Inverse problem modeling of particulate systems

Alan Waite Mahoney, Purdue University

Abstract

Particulate systems are widely used in the chemical industry both for final product properties and for convenience of processing. For these purposes, the particle size distribution affects the product value or processing cost, and therefore is an important factor in design and control. These goals are complicated by the nonlinear, distributed nature of the system and the poor availability of predictive models. This work presents methods for the determination of models, techniques for simulation, and strategies for control based on transformations of the population balance equation, the underlying framework that links the behavior of the distribution of the population as a whole to the dynamics of individual particles. By focusing on the level of individual particle dynamics, models are obtained that are sufficiently general for extrapolation to new reactor geometries and product distributions, yet are obtainable from measurements of the particle size distribution. Traditional methods for obtaining these models require fundamental physical understanding or considerable experimental data. A new technique based on an inverse problem approach to the population balance uses explicit solutions based on the method of characteristics and the method of weighted residuals (MWR) to directly determine the model form from measurement data from batch, semi-batch, or continuous systems. This allows application to complex molecules where theoretical insights are not accessible. The complexity of the system usually requires numerical solution. Two associated problems are the computational expense of evaluating the integral terms arising from aggregation and numerical diffusion along discontinuities arising from the separatrix. Refinements to MWR on finite elements are proposed that address these problems. Rearrangement of the required integrals allows their off-line calculation. Augmenting MWR with the method of characteristics allows explicit calculation along the interfaces associated with discontinuities. Control of the particle size distribution requires both system models and current state information. A nonlinear observer based on the inverse problem allows identification of model parameters on-line from measurements. Observability of the full system state from secondary measurements is investigated using both continuous and discrete system representations. A model predictive control application is shown incorporating the identification and prediction techniques developed here.

Degree

Ph.D.

Advisors

Doyle, Purdue University.

Subject Area

Chemical engineering

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