This invention is accomplished, tested and applied through many summer research stays during 2005 until 2011 at the Institute of Process Engineering (http://www.uni-kl.de/tvt/tvtlehrstuhl/tvtehemalige/tvtattarakih/) and Fraunhofer Institute for Industrial Mathematics (http://www.itwm.fraunhofer.de/ Transport Phenomena Group/ The University if Kaiserslautern/Germany & published in a series of papers in the European Symposium on Computer-Aided Process Engineering & International Conferences on Population Balance Modeling.
The invention is related generally to the field of mathematical & numerical modeling of population balances as a framework for modelling discrete systems. The invention provides an accurate framework for numerical modelling of such discrete systems, which arise naturally in chemical, physical and biological systems. Particular examples are the two-phase chemical reactors (polymer, two-liquid phase, gas-liquid phase & solid-liquid phase), separation processes (solvent liquid extraction, crystallization, gas absorption & distillation), biological systems and aerosol formation. The invented numerical framework introduces the idea of two types of particles: secondary and primary particles, which can fully describe the moments and the shape of the particulate distribution. The interaction of secondary particles can capture discontinuous jumps in the population states as a result of particle splitting, aggregation and nucleation events. The invention provides a hierarchy and evolution in the numerical modelling of discrete systems, which starts by simple one primary and one secondary particles (two-population group model) and evolves to the more complex and rich numerical presentation of the discrete system properties. The invention is already linked to popular commercial CFD solvers such as FLUENT, OPENFOAM and NOGRID. Currently, this discrete population balance model is being coupled to FPM software, which is a property of Fraunhoffer Institute for Industrial mathematics/ Kaiserslautern/ Germany.