Population-balance equation moment closure

This implies that under the condition of a maximum of one TDB per chain, the set of population balance equations of the TDB branching moment variant of the model is solvable without requiring any additional closure assumption. The results obtained with the pseudo-distribution model are identical to those obtained with the classes model shown before (see Figure 9.6). 

C.3. In the polycondensation reactor example above, we reduced the number of equations by deriving moment equations. This required a closure approximation to estimate the value of A.3 given A,o, A,i, A.2. Test this approximation by solving the complete set of population balance equations... 

When the population balance is written in terms of one internal coordinate (e.g., particle diameter or particle volume), the closure problem mentioned above for the moment equation has been successfully relaxed for solid particle systems by the use of a quadrature approximation. 

The method of moments is the most well-known method for solving polymerization problems [1-3]. The equations are derived from the population balances. This is realized in a straightforward way for the radical polymerization system of Table 9.1, a ID problem. Table 9.2 presents the original population balances and Table 9.3 the resulting moment equations, up to the 4th moment. The linear part of this problem can be solved without additional assumptions, but the nonlinear part leads to a closure problem. This will be discussed next. Some results and a discussion on the validity of the method will be given in Section 9.4, in a comparison with the Galerkin-FEM method. 

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