Modeling and simulation of crystallization processes using parsival

Wulkow, Michael; Gerstlauer, Andreas; Nieken, Ulrich

doi:10.1016/s0009-2509(00)00432-2

Cited by 117 publications

(72 citation statements)

References 16 publications

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“…Using these parameters >99.9% of droplets formed lay within the volume range from 0 to Vp and the mass balance could be conserved adequately. The commercial software PARSIVAL ® (Wulkow et al, 2001) was used to solve the partial differential equation of the PBE with coupled mass balance. The numerical parameters of the breakage and coalescence rate of the different models were fitted to experimental data using the implemented parameter estimation routine by minimising the residual between experimental and simulated data.…”

Section: Numerical Investigations and Parameter Estimationmentioning

confidence: 99%

Coalescence efficiency model including electrostatic interactions in liquid/liquid dispersions

Kamp¹,

Kraume²

2015

Chemical Engineering Science

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The drop size distribution is an essential process variable in liquid/liquid systems and relevant in many technical applications. It can be described by population balance equations. A coalescence efficiency model was developed to be able to describe the well-known coalescence inhibition due to changing pH value or salt concentration. The model includes the attractive van der Waals and repulsive electrostatic force according to the DLVO theory into the population balance equation framework. This DLVO model can extend existing simulations in a straightforward manner due to a conceptual implementation. Moreover, zeta potential measurements were performed and the model was applied to simulate experiments in a stirred tank. Hence, the drop size distribution could be predicted well with changing pH value. The results are discussed in comparison to simulations with existing models in literature.

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Section: Numerical Investigations and Parameter Estimationmentioning

confidence: 99%

Coalescence efficiency model including electrostatic interactions in liquid/liquid dispersions

Kamp¹,

Kraume²

2015

Chemical Engineering Science

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“…In the numerical study, reference simulations with the error controlled, adaptive population balance solver Parsival 23 are performed in order to asses the overall error of QMOM. In Parsival, the relative weighted error of the particle-size distribution can be controlled up to a user specified tolerance.…”

Section: Numerical Studiesmentioning

confidence: 99%

“…17 In our case studies, we compare QMOM results to solutions obtained with Parsival. 23 Parsival uses an hp-adaptive discontinuous FEM, where the user can prescribe a relative error bound on the solution that is guaranteed by the algorithm. Therefore, Parsival provides a highly accurate reference solution.…”

Section: Introductionmentioning

confidence: 99%

Generalization and numerical investigation of QMOM

et al. 2006

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in Wiley InterScience (www.interscience.wiley.com).A generalized framework is developed for the quadrature method of moments (QMOM), which is a solution method for population balance models. It further evaluates the applicability of this method to industrial suspension crystallization processes. The framework is based on the concepts of generalized moments and coordinate transformations, which have been used already in earlier solution approaches. It is shown how existing approaches to QMOM are derived from the suggested unified framework. Thus, similarities and differences between the various QMOM methods are uncovered. Further, potential error sources involved in the different approaches to QMOM are discussed and assessed by means of a series of test cases. The test cases are selected to be challenging. The error in the QMOM solution is evaluated by comparison to an adaptive, error controlled solution of the population balance. The behavior of a range of different QMOM formulations is analyzed by means of numerical quadrature, dynamic simulation, as well as numerical continuation and bifurcation analysis. As a result of this detailed analysis, some general limitations of the method are detected and guidelines for its application are developed. This article is limited to lumped population balance models with one internal coordinate.

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“…To investigate the model, we considered different different temperatures of synthesis and different values of the pH of the reactive mixture. To solve the model, we used the numerical code Parsival, which solves population balance equations for lumped systems [11].…”

Section: Introductionmentioning

confidence: 99%

A mathematical investigation of the Turkevich organizer theory in the citrate method for the synthesis of gold nanoparticles

Agunloye

Gavriilidis

Mazzei

2017

Chemical Engineering Science

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Abstract-Gold nanoparticles are commonly synthesized by reducing chloroauric acid with sodium citrate. This method, referred to as the citrate method, can produce spherical gold nanoparticles (NPs) in the size range 10-150 nm. Gold NPs of this size are useful in many applications. However, the NPs are usually polydisperse and irreproducible. A better understanding of the synthesis mechanisms is thus required. This work thoroughly investigated the only model that describes the synthesis. This model combines mass and population balance equations, describing the NPs synthesis through a sequence of chemical reactions. Chloroauric acid reacts with sodium citrate to form aurous chloride and dicarboxy acetone. The latter organizes aurous chloride in a nucleation step and concurrently degrades into acetone. The unconsumed precursor then grows the formed nuclei. However, depending on the pH, both the precursor and the reducing agent react differently thus affecting the synthesis. In this work, we investigated the model for different conditions of pH, temperature and initial reactant concentrations. To solve the model, we used Parsival, a commercial numerical code, whilst to test it, we considered various conditions studied experimentally by different researchers, for which results are available in the literature. The model poorly predicted the experimental data. We believe that this is because the model does not account for the acid-base properties of both chloroauric acid and sodium citrate.

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Modeling and simulation of crystallization processes using parsival

Cited by 117 publications

References 16 publications

Coalescence efficiency model including electrostatic interactions in liquid/liquid dispersions

Coalescence efficiency model including electrostatic interactions in liquid/liquid dispersions

Generalization and numerical investigation of QMOM

A mathematical investigation of the Turkevich organizer theory in the citrate method for the synthesis of gold nanoparticles

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