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Aim of this work was the extension and development of a coupled Computational Fluid Dynamics (CFD) and population balance model (PBM) solver to enable a simulation aided design of stirred liquid-liquid extraction columns. The principle idea is to develop a new design methodology based on a CFD-PBM approach and verify it with existing data and correlations. On this basis, the separation performance in any apparatus geometry should be possible to predict without any experimental input. Reliable “experiments in silico” (computer calculations) should give the engineer a valuable and user-friendly tool for early design studies at minimal costs.
The layout of extraction columns is currently based on experimental investigations from miniplant to pilot plant and a scale-up to the industrial scale. The hydrodynamic properties can be varied by geometrical adjustments of the stirrer diameter, the stirrer height, the free cross sectional area of the stator, the compartment height as well as the positioning and the size of additional baffles. The key parameter for the liquid–liquid extraction is the yield which is mainly determined at the in- and outlets of the column. Local phenomena as the swirl structure are influenced by geometry changes. However, these local phenomena are generally neglected in state-of-the are design methodologies due to the complex required measurement techniques. A geometrical optimization of the column therefore still results in costs for validation experiments as assembly and operation of the column, which can be reduced by numerical investigations. The still mainly in academics used simulation based layout of counter-current extraction columns is based at the beginning of this work on one dimensional simulations of extraction columns and first three dimensional simulations. The one dimensional simulations are based on experimental derived, geometrical dependent correlations for the axial backmixing (axial dispersion), the hold-up, the phase fraction, the droplet sedimentation and the energy dissipation. A combination of these models with droplet population balance modeling resulted in a description of the complex droplet-droplet interactions (droplet size) along the column height. The three dimensional CFD simulations give local information about the flow field (velocity, swirl structure) based on the used numerical mesh corresponding to the real geometry. A coupling of CFD with population balance modeling further provides information about the local droplet size. A backcoupling of the droplet size with the CFD (drag model) results in an enhancement of the local hydrodynamics (e.g. hold-up, dispersed phase velocity). CFD provided local information about the axial dispersion coefficient of simple geometrical design (e.g. Rotating Disc Contactor (RDC) column). First simulations of the RDC column using a two dimensional rotational geometry combined with population balance modeling were performed and gave local information about the droplet size for different boundary conditions (rotational speed, different column sizes).
In this work, two different column types were simulated using an extended OpenSource CFD code. The first was the RDC column, which were mainly used for code development due to its simple geometry. The Kühni DN32 column is equipped with a six-baffled stirring device and flat baffles for disturbing the flow and requires a full three dimensional description. This column type was mainly used for experimental validation of the simulations due to the low required volumetric flow rate. The Kühni DN60 column is similar to the Kühni DN32 column with slight changes to the stirring device (4-baffles) and was used for scale up investigations. For the experimental validation of the hydrodynamics, laser based measurement techniques as Particle Image Velocimetry (PIV) and Laser Induced Fluorescence (LIF) were used. A good agreement between the experimental derived values for velocity, hold-up and energy dissipation, experimentally derived correlations from literature and the simulations with a modified Euler-Euler based OpenSource CFD code could be found. The experimental derived axial dispersion coefficient was further compared to Euler-Lagrange simulations. The experimental derived correlations for the Kühni DN32 in literature fit to the simulated values. Also the axial dispersion coefficient for the dispersed phase satisfied a correlation from literature. However, due to the complexity of the dispersed phase axial dispersion coefficient measurement, the available correlations gave no distinct agreement to each other.
A coupling of the modified Euler-Euler OpenSource CFD code was done with a one group population balance model. The implementation was validated to the analytical solution of the population balance equation for constant breakage and coalescence kernels. A further validation of the population balance transport equation was done by comparing the results of a five compartment section to the results of the commercial CFD code FLUENT using the Quadrature Method of Moments (QMOM).
For the simulation of the droplet-droplet interactions in liquid-liquid extraction columns, several breakage and coalescence models are available in the literature. The models were compared to each other using the one-group population balance model in Matlab which allows the determination of the minimum stable droplet diameter at a certain energy dissipation. Based on this representation, it was possible to determine the parameters for a specific breakage and coalescence model combination which allowed the simulation of a Kühni miniplant column at different rotational speeds. The resulting simulated droplet size was in very good agreement to the experimental derived droplet size from literature. Several column designs of the DN32 were investigated by changing the compartment height and the axial stirrer position. It could be shown that a decrease of the stirrer position increases the phase fraction inside the compartment. At the same time, the droplet size decreases inside the compartment, which allows a higher mass transfer due to a higher available interfacial area. However, the shifting results in an expected earlier flooding of the column due to a compressed flow structure underneath the stirring device. In a next step, the code was further extended by mass transfer equations based on the two-film theory. Mass transfer coefficient models for the dispersed and continuous phase were investigated for the RDC column design.
A first mass transfer simulation of a full miniplant column was done. The change in concentration was accounted by the mixture density, viscosity and interfacial tension in dependence of the concentration, which affects the calculation of the droplet size. The results of the column simulation were compared to own experimental data of the column. It could be shown that the concentration profile along the column height can be predicted by the presented CFD/population balance/mass transfer code. The droplet size decreases corresponding to the interfacial tension along the column height. Compared to the experimental derived droplet size at the outlet, the simulation is in good agreement.
Besides the occurrence of a mono dispersed droplet size, high breakage may lead to the generation of small satellite droplets and coalescence underneath the stator leads to larger droplets inside the column and hence to a change of the hold-up and of the flooding point. A multi-phase code was extended by the Sectional Quadrature Method of Moment (SQMOM) allowing a modeling of the droplet interactions of bimodal droplet interactions or multimodal distributions. The implementations were in good agreement to the analytical solution. In addition, the simulation of an RDC column section showed the different distribution of the smaller droplets and larger droplets. The smaller droplets tend to follow the continuous phase flow structure and show a higher distribution of inside the column. The larger droplets tend to rise directly through the column and show only a low influence to the continuous phase flow.
The current results strengthen the use of CFD for the layout of liquid-liquid extraction columns in future. The coupling of CFD/PBM and mass transfer using an OpenSource CFD code allows the investigation of computational intensive column designs (e.g. pilot plant columns). Furthermore the coupled code enhances the accuracy of the hydrodynamics simulations and leads to a better understanding of counter-current liquid-liquid extraction columns. The gained correlation were finally used as an input for one dimensional mass transfer simulations, where a perfect fit of the concentration profiles at varied boundary conditions could be obtained. By using the multi-scale approach, the computational time for mass transfer simulations could be reduced to minutes. In future, with increasing computational power, a further extend of the multiphase CFD/SQMOM model including mass transfer equation will provide an efficient tool to model multimodal and multivariate systems as bubble column reactors.
Modeling of solid-particle effects on bubble breakage and coalescence in slurry bubble columns
(2020)
Solid particles heavily affect the hydrodynamics in slurry bubble columns. The effects arise through varying breakup and coalescence behavior of the bubbles with the presence of solid particles where particles in the micrometer range lead to a promotion of coalescence in particular. To simulate the gas-liquid-solid flow in a slurry bubble column, the Eulerian multifluid approach can be employed to couple computational fluid dynamics (CFD) with the population balance equation (PBE) and thus to account for breakup and coalescence of bubbles.
In this work, three approaches are presented to modify the breakup and coalescence models to account for enhanced coalescence in the coupled CFD-PBE framework. The approaches are applied to a reference simulation case with available experimental data. In addition, the impacts of the modifications on the simulated bubble size distribution (BSD) and the applicability of the approaches are evaluated. The capabilities as well as the differences and limits of the approaches are demonstrated and explained.
In this paper we present the comparison of experiments and numerical simulations for bubble cutting by a wire. The air bubble is surrounded by water. In the experimental setup an air bubble is injected on the bottom of a water column. When the bubble rises and contacts the wire, it is separated into two daughter bubbles. The flow is modeled by the incompressible Navier–Stokes equations. A meshfree method is used to simulate the bubble cutting. We have observed that the experimental and numerical results are in very good agreement. Moreover, we have further presented simulation results for liquid with higher viscosity. In this case the numerical results are close to previously published results.
This work reviews the state-of-the-art models for the simulation of bubble columns and focuses on methods coupled with computational fluid dynamics (CFD) where the potential and deficits of the models are evaluated. Particular attention is paid to different approaches in multiphase fluid dynamics including the population balance to determine bubble size distributions and the modeling of turbulence where the authors refer to numerous published examples. Additional models for reactive systems are presented as well as a special chapter regarding the extension of the models for the simulation of bubble columns with a present solid particle phase, i.e., slurry bubble columns.
Measuring Particle Size Distributions in Multiphase Flows Using a Convolutional Neural Network
(2019)
The efficiency of many chemical engineering applications depends on the surface/volume ratio of the dispersed phase. Knowledge of this particle size distribution is a key factor for better process control. The challenge of measurements acquired by optical imaging techniques is the segmentation of overlapping particles, especially in high phase fraction flows. In this work, a convolutional neural network is trained to segment droplets in images acquired by a shadowgraphic approach. The network is trained on artificial images and implemented into a droplet size algorithm. The results are compared to an OpenSource segmentation approach.
Reactive bubble columns are omnipresent in the chemical industry. The layout of these columns is still limited by correlations and therefore improved simulation techniques are required to describe the complex hydrodynamics/reaction interaction. In this work, we focus on the numerical and experimental study of the viscosity influence on bubble motion and reaction using an Euler-Lagrange framework with an added oscillation and reaction model to bring the column layout base closer to a predictive level. For comparison and validation, experimental data in various water-glycerol solutions was obtained in a cylindrical bubble column at low gas hold-up, where the main parameters such as bubble size, motion, and velocities were detected. Glycerol leads thereby to a change in viscosity and surface tension. Further, the surface tension was modified by addition of a surfactant. The bubble oscillating motion in low to higher viscosity could be described using an Euler-Lagrange framework and enables a description of industrial bubble flows. In addition, the simulations were in good agreement concerning reactive mass transfer investigations at higher viscosity of the liquid which led to an overall lower mass transfer compared to the cases with lower viscosity.
The generation of liquid-liquid dispersions with defined droplet size distributions is an important aspect for process equipment design. In this work, two centrifugal pumps with different impeller diameters were used to generate dispersions at selected operating points for a paraffin oil-water system. The droplet break-up phenomena within the centrifugal pumps were analyzed using a transparent pump design in combination with high-speed imaging. Droplet size distributions at centrifugal pump discharge nozzle were recorded with optical probe measurement technologies and evaluated by means of image processing using a neural network. The influence of impeller diameter, rotational speed, volumetric flow rate and dispersed phase fraction are discussed. Experimental data is correlated using fluid properties, operating data as well as centrifugal pump dimensions. The correlations developed from results of this work serve as a basis for the equipment design of centrifugal pumps.
The digitization of extraction columns requires a profound knowledge of the present hydrodynamics/mass transport interaction as well as appropriate measurement techniques for the detection of relevant input and target values. In this article, the different techniques for droplet size distribution as well as concentration determination are presented and new methods for online evaluation are discussed. In combination with the simulation of droplet size, holdup and solute concentration distribution, an online-capable process tool for controlling and optimizing extraction columns will be obtained.
Both solid particles and column diameter affect the gas holdup and flow regimes in slurry bubble columns, but investigations of the combined effects are not to be found. This study shows the simultaneous impacts on the overall gas holdup and flow regime transitions and determines the dominant effects in slurry bubble columns on the centi-scale containing solid particle concentrations up to 20 vol %. Additional tomography measurements are presented to visualize the gas phase flow and the spatial gas phase distribution in the column.
In gravity separators, also known as settlers, two immiscible liquid phases separate due to differences in density. In extraction mixer-settler units, a dispersion needs to be separated within the separator unit. In order to overcome the hitherto purely experimental design, a knitted mesh adapted model as well as an automated test facility were developed in this work, which easily enable a scale-up to industrial units. An automation allows for a controlled investigation of knitted meshes as coalescing aids in settlers, and this was achieved via photo-optical probes with an optimized image analysis technique. It overcomes the limitations of neuronal network training based on manually annotating images using computer-generated image data. Therefore, the new methodology and setup are explained in detail, and the derivation and application of a new model to design separators with knitted meshes as coalescing aid is presented and compared to experimental results using meshes of different structures and materials. Finally, case studies and scale-up are discussed.