The Solution of Population Balance Equations

A particularly attractive approach that has evolved more recently is that of discretizing population balance equations and solving the discrete equations numerically. The effectiveness of this technique lies in rapid solutions of selected properties of the population that may be of interest to a specific application. 

Lastly, we shall explore Monte Carlo simulation techniques, which, with an abundance of computing power, have an incomparable degree of omnipotence. 

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Gimbun, j., Nagy, Z. K. Rielly, C. D. 2009 Simultaneous quadrature method of moments for the solution of population balance equations, using a differential algebraic equation framework. Industrial U Engineering Chemistry Research 48, 7798-7812. 

Kumar, S. Ramkrishna, D. 1996a On the solution of population balance equations by discretization -1. A fixed pivot technique. Chemical Engineering Science 51, 1311-1332. 

Chapter 4 deals with methods for the solution of population balance equations. It also probes into Monte Carlo simulation techniques. In Chapter 5, the self-similarity behavior of solutions to the population balance equations is considered with various examples. The subject of inverse problems for the identification of population balance models from experimental data on dynamic particle distributions is treated in Chapter 6. The exploitation of self-similar solutions in inverting experimental data is of particular interest. 

When the particle densities are not small, the coupled equations (2.11.1) and (2.11.2) must be solved simultaneously. Generally, such solutions can only be obtained numerically. The solution of population balance equations is of concern in Chapter 4. 

Before we conclude our discussion on discretization, we consider the solution of population balance equations with growth terms, which were excluded from prior discussions. 

Because the literature on approximate methods for the solution of population balance equations has grown substantially over the years, an exhaustive coverage of the same has been difficult. It must also be said, however, that not infrequently papers display different techniques to solve the same set of problems rather than generalizations expanding the scope of problems solved. 

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