DCMD Desalination

7/29/2019 DCMD Desalination

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Spatial variations of DCMD performance for desalinationthrough countercurrent hollow fiber modules

Li-Hua Cheng, Ping-Chung Wu, Cho-Kai Kong, Junghui Chen*

R&D Center for Membrane Technology and Department of Chemical Engineering,

Chung Yuan University, Chungli 320, Taiwan

Tel. 886(3)2654107; Fax 886(3)2654199; email: [email protected] 1 July 2007; accepted revised 25 September 2007

Abstract

To understand the spatial variations of the desalination behavior, a mathematical model is systematicallyformulated to simulate a direct contact membrane distillation (DCMD) with the hollow fiber module for desalina-tion. The model equation for the entire module is derived by integrating the mass, momentum and energy balanceson both feed and permeate sides with the permeate flux across the membrane. The property variations of feed and

permeate sides along the length of the membrane module are thoroughly simulated. Sensitivity of the permeateflux and the thermal efficiency along the fiber length to operating conditions is further investigated over a range oftemperature and flow rate. It is shown that both permeate flux and thermal efficiency decrease along the fiberlength as the feed gets cooled down. Although the velocity variations of both streams are not big, the flow rateratio of the hot feed to the cold solution has a dramatic impact on the distribution of the permeate flux and thethermal efficiency along the fiber length. The effect analysis could potentially be applied to optimal design andscale-up of hollow fiber DCMD modules.

Keywords: Direct contact membrane distillation; Hollow fiber module; Membrane distillation; Modeling;Simulation

1. Introduction

Membrane distillation (MD) is a thermally

driven process, in which only vapor molecules

are transported through porous hydrophobic

membranes. The potential advantages of the MD

process in comparison with the conventional

processes lie in the lower operating temperature

and the hydrostatic pressure, insensitivity to

salt concentration, along with the merits in

utilizing low-grade waste and/or alternative energy

sources [1]. Although MD was introduced as a*Corresponding author.

Presented at the Fourth Conference of Aseanian Membrane Society (AMS 4), 1618 August 2007, Taipei,

Taiwan.

Desalination 234 (2008) 323334

0011-9164/08/$ See front matter# 2008 Published by Elsevier B.V.

doi:10.1016/j.desal.2007.09.101


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water desalination process in 1963, it is not

industrially implemented on any large scale

plants even today. Besides the development of

membrane, the commercialization of the MD

process will, to a large extent, depend upon theappropriate design of module. Compared with

plate and frame modules, hollow fiber-based

membrane devices for MD are more likely to

be of considerable utility because they are

simple, potentially scalable, and they can often

pack a large membrane surface area per unit

device volume without any need for a support-

ing structure [2]. Hollow fiber module also

shows the least temperature polarization among

various types of membrane modules [3]. Some

research on MD has employed hollow fibermembrane modules. For example, Gryta and

Tomaszewska presented and verified the heat

transport in MD capillary modules [4]. Lagana

et al. developed a model of tubular membrane

(with relative large fiber diameter) for effect

evaluation of membrane morphology, such as

thickness, elastic modules and pore radius distri-

bution on permeate flux [5]. Hollow fibers of

relatively larger wall thickness, considerable

porosity and increased internal diameter werepreferred for the performance improvement of

direct contact membrane distillation (DCMD) [6].

Preliminary experimental MD investigations

on a small scale using hollow fiber membranes

illustrated by Li and Sirkar showed a remarkably

high water vapor flux up to 79 kg/m2 h high

module productivity [2].

Although past research on MD has adopted

hollow fiber module, modeling of hollow fiber

MD modules has not been seriously and system-

atically studied due to the complex nature ofthe MD process itself and the flow through fiber

modules. The primary goal of currently available

MD models is to predict the values of the

permeate flux other than the estimation of the

temperature and the concentration polarization

coefficients [1]. El-Bourawi et al. pointed out

the issue that only a mean temperature and a

mean concentration were considered when

modeling MD processes [1]. This will increase

the risk of membrane pore wetting because of

the hydrostatic pressure drop along the length

of the membrane module. To simulate a hollowfiber MD module, three sub-models are required.

Two sub-models are used to describe the flow on

each side of the membrane, and the third model

characterizes the separative properties of the

membrane. A general approach to modeling

membrane modules has been reported [7];

however, the case study on MD has not been

involved. For the commonly adopted type of the

hollow fiber DCMD module, spatial variations

of parameters, like temperature, velocity and

concentration, etc. along the fiber length are ofconsiderable importance for modeling and its

scale-up, which has not been thoroughly studied

to our best knowledge. Furthermore, thermal

efficiency, which depicts the fraction of energy

used for the vaporization of water, is also an

important factor for the evaluation of the MD

process with the non-isothermal characteristics.

It can be used as a criterion for improvement.

In this paper, systematical model formulations

of DCMD for desalination through countercur-rent hollow fiber modules are derived from

rigorous mass, momentum and energy balances

of both the feed and permeate sides coupled to

the simultaneous mass and heat transfer across

the membrane. The simulations can help us esti-

mate the axial variation of properties, such as the

feed and permeate flow rates, retentate and

permeate temperatures, hydrostatic pressure, flux

and thermal efficiency, etc. An attempt can be

carried out to further understand the sensitivity

of the process efficiency to operating conditionsalong the fiber length.

2. Hollow fiber DCMD module model

Hollow fiber modules contain a large number

of membrane fibers housed in a module shell.

Feed can be introduced on either the fiber or

324 L.-H. Cheng et al. / Desalination 234 (2008) 323334


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the shell side and permeate is withdrawn in aco-current or a countercurrent, where the latter

is generally more effective [8]. A schematic

representation of the flow pattern in a hollow

fiber module with the fiber side feed and the

countercurrent permeate stream is illustrated in

Fig. 1. The zoom of the fiber shown at the bottom

of Fig. 1 describes the transport of the water vapor

from the feed side to the permeate side through

the porous and hydrophobic membrane. The cor-

responding variables are labeled on the module.

To describe the hollow fiber module transportbehavior, the transport equations are derived for

the retentate as well as for the permeate side of the

module as the flux depends on both of the feed

and permeate side conditions. For the simulation

with reasonable computational expense, the fol-

lowing assumptions for the transport equations

are made to describe the flow on each side of the

membrane: (i) steady incompressible flow, (ii)

lubricating approximation at the feed side, (iii)

negligible axial diffusion compared to convection,(iv) negligible channeling when the uniform flow

exists and (v) negligible heat loss to environment.

2.1. Feed side in tube

On the basis of the momentum, mass and

energy balances in the feed side, the following

equations in terms of pressure (PF), velocity

(vF), salt compositions (xFs ) and temperature

(TF) are derived

dPF

dz

32F

d2ivF 1

1

VFdvF

dz

vF

VF 2Ms

s

Mw

w

dxFsdz

4Jdo

MFd2i

2

xFsVF

dvF

dz

vFMw

w VF 2

dxFsdz

0 3

dF

vF

CF

p TF

dz 4Q

F

Nd2i4

where di and do are the inside and outside

diameters of the fiber, respectively. CFp is the spe-

cific heat of the feed. F andw are the densities

of feed and water. VF is the feed molar volume.

Jis the mass flux. Ms, Mw andMF are the mole-

cular weights of salt, water and feed. F is theviscosity of the feed.

2.2. Permeate side in shell

In the permeate side, the differential equa-

tions in terms of pressure (PP), velocity (vP) and

temperature (TP) are derived

dPp

dz

32P

d2hvp 5

dv

P

dz 4V

P

NJdoMP d2s Nd

2o

6

dPvpCPp Tp

dz

QP

d2s Nd2o

7

The composition term is neglected due to the

nearly 100% rejection of non-volatile ionic

r

z

vF

m

di d

o

vP

ds

RetentateFeed inlet

Cooling water

Permeate

Permeate

Permeate

Retentate

Fig. 1. Hollow fiber module with tube side feed flow.

L.-H. Cheng et al. / Desalination 234 (2008) 323334 325


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solutes in DCMD of desalination. dh is the

hydraulic diameter of the shell, which is a func-

tion of the packing density of the module ,

dh 1 do and N

dods

2

. ds is the inside

diameter of the hollow module shell. N is the

number of fibers. All the other variables are

identical to those variables in the feed side, but

the superscript is for the permeate side.

2.3. Flux across the membrane

The above two side modules are completely

independent except for the coupling terms which

describe energy flux (Q) and mass flux (J)through the membrane simultaneously occurring

in the radial direction shown in Fig. 2, where TFmand TPm are temperatures at both sides of the

membrane, respectively.

2.3.1. Heat transfer

The heat transfer process of DCMD includes

the heat transferred through the boundary of the

feed side (QF

) and the permeate side (QP

), andacross the membrane (Qm).

(i) Within the boundary of the tube feed side:

QF hFAFr TF TFm

8

where AFr

1 and Ndi. The heat transfer

coefficient in the tube side hF may be described

in a number of ways. Only one of them is chosen

here because of its relative simple form and wide

adoption [4]:

NuF hFdi

kF

1:62ReF0:33PrF0:33di

L

0:33ReF < 2100

0:023ReF0:8PrF0:33 ReF ! 2100

8>:9

where ReF div

FF

Fand PrF

CFp F

kF.

(ii) Across the membrane:

Qm Amr JH km

mTFm T

Pm

!10

where Am

r dlm=di and dlm is the log-meanradius difference of the fiber.H is the enthalpyof evaporation which is determined based on the

mean temperature of feed and permeate side

temperatures, TFm TPm

=2 [9]. m is the mem-

brane thickness. km is the thermal conductivity.

km "kmg 1 " kms, " is the porosity andkmg andkms refer to the conductive coefficients

of air within the membrane pore and solid

membrane, respectively.

(iii) Within the boundary of the shell cold side:

QP hPAPr TPm T

P

11

where APr do=di anddo is the outside diameterof the fiber. The heat transfer coefficient in the

shell side of the hollow fiber module hP could

be described by correlation similar to Eq. (9),

m

TF

PF

TP

PP

TF

PF

TP

PP

m

m

m

m

Membrane

Vapor

Vapor

Vapor

Fig. 2. Mass and heat transfers during MD.



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but the heat transfer refers to the hydraulic

diameter of shell dh [10].

According to the energy conservation, at

steady state, the amount of heat transferred

through the above three phases is equal,

QF Qm QP 12

2.3.2. Mass transfer

The mass transfer process in DCMD has two

steps. The volatile component passes through

the concentration boundary on the feed side of the

membrane and then through the porous mem-

brane itself. Since the mean free molecular path

of saturated water vapor under typical DCMDoperating conditions is comparable to the typical

membrane pore size used in MD, the Knudsen

diffusion Molecular diffusion Poiseuilleflow transition [11] is chosen among the numerous

expressions of mass transfer of MD.

J R1K R1

M

1 R1P

n oPFm P

Pm

13

where PFm and PPm are the vapor pressures on

the feed and permeate sides of the membrane.The difference of both pressures is the driv-

ing force of the MD process. R1K CKMwRTm

0:5,

R1M CMDMw

PaMRTm

and R1P CP

MwPmRTm

. CK,

CM, andCP represent the individual contribu-

tion of Knudsen diffusion, molecular diffusion

and Poiseuille flow, respectively. The diffusion

coefficient D depends on temperature and pres-

sure [11]. Water vapor pressures are calculated

using the Antoine equation. The diffusion modelspresented above have to be modified to account

for the reduction in vapor pressure caused by

dissolved species. For dilute salt solutions,

Raoults law can be used,

PFm Psat 1 xFs

14

where Psat is the saturated vapor pressure of

water at TFm . Based on the relationship of the

mass and heat transfers through membrane,

the temperatures (TFm andTPm) and the flux (J) are

determined by solving the non-linear leastsquares optimization problem using MATLAB.

2.4. Solution of model

The hollow fiber module parameters used for

the simulation are listed in Table 1. For full infor-

mation, please refer to [11]. The coupled ordinary

differential equations, including the flow on each

side of the membrane and the characterization of

hydrophobic membrane, are solved numericallywith the following boundary conditions

For the feed side

T0 TFin; v0 vFin; x

Fs 0 xs;in;

PFL P0 15

For the permeate side

TL TPin; vL vPin; x

Ps0 0;

Pp0 P0 16

P0 is equal to the ambient atmospheric pressure

at both outlets of the streams. In order to apply

the numerical method to the operation in a

Table 1

Characteristics of the membrane module

Hollow fiber membrane module PVDF

Length of fibers (L, m) 0.34

Shell diameter (ds, m) 0.03Number of fibers (N) 3000

Inner diameter of fibers (di, mm) 0.30

Membrane thickness (m, mm) 60Nominal pore diameter (mm) 0.2

Packing density (, %) 60Porosity (", %) 75



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countercurrent manner, the outlet condition for the

permeate side on a trial basis should be estimated.

It has to be found out if its entrance condition in

Eq. (16) is satisfied. If not, make another guess and

try again. The simulated system is repeated untilthe entrance condition is satisfied.

3. Results and discussion

3.1. Spatial variations

3.1.1. Temperature variation

The variations ofTF, TP, TFm andTPm as func-

tions of the fiber length are shown in Fig. 3,

where the corresponding operation condition is

added to the caption. v

F

in andv

P

in are the volumeflow rates, and wFin is the mass fraction of salt

in the feed inlet. All these temperatures change

almost linearly along the fiber length. TF

decreases from the inlet 343 K to outlet

312.5 K, while TP increases from the inlet

298 K to outlet 330 K. Because of the counter-

current flow fashion, nearly constant transmem-

brane temperature difference is maintained

throughout the membrane module. It can be seen

that with the temperature dropping by 30 K at

the feed side, the transmembrane temperatureranges 36 K, whereas the temperature at the

permeate side increases by 30 K.

Fig. 3 also shows the obvious temperature

polarization as the transmembrane temperature

difference is almost equal to those at the bound-

aries of the feed side and the permeate side. It

might be alleviated by increasing the flow ratesof both feed and permeate.

3.1.2. Velocity variation

Fig. 4 shows the velocity variation of both

retentate and permeate along the fiber length

axial position. Because of the countercurrent flow

fashion and the cumulative changes of permeate

flux along the fiber length, the feed side velocity

vF decreases from the inlet 0.472 m/s to the outlet

0.455 m/s, while the permeate side velocity vP

increases from the inlet 0.332 m/s to the outlet

0.343 m/s. The relative small velocity variation

at the permeate side is attributed to the larger

cross-sectional area when the packing density

is 0.6. The velocity variations of both retentate

and permeate are not significantly big enough;

however, they have great effect on the trans-

membrane hydrostatic pressure.

3.1.3. Hydrostatic pressure variation

The bulk pressure along the length of module

is a function of both fluid velocity and fiber

length as expressed in Eqs. (1) and (5). Fig. 5

0 0.05 0.1 0.15 0.2 0.25 0.3

300

305

310

315

320

325

330

335

340

345

z, m

T,

K

TF

TP

TF

TP

m

m

Fig. 3. Temperature as a function of the fiber length (TFin

343 K, TPin 298 K, vFin v

Pin 6 L/min, w

Fin 0:025:

0.45

0.46

0.47

0.48

z, m0 0.05 0.1 0.15 0.2 0.25 0.3

0.33

0.335

0.34

0.345

vP,

m/s

vF,

m/s

vF

vP

Fig. 4. Velocity as a function of the fiber length (TFin

343 K, TPin 298 K, vFin v

Pin 6 L/min, w

Fin 0.025).



7/12

shows the local hydrostatic pressure drop of both

feed and permeate sides along the fiber length.

When both outlets of retentate and permeate

are required to be the ambient atmospheric pres-

sure, the inlet feed pressure reaches 131 kPa

while the inlet permeate pressure is 125 kPa.

The relatively lower pressure drop at the perme-

ate side is attributed to the countercurrent flow

fashion, the cumulative permeate flux from the

feed side to the permeate side as well as the

relative larger cross-sectional area at the per-

meate side with packing density of 0.6. Nazish

et al. also reported the downstream pressure

build-up in case of the hollow fiber module for

pervaporation [12].

Variation of hydrostatic pressure has no

influence on flux since the DCMD driving force

is the function of the vapor pressure difference

between both membrane sides. However, it willincrease the risk of membrane pore wetting

because membranes used in MD requires being

non-wetting [1]. For a typical PVDF membrane

contact angle of 130, the penetration pressure

of a cylindrical of the maximum pore diameter

1 mm is only 185 kPa. When longer fiber, 1.2 m,

is adopted, for instance, liquid entry pressure

of 185 kPa would have been reached when both

inlet flow rates are maintained at 6 L/min. The

effect of pressure drop may be reduced by

increasing the fiber diameter or shortening

the fiber length at the cost of high membrane

area packing density. Therefore, there is a

trade-off between the module volume and

attained separation, showing the necessity to

optimize the fiber dimensions for the hollow

fiber DCMD module.

3.1.4. Permeate flux and thermal

efficiency variation

As DCMD is a non-isothermal process, the

properties of interests, the permeate flux Jzand the thermal efficiency z along the lengthof fiber should be computed locally. The thermal

efficiency is defined as

z JzHTz

JzHTz kmm TFm z T

Pm z

17

which depicts the fraction of energy that has

been used for the vaporization of water.

Fig. 6 shows the variations ofJz andzwith the fiber length. Both of them decrease

0 0.05 0.1 0.15 0.2 0.25 0.3100

105

110

115

120

125

130

135

z, m

P,

kPa

PF

PP

Fig. 5. Hydrostatic pressure as a function of the fiber

length (T

F

in 343 K, TP

in 298 K, vF

in vP

in 6 L/min,wFin 0:025).

0 0.05 0.1 0.15 0.2 0.25 0.30

5

10

15

20

J,

kg/m2h

z, m

0

0.2

0.4

0.6

0.8

J

Fig. 6. Permeate flux and thermal efficiency as a

function of the fiber length (TFin 343 K, TPin 298 K,

vFin vPin 6 L/min, w

Fin 0:025).



8/12

along the fiber length because DCMD driving

force comes from the vapor pressure difference

between both membrane sides. Although the

transmembrane temperature difference keeps

almost constant as shown in Fig. 3, the vaporpressure difference has significantly changed

since the vapor pressure with the Antoine

Equation is an exponential depending on tem-

perature. It can be seen that J(z) decreases from

the inlet 18 to the outlet 3 kg/m2 h, which is

corresponding to transmembrane difference of

3 and 6 K as shown in Fig. 3, respectively.

Because of the almost constant transmembrane

temperature difference of 36 K, the conductive

heat transfer keeps nearly unchanged. Therefore,

with the decrease in Jz and the linear decreaseof H with the temperature along the fiber

length, it is expected that z decreases linearlyaccording to Eq. (17) as shown in Fig. 6.

3.1.5. Concentration variation

The salinity of the retentate increases parabo-

lically along the fiber length as shown in Fig. 7,

in which wFS is the mass fraction of salt in the

feed side. It is also attributed to the permeateflux changed along the fiber. Nevertheless, the

change in salinity is very small because of single

pass through the fiber.

3.2. Effect of operating variables

3.2.1. Effect of temperature

In Fig. 8(a), the spatial variations of Jz

change significantly with TFin, because the expo-

nential increase of the vapor pressure of the feed

0 0.05 0.1 0.15 0.2 0.25 0.30.025

0.0252

0.0254

0.0256

0.0258

0.026

0.0262

z, m

wF s

Fig. 7. Retentate salinity as a function of the fiber

length (TFin 343 K, TPin 298 K, v

Fin v

Pin 6 L/min,

wFin 0:025).

(a)

0 0.05 0.1 0.15 0.2 0.25 0.30

5

10

15

20

25

30

z, m

J,

kg/m2h

TF

in

TF

in

=

313 K

323 K

333 K

343 K

353 K

(b)

0 0.05 0.1 0.15 0.2 0.25 0.30

0.2

0.4

0.6

0.8

1

z, m

=

313 K

323 K

333 K

343 K

353 K

Fig. 8. The effect of the inlet temperature of the feed

solution on the spatial variations of (a) the permeate

flux and (b) the thermal efficiency (TPin 298 K, vFin

vPin 6 L/min).



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solution with temperature would increase the

transmembrane vapor pressure difference as all

the other involved parameters are maintained

invariables. It is consistent with the general

conclusion that the permeate flux increases asTFin increases when the whole fiber length is

investigated. The higher z also occurs at

the front of the fiber length as TFin increases

(Fig. 8(b)). This indicates that it is not worthy

to increase the fiber length without consider-

ing z.As the feed temperature is kept constant and

lowerTPin is adopted in Fig. 9(a), the transmem-

brane vapor pressure difference at largerT

TFm TPm and lowerT

Fin would be the same as the

one at smallerT and higherTFin in the case of

higher TPin. It is because the transmembrane

vapor pressure based on the Antoine equation

has the exponential change in TFin. Therefore,

lowering TPin may not increase permeate flux

when the whole fiber length is investigated.

Nevertheless, it decreases thermal efficiency as

shown in Fig. 9(b). Hence, there is a trade-off

between the permeate flux and the thermal effi-

ciency as the permeate temperature increases.

3.2.2. Effect of flow rate

In Fig. 10, the spatial variations ofJz andz change dramatically along the fiber length

at different vFin when vPin remains constant. It also

indicates that Jz and z increase at the

higher feed flow rate with the increase of vFin.

The effect of feed velocity can increase the heat

transfer coefficient and then reduce the tempera-ture and the concentration polarization effect at

both boundary sides of bulk streams. On the other

hand, because of the shorter retention time of the

stream within the hollow fiber module, the higher

transmembrane difference is maintained along

the fiber length. Thus, this can increase the process

driving force and yield higher permeate flux.

The effect of stream velocity on the spatial

variations ofJz andz demonstrates that the

ratio of the hot feed to the cold solution plays animportant role in the distribution of transmem-

brane temperature difference along the fiber

length. When the ratio is lower than 1, the effec-

tive fiber length reduces as shown in Fig. 10(a).

For example, Jz decreases from the inlet22.5 kg/m2 h to almost 0 at the fiber length of

0.15 m at the feed flow rate of 2 L/min and

(a)

0 0.05 0.1 0.15 0.2 0.25 0.3 0.350

5

10

15

20

25

z, m

J,

kg/m2h

=

290 K

293 K

298 K

308 K318 K

(b)

0 0.05 0.1 0.15 0.2 0.25 0.30

0.2

0.4

0.6

0.8

1

z, m

=

290 K

293 K

298 K

308 K

318 K

TPin

TP

in

Fig. 9. The effect of the inlet temperature of cold water

on the spatial variations of (a) the permeate flux and

(b) the thermal efficiency (TFin 343 K, vFin v

Pin

6 L/min).



10/12

the permeate flow rate of 6 L/min. With the

increase of the ratio, the permeate flux drop alongthe fiber length decreases gradually. When the

ratio increases to more than 1, the Jz distribu-tion along the fiber length becomes even as

shown in Fig. 10 (a), indicating the full utilization

of the membrane area of the process.

On the contrary, although both Jz andzchange along the fiber length at different vPin

when vFin is maintained constant as shown in

Fig. 11, the distribution of Jz could be chan-

ged drastically throughout the whole fiberlength. When the flow rate of the hot feed is

much greater than that of the cold solution, more

permeate flux occurs at the end of the fiber

length. This is because the larger transmem-

brane temperature difference is maintained near

the inlet of permeate, and the driving force

reduces with the rapid temperature rise of

(a)

0 0.05 0.1 0.15 0.2 0.25 0.30

5

10

15

20

25

z,m

J,

kg/m2h

vF

in=

2 L/min

4 L/min

6 L/min

8 L/min10 L/min

(b)

0 0.05 0.1 0.15 0.2 0.25 0.30

0.2

0.4

0.6

0.8

1

z,m

=

2 L/min

4 L/min

6 L/min

8 L/min

10 L/min

vF

in

Fig. 10. Spatial variations of the permeate flux (a) and

the thermal efficiency (b) as a function of the inlet flow

rate of the feed solution (vPin 6 L/min, TFin 343 K,

TPin 298 K).

(a)

0 0.05 0.1 0.15 0.2 0.25 0.30

5

10

15

20

25

30

z,m

=

2 L/min

2.5 L/min

3 L/min

4 L/min

6 L/min

8 L/min

10 L/min

(b)

0 0.05 0.1 0.15 0.2 0.25 0.30

0.2

0.4

0.6

0.8

z,m

=

2 L/min

2.5 L/min

3 L/min

4 L/min

6 L/min

8 L/min10 L/min

J,

kg/m2h

vPin

vPin

Fig. 11. Spatial variations of the permeate flux (a) and

thermal efficiency (b) as a function of the inlet flow

rate of cold water (vFin 6 L/min, TFin 343 K, T

Pin

298 K).



11/12

permeate along the fiber length. Similarly, when

the flow rate of the hot feed is much lower than

that of the cold solution, the lower Jz iscovered at the end of the fiber length. Therefore,

to obtain higher productivity, the membranearea of the module should be fully utilized and

the flow rate ratio of the hot feed and the cold

solution should be appropriately adjusted.

4. Conclusions

The detailed DCMD model is developed by

integrating the permeate flux through the mem-

brane with rigorous mass, momentum and energy

balance on both feed and permeate sides. In this

paper, the use of the model is demonstrated toinvestigate complex spatial property variations

of feed and permeate sides along the fiber length

in a desalination system during DCMD.

Even if nearly constant transmembrane tem-

perature difference is maintained in the counter-

current operation, both permeate flux and thermal

efficiency decrease along the fiber length as the

feed gets cooled down or the permeate is heated

up. Although the velocity variations of both

streams are not great, the risk of membranepore wetting increases dramatically because of

the hydrostatic pressure build-up. Although the

operating condition in DCMD processes can be

adjusted any time, it is difficult to fully under-

stand how well the process is operated. Further-

more, the simulated DCMD results depicting the

flow rate ratio of the hot feed to the cold solution

has a dramatic effect on distribution of permeate

flux and thermal efficiency along the fiber

length. With the increase of the ratio, the effective

fiber length increases, resulting in the increase ofboth the flux and the thermal efficiency.

As shown in this paper, the detailed model is

essential to the design of the DCMD module

with the trade-off between the permeate flux and

the thermal efficiency as the permeate condition

varies. It is also necessary to optimize fiber

dimensions and operating conditions so that the

performance can be optimized in the hollow

fiber DCMD system for the desalination. More-

over, the channeling problem exists in the

practical application when the longer fiber is

applied. The model to be modified for optimaldesign of DCMD systems will be investigated

in our future work.

Acknowledgements

This work was sponsored by the Center-

of-Excellence Program on Membrane Technol-

ogy, the Ministry of Education, Taiwan, R.O.C.

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DCMD Desalination

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