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Journal of Membrane Science 325 (2008) 809–822

Contents lists available at ScienceDirect

Journal of Membrane Science

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

umerical study of two-dimensional multi-layer spacer designs for minimumrag and maximum mass transfer

.A. Fimbres-Weihs, D.E. Wiley ∗

chool of Chemical Engineering and Industrial Chemistry, UNESCO Centre for Membrane Science and Technology, University of New South Wales, Sydney, NSW 2052, Australia

r t i c l e i n f o

rticle history:eceived 2 July 2008eceived in revised form 24 August 2008ccepted 3 September 2008vailable online 16 September 2008

a b s t r a c t

Based on the insights gained from previous published works, a series of multi-layer spacer designs foruse in spiral wound membrane modules are proposed and evaluated via computational fluid dynamicssimulations. The filament diameter to channel height ratio of traditional cylindrical filaments is reducedfrom 0.6 to 0.4 and 0.3, and one or two layers of elliptical filaments with various attack angles are intro-duced in the middle region of the channel. The mass transport equations are solved in conjunction with

eywords:omputational fluid dynamicsass transferovel spacerpacer designulti-layer spacer

the momentum and continuity equations for a solute with Schmidt number of 600, and the hydraulicReynolds number is varied from 50 up to 800. Spacer performance is evaluated via a basic permeate pro-cessing cost analysis. The proposed designs did not lower processing costs when operating at hydraulicReynolds numbers above 200, but showed potential for reducing costs in the steady laminar flow regime,at hydraulic Reynolds numbers equal to or less than 200. Implications for design improvements of spacermeshes, such as extra layers of spacer filaments to direct the bulk flow towards the membrane walls, andchanges to the filament profiles to reduce form drag are discussed.

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. Introduction

The spacer meshes in spiral wound membrane (SWM) moduleshat help keep the membrane leaves apart also serve other pur-oses. Flow disruption and boundary layer destabilization causedy the obstruction of the channel due to the spacer filamentsesult in increased mixing and mass transfer, albeit at the expensef increases in energy losses. These effects have been demon-trated in various published works [1–7]. The benefits of massransfer enhancement often outweigh the disadvantages caused byncreased energy losses, such that it becomes more economicallyttractive to operate membrane systems that utilize spacer meshes,ompared to those that do not [3,8].

Despite the beneficial impact of spacer meshes on mass transfer,ome energy losses do not translate into enhanced mass trans-er [7]. Different spacer configurations will lead to different massransfer to energy losses ratios [9]. In addition, recent studies [6,7]uggest that certain flow characteristics lead to increased mass

ransfer (e.g. flow towards the membrane wall and wall shear per-endicular to the bulk flow direction). Therefore, it is expected thatpacer filament designs that promote these flow characteristics,hile keeping increases in energy losses to a minimum, would

∗ Corresponding author. Tel.: +61 2 9385 5541.E-mail address: d.wiley@unsw.edu.au (D.E. Wiley).

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376-7388/$ – see front matter © 2008 Elsevier B.V. All rights reserved.oi:10.1016/j.memsci.2008.09.005

© 2008 Elsevier B.V. All rights reserved.

esult in further economic improvements for the operation of mem-rane units.

Spacer configurations consisting of more than the typical twoayers of filaments have been proposed [10,11]. The efficacy of

ulti-layer spacers is due to the ability of smaller near-wall fila-ents to promote the formation of recirculation regions and vortex

hedding in the vicinity of the membrane wall, thus disruptinghe boundary layer. Additionally, the middle spacer filament layerr layers serve the purpose of re-directing the low-concentrationulk flow towards the membrane walls. Since form drag causedy the recirculation regions and vortex shedding behind theiddle layers does not result in boundary layer separation or

eattachment, it is therefore possible to reduce energy lossesy optimizing the filament profile of the middle layer spacerlaments.

Kim and Kim [12] developed a numerical algorithm to calculatehe minimum drag profile in 2D flow. They found that this profileepends on the Reynolds number. They also found that ellipticalrofiles are very close to the optimal profiles, with a total drag neverore than 0.1% higher. The total drag of a circular profile was 4.54%

igher at a Reynolds number of 1, but this ratio quickly increased to

bove 30% higher at a Reynolds number of 40. As elliptical filamentsresent desirable drag characteristics, they appear as the obviouslternative for a middle-layer spacer filament. Moreover, the abilityo manufacture elliptical filament profiles should only depend onhe ability to extrude this desired profile shape before constructing

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10 G.A. Fimbres-Weihs, D.E. Wiley / Journa

he spacer mesh, which is not considered a difficult task for modernxtrusion equipment.

This paper considers possible multi-layer spacer configurationesigns for improving the mass transfer enhancement char-cteristics of typical zigzag spacers. For this purpose, variousonfigurations incorporating elliptical filaments as the middlepacer layers are simulated and analyzed. Due to the higher num-er of degrees of freedom in 3D spacer geometries, only 2D flow isonsidered in this study. The reason for this is that the main aimf this work is to understand the effect of these multi-layer spaceresigns on mass transfer, serving as a screening tool for furtheretailed analysis and design of spacers.

Williamson [13] reported that, under ideal conditions, the tran-ition from 2D to 3D flow in a cylinder wake occurs at a cylindereynolds number of about 194, which translates to hydrauliceynolds numbers above 500 for all of the geometries consid-red in this work, and above 745 for the geometries with a df/hchatio of 0.3. In addition, Zovatto and Pedrizzetti [14] showed thathe presence of nearby walls further delays the transition to 3Dow. Furthermore, Iwatsu et al. [15,16] suggest that for hydrauliceynolds numbers above 800 the differences between 2D and 3Dow are significant, such that the characteristics of 3D flow cannote extrapolated from 2D calculations. Therefore, laminar steadynd unsteady flow conditions with hydraulic Reynolds numbersp to 800 are investigated in this paper for spacer-filled channels.oreover, an economic analysis is carried out in order to compare

he relative performance of the spacer designs in terms of overallost-effectiveness of the entire channel.

. Problem description, assumptions and methods

The commercial CFD code ANSYS CFX-11.0 is used to solve theontinuity, momentum and mass transport equations [17] in apacer-filled channel. Previous work [18,19] has shown that nei-her gravity nor density variation will have a significant effect onhe solutions obtained, therefore constant properties are employednd the effect of gravity was excluded. In order to further simplifyhis system the fluid is assumed to be Newtonian, the flow two-imensional, and a binary mixture of water and salt is considered,ith no sources of salt in the fluid. Mass transfer is incorporated

n the form of a dissolving wall boundary condition. Althoughpermeable wall boundary condition [19,20] in which the wallass fraction is dependent on the permeation velocity would beore physically accurate, the relative magnitude of the permeation

elocity is usually a few orders of magnitude smaller than the aver-ge fluid velocity, such that the effect of permeation on wall shearnd mass transfer enhancement is minimal [21]. In addition, forhannel geometries and flow conditions typically found in NF andO, Geraldes and Afonso [22] have recently demonstrated that Sher-ood numbers obtained for cases without permeation can be used

o predict the wall conditions in cases where permeation is present.he impermeable-dissolving wall model is therefore capable of pro-iding valuable insights into the flow field-induced mass transferhenomena taking place inside narrow channels, and the resultsbtained should still represent a good approximation of the flownd mass transfer in SWM modules.

The geometries analyzed in this paper are variations of the 2Digzag spacer arrangement [6,23–25]. A basic zigzag geometry washosen because it presents the most similarities to spacers used in

eal membrane modules. Moreover, using parameters df/hch = 0.6nd lm/hch = 4, it was also found to be better performing than thether geometries studied by Schwinge et al. [24], with regards tots mass transfer and pressure loss characteristics. Modifications tohis configuration were made by decreasing the df/hch ratio while

dtawi

embrane Science 325 (2008) 809–822

eeping the ratio of lm/df constant, and by introducing a middlepacer layer consisting of submerged elliptical filaments with vari-us angles of attack (�e). The lm/df ratio was kept constant in ordero maintain the same membrane area covered by the spacer mesh.s a consequence of keeping the lm/df ratio constant, changes inlament diameter for a given Reynolds number do not affect thespect ratio (length to height) of the recirculation regions formedue to the presence of the obstruction.

Comparisons of different mass transfer enhancement tech-iques are often made at the same Reynolds number [5]. However,his may not be the best option when energy losses are significant.uang and Tao [26] proposed making comparisons at the sameressure drop and at the same pumping power. From the defini-ion of the Fanning friction factor used in this paper, the necessaryumping power per unit length can be calculated by

Ws

L= Q�pch

L= 2fATε�u3

effdh

= 2ATε�3

�2d4h

Re3hf (1)

From Eq. (1) it can be seen that for two different flows of theame fluid to have the same pumping power per unit length, theollowing condition must be satisfied:

Re3h1f1ε1AT1

d4h1

= Re3h2f2ε2AT2

d4h2

(2)

The geometries considered in this work were chosen to have theame ε/d4

h ratio, such that comparisons at the same Power numberRe3

hf ) value would have the same pumping power requirementser unit volume of the respective channel As a result, increases

n mass transfer performance at the same Re3hf value are directly

elated to changes in spacer arrangement, and would represent aetter performing spacer configuration regardless of the economic

mpact of pumping costs.A general unit cell for the family of geometries considered in this

aper is shown in Fig. 1. The aspect ratio of the elliptical filamentsaE/ae) was chosen such that it was as close as possible as that ofhe optimal ellipse for minimum drag, as reported by Kim and Kim12]. This gave an aE/ae ratio of 5 for the cases with a df/hch ratio of.4, and an aE/ae ratio of 4 for the cases with a df/hch ratio of 0.3. Forhe cases where the angle of attack of the elliptical filaments wasot zero, the elliptical filaments were tilted in opposite directions

n order for the lift generated by these filaments to cancel eachther. The distance from the centre of the elliptical filaments to thehannel walls was chosen to be either half of the channel height ors given by the following equation:

e = 13 (hch − ae) + 0.3df (3)

The configurations considered are portrayed in Fig. 2. In the-layer (3L) configuration, the elliptical filaments are placedqui-distant from both membrane walls. In the 4-layer (4L) con-gurations, successive elliptical filaments are placed at a distance

rom one of the membrane walls as given by Eq. (3). This was donen order to allow a reduction in elliptical filament size while keep-ng the spacer configuration representative of a real-world spacer

esh, i.e. without leaving gaps in the channel height. For each 4Lpacer there are two possible locations for the first elliptical fil-ment, depending on which membrane wall it is closer to. If therst elliptical filament is closer to the membrane wall to whichhe upstream circular filament is attached, the configuration is

esignated as “Low” (-L). Conversely, if the filament is closer tohe membrane wall to which the downstream circular filament isttached, then it is designated as “High” (-H). The designation byhich each spacer configuration will be referred to in this paper is

ndicated in parentheses in Fig. 2.

G.A. Fimbres-Weihs, D.E. Wiley / Journal of Membrane Science 325 (2008) 809–822 811

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Fig. 1. Generic unit cell geometry o

It must be noted that geometries 2L04 and 2L03 are not repre-entative of typical spacer geometries because the spacer height ismaller than the channel height, and a gap is present in between thepacer filaments, as seen in Fig. 2. In real world membrane modules,he spacer filaments usually touch each other, as they are weldedogether in layers or woven so as to keep the membrane leavespart. Nonetheless, these geometries could be manufactured if ahird filament parallel to the flow is introduced, or via the use ofpacer protuberances. This paper does not consider the additionalanufacturing costs that such designs might incur.For steady laminar flow at low Reynolds numbers, it generally

akes several repetitions of the unit cell before the Sherwood num-er reaches a limiting value. In order to avoid the need to simulaten excessively long channel at low Reynolds numbers, two sepa-ate simulations were carried out. The first consisted of an arrayf at least eight repetitions of the unit cell, where the entrancend exit length dimensions were chosen based on the findings ofchwinge et al. [24]: an entrance length of 10 times the channeleight and an exit length twice as long as the entrance length. These

ong entrance and exit lengths were necessary to fully develop the

elocity profiles before the beginning of the spacer array, and to pre-ent the outlet condition interfering with the recirculation regionsfter the last filament. The second simulation involved three repe-itions of the unit cell and the application of the methodology for

a

fid

Fig. 2. Schematic of the unit cells for the different s

pacer type modeled in this paper.

eriodic wrapping described by Fimbres-Weihs and Wiley [7]. Therst simulation allows quantification of the entrance effects in thehannel, while the second simulation permits the calculation of theharacteristics far away from the channel inlet.

For unsteady flow, the Sherwood number achieves its limit-ng value much closer to the channel entrance than in the case ofteady laminar flow, often after as few as five repetitions of theeriodic unit cell [27]. In addition, the results of Fimbres-Weihs etl. [6] revealed that at least six spacer filaments were necessary forortices to appear in unsteady flow. Therefore, the same channelharacteristics were used for the unsteady runs as for the entranceegion runs under steady laminar flow.

As in our previous works [6,7], a Schmidt number of 600 washosen, which is characteristic of typical monovalent salts, suchs sodium chloride. The channel walls over the entrance and exitengths as well as the spacer surfaces are treated as non-slip walls

ith no mass transfer, where both velocity components and theass fraction gradient normal to the boundary are set to zero (u == 0 and ∂Y/∂nw = 0). The membrane walls are also treated ason-slip walls (u = v = 0), but the mass fraction at the wall is fixed

t a constant value (Y = Yw).

For the entrance region and unsteady runs, a flat velocity pro-le with u = uavg, v = 0 and Y = 0 is specified at the inlet of the flowomain. At the outlet, an average reference pressure of zero is spec-

pacer configurations analyzed in this paper.

8 l of Membrane Science 325 (2008) 809–822

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12 G.A. Fimbres-Weihs, D.E. Wiley / Journa

fied. For the steady laminar runs under fully developed conditions,he inlet and outlet boundaries were treated as fully developedelocity and mass fraction profiles, using the approach described byimbres-Weihs and Wiley [7]. The results were taken from the mid-le unit cell, following the approach of Rosaguti et al. [28], in ordero avoid the error introduced due to the lack of gradient informationt the periodic boundaries.

Mesh independent solutions were obtained using an unstruc-ured mesh with element sizes of the order of at most 3% of theircular filament diameter. This element size was determined afterseries of runs with increasingly finer meshes. Inflated boundariesere used for all the boundaries with a non-slip condition, where

he thickness of the first grid element layer was of the order of atost 0.15% of the circular filament diameter. Angular resolution

n the surfaces of the filaments was set to 17◦, and to 15◦ for thecorners” between the filaments and the membrane wall.

The time steps used for the unsteady runs were determined byecreasing the time step size until the solution did not depend onhis parameter. Typically, the RMS Courant number for the unsteadyuns was less than 0.2, and the maximum Courant number wasess than 3. Following the approach used by Fimbres-Weihs et al.6], an approximate steady-state solution was chosen as the initialtate (t = 0) for the transient simulations. Using this initial condi-ion, the statistical quantities of all the variables stabilized afterpproximately one residence time.

.1. Channel interpolation

In this work, solutions to the momentum and mass transportquations are obtained for the entrance region and for condi-ions of fully developed velocity and mass fraction profiles. Thesewo results can be used to estimate the mass transfer and pres-ure drop conditions for the region where entrance effects areot dominant, but the mass transfer conditions are not yet fullyeveloped. Churchill and Usagi [29] developed a simple correlationo approximate intermediate solutions for transfer processes forhich asymptotic solutions are known at large and small values of

he independent variable. Mass transfer in a narrow channel underaminar flow, such as investigated in this paper, fits this categoryf problems with the Sherwood number as the dependent variable,nd the dimensionless channel length as the independent variable.ollowing the approach of Churchill and Usagi, the following is auitable interpolation expression:

h = [(AxB∗ )N + ShNfd]

1/N(4)

A similar expression is also applicable for the friction factor:

= [(AxB+)N + f Nfd]

1/N(5)

Entrance region effects are quantified by parameters A and B inq. (4), and parametersA andB in Eq. (5). ParametersN andNquan-ify the transition from entrance region to fully developed flow, aseen in Fig. 3, i.e. a very highN orNwould signify a sharp transition,hich would follow the entrance region trend until it reaches with

he fully developed value, and then follow the latter. A lower N orNould result in a smoother transition. Such a function is similar tohyperbolic function that describes the decline in Sherwood num-er and friction factor over the entrance region, and that decays tohe asymptotic value for far downstream regions of the channel ashown in Fig. 3. The parameters in Eqs. (4) and (5) were estimated

ia a non-linear regression using the results from the channel sim-lations in the laminar regime. Using this interpolation method, aingle equation for each of Sh and f can therefore be obtained usinghe data from the two different simulations in this paper. The singlequation should be suitable for describing the Sherwood number

dwita

ig. 3. Conceptual diagram of interpolation functions, as defined by Eqs. (4) and (5),howing asymptotes and interpolation curves.

nd friction factor behavior of an entire spiral wound module at aiven Reynolds number.

.2. Cost estimation

In order to effectively compare the relative performance of dif-erent spacer geometries in real-world operations, an economicnalysis is needed. However, a thorough economic analysis wouldave to take into account many factors that vary greatly with geo-raphical region and also over time including salaries, equipmentost and interest rates. Such a complete analysis is outside the scopef this paper. However, it is possible to obtain an approximation ofotal costs by analyzing the direct costs for the production of per-

eate, without taking into account pre-treatment costs, which arendependent of the spacer geometry in the SWM units. In addition,

askan et al. [30] explain that cleaning costs are largely propor-ional to the membrane area, and can therefore be considered aseing incorporated with the membrane cost. Moreover, due to theature of the spacer prototypes considered in this chapter, estima-ion of their manufacturing costs would be outside the scope ofhis work. Therefore, the cost analysis carried out in this chapteroes not directly take into account membrane cleaning costs, and

gnores pre-treatment and spacer costs, focusing instead on directermeate processing costs.

.2.1. Permeate calculationThe local permeate flux can be calculated following the approach

f Kedem and Katchalsky [31] and Merten [32], which yields theollowing expression:

sln = Lp(�ptm − ��tm) (6)

The osmotic pressure of the solute can be approximated by ainear expression [33]:

= ϕY (7)

here the value for the osmotic pressure coefficient (ϕ) used washe value reported by Geraldes et al. [34], and is shown in Table 1.qs. (6) and (7) can be combined to obtain an expression for theocal permeate flux in terms of the local wall solute mass fraction.

The local solute mass fraction at the membrane wall can be

irectly obtained from CFD simulation results using a permeableall boundary condition. However, since the simulations reported

n this paper use an impermeable wall, i.e. a dissolving wall wherehere is no fluid permeating through the wall, a more convenientpproach is to use the mass transfer coefficient data obtained from

G.A. Fimbres-Weihs, D.E. Wiley / Journal of M

Table 1Case study parameters for cost analysis

Module length (L) 90 cmChannel width (wch) 90 cmSalt rejection 99.6%Feed mass fraction (Yb,in) 0.025Inlet transmembrane pressure (�ptm,in) 60 atmReflection coefficient (�) 1Osmotic pressure coefficient (ϕ) 8.051 × 107 PaMembrane permeability (Lp) 3.94 × 10−6 m/(s atm)Channel height (hch) 0.001 mEnergy cost (Ce) $0.10 kW/hM 2

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embrane cost (Cm) $100/mmortization factor (Fa) 0.4/yrump efficiency (�pump) 0.6peration time (top) 8000 h/yr

he simulations. The local mass transfer coefficient is defined as

mt = D

(Yw − Yb)

(∂Y

∂y

)w

(8)

From the mass balance of solute at the membrane surface, it islso known that:

slnYw = �D(∂Y

∂y

)w

+ JslnYp (9)

Combining these equations yields the following expression forhe permeate flux:

sln = 12

(Lp�ptm + �kmt)

−√[

12

(�kmt − Lp�ptm)]2

+ �kmtLp�ϕ(Yb − Yp) (10)

Eq. (10) can be used to calculate the local permeate flux inerms of the operating parameters and the mass transfer coefficient.owever, the mass transfer coefficient obtained from the CFD sim-lation results in this paper is calculated using impermeable wallonditions. In the real case, the permeation of fluid through theembrane wall alters the mass transfer conditions, and hence theass transfer coefficient, when compared to the dissolving wall

ase. Geraldes and Afonso [22] have shown that the mass trans-er coefficients for permeable wall conditions can be related to thempermeable (dissolving wall) mass transfer coefficients using theollowing relationship.

= Shper

Shimp= kmt,per

kmt,imp= + (1 + 0.26 1.4)

−1.7(11)

here the variable is the ratio of permeation Peclet number tohe impermeable Sherwood number, and can be calculated usinghe following equation:

= Jsln

�kmt,imp(12)

Therefore, Eqs. (10)–(12) can be used to calculate the local per-eate flux at given operating conditions�ptm, kmt and Yb.Now the permeate flux is an input required for calculating the

ermeable wall mass transfer coefficient. Thus, an iterative proce-ure is used to obtain an estimate of the permeate flux accurate toix significant figures.

The permeate production of a membrane module is directly pro-

ortional to the average permeate flux, and can be calculated usinghe following expression:

p = AmJsln,avg

�(13)

fl

C

embrane Science 325 (2008) 809–822 813

here the membrane area (Am) is the product of the width andength of the channel, and the average permeate flux (Jsln,avg) cane estimated as the average of the local permeate flux values cal-ulated for the inlet and outlet flow conditions of the membraneodule.In this paper, the permeate flux at the inlet flow conditions is

alculated using Eq. (10) and the inlet conditions (�pin, kmt,in,pernd Yb,in). Likewise, the permeate flux at the outlet is calculatedsing Eq. (10) and the outlet conditions (�pout, kmt,out,per and Yb,out)

n an iterative manner. In order to calculate the outlet operatingonditions, the following relationships are used:

in = uavg,inhchwch (14)

out = Qin − Qp (15)

b,out = QinYb,in − QpYp

Qout(16)

avg,out = Qout

hchwch(17)

ptm,out =�ptm,in −�pch (18)

pch = 2�2L

�d3h

Re2h,avgf (19)

In Eq. (19), the average Reynolds number is calculated as theverage of the inlet and outlet Reynolds numbers. The iterativerocedure for the calculation of the permeate flux at the outlet islightly more complex than that for the permeate flux at the inlet.his is because the outlet permeate flux estimate is also used foralculating the permeate flow (Qp) through Eq. (13), which in turns used for calculating the outlet Reynolds number through Eqs.15) and (17). The impermeable Sherwood numbers and frictionactors used for calculating the inlet and outlet permeate fluxes arebtained using the interpolation Eqs. (4) and (5), respectively. Thearameters in the interpolation equations are, in turn, estimated vianon-linear regression using the results from the entrance regionnd fully developed channel simulations, as described in Section.1. Once converged values for both the inlet and outlet permeateuxes are obtained, the value for the permeate flow can be obtainedhrough Eq. (13).

.2.2. Cost calculationKnowing the permeate flow, the capital cost for the membrane

nit per cubic meter of permeate flow can be calculated using theollowing expression:

c = AmCmFa

Qptop(20)

Operating costs are proportional to the pumping energy, whichs equal to:

s =�pchQin (21)

The operating cost per cubic meter of permeate flow is theniven by

op = WsCe

Qp�pump(22)

Finally, the total processing cost per cubic meter of permeateow is calculated as the sum of the operating and capital costs:

tot = Cop + Cc (23)

814 G.A. Fimbres-Weihs, D.E. Wiley / Journal of Membrane Science 325 (2008) 809–822

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3

3

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cttsicRltti

Fc

Fe

an

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wamic

ig. 4. Friction factor dependence on hydraulic Reynolds number for 2-layer spacer-lled channels with varying df/hch ratios.

. Results and discussion

.1. Two-layer spacer geometries

The first series of runs conducted was for 2-layer (2L) spacersith circular filaments, i.e. without elliptical filament layers. The

f/hch ratio was varied from 0.6 down to 0.3, while keeping theatio of lm/df at a constant value of 6.667. As the filament diameters decreased, the cross-section of the channel that is obstructeds also decreased. It is therefore expected that for lower filamentiameter to channel height ratios the friction factor will be lower,pproaching the value for an empty channel. Fig. 4 shows that thiss the case.

The effect of filament diameter on Sherwood number is moreomplex than its effect on the friction factor. For empty channels,he Sherwood number for flow with a fully developed concentra-ion profile does not depend on the Reynolds number. However, ashown in Fig. 5, for spacer-filled channels the Sherwood numberncreases as the Reynolds and Power numbers are increased, as aonsequence of increased boundary layer destabilization at highereynolds numbers. At low Reynolds numbers, where no boundary

ayer separation occurs and creeping flow conditions are prevalent,he Sherwood number will be lower for the spacer-filled channelshan for the empty channel as a result of the spacer filaments cover-ng the membrane surface and reducing the available mass transfer

ig. 5. Sherwood number dependence on Power number for 2-layer spacer-filledhannels with varying df/hch ratios.

bt

RSfesptsfatFnne

3

fir

ig. 6. Sherwood number distribution along channel length for spacer-filled andmpty channels, at a hydraulic Reynolds number of 200.

rea, i.e. “membrane coverage”. This effect is evidenced for Powerumbers below 105 in Fig. 5.

For empty channels, entrance region effects caused by the devel-ping boundary layer result in a higher Sherwood number nearhe channel inlet [35]. As the distance from the channel inlet isncreased, the Sherwood number eventually reaches its asymptoticalue. Since further increases in channel length do not affect theherwood number, the concentration profile is considered to befully developed”. This phenomenon is also encountered in spacerlled channels as can be observed in Fig. 6, which was obtainedy making use of the interpolation functions described by Eqs. (4)nd (5). As a consequence of the entrance region effect, the ratio ofnergy losses to mass transfer is increased as the channel length isncreased. This suggests that short and wide channels will result inower energy needs for given mass transfer needs.

As mentioned in Section 2. the geometries considered in thisork were chosen to have the same ε/d4

h in order for comparisonst the same Re3

hf value to have the same pumping power require-ents per unit volume of the respective channel. The group Re3

hfLs therefore a measure of accumulated energy losses at a specifiedhannel length (L). In order to make this value dimensionless, it can

e multiplied by ε14 /dh (which was kept constant for all the geome-

ries modeled in this paper), thus giving the dimensionless group

e3hfε

14 L/dh. From Fig. 6 it can be seen that for a given energy loss, the

herwood number is always higher for spacer filled channels thanor an empty channel. In addition the empty channel requires lessnergy to attain a fully developed concentration profile than thepacer-filled geometries tested. This is to be expected given thatressure drop for the empty channel is significantly lower than forhe spacer-filled cases, as was shown in Fig. 4. In addition, Fig. 6hows that the geometries with a higher Sherwood number underully developed concentration profile conditions will usually havehigher Sherwood number at any given value for the energy loss

hroughout the entire length of the channel. This is confirmed inig. 6, where it is shown that the lines for the different spacers doot intersect each other, and the asymptotic value of the Sherwoodumber for the 2L03 geometry is slightly higher than that for thempty channel.

.2. Multi-layer spacer geometries

In order to assess the effect of the angle at which the ellipticallaments intersect the oncoming bulk flow, simulations of configu-ations with different angles of attack were undertaken. Because of

l of Membrane Science 325 (2008) 809–822 815

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G.A. Fimbres-Weihs, D.E. Wiley / Journa

he large number of geometric variations explored in this paper,nd due to the high computational and time demands of tran-ient simulations, it would not have been practical to carry outransient simulations for all of the spacer geometries. Therefore,or the purposes of isolating the effect of the angle of attack, theydraulic Reynolds number was not varied and kept constant atvalue of 200, which is the highest hydraulic Reynolds number

or which all of the geometries present steady flow conditions. Inddition, this Reynolds number is representative of typical operat-ng conditions in real-world membrane systems which operate inhe steady-laminar flow regime.

Aerodynamic studies show [36] that for airfoils, form drag andts variation are small at small angles of attack. Moreover, as thengle of attack is increased above a threshold value (usually in theange of 5◦ to 15◦ for Reynolds numbers of the order of 100,000)ow separation causes form drag to increase drastically (usuallyoubling or tripling its value). Therefore, the angle of attack of thelliptical filaments in this study was kept within the range of +10◦

o −10◦.Due to the relative positioning of the circular and elliptical

pacer filaments and the definition of the angle of attack, a negativengle of attack is expected to align the elliptical spacer filamentith the bulk flow such that form drag is reduced. Fig. 7 shows

hat as the attack angle increases, a larger region of stagnant fluidorms downstream of the elliptical filaments, thus increasing formrag. It can also be seen that this region of stagnant flow, causedy boundary layer separation, is smaller for the negative angles ofttack than for the positive values. At an angle of −5◦ the veloc-ty of the fluid flowing above and below the elliptical filament ispproximately equal and the stagnant region is smaller than at thether angles of attack. Therefore, for the 3L04 spacer, form drag isxpected to be lower for an attack angle of −5◦ than for the otheralues.

The effect of the angle of attack on form drag for all spacer con-gurations and angles of attack can be seen in Fig. 8. For all theseonfigurations the lowest percentage of energy losses due to formrag is attained at an angle in the range of −5◦ to −7.5◦. In the case ofhe 3L04 configuration, form drag is reduced as the angle of attack is

educed from 0◦ to −5◦, and increases again as the angle is reducedurther to −10◦. This suggests that, as expected from Fig. 7, an anglef −10◦ overshoots the negative angle value necessary to align thelliptical filament with the bulk flow. As a result, this angle causes

ig. 7. Velocity contour plots for the 3L04 spacer configurations at various angles ofttack, and a hydraulic Reynolds number of 200.

ctalwc

Ft

ig. 8. Variation of the percentage of energy losses due to form drag with angle ofttack for multi-layer spacer geometries, at a hydraulic Reynolds number of 200.

larger region of stagnant fluid behind the obstacle, thus leadingo a larger percentage of form drag than at a −5◦ angle.

Since form drag is the main component of pressure drop, itan provide an indication of the behavior of the friction factor ashe angle of attack is changed. As can be seen in Fig. 9, however,he pattern of lower friction factor for negative angles of attack isnly followed by the 4L04L and 4L03L configurations. For the 3L04,L04H and 4L03H configurations the friction factor is at its lowestalue at an angle of attack between −5◦ and 0◦. The increase in fric-ion factor at negative angles of attack for the -L configurations isue to an increase in the viscous drag. Fig. 8 confirms that the per-entage of pressure drop due to form drag for these cases is lowerhan for the other configurations.

The reason for the increase in viscous drag is visualized in Fig. 10.t can be seen in this figure that for the 4L03L and 4L04L config-rations the relative positioning of the elliptical filament to theircular filaments causes most of the fluid to flow on one side ofhe elliptical filaments. This channeling of the fluid creates a large

rea of stagnant or slow moving fluid downstream of the circu-ar filaments, between the elliptical filaments and the membraneall. The relatively slow flowing fluid does not contribute signifi-

antly to viscous drag on the elliptical filament and the membrane

ig. 9. Dependence of friction factor on angle of attack for multi-layer spacer geome-ries, at a hydraulic Reynolds number of 200.

816 G.A. Fimbres-Weihs, D.E. Wiley / Journal of Membrane Science 325 (2008) 809–822

Ffi

wtfibtfa

bwbwazfdnloacTttriit

Fg

isi

bbtaa

lTecSafFwatbattack. Both the 4L04L and 4L03L configurations show a higher

ig. 10. Velocity contour plots for the 4L03H, 4L03L, 4L04H and 4L04L spacer con-gurations at an attack angle of −10◦ , and a hydraulic Reynolds number of 200.

all surfaces. In contrast, for the 4L03H and 4L04H configurationshe flow is more evenly distributed on both sides of the ellipticallament. Therefore, both sides of the elliptical filaments and mem-rane walls experience higher viscous drag in the -H configurationshan in the -L configurations. This results in a higher friction factoror the -H configurations at the −10◦ angle of attack than at the 0◦

ngle, despite form drag being lower for the negative angle.For the effect of the angle of attack on the Sherwood num-

er, it is expected that both positive and negative angles of attackould increase the average Sherwood number over the unit cell

y directing flow away from the bulk and towards the membranealls. As seen in Fig. 11, this is only the case for the 3L04 and (tolesser extent) 4L04H configurations. For those cases, the non-

ero angles of attack cause low concentration fluid to be divertedrom the bulk flow towards the membrane surface, causing a largeregree of boundary layer renewal and thus a higher Sherwoodumber. In contrast, the 4L03H and 4L03L configurations show a

ocal minima for the average Sherwood number when the anglef attack is −10◦ or +10◦. In these latter cases, the large angles ofttack reduce the velocity of the fluid flowing between the ellipti-al filament and the membrane wall as shown previously in Fig. 10.his in turn reduces the wall shear rate and increases the concen-ration boundary layer thickness. Since less fluid is being forcedo make contact with the membrane surface, less boundary layer

enewal occurs and, as a result, the average Sherwood numbers also reduced. This effect is evidenced by comparing the veloc-ty and mass fraction contour plots in Fig. 12, which show thathe bulk of the fluid channels past the flow obstructions follow-

SIsa

Fig. 12. Velocity and solute mass fraction contour plots for the 4L03L spacer config

ig. 11. Dependence of Sherwood number on angle of attack for multi-layer spacereometries, at a hydraulic Reynolds number of 200.

ng a zigzag path, and generates large stagnant areas where theolute concentration builds up and mass transfer into the bulk fluids low.

For the case of the 4L04L configuration, the Sherwood num-er tends to increase as the angle of attack is increased. This isecause the negative angle of attack reduces the amount of fluidhat flows near the membrane wall, whereas the positive angle ofttack increases the amount of low concentration bulk fluid thatpproaches the membrane wall.

It is well known that mass transfer can be enhanced by boundaryayer destabilization through the use of flow obstructions [1,37–39].hese obstructions, in turn, increase the channel pressure drop, i.e.nergy losses. Since different angles of attack result in differentombinations of mass transfer enhancement and energy losses, theherwood number to friction factor ratio can be used to identify thengle of attack that achieves the best balance between mass trans-er enhancement and energy losses. This comparison is shown inig. 13. For all but the 4L04L and 4L03L configurations, the Sher-ood number to friction factor ratio was higher at a zero angle of

ttack. This means that for all but the 4L04L and 4L03L configura-ions, the benefit of an increased Sherwood number is outweighedy the increase in energy losses caused by a non-zero angle of

herwood number to friction factor ratio at the −5◦ angle of attack.t is interesting to note that, although both the 4L04L and 4L03Lpacer configurations showed a lower friction factor due to the neg-tive angle of attack, the 4L03L configuration prevented flow from

uration for various angles of attack, at a hydraulic Reynolds number of 200.

G.A. Fimbres-Weihs, D.E. Wiley / Journal of Membrane Science 325 (2008) 809–822 817

Fa

rc

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Fs2

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ig. 13. Dependence of the Sherwood number to friction factor ratio on angle ofttack for multi-layer spacer geometries, at a hydraulic Reynolds number of 200.

eaching the region near the membrane wall, whereas the 4L04Lonfiguration did not exhibit this behavior.

For the 3L04 spacers, the configuration with a −10◦ angle ofttack is aligned with the flow, and has lower friction factor thanhe configuration with a +10◦ angle of attack. From Fig. 14 it cane seen that the configuration with a −10◦ angle of attack also hasore evenly distributed local Sherwood number values along theembrane wall than the other angles of attack, which results in one

f the highest overall Sherwood numbers of this series of spacers.owever, these overall Sherwood number values are still lower than

or the configuration without an elliptical filament (2L04).In general, it can be said that increases in the angle of attack

ead to increases in both the friction factor and Sherwood number.lthough there are specific situations in which due to the geomet-ical alignment of the spacer filaments this relationship might notold, it has been shown that this trend is generally followed. In addi-ion, positioning the elliptical filaments in the -L configuration willesult in higher Sherwood numbers. It must be said, however, thathis trend was found at a constant lm/df ratio of 6.667, and theres the possibility of a different trend if the lm/df ratio is changedignificantly from this value.

.3. Economic analysis of spacer performance

The economic analysis of the different spacer configurationsas carried out following the approach described in Section 2.2.

n order to isolate the impact of the spacer configuration used,nly processing costs were calculated, i.e. feed pre-treatmentosts and operating costs other than pumping through the mem-

ig. 14. Local Sherwood number for the bottom membrane wall of 2L04 and 3L04pacer geometries with varying angles of attack, at a hydraulic Reynolds number of00.

iacbcicocwFtt

3

nlfip

ig. 15. Dependence of cost components on hydraulic Reynolds number for twoample geometries. A membrane cost of $100/m2 was assumed.

rane module (e.g. cleaning costs) were neglected. In addition,embrane-cleaning costs are assumed to be proportional toembrane area (and hence included in the membrane cost).

pacer manufacturing costs are also neglected. Therefore, the costseported in this section do not represent the total cost of perme-te production, and should only be considered as a comparativendicator of spacer performance, as explained in Section 2.2.

A set of cost parameters, representative of what is currentlyound in literature [3,9,40], was utilized for the cost analysis casetudy. These parameters are summarized in Table 1. In addition,hree different membrane costs were considered: a case study baseost of $100/m2, a higher cost of $500/m2, and a lower cost of10/m2 of membrane. The high membrane cost is representativef a membrane system which is very prone to fouling, and thusncludes the cost of cleaning and replacement in case of blockage.he low membrane cost is representative of the possible futureembrane costs, since current trends indicate that membrane pro-

uction costs will continue to decrease.As the Reynolds number is increased, the components of the

otal cost (Cc and Cop) vary in opposite directions. Given that energyosses increase as the Reynolds number increases, the operatingosts also increase. On the other hand, increases in Reynolds num-er lead to increases in Sherwood number, which in turn leadso decreased membrane area needs due to increased mixing and

ass transfer. Therefore, typical cost curves follow a “U” shapedrend (see Fig. 15). At low Reynolds numbers, well within the lam-nar flow regime, capital costs dominate due to low mass transfernd low energy losses. As the Reynolds number is increased andapital costs are reduced, operating costs are increased until theyecome the dominant component. In the region where operatingosts dominate, the total cost increases as the Reynolds number isncreased further. Therefore, there exists a point in any total costurve at which the total cost is minimized, and either an increaser decrease of Reynolds number would lead to an increase in totalost. The Reynolds number at which this minimum total cost occursill be referred to as the “optimal” Reynolds number for operation.

or the data presented in Fig. 15, the optimal Reynolds number forhe empty channel is between 1000 and 2000, and around 400 forhe 4L03H spacer geometry.

.3.1. Base membrane cost of $100/m2

Fig. 16 depicts the effect of filament diameter and Reynoldsumber on permeate processing costs for the geometries ana-

yzed in this paper. Despite energy losses encountered in spacerlled channels being larger than for empty channels, the cost ofermeate production using spacers is lower than the cost with-

818 G.A. Fimbres-Weihs, D.E. Wiley / Journal of Membrane Science 325 (2008) 809–822

F ic Reyl ts forc

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The scenario for the geometries at a df/hch ratio of 0.3 is some-what similar to that for the geometries at a df/hch ratio of 0.4. Asopposed to the cases at df/hch ratio of 0.4 and 0.6, transient simula-tions were carried out for the 4L03H geometries, and these results

ig. 16. Dependence of total processing cost per cubic meter of permeate on hydrauleft shows effect of filament diameter on cost. The graph on the right compares cosost of $100/m2 was assumed.

ut using spacers. Modules using spacers have smaller membranerea requirements due to the higher Sherwood numbers attained,hus offsetting the higher energy costs required for their opera-ion. This result agrees with previous studies [3,8]. However, atydraulic Reynolds numbers below 100, spacer geometries 2L03nd 2L04 do not present significant cost benefits over the emptyhannel. As explained in Section 3.1. This is due to the amount ofembrane area covered by the spacer filaments in these configura-

ions. Membrane coverage results in lower Sherwood numbers, andence higher permeate processing costs than for the channel with-ut spacers. In any case, operating at hydraulic Reynolds numberselow 100 would not be recommended under the conditions of thistudy, as Fig. 16 shows that lower permeate processing costs can bechieved by operating in the hydraulic Reynolds number range of00 to 1000. In addition, operating at low Reynolds numbers also

ncreases the potential impact of fouling.The results presented in Fig. 16 show that lower processing

osts are achieved by the 2L04 and 2L06 spacer geometries. Foroth of these geometries, as well as for the 2L03 spacer geom-try, the trends indicate lower costs as the Reynolds number isncreased. Given that it is not clear whether a minimum in theost curve has been reached at the highest Reynolds number forhich data was collected, it is unclear which filament diameter

o channel height ratio will achieve the lowest permeate process-ng cost. Moreover, flow becomes unsteady for these geometries ateynolds numbers higher than the ones presented in Fig. 16. There-ore, transient data is needed before the best performing spaceronfiguration for these cost parameters and flow conditions can beetermined. Nonetheless, one conclusion can be drawn from theseimulations results: for 2D 2L zigzag spacer meshes operating in theaminar flow regime, significant permeate cost reductions cannote achieved by reducing the filament diameter to channel heightatio from 0.6 to 0.4 or 0.3.

The multi-layer spacers geometries proposed in this paperhow lower permeate processing costs than the 2L06 geometryor hydraulic Reynolds numbers below 200. This is partially due to

he decrease in open volume inside the channel (due to the addedpacer layers) which leads to an increase in local velocity and wallhear rates. It is also due to the increased mass transfer enhance-ent caused by the elliptical filaments directing low concentration

uid towards the membrane wall. However, the added filament

Fhm

nolds number, for empty, 2-, 3- and 4-layer spacer-filled channels. The graph on theselected multi-layer spacers against empty channel and 2L06 spacer. A membrane

ayers also increase energy losses and, thus, operating costs. Atydraulic Reynolds numbers above 300 the ratio of energy costs toembrane costs is higher for the multi-layer configurations than

or the 2L06 spacer and, as a result, lower permeate processing costsre achieved with the 2L06 spacer at hydraulic Reynolds numbersbove 300.

Fig. 17 shows a comparison of the different geometries at a df/hchatio of 0.4. The results shown in Fig. 17 are similar to those seen inig. 16, in that multi-layer spacers present lower permeate process-ng costs at hydraulic Reynolds numbers below 200. In addition,he 3L04 spacer at an angle of attack of 0◦ results in lower costshan its 4L04H counterpart. From the trends shown in Fig. 16 its difficult to predict which geometry would be the better overallerformer as the Reynolds number is increased beyond 200, whichould lead to unsteady flow. Transients simulations would be nec-

ssary in order to determine which configuration would result inhe lowest permeate processing cost.

ig. 17. Dependence of total processing cost per cubic meter of permeate onydraulic Reynolds number, for spacer-filled channels with a df/hch ratio of 0.4. Aembrane cost of $100/m2 was assumed.

G.A. Fimbres-Weihs, D.E. Wiley / Journal of M

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ig. 18. Dependence of total processing cost per cubic meter of permeate onydraulic Reynolds number, for spacer-filled channels with a df/hch ratio of 0.3. Aembrane cost of $100/m2 was assumed.

re presented for the hydraulic Reynolds number of 800 in Fig. 18.t can be seen that the use of 4-layer spacer geometries resulted inower permeate processing costs for all of the Reynolds numbersested in the laminar flow regime, but the use of the 2L03 spaceresulted in the lowest processing costs in the unsteady flow regime,t a hydraulic Reynolds number of 800. From the data collectedrom the transient simulations, it can be concluded that underhe assumptions of this study, operating at such a high Reynoldsumber is not recommended for these 4-layer geometries as the

ncreased energy costs associated with the increased energy lossesutweigh the benefits of increased permeate production due toncreased mass transfer. However, operating at a high Reynoldsumber may be justified for other reasons not considered here,uch as reduced cleaning costs due to reduced fouling. Neverthe-ess, the low cost achieved by using the 2L03 spacer at a hydrauliceynolds number of 800 cannot be reduced by using the 4-layerpacers at a df/hch ratio of 0.3.

The economic impact of configuration variations was also ana-yzed. The effect of filament positioning and angle of attack onermeate processing cost for multi-layer spacer meshes are shown

n Fig. 19. From these results it can be seen that changes in posi-ioning of the elliptical filaments (i.e. -H or -L) have a larger effect

n permeate processing costs than changes to the angle of attack.egardless of the angle of attack, the -L configurations for the 4-

ayer spacers always resulted in lower permeate processing costshan the -H configurations. This result agrees with the predic-

ig. 19. Dependence of total processing cost per cubic meter of permeate on anglef attack of elliptical filaments, for multi-layer spacer-filled channels at a hydrauliceynolds number of 200. A membrane cost of $100/m2 was assumed.

enidetleflnm

3

db$ctbmmc

embrane Science 325 (2008) 809–822 819

ions using the Sherwood number to friction number ratio (seeig. 13), and can be attributed to the fluid channeling effects seenn Figs. 10 and 12. The positioning of the elliptical spacers in the -Lonfigurations generates channels of faster flowing low concentra-ion fluid, which cause larger velocity and concentration gradientst the membrane wall, thus resulting in higher mass transfer andower permeate processing costs.

Changes in the angle of attack for the 4L04H spacer do not appearo have a significant effect on permeate production costs (less than%). In contrast, increases to the angle of attack for the 4L04L con-guration decrease the total permeate processing cost, albeit onlyy a small amount (4.1%). In the case of the 3L04 spacer, both pos-tive and negative angles of attack result in a significant reductionf the total permeate processing cost (16% and 13%, respectively).owever, from the data presented in this paper, it is not possible

o determine either the value or the direction of the angle of attackhat would produce the lowest processing cost.

For multi-layer spacer meshes with a df/hch ratio of 0.3, the anglef attack has a significant effect on permeate processing costs, withhe difference between the lowest and highest processing costseing over 30% in the angle range studied. Fig. 19 suggests thathe “optimal” angle of attack is between +10◦ and −10◦. This isecause, as seen in Fig. 11, mass transfer is lower for the geome-ries at attack angles of +10◦ and −10◦ than for 0◦ and 5◦. Despitenergy losses being lower for the 4L03L case with an angle of attackf −10◦ than for 0◦ and 5◦ (see Fig. 9), the lower Sherwood num-er results in a lower permeate flux, which in turn increases theperating cost per cubic meter of permeate. Angles above +10◦ orelow −10◦ are unlikely to reduce processing costs, as aerodynamictudies [36] suggest that flow separation would cause significantncreases to form drag, and hence to operating costs. Given that theow Sherwood numbers observed for the attack angles of +10◦ and10◦ imply a low degree of mixing and boundary layer renewal, it

s unlikely that these configurations will achieve lower processingosts for higher Schmidt number solutes.

For the df/hch ratios of 0.4 and 0.3, the -L spacer configura-ions resulted in lower processing costs than the -H configurations.herefore, it can be concluded that for 2D 4-layer zigzag spac-rs with elliptical filaments as middle layers, the -L configurationill result in lower processing costs than the -H configuration, for

he cost parameter conditions used in this paper. Since the attackngles which produced the lowest permeate processing cost forach spacer configuration also presented the highest Sherwoodumbers, it can be said that mass transfer had the greatest impact

n determining the permeate processing costs in steady flow con-itions. The data collected suggests that positioning the middlelliptical filament layers such that they cause a change in the direc-ion of the bulk flow (via positive angles of attack) will result inower processing costs for the geometries analyzed, despite lowernergy losses occurring when the filaments are aligned with theow (at negative angles of attack). However, more data points areeeded before optimal operating angles of attack can be deter-ined for these geometries.

.3.2. Effect of changes in membrane costWhen higher membrane costs per unit area are assumed, the

ifference between spacer-filled channels and empty channelsecomes more evident. As seen in Fig. 20 for a membrane cost of500/m2, the permeate production cost when utilizing an emptyhannel is higher than for any of the spacer-filled channel geome-

ries tested within the Reynolds number range of this study. This isecause energy losses in the empty channel are up to an order ofagnitude lower than for the spacer-filled channels, and thereforeembrane costs account for most of the empty channel processing

osts. In addition, as membrane costs are increased, the Reynolds

820 G.A. Fimbres-Weihs, D.E. Wiley / Journal of M

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ig. 20. Dependence of total processing cost per cubic meter of permeate onydraulic Reynolds number, for empty, 2-, 3- and 4-layer spacer-filled channels.membrane cost of $500/m2 was assumed.

umber for minimum total cost is also increased. This effect islearly seen for the 4L03H spacer geometries, for which the process-ng costs in the unsteady flow regime (i.e. at a hydraulic Reynoldsumber of 800), are lower than in the steady laminar regime. Inontrast, at lower membrane costs, processing costs were highert a hydraulic Reynolds number of 800 than at the lower hydrauliceynolds number of 200 (see Fig. 16). Therefore, as membrane costsre increased, it becomes desirable from the economic viewpoint toperate in the unsteady flow regime. This is because the increasednergy losses and associated costs of operating in the unsteadyow regime are easily offset by the higher mass transfer rates andermeate fluxes attained at higher Reynolds numbers.

Conversely, at the lower membrane cost of $10/m2, the opti-al operating Reynolds number for every spacer configuration

s lower than the optimal Reynolds number at higher membraneosts. Fig. 21 shows that the advantage of spacer-filled channelsgainst the empty channel is reduced at this lower membrane cost,nd that the optimal Reynolds number for the empty channel isigher than the optimal Reynolds number for spacer-filled chan-els. The reason for this change is that at low membrane costs,

nergy costs become the main contributor to the total processingost, and the total cost curve approaches the operating cost curve.oreover, it can also be seen that the optimal Reynolds number

or the multi-layer spacer configurations is lower than the optimal

ig. 21. Dependence of total processing cost per cubic meter of permeate onydraulic Reynolds number, for empty, 2-, 3- and 4-layer spacer-filled channels.membrane cost of $10/m2 was assumed.

fatndmmamr

iwpintTi[lt

cs

embrane Science 325 (2008) 809–822

eynolds number for the 2L06 spacer. This suggests that operatingosts dominate in multi-layer spacers, mainly due to the increasedressure losses and form drag caused by the extra filament layers

n the multi-layer configurations. In other words, a geometry withlarger amount of form drag will have a lower optimal operatingeynolds number, while a geometry with less form drag will have aigher optimal operating Reynolds number. However, the value ofhe minimum permeate processing cost is not solely dependent onhe value of optimal Reynolds number. Therefore, form drag aloneannot determine which geometry will attain the lowest permeaterocessing costs. For this scenario, the best performing (lowest pro-essing cost) spacer geometry is the 2L06 spacer, followed by theL04 at an angle of attack of 0◦. The geometry with the highest pro-essing cost at the optimal Reynolds number is, as in the previouscenarios, the empty channel.

. Conclusions

A design study for novel multi-layer spacer configurationsncluding elliptical filament spacer layers was conducted. Singlend double layers of elliptical spacer filaments were incorporatednto 2D zigzag configurations of circular filaments. The expectedffect of the elliptical filaments was to direct low concentrationuid from the bulk to the near-wall region, and to increase theisruption of boundary layer formation caused by the circularlaments. In order to assess the benefits of this type of spacer con-guration, an economic analysis was also carried out using costarameters representative of those quoted in literature.

The results presented in this work show that, although aomparison of different spacer geometries via power consump-ion (Re3f) and mass transfer (Sh) is useful, an economic analysisncorporating permeate production provides a more realistic rel-tive performance assessment, as it accounts for the trade-offs inther performance characteristics. Therefore, in order to determinehich spacer geometries will yield lower permeate processing

osts, an economic analysis is recommended over a comparisonf mass transfer at similar energy losses.

According to the economic analysis, the optimal operatingeynolds number (at which total processing costs were minimizedor each spacer geometry) was found to be closely related to themount of form drag generated by the spacer filaments. For geome-ries with a higher amount of form drag the optimal Reynoldsumber was lower than for those with a lower amount of formrag. It was also found that for higher membrane costs, the opti-al operating Reynolds number was increased. For the highestembrane cost assumed in this paper ($500/m2), the optimal oper-

ting Reynolds number fell in the unsteady flow regime. For lowembrane costs of $10/m2, operating in the laminar flow regime

esulted in the lowest processing costs.One of the main components of processing cost which was not

ncorporated into the economic analysis carried out in this workas that of fouling and cleaning. Since this cost is usually pro-ortional to the membrane area, it was therefore assumed to be

ncluded in the membrane cost. If fouling and cleaning costs are sig-ificant, the analysis presented in this work suggests that increasinghe operating Reynolds number will reduce total processing costs.he direct effect of multiple spacer layers on fouling was not stud-ed in this paper. However, based on the study of Schwinge et al.10] and on the results presented here, it is expected that the higher

ocal velocities and shear rates at the membrane wall will reducehe extent of fouling.

Another cost component not taken into account in the analysisarried out in this work was the cost of production of the novelpacer geometries. Although new techniques are available for the

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The authors would like to acknowledge the Australian ResearchCouncil for funding this project through a Discovery grant. One ofus (G. F.-W) would like to thank the University of New South Walesand the Faculty of Engineering for scholarship funding.

Nomenclature

ae ellipse minor axis (m)aE ellipse major axis (m)Am membrane area (m2)AT channel cross-section area (m2)A,A,B,B Empirical constantsCc capital cost ($/m3)Ce energy cost ($/kWh)Cm membrane cost ($/m2)Cop operating cost ($/m3)Ctot total permeate processing cost ($/m3)de equivalent diameter (m)df filament diameter (m)dh hydraulic diameter (m)D diffusion coefficient (m2/s)f = dh

2�u2eff

�pL Fanning friction factor

Fa amortization factor (1/yr)he height to ellipse (m)hch channel height (m)Jsln flux of solution through the membrane (kg/m2 s)kmt mass transfer coefficient (m/s)lm mesh length (m)L channel length (m)Lp specific permeate flux of membrane, permeability

coefficient (kg/Pa m2 s)n distance in the direction normal to a surface (m)N,N Empirical constantsp pressure (Pa)�pch channel pressure drop (Pa)Pn = Re3

hf Power numberQ volumetric flow (m3/s)Reh =�ueffdh/� hydraulic Reynolds numberSc =�/�D Schmidt numberSh = kmtdh/D Sherwood numberShloc = (dh/Yw − Yavg)(∂Y/∂y)w local Sherwood numbert time (s)top operating time (h/yr)u velocity in x direction (m/s)ueff = uavg/ε effective velocity (m/s)v velocity in y direction (m/s)Vtot volume of fluid in the channel (m3)wch channel width (m)Ws pumping energy (W)x distance in bulk flow direction (m)x+ = L/dhRe dimensionless friction distancex* = L/dhReSc dimensionless mass transfer distancey distance in direction perpendicular to bulk flow (m)Y salt mass fraction

Greek letters

G.A. Fimbres-Weihs, D.E. Wiley / Journa

roduction of new spacer designs [11,41], common mass producedpacers are currently available at much lower costs, which will haven impact on the economic results presented here. Incorporationf the capital costs of spacers would give an economic advantage toraditional 2-layer spacers over new multi-layer designs, which are

ore expensive to produce. Therefore, new designs must increaseermeate production substantially in order to provide an economic

ncentive for their production.The multi-layer configurations with elliptical filaments showed

otential for increased productivity due to mass transfer enhance-ent. However, lower permeate processing costs were obtained

y using a simple 2D zigzag spacer (2L06). The middle layers oflliptical filaments in multi-layer spacer configurations promotedass transfer enhancement when compared to 2-layer spacer

lled channels with the same df/hch ratios. However, stagnant fluidegions near the membrane walls resulted in lower mass trans-er for the multi-layer spacer configurations than for the 2L06 andL04 spacers. Variation of the angle of attack of the elliptical fila-ents showed potential to increase mass transfer enhancement

t the same or lower energy losses by optimizing the profile ofhe middle spacer layer, such that little or no recirculation regionsre formed on its downstream side. In addition, multi-layer spacerhowed potential for reducing processing costs in high-membraneost scenarios.

Although negative attack angles usually reduced energy losses,hey failed to direct flow towards the membrane wall, and thusesulted in lower mass transfer and hence higher operating costser unit volume of permeate. On the other hand, positive angles ofttack generally resulted in lower total permeate processing costs,ue to increased mass transfer. Thus, mass transfer performanceas the main factor in determining the total processing costs for

he conditions of this study. As such, improvements in mass transfernhancement have the potential to reduce both capital and operat-ng processing costs per unit volume of permeate produced. This isossible even if energy losses are increased, since larger permeateuxes will reduce the operating cost per unit volume of permeate.

With regards to the relative positioning of circular and ellipti-al filaments in 4-layer spacers, it was found that the “low” (-L)onfiguration resulted in higher mass transfer enhancement, andence lower permeate processing costs. 4L spacers in the -L con-guration, coupled with positive angles of attack for the ellipticallaments were found to be the most effective in disrupting flownd redirecting low concentration fluid towards the membranealls. However, further studies are required in order to optimize

he hydrodynamic profile and angle of attack of the submerged lay-rs, and thus reduce the energy losses incurred by the addition ofurther flow obstacles. Variation of the filament length to channeleight ratio (lm/hch) should also be explored. In addition, three-imensional simulations of real-world multi-layer spacer designsre needed in order to investigate the 3D flow and mass transferffects that have not been taken into account in this paper.

Current trends indicate that energy costs are increasing, and thatembrane production costs are decreasing. This accentuates the

eed for improved spacer meshes which reduce energy losses ineneral, and detrimental form drag in particular, in order to reducerocessing costs for membrane operations. Multi-layer spacereshes represent a potential alternative to traditional 2-layer

pacer meshes, but further optimization of geometric parametersnd filament profiles are required. Although none of the proposedulti-layer designs resulted in lower processing costs than tradi-

ional 2-layer configurations, especially at lower membrane costs,urther study into the 3D flow and mass transfer effects of the mid-le layer spacer filaments would provide invaluable information toither support or rule out multi-layer spacers as a real alternativeo traditional spacer meshes.

embrane Science 325 (2008) 809–822 821

cknowledgements

ε void fraction, porosity�pump pump efficiency�e angle of attack of elliptical filament (◦)� dynamic viscosity of the fluid (kg/m s)

822 G.A. Fimbres-Weihs, D.E. Wiley / Journal of M

ratio of permeable to impermeable Sherwood num-ber

osmotic pressure (Pa)� density of the fluid (kg/m3)� reflection coefficientϕ osmotic pressure coefficient (Pa) ratio of permeation Peclet number to impermeable

Sherwood number

Subscriptsavg average value integrated over channel cross-sectionb mass flow average or bulk flow valuefd value at fully developed boundary layer conditionsin value at the domain inletloc value at the local flow conditionsout value at the domain outletp value for the permeate

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eferences

[1] D.G. Thomas, Forced convection mass transfer. Part II. Effect of wires locatednear the edge of the laminar boundary layer on the rate of forced convectionfrom a flat plate, AIChE J. 11 (1965) 848–852.

[2] D.G. Thomas, Forced convection mass transfer. Part III. Increased mass transferfrom a flat plate caused by the wake from cylinders located near the edge ofthe boundary layer, AIChE J. 12 (1966) 124–130.

[3] A.R. Da Costa, A.G. Fane, C.J.D. Fell, A.C.M. Franken, Optimal channel spacerdesign for ultrafiltration, J. Membr. Sci. 62 (1991) 275–291.

[4] R.E. Hicks, W.G.B. Mandersloot, The effect of viscous forces on heat and masstransfer in systems with turbulence promoters and in packed beds, Chem. Eng.Sci. 23 (1968) 1201–1210.

[5] G. Schock, A. Miquel, Mass transfer and pressure loss in spiral wound modules,Desalination 64 (1987) 339–352.

[6] G.A. Fimbres-Weihs, D.E. Wiley, D.F. Fletcher, Unsteady flows with mass transferin narrow zigzag spacer-filled channels: a numerical study, Ind. Eng. Chem. Res.45 (2006) 6594–6603.

[7] G.A. Fimbres-Weihs, D.E. Wiley, Numerical study of mass transfer in three-dimensional spacer-filled narrow channels with steady flow, J. Membr. Sci. 306(2007) 228–243.

[8] D.G. Thomas, W.L. Griffith, R.M. Keller, The role of turbulence promoters inhyperfiltration plant optimization, Desalination 9 (1971) 33–50.

[9] A.R. Da Costa, A.G. Fane, Net-type spacers: effect of configuration on fluid flowpath and ultrafiltration flux, Ind. Eng. Chem. Res. 33 (1994) 1845–1851.

10] J. Schwinge, D.E. Wiley, A.G. Fane, Novel spacer design improves observed flux,J. Membr. Sci. 229 (2004) 53–61.

11] F. Li, W. Meindersma, A.B. De Haan, T. Reith, Novel spacers for mass transferenhancement in membrane separations, J. Membr. Sci. 253 (2005) 1–12.

12] D.W. Kim, M.-U. Kim, Minimum drag shape in two-dimensional viscous flow,Int. J. Numer. Methods Fluids 21 (1995) 93–111.

13] C.H.K. Williamson, Vortex dynamics in the cylinder wake, Ann. Rev. Fluid Mech.28 (1996) 477–539.

[

[

[

embrane Science 325 (2008) 809–822

14] L. Zovatto, G. Pedrizzetti, Flow about a circular cylinder between parallel walls,J. Fluid Mech. 440 (2001) 1–25.

15] R. Iwatsu, K. Ishii, K. Kawamura, K. Kuwahara, J.M. Hyun, Numerical simula-tion of three-dimensional flow structure in a driven-cavity, Fluid Dynam. Res.5 (1989) 173–189.

16] R. Iwatsu, J.M. Hyun, K. Kuwahara, Analyses of three-dimensional flow calcula-tions in a driven cavity, Fluid Dynam. Res. 6 (1990) 91–102.

17] R.B. Bird, W.E. Stewart, E.N. Lightfoot, Transport Phenomena, Wiley, New York,1960.

18] D. Wiley, D.F. Fletcher, Techniques for computational fluid dynamics modellingof flow in membrane channels, J. Membr. Sci. 211 (2003) 127–137.

19] D.F. Fletcher, D. Wiley, A computational fluids dynamics study of buoyancyeffects in reverse osmosis, J. Membr. Sci. 245 (2004) 175–181.

20] A. Subramani, S. Kim, E.M.V. Hoek, Pressure, flow, and concentration pro-files in open and spacer-filled membrane channels, J. Membr. Sci. 277 (2006)7–17.

21] N.V. Ndinisa, D.E. Wiley, D.F. Fletcher, Computational fluid dynamics sim-ulations of Taylor bubbles in tubular membranes—model validation andapplication to laminar flow systems, Chem. Eng. Res. Des. 83 (2005)40–49.

22] V. Geraldes, M.D. Afonso, Generalized mass-transfer correction factor fornanofiltration and reverse osmosis, AIChE J. 52 (2006) 3353–3362.

23] J. Schwinge, D. Wiley, D.F. Fletcher, Simulation of the flow around spacer fila-ments between channel walls. 1. Hydrodynamics, Ind. Eng. Chem. Res. 41 (2002)2977–2987.

24] J. Schwinge, D. Wiley, D.F. Fletcher, Simulation of the flow around spacer fila-ments between channel walls. 2. Mass-transfer enhancement, Ind. Eng. Chem.Res. 41 (2002) 4879–4888.

25] J. Schwinge, D. Wiley, D.F. Fletcher, Simulation of unsteady flow and vortexshedding for narrow spacer-filled channels, Ind. Eng. Chem. Res. 42 (2003)4962–4977.

26] H.-Z. Huang, W.-Q. Tao, An experimental study on heat/mass transfer andpressure drop characteristics for arrays of nonuniform plate length positionedobliquely to the flow direction, J. Heat Trans. T. ASME 115 (1993) 568–575.

27] Z.-X. Yuan, W.-Q. Tao, Q.-W. Wang, Numerical prediction for laminar forcedconvection heat transfer in parallel-plate channels with streamwise-periodicrod disturbances, Int. J. Numer. Methods Fluids 28 (1998) 1371–1387.

28] N.R. Rosaguti, D.F. Fletcher, B.S. Haynes, Laminar flow and heat transfer in aperiodic serpentine channel, Chem. Eng. Technol. 28 (2005) 353–361.

29] S.W. Churchill, R. Usagi, A general expression for the correlation of rates oftransfer and other phenomena, AIChE J. 18 (1972) 1121–1128.

30] F. Maskan, D.E. Wiley, L.P. Johnston, D.J. Clements, Optimal design of reverseosmosis module networks, AIChE J. 46 (2000) 946–954.

31] O. Kedem, A. Katchalsky, Thermodynamic analysis of the permeability of bio-logical membranes to non-electrolytes, Biochim. Biophys. Acta 27 (1958) 229.

32] U. Merten, Flow relationships in reverse osmosis, Ind. Eng. Chem. Fundam. 2(1963) 229.

33] S. Sourirajan, Reverse Osmosis, Academic Press, New York, NY, 1970.34] V. Geraldes, V. Semiao, M.N. de Pinho, Flow and mass transfer modelling of

nanofiltration, J. Membr. Sci. 191 (2001) 109–128.35] A.H.P. Skelland, Diffusional Mass Transfer, John Wiley & Sons, New York, 1974.36] J.D. Anderson, A History of Aerodynamics, Cambridge University Press, Cam-

bridge, 1997.37] P. Feron, G.S. Solt, The influence of separators on hydrodynamics and mass

transfer in narrow cells: flow visualisation, Desalination 84 (1991) 137–152.38] G. Belfort, G.A. Guter, An experimental study of electrodialysis hydrodynamics,

Desalination 10 (1972) 221–262.

39] W.W. Focke, On the mechanism of mass transfer enhancement by eddy pro-

moters, Electrochim. Acta 28 (1983) 1137–1146.40] D.E. Wiley, C.J.D. Fell, A.G. Fane, Optimisation of membrane module design for

brackish water desalination, Desalination 52 (1985) 249–265.41] J. Balster, I. Pünt, D.F. Stamatialis, M. Wessling, Multi-layer spacer geometries

with improved mass transport, J. Membr. Sci. 282 (2006) 351–361.