Although use of computational fluid dynamics (CFD) for simulating precipitation (and particulate systems in general) is becoming a standard approach, a number of issues still need to be addressed. One major problem is the computational expense of coupling a standard discretized population balance (DPB) with a CFD code, as this approach requires the solution of an intractably large number of transport equations. In this work the quadrature method of moments (QMOM) is tested for size-dependent growth and aggregation. The QMOM is validated by comparison with both Monte Carlo simulations and analytical solutions using several functional forms for the aggregation kernel. Moreover, model predictions are compared with a DPB to compare accuracy, computational time, and the number of scalars involved. Analysis of the relative performance of various methods for treating aggregation provides readers with useful information about the range of application and possible limitations.

Quadrature method of moments for population‐balance equations

https://spiral.imperial.ac.uk/bitstream/10044/1/42571/2/PECS_revision_manuscript.pdf

Population balance modelling of polydispersed particles in reactive flows

Antisolvent crystallization is widely used in the production of pharmaceuticals. Although it has been observed experimentally that the crystal size distribution is strongly influenced by the imperfect mixing of the antisolvent with the solution, these effects have not been adequately quantified. In this work, a turbulent computational fluid dynamics (CFD) code was coupled with a multienvironment probability density function (PDF) model, which captures the micromixing in the subgrid scale, and the population balance equation, which models the evolution of the crystal size distribution. The population balance equation (PBE) was discretized along the internal coordinate using a high-resolution central scheme. The presence of solids was addressed by treating the suspension as a pseudo-homogeneous phase with a spatial variation in the effective viscosity. This coupled CFD-PDF-PBE algorithm was applied to an antisolvent crystallization process in an agitated semibatch vessel, where the rising liquid level was m...

Simulation of Mixing Effects in Antisolvent Crystallization Using a Coupled CFD-PDF-PBE Approach

In this work barium sulfate precipitation is studied in a tubular reactor in a wide range of operating conditions. The effect of reactant concentrations and barium or sulfate excess on crystal-size distribution and morphology is investigated. Experimental results show that ion excess has a strong influence and that at high concentration aggregation takes place. Computational fluid dynamics is coupled with the finite-mode probability density function approach for taking into account both macro- and micromixing, whereas the population balance is treated by using the standard moment method. Comparison with experimental data suggests that when micromixing and agglomeration are properly taken into account, the agreement is improved. However, this statement is partially affected by the lack of knowledge in barium sulfate kinetics.

Nucleation, growth, and agglomeration in barium sulfate turbulent precipitation

The generation of nanostructured particles in high-temperature flames is important both for the control of emissions from combustion devices and for the synthesis of high-value chemicals for a variety of applications. The physiochemical processes that lead to the production of fine particles in turbulent flames are highly sensitive to the flow physics and, in particular, the history of thermochemical compositions and turbulent features they encounter. Consequently, it is possible to change the characteristic size, structure, composition, and yield of the fine particles by altering the flow configuration. This review describes the complex multiscale interactions among turbulent fluid flow, gas-phase chemical reactions, and solid-phase particle evolution. The focus is on modeling the generation of soot particles, an unwanted pollutant from automobile and aircraft engines, as well as metal oxides, a class of high-value chemicals sought for specialized applications, including emissions control. Issues arising due to the numerical methods used to approximate the particle number density function, the modeling of turbulence-chemistry interactions, and model validation are also discussed.

Modeling of Fine-Particle Formation in Turbulent Flames

The 4-environment generalized micromixing (4-EGM) model is applied to describe turbulent mixing and precipitation of barium sulfate in a tubular reactor. The model is implemented in the commercial computational fluid dynamics (CFD) software Fluent. The CFD code is first used to solve for the hydrodynamic fields (velocity, turbulence kinetic energy, turbulent energy dissipation). The species concentrations and moments of the crystal size distribution (CSD) are then computed using user-defined transport equations. CFD simulations are performed for the tubular reactor used in an earlier experimental study of barium sulfate precipitation. The 4-EGM CFD results are shown to compare favourably to CFD results found using the presumed beta PDF model. The latter has previously been shown to yield good agreement with experimental data for the mean crystal size at the outlet of the tubular reactor.



On a applique un modele de micromelange generalise a 4 environnements (4-EGM) afin de decrire le melange turbulent et la precipitation du sulfate de baryum dans un reacteur tubulaire. Ce modele a ete implante dans le logiciel de CFD commercial Fluent. Le programme de CFD est d'abord utilise pour calculer les champs hydrodynamiques (vitesse, energie cinetique de turbulence, dissipation d'energie turbulente). Les concentrations d'especes et les moments de la distribution de taille des cristaux (CSD) sont ensuite calcules par ordinateur a l'aide des equations de transport definies par l'usager. Des simulations de CFD sont realisees pour le reacteur tubulaire utilise dans une etude experimentale anterieure de la precipitation du sulfate de baryum. On montre que les predictions du 4-EGM se comparent favorablement a celles du modele beta PDF. II a ete montre anterieurement que ce dernier presentait un bon accord avec les donnes experimentales pour la taille moyenne des cristaux a la sortie du recteur tubulaire.

Bruno Marcant

Papers

Simulation of fine particle formation by precipitation using computational fluid dynamics