modeling and simulation of membrane distillation md

7/24/2019 modeling and simulation of membrane distillation MD

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Desalination by solar powered membrane distillation systems

Mohammed Rasool Qtaishat a,, Fawzi Banat b

a Department of Chemical Engineering, University of Jordan, Amman, Jordanb Department of Chemical Engineering, The Petroleum Institute, PO Box 2533 Abu Dhabi, UAE

a b s t r a c ta r t i c l e i n f o

Article history:

Received 18 October 2011

Received in revised form 14 January 2012

Accepted 22 January 2012Available online 25 February 2012

Keywords:

Membrane distillation

Desalination

Solar energy

Solar collectors

Membrane distillation (MD) is a hybrid membrane-evaporative process which has been of interest for desa-

lination. MD requires two types of energy, namely, low temperature heat and electricity. Solar collectors and

PV panels are mature technologies which could be coupled to MD process. The interest of using solar pow-

ered membrane distillation (SPMD) systems for desalination is growing worldwide due to the MD attractive

features. Small scale SPMD units suitable to provide water for human needs in remote areas where water and

electricity infrastructures are currently lacking have been developed and tested by a number of researchers.

The combination of solar energy with MD has proven technically feasible; however, the cost of produced

water is relatively high compared with that produced from the commercial PVRO process. The production

of commercial, reliable, low cost and long lasting MD modules will put this process on the front edge of

desalination technologies. The aim of this article is to present the main features of MD along with its basic

principles. Efforts of researchers in coupling MD with solar energy and their costestimates are reviewed as well.

2012 Elsevier B.V. All rights reserved.

1. Introduction

The demand on fresh water is growing steadily and is becomingone of the worldwide challenges. The World Health Organization

(WHO) estimates that 20% of the world's population has inadequate

access to drinking water. Although over two-thirds of the planet is

covered with water, 99.3% of the total water is either too salty (sea-

water) or inaccessible (ice caps). Since water is potable only when

it contains less than 500 ppm of salt, much research has gone intonding efcient methods of removing salt from seawater and brack-

ish water. These are called desalination processes. Desalination of

seawater is a promising alternative to compensate for the shortage

of drinking water. Generally, desalination can be accomplished

using a number of techniques. These may be classied under the fol-

lowing categories:Thermal processes that involve phase change such

as Multi-Effect Distillation (MED) and Multi Stage Flash (MSF). Mem-

brane processes that do not involve phase change such as Reverse

Osmosis (RO) and electro dialysis (ED).Hybrid process that involve

bothmembraneand phase change such as membrane distillation (MD).

The thermal desalination processes depend on the evaporation of

water by the addition of heat provided by the sun or by combustion

processes, this was one of mankind's earliest forms of water treat-

ment and is still a popular treatment solution. On the other hand,

the development of modern polymeric materials in recent years has

led to the production of membranes which allow the selective

passage of water in liquid or vapor state or ions and thus providing

the basis for membrane desalination processes. Among those mem-

brane processes, RO is the leading commercial membrane desalina-tion process which requires applying high pressure to overcome the

osmotic pressure.

It is worth mentioning that both, thermal and RO are the leading

desalination processes in the water market[1]. However, those pro-

cesses suffer from drawbacks and some technical difculties which

are: i) They are considered energy intensive either by the heat demand

(i.e. thermal processes) or by the high pressure demand as in reverse

osmosis process, this high energy consumption generates more pollut-

ants and undesired emissions. ii) The scaling and fouling problem is one

of the major challenges that adds to the complexity and cost of those

processes. iii) The membrane cost and its durability in the membrane

processes are still immature subjects that require more research and

development.

These drawbacks affected the economic feasibility of those pro-

cesses, which necessitates the search for alternative, environment

friendly and sustainable desalination.

Membrane distillation (MD) is a promising new comer to the

desalination processes which can be coupled to low-grade and renew-

able energy source such as wind and solar energy.

The developments in the use of renewable energy sources (RES)

have demonstrated that it is ideally suited for desalination, when

the demand of fresh water is not too large. The rapid escalation in

the costs of fuels has made the RES alternative more attractive. In cer-

tain remote arid regions, this may be the only alternative.

The interdependence of water and energy is increasingly evident

due to their territorial, environmental and economic implications.

Desalination 308 (2013) 186197

Corresponding author.

E-mail addresses:[email protected](M.R. Qtaishat),[email protected]

(F. Banat).

0011-9164/$ see front matter 2012 Elsevier B.V. All rights reserved.

doi:10.1016/j.desal.2012.01.021

Contents lists available at SciVerse ScienceDirect

Desalination

j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / d e s a l
http://dx.doi.org/10.1016/j.desal.2012.01.021http://dx.doi.org/10.1016/j.desal.2012.01.021http://dx.doi.org/10.1016/j.desal.2012.01.021mailto:[email protected]:[email protected]://dx.doi.org/10.1016/j.desal.2012.01.021http://www.sciencedirect.com/science/journal/00119164http://www.sciencedirect.com/science/journal/00119164http://dx.doi.org/10.1016/j.desal.2012.01.021mailto:[email protected]:[email protected]://dx.doi.org/10.1016/j.desal.2012.01.021


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Innovations in the area of energy supply can improve the economic

viability of prospective desalination plants considerably. Recently,

considerable attention has been given to the use of renewable energy

including solar, wind and geothermal as sources for desalination,

especially in remote areas and islands, because of the high costs of

fossil fuels.

Solar energy can be used for seawater desalination either by produc-

ing the thermal energy required to drive the phase-change processes or

by producing the electricity required to drive the membrane processes.It should be claried that membrane distillation (MD) has not

been yet commercialized for large-scale desalination plant in spite

of its attractive features especially the possibility of coupling to low-

grade source of energy, this is due to the lower ux of MD and

some technical problems such as the membrane wetting. However,

much research has gone into developing new membranes for MD

that overcomes those membrane design drawbacks[26].

MD applications are not limited only to desalination, since lower

operating temperatures have also made membrane distillation attrac-

tive in the food industry where concentrated fruit juices and sugar so-

lutions can be prepared with better avor and color[7], in medical

eld where high temperatures can sterilize biological uids[8], and

in the environmental applications such as removal of benzene and

heavy metals from water[36].

The purpose of this research paper is to provide a state-of-the-art

review on membrane distillation systems associated with solar ener-

gy for seawater and brackish water desalination. This article presents

the membrane distillation principle, congurations, mathematical

models and economic feasibility.

2. Membrane distillation process

Membrane distillation (MD) is a hybrid of thermal distillation and

membrane processes. MD is a relatively new process that is being in-

vestigated worldwide as a low cost and energy saving alternative to

conventional separation processes such as distillation and reverse os-

mosis[26]. Membrane distillation (MD) process is not commercial-

ized yet for large scale industry. The reason behind this is that MDprocessux is lower than the commercialized separation processes.

The principle of membrane distillation is illustrated inFig. 1. Con-

ventionally, membrane distillation (MD) is a thermally driven process

in which a microporous membrane acts as a physical support separat-

ing a warm solution from a cooler chamber, which contains either a

liquid or a gas.

As the process is non-isothermal, vapor molecules (water vapor in

the case of concentrating non-volatile solutes) migrate through the

membrane pores from the high to the low vapor pressure side; that

is, from the warmer to the cooler compartment.

Generally, the transport mechanism of MD can be summarized in

the following steps:

Evaporation of water at the warm feed side of the membrane.

Migration of water vapor through the non-wetted pores.

Condensation of water vapor transported at the permeate side of

the membrane.

2.1. Membrane distillation congurations

Among membrane distillation processes, variation exists as to the

method by which the vapor is recovered once it has migrated through

the membrane. These alternatives are as follows:

2.1.1. Direct contact membrane distillation (DCMD)

DCMD is the oldest and most widely used process, having liquid

phases in direct contact with both sides of the membrane. The vapor

diffusion path is limited to the thickness of the membrane, thereby

reducing mass and heat transfer resistances. Condensation within the

pores is avoided by selecting appropriate temperature differences

across the membrane.

It is worth mentioning that in DCMD conguration the heat losses

by conduction through the membrane matrix is higher than other

conguration due to the existence a continuous contact betweenthe membrane surfaces and the feed (hot) and permeate (cold)

solutions.

2.1.2. Air gap membrane distillation (AGMD)

AGMD has an additional air gap interposed between the mem-

brane and the condensation surface. This gives rise to higher heat

and mass transfer resistances. Although heat loss by conduction is re-

duced, the penalty is ux reduction. The use of an air gap congura-

tion allows larger temperature differences to be applied across the

membrane, which can compensate in part for the greater transfer

resistances.

2.1.3. Vacuum membrane distillation (VMD)

The vapor is withdrawn by applying a vacuum on the permeateside. The permeate-side pressure is lower than the saturation pres-

sure of the evaporating species and the condensation of the permeate

takes place outside the module.

2.1.4. Sweeping gas membrane distillation

The permeating vapor is removed by using an inert gas stream

which passes on the permeate side of the membrane. Condensation

is done externally and involves large volumes of the sweep gas

and vapor stream.Fig. 2shows the different congurations of MD.

2.2. Membrane distillation advantages

The benets of membrane distillation compared to other more

popular separation processes stem from:

100% (theoretical) rejection of ions, macromolecules, colloids, cells

and other non-volatiles;

lower operating temperatures than conventional distillation;

lower operating pressures than conventional pressure-driven

membrane separation processes;

reduced chemical interaction between membrane and process

solution;

less demanding membrane mechanical property requirements;

reduced vaporspaces compared to conventional distillation processes.

The last benet is considered one of the amazing advantages of

MD process, since the large vapor space required in conventional dis-

tillation column is replaced in MD by the pore volume of a micropo-

rous membrane, which is generally of 100m thick.

Membrane

Membrane pores

Feed side

(Hot)

Permeate side

(Cold)

Fig. 1.Principle of membrane distillation.

187M.R. Qtaishat, F. Banat / Desalination 308 (2013) 186197


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Conventional distillation relies on high vapor velocities to provide

intimate vapor-liquid contact while MD employs a hydrophobic mi-

croporous membrane to support a vaporliquid interface.

As a result, MD process equipment can be much smaller, which

translates to saving in terms of footprint, and the required operating

temperatures are much lower, because it is not necessary to heat

the process liquids above their boiling points. Feed temperature in

membrane distillation typically ranged from 60 to 90 C, although

temperature as low as 30 C has been used [16]. Therefore, low-

grade, waste and/or alternative energy sources such as solar and geo-

thermal energy can be coupled with MD systems for a cost efcient,

energy efcient liquid separation system.

2.3. Membrane distillation disadvantages

The main disadvantage of MD process is the drawback of mem-

brane wetting. The wettability of the microporous membranes is a

function of three main factors: the surface tension of the process so-

lution, membrane material and the membrane structure.

To overcome the membrane wetting: the process solution must be

aqueous and sufciently dilute. This limits MD for certain applications

such as desalination, removal of trace volatile organic compounds

from wastewater and concentration of ionic, colloids or other non-

volatile aqueous solutions[9].

2.4. Membrane distillation membrane

As a matter of fact, commercial microporous hydrophobic mem-

branes, made of polypropylene (PP), polyvinylidene uoride (PVDF)

and polytetrauoroethylene (PTFE, Teon), available in capillary or

at-sheet forms, have been used in MD experiments although these

membranes were prepared for microltration purposes[9]. Table 1

summarizes some of the commercial membranes commonly used in

MD processes together with some of their characteristics [9].

Recently, the desired characteristics for MD membranes have been

specied,[10]. As it is well known, a MD membrane must be porous

and hydrophobic, with good thermal stability and excellent chemical

resistance to feed solutions. The characteristics needed for MD mem-

branes are the following:

2.4.1. High liquid entry pressure (LEP)

This is the minimum hydrostatic pressure that must be applied

onto the liquid feed solution before it overcomes the hydrophobic

forces of the membrane and penetrates into the membrane pores.

LEPis characteristic of each membrane and permits to prevent wetting

of the membrane pores. HighLEPmay be achieved using a membrane

material with high hydrophobicity (i.e. large water contact angle) and

a small maximum pore size. However, as the maximum pore size

decreases, the mean pore size of the membrane decreases and the

permeability of the membrane becomes low.

2.4.2. High permeabilityThe MD ux will increase with an increase in the membrane

pore size and porosity, and with a decrease of the membrane thick-

ness and pore tortuosity. In other words, to obtain a high MD perme-

ability, the surface layer that governs the membrane transport must

be as thin as possible and its surface porosity as well as pore size

must be as large as possible.

In fact, the relationship between the membrane pore size and the

mean free path of migrating molecules determines the dominant dif-

fusion mechanism. In MD, air is trapped within the membrane pores

with pressure values close to the atmospheric pressure if no vacuum

SGMD

Feed in

Vacuum pump

membrane

Feed out

Permeate

Condenser

VMD AGMD

Feed in

Sweep gas outmembrane

Feed out Sweep gas in

Product

Condenser

DCMD

Feed inLiquid

permeate out

membrane

Feed outLiquid

permeate in

Feed in Coolant out

membrane

Feed out Coolant in

Air gap

Condensing

plate

Product

Fig. 2.Membrane distillation congurations.

Table 1Some commercial membranes commonly used in membrane distillation.

Membrane Manufacturer Material Thickness

(m)

Average pore

size (m)

Porosity

(%)Trade name

TF200 0.20

TF450 Gelman PTFE/PPa 178 0.45 80

TF1000 1.00

GVHP Millipore PVDFb 110 0.22 75

HVHP 140 0.45

S6/2 AkzoNobel PPc 450 0.2 70

MD020CP2N Microdyn

a Flat-sheet polytetrauoroethylene membranes supported by polypopylene net.b Flat-sheet polyvinylidene uoride membranes.c Polypropylene capillary membrane: number of capillaries in a membrane module:

40; effective ltration area: 0.1 m2, inner capillary diameter: 1.8 mm; length of capil-

laries: 470 mm.

188 M.R. Qtaishat, F. Banat / Desalination 308 (2013) 186197


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is applied vapor permeates through the porous membrane, as a result

of molecular diffusion, Knudsen ow and/or the transition between

them[26]. The calculated MD ux considering Knudsen mechanism

is higher than that considering the combined Knudsen/molecular dif-

fusion mechanism.

2.4.3. Low thermal conductivity

In MD heat loss by conduction occurs through both the pores and

the matrix of the membrane. The conductive heat loss is greater forthinner membranes. Various possibilities may be applied to diminish

the conductive heat loss by using:

i) Membrane materials with low thermal conductivities. This

does not necessarily guarantee the improvement of the MD

process because most hydrophobic polymers have similar

heat conductivities; at least the materials have thermal con-

ductivities with the same order of magnitude.

ii) Membranes with high porosity, since the conductive heat

transfer coefcient of the gas entrapped within the membrane

pores is an order of magnitude smaller than that of the mem-

brane matrix. This possibility is parallel to the need of high

DCMD permeability as the available surface area of evaporation

is enhanced.

iii) Thicker membranes. However, there is a conict between therequirements of high mass transfer associated with thinner

membranes and low conductive heat transfer through the

membrane obtained by using thicker membranes.

MD can be commercialized for large scale industry if the above

listed membrane requirements are satised, as a result, in recent

years, the MD research attention has gone into preparing membranes

specically for the MD applications. For example, Fang et al. 2004

[11], prepared asymmetric at-sheet membranes from poly (vinyli-

dene uoride-co-tetrauoroethylene) by the phase inversion meth-

od. Those membranes were tested by DCMD conguration and the

results were compared to PVDF at-sheet membranes prepared by

the same procedure. Their new membranes exhibited higher ux

than those of the PVDF membranes. They also prepared membranes

from poly(vinylidene uoride-co-hexauoro propylene) [12] andfound that the DCMD performance of these membranes was better

than that of the PVDF membrane. Li and Sirkar 2005 [13]and Song

et al. 2007[14], designed novel hollow ber membrane and device

for desalination by VMD and DCMD. The membranes were commer-

cial polypropylene (PP) membranes coated with plasma polymerized

silicone uoropolymer. Permeate uxes as high as 71 kg/m2.h were

achieved. Bonyadi and Chung 2007[15], used the co-extrusion method

to prepare dual layerhydrophilic/hydrophobichollow ber membranes

for MD. PVDF was used as a host polymer in the dope solution, where

hydrophobic and hydrophilic surfactants were added. A ux as high as

55 kg/m2.h was achieved using DCMD conguration.

In a series of publications, Qtaishat et al. 2009 and 2010 [1621],

presented the concept of hydrophobic/hydrophilic composite mem-

branes for MD. It was shown that this type of membranes satisesall the requirements of higher ux MD membranes as mentioned ear-

lier. Since the very thin hydrophobic layer is responsible for the mass

transfer, on the other hand the thick hydrophilic layer, the pores of

which are lled with water, will contribute to preventing the heat

loss through the overall membrane.

The hydrophobic/hydrophilic membrane was prepared by phase

inversion method in a single casting step. A hydrophobic surface

modifying macromolecules (SMMs) was blended with a hydrophilic

base polymer. During the casting step, the SMMs migrated to the

air/polymer interface since they have lower surface energy. Conse-

quently, the membrane top-layer becomes hydrophobic while the

bottom layer becomes hydrophilic. These membrane were proved to

be workable membranes in MD, furthermore, their ux data were

much higher than the commercial PTFE membranes.

3. Heat and mass transfer membrane distillation

In MD, the driving force for water vapor migration through the

membrane pores is the temperature difference between the feed/

membrane interface temperature (Tmf) and the permeate/membrane

interface temperature (Tmp). Due to the heat losses in MD process, the

membrane/interface temperatures are different from the bulk tem-

peratures. This could be considered as one of the MD process draw-

backs. This temperature difference leads to a decrease from thetheoretical driving force, which is dened as the difference between

the bulk feed temperature (Tbf) and the bulk permeate temperature

(Tbp). This phenomenon is known as temperature polarization. The

temperature polarization coefcient (TPC) is dened as the ratio be-

tween the actual driving force and the theoretical driving force[22];

as a result the temperature polarization coefcient is expressed

mathematically as the following:

TP CTmfTmpTbfTbp

: 1

It is impossible to measure the membrane/interface temperatures

experimentally; usually these temperatures are evaluated by per-

forming a heat balance that relates them to the bulk temperatures

[22]. In order to solve this heat balance for membrane interface tem-

peratures, the heat transfer coefcients in the adjoining liquid bound-

ary layers to the membrane should be evaluated. Generally, the

boundary layer heat transfer coefcients are evaluated using empiri-

cal correlations for the determination of Nusselt number, and a wide

variety of these correlations is shown inTable 2[22]. It is worth men-

tioning that each shown empirical correlation is valid for certain ow

regime and module geometry. In a recent article, Qtaishat et al. [23]

solved the heat balance and evaluated experimentally the membrane

surface temperatures via applying different empirical correlation that

takes into account the temperature variation effect on the physical

properties of both feed and permeate solutions.

3.1. Heat transfer

The following heat transfer analysis considers the DCMD congu-

ration; however the same analysis could be applied to other MD con-

guration with some modications. In DCMD, the heat transfer can be

divided into three regions as shown inFig. 3; that are: (i) heat trans-

fer in the feed boundary layer, Qf; (ii) Combination of both conductive

heat transfer through the membrane and heat transferred because of

water vapor migration through the membrane pores, Qf; (iii) heat

transfer in the thermal permeate boundary layer,Qp.

Table 2

Empirical correlations for evaluating Nusselt number in MD.

Empirical correlation[22] Flow regime

Nu 1:86 RePr 1

3= Laminar

Nu = 3.66 Laminar

Nu = 4.36 Laminar

Nu =0.097Re0.73Pr0.13 Laminar

Nu 1:95 RePr 1

3= Laminar

Nu 0:13Re0:64 Pr1

3= Laminar

Nu 0:023Re0:8Pr1

3= Turbulent

Nu 0:036Re0:8Pr1

3= Turbulent

Nu 0:027Re0:8Prc bfmf

0:14Turbulent

Nua f=8 RePr1:0712:7 f=8

12= Pr

23=1

Turbulent

Nua f=8 Re1000 Pr112:7 f=8

12= Pr

23= 1

Turbulent

aThe friction factor, f, in these correlation was estimated by:

f=(0.79 ln(Re)

1.64)2

.



5/12

These heat transfer mechanisms can be expressed mathematically

as follows:

Through the feed solution thermal boundary layer:

Qf hf TbfTmf

: 2

Through the membrane:

Qm hm TmfTmp

JwHv: 3

Through the permeate solution thermal boundary layer:

Qp hp TmpTbp

: 4

In the above equations,hfis the feed boundary layer heat transfercoefcient, hp is the permeate boundary layer heat transfer coef-

cient.Jwis the permeate ux,TmfandTmpare the membrane/feed in-

terface temperature and membrane/permeate interface temperature,

respectively.Hv is the latent heat of vaporization, hm is the heat

transfer coefcient of the hydrophobic membrane, which can be cal-

culated from the thermal conductivities of the hydrophobic mem-

brane polymer (km) and air trapped inside the membrane pores (kg).

hmkgkm 1

5

where and are the thickness and porosity of the hydrophobic

membrane, respectively.The evaporation efciency,EE, is dened as the ratio between the

heat transferred because of water vapor migration through the mem-

brane pores and the total heat transferred through the membrane

[22]. Mathematically, the evaporation efciency is expressed by

EEQm;M:T

Qm;M:T Qm;cond

JwHv

JwHvhm TmfTmp

: 6

At steady state, the overall heat transfer ux through the whole

DCMD system, Q, is given by

Qf

Qm

Qp

Q: 7

Combining Eqs.(2)(4), the heat ux can be written as follows:

Q 1

hf

1

hm JwHvTmfTmp

1

hp

0@

1A1

TbfTbp

: 8

As a result, the overall heat transfer coefcient (U) for the DCMD

process may be written as:

U 1

hf

1

hm JwHvTmfTmp

1

hp

0@

1A1: 9

3.2. Mass transfer

In MD process, the mass transport is usually described by assum-

ing a linear relationship between the mass ux (Jw) and the water

vapor pressure difference through the membrane distillation coef-

cient (Bm)[22]:

Jw Bm pmfpmp

10

wherepmfand pmpare the partial pressures of water at the feed andpermeate sides evaluated by using Antoine equation at the tempera-

turesTmfandTmp, respectively; such as the following

Pv

exp 23:3283841

T45

: 11

where Pv is the water vapor pressure in Pascal and T is the corre-

sponding temperature in Kelvin. However, the water vapor pressure

decreases with increasing the salt concentration in the feed water

according to Raoult's law as follows[9]:

Pvi 1xi P

v12

wherexiis the weight fraction of salt in water.

Various types of mechanisms have been proposed for transportof gasses or vapors through porous membranes: Knudsen model, vis-

cous model, ordinary-diffusion model, and/or the combination there-

of. The governing quantity that provides a guideline in determining

which mechanism is operative under a given experimental condition

is the Knudsen number,Kn, dened as the ratio of the mean free path

() of the transported molecules to the pore size (diameter, d) of the

membrane; i.e.Kn =/d.

In MD, mass transport across the membrane occurs in three regions

depending on the pore size and the mean free path of the transferring

species[22]: Knudsen region, continuum region (or ordinary-diffusion

region) and transition region(or combined Knudsen/ordinary-diffusion

region). If the mean free path of transporting water moleculesis large in

relation with the membrane pore size (i.e.Kn >1 orrb0.5, whereris

pore radius), the molecule-pore wall collisions are dominant over themoleculemolecule collisions and Knudsen typeofowwill be the pre-

vailing mechanism that describes the water vapor migration through

the membrane pores. In this case, the net MD membrane permeability

can be expressed as follows.

BKm

2

3

r

8M

RT

1=2

13

Where , , r, are the porosity, pore tortuosity, pore radius and

thickness of the hydrophobic membrane, respectively; Mis the mo-

lecular weight of water, R is the gas constant and Tis the absolute

temperature. The pore tortuosity is usually in the range of 12. How-

ever, it cannot be measured experimentally directly. It is possible to

evaluate the effective porosity per effective unit length of the

Tb,f

Permeate

boundary

layer

Hydrophobic

membrane

Dry pore

Heat and mass

fluxes

Tb,p

Tm,f

Jw

Feed in

Mf, inTbf, in

Feed out

Mf, outTbf, out

Permeate in

Mp, inTbp, in

Permeate out

Mp, outTbp, out

Feed

boundary

layer

Tm,p

Fig. 3.Heat and mass transfer in DCMD.



6/12

membrane (/) by performing the gas permeation test that is de-

tailed elsewhere[9].

In MD process, air is always entrapped within the membrane

pores with pressure values close to the atmospheric pressure. There-

fore, ifKnb0.01 (i.e.r> 50), molecular diffusion is used to describe

the mass transport in continuum region caused by the virtually stag-

nant air trapped within each membrane pore due to the low solubility

of air in water. In this case the following relationship can be used for

the net DCMD membrane permeability.

BDm

PD

Pa

M

RT 14

WherePais the air pressure (assumed to be 1 atm), Pis the total

pressure inside the pore assumed constant and equal to the sum of

the partial pressures of air and water liquid, and D is the water diffu-

sion coefcient. The value ofPD(Pa m2/s) for waterair can be calcu-

lated from the following expression[9,22].

PD 1:895105

T2:072

15

Finally, in the transition region, 0.01bKnb1 (i.e. 0.5brb50),

the molecules of water liquid collide with each other and diffuse

among the air molecules. In this case, the mass transport takesplace via the combined Knudsen/ordinary-diffusion mechanism

and the following equation is used to determine the water liquid

permeability[22].

BCm

3

2

r

RT

8M

1=2

PaPD

RT

M

1

16

4. Solar collecting technologies coupled with membrane

distillation

Solar collectors can be used to provide the heat (Solar Thermal) or

electrical energy (Solar Photovoltaic) requirements to operate a

membrane distillation system. The main solar technologies thatcould be coupled with membrane distillation are briey reviewed

below.

4.1. Solar photovoltaic

Photovoltaic (PV) cells are key components of PV applications that

convert solar energy into electricity through the transfer of electrons.

PV can be thought as a direct current (DC) generator powered by the

sun. At present, there are three generations of PV cells: crystalline sil-

icon (c-Si) technologies (1st generation), amorphous silicon thin-lm

(TF) technologies (2nd generation) and Nano-PV technologies (3rd

generation). Crystalline silicon are mature and reliable technologies

currently dominating the PV market (about 82% of global cell produc-

tion in 2009)[23]. The conversion efciency of c-Si lies between 15%and 18%[24]. The TF technologies are currently the main alternative

to c-Si (17% market share in 2009) [23]. In addition, thin lm (TF)

PV technologies are presently the lowest-cost to manufacture. The

production cost of cadmium telluride (CdTe) thin lm module is cur-

rently the least; $0.76/Wp[23]. However, scarcity of key component

materials has been highlighted as a potential barrier to both large

scale deployment and reductions in TF technology cost. In particular,

major concerns have been raised for indium and tellurium availability

and potential risks for the TF PV technologies that utilize them, i.e.

cadmium telluride (CdTe) and copper indium gallium (di) selenide

(CIGS)[28].

The photovoltaic cell photo current is directly proportional to the

solar intensity. The performance of the solar cell depends on the cell

temperature. Solar cells work best at low temperatures, as

determined by their material properties. All cell materials lose ef-

ciency as the operating temperature rises. The high temperature has

negative effect on the electrical output of the PV module, especially

the dominant crystalline Si based cells, where their conversion ef-

ciency degrades by about 0.40.5% per degree rise in temperature

[25]. Tan et al. [26]performed high temperaturehumidity tests on

performance degradation of PV cells. It was found that the degrada-

tion is directly related to the passivation integrity, and the inception

of moisture causes a signi

cant degradation in the short circuit cur-rent and maximum power output.

The tracking at PV system is one of the methods to increase the

PV power generation. The increase of solar energy capture due to

sun tracking is region by region depending on the local meteorologi-

cal conditions. Abu-Khader et al. [27]performed an experimental in-

vestigation on the effect of using two-axis sun-tracking systems on

the electrical generation of a at photovoltaic system to evaluate its

performance under Jordanian climate. It was experimentally found

that there was an increase of about 3045% in the output power for

the NorthSouth axes-tracking system compared to the xed one.

PV electricity generation costs currently lies between 0.24 and

$0.72/kWh, according to the system type and the solar irradiation.

Such costs are expected to descend to the $0.130.31/kWh range

[29].

Power conditioning equipment (e.g. charge controller, inverters)

and energy storage batteries may be required to supply energy to a

desalination plant. Charge controllers are used for the protection of

the battery from overcharging. Inverters are used to convert the di-

rect current from the photovoltaic module system to alternating cur-

rent. The electricity produced can be used to power pumps for

desalination, mostly for membrane technologies. The photovoltaic

technology connected to a reverse osmosis (RO) system is commer-

cial nowadays. However, the high cost of PV cells is still one of the

major challenges facing the widespread use of this technology.

4.2. Solar thermal

Solar collectors are well-known devices which are usually used to

absorb and transfer solar energy into a collection uid. The thermalenergy can be achieved in solar stills, collectors, or solar ponds.

Solar collectors are usually classied according to the temperature

level reached by the thermal uid in the collectors (Table 3) [29].

Low temperature collectors are those operating in the range below

80 C while medium temperature collectors are those operating in

the range from 80 to 250 C. Low temperature collectors provide

low-grade heat that is not useful to serve as a heat source for conven-

tional desalination distillation processes but is of interest for mem-

brane distillation process. Medium temperature collectors can be

used to provide heat for thermal desalination processes by indirect

heating with a heat exchanger. Evacuated tube collectors produce

temperatures of up to 200 C and thus can be used as an energy

source for thermal desalination processes [30].

High temperature collectors such as parabolic troughs or dishes orcentral receiver systems can concentrate the incoming solar radiation

onto a focal point, from which a receiver collects the energy using a

heat transfer uid. The high thermal energy content can be used di-

rectly in thermal desalination processes or can be used to generate

electricity using a steam turbine. Sun tracking can improve the collec-

tor efciency. Large-scale desalination applications require large col-

lector areas.

A solar pond is a body of liquid which collects solar energy by ab-

sorbing direct and diffuse sunlight and stores it as a heat. Salt gradient

solar ponds (SGSP) rely on a salt solution (the salts most commonly

used are NaCl and MgCl2) of increasing concentration with depth to

suppress natural convection. Warm concentrated brine at the bottom

of the pond is prevented from rising to the surface and losing its heat

because the upper portion of the pond contains less salt and is,



7/12

therefore, less dense than the lower portion. Whereas the top tem-

perature is close to ambient, a temperature of 90 C can be reached

at the bottom of the pond where the salt concentration is highest. A

typical prole of density and temperature within a solar pond is

shown inFig. 4. Heat is extracted by passing the brine from the stor-

age zone through an external heat exchanger. This heat can be used in

a special organic-uid turbine to generate electricity, provide energy

for desalination, and to supply energy for space heating in buildings.

Solar ponds have large storage capacity allowing seasonal as well as

diurnal thermal energy storage. The annual collection efciency of

useful heat for desalination is around1015%. Larger ponds tend to

be more efcient than smaller ones due to losses at the pond edge.

Solar ponds are particularly suitable for desalination plants as waste

brine from desalination can be used as the salt source for the solar

pond density gradient. Using desalination brine for solar ponds not

only provides a preferable alternative to environmental disposal,

but also a convenient and inexpensive source of solar pond salinity.

Gracia-Roderiquez (2002)[21]reported that solar pond-powered de-

salination is one of the most cost-effective methods.

Many projects are currently under preparation to make possible

large concentrating solar power (CSP) plant developments in arid re-

gions, such as the Shams 1 solar power station initiative. The Shams 1CSP will feature 768 parabolic trough collectors over 6,300,000 ft2 of

land. Shams 1's parabolic trough collectors collect sunlight and con-

vert it into thermal energy. The Shams solar power station is being

built in the city of Madinat Zayed, located 120 km south west of

Abu Dhabi, in the United Arab Emirates (UAE). Construction of

phase 1 of the solar project, Shams 1, commenced in July 2010 and

is expected to be completed by 2012. Upon completion, Shams 1

will be the rst solar farm in the Middle East and the largest concen-

trated solar power (CSP) plant in the world. The project is estimated

to cost $600 m[31].

Palenzuela et al. [32]considered the combination of desalination

technology into concentrating solar power (CSP) plants for the

planned installation of CSP plants in arid regions. The authors pre-

sented a thermodynamic evaluation of different congurations for

coupling parabolic-trough (PT) solar power plants and desalination

facilities in Abu Dhabi as a case for dry locations in the Middle East

and North Africa (MENA) region.

Since solar insolation is intermittent, a thermal energy storage sys-

tem should be incorporated to run the desalination process round theclock. One of the solutions to utilize uctuating solar energy on a con-

tinuous basis is to incorporate thermal energy storage (TES) system.

Three types of TES systems are in commercial use; (1) sensible heat

storage, (2) latent heat storage, and (3) thermo chemical storage sys-

tems. Themost widely used TES is the sensible heatstorage system [33].

4.3. Performance parameters in SPMD

The gained output ratio (GOR) and the thermal recovery ratio

(TRR) of the system are the most important performance parameters

used in thermal desalination processes as well as in solar powered

membrane distillation processes. The GOR is the ratio of thermal en-

ergy required to produce distillate water to the actual thermal energy

consumed in the feed side. Mathematically, the GOR is calculated

from:

GOR mdHv

mhCp ThiTho 17

wheremdis the distillate ow rate (kg/h), the latent heat of vapor-

ization (J/kg),mhthe feed ow rate (kg/h), Cp the feed specic heat

(J/kg K), Thi, Tho the feed temperatures (in K) at the module inlet

and outlet.

The TRR is the theoretical energy needed for distillate produced

divided by the total thermal energy input. In the SPMD, the total ther-

mal energy input is the solar energy incident on the solar collector. As

such, the TRR can be de

ned as:

TRR mdHv

AI 18

whereAis the solar collector area (m2), andIis the global irradiation

(W/m2). TheTRR of a SPMD plant is measure of its efciency to pro-

duce distillate.

5. Coupling membrane distillation with solar energy collectors

Coupling membrane distillation modules with solar energy collec-

tors has been of interest for many researchers over the world because

MD can tolerate uctuating and intermittent operating conditions as

well as it requires low grade thermal energy. Two alternative cong-urations of coupling solar energy with MD are illustrated in Fig. 5.

The solar-assisted MD desalination system (Fig. 5a) comprises solar

thermal collectors which feeds hot water to the MD module. The

heat is supplied to the MD module either directly or through a heat

exchanger. Electricity needed is either supplied from the electric

grid or from an auxiliary diesel generator to drive all pumps and

other electrically powered devices. The solar stand-alone MD desali-

nation system (Fig. 5b) is similar to the solar-assisted MD desalina-

tion system in all aspects except that solar powered PV collectors

integrated with direct current (DC) battery cells and electric current

inverters are used instead of the diesel generator to supply the neces-

sary electricity. Membrane distillation modules were coupled withat plate collectors, vacuum collectors, solar ponds, solar stills, and

parabolic troughs as detailed below.

Table 3

Solar energy collectors[29].

Collector type Concentration

ratio

Typical temperature

range (C)

Tracking

Solar pond 1 50100 No

Flat plate (FPC) 1 3080 No

Improvedat plate (IFPC) 1 80120 No

Evacuated tube (ETC) 1 50190 No

Compound Parabolic

Collectors (CPC)

15 70240 No

Par ab olic tr ou gh (PTC ) 1 540 70400 Single axis

Linear Fresnel (LFC) 1540 70290 Single axis

Parabolic dish reector (PDR) 1001000 70930 Two axes

Central receiver 1001500 1302700 Two axes

Fig. 4.Typical salt gradient solar pond.



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5.1. Coupling with vacuum orat plate collectors

The rst publication in this eld came from Australia where Hogan

et al. [34] from the University of New South Wales described a

0.05 m3/day system using a 3 m2 at plate solar collectors. Hollowber membrane distillation module with heat recovery was used

in their study. The authors reported that the thermal and electrical

energy consumption was 55.6 kWh/m3. The calculated ux of 17 li-

ters per day per square meter of collector area was comparable tothat reported for solar MSF and ME plants.

As reported by Thomas[35]a solar-powered membrane distilla-

tion system was installed by the Water Re-use Promotion Center in

Tokyo, Japan, in 1994. Flat plate module and a 12 m2 eld of vacuum

tube collectors were used. Automatic controls start up the desalina-

tion system whenever sufcient sunlight is present to provide hot

water and electricity for pumping from the solar collectors and PV

panels. The plant had a maximum productivity of 40 liters per hour.

Four autonomous solar-powered membrane distillation plants

were developed through SMADES EU-funded project [36]. First a

so-called compact system was designed and tested to generate

process parameters for the design of the so-called large system.

Three compact systems were installed in Jordan, Morocco, and

Egypt. The compact system is simple one loop desalination designed

to produce about 100 l of distilled water per day. As such, no thermal

heat storage tanks, no electrical storage (battery), no complex but a

simple and reliable control was needed. The main components of the

system are: two at-plate solar collectors with a corrosion-free ab-

sorber that can directly be used to heat up the salty water, one spiral

wound membrane distillation module with heat recovery, feed

pumps, PV module with a DC/AC converter, and feed and distillate

storage tanks (Fig. 6). One of the compact units was installed in

the city of Irbid in northern Jordan in August 2005 and fed with

brackish water[37,38]. The key design data of the compact system

are listed in Table 4. The distillate ow rate was about 120 liters

per day during the summer months, and about 50 liters per day dur-

ing the cloudy winter days. The distillate conductivity was less than

600S/cm.

The large system was installed in the city of Aqaba on the Red Sea

coast and fed with untreated seawater in February 2006 [37,38].The

system consists of two loops. The desalination loop is operated with

seawater and is separated from the collector loop (operated with

tap water) by a titanium corrosion resistant heat exchanger. Thisarrangement allows for the use of economic standard components

in the solar collector without the need of cost-intensive corrosion

resistant materials. Four spiral wound membrane distillation modules

exactly the same as those used in the compact systems were operated

in parallel. A schematic of the setup is shown in Fig. 7. The design

capacity of the Aqaba system was 1 m3/day. The key design data of

this system are listed inTable 5.

A DC/AC converter was used to convert 24 VDC delivered from the

batteries into 230 V AC. The capacity of the battery storage was

300 Ah. A thermal heat storage vessel was used to store the surplus

energy in order to be used whenever sufcient solar radiation is not

available. Due to natural uctuations of solar radiation and tempera-

ture, the water production rate and energy requirements uctuated

between 600 and 800 liter per day and 200 and 250 kWh/m3,

respectively.

During the rst month of operation (February 2006), the quality of

produced distillate was very good with a conductivity of less than

10S/cm. In March 2006, an increase in the distillate conductivity

was noticed. After a thorough evaluation, it was decided to remove

the deteriorated module and to operate the system with three mem-

brane modules instead of four. The ux obtained varied between 2

and 11 liters per day per meter squared of collector area.

Experimental results from the large system showed a gradual de-

cline of the permeate ux and quality during the rstve months of

operation. Heating of seawater to temperatures up to 80 C caused

scale deposit on the membrane surface. Cleaning the membrane

with dilute formic acid resulted in the dissolution of the deposit on

the membrane surface, and the initial membrane permeability was

restored[39]. Nevertheless, the information related to the membranedurability in membrane distillation (MD) is still immature. It is docu-

mented that the membrane wetting and the scale deposition on the

membrane surface are the most serious problems that make the

membrane unworkable in MD [4]. However, there are many mem-

brane designers considered designing the membranes to avoid or

minimize those drawback effects. Their results were very promising

[1321].

Wang et al. [40] has recently described the performance of a

solar-heated hollowber vacuum membrane distillation (VMD) sys-

tem for potable water production from underground water. The

Fig. 5.Solar-assisted (a) and stand-alone (b) desalination systems.

Solarcollector

PVDistillate

PV module

Feedtank

Over flow

Background

container

Refilling pump

Solarirradiation

Feedpump

MDmodule

Fig. 6.Schematic drawing of the compact system (one loop desalination system).

http://localhost/var/www/apps/conversion/tmp/scratch_3/image%20of%20Fig.%E0%B6%80http://localhost/var/www/apps/conversion/tmp/scratch_3/image%20of%20Fig.%E0%B6%80http://localhost/var/www/apps/conversion/tmp/scratch_3/image%20of%20Fig.%E0%B6%80http://localhost/var/www/apps/conversion/tmp/scratch_3/image%20of%20Fig.%E0%B6%80http://localhost/var/www/apps/conversion/tmp/scratch_3/image%20of%20Fig.%E0%B6%80http://localhost/var/www/apps/conversion/tmp/scratch_3/image%20of%20Fig.%E0%B6%80http://localhost/var/www/apps/conversion/tmp/scratch_3/image%20of%20Fig.%E0%B6%80http://localhost/var/www/apps/conversion/tmp/scratch_3/image%20of%20Fig.%E0%B6%80http://localhost/var/www/apps/conversion/tmp/scratch_3/image%20of%20Fig.%E0%B6%80http://localhost/var/www/apps/conversion/tmp/scratch_3/image%20of%20Fig.%E0%B6%80http://localhost/var/www/apps/conversion/tmp/scratch_3/image%20of%20Fig.%E0%B6%80http://localhost/var/www/apps/conversion/tmp/scratch_3/image%20of%20Fig.%E0%B6%80http://localhost/var/www/apps/conversion/tmp/scratch_3/image%20of%20Fig.%E0%B6%80http://localhost/var/www/apps/conversion/tmp/scratch_3/image%20of%20Fig.%E0%B6%80http://localhost/var/www/apps/conversion/tmp/scratch_3/image%20of%20Fig.%E0%B6%80http://localhost/var/www/apps/conversion/tmp/scratch_3/image%20of%20Fig.%E0%B6%80http://localhost/var/www/apps/conversion/tmp/scratch_3/image%20of%20Fig.%E0%B6%80http://localhost/var/www/apps/conversion/tmp/scratch_3/image%20of%20Fig.%E0%B6%80http://localhost/var/www/apps/conversion/tmp/scratch_3/image%20of%20Fig.%E0%B5%80


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system has fourmajor components, a solar energy collector, a hollow

ber membrane module, a permeation condenser and two mechan-

ical pumps (Fig. 8). The area of the solar energy collector is 8 m2 and

the membrane total area is about 0.09 m2. The membrane is 0.1m

hollow ber membrane made from polypropylene, with the inner

diameter 371 mm, wall thickness 35 mm, and ber operative length

0.14 m. The experiment results showed that the pure water ux of

the system could reach 32.2 kg per hour per square meter mem-

brane area.

The performance of a desalination plant based on coupling an air-

gap membrane distillation module with a solar pond was tested by

Walton et al. [41]. Low grade thermal energy (between 13 and

75 C) was extracted from the pond and supplied via a heat exchanger

to the membrane module. The membrane area was 2.94 m2. The

Swedish rm SCARAB (http://www.hvr.se) has built and supplied

the membrane distillation module in addition to the controlling

pumps and heaters.

As shown inFig. 9, hot brine was pumped from the bottom of the

solar pond and circulated through a heat exchanger to supply heat to

the saline solution. Cold water from the solar pond surface was

passed through another heat exchanger to provide cooling. High

and low temperatures for system operation were obtained by changing

theow rates for solar pond hot and cold water.

The research included measuring the ux per unit area of mem-

brane surface and conductivity of permeate over a range of feed

water salinities and temperature as well as an assessment of mem-

brane fouling. The permeate ux was uctuating and reached a max-

imum of 6 L/m2.h.Theoretical calculations, based upon measured results, indicate

that membrane distillation with latent heat recovery is necessary to

make the process being competitive with other thermal technologies

in terms of energy use. Walton et al. (2004) [41]reported that mem-

brane distillation is only competitive relative to reverse osmosis

when low cost heat energy is available and/or when the water

chemistry of the source water is too difcult for treatment with re-

verse osmosis.

Suareza et al.[42]developed a heat and mass transport model to

evaluate the feasibility of coupling a DCMD module with an SGSP

for sustainable freshwater production in an environment such as

that at Walker Lake. They reported that the coupled DCMD/SGSP

system is capable of providing freshwater for terminal lakes recla-

mation. The coupled system shown inFig. 10was found to produce

water ows on the order of 1.6103 m3 per day per m2 of SGSP

with membrane areas ranging from 1.0 to 1.3103 m2 per m2 of

SGSP.

Mericqa et al. [43]has studied the simulation of coupling VMDwith solar energy to produce distillate from seawater. For this pur-

pose solar collectors (SC) as well as salt gradient solar ponds (SGSP)

were considered. Simulation results showed that VMD/SGSP could

induce marked concentration and temperature polarization phenom-

ena that reduced uxes because of the difculty to create turbulence

in the feed seawater when SGSP are used. Using the combination of

VMD/SC was more practical, as they concluded.

5.2. Coupling with parabolic trough collectors

Within the frame of MEDESOL (Seawater Desalination by Innova-

tive Solar-Powered Membrane Distillation System) project the tech-

nical feasibility of producing fresh water from seawater by

integrating several MD modules (a multi-stage MD system) for a ca-pacity range 0.550 m3/d will be evaluated. The heat source of the

process will be from an advanced compound parabolic solar concen-

trator, especially developed to achieve the specic needed range of

temperatures. The seawater heater will include the development of

an advanced non-fouling surface coating, as reported by Glvez et

al. (2009)[44].

Table 4

Specications of the compact system.

Compact system

Plant capacity (Average) 100 l/day

Membrane area 10 m2

Solar collectors area 5.73 m2

PV-module 106 Wp

Battery

Collector

tank

Brine

unit

Solar

irradiation

PV

Control

AC

Storage

PV array

Heatexchanger

Feed

pump

PV

MD modulesDistillate

Expansionvessel

DC

feild

Fig. 7.Schematic drawing of the large system (two loop desalination system).

Table 5

Specications of the large unit.

Design capacity (m3/day) 1

Collector area (m2) 72

Collector type Flat plate

Heat storage capacity (m3) 3

Number of membrane modules 4

PV (kWp) 1.44

PV area (m2) 14

http://www.hvr.se/http://www.hvr.se/


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5.3. Coupling with solar stills

Banat et al.[45]described a solar still-membrane distillation inte-

grated system operated with articial seawater. Hot water from the

still was circulated into a tubular membrane distillation module be-

fore being returned back to the still. As such, distilled water was pro-

duced from both the solar still and the membrane distillation module.

The ux of the MD module was four times higher than the ux

obtained from the solar still.

6. Availability and cost

Solar energy can be harnessed for MD desalination by producing

the thermal energy required to drive the evaporation and by produc-ing the electricity required to drive the pumps. The main energy re-

quirement for membrane distillation is thermal energy. Electricity

demand is low and is used for auxiliary services such as pumps, sen-

sors, controllers etc However, the high cost of PV modules and to

less extent the high cost of solar collectors hinders the use of solar en-

ergy on wide scale. Capital costs of MD modules and corrosion resis-

tant heat exchangers are important also. At present, no commercial

MD modules are available and researchers either use modules

designed for other membrane separations or design and build their

specic modules. Therefore, it is difcult to conclude if the SPMD pro-

cess is really competitive with other solar driven conventional desali-

nation processes.

Very few studies on the cost of solar powered MD desalination

plants have been reported in literature. Kullab and Martin[46]have

presented the cost for a scaled-up solar powered air gap membrane

distillation. Evacuated tube solar collectors were used to supply the

thermal energy. For a yearly production of 24,000 m 3 of pure water,

the cost of water production was estimated at 8.9$/m3. Around 70%

of this cost was associated with the solar collectors. Banat and Jwaied

[47]estimated the cost of potable water produced by the stand-alone

compact unit to be 15$/m3 and 18$/m3 for water produced by the

large unit. The authors pointed out that membrane lifetime andplant lifetime are key factors in determining the water production

cost. The cost decreases with increasing the membrane and/or plant

lifetime.

Integrating solar power and membrane distillation desalination

plants is not yet a straightforward issue and many technological as-

pects remain to be discussed. Large seawater SPMD desalination

plants need, obviously, facilities to be located near the sea, where

land cost and availability could be a signicant problem. Furthermore,

Fig. 8.Flow sheet of the solar-heated MD system for producing potable water.

Fig. 9.Flow schematic of SPMD[41].

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the solar direct normal irradiance (DNI) is normally lower on areas

close to the sea, which makes concentrating solar power (CSP) plants

most optimal locations to be separated from the coast. Other thermal

desalination technologies such as MED or MSF could also be coupled

with membrane distillation to minimize the production cost. To an-

swer all of these issues, techno-economic analysis is needed to dene

the best schemes of the integration of a membrane distillation with

solar energy.

7. Summary

Several small and lab scale plants for MD desalination using solar

energy have recently been tested. The process is deemed suitable to

operate in conjunction with solar energy for small capacities. The

main cost is in the initial investment. However, once the system is op-

erational, it is extremely inexpensive to maintain and the energy has

minimal or even no cost. The availability and cost of MD modules is

still a serious and important issue. People not only in remote regions

but also in urban areas will benet if low cost stand-alone MD

systems are developed commercially.

Nomenclature

SymbolsA Solar collector area (m2)

Bm net DCMD permeability (s/m)

d mean pore size (nm)

D water diffusion coefcient (m2 s1)

EE evaporation efciency

f the friction factor

GOR The gained output ratio

h heat transfer coefcient (W m2 K1)

H Enthalpy (J/kg)

I Global irradiation (W/m2)

Jw DCMD ux (m/s)

k thermal conductivity (w m1 K1)

Kn Knudsen number

Nu Nusselt numberM molecular weight of water (kg mol1)

md Distillate ow rate (kg/h)

mh Feed ow rate (kg/h)

p liquid pressure (Pa)

Pv vapor pressure of water (Pa)

P total pressure (Pa)

Pa air pressure (Pa)

Pr Prandtl number

Q heat ux (W m2)T absolute temperature (K)

TPC Temperature polarization coefcient

TRR The thermal recovery ratio

r mean pore radius (nm)

R gas constant (J mol1

K1

)

Re Reynolds number

xi solute mole fraction

Greek letters

total membrane thickness (m)

porosity (%) Density (kg/m3)

mean free path (nm)

water dynamic viscosity (kg m1 s1)

tortousityHv latent heat of vaporization (kJ/mol)

Superscripts

K Knudsen

D molecular-diffusionC combined Knudsen/ordinary-diffusion

s aqueous NaCl solution

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