One-Group Reduced Population Balance Model for CFD Simulation of a Pilot-Plant Extraction Column

Abstract

In this work, a one-group reduced population balance model based on the one primary and one secondary particle method (OPOSPM) developed recently by Attarakih et al. ( Jezowski J. Thullie J. Proceedings of the 19th European Symposium on Computer Aided Process Engineering, ESCAPE-19, Cracow, Poland, June 14−17, 2009New York2009978-0-444-53433-0) is implemented in the commercial computational fluid dynamics (CFD) package FLUENT 6.3 for solving the population balance equation in a combined CFD−population balance model (PBM). The one-group reduced population balance conserves the total number (N) and volume (α) concentrations of the population by directly solving two transport equations for N and α and provides a one-quadrature point for closing the unclosed integrals in the population balance equation. Unlike the published two-equation models, the present method offers accuracy improvement and internal consistency (with respect to the continuous population balance equation) by increasing the number of primary particles (sections). The one-group reduced population balance provides the possibility of a one-equation model for the solution of the PBM in CFD based on the mathematically consistent d 30 instead of the classical d 32 mean droplet diameter. Droplet breakage and coalescence are considered in the PBM, which is coupled to the fluid dynamics in order to describe real droplet behavior in a stirred liquid−liquid extraction column. As a case study, a full pilot-plant extraction column of a rotating disk contactor (RDC) type consisting of 50 compartments was simulated with the new model. The predicted results for the mean droplet diameter and the dispersed-phase volume fraction (holdup) agree well with literature data. The results show that the new CFD−PBM model is very efficient from a computational point of view (a factor of 2 less than the QMOM and a factor of 5 less than the method of classes). This is because the one-group reduced population balance requires the solution of only one equation (the total number concentration) when coupled to the CFD solver. It is therefore suitable for fast and efficient simulations of small-scale devices and even large-scale industrial processes.

Modelling the Hydrodynamics of Bubble Columns using Coupled OPOSPM-Maximum Entropy Method

“…By following Coulaglou and Tavlarides (1977), they derived bubble breakage and coalescence kernels which were included in the source terms (S b and S c ). This approach has two major disadvantages: Firstly, it complicates the addition of new bubble kernels to the IACE, and secondly, it prevents increasing the numerical accuracy of the model by further increasing the order of quadrature approximation of the integrals in the source term (Drumm et al, 2010). This approach has two major disadvantages: Firstly, it complicates the addition of new bubble kernels to the IACE, and secondly, it prevents increasing the numerical accuracy of the model by further increasing the order of quadrature approximation of the integrals in the source term (Drumm et al, 2010).…”

“…This approach has two major disadvantages: Firstly, it complicates the addition of new bubble kernels to the IACE, and secondly, it prevents increasing the numerical accuracy of the model by further increasing the order of quadrature approximation of the integrals in the source term (Drumm et al, 2010). This is because d 30 is a quadrature node based on OPOSPM (Drumm et al, 2010) while d 32 is only a physical definition which is not related to a quadrature approximation of the source terms in the PBE. This is because d 30 is a quadrature node based on OPOSPM (Drumm et al, 2010) while d 32 is only a physical definition which is not related to a quadrature approximation of the source terms in the PBE.…”

Evaluating Sampling Strategies for Visualizing Uncertain Multi-Phase Fluid Simulation Data

“…Using multi-phase fluid simulations, the interaction of liquid or gaseous media can be studied. For this purpose, Eulerian-Eulerian methods such as the Method of Moments [11] have long been in the focus of research, with a number of improvements regarding performance and flexibility being proposed [12,13,14,9]. A fundamental aspect common to all these variants is that bubbles are not represented explicitly.…”

“…The third moment M 3 (x) is related to the volume of the bubble distribution. It can be used to calculate the size of individual bubbles [14]. Even though this size has no influence on the bubble positions, it is needed afterwards for the visualization [10].…”

A pseudo-3D model with 3D accuracy and 2D cost for the CFD–PBM simulation of a pilot-scale rotating disc contactor

“…Actually, it can be treated as a combination of the CM and the QMOM to minimize their respective drawbacks. The SQMOM was successfully implemented by Drumm et al (2010) for the CFD-PBM simulation of extractors with its simplest form: one primary and one secondary particle method (OPOSPM). The results indicated that the OPOSPM is an effective and cost-saving method, and only one scalar equation must be solved for the PBM.…”