Walter R. Witkowski
Ph.D., University of Texas at Austin, 1990
The model identification technique presented is flexible in model formulation and inclusion of available experimental measurements. In contrast to methods used in the literature, this approach allows the assessment of the parameter estimate reliability, providing a measure of the accuracy and validity of a model.
Accurate model solution methods are necessary for efficient and reliable parameter identification. Three different formulations of the method of weighted residual approach are used. The results using Galerkin's technique with Laguerre polynomials, orthogonal collocation, and the standard finite element method are compared in two crystallization case studies. Issues such as numerical stability, efficiency, and solution convergence are discussed.
A lack of sufficient process measurements is the primary problem to be overcome in developing a reliable model identification and verification scheme. A measure of the solute concentration is available. To provide additional process information, a Malvern 3600Ec Particle Sizer, which is based on Fraunhofer light scattering theory, is used to measure the crystal size distribution (CSD).
A numerical study is performed to determine if the parameter estimation problem using the available concentration and CSD information is possible. Using pseudo-experimental data, generated by solving the model and adding random noise, reliable process measurements are produced. It is shown that while solute concentration data is sufficient to estimate the kinetic growth parameters, additional process information is necessary to evaluate the nucleation parameters. The Malvern's obscuration measurement is the most accurate concerning the CSD. Using this measurement along with concentration allowed accurate identification of all of the kinetic parameters. Complete identification is not achieved using only the concentration data along with the CSD size class information. These conclusions involving the effectiveness of various measurements are verified using the experimental data.
The classical model formulation is found to be adequate to describe the process dynamics at different operating conditions. Operating conditions that are tested include seed loading, seed size and stirrer speed.
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University of Wisconsin
Department of Chemical Engineering
Madison WI 53706