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Dimension reduction of bivariate population balances using the quadrature method of moments
2011
Computers and Chemical Engineering
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We propose a model reduction based on the quadrature method of moments (QMOM). Using this method a two-dimensional population balance is reduced to a system of one-dimensional advection equations. ...
Despite the dimension reduction the method keeps important volume dependent information of the crystal size distribution (CSD). ...
The population balance The growth process of crystals showing direction-dependent growth can be modelled using a multi-dimensional population balance. ...
doi:10.1016/j.compchemeng.2010.06.012
fatcat:7btbaqj2qveavlrfl7bpqj42yi
Comminution process modeling based on the monovariate and bivariate direct quadrature method of moments
2014
AIChE Journal
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However, other properties, such as the particle strength, also influence the grinding kinetics. A bivariate PBE was developed and resolved by the direct quadrature method of moments. ...
Population balance equations (PBE) applied to comminution processes are commonly based on selection and breakage functions, which allow the description of changes of particle-size distributions vs. time ...
Introduction Population balance equations (PBE) are commonly used to model particulate processes. ...
doi:10.1002/aic.14358
fatcat:ilkc44ebr5dgjkwzg7el4hrxmm
Batch Cooling Crystallization of Plate-like Crystals: A Simulation Study
2015
Periodica Polytechnica: Chemical Engineering
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The population balance equation is reduced to a system of equations for the bivariate mixed moments of internal variables, which are solved by means of the quadrature method of moments. ...
The population balance approach is used to describe a seeded crystallization process, developing a bivariate morphological population balance model including nucleation and size dependent crystal growth ...
Acknowledgements The financial support of the Hungarian Scientific Research Fund under Grant K 77955 and the Collegium Talentum is gratefully acknowledged. ...
doi:10.3311/ppch.7581
fatcat:7eowlijnmveaboe5hy773gc7mm
Numerical solution of the bivariate population balance equation for the interacting hydrodynamics and mass transfer in liquid–liquid extraction columns
2006
Chemical Engineering Science
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These methods are the generalized fixed-pivot technique (GFP) and the quadrature method of moments (QMOM). ...
A comprehensive model for predicting the interacting hydrodynamics and mass transfer is formulated on the basis of a spatially distributed population balance equation in terms of the bivariate number density ...
Acknowledgements The authors wish to thank the DFG and DAAD for supporting this work. ...
doi:10.1016/j.ces.2004.12.055
fatcat:rhlnw6d7enhk5m2n2hs6rxpwuq
Approximate Moment Methods for Population Balance Equations in Particulate and Bioengineering Processes
2020
Processes
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A specific class of solution algorithms, so-called moment methods, is based on the reduction of complex models to a set of ordinary differential equations characterizing dynamics of integral quantities ...
In this contribution, a concise overview of the most prominent approximate moment methods is given. ...
The method uses a Gauss-Christoffel quadrature rule and shows good results in comparison to experimental data.
• The bivariate moment projection algorithm is presented in [138] . ...
doi:10.3390/pr8040414
fatcat:lszkh5hdbffljb3aurq45mojwq
Comparison of methods for multivariate moment inversion—Introducing the independent component analysis
2014
Computers and Chemical Engineering
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Despite the advantages of the moment based methods in solving multivariate population balances models, these methods still suffer with the so-called multivariate moment inversion problem. ...
This work presents a comparative analysis of the existing methods regarding their accuracy and robustness. ...
The multivariate moment inversion using optimization was first reported by Wright et al. (2001) for a bivariate population balance problem. ...
doi:10.1016/j.compchemeng.2013.08.006
fatcat:ioxtaueakjcmtjik44e4xushbu
Modelling of Particulate Processes
2005
Kona : Powder and Particle
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We review the method of moments, sectional, finite element, and Monte Carlo methods and give examples of their applications in f lame synthesis. ...
We review models and numerical methods used in f lame synthesis of organic and inorganic nanoparticles. ...
Acknowledgements The author would like to thank the members of the Computational Modelling Group in Cambridge, in par ticular my students Neal Morgan, Rober t Patterson, Jasdeep Singh, and Sebastian Mosbach ...
doi:10.14356/kona.2005007
fatcat:alsno7jdubcgpiqe6amtlne3yq
Simulation and control of nanoparticle size distribution in a high temperature reactor
2012
Polish Journal of Chemical Technology
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The proposed method "which is the application of reduced population balance model" shows that there is some dependence of the average particle diameter on the wall temperature and the model can thus be ...
The simulation results from the above model demonstrated that the reduced population balance can be effectively used to control the PSD. ...
Wright et al 26 used the bivariate extension of the quadrature method of moments (QMOM) to effi ciently model the dynamic of a population of inorganic nanoparticles undergoing simultaneous coagulation ...
doi:10.2478/v10026-012-0052-y
fatcat:wibhlpuli5e55i7imiamokby4q
Solution of population balance equations in applications with fine particles: Mathematical modeling and numerical schemes
2016
Journal of Computational Physics
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quadrature method of moments (EQMOM) based on the work of Yuan et al. ...
For this purpose, two types of methods are investigated for solving the population balance equation with aggregation, continuous particle size change (growth and size reduction), and nucleation: the extended ...
Moreover, the moment space is described in each
Population balance equation (PBE) Let us consider the volume v as the only internal variable. ...
doi:10.1016/j.jcp.2016.08.017
fatcat:x6qetqir4be7lkbvx5rte6ipca
Quadrature-Based Methods for Obtaining Approximate Solutions to Nonlinear Asset Pricing Models
1991
Econometrica
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The method works by using numerical quadrature rules to approximate the integral operators that arise in stochastic intertemporal models. ...
An empirical application uses the method to study the relationship between the risk premium and the conditional variability of the equity return under an ARCH endowment process. ...
Burnside (1989) uses versions of the method to approximate predicted population moments for method of moments estimation of financial models. ...
doi:10.2307/2938261
fatcat:23wqkgfcpzcdzpva6odrczmseu
Strongly coupled fluid-particle flows in vertical channels. II. Turbulence modeling
2016
Physics of Fluids
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Here, data from the EL simulations are used to validate a multiphase Reynolds-stress model (RSM) that predicts the wall-normal distribution of the two-phase, one-point turbulence statistics up to second ...
Finally, an algebraic stress model for the PA particle-phase pressure tensor and the Reynolds stresses is derived from the RSM using the weak-equilibrium assumption. ...
Population balance equation (PBE) Let us consider the volume v as the only internal variable. ...
doi:10.1063/1.4943234
fatcat:jmohocqth5bypbdkpvbs4us4em
Experimental and numerical study on the effect of oxymethylene ether-3 (OME3) on soot particle formation
2021
Fuel
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2021 pre-print arXiv:2104.12873v1 fatcat:nus5n6vrjngspix47vwadhrjn4
Particle size distribution (PSD) and Laser Induced Fluorescence (LIF) and Incandescence (LII) along with numerical (Conditional Quadrature Method of Moments - CQMOM, based on D'Anna physico-chemical soot ...
The soot volume fraction and PSD indicate a reduction in the total number and the size of the soot particles at all equivalence ratios, while the number of small nanoparticles remains almost unchanged. ...
Acknowledgments The ...
doi:10.1016/j.fuel.2020.119353
fatcat:oh3qsaq5ojadncim5jemfvtnke
Particle formation in oxymethylene ethers (OMEn, n = 2-4) / ethylene premixed flames
[article]
2022
arXiv
pre-print
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In the numerical simulations, the kinetic mechanism is combined with a detailed quadvariate soot model which uses the Conditional Quadrature Method of Moments and validated with Laser-Induced Fluorescence ...
Furthermore, the extent of soot reduction is comparable among the three OMEn. The trends and overall reduction are very well captured by the model. ...
Acknowledgments The authors gratefully acknowledge the funding by the German Federal Ministry of Education and Research (BMBF) as part of the NAMOSYN Project (project number 03SF0566R0). ...
arXiv:2204.10733v1
fatcat:ilkjwhttj5egfn5l5vpiggytqa
Modelling of Soot Aerosol Dynamics in Turbulent Flow
2019
Flow Turbulence and Combustion
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Comprehensive modelling of soot formation in combustion processes requires coupling of the population balance equation, which is the fundamental equation governing aerosol dynamics, with the equations ...
emissions require control of the number of smaller particles. ...
Acknowledgments The author wishes to thank Prof. W. P. Jones for feedback on an early version of this paper. ...
doi:10.1007/s10494-019-00054-8
fatcat:s63b4g65irhshc4srsyzeas3du
Chapter 40 Classical estimation methods for LDV models using simulation
[chapter]
1994
Handbook of Econometrics
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We are grateful to the National Science Foundation for partial financial support, under grants SES-929411913 (Hajivassiliou) and SES-9122283 (Ruud). ...
It is crucial to stress that such numerical quadrature methods offer only poor approximations to integrals of such dimension. ...
Let s be the time in seconds a given computer requires to approximate a 16-dimensional integral by numerical quadrature methods. ...
doi:10.1016/s1573-4412(05)80009-1
fatcat:2r67s6yl3rferkwo6slim5gf5i
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