Abstract
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.
Highlights
Bulk materials typically consist of individual non-uniform particles having different parameters, which vary in a certain range
This contribution proposes a new method for formulating transformation matrices using population balance equations (PBE) for agglomeration and milling processes
These parameters are referred to as distributed and include, for example, the diameters of particles, their densities, or porosities. These parameters can physically be fairly accurately described by continuous distribution functions, such a representation is not always convenient for numerical analysis and modelling
Summary
Bulk materials typically consist of individual non-uniform particles having different parameters, which vary in a certain range. Processes 2019, 7, 535 models [2]; the distributions of granules by porosity and saturation are important for breakage rate in some apparatuses [3]; and the moisture content of particles plays a significant role in dryers [4] Such a diversity of models and their parameters makes the simulation process much more challenging when trying to combine their different types in a single flowsheet. Consider a flowsheet where a screen and a dryer are connected in series, and the solid phase is distributed according to particle size and moisture content In this case, the screen unit, usually performing separation of particles only according to size, will fail to determine their moisture properly, which is important for the dryer. Their application, instead of explicit calculation of output flows, enables the usage of more material parameters in a proper way and implicitly preserves information about all secondary distributions and their dependencies at any time point in the unit
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