Generalized population balance equation moment method

Thus (4.4.8) shows how any term in the population balance equation involving the number density can be expressed purely in terms of the first M integral moments. While the use of generalized Laguerre polynomials with additional parameters provided some flexibility for the method of moments, Hulburt and Akiyama have reported difficulties with this method. 

General solution of the population balance is complex and normally requires numerical methods. Using the moment transformation of the population balance, however, it is possible to reduce the dimensionality of the population balance to that of the transport equations. It should also be noted, however, that although the mathematical effort to solve the population balance may therefore decrease considerably by use of a moment transformation, it always leads to a loss of information about the distribution of the variables with the particle size or any other internal co-ordinate. Full crystal size distribution (CSD) information can be recovered by numerical inversion of the leading moments (Pope, 1979 Randolph and Larson, 1988), but often just mean values suffice. 

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