MODELING OF CRYSTALLIZATION SYSTEMS VIA GENERALIZED ORTHOGONAL POLYNOMIALS METHOD

Abstract

The population balance equation which is used to describe the dynamic of crystallization processes is simulated by the proposed generalized orthogonal polynomials (GOP). Examples of modeling include the ordinary differential equation for MSMPR crystallization processes, the partial differential equation for transient batch crystallization processes and the functional differential equation for breakage of crystals within the crystallizer. The key idea is to express the population density function by. a generalized orthogonal polynomials series. The ordinary (or partial, or functional) differential equation is then transformed into a set of algebraic (or ordinary differential, or algebraic) equations of expansion coefficients through the integration operation matrix. The advantage of using GOP approximation is that almost any kind of orthogonal polynomials can be used to approximate the system with very accurate results. Furthermore, it is very easy to calculate the expansion coefficients by using the present proposed operation matrix and the recursive formula.

KEYWORDS:

• Crystallization
• Generalized orthogonal polynomials
• Population balance

Additional information

Notes on contributors

MAW-LING WANG

To whom all correspondence should be sent.