Use of axial dispersion model for determination of Sherwood number and mass transfer coefficients in a perforated rotating disc contactor

Mehdi Asadollahzadeh*,Alireza Hemmati,Meisam Torab-MostaediMansour Shirvani,Ahad Ghaemi,ZahraSadat Mohsenzadeh

1Nuclear Fuel Cycle Research School,Nuclear Science and Technology Research Institute,P.O.Box:11365-8486,Tehran,Iran

2School of Chemical Engineering,Iran University of Science and Technology,Tehran,P.O.Box 16765-163,Iran

3Department of Chemical Engineering,Faculty of Engineering,South Tehran Branch,Islamic Azad University,Iran

1.Introduction

Mass transfer performance of a system is an inseparable part of many chemical engineering operations in two-phase systems.Solvent extraction(SE)is one of these chemical operations which applied in an enormous number of industrial systems.The solvent extraction process can be conducted in a number of different extraction columns.These extraction columns are divided into non-agitated and agitated extraction columns[1,2].The rotating disk contactor(RDC)is one of the most important agitated extraction columns.This type of extraction column has been widely used in chemical industries and petroleum refining due to its high throughput,low investment,low energy consumption,and easy operation and maintenance[3].However,this extraction column has some limitations due to its structure.There have been some drawbacks including severe axial back mixing and inappropriate drop distribution which cause a reduction in the mass transfer efficiency of commercial RDCs,particularly for low inter facial tension systems.Both the continuous and dispersed phases as they pass through the extraction column can affect axial mixing[4,5].For these reasons,modified RDCs are developed to overcome the mentioned issues.Perforated rotating disk contactor is one of these modified extraction columns that leads to the enhancement in the mass transfer performance of a system.PRDC extraction column is considered as a subset of the RDC extraction column with improved structure,for instance,the RDC with sieved disks[6,7].Better drop dispersion,lower bond drops,more contact time and at the last count,the higher mass transfer are the advantages of PRDC extraction column in comparison to RDC extraction column[8].Furthermore,low operating expenses,easy manufacturing in the industrial scale compared to other agitated columns,and easy scale up to commercial scale are the other plus points of PRDC extraction columns.Sieved disks were apparently more appropriate to liquid–liquid systems with low interfacial tension[9].Based on the obtained experimental results[9],the height of the transfer unit for the sieved disk extraction columns is much lower than that of the rotating disk extraction columns.PRDCs are also used by Fanet al.[10]for phenol removal using liquid membrane separation.According to their conclusion,the mass transfer performance of sieved disk extraction columns is much better than that of the RDC[10].Wanget al.[5]investigated how the perforations on disks cut the droplets and disperse them in the continuous phase.The droplet size in the PRDC extraction column can be controlled using holes on sieved disks and is rather uniform.Thus,it is expected that the extraction column with sieved disks has suitable mass transfer performance and controllability compared to the rotating disk extraction column[5].

The design and scale up of an extractor need the calculation of two independent parameters including the cross-sectional area and the height of the column.The first one is required to accommodate the desired flows without flooding and the second one should be determined to reach the appropriate performance of extraction columns.Ideal plug flow conditions were considered in continuous and dispersed phases for the calculation of the height needed for a separation system in early design and scale-up procedures.However,it is now accepted that axial mixing in the extraction column for one or two phases can lead to the enhancement of the required height for reaching desired separation[11].Using a diffusion or back flow model for design and scale-up is now developed for determination of the height of the extraction column.In this method one parameter is considered for all deviations from the ideal plug flow conditions[12].As a result,widespread availability of reliable correlations for calculation of mass transfer coefficients is required to develop an extraction column design. On the other hand, determining mass transfer coefficient in an extractor is difficult due to significant uncertainty. Although the PRDCwas applied appropriately for a number of separation processes, limited experimental data are available from the literature on the mass transfer performance of PRDC extraction columns. In the current study, the

In the current study,the volumetric overall mass transfer coefficients of a pilot scale perforated rotating disk contactor have been determined.A thorough research was carried out for calculation of operating variable effects which include disk rotational speed, flow rates of continuous and dispersed phase on mass transfer performance of the extraction column for a water–acetone–toluene liquid–liquid system.Additionally,experimental results are compared with Kumar and Hartland[13]correlations and new correlations are developed so that the overall mass transfer coefficient can be precisely foreseen.

2.Experimental

2.1.PRDC pilot scale unit

A pilot scale unit of a perforated rotating extraction column was constructed.Internal diameter of the perforated rotating disk cont actor is 113 mm and it has 43 stages.The accessory equipment contains storage tanks,pumps and rota meters.The rotor shaft carries sieved disks with a diameter of 0.07 m and drilled with 30 holes of 0.015 cm diameter.All internal parts of the column and the blade impellers were made of AISI 316 stainless steel.The blade impellers are mounted on a shaft,which is driven by an electric motor via a variable speed gear box.An optical sensor was used to interface the location of two phases at the top of the extraction column which was automatically controlled.Centrifugal pumps(Penax model)were used to circulate both liquid phases through the column.A schematic of the PRDC pilot-scale unit used in this study is depicted in Fig.1.The geometrical data of the investigated extraction column are given in Table 1.

2.2.Liquid–liquid system

All experiments were conducted at ambient temperature,using a liquid–liquid system according to the recommendations of the European Federation of Chemical Engineering[14].The system was toluene–acetone–water.Distilled water was used as continuous phase in all experiments.The physical properties of this system are given in Table 2.Liquid–liquid equilibrium data of the system was taken from Mí?eket al.'s[14]paper.All experiments were performed with acetone concentrations of approximately 3.5 wt%.

Fig.1.A schematic diagram of the perforated rotating disk contactor(PRDC).

Table 1The main dimensions of the PRDC column

2.3.Experimental procedures

Before running each experiment,the continuous and dispersed phases were mutually saturated,after which acetone was added to the toluene.The acetone content is approximately 3.5 wt%in organic phase.The extraction column was filled with the continuous phase and the agitation rate is then adjusted to the exact amount. Next, the organic phase as dispersed phasewas entered into the extraction column. Optical sensor was applied to maintain the interface position at the desired height. The systemwas permitted to achieve steady state. Samples of aqueous and organic phases at 7 points along the extraction column were collected for determination of acetone concentration. Solute concentrations were then determined by UV–visible spectroscopy. The photography approach using a Nikon D3100 digital camera is used for determination of drop size. Several photographs of the extraction column contents were taken. The photos were analyzed by Digimizer Image Analysis software. The drops were compared with the size of the disks or stator thickness served as the reference for the drop size measurements. Most of the droplets are spherical based on experimental observations. For elliptical drops both the vertical and horizontal axes were measured and the following equation was used to calculate the mean drop size of droplets.

The Sauter mean diameter is then determined as follows:

whereniis the number of mean diameter drop.

The hold-up is defined as the ratio of the dispersed phase to the total volume of the extraction region.At the end of each experiment,displacement approach was applied for determination of hold-up of dispersed phase in the extractor[15].The holdup of dispersed phase was determined using change of interfacial height after coalescence of dispersed phase droplets.

3.Modeling

According to the axial diffusion model and material balance in the extraction column,over the differential elements of the extraction column with a total effective height,H,the equation set for the steady state process is established using following equation,under the constant super ficial velocitiesVcandVdat any given agitation rate[16]:

It should be noted that in Eqs.(3)and(4)Noc=KocaH∕Vcrepresents(NTU)oc=H∕(HTU)oc.PecandPedare the Peclet number and may be represented as Eqs.(5)and(6):

The axial mixing in the dispersed phase is generally less pronounced than that in the continuous phase.In the present work,dispersed phase axial dispersion is assumed to be negligible.The following boundary conditions can be used for the extraction column:

For calculation of continuous phase volumetric overall mass transfer coefficient from Eqs.(3)and(4),the axial dispersion coefficient,the measured concentrations of continuous and dispersed phase and boundary conditions along with the equilibrium data are required.

The specific interfacial area is obtained by the following equation:

4.Results and Discussion

4.1.Effect of agitation rate

The influence of agitation rate on the volumetric overall mass transfer coefficient,mean drop size and holdup is shown in Fig.2(a,b and c).It can be seen that higher agitation rate results in the enhancement of holdup but the reduction of mean drop size.Consequently,decreasing the mean drop size and increasing holdup would increase the interfacial area for mass transfer.However,a decrease in drop size causes a reduction of the overall mass transfer coefficient because of decreasing the internal circulations inside the droplets.Since the latter effect is not dominant,the overall result is the enhancement of the overall mass transfer coefficient via increasing the agitation rate.

Fig.2.(a)The volumetric overall mass transfer coefficient as a function of agitation rate and mass transfer direction,(b)the Sauter mean drop diameter as a function of agitation rate and mass transfer direction,(c)the dispersed phase holdup as a function of agitation rate and mass transfer direction.

Fig.2 also reveals that the extraction column performance changes with the mass transfer direction.When the mass transfer carries out from the continuous(c)to the dispersed phase(d),acetone concentration at the top of the drop is lower than the bottom of the drop.This interfacial tension driving force results in the interface moving in opposition to the direction of the inner circulation generated in the droplet.So,interface deformation can happen when the direction of mass transfer is c→d.Drop deformation such as the break-up process leads totheenhancementofmasstransfer.Ford→c mass transfer,the interfacial tension driving force is opposite.The interface motion and the inner circulation are in the same direction.Consequently,the droplets can be more stable than in the c→d direction.Therefore,drops tend to be smaller in c→d mass transfer than the opposite direction(see Fig.2(b)).In addition,the dispersed phase holdup is larger for c→d acetone transfer because of the smaller droplet formation(see Fig.2(c)).Finally,in the case of the c→d direction,the interfacial area is higher than that of in the d→c because of the lower drop size and higher holdup.

The higher mass transfer coefficient in the d→c direction than c→d direction for acetone transfer can be explained via the interfacial turbulence induction of local differences in the acetone concentration.The interfacial tension driving force occurs due to interfacial movement and internal circulation generated in the drop.The latter mentioned phenomena are in the same direction in c→d acetone transfer,while in d→c acetone transfer,they are in the opposing directions.For the mentioned reason,internal agitation within the drop would carry out in d→c transfer systems which results in higher mass transfer coefficient than that realized for c→d transfer systems.It is seen that the influence of interfacial area on the mass transfer performance of the extraction column is lower than that of the over all mass transfer coefficient.Consequently,mass transfer in the direction of dispersed phase to continuous leads to appropriate column performance[17,18].

4.2.Effect of continuous phase velocity

The influence of continuous phase velocity on volumetric overall mass transfer coefficient,mean drop size and holdup is shown in Fig.3(a,b and c).According to Fig.3,generally,an increase in the velocity of the continuous phase has a minor effect on the volumetric overall mass transfer coefficient,mean drop size and holdup.From Fig.3(b),it can be seen that the Sauter mean drop diameter changes slightly with the increase of the continuous phase velocity.Also,based on section(c)in Fig.3,there has been an increase in the dispersed phase hold-up with an increase in continuous phase velocity.This observation could be attributed the increment of drag force between the continuous phase and the drops.The interfacial area increases with the enhancement of dispersed phase holdup,when the mean drop size is almost constant.It can be also seen that the overall mass transfer coefficient increases a little with an increase in the continuous phase velocity.Thus,the extraction column mass transfer performance will improve slightly due to slight variation in the hold-up and mean drop size with variation of velocity of the continuous phase.

4.3.Effect of dispersed phase velocity

Fig.4(a,b and c)shows the influence of dispersed phase velocity on volumetric overall mass transfer coefficient,mean drop size and holdup respectively.As it can be seen from Fig.4(b)and(c),the Sauter mean drop diameter and dispersed phase holdup increase with the enhancement of dispersed phase velocity in the c→d and d→c mass transfer directions,although,the influence of the dispersed phase holdup on the interfacial area is dominant than that of the mean drop size.Thus,there is an increase in the interfacial area with the increase of dispersed phase velocity.As it is also seen,the overall mass transfer coefficient increases with the enhancement of the dispersed phase velocity for the d→c and c→d directions.For both mass transfer directions,the mass transfer performance in the extraction column would enhance with an increase in both overall mass transfer coefficient and the interfacial area.

Fig.3.(a)The volumetric overall mass transfer coefficient as a function of the continuous phase velocity,(b)the Sauter mean drop diameter as a function of the continuous phase velocity and(c)the dispersed phase holdup as a function of the continuous phase velocity.

Fig.4.(a)The volumetric overallmass transfer coefficient as a function of the dispersed phase velocity, (b) the Sauter mean drop diameter as a function of the dispersed phase velocity and(c) the dispersed phase holdup as a function of the dispersed phase velocity..

Fig.5.Comparison of the experimental overall mass transfer coefficient data with the correlation by Kumar and Hartl and[19]for water–acetone–toluene.

4.4.Predictive correlation of the overall mass transfer coefficient

Development of new correlation for overall mass transfer coefficient in a perforated rotating disk column is one of the aims of the current study.Kumar and Hartland[19]proposed semi-empirical predictive correlations for the individual mass transfer coefficients of the dispersed and continuous phases in different kinds of extraction columns including spray,Kühni,rotating disk,EC and PSE columns.The developed correlations for the RDC extraction column may be written as follows[19]:

The overall mass transfer coefficient is determined by Eq.(14).The experimental continuous phase overall mass transfer coefficient for the water–acetone–toluene system is compared with the obtained result from the developed correlation by[19].Fig.5 compares the experimental values with determined results using proposed correlations.The average absolute value of the relative error is calculated as 44.43%.

Table 3 is provided for comparison of experimental results of overall mass transfer coefficient with the results of previous studies.Average Absolute Relative Error(AARE)is used to determine the accuracy of the current work.According to Table 3,it can be resulted that none of the previous correlations are suitable for determination of mass transfercoefficient in the perforated rotating disk contactor.Also,the comparison between experimental data and the investigated data by Korchinsky[20]in the same experimental conditions was shown in Table 4.It is observed that the performance of the PRDC column improved better than the RDC column.

Table 3The AARE values in the predicted values of Kocobtained by the previous correlation to the experimental data

Table 4The comparison between the performance of PRDC and RDC columns

Consequently,based on the Sherwood number,Reynolds number and dispersed phase holdup in the differing directions of mass transfer novel empirical correlations are developed in order to predict overall mass transfer coefficients.The following correlations are calculated for the water–acetone–toluene system in the PRDC column:

After calculation of the Sherwood number using Eqs.(15)and(16),the overall mass transfer coefficient of continuous phase can be determined via the following equation:

Also,the Reynolds number in Eqs.(15)and(16)is calculated by Eq.(18).In which,Vsis the slip velocity between the continuous and dispersed phases through the extraction column.The slip velocity between the continuous and dispersed phases is obtained by Eq.(19).

The comparison of experimental data with those calculated by Eqs.(15)and(16)is shown in Fig.6.The average absolute value of the relative error for prediction of the overall mass transfer coefficient using the proposed correlations for the water–acetone–toluene system is 12.53%.

Finally,mass transfer data for the water–acetone–toluene system in this study is compared with mass transfer data for other types of extraction columns which was obtained by Kumar and Hartl and[19].Fig.7 shows the relation bet weenRe·Scand the Sherwood number in different extraction columns.It is observed that the mass transfer behavior of the PRDC extraction column is the same as the RDC extraction column.

4.5.Axial mixing coefficients for continuous and dispersed phases

The effect of rotor speed on the mass transfer and axial mixing coefficients for the continuous and dispersed phase was observed in Table5.It is shown that the values of axial mixing coefficients for the dispersed phase were lower than the continuous phase and the neglect from these values in modeling equations is correct.

Fig.6.Comparison of the experimental values of overall mass transfer coefficient with the correlations developed in the current study.

Fig.7.The relationship between Re·Sccand Shocin different extraction columns[19].

4.6.Errors of d32 and acetone concentration

The experimental errors such as errors in measuring droplet size from pictures and errors in acetone concentration from eachexperiment may occur in the experimental work.Therefore,measurements for determination of the Sauter mean drop diameter were made in triplicate to verify experimental reproducibility.The Sauter mean drop diameter for each run was determined by the obtained average results from taking photos.The average of the Sauter mean drop diameter with a standard deviation for one of the experiments is shown in Fig.8.The acetone concentrations were obtained after steady conditions with the five measurements fromeach valve in 10min intervals to verify experimental reproducibility..The average of acetone concentrations with a standard deviation for one of the experiments is shown in Fig.9.

5.Conclusions

In the current study, the mass transfer performance of the perforated rotating disk contact or for the water–acetone–toluene system isinvestigated.The effect of operating parameters including dispersed and continuous phase velocities and agitation rate is considered for investigation of mass transfer in the PRDC extraction column.The results revealed that the column performance increased with an increase in agitation rate,whereas it changes slightlywith the continuous phase velocity..It is also indicated that the mass transfer performance increases with the dispersed phase velocity for c→d and d→c transfer.The results indicated that the volumetric overall mass transfer coefficient is higher for acetone transfer in the direction of continuous to dispersed phase because of the smaller drop size and higher hold-up for mass transfer.Furthermore,continuous phase overall mass transfer coefficients are predicted using new correlations which are developed in this study.The proposed correlations can be applied to determine the extraction column height for various extraction processes.

Table 5Axial mixing coefficients for continuous and dispersed phases

Fig.8.Average Sauter mean drop diameter and standard deviation for toluene–water.

Fig.9.Average acetone concentration and standard deviation for toluene–water.

Nomenclature

ainterfacial area,m2·m-3

Dmolecular diffusivity,m2·s-1

Dccolumn diameter,m

Dirotor diameter,m

d32Sauter mean drop diameter,m

Eaxial mixing coefficient,m2·s-1

gacceleration due to gravity,m·s-2

Heffective height of the column,m

Koverall mass transfer coefficient,m·s-1

Nrotor speed,s-1

PePéclet number(=HV∕E)

Peccontinuous-phase Péclet number(=d32Vs∕Dc)

Qflow rate of the continuous or dispersed phase,m3·s-1

ReReynolds number(=d32Vsρc∕ μc)

ScSchmidt number(=μ ∕ (ρD))

ShSherwood number(=kd32∕D)

Shocoverall continuous-phase Sherwood number(=Kocd32∕D)ttime,s

Vsuperficial velocity,m·s-1

Vsslip velocity,m·s-1

Vtterminal velocity,m·s-1

xmass fraction of acetone in continuous phase

x* equilibrium mass fraction

ymass fraction of acetone in dispersed phase

Δρ density difference between phases,kg·m-3

κ viscosity ratio(μd/μc)

μ viscosity,Pa·s

ρ density,kg·m-3

σ inter facial tension,N·m-1

φ dispersed phase holdup

ψ power dissipated per unit mass,m2·s-3

Subscripts

c continuous phase

d dispersed phase

o overall value

x x-phase(continuous phase in present case)

y y-phase(dispersed phase in present case)

Superscripts

* equilibrium value

° inlet to column

[1]M.Ghadiri,S.N.Ashrafizadeh,M.Taghizadeh,Study of molybdenum extraction by trioctylamine and tributylphosphate and stripping by ammonium solutions,Hydrometallurgy144–145(2014)151–155.

[2]A.Rahbar-Kelishami,H.Bahmanyar,New predictive correlation for mass transfer coefficient in structured packed extraction columns,Chem.Eng.Res.Des.90(2012)615–621.

[3]G.V.Jeffreys,K.K.M.Al-aswad,C.J.Mumford,Drop-size distribution and dispersed phase hold-up in a large rotating disc contactor,Sep.Sci.Technol.16(1981)1217–1245.

[4]T.Murugesan,I.Regupathi,Prediction of continuous phase axial mixing in rotating disc contactors,J.Chem.Eng.Jpn.37(2004)1293–1302.

[5]Y.D.Wang,W.Y.Fei,J.H.Sun,Y.K.Wan,Hydrodynamics and mass transfer performance of a modified rotating disc contactor(MRDC),Chem.Eng.Res.Des.80(2002)392–400.

[6]J.S.R.Coimbra,F.Mojola,A.J.A.Meirelles,Dispersed phase hold-up in a perforated rotating disc contactor(PRDC)using aqueous two-phase systems,J.Chem.Eng.Jpn.31(1998)277–280.

[7]L.A.Sarubbo,L.A.Oliveira,A.L.F.Porto,G.M.Campos-Takaki,E.B.Tambourgi,Studies of efficiency in a perforated rotating disc contactor using a polymer–polymer aqueous two-phase systems,Braz.J.Chem.Eng.22(2005)489–493.

[8]A.L.F.Porto,L.A.Sarubbo,K.A.Moreira,H.J.F.d.Melo,J.L.Lima-Filho,G.M.Campos-Takaki,E.B.Tambourgi,Recovery of ascorbic oxidoreductase from crude extract with an aqueous two-phase system in a perforated rotating disc contactor,Braz.Arch.Biol.Technol.47(2004)821–826.

[9]M.M.Krishnaiah,M.U.Pai,M.V.R.Rao,S.R.S.Sastri,Performance of a rotating disk contactor with perforated rotors,Br.Chem.Eng.12(1967)719–721.

[10]Z.L.Fan,Y.R.Feng,Y.T.Qiu,J.Shi,A preliminary study on liquid membrane separation in rotating disk contactors with perforated discs,J.Chem.Ind.Eng.2(1987)208–217.

[11]H.R.C.Pratt,G.W.Stevens,Axial Dispersion,Oxford University Press,United States,1992.

[12]H.G.Bart,C.Drumm,M.M.Attarakih,Process intensification with reactive extraction columns,Chem.Eng.Process.47(2008)57–65.

[13]A.Kumar,S.Hartland,Mass transfer in a Kuehni extraction column,Ind.Eng.Chem.Res.27(1988)1198–1203.

[14]T.Mi?ek,R.Berger,J.Schroter,Standard test systems for liquid extraction studies,EFCE Publ.Ser.46(1),1985.

[15]L.M.Rincón-Rubio,A.Kumar,S.Hartland,Characterization of flooding in a Wirz extraction column,Can.J.Chem.Eng.71(1993)844–851.

[16]A.Kumar,S.Hartland,Prediction of axial mixing coefficients in rotating disc and asymmetric rotating disc extraction columns,Can.J.Chem.Eng.70(1992)77–87.

[17]M.Torab-Mostaedi,J.Safdari,M.A.Moosavian,M.G.Maragheh,Stage efficiency of Hanson mixer–settler extraction column,Chem.Eng.Process.Process Intensif.48(2009)224–228.

[18]C.Gourdon,G.Casamatta,influence of mass transfer direction on the operation of a pulsed sieve-plate pilot column,Chem.Eng.Sci.46(1991)2799–2808.

[19]A.Kumar,S.Hartland,Correlations for prediction of mass transfer coefficients in single drop systems and liquid–liquid extraction columns,Chem.Eng.Res.Des.77(1999)372–384.

[20]W.J.Korchinsky,A.M.Ismail,Mass transfer parameters in rotating-disc contactors:influence of column diameter,J.Chem.Technol.Biotechnol.43(1988)147–158.

[21]A.C.L.a.P.H.Calderbank,Mass transfer in the continuous phase around axisymmetric bodies of revolution,Chem.Eng.Sci.19(1964)471–484.

[22]A.Kumar,S.Hartland,Correlations for prediction of mass transfer coefficients in single drop systems and liquid–liquid extraction columns,Chem.Eng.Res.Des.77(1999)372–384.

[23]M.E.Weber,Mass transfer from spherical drops at high Reynolds numbers,Industrial Engineering Chemistry Fundamentals 1975,pp.365–366.

[24]L.Steiner,Mass transfer rates from single drops and drop swarms,Chem.Eng.Sci.41(1986)1979.

[25]G.A.Hughmark,Liquid–liquid spray column drop size,holdup,and continuous phase mass transfer,Industrial Engineering Chemistry Fundamentals 1967,pp.408–413.

[26]M.Torab-Mostaedi,A.Ghaemi,M.Asadollahzadeh,Prediction of mass transfer coefficients in a pulsed disc and doughnut extraction column,Can.J.Chem.Eng.90(2012)1569–1577.

[27]M.Torab-Mostaedi,A.Ghaemi,M.Asadollahzadeh,P.Pejmanzad,Mass transfer performance in pulsed disc and doughnut extraction columns,Braz.J.Chem.Eng.28(2011)447–456.

[28]M.Torab-Mostaedi,S.J.Safdari,M.A.Moosavian,M.G.Maragheh,Mass transfer coefficients in a Hanson mixer–settler extraction column,Braz.J.Chem.Eng.25(2008)473–481.