Special Issue "Recent Advances in Population Balance Modeling"

A special issue of Processes (ISSN 2227-9717). This special issue belongs to the section "Materials Processes".

Deadline for manuscript submissions: closed (31 December 2018)

Special Issue Editors

Guest Editor
Prof. Dr. Krist V. Gernaey

Department of Chemical and Biochemical Engineering, Technical University of Denmark, Søltofts Plads, Building 229, 2800 Kgs. Lyngby, Denmark
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Interests: industrial fermentation technology; scale-up/scale-down; resource recovery; continuous production processes; mathematical modeling; process analytical technology (PAT)
Guest Editor
Prof. Dr. Ingmar Nopens

Department of Data analysis and mathematical modelling, Ghent University, St. Pietersnieuwstraat 33, 9000 Gent, Belgium
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Interests: population balance modelling; kinetic modelling; Computational Fluid Dynamics; resource recovery; pharmaceutical engineering
Guest Editor
Assist. Prof. Dr. Seyed Soheil Mansouri

Department of Chemical and Biochemical Engineering, Technical University of Denmark, 2800 Kongens Lyngby, Denmark
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Interests: process system engineering; process control and optimization; downstream process development; chemical and biochemical process intensification
Guest Editor
Prof. Dr. Heiko Briesen

Chair of Process Systems Engineering, TUM School of Life Sciences, Technical University of Munich, Germany
Website | E-Mail
Interests: Modeling and simulation, multiscale modeling, population balance modeling, particulate processes, crystallization

Special Issue Information

Dear Colleagues,

Population Balance Modelling is a powerful modelling framework that allows predicting the dynamics of distributed properties of a population of individuals at the mesoscale. This is of particular interest when such a property is a critical quality attribute of a production system (e.g., particle size distribution, particle composition, etc.). The framework finds its roots in chemical engineering in the 1960s and boomed in the late 1990s with increasing computational power. It is now gaining ground in other application fields, such as pharmaceutical engineering and biotechnology.

Population balance models come in different forms. They can be formulated taking into account different continuous and discrete mechanisms such as growth, aggregation and breakage. For these mechanisms, process rates or kernels need to be defined. Calibration and validation of these kernels based on experimental data is of particular interest to secure the model’s predictive power and, hence, successful use in scenario analysis for process operational and design optimization.

Moreover, PBMs can include one or more distributed properties and either be embedded in a Computational Fluid Dynamics framework or spatial compartments to include the effect of spatial heterogeneities. Specific numerical and computational burden challenges arise when doing so.

The latest research in this intriguing field of research is being shown and discussed at the 6th International Conference on Population Balance Modelling ( PBM2018) held in Ghent, Belgium on 7–9 May, 2018. The issue is a reflection of high-quality papers presented at PBM2018. This Special Issue on “Population Balance Modeling” aims at showing the most recent advances in formulation, solution methods and application areas of population balance modelling.

All the authors of accepted contributions at PBM2018 are invited to submit manuscripts.

Prof. Dr. Krist V. Gernaey
Prof. Dr. Ingmar Nopens
Dr. Seyed Soheil Mansouri
Prof. Dr. Heiko Briesen
Guest editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Processes is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1100 CHF (Swiss Francs). Please note that for papers submitted after 30 June 2019 an APC of 1200 CHF applies. Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • population balance model
  • formulation
  • numerical solution method
  • spatial heterogeneity
  • calibration
  • validation

Published Papers (10 papers)

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Research

Open AccessFeature PaperArticle An Analysis of Uncertainty Propagation Methods Applied to Breakage Population Balance
Processes 2018, 6(12), 255; https://doi.org/10.3390/pr6120255
Received: 29 October 2018 / Revised: 21 November 2018 / Accepted: 6 December 2018 / Published: 8 December 2018
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Abstract
In data-driven empirical or hybrid modeling, the experimental data influences the model parameters and thus also the model predictions. The experimental data has some variability due to measurement noise and due to the intrinsic stochastic nature of certain pharmaceutical processes such as aggregation [...] Read more.
In data-driven empirical or hybrid modeling, the experimental data influences the model parameters and thus also the model predictions. The experimental data has some variability due to measurement noise and due to the intrinsic stochastic nature of certain pharmaceutical processes such as aggregation or breakage. To use predictive models, it is imperative that the accuracy of the predictions is known. To this extent, various uncertainty propagation techniques applied to a predictive breakage population balance model are studied. Three uncertainty propagation techniques are studied: linearization, sigma point, and polynomial chaos. These are compared to the uncertainty obtained from Monte Carlo simulations. Linearization performs the worst in the given scenario, while sigma point and polynomial chaos methods have similar performance in terms of accuracy. Full article
(This article belongs to the Special Issue Recent Advances in Population Balance Modeling)
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Open AccessFeature PaperArticle Dual Population Balance Monte Carlo Simulation of Particle Synthesis by Flame Spray Pyrolysis
Processes 2018, 6(12), 253; https://doi.org/10.3390/pr6120253
Received: 31 October 2018 / Revised: 27 November 2018 / Accepted: 29 November 2018 / Published: 6 December 2018
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Abstract
The Dual Population Balance Monte Carlo Method (DPBMC) takes into account the full size spectrum of the droplet and particle phase. Droplet and particle size distributions are rendered by weighted simulation particles. This allows for an accurate description of particle nucleation and coagulation [...] Read more.
The Dual Population Balance Monte Carlo Method (DPBMC) takes into account the full size spectrum of the droplet and particle phase. Droplet and particle size distributions are rendered by weighted simulation particles. This allows for an accurate description of particle nucleation and coagulation and droplet combustion, simultaneously. Internal droplet properties such as temperature and concentrations fields are used to define criteria for the onset of droplet breakage in the framework of weighted Monte Carlo droplets. We discuss the importance of droplet polydispersity on particle formation in metal oxide particle synthesis, which is shown to strongly affect particle formation and growth. The method is applied to particle synthesis from metal nitrate precursor solutions with flame spray pyrolysis (FSP) and compared to experiments from literature. Full article
(This article belongs to the Special Issue Recent Advances in Population Balance Modeling)
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Open AccessFeature PaperArticle Modeling and Simulation Studies of a Novel Coupled Plug Flow Crystallizer for the Continuous Separation of Conglomerate-Forming Enantiomers
Processes 2018, 6(12), 247; https://doi.org/10.3390/pr6120247
Received: 15 October 2018 / Revised: 19 November 2018 / Accepted: 27 November 2018 / Published: 1 December 2018
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Abstract
Separation of enantiomers is a major concern in pharmaceutical industries due to the different therapeutic activities exhibited by the enantiomers. Preferential crystallization is an attractive means to separate the conglomerate-forming enantiomers. In this work, a simulation study is presented for a proposed novel [...] Read more.
Separation of enantiomers is a major concern in pharmaceutical industries due to the different therapeutic activities exhibited by the enantiomers. Preferential crystallization is an attractive means to separate the conglomerate-forming enantiomers. In this work, a simulation study is presented for a proposed novel preferential crystallization configuration that involves coupled plug flow crystallizers (PFCs). The PFCs are coupled through liquid phase exchange which helps the enrichment of the preferred enantiomer in the liquid phase. A set of coupled population balance equations (PBEs) are used to describe the evolution of the crystal size distribution (CSD) in the PFCs. The PBEs and the relevant mass balance equations are solved using the high-resolution finite-volume method. The simulation results predict that the proposed configuration has higher productivity compared to the currently used crystallization configurations while maintaining the same level of purity. Moreover, the effect of process variables, such as the extent of liquid phase exchange and the location of the PFC where liquid phase exchange occurs, are studied. The insights obtained from this simulation study will be useful in design, development, and optimization of such novel crystallization platforms. Full article
(This article belongs to the Special Issue Recent Advances in Population Balance Modeling)
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Open AccessFeature PaperArticle Parameter Identification For Continuous Fluidized Bed Spray Agglomeration
Processes 2018, 6(12), 246; https://doi.org/10.3390/pr6120246
Received: 30 October 2018 / Revised: 26 November 2018 / Accepted: 27 November 2018 / Published: 30 November 2018
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Abstract
Agglomeration represents an important particle formation process used in many industries. One particularly attractive process setup is continuous fluidized bed spray agglomeration, which features good mixing as well as high heat and mass transfer on the one hand and constant product throughput with [...] Read more.
Agglomeration represents an important particle formation process used in many industries. One particularly attractive process setup is continuous fluidized bed spray agglomeration, which features good mixing as well as high heat and mass transfer on the one hand and constant product throughput with constant quality as well as high flow rates compared to batch mode on the other hand. Particle properties such as agglomerate size or porosity significantly affect overall product properties such as re-hydration behavior and dissolubility. These can be influenced by different operating parameters. In this manuscript, a population balance model for a continuous fluidized bed spray agglomeration is presented and adapted to experimental data. Focus is on the description of the dynamic behavior in continuous operation mode in a certain neighborhood around steady-state. Different kernel candidates are evaluated and it is shown that none of the kernels are able to match the first six minutes with time independent parameters. Afterwards, a good fit can be obtained, where the Brownian and the volume independent kernel models match best with the experimental data. Model fit is improved for identification on a shifted time domain neglecting the initial start-up phase. Here, model identifiability is shown and parameter confidence intervals are computed via parametric bootstrap. Full article
(This article belongs to the Special Issue Recent Advances in Population Balance Modeling)
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Open AccessFeature PaperArticle Influence of Thermal Conditions on Particle Properties in Fluidized Bed Layering Granulation
Processes 2018, 6(12), 235; https://doi.org/10.3390/pr6120235
Received: 25 September 2018 / Revised: 16 November 2018 / Accepted: 16 November 2018 / Published: 22 November 2018
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Abstract
Fluidized bed layering granulation is frequently used to formulate particles of high quality. From previous studies, it is well known that the dynamic behavior of the process, as well as the product properties depend on operating parameters. The process is characterized by heat [...] Read more.
Fluidized bed layering granulation is frequently used to formulate particles of high quality. From previous studies, it is well known that the dynamic behavior of the process, as well as the product properties depend on operating parameters. The process is characterized by heat and mass transfer between fluidized particles and the surrounding fluidization medium. To investigate the mutual influence between particle phase and fluidization medium, a dynamic model is introduced. The model comprises two parts: a population balance model to describe the evolution of the particle sizes and a system of ordinary differential equations to account for thermal conditions. For the first time, the dynamic model considers the bidirectional coupling of particles and fluidization medium in fluidized bed layering granulation. By means of simulations, it is shown that the derived model is capable of reproducing the experimental findings. Full article
(This article belongs to the Special Issue Recent Advances in Population Balance Modeling)
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Open AccessArticle Local Fixed Pivot Quadrature Method of Moments for Solution of Population Balance Equation
Processes 2018, 6(11), 209; https://doi.org/10.3390/pr6110209
Received: 16 September 2018 / Revised: 18 October 2018 / Accepted: 25 October 2018 / Published: 31 October 2018
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Abstract
A local fixed pivot quadrature method of moments (LFPQMOM) is proposed for the solution of the population balance equation (PBE) for the aggregation and breakage process. First, the sectional representation for aggregation and breakage is presented. The continuous summation of the Dirac Delta [...] Read more.
A local fixed pivot quadrature method of moments (LFPQMOM) is proposed for the solution of the population balance equation (PBE) for the aggregation and breakage process. First, the sectional representation for aggregation and breakage is presented. The continuous summation of the Dirac Delta function is adopted as the discrete form of the continuous particle size distribution in the local section as performed in short time Fourier transformation (STFT) and the moments in local sections are tracked successfully. Numerical simulation of benchmark test cases including aggregation, breakage, and aggregation breakage combined processes demonstrate that the new method could make good predictions for the moments along with particle size distribution without further assumption. The accuracy in the numerical results of the moments is comparable to or higher than the quadrature method of moment (QMOM) in most of the test cases. In theory, any number of moments can be tracked with the new method, but the computational expense can be relatively large due to many scalar equations that may be included. Full article
(This article belongs to the Special Issue Recent Advances in Population Balance Modeling)
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Open AccessFeature PaperArticle Mathematical Modelling and Simulation of a Spray Fluidized Bed Granulator
Processes 2018, 6(10), 195; https://doi.org/10.3390/pr6100195
Received: 11 September 2018 / Revised: 9 October 2018 / Accepted: 16 October 2018 / Published: 18 October 2018
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Abstract
In this present work, a study of the modelling and simulation for a top-sprayed fluidized bed granulator (SFBG) is presented, which is substantially used by the pharmaceutical industry to prepare granules. The idea is to build a number-based mathematical model using the notion [...] Read more.
In this present work, a study of the modelling and simulation for a top-sprayed fluidized bed granulator (SFBG) is presented, which is substantially used by the pharmaceutical industry to prepare granules. The idea is to build a number-based mathematical model using the notion of population balances by dividing a top SFBG into two different zones, namely the wet zone and dry zone. To solve a two-compartment model, an existing accurate and efficient finite volume scheme is implemented. In order to validate the compartmental model, a new class of analytical moments is derived corresponding to various combinations of aggregation and breakage kernels. To verify the accuracy of a modified finite volume scheme, the zeroth and first order moments computed using the finite volume scheme are compared with the newly-derived analytical results. Moreover, the stability of the compartmental model and the numerical scheme is tested by varying the size of the wet zone. It is also shown that the relative errors in both order moments increase with the increase in the size of the wet zone. Full article
(This article belongs to the Special Issue Recent Advances in Population Balance Modeling)
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Open AccessFeature PaperArticle A Novel Framework for Parameter and State Estimation of Multicellular Systems Using Gaussian Mixture Approximations
Processes 2018, 6(10), 187; https://doi.org/10.3390/pr6100187
Received: 6 September 2018 / Revised: 2 October 2018 / Accepted: 6 October 2018 / Published: 10 October 2018
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Abstract
Multicellular systems play an important role in many biotechnological processes. Typically, these exhibit cell-to-cell variability, which has to be monitored closely for process control and optimization. However, some properties may not be measurable due to technical and financial restrictions. To improve the monitoring, [...] Read more.
Multicellular systems play an important role in many biotechnological processes. Typically, these exhibit cell-to-cell variability, which has to be monitored closely for process control and optimization. However, some properties may not be measurable due to technical and financial restrictions. To improve the monitoring, model-based online estimators can be designed for their reconstruction. The multicellular dynamics is accounted for in the framework of population balance models (PBMs). These models are based on single cell kinetics, and each cellular state translates directly into an additional dimension of the obtained partial differential equations. As multicellular dynamics often require detailed single cell models and feature a high number of cellular components, the resulting population balance equations are often high-dimensional. Therefore, established state estimation concepts for PBMs based on discrete grids are not recommended due to the large computational effort. In this contribution a novel approach is proposed, which is based on the approximation of the underlying number density functions as the weighted sum of Gaussian distributions. Thus, the distribution is described by the characteristic properties of the individual Gaussians, like the mean and covariance. Thereby, the complex infinite dimensional estimation problem can be reduced to a finite dimension. The characteristic properties are estimated in a recursive approach. The method is evaluated for two academic benchmark examples, and the results indicate its potential for model-based online reconstruction for multicellular systems. Full article
(This article belongs to the Special Issue Recent Advances in Population Balance Modeling)
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Open AccessFeature PaperArticle Modeling the Separation of Microorganisms in Bioprocesses by Flotation
Processes 2018, 6(10), 184; https://doi.org/10.3390/pr6100184
Received: 22 August 2018 / Revised: 27 September 2018 / Accepted: 30 September 2018 / Published: 6 October 2018
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Abstract
Bioprocesses for the production of renewable energies and materials lack efficient separation processes for the utilized microorganisms such as algae and yeasts. Dissolved air flotation (DAF) and microflotation are promising approaches to overcome this problem. The efficiency of these processes depends on the [...] Read more.
Bioprocesses for the production of renewable energies and materials lack efficient separation processes for the utilized microorganisms such as algae and yeasts. Dissolved air flotation (DAF) and microflotation are promising approaches to overcome this problem. The efficiency of these processes depends on the ability of microorganisms to aggregate with microbubbles in the flotation tank. In this study, different new or adapted aggregation models for microbubbles and microorganisms are compared and investigated for their range of suitability to predict the separation efficiency of microorganisms from fermentation broths. The complexity of the heteroaggregation models range from an algebraic model to a 2D population balance model (PBM) including the formation of clusters containing several bubbles and microorganisms. The effect of bubble and cell size distributions on the flotation efficiency is considered by applying PBMs, as well. To determine the sensitivity of the results on the model assumptions, the modeling approaches are compared, and suggestions for their range of applicability are given. Evaluating the computational fluid dynamics (CFD) of a dissolved air flotation (DAF) system shows the heterogeneity of the fluid dynamics in the flotation tank. Since analysis of the streamlines of the tank show negligible back mixing, the proposed aggregation models are coupled to the CFD data by applying a Lagrangian approach. Full article
(This article belongs to the Special Issue Recent Advances in Population Balance Modeling)
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Open AccessFeature PaperArticle Population Balance Modeling and Opinion Dynamics—A Mutually Beneficial Liaison?
Processes 2018, 6(9), 164; https://doi.org/10.3390/pr6090164
Received: 16 August 2018 / Revised: 3 September 2018 / Accepted: 7 September 2018 / Published: 11 September 2018
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Abstract
In this contribution, we aim to show that opinion dynamics and population balance modeling can benefit from an exchange of problems and methods. To support this claim, the Deffuant-Weisbuch model, a classical approach in opinion dynamics, is formulated as a population balance model. [...] Read more.
In this contribution, we aim to show that opinion dynamics and population balance modeling can benefit from an exchange of problems and methods. To support this claim, the Deffuant-Weisbuch model, a classical approach in opinion dynamics, is formulated as a population balance model. This new formulation is subsequently analyzed in terms of moment equations, and conservation of the first and second order moment is shown. Exemplary results obtained by our formulation are presented and agreement with the original model is found. In addition, the influence of the initial distribution is studied. Subsequently, the Deffuant-Weisbuch model is transferred to engineering and interpreted as mass transfer between liquid droplets which results in a more flexible formulation compared to alternatives from the literature. On the one hand, it is concluded that the transfer of opinion-dynamics problems to the domain of population balance modeling offers some interesting insights as well as stimulating challenges for the population-balance community. On the other hand, it is inferred that population-balance methods can contribute to the solution of problems in opinion dynamics. In a broad outlook, some further possibilities of how the two fields can possibly benefit from a close interaction are outlined. Full article
(This article belongs to the Special Issue Recent Advances in Population Balance Modeling)
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