Markov Processes in Stochastic Modeling of Transport Phenomena: from Application to Theory

The present work discusses the development of mathematical theory in order to satisfy the need for rigorous and applicable modeling of transport phenomena in chemical engineering science. An underlying background in applications and examples are common to all the different following topics. The first object of investigation is Danckwerts' law. It states that the expected residence time of a particle in a processing vessel with steady and constant in- and outflow is given by the volume of the vessel divided by the in-/outflowrate. Its implementation for discrete Markov chains and onedimensional diffusion processes is shown. Therefore relations of the theory of strongly continuous semigroups and their generators to diffusion processes are presented and used. Furthermore multiphase processes are introduced and characterized. A limit theorem for these multiphase processes is formulated and proved. Finally a heterogeneous stochastic model for transport in slugging fluidized bed reactors is illustrated.