Mathematical models for industrial reactors

Throughout this chapter we have discussed how phenomena taking place in micro-, meso-and macroscale influence olefin polymerization rates and polyolefin microstructure. The catalyst type ultimately determines the polymer microstructure for given a set of polymerization conditions such as temperature and concentration of monomer, comonomer, and chain transfer agent, but also the polymerization conditions themselves are a consequence of the type of support and reactor used to produce the polyolefin. 

A complete phenomenological mathematical model for olefin polymerization in industrial reactors should, in principle, include a description of phenomena taking place from microscale to macroscale. It may come as a disappointment to learn that most mathematical models for industrial reactors ignore several of these details. In fact, most models assume 

If it is known that this hypothesis is an oversimpMfication, then why is it made so often Mostly, because the additional effort required to integrate micro-, meso- and macroscale phenomena in a single model does not necessarily lead to better quantitative predictions when it comes to industrial reactors. Uncertainties on model parameter values are, most often, too high to try to decouple true polymerization kinetic parameters from mass and heat transfer effects often apparent kinetic parameters will do an equally good job from an engineering perspective [86]. 

Therefore, the equations shown in Table 2.10, either in transient or steady-state, are usually applied to industrial reactors as well. To these equations may be added an energy balance to model non-isothermal reaction operation d T 

For gas-phase or liquid propylene bulk reactors, the bulk monomer concentration in the reactor must be converted to concentration in the polymer phase surrounding the active sites with a thermodynamic relationship. Generally, a simple partition coefficient such as the one used in Equation 2.136a is used. For diluent slurry reactors, where the monomer is introduced in the gas phase, a partition coefficient such as Herny s law constant must also be used to calculate the concentration of monomer in the diluent which, in turn, is used to estimate the concentration of monomer in the polymer phase surrounding the active sites. Evidently, more sophisticated thermodynamic relationships relating the concentration of monomer in the gas phase, diluent and polymer can be used but, from a practical point of view, are only justified when the polymerization kinetic constants are very well known. Similar considerations apply to calculate the concentrations of comonomers, hydrogen and any other reactant in the system. 

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