Extension and Violations of the MSMPR Model

As is the case for all balance equations, we can generalize the population balance. The details of the derivation are presented elsewhere (Randolph and Larson 1988). 

The basis of the derivation is the concept of particle phase space, of a system, i.e., the least number of independent coordinates that allows a complete description. These coordinates are either internal, which describe properties independent of position, or external, which describe spatial distribution. 

Reduction of the Macro-Distributed Population Balance for an MSMPR Crystallizer 

No breakage or agglomeration occurs in an MSMPR crystallizer so B = D = 0. The internal coordinate of interest is particle length so, V = G = dLjdt. Furthermore, 

The macro-distributed population balance also permits us to analyze the performance of a continuous crystallizer, which is not at steady state. The population balance reduces to 

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