(373a) Numerical Bifurcation Analysis of Periodic Solution of Population Balance Models

Periodic oscillations in crystallization processes have been found by various authors in theoretical and experimental studies. Such results are important in applications, because the oscillations should be avoided for a better product quality. Conversely in special cases the periodic oscillations may be useful for industrial applications [3].

The main aim of the contribution is to develop a numerical tool for the nonlinear analysis of periodic solutions for particulate processes. A crystallization process is considered as an example. The process is described by a population balance model including fines dissolution and classified product removal, which are possible sources of nonlinear behavior [2]. The nonlinear analysis of the discretized population balance model is difficult due to the high order and integral terms in the model. The problem is solved by applying the recursive projection method [4,1].

The results show that the analysis of periodic solutions in population balance models can be done efficiently by the recursive projection method in combination with conventional numerical algorithms for the nonlinear analysis.

Bibliography

1 K. Lust. Numerical bifurcation analysis of periodic solutions of partial differential equations. PhD thesis, Katholieke Universiteit Leuven, Leuven, Belgium, 1997.

2 P. K. Pathath and A. Kienle. A numerical bifurcation analysis of nonlinear oscillations in crystallization processes. Chemical Engineering Science, 57(10):4391-4399, 2002.

3 R. Radichkov, T. Müller, A. Kienle, S. Heinrich, M. Peglow, and L. Mörl. A numerical bifurcation analysis of continuous fluidized bed spray granulation with external product classification. Chemical Engineering and Processing, 45(10):826-837, Oct. 2006.

4 G. M. Shroff and H. B. Keller. Stabilization of unstable procedures: The recursive projection method. SIAM Journal on Numerical Analysis, 30(4):1099-1120, Aug. 1993.