Title  :  Modeling coupled processes by multidimensional population assessment

Animators  : Christine Frances – Philippe Villedieu

In real processes, the transformation processes of morphological properties are very often coupled. In the case of a precipitation process, for example, the nucleation, growth, agglomeration and breakage processes often take place simultaneously. Similarly, the formation of granules in water treatment processes relies on the combination of aggregation, flocculation, rupture and re-structuring mechanisms.

The writing of a multidimensional population balance, based on the physical, chemical and morphological parameters, requires a certain number of precautions and involves difficulties due to the coexistence of kinetic processes (such as crystal growth or erosion) and catastrophic events (such as nucleation or breakage) that only a common work of applied mathematicians and physicists can overcome. Numerical resolution ways are multiple; several methods have been proposed for one-dimensional population balancess  (class methods, moment methods, or also Monte-Carlo simulations). The extension of these methods to the multidimensional problem, is a real challenge considering the current computing means. A reflection on the quantification of the performances of the various numerical methods and their optimization is essential.  In addition, some methods of population balance resolution describe the moments of a distribution, but users (researchers or industry) are more familiar with data expressed as property distribution functions. This raises the problem of reconstructing distributions from the knowledge of moments.

 In this area, the research is related to   :

– real-life experiments conducted on research pilots or industrial units to collect the data needed for morphological analysis,

– the modeling of phenomena coupled by the multidimensional population balance approach according to the different resolution methods proposed and the possible coupling with the spatial heterogeneities of the imposed constraints

– development of methods for reconstructing population property distributions. Optimization tools (optimization of a variational criterion or integral convex criteria, of entropic type) could be used as well as the development of state-observable models studied from the angle of the filtering (linear filtering of the Kalman type extended, or nonlinear filtering, based on empirical measurements of particles evolving according to markovian dynamics).