    model. Chemical Engineering Science. 41, 3083-
    3093.
[4] Iedema, P.D., M. Wulkow and C.J. Hoefsloot (2000).
    Modeling Molecular Weight and Degree of
    Branching Distribution of Low-Density
    Polyethylene. Macromolecules. 33(19), 7173-
    7189.
[5] Keramopoulos, A. and C. Kiparissides (2002).
    Development of a comprehensive model for
    diffusion-controlled free-radical
    copolymerization reactions. Macromolecules. 35,
    4255-4272.
[6] Kumar, S. and D. Ramkrishna (1996). On the
    solution of population balance equations by
    discretization - I. A fixed pivot technique.
    Chemical Engineering Science. 51, 1311-1332.
[7] Lorenzini P., M. Pons and J. Villermaux (1992)
    Free-radical polymerization engineering - III.
    Modelling homogeneous polymerization of
    ethylene: mathematical model and new method
    for obtaining molecular - weight
    distribution. Chemical Engineering Science. 47,
    3969-3980.
[8] Nele, M., C. Sayer and J.C. Pinto (1999).
    Computation of molecular weight distributions
    by polynomial approximation with complete
    adaptation procedures. Macromolecular Theory
    and Simulations. 8, 199-213.
[9] Nordhus, H., O. Moen and P. Singstad (1997).
    Prediction of molecular weight distribution and
    long - chain branching distribution of low-density
    polyethylene from a kinetic model. J.M.S.-Pure
    Appl. Chem. A34, 1017-1028.
[10] Pladis, P. and C. Kiparissides (1998). A
     comprehensive model for the calculation of
     molecular weight - long chain branching
     distribution in free-radical polymerizations.
     Chemical Engineering Science. 53, 3315-3333.
[11] Teymour, F. and J.D. Campbell, (1992). In
     Proceedings of the 4th International Workshop on
     Polymer Reaction Engineering, eds K.H.
     Reichert, H.U. Moritz, DECHEMA Vol. 127, p.
     149. VCH, Weinheim.
[12] Thomas, S. (1998). Measurement and modeling of
     long chain branching in chain growth
     polymerization. PhD Thesis, Mc Master
     University.
[13] Tobita, H. (1996). Random degradation of branched
     polymers. 1. Multiple branches. Macromolecules.
     29, 3010-3023.
[14] Tobita, H. and K. Hatanaka (1996). Branched
     structure formation in free radical polymerization
     of vinyl acetate. Journal of Polymer Science. 34,
     671-681.
[15] Wulkow, M. (1995). The simulation of molecular
     weight distributions in polyreaction kinetics by
     discrete Galerkin methods. Macromol. Theory
     Simul., 5, 393-407.