A large number of chemical engineering processes are operated with one or more dispersed phases that can be modelled by the population balance approach comprising partial differentials of first order and integral terms over the population domain (1,2). The integral terms characterize intra particle phenomena e.g. breakage or agglomeration of particles. The population balance approach leads to partial differential equations (PEDs) or integro partial differential equations (IPDEs) which must be preprocessed for the application of standard numerical simulation or optimization tools. The PDEs, IPDEs and the related boundary conditions can be transformed into differential algebraic equations (DAEs) using the Method-of-Lines (MOL) approach (3). Thereby, a special treatment of the integral terms has to be considered. For the resulting overall DAEs, efficient numerical routines are available in simulation tools like Diva (4) or gPROMS (5).
展开▼
