The mathematical models of particulate processes include a population balance equation (PBE) to describe the evolution of the particle size distribution (PSD) complemented with balance equations for the states of the continuous phase. In this work on particulate processes three main topics are addressed: the numerical solution of a one dimensional PBE, time optimal control of a particulate system in a semi-batch reactor, and the solution of inverse problems to extract the kernels of the PBE from available data.
The objective of the research in the field of the numerical solution of the PBE reported in this thesis is to determine the most appropriate numerical method among several high resolution methods in terms of computation time and accuracy. Additionally the potential advantage of grid adaptation to improve the performance of the most promising numerical methods is studied.
Because of the dependency of the properties of a particulate system on the PSD, control of the PSD is of extreme interest. The control concept studied here is direct optimizing control. The objective of the control problem is the time optimal production of a product with a target PSD in a semi-batch reactor. Since usually not all states are measurable, incorporating an extended Kalman filter in the control loop for state estimation is considered.
The last part of the thesis presents the application of techniques to extract kernels from available data. The novel approach presented for the solution of inverse problems can be used for extracting a general growth kernel from PSD measurements. It is also shown that the approach can be used for describing pure aggregation processes.
Throughout this thesis emulsion polymerization processes are selected as an example to illustrate the concepts investigated and developed in this work. The obtained conclusions and results however, can be extrapolated straightforwardly to other particulate processes.