Simulation of solar vacuum membrane distillation unit

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˙moxy auxiliary mass flow. ˙me mass flow of the entry of the module. ˙mret ... compared to the convection heat flow. The heat balance is reduced to v. dT dz. =.
Desalination 324 (2013) 87–92

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Desalination journal homepage: www.elsevier.com/locate/desal

Simulation of solar vacuum membrane distillation unit Samira Ben Abdallah ⁎, Nader Frikha, Slimane Gabsi Unit of research: Environment, Catalysis and Analysis Processes, University of Gabes National Engineering school of Gabès, Street Omar Ibn ElKhattab, 6029 Gabès, Tunisia

H I G H L I G H T S • The coupling of the solar energy with the hollow fibres module. • Modeling of heat and mass transfer in vacuum membrane desalination coupled with solar energy. • The determination of daily and yearly desalination unit production.

a r t i c l e

i n f o

Article history: Received 28 February 2013 Received in revised form 30 May 2013 Accepted 2 June 2013 Available online xxxx Keywords: Seawater desalination Membrane Distillation Solar energy Modeling

a b s t r a c t The present research work is interested in modelling and simulating a plant of vacuum membrane distillation (VMD) for seawater desalination coupled with solar energy. Its aim is not only to develop a mathematical model describing the functioning of VMD hollow fibre module coupled with a flat solar collector, but also to determine the daily productivity of this unit. The mathematical model shows that the daily production can reach 38 kg/day. The integration of the solar energy allows the improvement of the desalination plant productivity. © 2013 Elsevier B.V. All rights reserved.

1. Introduction The desalination of seawater is considered as the most important source of potable water for arid and semiarid zones [1]. Although its technologies are operational for many years, their cost often limits their use only to the rich countries. The possibility of designing innovative processes based on the coupling of this technology with the solar energy is becoming an attractive way to reduce the production costs and to increase the process performance [2]. For solar-powered desalination units, two different layouts are developed: compact system and two-loop system, in which seawater is heated directly inside collectors or by means of an intermediate heat exchanger, respectively [3]. Membrane distillation (MD) is a relatively new process that is investigated worldwide as a conventional separation process [4], such as distillation and reverse osmosis. Actually, it is a thermal membrane separation process that involves the transport of vapour through micro-porous hydrophobic membranes and operates on the principle of vapour–liquid equilibrium as a basis for molecular separation [5–8]. MD systems can be classified into four different configurations: direct contact MD (DCMD), air-gap MD (AGMD), sweeping gas MD (SGMD) and vacuum MD (VMD). The DCMD, AGMD and VMD are ⁎ Corresponding author. Tel.: +216 21572984; fax: +216 74 275595. E-mail address: [email protected] (S.B. Abdallah). 0011-9164/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.desal.2013.06.001

the best suited for desalination applications [6,9,10]. An experimental study carried out by Huayan et al. [11] to compare the efficiency of DCMD, SGMD and VMD, using a salt solution feed. They showed that the VMD presented the highest flux among the three MD configurations. Therefore, the VMD is chosen for the MD configuration adopted in this work. The VMD process is based on the evaporation of solvents through hydrophobic porous membranes improved by applying vacuum or low pressure on the permeate side [12]. Permeate condensation takes place outside the module, inside a condenser or a trap containing liquid nitrogen [7]. The analysis of the operating conditions shows that the parameters key is a relatively low temperature and pressure. Moreover, the process coupling VMD with a source of energy (solar or geothermal) could compete with reverse osmosis [3,7,14,15]. Being capable of directly using solar thermal energy, the solar membrane distillation desalination system has evolved as a promising green technology for alleviating the water resource problem [15,17]. R. B. Saffarini et al. [16] showed that solar heater costs accounted for over 70% of the total cost for all systems, suggesting the desirability of using alternative sources of thermal energy, such as solar energy. Since the majority of research studies concern the coupling of solar collectors with the other configurations of the DM such as DCMD [17,18] and AGMD [19–21], Wang et al.[22] were among the first to

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Nomenclature seawater heat storage capacity Cp D_ mass flow of the distillate molar water flow Jv Knudson permeability Km L module length _ oxy auxiliary mass flow m _e mass flow of the entry of the module m _ ret mass flow of retentate m _s mass flow at the exit m Pvacuum vacuum pressure R radius T temperature Intefacial temperature Ti ambient temperature Ta tank temperature Tr retentate temperature Tret V tank volume mean velocity vm

Subscripts CC central compartment CE external compartment CM compartment in the medium Int interior Ext external

Greek symbols ω recycling ratio λ water conductivity ρ water density

couple VMD with solar energy. Their study shed the light on a designed and tested solar-heated hollow-fibre-based VMD system. The largest permeate flux obtained is 32.19 L m−2 h−1 of membrane area with an 8-m2 solar energy collector. Therefore, Mericq et al. [10] studied the possibility of submerging the plate DMV membrane in the salinity gradient solar ponds and the solar collector. The use of solar collector does not only seem to be the most interesting solution but also allows a maximum permeate flux of 142 L m−2 h−1 to be reached with permeable membrane. In this research work, a study of the effect of coupling solar energy with the VMD module on the permeate stream is realized. This study is carried out in step three: • A modeling of functioning of a plane solar collector, • A modeling of the heat and mass transfer within the hollow fibre module, • Finally, a coupling of two models by performing a balance sheet on the whole installation. Such a global model allows the determination of the instantaneous variation of the distillate flow as well as the daily productivity. 2. Modelling of the functioning of the vacuum desalination membrane coupled with the solar collector Vacuum membrane distillation is a complicated physical process in which both heat and mass transfers are involved. Indeed, the coupling of the heat and mass transfer equations in each part of the unit; the module, the collector and the tank, lead to the establishment of a model

describing the functioning of the desalination unit. The variations of the temperature and distillate quantity during the day were determined. The model is developed to calculate the effect of the solar energy on the permeate flux. Fig. 1 shows the plan for the installation. In fact, the hollow fibre module was coupled with a solar flat plate collector to improve its productivity and received a water flow not only to be treated from the tank, but also to provide an elevation of water temperature function of the solar radiation received by the collector. The tank was fed with fresh sea water and retentate flow. 2.1. Solar collector The coupled collector chosen for this installation is a flat plate collector with a slope of 30°. It was made up of 30 tubes having the length of 2 m and the diameter of 8 mm. The collector exit temperature was determined using a model developed by Frikha et al. [23]. This model allows calculating daily exit temperature variation according to the solar radiation. The latter is calculated using EUFRAT model that determines the different types of radiation as a function of climatic parameters [24,25]. Fig. 2 represents the instantaneous variation of the collector exit temperature for the four typical days of the year which represent the equinox and solstices. With the equinox was the date when day and night are of approximately equal length marking the beginning of spring and autumn. The solstices were both the longest day of the year (in summer) and the shortest day of the year (in winter). This temperature gradually increased for the first few hours of the day and then steadily decreased at the end of the day. So the temperature level depends on the insulation. For the four typical days, the temperature does not exceed the 80 °C which is the membrane temperature permissible. The temperature reached its maximum value, about 80 °C in June. What is worthy to be noted is that these maximum values range from 12 to 13 h, which is the time interval during which the collector received the maximum insulation. This first part gives us the collector exit temperature variation as a function of the collector feed temperature and solar radiation which it subsequently used. 2.2. Hollow fibre module Firistly, we have developed a model describing the heat and mass trasfer in the hollow fobre module. This module allows to determine the module exit temperature and permate flow variation as a function the module feed temperature wich the collector exit température in this case [5,12,26]. The hollow fibre module configuration is external–internal. Indeed, the feed fluid circulates outside the fibre and the depression is applied inside the fibre. Hence, the direction of permeate flow is from outside towards the inside [27]. The heat transfered inside the module is coupled with a mass transfer through the membrane, which is due to the difference in pressure on both sides of the membrane. The establishment of a rigorous model describing the heat and mass transfer inside the hollow fibre module is very complex. Some assumptions are followed to mitigate and deal with the problem as shown in Fig. 3. In fact, the angular distance between fibres is little compared to the radial one. We supposed that the fibres are placed the ones with the dimensions of the others according to the angular distance by forming an assembly of coaxial cylinders. Thus, we consider that the internal fibre diameter represents the vacuum thickness compartment. The fibre thickness represents the membrane thickness and the distance between fibres represents the water thickness compartment. The module consists of a whole coaxial cylinders with alternate compartments water membrane–vacuum membrane where a mass transfer through the membrane happens under the gradient pressure effect.

S.B. Abdallah et al. / Desalination 324 (2013) 87–92

89

Hollow fibre module

Solar flat plate collector

Retentate

Distillate

Appoint flow Fig. 1. Schematic diagram of hollow fibres modules.

The determination of the module temperature profile requires developing a heat balance in each water compartment. The heat balance in water compartment was written as: !   dT 1d dT d2 T ρ Cp v ¼λ r þ 2 dz r dr dr dz

ð1Þ

In general, the conduction heat in the axial direction can be neglected compared to the convection heat flow. The heat balance is reduced to   dT λ 1d dT v ¼ r dz ρ C p r dr dr

ð2Þ

The transfer of water molecules in gas phase through the membrane pores is given by the mechanism of Knudsen diffusion [21]. The molar water flow Jv crossing the membrane is described by the following equation:  JV ¼ K m

 exp c−

  d −P vacuum T i −e

ð3Þ

−0:5

Km ¼ α Ti

with α ¼

2 ε rp 1 3 χ δR

rffiffiffiffiffiffiffiffi 8 R π

We consider a module with n compartments of water. We have one exterior compartment, one central and n − 2 compartments located in the middle between two vacuum compartments. The membrane interface temperature is determined by solving the equations describing the mass and heat transfer for each type of compartments. The interface temperature is determined by a heat balance in each compartment (DWT): • For external compartment (CE): ρ C p vm −

 ρ C p vm −

70 60

!   2 RintCE dT 1d dT  2  J Ζ −λ r ¼0 vintCE dz r dr dr ρ R extCE −R2 intCE

ð5Þ

   2 dT 1d dT J vextCC z −λ r ¼0 ρ RextCC dz r dr dr

ð6Þ

With 0 ≤ z ≤ L and 0 ≤ r ≤ RextCC • For n − 2 compartments in the medium

50

ρC p vm −

21 March

40

21 June

!   2ðJ vintCM RintCM þ J vextCM RextCM Þ dT 1d dT  2  −λ r ¼0 z 2 dz r dr dr ρ R extCM −R intCM

ð7Þ

21 September

30

21 December

with 0 ≤ z ≤ L and RextCM ≤ r ≤ RextCM

20 10

ð4Þ

With 0 ≤ z ≤ L and RintCE ≤ r ≤ RextCE • For the central compartment (CC):

80

Exit collector temperature (°C)

The coefficient of the membrane permeability or the Knudson permeability Km can be related to the membrane structural properties such as porosity (ε), thickness (δ), tortuosity (λ) and the pores radius (rp) and at the membrane interface temperature (Ti) [5–28]. Pvacuum: vacuum pressure; antoine constants: c = 23.1964, d = 3816.44, e = 46.13

The mass transfer equation for each type of compartment gives the distillate flow: 6

8

10

12

14

16

18

20

Time (h) Fig. 2. instantaneous variation of the outlet temperature for different day (feed temperature = 25 °C).

• For external compartment (CE): L

DCE ¼ ∫0 J vextCE 2 π RintCE dz

ð8Þ

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JvintCE JvextCM JvinCM JvextCC

CC

CM CE

Fig. 3. Cross section of the module. CC: central water compartment. CE: external water compartment. CM: water compartment in the medium located between two vacuum compartments.

• For the central compartment (CC): L

DCC ¼ ∫0 J vextCC 2 π RextCC dz

3. Result and discussion ð9Þ

• For n − 2 compartments in the medium located between two vacuum compartments (CM): L

DCM ¼ ∫0 ðJvintCM RintCM þ JvextCM RextCM Þ2 π dz

ð10Þ

The total distillate flow D is equal to the sum of the various flows in each compartment Di D ¼ ∑ Di

ð11Þ

n

The above equation resolution is used to determine the variation of the permeate flow and module exit temperature to the module feed temperature. On the other hand, we have developed a second model describing the functioning of a hollow fibre module coupled with plate solar collector that operates with retentate recycling [5,12]. The retentate flow at the module exit is equal to the remaining quantity: _ e −D_ _s¼m m

ð12Þ

_s _ ret −m m _ ret m

ð13Þ

So the auxiliary flow was: _ ret þ D_ ¼ ð1−ωÞm _ e þ ωD_ _ oxy ¼ ð1−ωÞm m

ð14Þ

Heat balance on the tank:     _ e þ ωD_ C p T a þ ω m _ e −D_ C p T ret ðt Þ ð1−ωÞm _ e T r Cp þ ρ Cp V ¼m

dT dt

3.1. Feed and exit module temperature In order to study the effect of the retentate recycling, the daily variation of feed and exit module temperature were determined. Fig. 4 shows the variation of feed and exit module temperature along the day for 21 June. The curves are seen to be similar. Indeed, the temperature increases gradually at the beginning of the day to reach its maximum between 12 and 13 h and then decreases. The temperature evolution is found to be influenced by the insulation. Besides, the exit temperature is always lower than the feed temperature. This decrease, which reaches 15 °C at 12 h, is caused by the evaporation power need. Whereas the exit temperature is practically always higher than the ambiant temperature that is favorable for a module functioning with recycling by taking into account the retentate heat recovered quantity. The retentate can reach a maximum temperature of about 62 °C. This value does not exceed the limit of the permissible operating membrane temperature which is on the order of 80 °C. It is to be noted that the temperature inside the membrane must be controlled in order to protect the membrane structure. 3.2. Permeate flow

The recycling ratio expressed by: ω¼

The fibres module characteristics that are selected to support high temperatures at the membrane wall have a good permeability. Table 1 shows the characteristics of hollow fibre module.

ð15Þ

We made use of a program using the Matlab calculation software which allows the equations to be presented in the previous model. The resolution is fully developed by the Ruge Kutta method using the predefined function in Matlab ode 23. This function is executed to solve non-stiff differential equations, low order method. A coupling between the balance equations on each part of the installation allows us to determine daily temperature variations at the exit collector (feed module) as well as the produced permeate flow.

The established model allows the determination of the profile of permeate flow along the day. The instantaneous variation of the permeate flow in different typical days are reported in Fig. 5. These results are obtained with the total recycling of the retentate flow (W = 1). Taking into account that the feed water flow was 256 kg/h, the permeate flow is found to reach a maximum at the hours when the received sunshine by the collector was higher. This maximum that reached 2.5% of the feed water flow varies according to the season, from almost 6 kg/h in summer (21 June) to 3.6 kg/h in winter

Table 1 Characteristics of hollow fibre module. Nature

PVDF

Internal fibre diameter (mm) Membrane thickness (mm) Length (m) Fibres number Diameter module (cm) Maximum temperature (°C) Permeability (m/s) (Ti in K) Vacuum pressure (Pa) Water flow rate (m/s)

2.6 0.4 1 18 2 80 Km = 7.8 × 10 1000 0.1 ≤ v ≤ 1

−6

× Ti−0.5

S.B. Abdallah et al. / Desalination 324 (2013) 87–92 Table 2 Quantities of permeate and productivity of the plant to four typical days.

80 70

Temperature (°C)

91

60

Date

21 March

21 June

21 September

21 December

Total distillate (kg) Average productivity (kg/(h m2))

39.47 17.32

46.54 20.42

36.86 16.18

24.32 10.68

50 40

The desalination plant yearly production variation varies seasonally. This is surely attributable to the variation of solar radiation. Indeed, Fig. 6 follows a very similar trend to the radiation level throughout 1 year. It varies from a minimum of 24 kg/day in winter to a maximum of 49 kg/day in summer. This module produces 13648 kg of water per year, which represents a daily production of 38 kg/day.

Feed module Exit module

30 20 10

8

6

10

12

14

16

18

20

4. Conclusion

Time (h) Fig. 4. Instantaneous variation exit module temperature along the day to 21 June.

(21 December). Such a variation depends on the out temperature of the collector, essentially of the received sunshine by this collector. As for the average productivity of the installation, it is represented in this case by the quantity of permeate per hour per unit of membrane surface. Table 2 compares the total distillate and average productivity of the four typical days. The daily water production thus ranges from 24.32 kg in winter to 46.54 kg in summer. Therefore, the average productivity of this installation increases according to the month. Actually, it reaches its maximum of 20.42 kg (per h m2 of the membrane) in June and is directly related to the feed temperature of the module as well as to the solar flow received by the collector.

The present research work aims at studying the simulation of a desalination membrane coupled with a solar collector. In order to study the contribution of solar energy effect, a model describing the solar desalination plant running is developed. This model considers the transfer phenomena for each part of the installation. The obtained results show that the desalination plant performance is remarkably influenced by the amount of energy transported to the feed. The coupling of the solar energy with the hollow fibres module allows the improvement of the desalination plant capacity that can be reached during daily production about 38 kg/day, but this production can be better if more than one module or a more effective solar collector such as a CCP is used, which can ensure high elevations of temperatures. A solar DMV unit was installed in the village of orphaned children (SOS MAHRES) in the coastal region Mahres. This work is carried within the framework of MEDINA project (Membrane-based Desalination: An Integrated Approach). An experimental study of this desalination unit is in progress.

3.3. Yearly variation of the desalination plant production The simulation program is also used to perform the desalination plant over a period of 1 year. The knowledge of the production of the module per day and the variation of the plant production along the year are presented in Fig. 6.

Acknowledgment This research work was supported by European commission within the sixth framework programme PCRD (project MEDINA no. 036997).

6 21 March

50

21 June 21 September

5

45

4

Production (kg)

Permeate flow (kg/h)

21 December

3

2

40

35

30

1 25 0

6

8

10

12

14

16

18

20

Time (h)

20

0

50

100

150

200

250

Day Fig. 5. Instantaneous variation of the permeate flow for different day (mfeed = 256 kg/ h; V = 50 L; R = 0.01 m; L = 1 m.).

Fig. 6. variation of the daily module production.

300

350

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