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Publisher DOI: 10.3390/pr7080535
Title: Application of transformation matrices to the solution of population balance equations
Language: English
Authors: Skorych, Vasyl 
Das, Nilima 
Dosta, Maksym 
Kumar, Jitendra 
Heinrich, Stefan 
Keywords: population balance equation;dynamic flowsheet simulation;transformation matrix;process modelling;agglomeration;milling;solids;multidimensional distributed parameters
Issue Date: 14-Aug-2019
Publisher: Multidisciplinary Digital Publishing Institute
Source: Processes 7 (8): 535 (2019)
Journal or Series Name: Processes 
Abstract (english): The development of algorithms and methods for modelling flowsheets in the field of granular materials has a number of challenges. The difficulties are mainly related to the inhomogeneity of solid materials, requiring a description of granular materials using distributed parameters. To overcome some of these problems, an approach with transformation matrices can be used. This allows one to quantitatively describe the material transitions between different classes in a multidimensional distributed set of parameters, making it possible to properly handle dependent distributions. This contribution proposes a new method for formulating transformation matrices using population balance equations (PBE) for agglomeration and milling processes. The finite volume method for spatial discretization and the second-order Runge–Kutta method were used to obtain the complete discretized form of the PBE and to calculate the transformation matrices. The proposed method was implemented in the flowsheet modelling framework Dyssol to demonstrate and prove its applicability. Hence, it was revealed that this new approach allows the modelling of complex processes involving materials described by several interconnected distributed parameters, correctly taking into consideration their interdependency.
DOI: 10.15480/882.2386
ISSN: 2227-9717
Other Identifiers: doi: 10.3390/pr7080535
Institute: Feststoffverfahrenstechnik und Partikeltechnologie V-3 
Type: (wissenschaftlicher) Artikel
Funded by: Deutsche Forschungsgemeinschaft (DFG)
German Academic Exchange Service (DAAD)
Project: Open Access Publizieren 2018 - 2019 / TU Hamburg 
SPP 1679: Dynamische Simulation vernetzter Feststoffprozesse 
Physics Embedded Approximations of Aggregation and Breakage Kernels for Population Balances 
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