numerical analysis of drops coalescence and breakage...

13
This article was downloaded by: [31.214.81.65] On: 04 April 2013, At: 14:56 Publisher: Taylor & Francis Informa Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK Separation Science and Technology Publication details, including instructions for authors and subscription information: http://www.tandfonline.com/loi/lsst20 Numerical Analysis of Drops Coalescence and Breakage Effects on De-Oiling Hydrocyclone Performance S. Noroozi a , S. H. Hashemabadi a & A. J. Chamkha b a Computational Fluid Dynamics Research Laboratory, School of Chemical Engineering, Iran University of Science and Technology, Tehran, Iran b Manufacturing Engineering Department, The Public Authority for Applied Education & Training, Shuweikh, Kuwait Accepted author version posted online: 07 Jan 2013.Version of record first published: 27 Mar 2013. To cite this article: S. Noroozi , S. H. Hashemabadi & A. J. Chamkha (2013): Numerical Analysis of Drops Coalescence and Breakage Effects on De-Oiling Hydrocyclone Performance, Separation Science and Technology, 48:7, 991-1002 To link to this article: http://dx.doi.org/10.1080/01496395.2012.752750 PLEASE SCROLL DOWN FOR ARTICLE Full terms and conditions of use: http://www.tandfonline.com/page/terms-and-conditions This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The accuracy of any instructions, formulae, and drug doses should be independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims, proceedings, demand, or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material.

Upload: lamkhuong

Post on 08-Jul-2018

241 views

Category:

Documents


0 download

TRANSCRIPT

This article was downloaded by: [31.214.81.65]On: 04 April 2013, At: 14:56Publisher: Taylor & FrancisInforma Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House,37-41 Mortimer Street, London W1T 3JH, UK

Separation Science and TechnologyPublication details, including instructions for authors and subscription information:http://www.tandfonline.com/loi/lsst20

Numerical Analysis of Drops Coalescence and BreakageEffects on De-Oiling Hydrocyclone PerformanceS. Noroozi a , S. H. Hashemabadi a & A. J. Chamkha ba Computational Fluid Dynamics Research Laboratory, School of Chemical Engineering, IranUniversity of Science and Technology, Tehran, Iranb Manufacturing Engineering Department, The Public Authority for Applied Education &Training, Shuweikh, KuwaitAccepted author version posted online: 07 Jan 2013.Version of record first published: 27 Mar2013.

To cite this article: S. Noroozi , S. H. Hashemabadi & A. J. Chamkha (2013): Numerical Analysis of Drops Coalescence andBreakage Effects on De-Oiling Hydrocyclone Performance, Separation Science and Technology, 48:7, 991-1002

To link to this article: http://dx.doi.org/10.1080/01496395.2012.752750

PLEASE SCROLL DOWN FOR ARTICLE

Full terms and conditions of use: http://www.tandfonline.com/page/terms-and-conditions

This article may be used for research, teaching, and private study purposes. Any substantial or systematicreproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form toanyone is expressly forbidden.

The publisher does not give any warranty express or implied or make any representation that the contentswill be complete or accurate or up to date. The accuracy of any instructions, formulae, and drug doses shouldbe independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims,proceedings, demand, or costs or damages whatsoever or howsoever caused arising directly or indirectly inconnection with or arising out of the use of this material.

Numerical Analysis of Drops Coalescence and BreakageEffects on De-Oiling Hydrocyclone Performance

S. Noroozi,1 S. H. Hashemabadi,1 and A. J. Chamkha21Computational Fluid Dynamics Research Laboratory, School of Chemical Engineering,Iran University of Science and Technology, Tehran, Iran2Manufacturing Engineering Department, The Public Authority for Applied Education& Training, Shuweikh, Kuwait

This work investigated the effects of breakage and coalescenceon de-oiling hydrocyclone performance utilizing ComputationalFluid Dynamics (CFD). It was found that an increase in theentrance flow rate with low entrance oil concentration not onlydid not increase the separation performance of the hydrocyclonebut it also decreased the separation efficiency. On the contrary,the hydrocyclone performance was enhanced with increasing theinlet velocity. Furthermore, a comparison between the standarddesign and the conical inlet chamber design was drawn in termsof separation efficiency for low entrance oil concentration; theresults depicted that the conical design had higher separationefficiency.

Keywords coalescence; computational fluid dynamics (CFD);deoiling; droplets breakage; hydrocyclone

INTRODUCTION

Hydrocyclones are originally designed for solid-liquidseparations, but at the present time they are also used forliquid-liquid and gas-liquid separations. Despite the com-mon use of hydrocyclones, their exact design is often diffi-cult because there exist many mathematical relationships topredict the separation efficiency and the pressure dropbased on semi-empirical models. Moreover, these correla-tions are restricted to particular cyclone geometry andoperating conditions. In recent years, applications of longliquid-liquid hydrocyclone have been extended in manyways. Some specific features of hydrocyclones such aslow maintenance cost due to the lack of moving parts,simple operation, and installation make them proper andfunctional devices for separation processes.

Some CFD simulations of liquid-liquid flow throughhydrocyclones have been published in which the

droplet-droplet interactions have been ignored. Gradyet al. (1) utilized the RSM turbulence and algebraic slipmixture model for the calculation of the velocity field andseparation efficiency in 10mm de-oiling hydrocyclone.Paladino et al. (2) applied similar methods for multiphaseflow simulation in low oil concentration at the hydrocy-clone feed. Huang (3) used the RSM (Reynolds StressModel) model for modeling turbulent flow andEulerian-Eulerian approach for the prediction of flowbehavior in high concentration of oil in the entrance feedthrough the Colman-Thew hydrocyclone type. Norooziand Hashemabadi (4) studied numerically the influence ofdifferent inlet designs on the de-oiling hydrocycloneefficiency. In another work, Noroozi and Hashemabadi(5) investigated the inlet chamber body profile effects onde-oiling hydrocyclone efficiency utilizing CFD simulation.Their results show that the separation efficiency can beimproved with appropriate hydrocyclone body design.

Separation processes in liquid-liquid systems with turbu-lent flow are affected by shear forces that can cause thedroplet to break and coalesce. This phenomenon can bringabout the droplet size distribution change which has a greateffect on separation efficiency. A transient droplet size dis-tribution is modeled utilizing population balance equationscoupled with momentum equations. CFD simulations ofdroplet coalescence and breakage in turbulent flows havebeen attempted for the prediction of separation efficiencyin liquid-liquid industrial processes in the literature.

Alopaeus et al. (6) used population balance coupledwith turbulent flow equations to develop a drop populationmodel in a stirred tank. Lasheras et al. (7) considered thestatistical description of the break-up of an immiscible fluidlump immersed into a fully developed turbulent flow. Intheir work, particle fragmentation was caused only by tur-bulent velocity fluctuations. Vikhansky et al. (8) proposedan extension of the Euler-Lagrangian approach for liquid–liquid two phase flows in a highly dispersed phase volumefraction. Attarakiha et al. (9) developed a numerical

Received 21 June 2012; accepted 21 November 2012.Address correspondence to Seyed Hassan Hashemabadi,

Computational Fluid Dynamics Research Laboratory, Schoolof Chemical Engineering, Iran University of Science and Tech-nology, 16846, Tehran, Iran. Fax: þ(9821) 7724-0495. E-mail:[email protected]

Separation Science and Technology, 48: 991–1002, 2013

Copyright # Taylor & Francis Group, LLC

ISSN: 0149-6395 print=1520-5754 online

DOI: 10.1080/01496395.2012.752750

991

Dow

nloa

ded

by [

31.2

14.8

1.65

] at

14:

56 0

4 A

pril

2013

algorithm to solve the PBE (Population Balance Equation)for considering the hydrodynamics of interacting liquid–liquid dispersions and droplet interactions (breakage andcoalescence). Andersson et al. (10) studied the effect of tur-bulence on droplet size distributions in a novel multiphasereactor. In this work, they studied the wide range of turbu-lence intensities for different dispersed phase hold-ups.Schmidt et al. (11) studied the hydrodynamic and masstransfer behavior of a rotary disc column (RDC) basedon a population balance model. Hu et al. (12) used thepopulation balance equations to predict phase inversionin liquid–liquid dispersed pipeline flows. Kankaanpaa(13) considered the coalescence and breakage in a solventextraction settler system with the aim of optimizing thedesign parameters. Patrunoa et al. (14) considered fourdifferent breakage kernels in order to predict a size distri-bution in a stirrer tank including a benzene–carbontetrachloride mixture.

There exist a few experimental and numerical studies ofdroplet breakage and coalescence effect on the separationefficiency in liquid-liquid hydrocyclones. Meyer andBohnet (15) investigated the effect of breakage and coalesc-ence of oil droplets in different feed oil concentration andentrance mean droplet size on the separation efficiencyfor a de-oiling hydrocyclone. Schutz et al. (16) studiedthe coalescence and breakage effects in a de-wateringhydrocyclone utilizing a CFD method. Furthermore, inthis study they considered the effect of the structure andtwo inlet designs on droplet size distribution through thehydrocyclone.

In the present investigation, the effects of different feedmass flow rates, inlet droplet size distributions andentrance oil concentration on droplets breakage andcoalescence were considered; the influence of these factorson the hydrocyclone separation efficiency was studied, aswell. Furthermore, the effect of a conical entrance chambercompared to the standard design has been discussed interms of separation efficiency, breakage and coalescenceof droplets.

MATHEMATICAL FORMULATION

The continuity equations for both the water and oilphases are expressed respectively as follows:

@ðaCoqCoÞ@t

þr � ðaCoqCouCoÞ ¼ 0 ð1Þ

@ðadqdÞ@t

þr � ðadqdudÞ ¼ 0 ð2Þ

where the subscripts Co and d represent continuous anddispersed phases (here water and oil), respectively, and ais the volume fraction. The coalescence and breakage ofoil droplets are computed as source terms in the oil phase

continuity equation. In this study, the dispersed phasewas assumed to be made of several numbers of particleclasses (size groups). This was done in order to considerthe oil droplets coalescence and breakage. The dropletbreakage and coalescence are taken into account as masstransfer source terms in the continuity equations. More-over, the breakage and coalescence of droplets is specifiedas mass transfer of each size group into the other ones.Moreover, similar properties have been assumed for all sizegroups (13). The continuity equation for each size group isrepresented as follows:

@ðad;iqd fiÞ@t

þr � ðad;iqdudfiÞ ¼ Si ð3Þ

where fi is the fraction of the dispersed phase volumefraction for each size group (ad,i¼ fi ad). Si is the sourceterm of interphase mass transfer including birth and deathrate of dispersed phase droplets due to breakage andcoalescence which can be symbolized as below:

Si ¼ BB �DB þ BC �DC ð4Þ

where BB and BC represent the birth rate and DB and DC

imply the death rate of droplets due to breakage andcoalescence, respectively (13). It is worth noting thatalthough the volume of oil in each droplet range throughbreakage and coalescence is changing, the total volume ofoil remains the same and therefore the sum of all dropletvolume fractions equals to the volume fraction of dispersedphase which can be given by:X

i

ad;i ¼ ad ð5Þ

Breakage Simulation

Since droplet breakup processes are complicated inturbulent flows, simplifications of the processes and flowconditions are crucial. The first assumption is the binarybreakup of particles: a particle breaks into two daughterparticles with equal or unequal sizes. The second one is thatthe particle size lies in the inertial sub-range: characteristicsof particle and eddy motion in turbulent flows can beexpressed as a function of the dissipation rate only (17).

The breakage is defined by the probability function,which is based on the energy level of the arriving eddies.The droplet breakage only occurs when the length scale ofeddies is equal or smaller than the droplet diameter. Thebreakage rate of droplets with volume nj (size dj) into dro-plets with volume ni (size di) can be expressed by (17,18,and 19):

XBðnj : niÞ ¼Z d

kmin

PBðnj : n i; kÞxB;kðnjÞ dk ð6Þ

992 S. NOROOZI, S. H. HASHEMABADI, AND A.J. CHAMKHA

Dow

nloa

ded

by [

31.2

14.8

1.65

] at

14:

56 0

4 A

pril

2013

where xB,k is the collision density of eddies of size between kand kþ dk on droplets of volume nj. The PB (nj: ni, k) is theprobability for a droplet of volume nj to break into twodroplets with volumes of ni (ni¼ nj fBV) and nh. kmin is theminimum eddy size which has the energy required for drop-let breakage. The breakage volume fraction, fBV, can bedefined in binary break-up as follows:

fBV ¼ ninj

¼ d3i

d3j

¼ d3i

d3i þ d3

h

ð7Þ

where di and dh are diameters of the daughter droplets of theparent droplet with diameter dj. The specific droplet break-age rate is obtained when the break-up model is calibratedby the coefficient fB and when Eq.6 is altered per thenumber of droplets yielding:

gðn j : niÞ ¼ fBXBðnj : niÞ1

nð8Þ

In this work, the Luo and Svendsen approach (17,18) hasbeen used for computing the eddy collision density. Luoand Svendsen (18) defined the collision frequency of eddiesof a size between k and kþ dk with droplets of size d in theinertial sub-range of isotropic turbulence. It can be writtenfor a droplet dj as follows:

xB;kðdjÞ ¼ 0:923 n ð1� adÞðeÞ1=3ð1þ nÞ2

d2j n

11=3ð9Þ

where n is the dimensionless size ratio of an eddy and drop-let (n¼ k=dj). The breakage probability of a droplet is equalto probability of the arriving eddy with size k which has akinetic energy level greater or equal than the minimumenergy required for droplet breakage expressed as follows:

PBðnj : n i; kÞ ¼ exp ð�vcÞ

¼ exp � 12ðf 2=3BV þ ð1� fBV Þ2=3 � 1Þrbqce2=3d

5=3j n11=3

!ð10Þ

where vc is the critical dimensionless energy for breakageand b is the empirical parameter from the turbulencetheory which is equal to 2.0 in this model and r demon-strates the surface tension between oil and water. As aresult, the break-up frequency of a mother droplet with sizedj splitting in two droplets of sizes di and dh¼ (d3

j –d3i )

1=3 isgiven by:

gðn j : niÞ ¼ 0:923 fB ð1� adÞðe

d2j

Þ1=3Z1nmin

ð1þ nÞ2

n11=3e�Xc dn

ð11Þ

where nmin is the dimensionless minimum size of eddies inthe inertial sub-range of isotropic turbulence and is definedby nmin¼ kmin=dj. Thus, nmin¼ 11.4g=dj, in which g is theKolmogorov length-scale (g ¼ ½ðlc=qcÞ3=e�1=4). Accord-ingly, the birth and death rate due to the larger dropletscan be obtained by the following equations:

BB ¼ qd ad ðXj>i

gðvj; viÞfiÞ ð12Þ

DB ¼ qd ad ðfiXj>i

gðvj; viÞÞ ð13Þ

Coalescence Simulation

In this study, droplet coalescence is computed using thePrince and Blanch approach (20). This model is based onthe turbulence dissipation of the continuous phase. In thismodel, the coalescence process has been assumed to takeplace in three steps which have been shown schematicallyin Fig. 1. At the first step, a small amount of continuousphase is entrapped between the droplets. Second, this liquidfilm is drained until it reaches the critical thickness andfinally, the critical film thickness between two droplets rup-tures and coalescence takes place.

In the Prince and Blanch approach (20), the coalescencefrequency of particles with volume vi to particles withvolume vj for the formation of particles with volume of(viþ vj) can be calculated by the following expression:

Cðvi; vjÞ ¼ ZAij ðutiÞ2 þ ðutjÞ

2h i1

2

expð�tij=TijÞ ð14Þ

where Z is the calibration factor and Aij represents thecross-sectional area of the colliding droplets expressed asfollows:

Aij ¼p4ðdi þ djÞ2 ð15Þ

It should be noted that uti and utj appearing in Eq. (14) rep-resent the turbulence velocities that can be assessed by:

uti ¼ffiffiffi2

pe1=3d1=3

i ; utj ¼ffiffiffi2

pe1=3d1=3

j ð16Þ

FIG. 1. Schematic diagram of coalescence stages. (Color figure available

online)

BREAKAGE AND COALESCENCE ON DE-OILING HYDROCYCLONE 993

Dow

nloa

ded

by [

31.2

14.8

1.65

] at

14:

56 0

4 A

pril

2013

Moreover, tij in Eq. (14) is the time required for thecoalescence of droplets of radius ri and rj and Tij is the con-tact time for the two particles which can be evaluated,respectively by the following terms:

tij ¼qcr

3ij

16r

!1=2

lnh0hcr

� �ð17Þ

Tij ¼r2=3ij

e1=3ð18Þ

where h0 and hcr are the initial and critical film thicknesseswhen rupture takes place, respectively. Initial film thicknessand critical film thickness at which rupture occurs were setto 1� 10�4m and 1� 10�8m in this study. Furthermore,the equivalent radius rij can be obtained as follows:

rij ¼didj

di þ djð19Þ

As a final point, the birth and death rate of coalescence aredefined as follows:

BC ¼ ðqdadÞ2 1

2

XXQðvj ; vkÞXjkifjfk

mj þmk

mjmk

!ð20Þ

DC ¼ ðqdadÞ2X

Qðvj; vkÞfifj1

mj

!ð21Þ

where Xjki is the coalescence mass matrix that is defined asthe fraction of mass due to coalescence between groups jwhich goes into group i(13):

Xjki ¼ðmjþmkÞ�mi�1

mi�mi�1if mi�1 < mj þmk < mi

miþ1�ðmjþmkÞmiþ1�mi

if mi < mj þmk < miþ1

0 otherwise

8<: ð22Þ

The Simulation Method for Liquid-Liquid Flow

In the current study, the liquid-liquid two-phase flow issimulated utilizing an Eulerian-Eulerian approach. In thisapproach, each phase is considered as a continuum anddescribed by averaged conservation equations. For incom-pressible fluids, the averaged momentum equations foreach phase (oil or water) may be obtained from the follow-ing equation (21):

@ðapqpupÞ@t

þ upr:ðapqpupÞ

¼ aprp�r:½apðslp þ stpÞ� þ apqpgþ FM ð23Þ

where g is the gravitational body force and p is the staticpressure. Moreover, the subscript ‘p’ is substituted by ‘c’

for the water phase (as continuous phase) and ‘d’ for oilphase (as dispersed phases). FM is the interphase momen-tum exchange or transfer term between the two phaseswhich is composed of all the correlated interphase forcessuch as drag, lift, virtual mass, and turbulent dispersionforces.

In this work due to the small diameter of droplets and theassumptions of spherical shape, the shear-lift force and thelift force caused by slanted wakes can be discounted (22).Also, because of very low concentration of oil in the feedand therefore a very low concentration of oil in the vicinityof the walls, the wall-lift (wall-lubrication) force was elimi-nated (22 and 23). Further, due to low density differencesbetween two liquids, virtual mass force is also negligible.In view of these assumptions, only drag and turbulentdispersion forces were considered. Drag force can becalculated as follows (21):

FDrag ¼3adacqcCD ud � ucj jðud � ucÞ

4ddð24Þ

On the grounds of the fact that the viscosity ratio of thetwo phases is very large (moil=mwater¼ 28), the drag coef-ficient can be obtained from the correlations based on asolid particle (4). In this work the following empiricalSchiller-Naumann correlation (24) is used for evaluationof the drag coefficient:

CD ¼24Red

1þ 0:15Re0:687d

� �Red � 1000

0:44 Red > 1000

�ð25Þ

where Red is the droplet Reynolds number defined as

Red ¼ qc uc � udj jddlc

ð26Þ

The interaction of drops dispersion due to turbulent flow istaken into account by the turbulent dispersion force givenas follows (25).

F td ¼ CTD CDnt;crt;d

radad

�racac

� �ð27Þ

where CTD is the turbulent dispersion coefficient and nt,c isthe turbulent kinematic viscosity for the continuous phaseand rt,d is the turbulent Schmidt number of dispersedphase. For the continuous phase, this force is equal butopposite in sign.

Turbulence Model

In this study, the Reynolds Stress Model (RSM)was chosen as the turbulence model. The RSM turbulencemodel is reported an effective and accurate model for

994 S. NOROOZI, S. H. HASHEMABADI, AND A.J. CHAMKHA

Dow

nloa

ded

by [

31.2

14.8

1.65

] at

14:

56 0

4 A

pril

2013

simulation of the velocity field through a hydrocyclone(26). The Reynolds stress model involves calculationof the individual turbulence stresses (Rij) using partialdifferential transport equations:

@

@tðqRijÞ ¼ �q Rik

@uj@xk

þ Rjk@ui@xk

� �|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}

Pij

þ

@

@xil@Rij

@xi

� �þ Cl

@

@xi

ltrk

@Rij

@xi

� �� @

@xiðquiRijÞ|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}

Dij

� eij þ Uij

ð28Þ

where Pij is the production of turbulence stresses and Dij

includes the molecular diffusion, turbulent diffusion andconvection of turbulence stresses (Rij). The kinetic energydissipation rate tensor (eij) which makes use of Kolmogrovassumption of local isotropy can be expressed as a functionof scalar kinetic energy dissipation rate (e), given by thefollowing partial differential equation:

eij ¼2

3edij ð29Þ

@e@t

þ @

@xiðuieÞ ¼

@

@xiCe

ekRij

@ui@xj

� �

� ek

2Ce1Rij@ui@xi

þ Ce2e

� �ð30Þ

The final term in Eq. (29), Uij simulates the re-distributionof turbulence by the pressure-strain gradient. Differentalternatives are presented in the literature for calculationof this term, Uij. In this work, the linear pressure straingradient was used which can be given by the followingexpression:

Uij ¼ �C1qej

Rij �2

3dijj

� �� C2 Pij �

2

3dijGk

� �ð31Þ

where all of the constants that were used in this work forthe RSM model equations are presented in Table 1.

HYDROCYCLONE GEOMETRIES, OPERATING, ANDBOUNDARY CONDITIONS

Geometries

In this work, two different geometries were used foranalysis of design effect on breakage and coalescence ofoil droplets; Fig. 2 shows the geometry parameters forboth designs in detail. The first design is according to thework of Meyer and Bohnet (15), and the second one isbased on the first one in which the cylindrical inlet cham-ber has been substituted for the conical chamber (angleof 15o).

Inlet Droplet Size Distribution

The properties for water and oil (along with surface ten-sion between oil and water) used in this study have beenpresented in Table 2. The inlet droplet size distributionswere subdivided into 12 size groups with two volume meandiameters according to Meyer and Bohnet (15). Each dis-crete size fraction has been defined in Table 3. The meandroplet diameter in two different droplet size distributions(ddsd,50), considered in this study, are 150 and 200 mm.Moreover, the droplet size distribution changes, due tothe breakage and coalescence, were considered by makinga comparison between entrance droplet size distributionand the so-called real droplet size distribution. The realdroplet size distribution can be obtained from the drop sizedistribution at the underflow and overflow conditionsrepresented as follows (15 and 16):

QrealðdÞ ¼ gQoverflowðdÞ þ fQunderflowðdÞ ð32Þ

The f and g are the integral droplet volume fraction at theunderflow and at the overflow, respectively.

In this simulation, the prescribed inlet velocity (3.2m=s)at the inlet boundary condition was used as a plug flow.The imposed mass flow rate boundary condition regardingoverflow split ratio Rf for outlets was set as a percentage ofinlet mass flow rate (40 percent in this work). The wallboundaries were subjected to no slip conditions and thestandard wall function was applied near the wall.

TABLE 1Constants for the RSM turbulence model equations

RSM modelconstants Cm C1 C2 Ce1 Ce2 Ce rk Cs

Value 0.24 �1.8 �0.6 1.4 1.92 0.13 0.82 0.09 FIG. 2. Geometry details of two de-oiling hydrocyclones with different

feed chamber.

BREAKAGE AND COALESCENCE ON DE-OILING HYDROCYCLONE 995

Dow

nloa

ded

by [

31.2

14.8

1.65

] at

14:

56 0

4 A

pril

2013

For the sake of computational time reduction the struc-tured hexahedral meshes were used. Moreover, by reasonof flow and hydrocyclone geometry complexity, 200,000,300,000, and 500,000 mesh densities for standard de-oilinghydrocyclones were examined and 300,000 mesh densitywas found as optimized mesh density in terms of accuracyand computational cost (the relative error of almost 3.75%compares to experimental error in terms of separationefficiency). Due to the high velocity gradient near the walland central regions through the hydrocyclone, the grid wasrefined at these regions as shown in Fig. 3. It is worth not-ing that the selected mesh as optimum mesh density hasbeen applied for all simulations. Furthermore, the coalesc-ence and breakage phenomena are applied in this study assource terms in continuity equation and are not a criterionfor mesh density.

The Semi-Implicit Pressure Linked Equations (SIM-PLE) algorithm is applied for coupling the continuity andmomentum equations for two-phase flows to gain thepressure field inside the hydrocyclone (24). The QuadraticUpstream Interpolation for Convective Kinetics (QUICK)scheme (26) is used for interpolation of variables from cellcenters to faces of control volumes that are recommendedfor higher accuracy in complex flow like in hydrocyclone

(27,28,29). Simulations are carried out for about 10,000incremental steps and the time step is 0.001 s. The conver-gence criteria have been assigned 10�3 for all equationsexcept the continuity equation and oil phase volumetricratio at which the criteria are 10�5.

RESULTS AND DISCUSSION

Model Verification

Prior to the application the numerical study of breakageand coalescence effect on oil-water separation efficiencythrough the hydrocyclone, it is compulsory to verify the mod-els which are used in the simulation. To this aim, the breakageand coalescence effects on drop size distribution and separ-ation efficiency in three different entrance oil drop size distri-butions was considered and the results were compared withthe reported experimental data (15). The inlet velocity wasconstant (3.2m=s) for the aforementioned conditions andthe separation efficiencywasdefinedas the ratioof oil flow rateat the overflow to feed flow rate (30), represented as follows:

E ¼ aoqoainqin

¼ 1� auquainqin

ð33Þ

FIG. 3. Cross section of structured grid for hydrocyclone CFD

simulation.

TABLE 3Discrete droplet size fraction (15)

Size groupnumber i ddsd,50¼ 150 mm

Particle numberddsd,50¼ 150 mm (number=s) ddsd,50¼ 200 mm

Particle numberddsd,50¼ 200 mm (number=s)

1 15 1112866 36.5 21090582 40.1 4811489 73.8 1138093 66.7 241781 92.7 1220044 89 21978 127.3 365905 111.1 11338 157.9 218126 130.2 4968 195.8 104157 145.8 8534 234.6 46418 195.8 1892 268.8 25649 229.4 764 301 2381

10 256.9 752 352.8 166311 307.9 1556 432.5 63412 431.5 3298 557.3 104

�droplet size distribution (dsd).

TABLE 2Physical properties of water and oil at 20�C

Density(kg=m3) Viscosity (Pa.s)

Surface tension(N=m)

oil 845 28 45.9� 10�3

water 998 1

996 S. NOROOZI, S. H. HASHEMABADI, AND A.J. CHAMKHA

Dow

nloa

ded

by [

31.2

14.8

1.65

] at

14:

56 0

4 A

pril

2013

Figures 4 and 5 show the real cumulative droplet sizedistribution, Eq. (32), for two different entrance size distri-butions (150 and 200 micron) produced by CFD simulationin comparison with the experimental data (Meyer andBohnet, 2003). According to these results the real size dis-tributions in the two cases (Figs. 4 and 5) have appropriateagreement with the experimental results (the mean

deviation of almost 17% compares to experimentalrecords). Moreover, the results revealed that the breakagein the 200 micron mean entrance droplet size is more.The results also illustrate that the breakage of the smallentrance diameter due to the small size of the dropletscompared to the eddy size almost does not happen.

Table 4 shows the separation efficiency obtained fromthe CFD simulation and the experimental work (Meyerand Bohnet, 2003) for two different entrance mean dropletdiameters. The results depicted the appropriate agreementwith experimental data (mean error of 3.75%). As shownin this table, the separation efficiency decreases withincreasing values of the inlet mean droplet diameterbecause of more droplet breakage as mentioned by Meyerand Bohnet (2003). Overprediction for droplet breakage(Fig. 5) causes more reduction of efficiency compared tothe experimental work.

Distribution of Size Groups in Hydrocyclone

Figure 6 (a, b) shows the contours of class distributionin a longitudinal cross section of the hydrocyclone for the

FIG. 4. Comparison the real droplet size distribution obtaining with

CFD and experimental work [15], ddsd,50,in¼ 150mm, ain¼ 0.5%,

Vin¼ 3.2m=s. (Color figure available online)

FIG. 5. Comparison the real droplet size distribution obtaining with

CFD and experimental work [15], ddsd,50,in¼ 200mm, ain¼ 0.5%,

Vin¼ 3.2m=s. (Color figure available online)

TABLE 4Comparison of separation efficiency for two inlets mean

droplet diameter (ain¼ 0.5%, Vin¼ 3.2m=s

Entrance meandrop sizedistribution(mm)

Efficiency(CFD)

(this work)

Efficiency(experimental)

(Meyer and Bohnet,2003)

150 0.95 0.93200 0.87 0.92

FIG. 6. Distribution of dispersed phase A) Twelfth size group, B) Second

size group, and C) Droplets Sauter mean diameter (ddsd,50,in¼ 150mm,

ain¼ 0.5%, Vin¼ 3.2m=s). (Color figure available online)

BREAKAGE AND COALESCENCE ON DE-OILING HYDROCYCLONE 997

Dow

nloa

ded

by [

31.2

14.8

1.65

] at

14:

56 0

4 A

pril

2013

twelfth (Fig. 6a) and the second (Fig. 6b) size groups, respect-ively. As shown in Fig. 6a, the fraction of the twelfth sizegroup is higher in the central regions concerning the otherzones. It might be attributed to themigration of droplets fromthe wall to the central zone due to high centrifugal force whichpromotes droplet collision probability; this fact makes dro-plets coalescence higher in these zones. In contrast, it is visua-lized well (Fig. 6b) that the accumulation of droplets with40mm diameter (second size group) in the near wall regionis higher than in other regions. This is related to dropletbreakage rate in these regions because the high dissipationrates of fluid kinetic energy near the wall. Moreover, Fig. 6cshows the Sauter Mean Diameter (SMD) of droplets whichillustrates the aggregation of coarse droplets in the centralzone and fine ones near the wall.

Effect of High Entrance Oil Volume Fraction

Figure 7 shows the real cumulative size distribution forthree different entrance size distributions for high oil vol-ume fraction (15%) in the standard hydrocyclone design(Fig. 2). According to these results, it is seen that for highentrance oil volume fraction the coalescence effect is adominant factor in two different entrance size distributions(150 and 200 mm). It might be related to the higher collisionprobability of droplets that leads to droplet coalescence inhigh oil volume fraction flows compared to the low oilvolume fraction.

Effect of Inlet Velocity

Figures 8 and 9 show the radial distribution of the tan-gential velocity and turbulent eddy dissipation rate at150mm from the top wall of the standard hydrocyclone(Fig. 2) for different inlet velocities, respectively. The meandiameter of entrance droplet size distribution for all inletvelocities and entrance oil concentration are 150 mm and

FIG. 7. Real cumulative size distribution for two different entrance size

distributions in high volume fraction (ain¼ 15% oil) versus the inlet drop-

let size distribution (Vin¼ 3.2m=s). (Color figure available online)

FIG. 9. Radial distribution of turbulence eddy dissipation rate in differ-

ent inlet velocities at 150mm from the top wall of standard hydrocyclone

(ain¼ 0.5%, ddsd,50,in¼ 150mm). (Color figure available online)

FIG. 8. Radial tangential velocity distribution in different inlet velocities

at 150mm from the top wall of standard hydrocyclone (ain¼ 0.5%,

ddsd,50,in¼ 150mm). (Color figure available online)

998 S. NOROOZI, S. H. HASHEMABADI, AND A.J. CHAMKHA

Dow

nloa

ded

by [

31.2

14.8

1.65

] at

14:

56 0

4 A

pril

2013

0.5%. As shown in these figures, increasing the inlet velo-city enhances the tangential velocity which causes the sep-aration efficiency to be promoted. In addition, increasingthe inlet velocity causes the eddy dissipation rate toincrease, which leads to higher droplet breakage especiallyin the regions near the wall due to the higher eddy dissi-pation rate. With respect to obtaining results, increasingthe entrance velocity not only cannot lead to the enhance-ment of separation efficiency in each operational conditionbut it may result in reducing the separation efficiency dueto the predominant effect of droplet breakage in high velo-city zones through the hydrocyclone.

Figure 10 shows the real cumulative droplet size distri-bution for six entrance velocities utilizing CFD simulationfor oil-water flow through the standard hydrocyclone(Fig. 2).The results depict that, although droplet breakageis more likely with high entrance velocities due to the higheddy dissipation rate in the vicinity of the wall; thisphenomenon brings about the reduction of separationefficiency. Moreover, the tangential velocity is high in theseranges of inlet velocity which can result in enhanced of sep-aration efficiency.

In contrast, in low velocity range, droplets breakage isminimal because of the lower effect of turbulence. Butthe lower tangential velocity can cause weaker back flowwhich leads to a reduction in the separation efficiency.

Figure 11 shows the separation efficiency at six differentinlet velocities. As shown in this figure, the separationefficiency increases up to a point and then gradually startsto decrease with increasing the inlet velocity. It seems thatthe optimum operational conditions can be gained with aninlet flow rate which leads to the minimum breakage. At

this operational condition the proper tangential velocitycan be specified in which minimum drop breakage and highvelocity to create strong back flow for separation of oilfrom water are met.

Effect of Inlet Chamber Design

Owing to the fact that the separation efficiencydecreases for large mean entrance droplet diameter in low

FIG. 10. Real cumulative size distribution for six different entrance velo-

cities (ain¼ 0.5%, ddsd,50,in¼ 150mm). (Color figure available online)

FIG. 11. Separation efficiency versus entrance velocity for standard

design (ain¼ 0.5%, ddsd,50,in¼ 150mm). (Color figure available online)

FIG. 12. Radial tangential velocity profile for two entrance chamber design

at 150mm from the top wall of standard and conical hydrocyclone

(ain¼ 0.5%, ddsd,50,in¼ 200mm, Vin¼ 3.2m=s). (Color figure available online)

BREAKAGE AND COALESCENCE ON DE-OILING HYDROCYCLONE 999

Dow

nloa

ded

by [

31.2

14.8

1.65

] at

14:

56 0

4 A

pril

2013

oil concentration at high inlet velocities, the effect of coni-cal inlet chamber design (Fig. 2) compared to the standardone was investigated with these conditions in this study.Figure 12 shows the tangential velocity profile in radialdirection at 150mm from the top wall of the hydrocyclonefor the two different designs. The results show that theconical design creates higher tangential velocity throughthe hydrocyclone with the same inlet velocity. This mightbe attributed to the stronger eddy recirculation effect inthe entrance chamber of the standard design (Norooziand Hashemabadi, 2011) which causes more breakagethrough more dissipation of energy in this region. Increas-ing of tangential velocity in conical design compared tostandard one causes the droplets to shift more to the cen-tral region due to the higher acceleration forces, whichresult in more accumulation of droplets in these regions.Figure 13 illustrates the real cumulative drop size distri-bution for two different hydrocyclone designs (Fig. 2).The results reveal that the droplet breakage effect decreasesconsiderably in the case of the conical design. In addition,contrary to the standard design, the coalescence is thedominant phenomenon in the conical design. Therefore,it can be concluded that the conical inlet chamber designproduces higher efficiency compared to the standard onefor low oil concentration in the inlet water.

CONCLUSION

In this investigation, the effects of droplets breakage andcoalescence on the separation efficiency of a de-oilinghydrocyclone were considered utilizing a CFD method.

The Eulerian-Eulerian multiphase approach and theRSM turbulence model were applied for the prediction ofphase distribution and understanding the hydrodynamicsof flow through the hydrocyclone. In order to take accountof the droplet-droplet interactions, the population balanceequation was solved along with the momentum equationsimultaneously. Furthermore, the Luo-Svendsen andPrince and Blanch approaches were used for the predictionof breakage and coalescence of droplets in each domain,respectively. With the aim of verification of the employedmethods, the results were compared with reportedexperimental data (Meyer and Bohnet, 2003). The meandeviation of CFD results from the experimental data wasapproximately 17%. In addition, the effect of oil concen-tration in coalescence and breakage of the droplets wasstudied. The results illustrated that increased feed oil con-centration enhanced breakage reduction due to increasingthe droplet collision. Therefore, this effect can augmentseparation efficiency. Additionally, the effect of the inletvelocity was also studied on the breakage and coalescencefor achieving the optimized velocity. The results showedthat an increase in the entrance flow rate for low entranceoil concentration can decrease the separation efficiencybecause of the dominant droplet breakage effect. Inaddition, the effect of the conical chamber design ondroplet breakage was also considered. According to theresults, using the conical entrance chamber leads to increas-ing tangential velocity compared to standard one; this canincrease the separation efficiency due to more dropsmigrating to the central regions.

ACKNOWLEDGEMENTS

We would like to express our gratitude to NationalIranian Oil Products Distribution Company for financialsupports.

NOMENCLATURE

A [m2] Cross-sectional area of the collidingdroplets

B [kg.m�3.s�1] Droplet birth termC [m3. s�1] Specific droplet coalescence rate

d [m] Droplet diameterD [kg.m�3.s�1] Droplet death termE [%] De-oiling efficiencyF [N. m�3] Interphase momentum transfer

termg [s�1] Specific Droplet Break-up RatefBV [-] Breakage volume fractionfB [-] Calibration coefficient of the breakagefi [-] Fraction of dispersed phase volume

fraction for each Size groupGk [J. s�1] Generation of turbulent kinetic

energyh [m] Film thickness

FIG. 13. Real cumulative size distribution for two different designs

(ain¼ 0.5%, ddsd,50,in¼ 200mm, Vin¼ 3.2m=s). (Color figure available online)

1000 S. NOROOZI, S. H. HASHEMABADI, AND A.J. CHAMKHA

Dow

nloa

ded

by [

31.2

14.8

1.65

] at

14:

56 0

4 A

pril

2013

k [-] Viscosity ratio of dispersed phase tocontinuous phase

L [mm] Lengthm [Kg] Massn [-] Number of dropletsPB [-] Breakage probability of a dropletp [N.m�2] Static pressureQ [m3.s�1] Specific Droplet Coalescence

RateQ(d) [-] Cumulative drop size distributionq [m3. s�1] Flow rateRe [-] Reynolds numberRij [N] Reynolds stressesrij [m] Equivalent radiusSi [kg. m�3.s�1] Mass transfer rate source

term due to breakage and coalescenceT [s] Contact timet [s] Timeu [m.s�1] Velocityx [-] CoordinatesZ [-] Calibration coefficient of the

coalescenceGreek Symbols

a [%] Volume fractionb [-] Constant parameter in Eq. (10)vc [-] Critical dimensionless energy for

droplet breakagedij [-] Kronecker deltae [J.s�1] Turbulent kinetic energy

dissipation rateCij [m�3.s�1] Coalescence rateg [m] Kolmogrov length scalej [J] Tturbulent kinetic energyk [m] Eddy sizel [kg. m�1.s�1] Dynamics viscosityhtij [m�3.s�1] Collision rate due to turbulenceq [Kg. m�3] Densityr [N.m�1] Interfacial tensions [pa] Stress tensorXB [m�3.s�1] Breakage ratexB,k [m�4.s�1] Collision densityn [-] Eddy=droplet size ratio

Subscripts

0 InitialB BreakageC Coalescencec Continuous phasecr Criticald Dispersed phasei, j, k Coordinate directionsin Inleth Daughter droplet diameterM Momentum

m Meanmax Maximum valuemin Minimum valueO Overflow orificereal Real droplet size distributiontd Turbulence DispersionU Underflow orifice

Superscript

L Laminart Turbulent

REFERENCES

1. Grady, S.A.; Wesson, G.D.; Abdullah, M.; Kalu, E.E. (2003) Predic-

tion of 10-mm hydrocyclone separation efficiency using computa-

tional fluid dynamics. Filtr. Sep., 40 (9): 40.

2. Paladino, E.E.; Nunes, G.C.; Schwenk, L. (2005) CFD analysis of the

transient flow in a low-oil concentration hydrocyclone. Proc. of the

Ann. Meeting AIChE, Cincinnati, OH, USA.

3. Huang, S. (2005) Numerical simulation of oil-water hydrocyclone

using Reynolds-Stress Model for Eulerian multiphase flows. Can.

J. Chem. Eng., 83: 829.

4. Noroozi, S.; Hashemabadi, S.H. (2009) CFD Simulation of inlet

design effect on de-oiling hydrocyclone separation efficiency. Chem.

Eng. Technol, 32 (12): 1885.

5. Noroozi, S.; Hashemabadi, S.H. (2011) CFD analysis of inlet chamber

body profile effects on de-oiling hydrocyclone efficiency. Chem. Eng.

Res. Des., 89: 968.

6. Alopaeus, V.; Koskinen, J.; Keskinen, K.I. (1999) Simulation of the

population balances for liquid-liquid systems in a non-ideal stirred

tank. Part 1 Description and qualitative validation of the model.

Chem. Eng. Sci., 54: 5887.

7. Lasheras, J.C.; Eastwood, C.; Bazan, C.M.; Montanes, J.L. (2002) A

review of statistical models for the break-up of an immiscible fluid

immersed into a fully developed turbulent flow. Int. J. Multiphase

Flow, 28: 247.

8. Vikhansky, A.; Kraft.M. (2004) Modelling of a RDC using a com-

bined CFD-population balance approach. Chem. Eng. Sci., 59: 2597.

9. Attarakiha, M.M.; Bart, H.J.O.; Faqir, N.M. (2004) Numerical sol-

ution of the spatially distributed population balance equation describ-

ing the hydrodynamics of interacting liquid–liquid dispersions. Chem.

Eng. Sci., 59: 2567.

10. Andersson, R.; Andersson, B.; Chopard, F.; Noren, T. (2004)

Development of a multi-scale simulation method for design of novel

multiphase reactors. Chem. Eng. Sci., 59: 4911.

11. Schmidt, S.A.; Simon, M.; Attarakih, M.M.; Lagar L.; Bart H.J.

(2006) Droplet population balances modeling: hydrodynamics and

mass transfer. Chem. Eng. Sci., 61: 246.

12. Hu, B.; Matar, O.K.; Hewitt, G.F.; Angeli, P. (2006) Population

balance modeling of phase inversion in liquid–liquid pipeline flows.

Chem. Eng. Sci., 61: 4994.

13. Kankaanpaa, T. (2007) CFD procedure for studying dispersion flows

and design optimization of the solvent extraction settler. Doctoral

Thesis, Helsinki University of technology.

14. Patrunoa, L.E.; Doraob, C.A.; Svendsena, H.F.; Jakobsena, H.A.

(2009) Analysis of breakage kernels for population balance modeling.

Chem. Eng. Sci., 64: 501.

15. Meyer, M.; Bohnet, M. (2003) Influence of entrance droplet size dis-

tribution and feed concentration on separation of immiscible liquids

using hydrocyclones. Chem. Eng. Technol., 26 (6): 660.

BREAKAGE AND COALESCENCE ON DE-OILING HYDROCYCLONE 1001

Dow

nloa

ded

by [

31.2

14.8

1.65

] at

14:

56 0

4 A

pril

2013

16. Schutz, S.; Gorbach, G.; Piesche, M. (2009) Modeling fluid behavior

and droplet interactions during liquid–liquid separation in hydrocy-

clones. Chem. Eng. Sci., 64: 3935.

17. Daeseong, J.; Shripad, T.R. (2011) Investigation of bubble breakup and

coalescence in a packed-bed reactor – Part 1: A comparative study of

bubble breakup and coalescence models. Int. J.Multiphase Flow, 37: 995.

18. Luo, H.; Svendsen, H.F. (1996) Theoretical model for drop and bub-

ble break up in turbulent dispersions. AIChE J., 42 (5): 1225.

19. Valdepenas, J.M.M.; Jimenez, M.A.; Barbero, R.; Martin Fuertes, F.

(2007) A CFD comparative study of bubble break-up models in a

turbulent multiphase jet. Heat Mass Transfer, 43: 787.

20. Prince, M.J.; Blanch, H.W. (1990) Bubble coalescence and break-up in

air-sparged bubble columns. AIChE J., 36 (10): 1485.

21. Ranade, V.V. (2002) Computational Flow Modeling for Chemical

Reactor Engineering; Academic Press: New York, U.S.A.

22. Ishii, M.; Hibiki, T. (2006) Thermo Fluid Dynamics of Two-Phase

Flow, 1st Ed.; Springer Science: New York.

23. Antal, S.; Lahey, R., Flaherty, J. (1991) Analysis of phase distribution

in fully-developed laminar bubbly two phase flow. Int. J. Multiphase

Flow, 7: 635.

24. Saboni, A.; Alexandrova, S. (2002) Numerical study of the drag on a

fluid sphere. AIChE J., 48 (12): 2992.

25. Burns, A.D.; Frank, T.; Hamill, I.; Shi, J.-M. (2004) The Favre aver-

aged drag model for turbulence dispersion in Eulerian multi-phase

flows. In: Proceedings of the Fifth Int. Conf. on Multiphase Flow,

ICMF, Yokohama, Japan.

26. Versteeg, H.K.; Malalasekera, W. (1995) An Introduction to Computa-

tional Fluid Dynamics, the Finite Volume Method; Longman Group

Ltd: New York.

27. Launder, B.E. (1989) Second-moment closure and its use in modeling

turbulent industrial flows. Int. J. Num. Methods in Fluids, 9 (8): 963.

28. Slack, M.D.; Del Porte, S.; Engelman, M.S. (2003) Designing auto-

mated computational fluid dynamics modeling tools for hydrocyclone

design. Minerals Eng., 17: 705.

29. Ko, J.; Zahrai, S.; Macchion, O.; Vomhoff, H. (2006) Numerical mod-

eling of highly swirling flows in a through-flow cylindrical hydrocy-

clone. AIChE J., 52 (10): 3334.

30. Gomez, C.; Caldenty, J.; Wang, S. (2002) Oil=water separation in

liquid=liquid hydrocyclons: Part 1- Experimental investigation. SPE

J., 7: 353.

1002 S. NOROOZI, S. H. HASHEMABADI, AND A.J. CHAMKHA

Dow

nloa

ded

by [

31.2

14.8

1.65

] at

14:

56 0

4 A

pril

2013