Experiments and modeling of a vacuum membrane distillation for high saline water

Journal of Industrial and Engineering Chemistry xxx (2013) xxx–xxx

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JIEC-1583; No. of Pages 10

Experiments and modeling of a vacuum membrane distillation for highsaline water

Gayathri Naidu a, Yongjun Choi b, Sanghyun Jeong a, Tae Mun Hwang c,Saravanamuthu Vigneswaran a,*a Faculty of Engineering and IT, University of Technology, Sydney (UTS), PO Box 123, Broadway, NSW 2007 Australiab University of Science and Technology, 113 Gwahangno, Yuseong-gu, Daejeon-si, Republic of Koreac Korea Institute of Construction Technology, Gyeonggi-do 411-712, Republic of Korea

A R T I C L E I N F O

Article history:

Received 20 June 2013

Accepted 21 September 2013

Available online xxx

Keywords:

High salinity

Modeling

Vacuum membrane distillation

A B S T R A C T

A modified design vacuum membrane distillation (VMD) system with high saline water was evaluated

using different operating conditions (sustainable low feed temperature and flow velocity). At high

salinity, a permeate flux of 13.9 to 15.8 L m�2 h�1 was achieved. Increasing the salinity from 1 to 3 M

NaCl reduced the permeate flux by 18–20%. An increase in bulk feed temperature (310.2–319.2 K)

significantly increased the permeate flux by 64%. The increase in flow velocity (1.1 to 2.2 m s�1) in turn

increased the permeate flux by 14–20%. Model fluxes predicted was a good fit to experimental fluxes

(R2 � 0.94).

� 2013 The Korean Society of Industrial and Engineering Chemistry. Published by Elsevier B.V. All rights

reserved.

Contents lists available at ScienceDirect

Journal of Industrial and Engineering Chemistry

jou r n al h o mep ag e: w ww .e lsev ier . co m / loc ate / j iec

1. Introduction

Seawater desalination technology offers the capacity toproduce freshwater from salt water, and sustain global demandsfor more water. Currently, 54% of the world’s seawater desalinationplants function on reverse osmosis (RO)-based technology [1,2].RO technology has grown rapidly in desalination plants due to itscapability to produce water with relatively less energy consump-tion compared to conventional thermal desalination technologies.The RO operation is also stable in having a high rejection rate ofdissolved salts in seawater [2]. However, the recovery rate in theRO process is still limited by 40 to 50% of the feed water while theremaining 50 to 60% (as saline RO brine or concentrate) is beingdiscarded [1]. For coastal desalination plants, this brine is mostlydischarged directly into the sea, which could have seriousimplications for marine ecology [3]. It requires more effort andenergy to treat RO brine because it has higher osmotic pressure.Hence, brine recovery in the RO system is significant in enhancingthe RO performance and having less impact on the marine ecology.The RO system combined with a post-treatment strategy has thepotential to improve the RO operation’s overall recovery rate.

Several technological options for treating RO brine have beenproposed, for example traditional solar evaporation, electro-

* Corresponding author. Tel.: +61 2 9514 2641; fax: +61 2 9514 2633.

E-mail address: [email protected] (S. Vigneswaran).

Please cite this article in press as: G. Naidu, et al., J. Ind. Eng. Chem

1226-086X/$ – see front matter � 2013 The Korean Society of Industrial and Engineer

http://dx.doi.org/10.1016/j.jiec.2013.09.048

dialysis, forward osmosis (FO) and membrane distillation (MD)[4]. Of these technologies, FO and MD have been shown to beeffective in the recovery of high salt concentration because theyare: first, less complex; and second, enable sustainable energyconsumption [5]. In the FO system, however, there are stillcommercial challenges associated with the selection of anappropriate draw solution and its additional treatment [6]. Onthe other hand, MD has a high water recovery rate of 80–90%especially when coupled with crystallization [7]. However, anindustrial-scale application of MD technology has not yet beenestablished [8].

MD is a desalination technology that integrates both thermaldistillation and membrane processes. MD differs from othermembrane technologies in that the driving force is the difference invapor pressure of water across the membrane, rather than totalpressure. In this type of operation, partial water vapor pressure willbe reduced slightly due to salt concentration. However, the drivingforce in the reduction of water vapor pressure is quite small andthe operation will continue producing a reasonable water output[5]. Therefore this technique is particularly useful for brinetreatment [9]. MD can achieve almost zero liquid discharge withhigh quality distillate when it is integrated into an RO process.Additionally, the thermal process in MD requires only lowoperating temperature. This makes it possible to utilize alternativeenergy sources such as waste heat or solar energy [10]. MDconsumes less electrical energy and therefore produces lessgreenhouse emissions. MD system can be constructed as a

. (2013), http://dx.doi.org/10.1016/j.jiec.2013.09.048

ing Chemistry. Published by Elsevier B.V. All rights reserved.


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Nomenclature

B VMD coefficient of the membrane

(kg m�2 s�1 Pa�1)

C solute concentration (mol L�1)

dh hydraulic diameter (m)

D diffusion coefficient of solute (m2 s�1)

Dkn Knudsen diffusion coefficient of solute (m2 s�1)

hw heat transfer coefficient (W m�2 K�1)

DHv latent heat of vaporization (J kg�1)

i molarity (mol L�1)

Jw water vapor flux (kg m�2 s�1)

K mass transfer coefficient (m s�1)

Km thermal conductivity (W m�1 K�1)

L length of the channel (m)

M molecular mass of water (kg mol�1)

N heat flux (J m�2 s�1)

P pressure (Pa)

R gas constant (J mol�1 K�1)

r pore size (m)

T temperature (K)

t time (min)

Greek symbols

d membrane thickness (m)

e porosity

t tortuosity

r density (kg m�3)

m viscosity (Pa s)

l mean free path of water molecules (m)

Subscript

f feed

bf bulk feed

h heating

m membrane surface

v vacuum

Groups

CP concentration polarization

CP0 concentration polarization at set vapor pressure

DCMD direct contact membrane distillation

FO forward osmosis

MD membrane distillation

Nu Nusselt number

Pr Prandtl number

Re Reynolds number

RO reverse osmosis

Sc Schmidt number

Sh Sherwood number

TP temperature polarization

TP0 temperature polarization at set vapor pressure

V-MEMD vacuum multi effect membrane distillation

VMD vacuum membrane distillation

G. Naidu et al. / Journal of Industrial and Engineering Chemistry xxx (2013) xxx–xxx2

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small-scale and compact unit; a smaller footprint compared to thetraditional distillation system.

The MD systems consist of various configurations. More than60% of MD studies have focused on the direct contact membrane


distillation (DCMD) system. This is because of its simpleconfiguration with condensation taking place within the system[10]. However, in DCMD, the direct contact element results inhigher heat loss by conduction in the membrane compared to otherconfigurations of the MD system [11]. On the contrary, vacuummembrane distillation (VMD) configuration has the potential toachieve higher flux, due to a higher driving force resulting fromdifferences in the feed water vapor pressure and vacuum pressure[12]. The vacuum also reduces the formation of boundary layer onthe feed side, which minimizes heat loss [13].

The performance of VMD is governed by operating parameterssuch as feed temperature, feed flow rate and water vapor pressure;these variables influence the permeate flux and feed concentrationas well as membrane characteristics (permeability) [10,11,13].Khayet [10] has reported VMD flux values ranging from 0.2 to36 L m�2 h�1 depending on factors such as operating parameters aswell as membrane type. However, these studies were done usinglow concentration salt solutions. Even though some studies werecarried out with high-salt concentration solutions, they wereperformed only on bench-scale equipment with a small membranearea (maximum 2 L d�1 water output capacity) [14–17]. Researchon small-scale equipment may not be able to represent theperformance of real conditions, such as elevation of polarizationeffect and the influence of operating parameters on these effects.These are important factors for estimating the water productionrate of a pilot scale MD application. Such aspects, however, can beachieved effectively on scaled-up equipment.

The objective of this paper was to evaluate the performance of aVMD system with an improved design to treat high saltconcentration. The system’s performance was evaluated in termsof permeate flux at different operating conditions (feed tempera-ture and flow velocity) at an initial feed concentration of 1 M NaCl.At the same time, a mathematical simulation was also conductedto fit the experimental data. This mathematical model was able to:first, assess the feasibility of the novel VMD system with high NaClconcentration; and second, analyze the influence of operatingconditions on VMD performance.

2. Materials and methods

2.1. Experimental method

All experiments were conducted with a modified VMD systemdesigned by Memsys (Fig. 1). Memsys is a technology companybased in Singapore and Germany providing a highly effectivepatterned design of thermal process modules for differentapplications. Memsys developed this commercial membranedistillation system that combines the advantages of multi-effectsand vacuum to achieve a highly efficient system of heat recovery[18]. This novel model, composed of a steam raiser, a membranemodule (vapor–liquid stage) and a condenser, combines the basicconcept of VMD with a multi-effect distillation process system[18]. As such three effects, namely heating effect (steam-raiser),evaporation-condensation effect and cooling effect (condensation)occur in one system. For easy reference, the term ‘one-stagevacuum multi- effect membrane distillation (V-MEMD)’ wasemployed to represent the VMD system used in the followingsections.

In a general VMD system design, vapor produced is condensedoutside the module without heat recovery. Similarly, the feedsolution is heated externally and then directed to the feed waterchannel for thermal evaporation. However, the V-MEMD systemdesign has the advantage of less heat loss due to internal heatingand condensation [18]. As shown in Fig. 2, in the one-stage V-MEMD system, water in the steam raiser unit (set at lower pressurethan the ambient pressure) is heated by an external heat source



Fig. 1. MemSYS VMD system.

Table 1Properties of membrane used in this study.

Material PTFE*

Manufacturer GE

Effective membrane area (m2) 0.16

Thickness (d) (mm) 179

Porosity (e) (%) 70–75

Mean pore size (r) (mm) 0.2

* PTFE—polytetrafluoroethylene.

G. Naidu et al. / Journal of Industrial and Engineering Chemistry xxx (2013) xxx–xxx 3

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and turned into steam. Hot steam flows and condenses at thecondensation foil, releasing heat to the feed water. The spacebetween the foil and membrane is the feed water channel. The feedwater is heated by the heat energy released from the steam raiserunit and evaporates under corresponding negative pressure.Vacuum is applied to the permeate side of the membrane. Thevapor produced is condensed in the condensing stage, and thenincorporated at the permeate side of the system. In this system,due to a constant heat loop inlet temperature, the pressure levelthroughout the module is stable and it is possible to achieve stablepermeate flux. The modular design of the V-MEMD system enablesless specific heat transfer and heat consumption [18]. At the sametime this configuration, which is assembled in a single plate andframe structure, makes the system easy to size up according tocapacity requirement. For instance, the one stage system can beincorporated with three to four membrane stages, increasing theoutput. This design also enables a compact-size system.

Membrane: The membrane used in this system was apolytetrafluoroethylene (PTFE) flat sheet hydrophobic membrane(General Electrics, US). The membrane size was 0.33 m � 0.48 m

Fig. 2. Schematic diagram of the water flow and temperature distribution (change) (T1>

temperature sensors—T1 = steam raiser (inlet) temperature/heating temperature, Th;

temperature, Tfb; T4 = feed temperature (outlet)/brine & internal temperatures—Tf = fee


with an effective membrane area of 0.16 m2. The porosity and thethickness of membrane were 70 to 75% and 179 mm, respectively(Table 1). Details of the membrane characteristics were obtainedfrom the manufacturer.

Feed water: The feed water solution was prepared by dissolvingNaCl in deionized (DI) water. The quality of feed water wasmeasured in terms of total dissolved solids (TDS) using conductiv-ity meter (WTW, LF330). Other sparingly dissolved salts such asCaCO3 and MgSO4 usually present in seawater or brackish waterwere not contained in the feed water.

Operating conditions: Fig. 2 shows the detailed schematicdiagram of the temperature distribution (change) in the one-stageV-MEMD. The temperature sensors (�0.1 8C) automaticallyrecorded the temperature values throughout the experiment. In thisstudy, two sets of experiment (Set I and Set II) were carried out atdifferent feed flow rates (Table 2). Each set consisted of three sub-experiments at different feed temperatures.

Flow rate: Feed water was circulated through the feed flowchannel at a feed flow rate of 50 L h�1 and 100 L h�1 whichcorresponds to a flow velocity of 1.1 m s�1 and 2.2 m s�1,respectively. This flow velocity was calculated based on thehydraulic area of the feed flow channel (a thickness of 1.50 mm).The condensation foil is made of polypropylene (PP) with athickness of 23 mm. This setting resulted in a 4.5 � 0.5 kPa ofvacuum pressure in the permeate side. However, the vacuumpressure rate changed slightly under different feed flow rates andtemperatures used in this study as shown in Table 2. In this system,the vacuum pump was used to suck non-condensable gases. If non-condensable gases are not removed, it accumulates in the system andreduces the heat and mass transport. Hence, the vacuum pump wasable to reduce the heat losses to obtain higher vapor flow rate in thesystem. The specific level of flux dependency to vacuum pressure wasnot considered in this study because the system was not designedwith a direct controllable vacuum pressure pump feature.

T2> T3> T4) through the one stage V-MEMD system (external temperatures from

T2 = steam raiser (outlet) temperature; T3 = feed temperature (inlet)/bulk feed

d temperature in membrane module; Tm = temperature on the membrane surface.



Table 2Experimental operating parameters of the V-MEMD system.

Experiment

set

Feed flow

rate (L h�1)

Temperature (K) Vacuum

pressure (Pp, kPa)Steam raiser (inlet, T1/Th) Steam raiser (outlet, T2) Feed (Inlet, T3/Tfb) Feed (brine/outlet, T4)

I 50 318.2 312.9 310.2 305.4 3.9

328.2 319.8 313.7 308.7 4.4

338.2 324.4 319.2 317.0 5.1

II 100 318.2 312.5 310.2 304.9 4.0

328.2 320.7 315.7 308.8 5.0

338.2 325.0 321.9 317.4 6.0

Fig. 3. The procedure (algorithm) used to calculate water flux.


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Permeate flux measurement: In this study, the producedpermeate was collected in a tank, which was then placed ontoan electronic balance. At the same time, the decreasing feed watervolume in the tank was recorded throughout the experimentperiod. The corresponding value (volume of decreased feed andproduced permeate) with the operation time was used to calculatethe permeate flux in kg m�2 s�1. The decreased feed volume wasconsistent with the collected permeate volume and evaporation orleakage was minimal or zero. Small losses incurred by evaporationin the heating pump can be neglected. During the experiment,stability was maintained in the system, which was mainly due tothe low feed temperature with minimum heat loss. After 20 min ofeach experimental run, the feed water temperature was stabilizedwith a slight variation (only �1.0–2.0 8C). Both experimental setswere duplicated but the average value was reported in this papersince the deviation in every set of measurements was less than 2%.

Temperature: Every experiment was carried out with 2 L ofdistilled water (fed from the permeate tank) for the heatingsystem. This water was heated (to the corresponding control paneltemperature, T1) in the additional tank and turned into steam inthe steam raiser. T1 (steam raiser inlet temperature) representedthe heating temperature, Th. The exchange (liquid to steam)required latent heat and as such T1 value was reduced to T2 (steamraiser outlet temperature). The temperature of the inlet feed waterincreased to T3 with the steam heat. T3 represented the bulk feedtemperature, Tfb. The temperature of the outlet feed water of thefeed channel (brine) was reduced to T4. The feed outlet water wasrecirculated to the feed tank for continuous operation. Meanwhilethe feed temperature inside the module is the feed temperature, Tf,while the feed temperature on the membrane surface is Tm (Fig. 2).

In this study, for steady state conditions, the heat transferred onthe membrane surface was considered equal to the amount of heattransferred inside the membrane. As an initial assumption only,the assumed value of feed temperature, Tf was taken to be the valueof the inlet feed temperature/bulk feed temperature (T3/Tfb)(Table 2). Thereafter, the feed temperature, Tf was determinedby continuously comparing the calculated and experimentalpermeate flux as discussed in the algorithm (Fig. 3). On the otherhand, the feed temperature at the membrane surface (Tm) wascalculated based on heat transfer coefficient, Eq. (10), using theexperimental permeate flux, through the modeling as described inFig. 3.

In the meantime, tap water was used as cooling water source forthe condenser. The cooling water was not recirculated to maintaina constant cooling temperature range. Outlet and inlet coolingtemperature values were retrieved from the temperature sensor.The inlet temperature was 296.4 � 0.1 K and the outlet temperaturewas 298.5 � 1.5 K.

In the V-MEMD system, direct control of the feed temperaturewas not possible. Consequently the experiments were carried outby adjusting the steam raiser temperature (T1/Th) from 318.2 K to338.2 K which was the maximum achievable temperature whenusing this system. The corresponding value of the bulk feedtemperature (T3/Tfb) was retrieved from the system’s control panel


data. The bulk feed temperature, Tfb changed systematically whenthe feed flow rate was increased. For both Set I and Set II, the feedwater was concentrated from 1 M to 3 M. In Set I, the feed flow ratewas set at 50 L h�1 (flow velocity =1.1 m s�1, Re = 6100) while thevalues of the three bulk feed temperature series were Tfb = 310.2,313.7 and 319.2 K, respectively. In Set II, the feed flow rate wasdoubled to 100 L h�1 (flow velocity = 2.2 m s�1, Re = 17, 300) whilethe values of the three bulk feed temperature series wereTfb = 310.2, 315.7 and 321.9 K, respectively. The different feedflow rates and bulk feed temperatures influenced the vacuumpressure slightly as shown in Table 2.




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It is important to highlight that the general feed temperaturesetting in MD systems ranges between 338.2 K and 358.2 K [19].Compared to a traditional VMD system, the setting of this modifiedV-MEMD design system was unique due to the integration of aninternal heating system. In this case, rather than the bulk feedtemperature, the heating temperature, Th was set between 318.2 Kand 338.2 K. This heat was channeled to the feed water. As such,the operating bulk feed temperature, Tfb was set at a lower range,between 310.2 K and 321.9 K. The presence of an internal heatingmade it possible to operate the system with lower Tfb, whileachieving reasonable permeate flux. Generally, the major energyconsumption in MD systems is attributed to the high feedtemperature settings [14,17]. Lower temperature enabled the V-MEMD system to operate more energy efficiently (i.e. lower bulkfeed temperature setting would potentially lower heat-loss withinthe system).

2.2. VMD modeling

A simple mathematical model was used to fit the experimentaldata. In a VMD process the driving force is maintained by applyinga continuous vacuum at the permeate side below the equilibriumvapor pressure. The hot feed solution is brought into contact withone side of a hydrophobic micro-porous membrane. When water ismass transported through the membrane, the water vapor flux, Jw

is expressed as follows [11,20]:

Jw ¼ B Pm Tm; Cmð Þ � Pvð Þ (1)

where, B is the VMD coefficient of the membrane, Tm is themembrane surface feed temperature, Cm is the solute concentra-tion on the membrane surface in the feed side, Pm (Tm, Cm) is thewater vapor pressure on the membrane surface in the feed side,and PV is the pressure in the vacuum side.

The water vapor pressure on membrane surface, Pm (Tm, Cm) canbe related to the feed temperature (in K) and feed solutionconcentration (in g kg�1). This is based on Raoult’s law wherebythe vapor pressure of saline water is equal to the vapor pressure ofwater in the pure state and as a function of the salinity. Raoult’slaw’s validity is 0 < T < 200 8C and 0 < S < 240 g kg�1 (T = tem-perature, S = salinity, and accuracy= 0.1%). Using Raoult’s law, themembrane surface vapor pressure, Pm (Tm, Cm) is expressed asfollows [21]:

PmðTm; CmÞ ¼exp �5:80 � 103=Tm þ 1:39 � 4:86 � 10�2Tm þ 4:18 � 10�5T2

m þ �1:45 � 10�8T3m

� �þ 6:55logðTmÞ

h i1 þ 0:57257 Cm= 1000 � Cmð Þð Þ (2)

The salt concentration profile on the membrane surface, Cm canbe calculated according to the following equation [10,22]. Thisequation is based on film theory, which incorporates concentrationpolarization as:

Cm

C f¼ exp

Jw

k

� �(3)

where Cf is the concentration in the bulk feed solution and k is themass transfer coefficient. The mass transfer coefficient, k, can becalculated by the relationship of the dimensionless number[23,24]:

k ¼ Sh � D

dh(4)


with

Sh ¼ 1:86 Re � Sc � dh

L

� �0:33

Re < 2100 : Laminar flow (5)

or

Sh ¼ 0:023 Re0:8Sc0:33 Re > 4000 : Turbulent flow (6)

where Sh is Sherwood number, Re is Reynolds number, Sc isSchmidt number, D is the diffusion coefficient of solute, dh is thehydraulic diameter and L is the length of the channel.

In general MD process, the mass transfer may be explained, inprinciple, using the Knudsen flow model, viscous flow model,molecular diffusion model, or a combination of them [11,20]. Twofactors that influence the mass transfer mechanism through aporous media are the membrane’s pore size and the mean freemolecular path of the transferring species. In a VMD configuration,the molecular diffusion model may not be an adequate represen-tation of mass transfer in view of the low partial pressure of airinside the pores. Thus, the mass transport mechanisms through theVMD’s hydrophobic micro-porous membrane could be explainedby the Knudsen flow model, viscous flow model or a combinationof both [24]. If transporting species have a mean free path, l, largerthan the membrane pore size (pore radius), the mass transportmechanisms through the pores are of the Knudsen diffusion type.The average pore diameter of the membrane used in theseexperiments was 0.2 mm which is smaller than the mean free pathof water vapor (2.8 mm at 30 8C). Hence, the Knudsen flow model isadopted because it represents the majority of mass transportmechanisms in the VMD process [25]. In the Knudsen flow modelthe membrane coefficient, B is expressed as follows [26]:

B ¼ MDkn

RTmd(7)

with

Dkn ¼ 2er

3t8RTm

pM

� �0:5

(8)

where e is porosity; r is the pore radius; d is the membranethickness; t is the pore tortuosity; M is the molecular mass ofwater; and R is the gas constant. The MD process involves bothmass transfer of water vapor as well as heat transfer across the

membrane. Heat transfer across the membrane boundary layerin an MD system is a limiting step for mass transfer. This isbecause a large amount of heat is needed to vaporize the liquid atthe vapor–liquid interface. In an MD system, heat transfer occursthrough latent heat transfer and conduction heat transfer [11].The presence of a boundary layer at the membrane surfaceresults in a lower temperature at the membrane surface, Tm,compared to the corresponding value at the feed temperature, Tf.In a V-MEMD configuration, however, the conductive heat acrossthe membrane is negligible due to the low pressure on thepermeate side of the membrane [11]. Hence, the heat flux, N

through the liquid boundary layer can be represented by thefollowing equation [12]:

hwðT f � TmÞ ¼ N � DHv (9)




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where DHv is the latent heat of vaporization, hw is the heat transfercoefficient, Tf is the feed temperature, and Tm is the membranesurface feed temperature. The heat transfer coefficient iscalculated using the following equation [25,27]:

hw ¼KmNu

dh(10)

with

Nu ¼ 1:86 Re � Pr � dh

L

� �0:33

Re < 2100 : Laminar flow (11)

or

Nu ¼ 0:023Re0:8 Pr0:33 Re > 4000 : Turbulent flow (12)

where Km is the thermal conductivity of the water, Nu, Re and Pr arethe Nusselt, Reynolds and Prandtl numbers, respectively.

In this analysis, the numerical influence of the temperaturepolarization (TP) and concentration polarization (CP) effect wastaken into account by the Newton–Raphson method with Jacobianmatrix. This is based on the Taylor expansion series forapproximation of the function values to obtain a better estimatedvalue of unknown variables. The Tm and Cm values were calculatedusing this method by considering TP and CP. In this context, as twoequations are being used simultaneously, the Jacobian matrix wasapplied to obtain the roots of the Newton–Raphson method.

f 1 ¼ exp

Bexp �5:80 � 103=Tm þ 1:39 � 4:86 � 10�2Tm þ 4:18 � 10�5T2

m þ �1:45 � 10�8T3m


h i1 þ 0:57257 Cm=ð1000 � CmÞð Þ � Pv

0@

1A

k� Cm (13)

f 1 ¼ T �

Bexp �5:80 � 103=Tm þ 1:39 � 4:86 � 10�2Tm þ 4:18 � 10�5T2

m þ �1:45 � 10�8T3m


h i1 þ 0:57257 Cm=ð1000 � CmÞð Þ � Pv

0@

1AHv

hw� Tm (14)

J ¼ d@ f 1;0

@x1

@ f 1;0

@x2

@ f 2;0

@x1

@ f 2;0

@x2e (15)

J ¼ d f 1 f 2 e (16)

Eqs (13) and (14) were represented in matrix form by Eqs (15)and Eq. (16). The matrix of Eq. (17) was used to modify Eqs (13) and(14) to Eq. (18), respectively. Eq. (18) was then rearranged toEq. (19). The two parameters (Tm and Cm) to be obtained in thematrix were solved using the Newton–Raphson method withJacobian matrix.

fxiþ1g ¼ fxig � J½ ��1f f g (17)

xiþ1 ¼ xi �f ðxiÞf 0ðxiÞ

(18)

f ðxiþ1Þ ¼ f ðxiÞ þ ðxiþ1 � xiÞ f 0ðxiÞ (19)

The model equations to calculate water flux were solved usingthe procedure (algorithm) shown in Fig. 3. Initially, the feedtemperature, Tf was assumed to be the value of the inlet feedtemperature/bulk feed temperature (T3/Tfb). The initial feed watermolarity (i) was 1 M. The mass transfer coefficient (k) wasobtained using Eq. (4) to Eq. (6), and the heat transfer coefficient(hw) was calculated using Eq (10) to Eq. (12). The initial Tm and Cm

values were calculated using Eqs (13) and (14). Eqs (15) and (16)


are the matrix form of Eqs (13) and (14). This was solved using theNewton–Raphson method with Jacobian matrix.

When modified to Eqs. (15) and (16), these two matrices can beused in the Newton–Raphson method. VMD coefficient (B) of themembrane is simultaneously calculated with Tm and Cm values,using Eqs. (7) and (8). Water vapor pressure on the membranesurface was obtained from Eq. (2) using the calculated Tm and Cm

values. Subsequently, the water flux, Jw was obtained using Eq. (1).This process was repeated for increased feed concentration from1 M to 3 M. When the feed water molarity (i) of 3 M was obtained,the calculation was stopped. Thereafter, the model flux and theexperiment flux were compared. If a minimum correlationcoefficient, R2 between the experimental flux and the model fluxwas not achieved, the iteration was restarted with a newlyassumed Tf.

It is important to highlight that the feed temperature, Tf

increases when it is heated by the steam from the steam raiser anddecreases due to the generated flux from different vapor pressuresbetween the feed and permeate sides in the module. Thus, heatexchange between the steam and the steam raiser, and betweenthe feed and the permeate side should be considered to calculatethe actual feed temperature, Tf along the length of the module.However, it was assumed that the feed temperature in the module,Tf remained the same along the length, because its calculation isintensely convoluted. Furthermore the quantity of steam heat fromthe steam raiser transferred to the feed water was much higherthan that of heat-loss when the feed water generated flux.

3. Results and discussion

The performance of the one-stage V-MEMD system (interms of permeate flux) was studied at different feedtemperatures and feed flow rates. The experimental valuesof the permeate flux when feed water was concentrated, withthe corresponding bulk feed temperatures, Tfb of 310.2 K,313.7 K and 319.2 K at a feed flow rate of 50 L h�1 (flowvelocity 1.1 m s�1) are presented in Fig. 4 (Set I). Fig. 5 (Set II)shows the permeate flux at doubled feed flow rate of 100 L h�1

(flow velocity 2.2 m s�1) with the corresponding bulk feedtemperatures, Tfb of 310.2 K, 315.7 K and 321.9 K. In both cases,the permeate flux increased as the feed flow rate and the feedtemperature also increased. This trend agrees with previousMD studies [10,28].

In terms of water quality, on the feed side, the average TDSvalue at the initial stage (1 M NaCl of feed concentration) for allexperiments were around 86.2 mS cm�1. The TDS value increasedto an average of 262.9 mS cm�1 at the end of the experiment (witha concentration factor of 3). On the permeate side, the TDS valueremained quite low with an average of 0.3 mS cm�1. As such, saltrejection was approximately 99.5% in all cases. The capacity toproduce high quality water is an advantage of the V-MEMDsystem, especially when saline water with high TDS value isconsidered.



0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

16.0

18.0

3.02.52.01.51.0

Per

mea

te F

lux

(L/m

2h)

NaCl Feed Conc entr ation (M)

Fig. 4. Permeate flux as a function of the feed concentration for different feed

temperatures at 50 L h�1 of feed flow rate (Set I) (feed temperature: * 319.2 K; ~

313.7 K; & 310.2 K).


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3.1. Effect of feed water concentration

The permeate flux decreased when the feed water concen-tration increased. For instance, the flux obtained at the initial saltconcentration of 1 M was 2.3 � 10�3 kg m�2 s�1 (8.4 L m�2 h�1).It reduced to 1.9 � 10�3 kg m�2 s�1 (6.9 L m�2 h�1) when NaClwas concentrated to 3 M (feed flow rate of 50 L h�1; Tfb of310.2 K) which was only an 18% reduction. The reduction inpermeate flux with feed water concentration was relativelyconstant under different conditions, regardless of the feed flowrate and feed temperature. The high salt concentration de-creased the water vapor pressure of the feed solution. Hence, asfeed salt concentration increased, the driving force for waterevaporation declined, resulting in a lower permeate flux. This isrepresented by Eq. (2).

3.2. Effect of feed water temperature

Increasing the feed temperature significantly improved thepermeate flux. The relationship between flux increment and feedtemperature can be suitably represented by Eqs (1) and (2), whichindicate the exponential relationship between water vaporpressure and temperature on membrane surface. At a feedconcentration of 1 M of NaCl and feed flow rate of 50 L h�1,

0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

16.0

18.0

3.02.52.01.51.0

Per

mea

te F

lux

(L/m

2h)

NaCl Fee d Concent ration (M)

Fig. 5. Permeate flux as a function of the feed concentration for different feed

temperatures at 100 L h�1 of feed flow rate (set II) (Feed temperature: * 321.9 K; D

315.7 K; & 310.2 K).


increasing the bulk feed temperature, Tfb by 9 K from 310.2 K to319.2 K, increased the permeate flux by 64%; from2.3 � 10�3 kg m�2 s�1 (8.4 L m�2 h�1) to 3.8 � 10�3 kg m�2 s�1

(13.5 L m�2 h�1). A similar pattern was observed for all theconcentrations.

3.3. Effect of feed flow rate

The influence of feed flow rate on permeate flux wasinvestigated by increasing the flow rate from 50 L h�1 to100 L h�1 (flow velocity from 1.1 m s�1 to 2.2 m s�1). A constantflux increment of around 14–20% was observed for all bulk feedtemperature values when the feed flow rate was doubled. Forinstance, at 1 M of feed concentration and Tfb of 310.2 K, thepermeate flux increased from 2.3 � 10�3 kg m�2 s�1

(8.4 L m�2 h�1) to 2.7 � 10�3 kg m�2 s�1 (9.6 L m�2 h�1) with anincrease of flow velocity from 1.1 m s�1 to 2.2 m s�1. This isbecause, at a higher flow velocity, turbulence increases. Corre-spondingly, heat and mass transfer increased from the bulk feed tothe membrane surface, increasing the permeate flux [13,17].However in this system, increasing the flow velocity from1.1 m s�1 to 2.2 m s�1 did not significantly contribute to permeateflux increment, indicating that a good mixing intensity was alreadyachieved at the lower flow velocity used in this study. Similarly,previous studies have shown that increasing the flow velocitybeyond the optimum hydrodynamic capacity of a system wouldnot significantly increase the permeate flux (asymptotic value)[14,29].

3.4. Model simulation

The modeling data of permeate flux with different saltconcentrations, feed temperature and flow rate were comparedwith the experimental values as shown in Fig. 6. The modelprediction agreed well with the experimental data, wherebyR2 � 0.94 was obtained. This indicated that the modeling datacould accurately predict the expected flux.

3.5. Polarization effect on V-MEMD system

In an MD system, the mass transfer is based on phasechange, whereby the latent heat of vaporization must beconverted from the feed temperature. The result is a lowertemperature formed at the boundary layer of the feed sidemembrane, creating a temperature difference. This is the effectof TP [30]. Meanwhile, when the mass transfer of non-volatilesalt occurs, a separation process takes place. Over time, theconcentration of salt at the membrane surface becomes higherthan that at the bulk feed, creating a concentration gradient,based on Eq. (3) [10]. This is the effect of CP. To analyze theeffect of TP and CP, values of feed temperature andconcentration close to the membrane surface (actual values)were calculated from the model equations as explainedin Fig. 3.

The effect of TP was calculated in terms of Tm/Tf, which is theratio between the feed temperature at the membrane surface(Tm) and the feed temperature (Tf) [14,17]. Due to the applicationof vacuum in this system, the boundary layer on the permeateside was not relevant and therefore not taken into considerationin the TP equation. A ratio value closer to 1 (higher value)indicates a lower polarization effect, while a lower valueindicates a higher effect of polarization. Meanwhile, the effectof CP was calculated in terms of Cm/Cf, which is the ratio betweenthe concentration in the feed (Cf) and the concentration at themembrane surface (Cm). Here, a higher ratio value indicates ahigher effect of polarization.



6.0

7.0

8.0

9.0

10.0

6.0 7.0 8. 0 9.0 10.0

Exp

erim

enta

l P

erm

eate

F

lux

(L/m

2h)

Model Fi t Fl ux (L/m2 h)

6.0

7.0

8.0

9.0

10.0

6.0 7.0 8. 0 9.0 10.0

Exp

erim

enta

l P

erm

eate

F

lux

((L

/m2

h)

Model Fit Fl ux (L/m2 h)

8.0

9.0

10.0

11.0

12.0

8.0 9.0 10.0 11.0 12.0

Exp

erim

enta

l P

erm

eate

F

lux

(L/m

2h)


8.0

9.0

10.0

11.0

12.0

8.0 9.0 10.0 11.0 12.0

Exp

erim

enta

l P

erm

eate

F

lux

(L/m

2h)

Model Fit Fl ux (L/ m2 h)

11.0

12.0

13.0

14.0

15.0

16.0

11.0 12.0 13.0 14.0 15.0 16.0

Exp

erim

enta

l P

erm

eate

F

lux

(L/m

2h)


11.0

12.0

13.0

14.0

15.0

16.0

11.0 12.0 13.0 14.0 15.0 16.0

Exp

erim

enta

l P

erm

eate

F

lux

(L/m

2h)


(a) (b)

(c) (d)

(f)(e)

Fig. 6. Comparison between modeling and experimental permeate flux (a) feed temperature: 310.2 K, feed flow rate: 50 L h�1, (b) feed temperature: 310.2 K, feed flow rate:

100 L h�1, (c) feed temperature: 313.7 K, feed flow rate: 50 L h�1, (d) feed temperature: 315.7 K, feed flow rate: 100 L h�1, (e) feed temperature: 319.2 K, feed flow rate:

50 L h�1, (f) feed temperature: 321.9 K, feed flow rate: 100 L h�1.


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Fig. 7 (a) and (c) shows the TP and CP ratio as a function offeed concentration with different feed temperatures and feedflow rates (Set I and Set II), respectively. This ratio is based onthe vacuum pressure values which change with feed flow ratesand feed temperatures (Table 2). In view of the deviation ofvacuum pressure values in permeate side (3.9 to 5.1 kPa at1.1 m s�1 and 4.0 to 6.0 kPa at 2.2 m s�1 as given in Table 2), itwas difficult to identify the influence of different operatingconditions on the effect of polarization. As such, the TP and CPratios were re-calculated based on a set (or reference) value of4.5 kPa of vacuum pressure, to compare their effects at aconstant (or reference) pressure value. The values of TP and CPcalculated based on the reference vacuum pressure value wererepresented as TP0 and CP0 (Fig. 7 (b) and (d)). The TP0 and CP0

ratio values were then used to directly identify the operatingparameters that significantly influenced the polarization factorfor the V-MEMD system. Table 3 shows the calculated ratio ofTP0 and CP0. Also, the predicted permeate flux, based on the


reference vacuum pressure value was used here. The CP and TPratio trend in Fig. 7 (a) and (c) was the same as the TP0 and CP0

ratio trend illustrated in Fig. 7 (b) and (d).In this study, the CP ratio was in the range of 1.15 to 1.40

while that of the TP ratio was much lower, from 0.96 to 0.99 forthe feed solution of 1 M of NaCl. Concentrating the feedsolution from 1 M to 3 M of NaCl reduced the effect of TPfurther by 0.5–1.0%. A previous study has also shown that theeffect of TP becomes insignificant at higher salinity concen-trated feed solution (1.0 M to 1.7 M NaCl) [30]. This is becauseat higher salt concentration, vapor pressure is reduced (Eq. (2)).Because lower separation is taking place, less latent heat isrequired and the feed temperature in the bulk side does notchange significantly [29,30].

Increasing the feed temperature increases the vapor pressure.The higher separation should increase the latent heat required,increasing the difference between the feed temperature and themembrane surface temperature. However, in this study, only a



II-1 I-1

II-2 I-2

II-3 I-3

I-3 II-3

I-2 II-2

I-1 II-1

0.95

0.96

0.97

0.98

0.99

1.00

1.0 1.5 2.0 2.5 3.0

TP

Rat

io

NaCl Fee d Conce ntration (M)1.0 1.5 2.0 2.5 3.0

0.95

0.96

0.97

0.98

0.99

1.00

NaCl Fee d Concentration (M)

TP

' Rat

io

1.00

1.10

1.20

1.30

1.40

1.50

1.0 1.5 2.0 2.5 3.0

CP

Rat

io

NaCl Fee d Conce ntration (M)1.0 1.5 2.0 2.5 3.0

1.00

1.10

1.20

1.30

1.40

1.50

NaCl Fee d Conce ntration (M)

CP

' Rat

io

(c) (d)

)b()a(

Fig. 7. Polarization effect in V-MEMD system (a) and (c) TP and CP ratio as a function of feed concentration with different feed temperatures and feed flow rates (Set I and Set II)

based on actual vacuum pressure value (b) and (d) TP0 and CP0 ratio as a function of feed concentration with different feed temperatures and feed flow rates (Set I and Set II)

based on reference value of 4.5 kPa vacuum pressure (———— 50 L h�1; ——100 L h�1; (I-1) 310.2 K (I-2) 313.7 K (I-3) 319.2 K (II-1) 310.2 K (II-2) 315.7 K (II-3) 321.9 K).

Table 3Influence of different operating conditions on the ratio of TP0 and CP0 .

Bulk feed temp., Tfb (K) Bulk feed conc., Cb (M) Flow rate (L h�1)

50 100

TP0 ratio CP0 ratio TP0 ratio CP0 ratio

310.2 1 0.99 1.15 0.99 1.15

2 0.99 1.13 0.99 1.12

3 0.99 1.10 0.99 1.10

313.7/315.7 1 0.97 1.26 0.98 1.25

2 0.98 1.23 0.98 1.23

3 0.98 1.20 0.98 1.20

319.2/321.9 1 0.96 1.40 0.96 1.38

2 0.96 1.36 0.96 1.35

3 0.97 1.33 0.97 1.32


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2–4% increase in the effect of TP was observed. This was attributedto the lower range of feed temperature used and the highhydrodynamic capacity of this system. Likewise, Cath et al. [9]investigated the performance of an enhanced DCMD configurationset at a low feed temperature of 313.2 K and a high flow velocity of2.2 m s�1 with the addition of vacuum on the permeate side. Theyalso observed a significantly smaller TP effect. However, a numberof studies on the VMD system have reported that the effect of TPwas dominant [24,30,31]. These studies were carried out on simplebench scale systems with external heating. In these studies thebulk feed temperatures were set high between 328.2 K and353.2 K. Furthermore, these experiments were conducted at a lowflow velocity (0.05 m s�1 to 0.5 m s�1).


In comparison, the advantage of the system used in this study(V-MEMD) was that the internal heating module enabled heat to beinternally transferred to the feed water at a lower temperaturerange (310.2–321.9 K). Consequently, heat-loss could be minimal,which would have led to TP having less effect. At the same time, thesystem was set at a high hydrodynamic capacity, with a flowvelocity of 1.1 m s�1 to 2.2 m s�1. This considerably reduced thepresence of polarization.

4. Conclusion

This study analyzed the feasibility of a modified design VMDsystem (V-MEMD) with high salinity water. Experiments were




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carried out with feed solution of 1 M of NaCl that was concentratedtill 3 M at different feed flow rates (flow velocity) and feedtemperatures. The results showed that the V-MEMD systememployed was suitable for producing high quality permeate (morethan 99.5% rejection rate) with highly saline water. The findings areas follows:

(1) The permeate flux reduced by only 18–20% for all conditionswhen 1 M NaCl was concentrated up to 3 M NaCl. An increase infeed temperature improved the permeate flux significant by64%.

(2) The model prediction was in good agreement with theexperimental data (R2 � 0.94). This indicated that the modelcan effectively predict the system’s performance under highsalt concentration.

(3) Maintaining a reasonable permeate flux with minimal polari-zation effect was important for the system’s efficiency. Acombination of higher temperature (321.9 K) in the experi-ments with high flow velocity (2.2 m s�1) created a higher flux.The V-MEMD system performed well under high salt concen-tration, achieving a permeate flux of 3.9 � 10�3 kg m�2 s�1

(13.9 L m�2 h�1) to 4.4 � 10�3 kg m�2 s (15.8 L m�2 h�1).

Acknowledgments

This study is supported by the National Centre of Excellence inDesalination Australia (NCEDA), which is funded by the AustralianGovernment through Water for the Future initiative. The authorswould also like to acknowledge Memsys Company for the V-MEMDunit.


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Experiments and modeling of a vacuum membrane distillation for high saline water

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