- Email: [email protected]
Study of evaporation efficiency in membrane distillation
DESALINATION ELSEVIER
Desalination 126 (1999) 193-198
www.elsevier.com/locate/desal
Study of evaporation efficiency in membrane distillation L. Martinez-Diez*, F.J. Florido-Diaz, M.I. V~quez-GonzS.lez Department of Applied Physics, Faculty of Science, University of Mdlaga, 29071 Mdlaga, Spain Tel. +34 (95) 213-1921; Fax +34 (95) 213-2000; email: [email protected]
Abstract
Membrane distillation experiments have been carried out by using a PTFE porous hydrophobic membrane and sodium chloride aqueous solutions. The effects of temperature, feed concentration and flow rate on permeate flux and heat lost by conduction through the membrane have been studied in a direct contact-type module. A method is introduced that allows the relation between the membrane thermal conductivity and the membrane permeability to be calculated.
Keywords:
Membrane distillation; Evaporation efficiency; Temperature polarization; Heat loss; Hydrophobic membranes
I. Introduction
Membrane distillation is a membrane technique that involves transport of water vapour through the pores ofhydrophobic membranes due to a vapour pressure driving force provided by temperature and/or solute concentration differences across the membrane. A variety of methods may be employed to impose this vapour pressure difference. In the present work, the direct contact membrane distillation method is *Corresponding author.
considered. In this configuration the surfaces of the membrane are in direct contact with two liquid phases, the feed (warm solution) and the permeate (cold solution), kept at different temperatures. A liquid vapour interface exists at the pore entrances where liquid-vapour equilibrium is established. Inside the pores only a gaseous phase is present through which vapour is transported as long as a partial pressure difference is maintained. The vaporization takes place at the feed membrane interface. The vapour flows through the membrane pores and condenses at the permeate membrane interface. Thus the
Presented at the Conference on Desalination and the Environment, Las Palmas, Gran Canaria, November 9-12, 1999. European Desalination Society and the International Water Services Association. 0011-9164/99/$- See front matter © 1999 Elsevier Science B.V. All rights reserved PII: S0011-9164(99)00174-5
194
L. Martinez-Diez et al. / Desalination 126 (1999) 193-198
separation mechanism of membrane distillation is based on a vapour-liquid equilibrium. The main advantage of membrane distillation over the traditional distillation process is associated with the possibility of working at low temperatures and/or using low-grade, waste or alternative energy sources. The possible applications of membrane distillation are limited by the wettability of the membrane, which is a function of the feed surface tension. Therefore, aqueous solutions containing inorganic solutes can be treated while solutions with surface-active components cannot. Pore size and porosity must also be taken into account. High porosities have special interest since the available area for evaporation is directly related to flux. However, high porosities are usually associated with large pore sizes which are undesirable because they increase the risk of membrane wetting. Membranes with 60% to 80% porosity and 0.1-0.5 #m pore size offer a suitable compromise. Hydrophobic materials such as polypropylene (PP), polytetrafluoroethylene (PTFE), polyethylene (PE) and polyvinylidene fluoride (PVDF) are used for manufacturing membrane distillation membranes. In membrane distillation the desired product can be either the permeate or the concentrate solution. Applications have been reported in the literature for (1) production of pure water from brackish water or seawater [1,2] and (2) concentration of fruit juices [3,4]. In the present work, membrane distillation is used for desalination and salt water is the hot feed solution. Pure water vapour passes through the membrane pores while the salts and other non-volatiles remain on the warm side of the membrane. In the process the heat requirements represent a significant part of the process cost. An analysis of the effective energy consumption when working at low temperatures is made. The importance of some factors relating to the membranes and the operation mode is analyzed.
2. Experimental Experimental tests have been performed using a flat PTFE membrane manufactured by Gelman Instruments as TF 200 (80% void fraction, 60/~m thickness, 0.2 #m pore size). This study was carried out in a direct contact membrane distillation module [5] with a flat sheet membrane. The membrane module is made up of nine feed channels and nine permeate channels each of 55.0 mm long, 7.0mm wide and 0.4mm high. In all experimental runs the membrane was maintained in a horizontal position. The feed solution was preheated in a thermostated bath and then pumped onto the membrane low surface. Water was likewise preheated (at a lower temperature than the feed solution) in another thermostated bath and then pumped onto the upper membrane surface. The recirculation of the fluids on both sides of the membrane was in countercurrent directions. Flow rates were maintained approximately equal for both streams. The temperatures of the bulk liquid phases were measured at the hot entrance (Tbl.in), the cold entrance (Tb>in), the hot exit (Tbl_ou0 and the cold exit (Tb2.out) of the membrane cell. All these temperatures were monitored by temperature sensors with 0.5°C accuracy. In the experimental set-up the permeate continuously flows out of the distillate reservoir, and the corresponding distillate flux was measured by collecting this liquid flowing out of the cold reservoir. Initial experiments were conducted using distilled water as feed. Further experiments were conducted using aqueous solutions of NaCl, with concentrations of 1 and 2 molar. Flow rates were varied from 8.0 cm3/s to 20.0 cm3/s (that is linear velocity down the channel was varied from about 32 cm/s to about 80 cm/s). In all the experiments the average temperature in the cold side of the membrane,
Tb2-in Tb2 +
=
2
out
(1)
L. Martlnez-Diez et al. / Desalination 126 (1999) 193-198 was maintained about 14 oC. Four different series of experiments were carried out at about 21, 29, 41 and 48°C as average temperatures in the hot side of the membrane,
Tbl :
T b l +- Tbl-out in 2
(2)
In order to have a negligible heat loss from the cold water to the environment, the membrane module (manufactured with plastic material) was covered with insulating material. Likewise the room temperature was close to the cooling water temperature (14 °C).
C=1.064--
~-~}
The system to be studied consists of a microporous hydrophobic membrane that separates two aqueous solutions maintained at different temperatures. Water vapour transport occurs through the membrane pores from the warm to the cold side. This transport phenomenon is usually described [6] by means of a linear relationship between the mass flux, J, and the driving force for the transport, which is the water vapour pressure difference between the feed (warm) and permeate (cold) sides of the membrane:
J : C6 Ogml-Pm2)
(4)
where r is the pore radius, e the membrane porosity, X the pore tortuosity, M the water molecular weight, R the gas constant and T the temperature. Simultaneously to mass transport, heat transport occurs across the membrane. Heat transfer within the membrane consists of the latent heat accompanying vapour flux and the heat conducted across the gas-filled membrane. km
Q = JAHvap + -~- (Tml-Tm2)
3. Theory
195
(5)
where AHvap is the latent heat of vaporization, k,, is the thermal conductivity of the porous membrane and Tml and Tin2 are the temperatures at the hot and cold membrane surfaces, respectively. The temperature difference (Tml- Tm2) is lower than the one corresponding to the bulk phases (Tbl- Tb2) due to the presence of boundary layers at both sides of the membrane. This phenomenon is called temperature polarization and it is quantified by the so-called temperature polarization coefficient
=
T 1- T 2
(6)
(3)
where 6 is the membrane thickness, and C is a phenomenological coefficient which measures the ability of the membrane to give membrane distillation fluxes. This coefficient may be related to the physical nature of the transport process [7] which is expected to be mainly a Knudsen-type diffusion,
In Eq. (5) only the latent heat of evaporation is the heat used effectively; however, the heat transferred by conduction is considered as heat lost:
km
196
L. Martinez-Diez et al. / Desalination 126 (1999) 193-198
The heat lost per mass flux unit can be expressed, taking into account Eqs. (3) and (7), as 31.o*c
Qlost km (T1 - Tin2) J C (Pm,-Pro2)
(8)
~
that for very dilute solutions and for low values of (T,, l- Tin2) may be approximated by [8]:
Qlost
J
~6
0
27.5"C
3 21.S*C
km
1
C(dp) -~
~---'--------~
(9) rm
v
I
I
I
I
0,5
1
1,5
2
17.50C 2,S
Feed concentration (mol/I)
where T m is the average temperature in the membrane, and where ( d p / d T ) T m c a n be evaluated from the Clausius-Clapeyron equation,
Fig. 1. Water flux vs. feed concentration for four average temperatures. The flow rate was 16 cm3/sand Tbl= 14°C. The solid lines are the linear fits of the experimental data.
6
(10)
i
i
i
4
using the Antoine equation to calculate p:
jo NE
P =exp(23.238
T-3841-45))
(11)
3 ? 0 •- 4
4. Results and discussion
Fig. 1 shows the distillate fluxes as a function of the feed salt concentration when different average temperatures in the membrane module are considered. A non-linear increase in the flux (Figs. 1,2) with increasing temperature reflects the exponential increase in the vapour pressure which provides the driving force. Fig. 1 also shows that the flux decreases in an approximately linear way with the salt concentration in the studied range. This linear behaviour is consistent with predictions based on the thermodynamics of irreversible processes and has been observed by
3 5
i
L
10
15 Flow
I
20
J2
25
rate (cmS/s)
Fig. 2. Water flux and heat lost per unit mass flux as a function of the flow rate. The feed concentration was 1 mol/l, and the average temperature 27.5°C. The solid lines are the fits of the experimental data to a quadratic function.
other authors [9]. Fig. 2 shows as the permeate flux increases when the recirculation rate increases. The effect of a higher recirculation rate
L. Martinez-Diez et al. / Desalination 126 (1999) 193-198 1
~
I
I
21.5"C4
-g
/ .2
197
._/-" 27.5"C
3
• 31.0"C
d"
v
-2 or
/
3
/
0
I
O,S Feed
[
I
I
1 1,5 2 concentration (mol/I)
I
4
2,5
Fig. 3. Heat lost per unit mass flux vs. feed concentration for three average temperatures. The flow rate was 16 cm3/s and Tbl = 14 ° C. The solid lines are the linear fits
I
I
6 1/dp/dT
8 (K/kPa)
Fig. 4. Fit of the experimental data to Eq. (9). The feed was water and the flow rate 16 cm3/s.
of the experimental data.
dp)-' Q,o , = (o.1+o.3) + (o.56±o.o5) [ =is to increase the heat transfer coefficient and thus reduce the effect o f temperature polarization. This means that the temperatures at the membrane surface more closely approximate that of the bulk streams, and thus the transmembrane temperature difference is greater. This produces a greater driving force and consequently enhances the flux. In order to estimate the heat lost, calculations were performed in the following way. The latent heat of evaporation is the heat used effectively and is obtained from the permeate flux. The increase in heat of the cooling water is a sum of the latent heat of evaporation and the conduction heat lost through the membrane from the feed to cooling water. The results obtained for different experimental conditions are shown in Figs. 2 and 3. In Fig. 4 an analysis as suggested for Eq. (9) is made from the Qlost/J results obtained when water is used as feed. The experimental points [(dp/dT)-l; Qlo~t/J] have been fitted to a linear function by a least-squares method. The result is
J
dT
and so a value of km/C = (56+5)x 10 7 kg m s -4 K 1 is obtained. From Eq. (4) and using a typical value of%~2 [8], the value of kin = 0.055 W/m K is obtained. By using Eq. (7), the corresponding z coefficient may be estimated. The obtained values vary between 0.7 and 0.6 decreasing with the mean temperature and increasing with the flow rate, as might have been expected. These ~: results allow us to explain the Qlost/J values shown in Figs. 2 and 3. In fact, heat transfer by conduction increases approximately linearly with temperature gradient, unlike the vapour pressure driving force (in MD the effects of concentration polarization are negligible) and thus flux. As a result, Qiost/d decreases as mean temperature increases, and Q~ostis approximately constant, unlike the vapour pressure driving force and thus flux. As a result, Qlost/Jincreases as feed concentration increases. Finally we can see how an increase in flow rate has a trend to decrease Qio~t/J, but the effect is not considerable [10].
198
L. Martinez-Diez et al. / Desalination 126 (1999) 193-198
0,7
J
J
i
km 0,65
0,6
M
B
p
m
Q
--
Qlost
--
r
R T 0,5520
t
24
i
28
32
---
Mass flux through the membrane, kg/m 2 s Thermal conductivity o f the membrane, W/m K Molecular weight o f water, kg/mol Pressure o f water vapour, Pa Heat flux, W/m 2 Heat lost, W/m 2 Pore radius, m Gas constant, J/mol K Temperature, K
Greek
Average temperature (*C)
6
Fig. 5. Temperature polarization vs. average temperature. The different symbols correspond to different flow rates and feed concentrations : &, 8 cma/s and 1 mol/1; V, 16 cma/s and water; O,16 cm3/s and 1 mol/l.
--
8
Subscripts b
--
m
5. Conclusions 1. The effects o f temperature, feed concentration and flow rate on permeate flux and heat lost were studied for a direct contact-type module. It was found that for the feed studied, both high temperature and flow rate promote permeate flux and decrease relative heat loss. 2. A method is introduced in order to evaluate the coefficient k m / C , a membrane coefficient directly related with the heat lost per mass flux unit. The materials for the membrane should be chosen so as to reduce the conduction heat loss through the membrane. 3. The high values obtained for the relative heat lost suggest that membrane distillation can be competitive only in situations where some source o f waste energy is available.
6. Symbols C
--
AHv - -
Phenomenological coefficient, kg/m s Pa Latent heat o f vaporization, J/g
Membrane thickness, m Porosity, dimensionless Pore tortuosity, dimensionless
1
--
2
--
In the bulk phase At the membrane surface Hot solution Cold water
References [1] P.A. Hogan, A.G. Fane and G.L. Morrison, Desalination, 81 (1991) 81. [2] A.G. Fane, R.W. Schofield and C.J.D. Fell, Desalination, 64 (1987) 231. [3] V. Calabr6, B.L. Jiao and E. Drioli, Ind. Eng. Chem. Res., 33 (1994) 1803. [4] J. Mansouri and A.G. Fane, J. Membr. Sci., 153 (1999) 103. [5] L. Martinez-Diez, M.I. V~quez-GonzAlez and F.J. Florido-Diaz, J. Membr. Sci., 1 (1998) 45. [6] K.W, Lawson and D.R. Lloyd, J. Membr. Sci., 124 (1997) I. [7] S. Bandini, C Gostoli and G.C. Sarti, J. Membr. Sci., 73 (1992) 217. [8] R.W. Schofield,A.G. Fane and C.J.D. Fell, J. Membr. Sci., 33 (1987) 299. [9] M.P. Godino, L. Pefia, C. Rinc6n and J.I. Mengual, Desalination, 108 (1996) 91. [10] K. Ohta, K. Kikuchi, I. Hayano, T. Okabe, T. Goto, S. Kimura and H. Ohya, Desalination 78 (1990) 177.
Desalination 126 (1999) 193-198
www.elsevier.com/locate/desal
Study of evaporation efficiency in membrane distillation L. Martinez-Diez*, F.J. Florido-Diaz, M.I. V~quez-GonzS.lez Department of Applied Physics, Faculty of Science, University of Mdlaga, 29071 Mdlaga, Spain Tel. +34 (95) 213-1921; Fax +34 (95) 213-2000; email: [email protected]
Abstract
Membrane distillation experiments have been carried out by using a PTFE porous hydrophobic membrane and sodium chloride aqueous solutions. The effects of temperature, feed concentration and flow rate on permeate flux and heat lost by conduction through the membrane have been studied in a direct contact-type module. A method is introduced that allows the relation between the membrane thermal conductivity and the membrane permeability to be calculated.
Keywords:
Membrane distillation; Evaporation efficiency; Temperature polarization; Heat loss; Hydrophobic membranes
I. Introduction
Membrane distillation is a membrane technique that involves transport of water vapour through the pores ofhydrophobic membranes due to a vapour pressure driving force provided by temperature and/or solute concentration differences across the membrane. A variety of methods may be employed to impose this vapour pressure difference. In the present work, the direct contact membrane distillation method is *Corresponding author.
considered. In this configuration the surfaces of the membrane are in direct contact with two liquid phases, the feed (warm solution) and the permeate (cold solution), kept at different temperatures. A liquid vapour interface exists at the pore entrances where liquid-vapour equilibrium is established. Inside the pores only a gaseous phase is present through which vapour is transported as long as a partial pressure difference is maintained. The vaporization takes place at the feed membrane interface. The vapour flows through the membrane pores and condenses at the permeate membrane interface. Thus the
Presented at the Conference on Desalination and the Environment, Las Palmas, Gran Canaria, November 9-12, 1999. European Desalination Society and the International Water Services Association. 0011-9164/99/$- See front matter © 1999 Elsevier Science B.V. All rights reserved PII: S0011-9164(99)00174-5
194
L. Martinez-Diez et al. / Desalination 126 (1999) 193-198
separation mechanism of membrane distillation is based on a vapour-liquid equilibrium. The main advantage of membrane distillation over the traditional distillation process is associated with the possibility of working at low temperatures and/or using low-grade, waste or alternative energy sources. The possible applications of membrane distillation are limited by the wettability of the membrane, which is a function of the feed surface tension. Therefore, aqueous solutions containing inorganic solutes can be treated while solutions with surface-active components cannot. Pore size and porosity must also be taken into account. High porosities have special interest since the available area for evaporation is directly related to flux. However, high porosities are usually associated with large pore sizes which are undesirable because they increase the risk of membrane wetting. Membranes with 60% to 80% porosity and 0.1-0.5 #m pore size offer a suitable compromise. Hydrophobic materials such as polypropylene (PP), polytetrafluoroethylene (PTFE), polyethylene (PE) and polyvinylidene fluoride (PVDF) are used for manufacturing membrane distillation membranes. In membrane distillation the desired product can be either the permeate or the concentrate solution. Applications have been reported in the literature for (1) production of pure water from brackish water or seawater [1,2] and (2) concentration of fruit juices [3,4]. In the present work, membrane distillation is used for desalination and salt water is the hot feed solution. Pure water vapour passes through the membrane pores while the salts and other non-volatiles remain on the warm side of the membrane. In the process the heat requirements represent a significant part of the process cost. An analysis of the effective energy consumption when working at low temperatures is made. The importance of some factors relating to the membranes and the operation mode is analyzed.
2. Experimental Experimental tests have been performed using a flat PTFE membrane manufactured by Gelman Instruments as TF 200 (80% void fraction, 60/~m thickness, 0.2 #m pore size). This study was carried out in a direct contact membrane distillation module [5] with a flat sheet membrane. The membrane module is made up of nine feed channels and nine permeate channels each of 55.0 mm long, 7.0mm wide and 0.4mm high. In all experimental runs the membrane was maintained in a horizontal position. The feed solution was preheated in a thermostated bath and then pumped onto the membrane low surface. Water was likewise preheated (at a lower temperature than the feed solution) in another thermostated bath and then pumped onto the upper membrane surface. The recirculation of the fluids on both sides of the membrane was in countercurrent directions. Flow rates were maintained approximately equal for both streams. The temperatures of the bulk liquid phases were measured at the hot entrance (Tbl.in), the cold entrance (Tb>in), the hot exit (Tbl_ou0 and the cold exit (Tb2.out) of the membrane cell. All these temperatures were monitored by temperature sensors with 0.5°C accuracy. In the experimental set-up the permeate continuously flows out of the distillate reservoir, and the corresponding distillate flux was measured by collecting this liquid flowing out of the cold reservoir. Initial experiments were conducted using distilled water as feed. Further experiments were conducted using aqueous solutions of NaCl, with concentrations of 1 and 2 molar. Flow rates were varied from 8.0 cm3/s to 20.0 cm3/s (that is linear velocity down the channel was varied from about 32 cm/s to about 80 cm/s). In all the experiments the average temperature in the cold side of the membrane,
Tb2-in Tb2 +
=
2
out
(1)
L. Martlnez-Diez et al. / Desalination 126 (1999) 193-198 was maintained about 14 oC. Four different series of experiments were carried out at about 21, 29, 41 and 48°C as average temperatures in the hot side of the membrane,
Tbl :
T b l +- Tbl-out in 2
(2)
In order to have a negligible heat loss from the cold water to the environment, the membrane module (manufactured with plastic material) was covered with insulating material. Likewise the room temperature was close to the cooling water temperature (14 °C).
C=1.064--
~-~}
The system to be studied consists of a microporous hydrophobic membrane that separates two aqueous solutions maintained at different temperatures. Water vapour transport occurs through the membrane pores from the warm to the cold side. This transport phenomenon is usually described [6] by means of a linear relationship between the mass flux, J, and the driving force for the transport, which is the water vapour pressure difference between the feed (warm) and permeate (cold) sides of the membrane:
J : C6 Ogml-Pm2)
(4)
where r is the pore radius, e the membrane porosity, X the pore tortuosity, M the water molecular weight, R the gas constant and T the temperature. Simultaneously to mass transport, heat transport occurs across the membrane. Heat transfer within the membrane consists of the latent heat accompanying vapour flux and the heat conducted across the gas-filled membrane. km
Q = JAHvap + -~- (Tml-Tm2)
3. Theory
195
(5)
where AHvap is the latent heat of vaporization, k,, is the thermal conductivity of the porous membrane and Tml and Tin2 are the temperatures at the hot and cold membrane surfaces, respectively. The temperature difference (Tml- Tm2) is lower than the one corresponding to the bulk phases (Tbl- Tb2) due to the presence of boundary layers at both sides of the membrane. This phenomenon is called temperature polarization and it is quantified by the so-called temperature polarization coefficient
=
T 1- T 2
(6)
(3)
where 6 is the membrane thickness, and C is a phenomenological coefficient which measures the ability of the membrane to give membrane distillation fluxes. This coefficient may be related to the physical nature of the transport process [7] which is expected to be mainly a Knudsen-type diffusion,
In Eq. (5) only the latent heat of evaporation is the heat used effectively; however, the heat transferred by conduction is considered as heat lost:
km
196
L. Martinez-Diez et al. / Desalination 126 (1999) 193-198
The heat lost per mass flux unit can be expressed, taking into account Eqs. (3) and (7), as 31.o*c
Qlost km (T1 - Tin2) J C (Pm,-Pro2)
(8)
~
that for very dilute solutions and for low values of (T,, l- Tin2) may be approximated by [8]:
Qlost
J
~6
0
27.5"C
3 21.S*C
km
1
C(dp) -~
~---'--------~
(9) rm
v
I
I
I
I
0,5
1
1,5
2
17.50C 2,S
Feed concentration (mol/I)
where T m is the average temperature in the membrane, and where ( d p / d T ) T m c a n be evaluated from the Clausius-Clapeyron equation,
Fig. 1. Water flux vs. feed concentration for four average temperatures. The flow rate was 16 cm3/sand Tbl= 14°C. The solid lines are the linear fits of the experimental data.
6
(10)
i
i
i
4
using the Antoine equation to calculate p:
jo NE
P =exp(23.238
T-3841-45))
(11)
3 ? 0 •- 4
4. Results and discussion
Fig. 1 shows the distillate fluxes as a function of the feed salt concentration when different average temperatures in the membrane module are considered. A non-linear increase in the flux (Figs. 1,2) with increasing temperature reflects the exponential increase in the vapour pressure which provides the driving force. Fig. 1 also shows that the flux decreases in an approximately linear way with the salt concentration in the studied range. This linear behaviour is consistent with predictions based on the thermodynamics of irreversible processes and has been observed by
3 5
i
L
10
15 Flow
I
20
J2
25
rate (cmS/s)
Fig. 2. Water flux and heat lost per unit mass flux as a function of the flow rate. The feed concentration was 1 mol/l, and the average temperature 27.5°C. The solid lines are the fits of the experimental data to a quadratic function.
other authors [9]. Fig. 2 shows as the permeate flux increases when the recirculation rate increases. The effect of a higher recirculation rate
L. Martinez-Diez et al. / Desalination 126 (1999) 193-198 1
~
I
I
21.5"C4
-g
/ .2
197
._/-" 27.5"C
3
• 31.0"C
d"
v
-2 or
/
3
/
0
I
O,S Feed
[
I
I
1 1,5 2 concentration (mol/I)
I
4
2,5
Fig. 3. Heat lost per unit mass flux vs. feed concentration for three average temperatures. The flow rate was 16 cm3/s and Tbl = 14 ° C. The solid lines are the linear fits
I
I
6 1/dp/dT
8 (K/kPa)
Fig. 4. Fit of the experimental data to Eq. (9). The feed was water and the flow rate 16 cm3/s.
of the experimental data.
dp)-' Q,o , = (o.1+o.3) + (o.56±o.o5) [ =is to increase the heat transfer coefficient and thus reduce the effect o f temperature polarization. This means that the temperatures at the membrane surface more closely approximate that of the bulk streams, and thus the transmembrane temperature difference is greater. This produces a greater driving force and consequently enhances the flux. In order to estimate the heat lost, calculations were performed in the following way. The latent heat of evaporation is the heat used effectively and is obtained from the permeate flux. The increase in heat of the cooling water is a sum of the latent heat of evaporation and the conduction heat lost through the membrane from the feed to cooling water. The results obtained for different experimental conditions are shown in Figs. 2 and 3. In Fig. 4 an analysis as suggested for Eq. (9) is made from the Qlost/J results obtained when water is used as feed. The experimental points [(dp/dT)-l; Qlo~t/J] have been fitted to a linear function by a least-squares method. The result is
J
dT
and so a value of km/C = (56+5)x 10 7 kg m s -4 K 1 is obtained. From Eq. (4) and using a typical value of%~2 [8], the value of kin = 0.055 W/m K is obtained. By using Eq. (7), the corresponding z coefficient may be estimated. The obtained values vary between 0.7 and 0.6 decreasing with the mean temperature and increasing with the flow rate, as might have been expected. These ~: results allow us to explain the Qlost/J values shown in Figs. 2 and 3. In fact, heat transfer by conduction increases approximately linearly with temperature gradient, unlike the vapour pressure driving force (in MD the effects of concentration polarization are negligible) and thus flux. As a result, Qiost/d decreases as mean temperature increases, and Q~ostis approximately constant, unlike the vapour pressure driving force and thus flux. As a result, Qlost/Jincreases as feed concentration increases. Finally we can see how an increase in flow rate has a trend to decrease Qio~t/J, but the effect is not considerable [10].
198
L. Martinez-Diez et al. / Desalination 126 (1999) 193-198
0,7
J
J
i
km 0,65
0,6
M
B
p
m
Q
--
Qlost
--
r
R T 0,5520
t
24
i
28
32
---
Mass flux through the membrane, kg/m 2 s Thermal conductivity o f the membrane, W/m K Molecular weight o f water, kg/mol Pressure o f water vapour, Pa Heat flux, W/m 2 Heat lost, W/m 2 Pore radius, m Gas constant, J/mol K Temperature, K
Greek
Average temperature (*C)
6
Fig. 5. Temperature polarization vs. average temperature. The different symbols correspond to different flow rates and feed concentrations : &, 8 cma/s and 1 mol/1; V, 16 cma/s and water; O,16 cm3/s and 1 mol/l.
--
8
Subscripts b
--
m
5. Conclusions 1. The effects o f temperature, feed concentration and flow rate on permeate flux and heat lost were studied for a direct contact-type module. It was found that for the feed studied, both high temperature and flow rate promote permeate flux and decrease relative heat loss. 2. A method is introduced in order to evaluate the coefficient k m / C , a membrane coefficient directly related with the heat lost per mass flux unit. The materials for the membrane should be chosen so as to reduce the conduction heat loss through the membrane. 3. The high values obtained for the relative heat lost suggest that membrane distillation can be competitive only in situations where some source o f waste energy is available.
6. Symbols C
--
AHv - -
Phenomenological coefficient, kg/m s Pa Latent heat o f vaporization, J/g
Membrane thickness, m Porosity, dimensionless Pore tortuosity, dimensionless
1
--
2
--
In the bulk phase At the membrane surface Hot solution Cold water
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