A New Framework and a Hybrid Method for One-Dimensional Population Balance Modeling of Batch Thermocycling Crystallization

2021 ◽  
pp. 107588
Author(s):  
Yung-Shun Kang ◽  
Jeffrey D. Ward ◽  
Zoltán K. Nagy
Keyword(s):  
Hybrid Method ◽  
Population Balance ◽  
Population Balance Modeling ◽  
One Dimensional ◽  
New Framework

A new framework for population balance modeling of spray fluidized bed agglomeration

Particuology ◽  
2015 ◽  
Vol 19 ◽  
pp. 141-154 ◽  
Author(s):  
Mubashir Hussain ◽  
Jitendra Kumar ◽  
Evangelos Tsotsas
Keyword(s):  
Fluidized Bed ◽  
Population Balance ◽  
Population Balance Modeling ◽  
Bed Agglomeration ◽  
New Framework

scholarly journals Comparison of One Dimensional and Two Dimensional Population Balance Model for Optimization of a Crystallization Process

2021 ◽  
Author(s):  
Tamar Rosenbaum ◽  
Victoria Mbachu ◽  
Niall Mitchell ◽  
John Gamble ◽  
Patricia Cho ◽  
...  
Keyword(s):  
Aspect Ratio ◽  
Crystallization Process ◽  
Population Balance ◽  
Seed Morphology ◽  
Balance Model ◽  
Population Balance Model ◽  
Two Dimensional ◽  
Population Balance Modeling ◽  
One Dimensional ◽  
The Impact

In this work, the advantage of two-dimensional population balance modeling (2D PBM) for a needle-shaped API is highlighted by comparing the one-dimensional population balance model (1D PBM) developed for an antisolvent crystallization with the 2D PBM. The API utilized for this work had extremely slow desupersaturation, and was not able to achieve solubility concentration despite a ~50 h seed bed age. While the 1D PBM is useful in optimizing the crystallization process to enhance desupersaturation, it is unable to match the particle size quantiles well. 2D PBM was necessary to probe the impact of crystallization process parameters on particle aspect ratio (AR). Simulations utilizing the 2D PBM indicated that regardless of antisolvent addition rate or seed morphology, the final material would still be high aspect ratio. This knowledge saved the investment of much time and efforts in trying to minimize particle AR with changes in crystallization processing parameters alone.

scholarly journals How Should We Categorize Approaches to the History of Political Thought?

2020 ◽  
Vol 83 (1) ◽  
pp. 91-114
Author(s):  
Adrian Blau
Keyword(s):  
Theoretical Analysis ◽  
Political Theory ◽  
Political Thought ◽  
Two Dimensional ◽  
History Of Political Thought ◽  
One Dimensional ◽  
History Of ◽  
New Framework

AbstractThis paper proposes a new framework for categorizing approaches to the history of political thought. Previous categorizations exclude much research; political theory, if included, is often caricatured. And previous categorizations are one-dimensional, presenting different approaches as alternatives. My framework is two-dimensional, distinguishing six kinds of end (two empirical, four theoretical) and six kinds of means. Importantly, these choices are not alternatives: studies may have more than one end and typically use several means. Studies with different ends often use some of the same means. And all studies straddle the supposed empirical/theoretical “divide.” Quentin Skinner himself expertly combines empirical and theoretical analysis—yet the latter is often overlooked, not least because of Skinner's own methodological pronouncements. This highlights a curious disjuncture in methodological writings, between what they say we do, and what we should do. What we should do is much broader than existing categorizations imply.

scholarly journals Special Issue on “Recent Advances in Population Balance Modeling”

Processes ◽  
2021 ◽  
Vol 9 (1) ◽  
pp. 122
Author(s):  
Seyed Soheil Mansouri ◽  
Heiko Briesen ◽  
Krist V. Gernaey ◽  
Ingmar Nopens
Keyword(s):  
Population Balance ◽  
Special Issue ◽  
Modeling Framework ◽  
Population Balance Modeling ◽  
Recent Advances

Population Balance Modeling (PBM) is a powerful modeling framework that allows the prediction of the dynamics of distributed properties of a population of individuals at the mesoscale [...]

scholarly journals Study on the regional characteristics during foam flooding by population balance model

2020 ◽  
pp. 014459872098361
Author(s):  
Zhongbao Wu ◽  
Qingjun Du ◽  
Bei Wei ◽  
Jian Hou
Keyword(s):  
Numerical Simulation ◽  
Simulation Model ◽  
Oil Recovery ◽  
Population Balance ◽  
Growth Zone ◽  
Balance Model ◽  
Population Balance Model ◽  
Liquid Ratio ◽  
One Dimensional ◽  
Foam Flooding

Foam flooding is an effective method for enhancing oil recovery in high water-cut reservoirs and unconventional reservoirs. It is a dynamic process that includes foam generation and coalescence when foam flows through porous media. In this study, a foam flooding simulation model was established based on the population balance model. The stabilizing effect of the polymer and the coalescence characteristics when foam encounters oil were considered. The numerical simulation model was fitted and verified through a one-dimensional displacement experiment. The pressure difference across the sand pack in single foam flooding and polymer-enhanced foam flooding both agree well with the simulation results. Based on the numerical simulation, the foam distribution characteristics in different cases were studied. The results show that there are three zones during foam flooding: the foam growth zone, stable zone, and decay zone. These characteristics are mainly influenced by the adsorption of surfactant, the gas–liquid ratio, the injection rate, and the injection scheme. The oil recovery of polymer-enhanced foam flooding is estimated to be 5.85% more than that of single foam flooding. Moreover, the growth zone and decay zone in three dimensions are considerably wider than in the one-dimensional model. In addition, the slug volume influences the oil recovery the most in the foam enhanced foam flooding, followed by the oil viscosity and gas-liquid ratio. The established model can describe the dynamic change process of foam, and can thus track the foam distribution underground and aid in optimization of the injection strategies during foam flooding.

Celebrating a milestone in Population Balance Modeling

2009 ◽  
Vol 64 (4) ◽  
pp. 627 ◽  
Author(s):  
Ingmar Nopens ◽  
Heiko Briesen ◽  
Joel Ducoste
Keyword(s):  
Population Balance ◽  
Population Balance Modeling

scholarly journals Population balance modeling of biopolymer production in cellular systems

2014 ◽  
Vol 47 (3) ◽  
pp. 1705-1710 ◽  
Author(s):  
Andre Franz ◽  
Robert Dürr ◽  
Achim Kienle
Keyword(s):  
Population Balance ◽  
Cellular Systems ◽  
Population Balance Modeling

Taylor series expansion scheme applied for solving population balance equation

2018 ◽  
Vol 34 (4) ◽  
pp. 561-594 ◽  
Author(s):  
Mingzhou Yu ◽  
Jianzhong Lin
Keyword(s):  
Series Expansion ◽  
Taylor Series ◽  
Numerical Study ◽  
Rapid Development ◽  
Taylor Series Expansion ◽  
Population Balance ◽  
Population Balance Modeling ◽  
Physicochemical Processes ◽  
Selection Of ◽  
Expansion Scheme

Abstract Population balance equations (PBE) are widely applied to describe many physicochemical processes such as nanoparticle synthesis, chemical processes for particulates, colloid gel, aerosol dynamics, and disease progression. The numerical study for solving the PBE, i.e. population balance modeling, is undergoing rapid development. In this review, the application of the Taylor series expansion scheme in solving the PBE was discussed. The theories, implement criteria, and applications are presented here in a universal form for ease of use. The aforementioned method is mathematically economical and applicable to the combination of fine-particle physicochemical processes and can be used to numerically and pseudo-analytically describe the time evolution of statistical parameters governed by the PBE. This article summarizes the principal details of the method and discusses its application to engineering problems. Four key issues relevant to this method, namely, the optimization of type of moment sequence, selection of Taylor series expansion point, optimization of an order of Taylor series expansion, and selection of terms for Taylor series expansion, are emphasized. The possible direction for the development of this method and its advantages and shortcomings are also discussed.

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