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J. of Supercritical Fluids 50 (2009) 61–68

Contents lists available at ScienceDirect

The Journal of Supercritical Fluids

journa l homepage: www.e lsev ier .com/ locate /supf lu

pplication of CFD in the study of supercritical fluid extraction withtructured packing: Wet pressure drop calculations

oão Fernandesa, Pedro F. Lisboaa, Pedro C. Simõesa,∗, José P.B. Motaa, Esteban Saatdjianb

REQUIMTE, Departamento de Química, Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa, Quinta da Torre, 2829-516 Caparica, PortugalLEMTA-CNRS, 2 ave. de la forêt de Haye, 54500 Vandoeuvre, France

r t i c l e i n f o

rticle history:eceived 2 January 2009

a b s t r a c t

Computational fluid dynamics (CFD) is used to study the complex multiphase flow inside Sulzer EXstructured gauze packing and to understand the influence of shape and geometry on the hydrodynamics

eceived in revised form 31 March 2009ccepted 1 April 2009

eywords:ressure dropFD modelling

of packed columns. Models for the estimation of both dry and wet pressure drops are presented. Theresults of these numerical simulations are compared to experimental data available in the literature, andgood agreement is found.

© 2009 Elsevier B.V. All rights reserved.

tructured packingupercritical fluids

. Introduction

In recent years supercritical fluid technology has been applied tohe extraction of raw materials from both solid matrices and liquid

ixtures. Examples of processes in which supercritical fluids areurrently used are the decaffeination of coffee or tea, removal ofesticides, batch hop extraction, and the continuous fractionationf beverages and oils [1–6]. Supercritical fluid extraction (SFE) fromiquid phase is usually carried out in packed extraction columns,

ith structured packing predominantly of the gauze type. Thisype of packing performs very well, even under supercritical condi-ions, due to its relatively high surface area and void volume; theseive rise to high mass-transfer efficiencies as well as high columnapacities. Gauze structured packing has, nevertheless, some dis-dvantages with respect to unstructured packing. The main onesre its high cost and its low efficiency and capacity at high flowates. In order to reduce the effect of these disadvantages, an accu-ate column design is required to increase the separation efficiencynd to decrease the associated costs. In particular, it is necessary toetermine the complex flow patterns of liquid and gas within theacking elements and to understand how they affect the pressurerop and mass-transfer efficiency. With the availability of such data

t is then possible to optimally design a SFE column [7].Computational fluid dynamics (CFD) has been extensively

eported in the literature as an effective numerical tool to get annderstanding of the complex flow pattern in packed columns;

∗ Corresponding author. Tel.: +351 212 948 300; fax: +351 212 948 385.E-mail address: pcs@dq.fct.unl.pt (P.C. Simões).

896-8446/$ – see front matter © 2009 Elsevier B.V. All rights reserved.oi:10.1016/j.supflu.2009.04.009

furthermore, the use of CFD reduces the extent and number ofrequired experiments. Various authors have studied fluid flowinside structured packing using CFD. Amongst the numerical stud-ies and computational models which have been proposed, are, e.g.,the works of Hodson et al. [8] (who presented a micro-scale simula-tion of the flow pattern of a vapor phase in a distillation column) andVan Gulijk [9] (who presented a simplified “Toblerone” model of apacking sheet to study transversal dispersion in structured pack-ing). Von Scala et al. [10] focused on the hydrodynamics and heattransfer inside structured packing. Petre et al. [11,12] representedthe structured packing as a combination of four representative ele-mentary three-dimensional (3-D) units (REU). The hydrodynamicsin each REU was studied using CFD, and the overall pressure dropwas reconstructed by adding the individual contributions of theREUs. Based on the work of Van Gulijk, Higler et al. [13] and vanBaten et al. [14] and Van Baten and Krishna [15] studied mixingand mass transfer of a liquid phase within a catalytic packed bedof the Katapak-S type. Gao et al. [16] studied the flow of a liquidphase in structured packing using a two-dimensional (2-D) model,and tracked the free surface of the liquid employing the volume-of-fluid (VOF) method. Another model to describe the flow of a liquidin a structured packing is the one proposed by Szulczewska et al.[17]. These authors employed a 2-D model, and assumed counter-current gas–liquid flow, to calculate the gas–liquid interfacial areaand to study the mechanisms of droplet formation and liquid film

breaking over both flat and corrugated vertical plates. Using theVOF approach, Raynal et al. [18] were able to successfully estimatethe thickness of the liquid film and consequently the liquid holdupin a structured packing. Later, the same authors presented a multi-scale approach for CFD calculations of gas–liquid flow within large

6 ercriti

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2 J. Fernandes et al. / J. of Sup

olumns [19]. In their approach, the authors start by determininghe thickness of the liquid film and holdup using a 2-D model. Theas velocity is then corrected using the estimated values of holdupnd mean thickness of the liquid film, and the pressure drop in aeriodic representative unit cell of the packing is calculated. Finally,rom these calculations the authors obtain directional resistanceoefficients, which allow them to model the whole packed bed asporous medium.

Haghshenas et al. [7] proposed a model for a whole packingodule, and calculated both dry and wet pressure drops. The mass-

ransfer efficiency of the packing was determined using a simplifiedeometry consisting of two packing sheets. Mahr and Mewes [20]roposed a model for the two-phase flow in columns equippedith structured packing. Their approach consists of calculating theressure drop in the packing at different angles/directions. Fromhese data, an estimate of an anisotropic gas flow resistance factoran be estimated, which allows the two-phase flow to be deter-ined. Instead of a uniform liquid phase, the liquid is split into

wo distinct phases, each of them representing a film flowing alongne preferential flow direction. Later, Khosravi Nikou and Ehsani21] applied different turbulence models to model flow throughtructured packing and to study heat and mass transfers.

Recently, we have estimated the dry pressure drop in the SulzerX structured gauze packing by performing CFD calculations withwo different geometric models [22]. The simpler model consistsf two corrugated packing sheets immersed into a parallelepipedf fluid with periodic boundary conditions and pressure-drivenow. The more complex model consists of thirteen packing sheets,hich represent one-third of the actual packing element, tightly

nserted into a cylindrical tube. In both cases the numerical gridas constructed in such a way as to capture the finite thickness of

he packing sheets. Each packing sheet was modelled as a pseudoorous medium with an imposed permeability to flow in the direc-ion perpendicular to the packing sheet. The components of theiscous and inertial resistance factors employed in the pseudoorous medium formulation were determined by measuring theressure drop incurred by water flowing across a single packingheet between two pipe sections. The predicted pressure dropsere extensively compared with experimental data for supercriti-

al carbon dioxide (the range of experimental data covered a wideange of temperatures and pressures) and air at ambient tempera-ure and pressure.

In the present paper we extend the previously employed grids,o that now the calculations are made for a whole Sulzer EX pack-ng element, and calculate wet pressure drops. Calculations arerst performed to calculate the dry pressure drops for the sys-ems operating at supercritical conditions. After these preliminaryalculations, the multiphase flow is modelled using a pseudo single-hase formulation as follows. First, the mean thicknesses of the

iquid film and the liquid holdup are determined for each operatingoint using classical correlations [23]. Then, the predicted holdup

s used to correct the gas velocity inside the packing and to estimatehe wet pressure drop. We assume that the packing is wetted by aalling liquid film, with uniform thickness predicted by correlations23], which drags the gas downwards at the liquid–gas interface.t is further assumed that the dragging velocity at the liquid–gasnterface is equal to the mean descending velocity of the liquid filmetermined from the values of liquid flow rate, holdup, and filmhickness. Since the film thickness is much smaller than the gridesolution, it is implicitly modelled by setting the slipping velocityt the surface of the packing sheets equal to the mean descend-

ng velocity of the liquid film with a correction for the angle of theorrugations.

In order to ascertain the validity of the assumption of uniformetting and film flow over the packing, simulations were carried

ut using the VOF method, as implemented in Fluent [24], for a 2-D

cal Fluids 50 (2009) 61–68

model that represents the space between two neighboring packingsheets and a reduced 3-D version of the whole packing element. TheVOF is a multiphase model in which the free surface of the liquidis tracked throughout the computational domain. This approachhas been used by other authors to model several flow conditions[18,25–27].

2. Numerical simulation

The transport equations are solved using a commercial CFDcode, Fluent v. 6.3. For turbulent flow calculations, the realizablek–ε turbulence model is employed with standard wall functions.Previous work has shown that this turbulent model can be success-fully applied to study both single-phase and multiphase flows instructured packed columns [18,22]. We refer to [22] for all detailsconcerning the model equations and turbulence model constants.

In the simulations involving the actual falling of the liquid phase,an Euler–Euler approach is adopted with a VOF formulation [23],in which both phases are treated as interpenetrating continua. TheVOF model is a surface-tracking technique applied to a fixed Eule-rian mesh. It is designed for two or more immiscible fluids wherethe interface between the fluids is of interest. Since the volume of aphase cannot be occupied by the other phases, the concept of phasevolume fraction, ˛, is introduced. The volume fractions are assumedto be continuous functions of space and time, and their sum is, bydefinition, always equal to one.

In the VOF model, a single set of momentum equations is sharedby all phases and the corresponding volume fractions in each com-putational cell are tracked throughout the computational domain.The set of momentum equations that must be solved can be writtenas:

∂

∂t(�−→v ) + ∇ · (�−→v −→v ) = −∇ · P + ∇ · [�(∇−→v + ∇−→v T )] + �−→g + −→

F ,

(1)

where � and � are the local density and viscosity, respectively, −→vis the velocity vector, −→g is the gravitational acceleration vector, P isthe pressure, and −→

F represents a source term. The solution of Eq. (1)depends on the volume fractions ˛i because they influence the localvalues of the physical and transport properties. This is taken intoconsideration in the calculations by computing volume-fractionaveraged properties in each computational cell. For example, thelocal value of � for a two-phase system is calculated as follows:

� = ˛1�1 + ˛2�2, (2)

where �i and ˛i are, respectively, the density and volume fractionof phase i; other properties are determined accordingly.

The tracking of the interface between phases is accomplishedby the solution of a continuity equation for the volume fraction ofeach phase; e.g., for the ith phase this equation takes the followingform:

∂

∂t(˛i�i) + ∇ · (˛i�i

−→vi ) = S˛i+

n∑j=1,j /= i

(mji − mij), (3)

where mij is the mass transfer from phase i to phase j and mji themass transfer from phase j to phase i. In the present case the terms

mij and mji are zero. However, the term S˛i

, which designates amass source/sink term for phase i, is set equal to the imposed liquidmass flux at the inlet/outlet boundaries of the domain for the liq-uid phase; this is discussed in more detail in Section 3. It is worthnoting that the volume fraction for one of the phases is not solved

J. Fernandes et al. / J. of Supercriti

Table 1Geometric data for Sulzer EX packing.

Internal diameter of column 24 mm

Material GauzeVoid fraction, ε 0.86Specific surface area, as (m2 m−3) 1710

f

∑

aaaitsiiufi

allbi

Channel diameter, dp (mm) 0.4912Hydraulic diameter, dh (mm) 1.886Inclination angle, � (◦) 45

or, because it is determined from the constraint:

n

i=1

˛i = 1. (4)

The VOF model is also able to include surface tension effectslong the interface between each pair of phases or even be furtherugmented if the contact angles between the phases and the wallsre specified. The surface tension and wall adhesion model usedn this work is the one presented by Brackbill et al. [28]. This ishe continuous surface force (CSF) model in which the addition ofurface tension to the VOF calculation results in a source term −→

Fn the momentum equations. The gravitational acceleration (�−→g )s included as a body force and the implicit body force treatment issed (this treatment improves solution convergence by accountingor the partial equilibrium of the pressure gradient and body forcesn the momentum equations).

The equations are integrated along the time coordinate using

n explicit scheme, and the interface between the gas andiquid phase is determined using the modified HRIC (high reso-ution interface capturing) scheme [26]. This scheme, which is alend of upwind and downwind differencing schemes, provides

mproved accuracy for VOF calculations and is less computa-

Fig. 1. (A) Photography of Sulzer EX structured gauze packing. (B) Computatio

cal Fluids 50 (2009) 61–68 63

tionally expensive than the traditional Geo-Reconstruct scheme[29].

For each simulation carried out, the fluids are assumed to beNewtonian, isothermal and incompressible; hence the propertiesare kept constant. The values for the thermophysical propertieswere obtained from NIST Thermodynamic Database. The values forthe surface tensions and contact angles of the liquids were takenfrom the literature [30,31].

3. Geometric models

The geometric characteristics of the Sulzer EX structured gauzepacking are listed in Table 1. The characteristic length of the packingis defined by the diameter of its channels, dp = 6(1 − ε)/as, where εis the void fraction and as is the surface area per unit volume ofpacking. The hydraulic diameter, dh, is defined as dh = 4ε/as.

The 3-D geometry created for the dry and pseudo-wet pres-sure drop calculations encompasses a whole packing element; themodel consists of thirteen packing sheets with finite thicknesstightly inserted into a cylindrical tube, the latter mimicking thecolumn wall. A photograph of the Sulzer EX packing element anda shaded rendering of the geometric model are depicted in Fig. 1Aand B, respectively.

In our geometric model adjacent sheets of the Sulzer EX elementtouch each other at the contact points of the corrugations, as in thereal packing, but a small gap of 0.5 mm exists between the packingelement and the cylindrical wall to prevent the meshing procedurefrom generating degenerated (poorly shaped) computational cells

adjacent to the wall. Unstructured hexahedral meshes with 2.0, 2.6,3.3, and 4.6 million elements were automatically generated for thegeometry by the CFD software. Preliminary tests showed that themesh with 2.6 million elements was the one that gave the bestcompromise between quality of mesh elements (in terms of aspect

nal domain for the pressure drop calculations—whole packing element.

6 ercritical Fluids 50 (2009) 61–68

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4 J. Fernandes et al. / J. of Sup

atio and skewness), CPU time, and numerical dispersion intro-uced by the spatial discretization method. The smallest element

n this mesh was 0.33 mm long.Periodicity of the flow in the axial direction, along the cylindri-

al tube, was enforced by imposing periodic boundary conditionst the bottom and top cross-sectional planes of the computationalomain (i.e., the flow fields over these two planes are identical or,quivalently, the outlet flow at one end of the packing element isqual to the inlet flow at the other end). This is the same as assum-ng that the flow is fully developed over the packing element. Theoundary condition at the column wall was defined as a no-slipoundary condition.

The porosity of the porous sheets was taken into account in theimulations by addition of a source term to the momentum flowquations in the cells meshing the volume of the sheets. The perme-bility, which contributes to the viscous loss term, and the inertialesistance factor were determined experimentally as discussed in22].

The VOF calculations were carried out primarily on the 2-Deometry shown in Fig. 2. This geometry corresponds to the spaceetween two neighboring packing sheets of a packing element. Theomputational domain was meshed with 11,400 cells; the grid den-ity was adapted in such a way that at least 8–10 grid points werelaced in the zone of the liquid film. The walls were defined witho-slip boundary conditions. Both the liquid and scCO2 inlet zonesere defined with uniform inlet velocity boundary conditions. The

utlets for scCO2 and liquid were defined with an outflow boundary

ondition.

Finally, 3-D simulations were performed on a coarse mesh (1.3illion elements) of the whole packing element model. Two cylin-

rical disks were added to the computational domain, one disk was

ig. 2. 2-D computational model used in conjunction with VOF model. Zoomedmage of the mesh.

Fig. 3. 3-D computational model used with VOF model.

placed over the top face of the domain and the other disk was placedbelow the bottom face. The top disk acts as a source term for the liq-uid phase, whereas the bottom disk acts as a sink term. Ultimately,the system will attain a steady state where the liquid holdup insidethe domain is constant. In order to be consistent with the assump-tion of periodic flow, the rates of generation and disappearanceof the liquid phase at the inlet/outlet boundaries have to be thesame. For this reason, the source and sink terms are set equal to theimposed liquid mass flux, but with a positive sign for the sourceterm and with a negative sign for the sink term (see Fig. 3).

4. Results and discussion

4.1. Dry pressure drops

In order to test the new grid, a few simulations were car-ried out to determine the dry pressure drop. The simulated datawere compared with the experimental data measured by Stock-fleth and Brunner [32,33], and Meyer [34] for scCO2. The rangeof experimental conditions simulated was reasonably large, span-ning a temperature range of 313–393 K and a pressure range of10–30 MPa, corresponding to a density range of the supercritical

−3 −5

fluid of 169–798 kg m and a viscosity range of 4.86 × 10 to2.34 × 10−3 Pa s.

In Fig. 4, the experimental and estimated dry pressure dropsare plotted as resistance factor, ϕ, versus the gas-phase Reynolds

Fig. 4. Resistance factors as a function of Reynolds number, data of Stockfleth andBrunner [32,33], and Meyer [34].

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sion and contact angle for this system (32 × 10−3 N m−1 and 130◦ forwater at the experimental pressure and temperature conditions),as measured by Jaeger and Eggers [30] and Jaeger [31], we shouldexpect initially the formation of drops of liquid in the corrugation

J. Fernandes et al. / J. of Sup

umber, ReG. The resistance factor is defined as,

= �P0

H

ε3dp

(1 − ε)�Gu2G

, (5)

here �P0 denotes the dry pressure drop, H is the packing height,G and uG are the density and superficial velocity of the gas, respec-

ively, and dp is the channel diameter defined above. The Reynoldsumber is defined as,

eG = uG�Gdp

�G, (6)

here �G is the viscosity of the gas. Fig. 4 compares the experi-ental results, the newly simulated data, and the simulated results

eported in our previous paper [22]. The results obtained with theew geometric model show less scattering than the previouslybtained data; this can be attributed to a more accurate descrip-ion of the velocity field, since the computational domain has beenxtended.

.2. Wet pressure drops

The wet pressure drops were determined using a pseudo single-hase formulation applied to the geometric model of the wholeacking. In this approach only the gas flow is explicitly modelledy CFD. The influence of the liquid phase on the velocity field ofhe gas phase is decoupled into two contributions – a static onend a dynamic one – which can be analyzed separately. Firstly, thexistence of liquid narrows the width of the channels along whichhe gas is flowing, because parts of the channels are occupied byiquid (static effect). Therefore, the average interstitial gas velocitys higher under wet conditions than under dry conditions for theame value of gas flow rate. Secondly, the falling liquid film dragshe gas downwards at the liquid–gas interface because the columns operated in counter-urrent mode (dynamic effect).

In order to analyze the two effects separately, simulations wererst performed assuming that the gas is not dragged by the liquidt the gas–liquid interface. For a Newtonian fluid and laminar flow,he mean thickness of the liquid film is [23]:

=(

3�LuL

�Lgap sin �

)0.5

, (7)

here �L and �L denote, respectively, the viscosity and density ofhe liquid phase, uL is the superficial velocity of the liquid, g is theravity acceleration, ap is the specific surface area of the packing,nd � is the angle with the horizontal of the corrugation. Assum-ng that the surface of the packing is completely wetted, the liquidoldup is simply given by,

L = apı. (8)

The effective interstitial velocities of the gas and liquid phasere,

Geff = uG

ε(1 − hL) sin �, uLeff = uL

εhL sin �(9a,b)

When the superficial velocity is corrected for the liquid holdupsing Eq. (9a), its value is seen to increase with hL. Hence the pres-ure drop for a given gas flow rate will be higher in the presence ofiquid holdup than without it.

In the second set of simulations, the dragging velocity at theiquid–gas interface was set equal to the mean descending velocity

f the liquid film, uL, determined from the values of liquid flow rate,oldup, and film thickness. Since the film thickness is much smallerhan the grid resolution, it is implicitly modelled by setting the slip-ing velocity at the surface of the packing sheets equal to the meanescending velocity of the liquid film. Under these assumptions, the

cal Fluids 50 (2009) 61–68 65

boundary conditions for the gas at the surface of the packing sheetcan be expressed as

�vG · �e⊥ = 0, �vG · �e|| = − uL

εhL, (10)

where �vG is the interstitial velocity vector of the gas, uL/(εhL) is themean interstitial descending velocity of the liquid, �e⊥ is the localunit vector perpendicular to packing sheet, and �e|| is the local unitvector parallel to the packing sheet. Since one of the assumptionsof the model is that of uniform wetting of the packing, the packingsheets are considered impermeable to the gas flow.

In this study we attempted to numerically reproduce the exper-imental data reported by Stockfleth and Brunner [32,33] for water,and Meyer [34] for T155 oil (soyabean oil deodorizer condensates)falling in Sulzer EX packed columns operating under supercriticalconditions. Table 2 gives the experimental conditions and physicalproperties of the fluids used in the simulations.

Fig. 5 shows our numerical results and the experimental data ofStockfleth and Brunner. The solid symbols denote the experimen-tal data, whereas the half-filled and open symbols represent thepredicted pressure drops. The half-filled symbols are the simulatedresults obtained when the superficial velocity of the gas is correctedonly for liquid holdup (static correction); the open symbols are theresults obtained when the gas velocity is corrected for both liquidholdup and downwards dragging by the falling liquid.

The results show that the major effect on the predicted pres-sure drop is the correction of the superficial gas velocity due toliquid holdup. Even though the predicted pressure drops are in rea-sonable good agreement with the experimental data, our modelconsistently underpredicts their values for the highest liquid flowrates. This can be due to an underestimation of the liquid velocityat the gas–liquid interface for high liquid flow rates (velocity profilemonotonically increasing from zero at the surface of the packing upto the highest value at the gas–liquid interface). Other sources forthis discrepancy can be extra effects that our simplistic approachdoes not take into account, such as non-uniform wetting of thepacking, eventual formation of drops, flow of the liquid throughpreferential paths, etc. From the experimental values of surface ten-

Fig. 5. Wet pressure drops for water–scCO2 at T = 313 K and P = 8.1 MPa. Filled dots:experimental data [32,33]; half-filled dots: simulated pressure drops obtained bycorrecting the superficial gas velocity for the liquid holdup, Eq. (9a); empty dots:simulated pressure drops obtained by correcting the superficial gas velocity for theliquid holdup and accounting for the dragging effect of the liquid on the gas phase.

66 J. Fernandes et al. / J. of Supercritical Fluids 50 (2009) 61–68

Table 2Experimental conditions and physical properties of the fluids used in the calculations.

Authors/system T(K) P (MPa) Viscosity (×105 Pa s) Density (kg m−3) Superficial tension (N m−1) Contact angle �

Dry pressure drops calculationsStockfleth and Brunner [32,33]

31310.1 4.86 634 – –

Gas: CO2 12.6 6.07 73013.1 6.24 740

Meyer [34] 353 18.0 189 695 – –Gas: CO2 23.0 157 798

363 21.0 234 553 – –26.0 198 673

373 20.0 16 524 – –30.0 43 698

393 10.0 8.0 169 – –20.0 129 42930.0 116 632

Wet pressure dropsStockfleth and Brunner [32,33] 313 8.1 4.42 × 10−2 132.0Gas: CO2 G: 32.2 × 10−4 G: 319.6Liquid: water L: 0.01 L: 998.0

ctpaatwva

Moaruoitpo

FdF

Meyer [34] 363 21.0Gs: CO2 G: 4.23 × 10−5

Liquid: T155 (oil) L: 4.07 × 10−2

hannels, and afterwards the formation of a thin film of liquid. First,he liquid drops emanating from the liquid phase start wetting theacking, they eventually join themselves, and then spread to formthin film. Nevertheless, Fig. 5 shows that our simulated values

re in good agreement with the experiments and that the generalrend in the variation of the pressure drop with liquid flow rate isell reproduced. It should be pointed out that the experimental

alues of pressure drop are quite small, so they may be affected bynon-negligible measurement error.

Fig. 6 compares the values of wet pressure drop measured byeyer and Brunner (solid symbols) and the values obtained with

ur model (open symbols). The two sets of points were obtainedt two different gas mass fluxes: 20,800 and 41,600 kg h−1 m−2,espectively. Again there is a good agreement between our sim-lated data and the experimental value of pressure drop. For theil–scCO2 system, even though the general trend in the increase

n the pressure drop is followed, the model slightly under predictshe pressure drop for the lower values of gas flow rate and overredicts the pressure drop for the highest flow rates. Since for thisil (T155), and for the pressure and temperature conditions con-

ig. 6. Wet pressure drops for oil (T155)–scCO2 [34] at T = 363 K, P = 21.0 MPa and twoifferent mass fluxes of gas: (�, ©) 20,800 kg h−1 m−2 and (�, �) 41,600 kg h−1 m2.illed and empty symbols denote experimental [34] and simulated data, respectively.

4.6 × 10−2 27.3G: 553.0L: 917.0

sidered, the value of surface tension is 2.3 × 10−3 N m−1 and thecontact angle is 23.7◦, it is expected that the liquid phase will forma film of uniform thickness. Given that one of the assumptions ofthe model [23] used to calculate the holdups and mean liquid filmthickness is that of a uniform wetted packing, our model shouldperform better in predicting the wet pressure drops for this lastcase. A comparison of Figs. 5 and 6 shows that this is indeed thecase.

4.3. VOF simulations

In order to verify the assumptions of uniform wetting ofthe packing we performed 2-D and 3-D simulations using theVOF (volume-of-fluid) model. In these simulations the effectsof superficial tension and contact angle have been included.Data for these properties were obtained from the literature

[30,31]. Fig. 7 shows the result of an unsteady-state simulationfor the system water–scCO2 (8.1 MPa, 313 K, uG = 0.01 m s−1, anduL = 2.8 × 10−3 m s−1). In this figure it is seen that water does forma uniform film (contour plot B); however, in the early stages of thesimulation there is the formation of drops (contour plot A). Since

Fig. 7. Contours of liquid holdup obtained from a dynamic VOF simulation ofwater–scCO2 for P = 8.1 MPa, T = 313K, uG = 0.01 m s−1, uL = 0.0028 m s−1 and t = 6.46 s(A), t = 85 s (B).

J. Fernandes et al. / J. of Supercriti

Flu

tothtlth

oulasatThffi

sotscs

FfP

ig. 8. Contours of liquid holdup obtained from a dynamic VOF simu-ation of Oil (T155)–scCO2 for P = 21.0 MPa, T = 363 K,uG = 1.215 × 10−3 m s−1,L = 5.579 × 10−3 m s−1 and t = 3.08 s (A), t = 9.75 s(B).

he initial drop formation is then replaced by a thin film, the validityf our initial assumption of uniform wetting of the packing provedo be correct. For the simulation shown, we calculated the liquidoldup based on the liquid fraction in the area corresponding tohe packing sheets. For the example under discussion the calcu-ated value of liquid holdup was 7.6%; this value is very close tohe value of 5.7% calculated from the classical correlations of liquidoldup and film thickness.

Fig. 8 shows an unsteady-state calculation of the fallingf an oil film of the system scCO2–T155 oil (21.0 MPa, 363 K,G = 1.215 × 10−3 m s−1, and uL = 5.579 × 10−3 m s−1). In this simu-

ation, the formation of the film started at the beginning of the runnd the film progressively wetted the full extent of the packingheets. This was expected, since the surface tension and contactngle of the oil are small. The oil film is also expected to be thickerhan the water film because the oil has a higher viscosity than water.he density of the supercritical fluid in the oil simulation was alsoigher than that in the water falling simulation, which contributed

or an increased holdup. This in turn gives rise to a thicker liquidlm.

Fig. 9 shows a 3-D simulation of the VOF model for the systemcCO2–T155 oil. Due to computational constraints only one-third

f the height of the packing element was simulated (the use ofhe VOF model increases considerably the computational load; theimulation reported here took almost three weeks of continuousomputation using eight processors working at 2.66 MHz). Fig. 9hows that the oil preferentially flows along the corrugations and

ig. 9. Contours of liquid holdup obtained from a 3-D VOF simulation of oil (T155)alling through structured packing against upwards CO2 flow. Simulated conditions:= 21.0 MPa, T = 363K, uG = 1.215 × 10−3 m s−1, uL = 5.579 × 10−3 m s−1, t = 5 s.

[

[

[

[

cal Fluids 50 (2009) 61–68 67

margins of the packing sheets. The liquid phase is also evenly dis-tributed over the packing.

5. Conclusions

A pseudo single-phase CFD model has been presented for thedetermination of wet pressure drops in the Sulzer EX structuredgauze packing. VOF simulations have enabled us to validate some ofthe assumptions underlying the single-phase model. The geomet-ric model employed in the pseudo single-phase CFD simulations isan extended version of the models reported in [22]. In this modelperiodicity of the flow is assumed along the axial direction. Twogeometric models have been employed in the VOF simulations. Thefirst model is 2-D and represents the space between two neighbor-ing packing sheets; the second model corresponds to one-third ofthe height of the packing element.

Simulations were carried out to determine the dry and wet pres-sure drops of Sulzer EX packing for various gas and liquid mass flowrates and various conditions of pressure (8.0–26.0 MPa) and tem-perature (313–393 K). The obtained results are in good agreementand the trends in the pressure drop with liquid and gas flow ratesare well predicted.

The 2-D VOF simulations confirm the validity of the assumptionsof uniform wetting of the packing and uniform liquid film thick-ness for the wet pressure drop calculations. This shows that theproposed pseudo single-phase modelling approach can be a com-putationally efficient method for predicting wet pressure drops incomplex packing geometries.

Acknowledgments

Financial support by Fundacão para a Ciência e Tecnologia,under project grant number POCTI/EME/61713/2004 and PhD grantSFRH/BD/19243/2004 is gratefully acknowledged.

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