Modeling the performance of flat and capillary membrane modules in vacuum membrane distillation

Journal of Membrane Science 447 (2013) 369–375

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Modeling the performance of flat and capillary membrane modules in vacuum membrane distillation A. Criscuoli a,n, M.C. Carnevale a, E. Drioli a,b a b

Institute on Membrane Technology, ITM-CNR, Via P. Bucci Cubo 17/C, 87030 Rende, CS, Italy Department of Chemical Engineering and Materials, University of Calabria, Via P. Bucci Cubo 42/A, 87030 Rende, CS, Italy

art ic l e i nf o

a b s t r a c t

Article history: Received 12 March 2013 Received in revised form 15 July 2013 Accepted 17 July 2013 Available online 25 July 2013

This paper deals with the modeling of the performance, in terms of energy consumptions and distillate flow rate produced, of flat and capillary membrane modules in vacuum membrane distillation (VMD). The developed model was validated by experimental tests carried out at lab-scale on a lab-made flat module of 40 cm2 membrane area, equipped with a commercial polypropylene membrane (pore size, 0.2 μm), and on a commercial capillary Microdyn module of 0.1 m2 membrane area. Once validated, the mathematical model was used to predict the performance of modules with higher membrane areas (up to 5 m2). The flat module resulted to perform better than the capillary one in terms of energy consumption/permeate flow rate ratios, the lowest value being 130 kW h/m3distillate for a 5 m2 membrane area, at 80 1C of feed temperature and 10 mbar of vacuum pressure. & 2013 Elsevier B.V. All rights reserved.

Keywords: Vacuum membrane distillation Modeling Flat and capillary membrane modules Energy consumptions

1. Introduction Membrane Distillation (MD) is a promising technology for different fields of industrial interest, like wastewater treatment, desalination, ultra-pure water production, concentration of nonvolatile components from aqueous solutions, etc. [1–3]. The large amount literature on the application of membrane distillation is clear evidence of the increasing interest in this technology. Research, mainly at the laboratory scale, has investigated areas such as the development of membranes with specific properties, the design of modules able to reduce polarization phenomena and the optimization of the operating conditions. Nowadays, the commercial modules developed for membrane distillation are mostly for carrying out Air Gap Membrane Distillation tests (AGMD) and they provide fluxes of the order of 4–10 L/m2 h at 70–80 1C with energy consumptions in the range of 97– 550 kW h/m3distillate [4–8]. Recently, a different MD configuration has been also considered by the Memsys clearwater distribution company [9], that developed vacuum multieffect membrane distillation units working stage-by-stage at progressively reduced temperatures and pressures. The distillate fluxes at 70–85 1C and a vacuum of 50–80 mbar are around 7–10 L/m2 h, whereas the energy consumptions range from 70 to 440 kW h/m3distillate [10]. It is well known that VMD is the configuration able to provide the highest trans-membrane fluxes. However, the need of a high

n

Corresponding author. Tel.: +39 0984 492118; fax: +39 0984 402103. E-mail address: [email protected] (A. Criscuoli).

0376-7388/$ - see front matter & 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.memsci.2013.07.044

vacuum pump and of a condensation unit outside the module increases the complexity of the system and, up to now, no modules have been designed to apply this MD configuration at large scale. Moreover, research works are mainly on lab-scale modules and addressed to the investigation of temperature polarization phenomena and heat efficiency analysis, and only few deals with the energy requirements of the system [11]. In this work, a mathematical model for simulating the performance, in terms of energy consumptions and distillate flow rate produced, of flat and capillary membrane modules in VMD, was developed. After its validation with experimental data obtained at lab-scale, the model was used to predict the effect of different operating conditions (feed flow rate and temperature, vacuum pressure at the permeate side), as well as the module design, on the performance of bigger modules (up to 5 m2). The main aim of the work was to calculate and compare the energy consumptions/distillate production of flat and capillary modules for large-scale applications of VMD.

2. Materials and methods 2.1. Experimental The experimental procedure and the scheme of the VMD set-up are those reported in reference [11]. The permeate was collected in a trap immersed in liquid nitrogen and located between the module and the vacuum pump.

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Table 1 Main membrane properties. Membrane

Flat

Capillary

Membrane material Nominal pore size (lm) Thickness Porosity

Polypropylene 0.2 91 mm 0.70

Polypropylene 0.2 0.4 mm 0.70

The same lab-plant was used for both modules. The flat module had an effective membrane area of 40 cm2 (height of the feed flow channel: 3.5 mm; width: 4 cm; length: 10 cm) [11], and was equipped with a commercial (Membrana, Germany) polypropylene membrane. The capillary module was the MD020CP2N, purchased by Microdyn (Germany), had a membrane area of 0.1 m2 and contained 40 polypropylene capillary fibers (inner fiber diameter (df): 1.8 mm; outer fiber diameter: 2.6 mm; fiber length: 47 cm). Main properties of the membranes used are summarized in Table 1. The pore tortuosity (τ) is linked to the membrane morphology/ structure and, then, to the manufacturing method. For both membranes it was calculated as a function of the porosity, by using the equation proposed for stretched membranes [12]: τ ¼ 1=ε ¼ 1:42

ð1Þ

Distilled water was employed as hot feed. With the flat module, the liquid stream was sent at the bottom plate and the vacuum applied at the upper plate, whereas, with the capillary module, the feed was circulated in the lumen side and vacuum applied at the shell side. Each experiment was repeated at least three times, for ensuring the reproducibility of results. The error bars reported in the figures of Section 3.1, showing experimental data, are the result of the difference in measured values during the repeated tests. The registered difference was quite low (5%) and it was due to the experimental error. 2.2. Theory A mathematical model to simulate the performance of flat and capillary membrane modules in VMD was developed. The program was realized in Turbo Pascal language and the main assumptions were: – liquid-free micropores; – vapor transport in the membrane of Knudsen type; – heat transfer through the membrane due to the water evaporation only; – negligible pressure drops of the liquid feed inside modules.

specific heat, Tref is the reference temperature and ΔHv the heat of vaporization of water. The decrease of the temperature along the module is due to the heat lost with the water evaporation. Eq. (4) is for mass flux and it reports a relationship between the distillate flux and the trans-membrane water vapor pressure difference (Pm  Pd) based on the Knudsen model: KKnud is the Knudsen coefficient, that depends on both temperature and geometric characteristics of the membrane, rp is the pore size, ε is the porosity of the membrane, δ is the membrane thickness, τ is the pore tortuosity, Pd is the pressure at the vacuum side, Pm is the water vapor pressure at the membrane surface temperature (Tm), Mw is the water molecular weight and R is the gas constant. Furthermore, as there is a heat transfer coupled with the mass transfer and, considering the temperature polarization phenomenon, the trans-membrane flux may be related with hl (the feed side heat transfer coefficient), as reported in the heat flux Eq. (5), where Tf is the feed temperature. The calculation of hl was made through the following equations: Nu ¼ 1:62ðRe Pr dh =LÞ0:33 Nu ¼ 0:023Re0:8 Pr0:33

ðlaminar flow; Léve` que equationÞ

ð6Þ

ðturbulent flow; Dittus–Boelter equationÞ ð7Þ

Reynolds (Re), Prandtl (Pr) and Nusselt (Nu) numbers were calculated considering the effective internal diameter for the capillary configuration, whereas the hydraulic diameter was used for the flat one. In Table 2 the expressions used to calculate both the hydraulic diameter and the passage section of the fluid are reported, being a and b the width and the height of the feed flow channel of the flat module, respectively (see Fig. 1). For both module geometries, the module length was divided in steps, each one of 1 cm. For each step, all variables (temperature, velocity, flux) were calculated by solving the relative equations. Tm was determined by the following procedure: 1. 2. 3. 4.

Tm was first fixed at 3 1C less than the feed temperature; Pm was calculated through the Antoine's equation; The flux was determined by Eq. (4); The new value of Tm was calculated by Eq. (5).

The iterative procedure (from 2 to 4) was repeated until the difference between the old and the new value of Tm was lower than 0.1 1C. Table 2 Hydraulic diameter and passage section of the fluid for the two modules.

The considered equations, for both configurations, are the following ones: ρ S dv=dAmb ¼ Flux

ð2Þ

ρcp S ½dðvT f Þ=dAmb –T ref dv=dAmb  ¼ –Flux ΔH v

ð3Þ

Flux ¼ K Knud ðP m P d Þ ¼ 1:064ðr p ε=δτÞðM w =RT m Þ0:5 ðP m P d Þ

ð4Þ

Flux ΔH v ¼ hl ðT f T m Þ

ð5Þ

Module

Flat

Capillary

Hydraulic diameter (cm) Passage section of the fluid (cm2)

dh ¼2(ab)/(a+b) S¼ ab

dh ¼df S¼ Nfπdh2/4

df

Eq. (2) is the mass balance along the module: S is the passage section of the fluid, Flux is the trans-membrane vapor flux, dAmb is the differential membrane area and ρ is the fluid density. The feed velocity decreases along the module, as the distillate is produced. Eq. (3) shows the energy balance along the module: cp is the

b Feed

a (1)

Feed

(2)

Fig. 1. Sections of passage of the feed for the flat (1) and capillary (2) membrane modules.

A. Criscuoli et al. / Journal of Membrane Science 447 (2013) 369–375

2.3. Application of the model The developed model was first validated by comparing its predictions to experimental results. Then, it was used to calculate the energy consumptions and distillate production of bigger flat and capillary modules (up to 5 m2). These calculations were made at: – different operating conditions (feed flow rate and temperature; vacuum pressure); – different feed flow channel width and feed path length for the flat module (at parity of membrane area); – different number and length of fibers for the capillary module (at parity of membrane area).

371

of feed, which is the typical value considered for commercial systems under vacuum [14]), η the pump efficiency (fixed at 0.8 for all calculations), Pa the atmospheric pressure, Pd the vacuum pressure. 2.3.3. Thermal energy for heating the feed (after the pre-heating with the retentate stream) TEf ¼ Q f ρcp ðT IN –T f Þ

ð11Þ

with TIN the feed temperature at the module inlet. Both thermal and electrical energies were obtained in kW, using the appropriate conversion factors.

3. Results and discussion The calculations of energy consumptions included: 3.1. Validation of the mathematical model – the electrical energy for pumping the feed stream; – the electrical energy of the vacuum pump; – the thermal energy for heating the feed (supposed to be at 25 1C) up to the operating temperature, when no feed is re-circulated to the module (continuous operation). In particular, the feed was first pre-heated by using the heat of the retentate stream (STEP 1) and, then, the desired temperature was reached by using external heat sources (STEP 2), see Fig. 2. The heat transferred from the retentate to the feed was not taken into account for the calculation of the thermal energy consumption, being an “available” heat for the system. Therefore, the thermal energy supplied to the system was only that needed to warm the pre-heated feed up to the desired temperature (STEP 2). The equation used for the feed pre-heating with the retentate stream is

3.2. Modeling of the flat membrane module 3.2.1. Lab-module The effect of the hot stream flow rate and temperature on the distillate flux is shown in Fig. 5. As reported in [11], the flux is 60

ð8Þ

with Qf the feed flow rate, Tf the feed temperature after the preheating with the retentate, Qr the retentate flow rate and Tr the retentate temperature. From (8) Tf was obtained. The equations used to calculate the electrical and thermal energy consumptions are reported below. 2.3.1. Electrical energy for pumping the feed

50

modeling 20 mbar; 40°C experimental 20 mbar; 60°C

30

modeling 20 mbar; 60°C experimental 40 mbar; 60°C 20

ð9Þ

10

with Pf the feed pressure inside the plant (fixed for all calculations at 1.1  105 Pa, which was the experimental pressure).

EEf ¼ Q f P f

0

modeling 40 mbar; 60°C

Fig. 3. Comparison between the experimental and theoretical distillate fluxes; vfeed ¼0.4 m/s. Flat membrane module (Amb ¼ 40 cm2).

2.3.2. Electrical energy of the vacuum pump [13] EEv ¼ 2:85  104 ðT p q0 =ηÞlog ðP a =P d Þ

ð10Þ

10

with Tp the permeate temperature, q0 the flow rate of the air to be evacuated from the permeate line (3 kg/h of air per each m3/h

8

External Heat

9 7

J (kg/m2h)

Retentate

experimental 20 mbar; 40°C

40

J (kg/m2h)

Q f cp ðT f 25Þ ¼ Q r cp ðT r 28Þ

Figs. 3 and 4 show a comparison between the experimental and theoretical distillate fluxes for the flat and the capillary membrane modules, respectively. The values of fluxes were obtained at different feed temperatures, feed velocities and vacuum pressures. It can be noticed that the distillate flux increases with the feed temperature and degree of vacuum, according to what reported in [11]. The model predictions are quite good, since they fall in the experimental measured range.

6 5 4 3 2

Feed

Heated Feed

Pre-heated Feed

STEP 1

1 0

STEP 2

Fig. 2. Feed heating step-by-step.

experimental 40 mbar; 40°C; 0.4 m/s

modeling

experimental 60 mbar; 50°C; 0.8 m/s

modeling

experimental 90 mbar; 60°C; 0.8 m/s

modeling

Fig. 4. Comparison between experimental and theoretical distillate fluxes at various feed temperatures, feed velocities and vacuum pressures. Capillary membrane module (Amb ¼ 0.1 m2).

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150

140

T=40°C

120

T=50°C

140 130

T=60°C

100

T=80°C 80 60

J (kg/m2h)

J (kg/m2h)

160

v=0.4 m/s 120

v=0.6 m/s v=0.8 m/s

110

v=1 m/s

40 100

20 0

0.4

0.6

0.8

90

1

10

20

Fig. 5. Trend of the distillate flux with feed velocity and feed temperature; Pd ¼ 10 mbar. Flat membrane module (Amb ¼40 cm2).

60

Fig. 7. Trend of the distillate flux with vacuum pressure and feed velocity; Tfeed ¼ 80 1C. Flat membrane module (Amb ¼ 40 cm2).

20000

4800

18000

4300

16000 14000

T=40°C

12000

T=50°C

10000

T=60°C

8000

T=80°C

6000 4000

3800 3300

v=0.4 m/s 2800

v=0.6 m/s

2300

v=0.8 m/s

1800

v=1 m/s

1300

2000 0

En.cons/Qp (kWh/m3)

En.cons/Qp (kWh/m3)

40

Pd (mbar)

v (m/s)

800

0.4

0.6

0.8

1

v (m/s) Fig. 6. Trend of the Energy consumption/permeate flow rate ratio with feed velocity and feed temperature; Pd ¼ 10 mbar. Flat membrane module (Amb ¼40 cm2).

strongly dependent on the hot stream temperature, and less dependent on the flow rate. In particular, the effect of the flow rate on the distillate flux is more evident at higher temperatures, due to the higher fluxes and, then, higher temperature polarization, that is reduced when the flow rate increases. For example, at 80 1C, for a 150% increase of the feed velocity the flux increased of 34%. However, this gain was always lower than that achieved by acting on the feed temperature: at 1 m/s of feed velocity, for a 100% variation of the average temperature the increment of flux was of about 400%. Fig. 6 reports the trend of the energy consumption/permeate flow rate ratio with feed velocity and feed temperature. It decreases with the feed temperature due to an increase of the distillate flow rate Qp, and increases with the feed velocity, because of the higher flow rate to be heated (that means higher thermal energy required). At 80 1C, for a 150% increase of the feed velocity the ratio increased of 64.4%, while it decreased of about 77% for a 100% increase of the feed temperature at 1 m/s. The lowest value (around 2.500 kW h/m3) is obtained at a hot stream temperature of 80 1C and at a velocity of 0.4 m/s. The variation of the distillate flux and energy consumption/ permeate flow rate ratio with the vacuum pressure, for the investigated range of feed velocities, is shown in Figs. 7 and 8, respectively. The flux increases with the degree of vacuum and with the feed velocity, due to the higher driving force. Conversely, the ratio increases with the feed velocity and the permeate pressure. This result is due to the fact that, as aforementioned, by increasing the feed velocity, a higher feed flow rate has to be heated, with a consequent increase of the energy consumption. Concerning the effect of the permeate pressure, higher values mean a lower driving force and, then, a lower flux and permeate

10

20

40

60

Pd (mbar) Fig. 8. Trend of the energy consumption/permeate flow rate ratio with vacuum pressure and feed velocity; Tfeed ¼ 80 1C. Flat membrane module (Amb ¼ 40 cm2).

production. At 80 1C and 1 m/s, for a 500% increase of the pressure at the permeate side the flux decreased of 11.4% while the energy consumption/permeate flow rate ratio increased of about 5.3%.

3.2.2. Bigger modules After the calculation performed on the 40 cm2 flat module, the mathematical model was applied to calculate the energy consumption/permeate flow rate ratios of bigger flat modules. Particular attention was devoted to the module design, specifically, to the width of the feed flow channel and to the feed path length. At parity of membrane area and height of the feed flow channel (that was fixed at the experimental value), the width of the feed flow channel was reduced while the feed path length was increased. In this way, by working at constant feed velocity, lower feed flow rates were needed as the passage sections for the fluid decreased, with a consequent reduction of the thermal energy consumptions. The effect of the feed flow channel width was studied for 0.05 m2 and 0.1 m2 membrane areas. Fig. 9a–d shows the different designs of the membrane module of 0.1 m2 consisting in a 20 cm  50 cm flat sheet. The width was progressively reduced from 20 cm down to 1 cm, which was considered to be the lowest value that can be realized in module manufacturing. As reported in Fig. 10, at parity of membrane area and operating conditions, the energy consumption/permeate flow rate ratio decreases as the passage section for the fluid is reduced (at lower feed flow channel width), because of the lower feed flow rate to be heated in order to operate at the same feed velocity. The lowest value of the energy consumption/permeate flow rate ratio (around 600 kW h/m3) is obtained for a width of 1 cm. In Fig. 11 it is reported a comparison, in terms of the energy consumption/permeate flow rate ratio, between modules of different

A. Criscuoli et al. / Journal of Membrane Science 447 (2013) 369–375

5000

Amb=0.1 m2 20 cm

Feed OUT

50 cm

En.cons/Qp (kWh/m3)

4500

Feed IN

Qfeed=504 L/h

4000 3500 3000 2500 2000 1500 Qfeed=126 L/h

1000

Qfeed=126 L/h

500

2

Feed IN

373

Amb=0.1 m

0

4cm

Module:4x10; Amb=40 cm^2; Re=17481 Module:1x500; Amb=0.05 m^2; Re=14088

20 cm

Module:1x1000; Amb=0.1 m^2; Re=14088 Feed OUT 50 cm Amb=0.1 m2

800

2.5cm

700 20 cm

Feed OUT

…and 5 more passages 50 cm

Feed IN

Amb=0.1 m2

En.cons/Qp (kWh/m3)

Feed IN

Fig. 11. Trend of the energy consumption/permeate flow rate ratio at different membrane areas. Flat membrane module; Tfeed ¼80 1C; vfeed ¼1 m/s; Pd ¼ 10 mbar.

600 500 400 300 200 100

1cm

0 20 cm Feed OUT

…and 17 more passages

Module 1x1000; σ=91μm

Module 1x1000; σ=0.4 mm

Fig. 12. Comparison between the energy consumption/permeate flow rate ratio at different membrane thickness: flat membrane module; Amb ¼0.1 m2; Tfeed ¼ 80 1C; vfeed ¼1 m/s; Pd ¼ 10 mbar; Re¼ 14,088.

50 cm Fig. 9. (a) Scheme of the 20  50 membrane module: feed flow channel width ¼ 20 cm; feed path length ¼ 50 cm. (b) Scheme of the 4  250 membrane module: feed flow channel width ¼ 4 cm; feed path length ¼ 250 cm. (c) Scheme of the 2.5  400 membrane module: feed flow channel width ¼ 2.5 cm; feed path length ¼400 cm. (d) Scheme of the 1  1000 membrane module: feed flow channel width ¼ 1 cm; feed path length¼ 1000 cm.

1600

En.cons/Qp (kWh/m3)

1400 1200 1000 800 600 400 200 0

Module:20x50; Re=18675

Module:4x250; Re=17481

Module:2.5x400; Re=16667

Module:1x1000; Re=14088

Fig. 10. Comparison among the energy consumption/permeate flow rate ratios for different module designs: flat membrane module; Amb ¼ 0.1 m2; Tfeed ¼80 1C; vfeed ¼ 1 m/s; Pd ¼10 mbar.

membrane areas, when operating at the same inlet conditions: the 0.05 m2 and the 0.1 m2 membrane modules (both with the lowest feed flow channel width of 1 cm and, then, working with the same feed flow rate). In the figure, the performance of the lab-tested module (40 cm2), working with a higher feed flow rate, is also shown. The difference in the ratio values is higher when moving

from 40 cm2 to 0.05 m2 or 0.1 m2, because of the higher feed flow rate to be heated in the case of the 40 cm2 module (504 L/h vs. 126 L/h), as well as the lower permeate produced through the smaller membrane area. The model was also used to investigate the effect of the membrane thickness on the performance of the process. In particular, the energy consumption/permeate flow rate ratio obtained by using a flat membrane with the same thickness of the capillary one (0.4 mm) was calculated and compared to that achieved with the experimental flat membrane thickness (91 mm). Fig. 12 reports the comparison between the energy consumption/permeate flow rate ratio at different membrane thickness for the 0.1 m2 module with the lowest feed flow channel width (1 cm). The ratio increases with the membrane thickness due to the increase of the membrane resistance. After the optimization of the feed flow channel width, the mathematical model was used to predict the energy consumptions and distillate flow rate of bigger modules (1 m2 and 5 m2, made of 10 and 50 optimized 0.1 m2 modules in series, respectively). In this case, in order to be able to compare the two configurations (flat and capillary), the membrane thickness was fixed at 0.4 mm, which was that of the capillary module used in the experiments. Fig. 13 reports the trend of the energy consumption/permeate flow rate ratio with the membrane area for modules with the same feed channel width (1 cm), and, then, working with the same feed flow rate. In this case the thermal energy is the same for the different modules, while the permeate production increases with the membrane area. Therefore, the energy consumption/permeate ratio decreases as the membrane area increases. When the membrane area is 5 m2, it is possible to obtain interesting values of energy consumption/permeate flow rate ratio due to at the

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900

1400 1200

700

En.cons/Qp (kWh/m3)

En.cons/Qp (kWh/m3)

800

600 500 400 300 200 100

1000 800 600 400 200

0 Module:1x1000; Amb=0.1 m^2

Module:1x10000; Amb=1 m^2

0 L=25 cm

Module:1x50000; Amb=5 m^2

highest quantity of distillate (Qp) produced in the process. The lowest value is around 130 kW h/m3 at Tfeed ¼80 1C, Pd ¼ 10 mbar and vfeed ¼2 m/s, at which corresponds a flux of 25 kg/h m2. It has to be pointed out that there will be a point where the energy/distillate ratio will reach an asymptotic value: if the membrane area continuously increases, at parity of feed flow rate the retentate temperature will decrease and there will be a reduction of the permeate flux that will be collected only until the driving force across the membrane will be guaranteed. Afterwards, the gain in permeate will stop and the energy consumption/permeate ratio will not further decrease. 3.3. Modeling of the capillary module Further modeling runs were carried out on the capillary membrane module. The design of the module was optimized by varying the length and the number of fibers, in order to reduce the passage section for the fluid, that implies, at parity of feed velocity, a lower feed flow rate to be treated and, consequently, a lower energy consumption. Fig. 14 shows the trend of the energy consumption/permeate flow rate ratio with the module length when working at the same operating conditions and with a membrane area of 0.1 m2. At parity of membrane area and feed velocity in the fibers, the energy consumption decreases with the length of the module because longer fibers leads to a reduction of their number and, thus, to a reduction of the section for the fluid flow and of the feed flow rate to be heated. The highest and lowest values are around 1200 kW h/m3 and 800 kW h/m3, at 25 cm and 1 m of length, respectively. The experimental length (47 cm) gives ratio values in between. The trend of the energy consumption/permeate flow rate ratio with the membrane area was also evaluated for modules of the same length. The ratio is independent on the membrane area, because, at parity of length, higher membrane areas correspond to an increase of the number of fibers and, then, of both the feed flow rate to be heated (higher energy consumptions) and of the distillate produced (higher permeate flow rates). 3.4. Flat vs. capillary membrane module Fig. 15 shows a comparison between the energy consumption/ permeate flow rate ratios for the two optimized membrane modules of 5 m2 membrane area, equipped with the same type of membrane (ε, 70%; δ, 0.4 mm; dp, 0.2 μm). Although the possibility of having flat and capillary membranes with the same structure and characteristics is somehow unrealistic, this type of calculation was performed to exclude any influence of the membrane on the final

L=1 m

Fig. 14. Trend of the energy consumption/permeate flow rate ratio with the length of the capillary membrane module: Amb ¼ 0.1 m2; vfeed ¼1 m/s (Re¼ 4886); Tfeed ¼ 80 1C; Pd ¼ 10 mbar.

1600

En.cons/Qp (kWh/m3)

Fig. 13. Trend of the energy consumption/permeate flow rate ratio with the membrane area: flat membrane module; s ¼ 0.4 mm; Tfeed ¼80 1C; Pd ¼ 10 mbar; vfeed ¼ 2 m/s.

L=47 cm

1400 1200 1000 800 600 400 200 0

FLAT 1x50000 dh=0.00519 m; Re=28176 HF L=1m dh=df=0.0018 m; Re=9772 HF L=1m dh=0.00519 m; Re=28176 Fig. 15. Comparison between the energy consumption/permeate flow rate ratio for the two membrane modules. Tfeed ¼ 80 1C; vfeed ¼ 2 m/s; Pd ¼ 10 mbar; Amb ¼ 5 m2.

performance and to link it to the module design only. In particular, for the capillary module, both the effective inner diameter of the fibers (that of the commercial capillary module used during the experimental tests) and the hydraulic diameter calculated for the flat module were considered in the Re, Nu and Pr equations. Latter case was analyzed to investigate the performance of the capillary module when equipped with fibers having as diameter the hydraulic diameter of the flat module. The figure shows that, at the same operating conditions, there is an evident difference between the two configurations. The lowest value (130 kW h/m3), and consequently the best result, is obtained when the vacuum membrane distillation is carried out on the flat module. The better performance of the flat module is linked to the possibility of reducing the feed flow rate and, then, the thermal energy needed, through a reduction of the section of passage of the fluid. The cross sections of the optimized flat and capillary 5 m2 modules are, in fact, 3.5  10  5 m2 and 2.25  10  3 m2, respectively. This means that higher feed flow rates have to be employed with the capillary module to work with the same feed velocity. The performance of the capillary module is reduced when the hydraulic diameter of the flat module (bigger than the effective inner diameter of fibers) is used for calculations, because of the higher overall cross section, that means higher feed flow rates to be heated in order to work at the same feed velocity. In Fig. 16 the values of the energy consumption as function of the yield (defined as the ratio between the produced permeate and the feed), is reported for the capillary (at the two different diameters) and the flat modules. Also in this case, the best configuration, in terms of minimum value of energy consumption and maximum value of yield, is the flat one, for which a yield of about 50% is obtained.

A. Criscuoli et al. / Journal of Membrane Science 447 (2013) 369–375

400

En. cons. (kW)

350 300 250 200 150 100 50 0 0.50

1.37

49.4

Y (%) HF L=1m dh=0.00519 m; Re=28176 HF L=1m dh=df=0.0018 m; Re=9772 FLAT 1x50000 dh=0.00519 m; Re=28176 Fig. 16. Energy consumption vs. yield for the two membrane modules. vfeed ¼2 m/s; Pd ¼ 10 mbar; Amb ¼ 5 m2.

4. Conclusions A mathematical model to simulate the performance, in terms of energy consumptions and distillate flow rate produced, of flat and capillary membrane modules in VMD, was developed. The model was first successfully validated by experimental results obtained at lab-scale and, then, employed to optimize the performance of bigger modules (up to 5 m2), to be used at large-scale. It was found that: 1. The energy consumption/permeate flow rate ratio decreases with the feed temperature and vacuum pressure, while increases with the feed flow rate. 2. The optimized design of the flat membrane module leads to lower energy consumptions/permeate flow rate ratio than the capillary one. 3. The value of 130 kW h/m3distillate, obtained at 80 1C and 10 mbar with the 5 m2 optimized flat module, is in the range of the energy consumptions reported for the modules already developed for large-scale applications of membrane distillation. Moreover, the distillate flux achievable is higher and of the order of 25 L/m2 h.

hl ΔHv J KKnud L Mw Nu Pa Pd Pf Pm Pr q0 Qf Qp Qr R Re rp S TEf Tf TIN Tm Tp Tr Tref v

375

feed side heat transfer coefficient (W/m2 K) heat of vaporization of water (J/kg) trans-membrane vapor flux (kg/m2 h) Knudsen coefficient (kg/m2sPa) length (m) water molecular weight (kg/mol) Nusselt number atmospheric pressure (Pa) pressure at the vacuum side (Pa) feed pressure inside the plant (Pa) water vapor pressure at the membrane surface (Pa) Prandtl number flow rate of the air (std ft3/min) feed flow rate (m3/h) distillate flow rate (m3/h) retentate flow rate (m3/h) gas constant (J/mol K) Reynolds number pore size (m) section of passage of the fluid (m2) thermal energy for heating the feed (J/h) feed temperature (K) feed temperature at the module inlet (K) temperature at the membrane surface (K) permeate temperature (1R) retentate temperature (K) reference temperature (K) feed velocity (m/s)

Greek symbols δ ε η ρ τ

membrane thickness (m) membrane porosity pump efficiency fluid density (kg/m3) pore tortuosity

References The obtained results show the potentiality of VMD for large-scale applications. However, the realization and testing of both optimized flat and capillary modules (with a membrane area of 5 m2) will be needed, to confirm the model predictions or to underline the eventual critical points (e.g., pressure drops inside modules) that must be incorporated into the simulation program to be able to better describe what occurs in real implementations. Acknowledgments This work has been partly carried out within the “Membrane distillation in remote areas—MEDIRAS” Project, Grant Agreement no. TREN/FP7/218938, funded by the European Commission—7th FP.

Nomenclature Amb cp df dh EEf EEv Flux

membrane area (m2) specific heat of the water (J/kg K) inner fiber diameter (m) hydraulic diameter (m) electrical energy for pumping the feed (J/h) electrical energy of the vacuum pump (Hp) trans-membrane vapor flux (kg/m2 s)

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