Macroscopic Reactor Modeling - Population Balances and the Method of Moments

Macroscopic Reactor Modeling - Population Balances and the Method of Moments 

In this section, we will first illustrate how to use the method of moments for homopolymerization and then show how these equations can be easily adapted to copolymerization using the method of pseudo-kinetic constants. 

In the following model development, we will use the polymerization kinetics mechanism described by Eqs. (1)-(14) to derive the population balances and moment equations for homopolymerization with a catalyst containing only one site type. Catalysts containing two or more site types are handled similarly by defining a set of equations with distinct polymerization kinetic constants for each different site type. 

For living polymer chains of length r 2 made in a CSTR, the dynamic population balance can be derived as Eq. (56). 

the reaction between catalyst and cocatalyst is considered instantaneous. Consequently, the term k CAl can be dropped from Eq. (58) and it is assumed that C (to) = C(to). 

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Macroscopic Reactor Modeling - Population Balances and the Method of Moments 411 Taking the first derivative of Eq. (68), one obtains Eq. (69). 

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