Investigation of an FFT-based solver applied to dynamic flowsheet simulation of agglomeration processes

Skorych, Vasyl; Dosta, Maksym; Hartge, Ernst‐Ulrich; Heinrich, Stefan; Ahrens, Robin; Borne, Sabine Le

doi:10.1016/j.apt.2018.12.007

Cited by 12 publications

(8 citation statements)

References 25 publications

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“…Various numerical approaches have been formulated. They include method of moments [1,7,8,25,91,92,102,107,160], sectional methods [44,59,68,69,72,73,80,83,131,134,157], finite volume schemes [12,30,31,70,71,109,110,119,126,130,132,136,138,139,142], finite element method [3,4,26,33,34,52,114], Adomain decomposition method [40], finite difference methods [95,96,145], tensor decomposition techniques [16,103] and Monte Carlo (MC) method [62,78,…”

Section: Why Numerical Methods?mentioning

confidence: 99%

Challenges and opportunities concerning numerical solutions for population balances: a critical review

Singh

Ranade²,

Shardt³

et al. 2022

J. Phys. A: Math. Theor.

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Population balance models are tools for the study of dispersed systems, such as granular materials, polymers, colloids and aerosols. They are applied with increasing frequency across a wide range of disciplines, including chemical engineering, aerosol physics, astrophysics, polymer science, pharmaceutical sciences, and mathematical biology. Population balance models are used to track particle properties and their changes due to aggregation, fragmentation, nucleation and growth, processes that directly affect the distribution of particle sizes. The population balance equation is an integro-partial differential equation whose domain is the line of positive real numbers. This poses challenges for the stability and accuracy of the numerical methods used to solve for size distribution function and in response to these challenges several different methodologies have been developed in the literature. This review provides a critical presentation of the state of the art in numerical approaches for solving these complex models with emphasis in the algorithmic details that distinguish each methodology. The review covers finite volume methods, Monte Carlo method and sectional methods; the method of moments, another important numerical methodology, is not covered in this review.

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Section: Why Numerical Methods?mentioning

confidence: 99%

Challenges and opportunities concerning numerical solutions for population balances: a critical review

Singh

Ranade²,

Shardt³

et al. 2022

J. Phys. A: Math. Theor.

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“…The flowsheet calculations can be used for four main purposes: modeling of process behavior, sensitivity analysis, process optimization and process control. In most cases, empirical or semi-empirical models are used for the simulations [2,3,12,13]. Therefore, only macroscopic states like mass flows, particle size distributions, temperatures, etc.…”

Section: Why Flowsheet Simulation?mentioning

confidence: 99%

Flowsheet simulation of solids processes: Current status and future trends

Dosta

Litster

Heinrich

2020

Advanced Powder Technology

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Complex manufacturing processes are nowadays applied for production of various solid products. It is very common that for production of particles with desired properties several transformation steps like drying, milling, classification, granulation, etc. should be involved. This leads to the process structures consisting of different apparatuses or transformation substeps connected with material and energy balances. Consequently, development of new processes or optimization of already existing, as well as an optimal control, is a very challenging task, which can be partially solved using numerical modelling.For the simulation of modern production processes, the flowsheet calculations can be effectively used. Starting from the 80s a lot of work focused on the flowsheet simulation of liquid-vapor systems has been done and as result various well-established systems exist today. With respect to the solid processes the intensive research has been started much later.In this contribution we present our view about a current role of flowsheet simulation for modeling of particulate materials and specify the open fields which can be covered in future research.

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“…In this paper we consider two common cases of collision kernels for diffusion and ballistic approaches and set the unit dimensionless temperature term KðTÞ ¼ 1. These expressions are often used in modelling in astrophysics, aerosol dynamics, flocculation and granulation [20,21,[12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27]…”

Section: Population Balance Modelmentioning

confidence: 99%

“…Using this approach, it is important to explore the formation of specific stationary size distributions of nanoparticles for different conditions of monomer-cluster and cluster-cluster collisions with accounting for various sources of binding monomers and seed clusters. This model can be considered as wellstudied for a case in presence of single monodisperse or smooth polydisperse source of particles [21][22][23][24].…”

Section: Introductionmentioning

confidence: 99%

Oscillating stationary distributions of nanoclusters in an open system

Matveev

Sorokin

Смирнов³

et al. 2020

Mathematical and Computer Modelling of Dynamical Systems

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Steady-state oscillations of nanoparticle populations in the system of colliding monomers and seed-clusters are observed for the range of the seed-cluster source with diffusion and ballistic collision kernels. The dynamics of nanoparticles in this system is driven by monomer-cluster and cluster-cluster irreversible aggregation and described in terms of the number of primary monomers per nanoparticle based on solving the population balance equations as described by the classical system of Smoluchowski equations. The oscillations of particles' concentrations arise with growing power of the source of seed-clusters and can remain visible for several orders of magnitute of particle sizes k. For the case of constant kinetic coefficients the novel semi-analytial solution of the utilized aggregation model is found and results of numerical simulations with use of up to 2 20 non-linear kinetic equations agree excellently with proposed theory.

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Investigation of an FFT-based solver applied to dynamic flowsheet simulation of agglomeration processes

Cited by 12 publications

References 25 publications

Challenges and opportunities concerning numerical solutions for population balances: a critical review

Challenges and opportunities concerning numerical solutions for population balances: a critical review

Flowsheet simulation of solids processes: Current status and future trends

Oscillating stationary distributions of nanoclusters in an open system

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