- Email: [email protected]

S1004-9541(15)00270-0 doi: 10.1016/j.cjche.2015.07.023 CJCHE 349

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Please cite this article as: Mark W. Hlawitschka, Menwer M. Attarakih, Samer S. AlZyod, Hans-J¨ org Bart, CFD based extraction column design - Chances and challenges, (2015), doi: 10.1016/j.cjche.2015.07.023

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ACCEPTED MANUSCRIPT CFD based extraction column design - Chances and challenges Mark W. Hlawitschka1,2, Menwer M. Attarakih3, Samer S. Al-Zyod3, Hans-Jörg Bart1,2，

University of Jordan, Department of Chemical Engineering, 11942-Amman, Jordan

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Center for Computational and Mathematical Modelling (CM²), TU Kaiserslautern, Kaiserslautern 67653, Germany

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Chair of Separation Science and Technology, POB 3049, TU Kaiserslautern, Kaiserslautern 67653, Germany

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Abstract

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This paper shows that one-dimensional (1-D) [and three-dimensional (3-D) computational fluid dynamics (CFD)] simulations can replace the state-of-the-art usage of pseudo-homogeneous dispersion or back mixing models. This is based on standardized lab-scale cell experiments for the determination of droplet rise, breakage, coalescence and mass transfer parameters in addition to a limited number of additional mini-plant experiments with original fluids. Alternatively, the hydrodynamic parameters can also be derived using more sophisticated 3-D CFD simulations. Computational 1-D modelling served as a basis to replace pilot-plant experiments in any column geometry. The combination of 3-D CFD simulations with droplet population balance models (DPBM) increased the accuracy of the hydrodynamics simulations and gave information about the local droplet size. The high computational costs can be reduced by open source CFD codes when using a flexible mesh generation. First combined simulations using a three way coupled CFD/DPBM/mass-transfer solver pave the way for a safer design of industrial-sized columns, where no correlations are available.

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Keywords: CFD, DPBM, Column design

Introduction

Solvent extraction columns are widely used in chemical, petrochemical, hydrometallurgical and nuclear processes. The main apparatus used for solvent extraction is still the mixer-settler or mixer-settler cascades because of easy design, reliability and high capacity. The main disadvantages are the large footprint of the mixer-settler, which is mainly determined by the settling zone and multiple pumps and piping requirements. By comparison, solvent extraction columns provide a high number of theoretical stages at high throughputs, requiring only a small footprint and low capital costs. Despite their advantages, solvent extraction columns are not widely applied due to their sophisticated layout and scale-up. Uncertainties mainly arise from the complex interactions of the liquid phases as for example back- and forward mixing and a changing droplet size distribution by coalescence and breakage. These phenomena * E-Mail: [email protected]

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finally have an impact on the operation limits (e.g. flooding) and the efficiency of the column. Hence, in the field of solvent extraction design, a scale-up from mini-plant columns to industrial sized columns has become an important feature. As the diameter of the column increases, the tendency for back mixing phenomena to occur increases, and this results in lower column efficiency during scale-up. Correlations derived on a pilot-plant scale will not accurately depict that behavior on an industrial scale, hence overdesign is a must.

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For improved and reliable design of solvent extraction columns, standardized labscale cells were developed that allow monitoring of single droplet behavior. Mini-plant column experiments could capture pilot-scale effects, especially during long duration runs. The hydrodynamics gap (droplet behavior, such as movement and size) between mini-plant experiments and pilot-plant scale could be partially closed by droplet population balance modelling (DPBM), based on geometrical identical column designs.

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1-D DROPLET POPULATION BALANCE MODELLING

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An enhancement of the axial dispersion or back mixing models was achieved by taking into account the changes in droplet size along the column height by DPBM for a differential height, , based on the droplet volume distribution is as follows [1]:

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(1)

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The left hand side of the Eq. 1 gives the transport of the population balance along the column height. On the right hand side, is the dispersed phase axial dispersion coefficient, is the volumetric inlet distribution and describes the net droplet volume production due to breakage and coalescence per unit time. In addition, two similar equations describe the solute balances of the dispersed and continuous phases: (2)

( 3)

In the linear driving force model, the overall mass transfer coefficient is defined by , the solute concentration in the continuous phase is given by and the distribution coefficient is . In addition, the surface area of droplets of volume are given by . The average solute concentration for all droplets having volume in the range at level is given by . The source term accounting for coalescence and breakage accounts in this context the mass transfer. In the given continuous phase solute balance (Eqn. 3), the axial dispersion is given by In addition the hold-up of dispersed phase is defined by: ,

( 4)

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Where and are the minimum and maximum droplet volume. The above equations can be easily adapted to any arbitrary column geometry when exchanging the required kernels for breakage and coalescence, energy dissipation, droplet velocity, mass transfer correlations and axial dispersion [11].

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3-D CFD MODELLING OF SOLVENT EXTRACTION COLUMNS

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3-D CFD simulations allow a description of column hydrodynamics without any geometrical constraints, where the geometrical possibilities are mainly limited by computational resources. The investigations of stirred solvent extraction columns started in 1993 with a publication of Weiss & Bart [12] describing the simulation of a single segment of an rotating disc contactor (RDC) column with the CFD code Fire. Rieger et al. [13] simulated a DN150 RDC column at low hold-up and employed the Euler-Euler model to predict the two-phase flow structure. Yundong et al. [14] measured and simulated the profile in a computational two dimensional represented RDC column using the CFD code PHOENICS. A validation of the velocity field was performed using the laser induced anemometer (LDA)-measurements of Fei et al. [15] with single phase flow in stirred solvent extraction columns. The residence time distribution was numerically and experimentally investigated by Modes & Bart [16] and recently by Gurker & Marr [17]. The two-phase flow field was simulated You & Xiao [18]. Ghaniyari-Benis et al. [19] simulated an RDC column using the Euler-Euler approach. The first study using CFD simulations for the optimization of solvent extraction columns was undertaken by Kolb [20] for a mini-plant Kühni column. An early extension of the two-phase flow accounting the droplet size distribution was reached by Vikhansky et al. [21]. Drumm [22] further extended CFD/DPBM research. Therefore, he implemented and applied several DPBM using the commercial CFD code FLUENT for the simulation of the droplet interactions in an RDC column. The concept of Kolb [20] and Drumm [22] was applied by Aksamija & Siebenhofer [23] for the optimization of an RDC column, where it could be shown that a stator less design could outperform the state-of-the-art design by 36% with regards to the HTU value. A first combination using a commercial CFD/DPBM/mass transfer code for the investigation of solvent extraction columns was done by Hlawitschka & Bart [24] and Jildeh et al. [25]. A further improvement regarding the simulation setup, computational time and flexibility can be reached by the extension of an OpenSource CFD code [26], namely OpenFOAM® (v171). The numerical framework of the modified “twoPhaseEulerFoam” code is based on a set of continuity and momentum equations for each phase. The continuity equation for the continuous phase is represented by: ,

( 5)

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where represents the source term due to possible mass transfer. The phase fraction in Eqn. 5 is represented by , the density of the continuous phase by and the velocity of the continuous phase by . The respective momentum conservation equation is given by: ( 6)

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In addition, the volume fraction must satisfy the following constraint for the given two phase flow: .

( 7)

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As previously stated in the works of Drumm [22] and the work of Wang & Mao [27], the dominant interphase interaction in agitated extraction columns is the drag force, which is calculated by: .

( 8)

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In the smaller sized columns with small sized rising droplets (<5 mm), the drag coefficient obtained by the model of Schiller & Naumann (1935) can be used:

, is defined as .

( 10)

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where the Reynolds number,

( 9)

Agitator movement is accounted for by the moving reference frame (MRF), where the rotation of the agitator is accounted for by source terms to the surrounding fluid. Turbulence is accounted by the mixture - model. The transport equation for the turbulent kinetic energy is given as: ( 11)

The density, viscosity and velocity is replaced by the mixture density, viscosity and velocity to account for the influences of the dispersed phase. The transport equation for the turbulent energy dissipation instead is derived from physical reasons [29]: ,

where the turbulent viscosity in Eqn. 12 is modelled as:

(12)

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(14)

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The generation of turbulent kinetic energy is derived from the mean rate-of-strain tensor:

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The model constants, which also have been applied in this work, are given as: ,

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=1.0 and

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(15)

represents the drag force per unit particle mass:

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where

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The mesh generation was optimized for the two Kühni and a RDC column from a single mesh generation for each column design to an automated mesh generation allowing a flexible design of the internals which is shown in Fig. 1 for the Kühni miniplant column (DN32, compartment height: 28 mm) with different agitator baffle heights. In total, the column is represented by eight compartments, as well as an inflow and outflow zone. Note that Fig. 1 shows the forth lowest compartment. It can be observed that the velocity inside a single compartment increases with increased agitator baffle heights. Besides the local hydrodynamics, the axial dispersion coefficient is a key value for liquid-liquid extraction column layout and is also required for the 1-D approach. It can be obtained by an additional Euler-Lagrange simulation. The main force balance equation for the Lagrangian particles is::

In Eqn. 15,

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is the fluid-phase velocity and

viscosity of the fluid is . The densities

and

is the particle velocity. The molecular describe the densities of the fluid

and particle respectively. The relative Reynolds number and drag coefficient are set as per the Eulerian model. For the determination of the axial dispersion coefficient, the Lagrangian particles were introduced as a Dirac function at the top of the column. The Lagrangian particles follow the continuous phase down the column and are tracked close to the outflow. The resulting distribution is then used to calculate the axial dispersion coefficient. For the three presented geometries, only a slight deviation in the axial dispersion coefficient of the continuous phase can be observed for 3.0 mm and 4.5 mm baffle heights (Fig. 2). The axial dispersion coefficient increases by 20 %, when the height is increased to 8.0 mm. Also the effect of different compartment heights can be studied using CFD simulations. In general, an

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increase of the axial dispersion coefficient can be observed at higher compartment heights and higher rotational speeds (Fig. 3), which also results from changes in the local flow structure resulting in larger dead zones underneath the stator plates. For the original design of the Kühni miniplant column (compartment height 28 mm, baffle height: 4.5 mm), the 3-D-CFD results follow the trend of the axial dispersion coefficient correlation developed by Breysee et al. [30].

Hr=3.0 mm

Hr=4.5 mm

Hr=8.0 mm -

-1

5E-05

Dc / m²s-1

4E-05 3E-05 2E-05 Hc = 33 mm

4.5 mm

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Fig. 1: Velocity fields in a Kühni mini-plant column at different agitator designs (baffle heights) at 6 m³ ·m ²·h and -1 a rotational speed of 200 r·min at a constant compartment height of 28 mm.

Fig. 2: Influence of the agitator baffle height on the -1 axial dispersion coefficient (6 m³·m ²·h ).

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Hc = 28 mm Hc = 23 mm

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Rotational speed / rpm

Fig. 3: Influence of the compartment height to the axial -1 dispersion coefficient (5 m³·m ²·h ) at a baffle height of 4.5 mm.

COMBINATION OF BOTH APPROACHES Both approaches, the 1-D and 3-D, have advantages and disadvantages concerning the computational effort, the accuracy and simulation time. The computational time for a mass transfer simulation heavily relies on the throughput. A simulation of the final steady state of a solvent extraction columns requires a simulation of 5-7 times of the residence time of the liquids inside the column. In contrast to this 3-D-CFD simulations are still based in literature on the simulation of time scales in the range of seconds and minutes due to the high computational load. As an example, the

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required time to reach steady state for a transient full mini-plant column simulation taking into account the mass transfer is approximated by one month on a modern cluster. The benefit is the full resolution of the local hydrodynamics, droplet size and mass transfer. The 1-D simulation instead, is able to simulate the transient behavior of the solute concentration within a few minutes including the simulation setup, but based is on experimental derived correlations (droplet velocity, slowing factor, axial dispersion coefficient, energy dissipation, mass transfer coefficient, droplet coalescence and breakup). Therefore, a combination of 3-D-CFD and 1-D-CFD seems to be straight forward to reduce experimental effort for the 1-D simulation and on the hand to reduce the computational time for mass transfer simulation. The main hydrodynamics correlations as the presented axial dispersion coefficient can be gained by 3-D-CFD simulations, where in addition, different geometrical modifications can be investigated. The geometry dependent correlations for the slowing factor, axial dispersion coefficient and energy dissipation can then be used as an input for the 1-D simulation. The concept can be readily extended to droplet resolved 3-D-CFD simulations, to obtain further information about the mass transfer coefficients of single droplets and droplet swarms.

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As a proof of concept, Fig. 4 shows the resulting droplet size distribution for a 1-D CFD full Kühni miniplant column simulation (Table. 1) compared to experimental data. Fig. 5 shows that a high accuracy between the simulated concentration profile and the experimental data could be obtained by using the mentioned 3-D-CFD correlations. Table 1: Principal design parameters of the used Kühni miniplant column.

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Number of compartments

40

Column width

32 mm

Compartment height

28 mm

Number of streambreakers

3 (120° to each other)

Agitator

6-baffled agitator

Agitator baffle height

4.5 mm

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Fig. 5: Comparison between the measured concentration

(Particulate Population Balance Laboratory) as compared to the measured outlet droplet size -1 distribution at 150 r·min and a throughput of 18.7 -1 m³·m ²·h .

profile and the 1-D simulation (Particulate Population -1 Balance Laboratory) simulation result for 150 r·min and a -1 throughput of 18.7 m³·m ²·h .

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CONCLUSIONS

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Fig. 4: Simulated droplet size using 1-D simulation

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The experimentally based design of solvent extraction columns can be supported by numerical modelling using 1-D and 3-D approaches. The 1-D simulation of solvent extraction columns was facilitated by modern tools using graphical user interfaces. The tools allow a description of the hydrodynamics (e. g. holdup), solute concentration and droplet size for different boundary conditions within minutes based on known or experimental derived correlations. The further development of the 3-D simulation reduces the required number of experimental correlations, due to a direct description of the local hydrodynamics (flow field, energy dissipation). A coupling of the 3-D CFD simulation with DPBM and mass transfer correlations allows the optimization of different column designs, including the column efficiency. Finally, by using the obtained correlations from the 3-D simulations (e.g. axial dispersion coefficients, energy dissipation) in the 1-D simulation, the computational time, especially for the mass transfer simulations, is reduced by keeping a good accuracy. The combination of both approaches is evidently the most promising technique for future column design. FUTURE CHALLENGES Despite the promising results using DPBM for extraction column design and the prediction of mass transfer, the numerical codes still do not cover all the effects observed in solvent extraction columns. Among them are wetting properties, the enrichment of impurities, crud formation and entrainment. In addition, these numerical tools were mainly tested for standard test systems and a common available column geometry. It will not reflect changes in column design and system properties, such as viscosity, interfacial tension and mass transfer rates, occurring in industrial applications. A further task is also the extension of the models to account for reactive extraction, which is essential for efficient recovery of ionic species (metal ions, organic acids, intermediates) in hydrometallurgy, urban mining, fine chemicals, bio and pharmaceutical fields.

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NOMENCLATURE solute concentration in the continuous phase, kg ·m-³

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solute concentration in the droplets, kg· m-³

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drag coefficient

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dispersed phase axial dispersion coefficient ,m² ·s-1 continuous phase axial dispersion coefficient, m² ·s-1 inlet droplet volume distribution acceleration of gravity, m· s-2 compartment height, m

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agitator height, m

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overall mass transfer coefficient, m· s-1 distribution coefficient Pressure, kg ·m-1 ·s-2

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droplet volume distribution

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Reynolds number

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net droplet volume production due to coalescence and breakage, s-1 surface area of droplet with volume , m² Time, s

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continuous phase velocity, m· s-1 disperse phase velocity, m· s-1 average velocity, m· s-1 particle velocity, m· s-1 droplet volume, m³ column height, m phase fraction

ε

turbulent energy dissipation, m² ·s-³ Viscosity, m² ·s-1 density , kg· m-³ diffusion term, kg· m-1 ·s-2 phase fraction

ACCEPTED MANUSCRIPT REFERENCES

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