Computational and experimental study of chromium (VI) removal in direct contact membrane distillation

Journal of Membrane Science 450 (2014) 447–456

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Computational and experimental study of chromium (VI) removal in direct contact membrane distillation Madhubanti Bhattacharya, Sajal Kanti Dutta, Jaya Sikder, Mrinal K. Mandal n Department of Chemical Engineering, National Institute of Technology Durgapur, Durgapur 713209, India

art ic l e i nf o

a b s t r a c t

Article history: Received 19 June 2013 Received in revised form 17 September 2013 Accepted 20 September 2013 Available online 1 October 2013

Computational and experimental study of a countercurrent direct contact membrane distillation (DCMD) module equipped with commercially available flat sheet hydrophobic polytetrafluoroethylene (PTFE) microporous membrane with polyethylene terephthalate (PET) and polypropylene (PP) support was investigated to remove toxic chromium (VI) from simulated water. PTFE/PET membrane exhibited better performance in terms of normalized flux. Liquid entry pressure (LEP) was used to characterize the thin film membrane. The effects of flowrate, chromium concentration, feed and permeate inlet temperature were studied with significant results on the flux and complete rejection. A two dimensional mathematical model was built up based on mass, momentum and energy balances to explore the effects of operating parameters on flux, flow conduit temperature distributions across entire domain and membrane surface temperatures across module length. The predictions exhibited good agreement with the experimental results using a modified coupled Knudsen and Poiseuille flow models. & 2013 Elsevier B.V. All rights reserved.

Keywords: Chromium (VI) removal Direct contact membrane distillation (DCMD) Computational study Knudsen diffusion Temperature polarization coefficient (TPC)

1. Introduction Chromium is known as a highly toxic metal, considered a priority pollutant contributed in the effluents produced from the electroplating, leather tanning, cement, mining, textile dyeing, manufacturing of dye, paper, ink, aluminum conversion coating operations, steel fabrication, plants producing industrial inorganic chemicals, wood treatment units, paints and pigments, metal cleaning, fertilizer and photography industries [1]. Uncontrolled or accidental release of chromium-bearing solutions from these various industrial applications seep into the soil and subsurface environment which results in groundwater contamination at nearby communities. Wastewater and solid waste from tanning operations often find their way into surface water, where toxins are carried downstream and contaminate water used for bathing, cooking, swimming and irrigation. South Asia, and in particular India and Pakistan, has the highest number of tanning industries, with South America also at risk of large populations being exposed to chromium contamination. According to the World Health Organization (WHO) and Bureau of Indian Standards (BIS) drinking water guidelines, the maximum allowable limit for total chromium is 0.05 mg/L [2,3]. Among two general forms Cr(III) and Cr (VI), trivalent chromium (chromium III) is a naturally occurring n

Corresponding author. Tel.: þ 91 343 275 4091; fax: þ 91 343 254 7375. E-mail addresses: [email protected], [email protected] (M.K. Mandal). 0376-7388/$ - see front matter & 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.memsci.2013.09.037

element, which is about 300 times less toxic than Cr(VI) that is relatively stable and innocuous, and can be found in plants, animals, and soil. Hexavalent chromium (chromium VI) is far more dangerous for humans, and is usually created by anthropogenic causes. It is a toxic human carcinogen that can cause or increase the rates of certain cancers. The concentrations of Cr(VI) in the wastewater of some industries like hardware factory is 60 mg/L [4], chrome tanning industry is 3.7 mg/L [5], 75.4 mg/L in electroplating industry [6], and 8.3 mg/L in tannery plant [7]. Due to the increasingly stringent environmental legislation, treatment of wastewater or contaminated groundwater laden with heavy metals has received considerable attention. Methods such as chemical precipitation, ion exchange resin, foam flotation, adsorption, and solvent extraction [8] are used for the removal of the chromium from industrial effluents although efficiency of removal is not satisfactory. Membrane methods like ultrafiltration, nanofiltration, reverse osmosis, electrodialysis, and liquid membrane are the other tools for separation with much better efficient exclusion [2]. Along with all these techniques, an emerging technology, membrane distillation is also suitable alternatives to the above mentioned methods. Unlike other conventional membrane separation techniques, MD is a thermally driven process. The transport mechanism of water vapor in the MD process can take place following Knudsen model, Poiseuille model or molecular diffusion model. Researches on removing heavy metals from waste or ground waters using membrane distillation is very few, likely, Macedonio

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and Drioli [9] and Qu et al. [10], conducted experiments in laboratory-scale utilizing direct contact membrane distillation (DCMD) modules with tubular geometries for separating arsenic. Qu et al. [10] testified that the concentration of arsenic in product water could be brought down to 10 mg/L with feed water arsenic concentrations as high as 40 mg/L and 2000 mg/L for As(III) and As (V), respectively. Almost similar results were reported by Macedonio and Drioli [9], although the feed water arsenic concentration was much lower in their studies. Air gap membrane distillation (AGMD) using a small-scale commercial prototype MD module was introduced by Islam [11] to study the arsenic separation and reported successful treatment of arsenic-contaminated water. Pal et al. [12], studied removal of arsenic from contaminated groundwater by solar driven membrane distillation, that for a 0.120 m3/h feed flow rate, 0.13 mm PVDF membrane yielded a high flux of 74 L/ m2 h at a feed water temperature of 40 1C and, 95 L/m2 h at a feed water temperature of 60 1C. In general MD models were developed, assuming that the process was one-dimensional using empirical heat and mass transfer equations. In very few studies, two-dimensional theoretical models were only considered, in which the feed and permeate temperatures along with the concentrations were performed along the longitudinal (x-axis) and transversal (y-axis) directions and local as well as total permeate fluxes were determined. The partial differential equations considered for the feed and permeate sides were coupled with the simultaneous mass and heat transfer equations through the membrane [13–17] to get the findings. The development of a transport model for a direct contact membrane distillation process in laminar flow was studied by RodriguezMaroto and Martinez [18] that allows knowing within the flow channels its velocity and temperature profiles which act as a function of externally measured temperatures just at the entrances and exits of the flow channels in the membrane module. The difference between the bulk temperatures and the externally measured one of a conventional membrane module can be calculated following the above model. In their study when working at low flow rates and high temperatures, moderately important differences between both temperatures were identified. A two dimensional DCMD model containing mass, energy and momentum balance was developed by Hwang et al. [19] for predicting production of permeate flux. The effect of linear velocity on permeation flux was examined where the effects of operating parameters such as flow mode, temperature difference, and NaCl concentration were also considered and validation of the simulated results with experimental results was compared. To validate the production of pure water from saline water theoretically, Chen et al. [20] designed a two-dimensional cocurrent flat-plate direct contact membrane distillation (DCMD) mathematical model. The partial differential equations are simplified to ordinary differential equations by finite difference technique. Simultaneous linear equations were evaluated with the help of fourth-order Runge–Kutta method. Knudsen and poiseuille flow models were combined for membrane co-efficient estimation, and validation of theoretical results with the experimental ones. Zhang et al. [21] developed a model containing mass and heat balance to predict the flux and evaporation ratio in direct contact membrane distillation (DCMD) using a compressible membrane. A dramatic flux decrease was found due to the use of compressible counter-current flat sheet PTFE membrane. The effect of linear velocity and the membrane length on permeation flux was investigated. Effect of different pressures on the membrane flux and temperature polarization was also calculated and validated with modeling results. In transient regime for SGMD process, Darcy–Brinkman–Forcheimer formulation was coupled with Navier–Stokes equations by Charfi et al. [22] for performing a two dimensional numerical simulation model. The fluids were

circulated across the membrane module in counter current mode. A solver based on the compact Hermitian method was incorporated to crack the derivative equations. The computed results obtained from numerical simulations were validated by comparison with experimental data. It was reported by Gostoli and Sarti [23] that the DCMD flux becomes independent on the membrane thickness when δ⪡km/h; where km denotes the thermal conductivity of the membrane and h, heat transfer coefficient combining both the feed and permeate boundary layers. A critical review of the most frequently used heat transfer empirical correlations in MD systems was presented by Mengual et al. [24]. The main objective of this work is to explore the effect of operating parameters on the fluxes of countercurrent flow mode. Commercially accessible porous hydrophobic membranes were used for the experimental purpose for removing chromium (VI) from contaminated water. The membrane chosen for this purpose only passes purified volatile water vapor through the membrane leaving the solute on the other end of the membrane. The PTFE commercial membrane was selected, as amount of flux obtained was much higher with respect to other commercial membrane [12]. Hydrophobic nature of the membrane with the micrometer pore size restrict membrane pore wetting irrespective of the fluctuating process pressure which retards the water molecule passage through the membrane for increasing the efficacy of the chromium removal. Comparative study between porous hydrophobic PTFE/PP and PTFE/PET membrane was also conducted. For studying the effects of flow rate, chromium concentration, feed and permeate inlet temperature on flux, a two dimensional theoretical model based on Navier–Stokes equation was considered. The flow mechanism was described by modified coupled Knudsen–Poiseuille diffusion model. All the physical properties related to model equations were considered as a function of temperature and flow model contributions (i.e., A(T) and B(T) respectively) in calculating the flux equation were also considered as temperature function. The differential equations obtained were discretized using finite difference technique. To describe the nature of DCMD process a detailed numerical analysis over mass, momentum and energy balances was conducted, and prediction was made on the water flux generation and finally predicted simulate results were validated with the experimental ones.

2. Experimental 2.1. Materials and chemicals Two commercial polytetrafluoroethylene (PTFE) membranes supported by a polyethylene terephthalate (PET) and polypropylene (PP), (Membrane solutions, Shanghai, China) were used in this study. Properties of membranes are mentioned in Table 1. The chemicals used were potassium dichromate, 1,5-diphenylcarbazide, concentrated sulfuric acid 98% and acetone (MERCK, India). Ultrapure water (Milli Q system, Waters, USA) was also used for various purposes.

Table 1 Membrane properties. Properties

PTFE/PET film

PTFE/PP film

Pore size (μm) Porosity (%) Thickness (μm) Thermal conductivity (W/m K)

0.22 80 370 0.25

0.22 80 163 0.28

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449

i=1

2

3

j=N

6

6

PERMEATE OUT

PERMEATE IN

1 5

i=M

j=1

j=N

4

5

FEED IN

FEED OUT

j= 1

i=M Length- 27.4 cm, Breadth- 6.4cm, Width- 1 cm

5

6

6

5

i=1

Fig. 2. Two dimensional counter current flow.

rejection (Rb) [25] are defined as follows:

7

V′ At 
 Cp Rb ¼ 1  Cf

ð1Þ

J¼

4

8

2 9

Fig. 1. Schematic flow-diagram of direct contact membrane distillation (DCMD) experimental set-up [1—permeate tank; 2—pump; 3—cooling coil/chiller; 4— rotameter; 5—pressure gauge; 6—temperature sensor; 7—membrane module; 8— heating coil in water bath; 9—feed tank].

2.2. Experimental methods A rectangular module with two halves (27.4 cm  6.4 cm  1 cm) was fabricated to carry out the experiments. A porous, flat sheet membrane was sandwiched between two halves of the module on finely perforated stainless steel plate. A schematic diagram of set up is shown in Fig. 1. The effective membrane surface area of module was 175.36 cm2. The hot feed solution was circulated along the lower channel of the membrane module and the cold permeate solution (pure water) along the upper channel countercurrent-wise to determine the effects of initial chromium concentration in the feed, its flowrate, temperature and permeate inlet temperature on chromium removal efficiency and flux. Temperatures and flow rates were controlled by regulating both the heating baths (Metrotech, India) and circulating peristaltic pumps (VSP-100, Miclins, India) respectively. Both the feed and permeate tank (SS-316) were insulated to avoid heat loss. Temperature, pressure, and flow rate were continuously monitored and controlled. The feed inlet temperature was varied from 40 1C to 70 1C, permeate temperature lies in the range from 18 1C to 25 1C with the feed flowrate from 50 LPH to 125 LPH, concentration of feed was increased from 200 ppb to 2000 ppb. Leakages were checked prior to each run. Amount collected in the permeate tank and outlet temperature of flow stream were recorded every 1 h interval at steady state and variation of pressure was also noticed. The difference in constant volume of permeate in the permeate tank over a time period was used to calculate the flux to minimize measurement errors (75%). Reproducibility of the values was checked by three separate runs conducted under same operating conditions. Samples of distillate collected at definite interval were analyzed for measurement of chromium (VI) concentration in the permeate by using a UV–vis spectrophotometer (CECIL 7000 series, GERMANY) at 540 nm wave length using 1,5-diphenylcarbazide as a color complexing agent, acetone as solvent and concentrated sulfuric acid to maintain the pH of the standard solution. 2.3. Parameters A set of parameters is used to describe the performance of the DCMD process. The widely accepted parameter flux (J) [12] and

ð2Þ

where V′, A, and t represent the volume of permeate sample (m3), the effective membrane area (m2) and the operating time (h), respectively. Cp and Cf represent permeate and feed concentrations respectively.

3. Theoretical models In computational study on DCMD process, three transport mechanisms were considered such as mass transfer through porous membrane layer, momentum transfer for the feed and permeate channel and energy transfer for all three layers. Three layers including the feed channel, porous membrane layer and permeate channel were constructed as shown in Fig. 2. The interfacial mechanism that controls the mass transfer resistance inside the thin film membrane is the mean free path (λ) for the vapor molecules and pore diameter (d). The partial pressure difference occurred due to the variation of the temperature causes the mass transfer (i.e., vapor molecule) across the membrane. The hydrophobic nature of the membrane and the higher LEP value may extend the interface at the permeate side of the membrane surface. The theoretical calculation procedures are sited in Appendix A. 3.1. Mass transfer The difference in saturated pressure (function of temperature) on both membrane surfaces is the main driving force for mass transfer through the membrane. The general mass flux form can be expressed as follows [20]: N″ ¼ C m ΔP sat ¼ C m ðP 1 sat  P 2 sat Þ sat

ð3Þ

sat

where P 1 and P 2 are the saturated vapor pressure of water on the hot and cold feed membrane surfaces, respectively. Cm is membrane coefficient which plays a substantial role for modeling and enormously affects the flux. Saturated vapor pressure can be described using the Antoine equation [26]:
 3816:44 P k sat ¼ exp 23:1964  ; k ¼ 1; 2 ð4Þ T k  46:13 where P k sat is in kPa and Tk is in 1C. To describe the mass flux across the hydrophobic porous membrane, Knudsen diffusion model (since mean free path of vapor molecules is larger than the membrane pore size), Poiseuille flow model (as momentum get transferred to the supported membrane) and molecular diffusion model (since the concentration gradient formed across the membrane) are considered to the

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three vital membrane flow models. The calculated Knudsen number is much greater than one (Kn⪢1), therefore Knudsen diffusion predominates the mass transfer process (i.e., molecule– pore wall collision). A modified coupled Knudsen and Poiseuille flow model is proposed in the present study and experimental results were validated with theoretical values. According, modified proposed Knudsen and Poiseuille flow model [19,27] can be described as sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ! 8 Ar 1 A r2 1 Pm M sat N″ ¼ ΑðΤÞ ð5Þ þ ΒðΤÞ ðP sat 1  P2 Þ 3 τδm 2πRMΤ m τδm 8μ RΤ m ΑðΤÞ ¼ 5  10

5

ðΤ 3f Þ  0:0085ðΤ 2f Þ þ 0:455Τ f

BðΤÞ ¼ 1  AðΤÞ

 7:05

ð6Þ ð7Þ

where A(T) and B(T) are Knudsen diffusion model and Poiseuille flow model contributions, respectively; Tf is the feed temperature, M is the molecular weight of water, Pm is the mean saturated pressure in membrane, R is the gas constant, r is the pore radius, Tm is the mean temperature in membrane, δm is the thickness of membrane, ε is the porosity of membrane, m is the water vapor viscosity and τ is the tortuosity factor. The tortuosity of the porous hydrophobic PTFE membrane can be written as [28] 1 τ¼ ε

ð8Þ

3.2. Momentum transfer Momentum balances are performed in both the feed and permeate channels using standard Navier–Stoke equation as follows [29]: Dv ρ ¼  ∇P þ μ∇2 v þ ρg Dt

ð9Þ

Therefore the reduced form of energy equation for feed and permeate side can be described as kj

∂2 T j ðx; yÞ ∂T j ðx; yÞ ¼ ρj cpj vj ðyÞ ∂x ∂y2

ð12Þ

where j symbolizes either feed or permeate side. The boundary conditions are as follows:  Kj

∂T j ðd; xÞ Km ¼ N″λ þ ½T ðd; xÞ  T p ðd; xÞ ∂y δm f

ð13Þ

Tð0; yÞ ¼ T j;in

ð14Þ

dTðx; 0Þ ¼0 dy

ð15Þ

where j symbolizes either feed or permeate side and negative sign of left hand side of Eq. (13) will be omitted for permeate side. km is the thermal conductivity of porous membrane and determined using the vapor of penetrating components (kg) and solid membrane thermal conductivities (ks) as km ¼ εkg þ ð1  εÞks

ð16Þ

3.4. Discretization The finite difference techniques were used to discretized the partial differential equation, Eq. (12), with boundary conditions into ordinary differential equations, for the purpose of obtaining a temperature distribution on both the channels. This technique was basically derived from Taylor's formula with second order accuracy by the three point forward and central difference formula as follows: f ′ðxÞ ¼

4f ðx þ hÞ  3f ðxÞ f ðx þ 2hÞ 2h

ð17Þ

f ðx þ hÞ  2f ðxÞ þ f ðx  hÞ

where ρ is the density of fluid, v is the fluid velocity vector, P is the pressure, μ is the viscosity and g is the gravity force. Under the following assumptions: (i) longitudinal direction of velocity (ii) fully developed (iii) steady state (iv) laminar flow (v) no gravity effect and appropriate boundary conditions, parabolic velocity profile is obtained from above equation as   y  y 2 v ¼ 6v  ð10Þ d d

f ″ðxÞ ¼

where y is transversal coordinate of height of each channel, d is the height of each channel and v is the average velocity. The ranges of Reynolds number for fluid flow in feed stream was 6.18–30.44 and in permeate stream it was 6.24-12.44.

where i is the grid line number along the x-direction, i.e., length of the channel and j is the grid line number along the y-direction, i.e., height of the channel.

By applying Eqs. (17) and (18) to Eqs. (12)–(15), the partial differential equations and its boundary conditions are rewritten as " # ∂T a ði; jÞ αa ði; jÞ T a ði; j þ 1Þ  2T a ði; jÞ þ T a ði; j  1Þ ¼ ð19Þ ∂x va ðyi ; jÞ ðΔyÞ2

αa ði; jÞ ¼ 3.3. Energy transfer

ð18Þ

2

h

ka ði; jÞ ρa;in cpa

ð20Þ

The boundary conditions are written as follows: In the present study, two-dimensional models are being derived to find out accurate temperature distribution profile within the channels. Accordingly, the three-dimensional governing equation obtained from energy balance was simplified into a two-dimensional model assuming the following factors: (i) laminar flow (ii) steady-state operation (iii) sole existence of longitudinal direction of velocity (iv) no internal generation of energy (v) symmetrical flow and temperature distribution and (vi) fully developed velocity profile. Considering such assumptions, two dimensional energy equation is obtained as [30]: ∇ðρvcp TÞ  ∇ðkð∇ΤÞÞ ¼ 0

ð11Þ

where k and cp are the fluid thermal conductivity and specific heat at constant pressure respectively.

T a ði þ 1; jÞ ¼

4T a ðiþ 1; j þ1Þ T a ði þ 1; j þ 2Þ 3

for

j¼1

ð21Þ

where, ‘a’ symbolizes either feed or permeate side for Eqs. (19)– (21). The linearized form of temperature profile equation at the membrane surface for feed side is written as  2Δy N″ði; jÞλði; jÞ kf ði; jÞ  km ðT f ði þ 1; j 1Þ  T p ðM  i; j  1ÞÞ =3 þ δ

T f ðiþ 1; jÞ ¼ 4T f ði þ 1; j 1Þ  T f ði þ 1; j 2Þ 

ð22Þ

M. Bhattacharya et al. / Journal of Membrane Science 450 (2014) 447–456

The ordinary differential equations (ODE), Eq. (19), with boundary conditions, Eqs. (21)–(23), were solved simultaneously using Method of Lines (MOL) [31] technique which is a combination of both finite difference techniques and fourth-order Runge– Kutta method. The simulating tool, FORTRAN (MicrosoftsDeveloper Studio; of 4.0.0.5277 version) was used for this purpose. The various parameters used in the above equations were considered as a function of temperature. Their dependence on temperature is as follows: ρa ði; jÞ ¼  0:4757T a ði; jÞ þ 1006:9

ð24Þ

cpa ði; jÞ ¼ 0:4846T a ði; jÞ þ 4184:9

ð25Þ

ka ði; jÞ ¼ 0:001T a ði; jÞ þ 0:5811

ð26Þ

μði; jÞ ¼ 4:0  10  8 T m ði; jÞ þ 8:0  10  6

ð27Þ

7 6 Normalized Flux (L/m2. h)

Similarly, linearized form of temperature profile equation at the membrane surface for permeate side is written as  2Δy N″ði; jÞλði; jÞ T p ði þ 1; jÞ ¼ 4T p ði þ 1; j  1Þ  T p ði þ 1; j  2Þ þ kp ði; jÞ  km ðT f ðM 1; j  1Þ  T p ði þ1; j  1ÞÞ =3 ð23Þ þ δ

451

5 4 3 2 1 0

PTFE/PET

PTFE/PP

Fig. 3. Comparison of normalized flux of PTFE/PET and PTFE/PP for a thickness of 200 mm. 5.0 experimental flux result theoretical flux result

4.5

ð28Þ

TPC ¼

T mf  T mp T bf  T bp

ð29Þ

where Tmf, Tmp, Tbf and Tbp represent temperatures at the membrane wall and bulk for both feed and permeate side respectively.

4.0 2

where, ‘a’ stands for either feed or permeate side and Tm is the mean temperature in membrane (1C). Temperature polarization coefficient (TPC) is also very important parameter to quantify the presence of thermal boundary layer around the membrane surfaces. Therefore it is written as [32]:

Flux (L/m . h)

λði; jÞ ¼  36306:0T f ði; jÞ þ 4:0  106

3.5

3.0

2.5

2.0 40

50

55

60

65

70

Feed Temperature (°C)

4. Results and discussion In the present work, parametric study on the effect of inlet temperature of the feed solution (40–70 1C), inlet concentration of feed solution (200–2000 ppb), flow rates (50–125 LPH) and inlet temperature of permeate solution (18–25 1C) are carried out to achieve maximum flux and rejection for PTFE/PET and PTFE/PP thin films. The effect of pressure has been neglected considering the economic senses of the process. The increase of process pressure may decrease the rate of evaporation of water vapor from mixture and increase the pore wetting of the membrane. This can cause the reduction of effectiveness of transmembrane flux and selectivity and make the process uneconomical. Comparison of these membranes is shown in Fig. 3 in terms of normalized flux (flux based on experimental results obtained for a particular membrane thickness with respect to actual thickness) obtained for a thickness of 200 mm under same operating conditions. The normalized fluxes are 7.11 L/m2 h and 1.41 L/m2 h for PET and PP supported PTFE membranes respectively. From the result, it can be concluded that PTFE membrane with PET support is much better than the membrane of same material of different support (PP). In this aspect PET supported PTFE membrane was utilized for the experimentation. Along with the other operating parameters, temperature distribution profile across the entire width of the both membrane channel and temperature over the membrane surface was also studied with the help of numerical simulation.

45

Fig. 4. Effect of feed inlet temperature on water flux at permeate inlet temperature 20 1C, 75 LPH and 50 LPH feed and permeate flow rates respectively and 500 ppb chromium concentration in feed.

4.1. Liquid entry pressure (LEP) The liquid entry pressure (LEP), defined as the minimum transmembrane pressure, required for distilled water or other feed solutions to enter into the pore by overcoming the hydrophobic forces, should be as high as possible. Otherwise, pore wetting will take place leading to the deterioration of the quality as well as rate of the production. The relationship of LEP with pore size, liquid– solid contact angle (θ) and liquid surface tension s (N m  1) can be expressed by the Laplace equation [33]: LEP ¼ 

2Xs cos θ r

ð30Þ

For cylindrical pore, X¼ 1 (where X is a geometric factor depending on pore structure) and r pore radius. At surface tension value, s¼ 0.0679 N/m [33] and contact angle, θ¼122 75% (measured for pure water with the help of Goniometer, Rame-Hart Inc. Imaging System, USA), calculated LEP value of 654.209 kPa was higher than the operating pressure.

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5.5

Experimental Flux Predicted Flux

4.0

5.0 4.5 2

Flux (L/m . h)

Flux (L/m2h)

3.5

3.0

2.5

4.0 3.5 3.0

2.0

2.5 2.0

1.5 17

18

19

20

21

22

23

24

25

26

40

Permeate Temperature (°C)

60

70

80

90

100

110

120

130

Feed Flowrate (LPH)

Fig. 5. Effect of permeate inlet temperature on water flux at feed inlet temperature 50 1C, 75 LPH and 50 LPH feed and permeate flow rates respectively and 500 ppb chromium concentration in feed.

Fig. 7. Effect of feed flow rate on water flux at feed inlet temperature 50 1C, permeate inlet temperature 20 1C, 50 LPH permeate flow rate and 500 ppb chromium concentration in feed.

1.0

6.0 5.5

0.8 5.0 2

Flux (L/m .h)

TPC (Temperature Polarization Co-efficient)

50

0.6

0.4

4.5 4.0 3.5 3.0 2.5

0.2

2.0 0

0.0 0.0000

200

400

600

800

1000 1200 1400 1600 1800 2000 2200

Feed Concentration (ppb) 0.0548

0.1096

0.1644

0.2192

0.2740

Length, X (m) Fig. 6. Variation of temperature polarization coefficient (TPC) along the length of the module.

4.2. Effect of temperature on flux The effects of temperature for feed and permeate side on flux are shown in Figs. 4 and 5 at permeate inlet temperature 20 1C and feed inlet temperature 50 1C, keeping 75 LPH and 50 LPH as feed and permeate flow rates respectively along with 500 ppb as chromium concentration in feed for both model predicted and experimental result correspondingly. From Fig. 4, it can be seen that experimental results on water flux goes up from 2.09 to 4.61 L/m2 h with increase in inlet feed temperature from 40 1C to 70 1C for PTFE/PET membrane. The model also depicts an increase in flux with rise in temperature. This rise in flux is mainly due to an increase in temperature dependent mass transfer driving force across the membrane surface which is governed by the Antoine equation, Eq. (4). At the higher temperature, it is obviously cleared that, temperature gradient between the feed and the permeate surface of membrane increases the driving force which higher flux. It can also be noted that rise in temperature large amount of vapor is produced from the feed solution which creates a higher vapor pressure inside the channel, may cause increase in flux through membrane pores. The agreement between the experimental results and theoretical prediction are fairly good.

Fig. 8. Effect of different feed concentration on permeate flux at feed inlet temperature 50 1C, permeate inlet temperature 20 1C, 75 LPH feed flow rate and 50 LPH permeate flow rate.

Similarly, Fig. 5 shows the variations in pure water flux across the membrane with a rise in inlet permeate temperature at a constant feed temperature and other conditions. The results show that flux decreases from 3.95 to 1.90 L/m2 h with an increase of temperature from 18 1C to 25 1C for model predicted and experimental result, which can be attributed to lowering of mass transfer driving force due to decrease in temperature difference between the feed and the permeate side. It can also be depicted that the model prediction on flux is similar to the experimental observation at low temperature and deviations are notable at higher permeate temperature. This decrease in flux may be because of temperature dependent flow model contributions, A(T) and B(T) Eqs. (6) and (7). These factors were established with the help of experimental results which indicate the extension of contribution on the model equations towards the permeability of penetrants. Furthermore, the reason for this difference might be the effect of temperature polarization where additional thermal boundary layer is formed next to the membrane surface, which reduces the driving force of evaporation. Temperature polarization coefficient (TPC), Eq. (29), reflects the presence of thermal boundary layer inside the flow module. Lower the value of TPC (TPC is always lower than unity), the greater is the effect of thermal boundary layer, as well as, temperature polarization, which is shown in Fig. 6. Therefore, the values of TPC should be as

M. Bhattacharya et al. / Journal of Membrane Science 450 (2014) 447–456

close to unity as possible. From the figure, it is clearly seen that temperature polarization effects increase as one moves towards the center of the module from both of its ends and decrease with rise in temperature.

0.020

Width, Y (m)

0.015

4.3. Effect of feed flowrate on flux Feed flowrate is another important parameter in a DCMD process and Fig. 7 shows the variations of water flux with feed flow rate in the laminar region at constant operating conditions for PTFE/PET membrane. It is observed that flux increases from 2.21 to 5.38 L/m2 h, with an increase of feed flow rate from 50 LPH to 125 LPH. This is due to reduction in concentration polarization phenomenon with increasing velocity which creates the turbulence in the flow channel and a decrease in the thickness of the temperature boundary layer [34]. Therefore, the higher driving force between free stream and membrane surface was attained which may accelerate transport of permeating components by increasing the convective heat transfer coefficient. Fig. 7 also predicts the variation of model predicted flux with constant or little upwind change. This is because of equation, Eq. (5), used for the calculation of flux, independent of feed flow rate. Flux equation used for this purpose, is exclusively dependent on several membrane properties and pressure term in Eq. (5), which is assumed to be constant value. Furthermore, slight enhancement of flux with increase in flow rate infers the variation of velocities during solving of mathematical equations. Eventually it is observed that there is no significant change of fluxes with the variation of permeate flow rate. Therefore observance of permeate flow rate may conclude to a low value of 50 LPH during the experimentation.

0.010

0.005

0.000 20

25

30

35

40

45

50

Temperature (°C) Fig. 9. Variation of temperature with depth of channel at 0.165 m length of the module.

50

Feed and Permeate Temperature (°C)

453

45

40

35

4.4. Effect of feed concentration on flux

30

Fig. 8 shows the variations of water flux with feed concentration at permeate and feed inlet temperature of 20 1C and 50 1C for PTFE/PET film respectively. From the fitted curve, it is observed that flux decreases from 5.77 to 2.31 L/m2 h exponentially (eventually attaining plateau) with an increase of chromium concentration in the feed from 200 ppb to 2000 ppb. Accordingly one may infer that vapor pressure of water decreases which reduces the transmembrane pressure gradient and lead to decrease in flux.

25

20 0.000

0.002

0.004

0.006

0.008

0.010

Width, Y (m)

Fig. 10. Temperature distribution contour profile along y direction at feed flowrate 75 LPH and permeate flowrate 50 LPH.

50

48

Feed Temperature (degree Centigrade)

50 46

48 46

44 44 42

42

40 38

0

40

0.002 36 0

0.004 0.05

0.1 Length, X (m)

m)

0.006 0.15

0.008 0.2

0.25

0.01

h,

idt

Y(

W

Fig. 11. Temperature variation across the entire module domain for feed side.

38

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M. Bhattacharya et al. / Journal of Membrane Science 450 (2014) 447–456

34 32 Permeate Temperature (degree Centigrade)

32 30

30

28 28 26 26

24 22

24 20 0.25 0.2 0.15

Le

ng

th

,X

(m

)

22 0.1 0.05 0 0.01

0 0.003 0.002 0.001 0.006 0.005 0.004 0.009 0.008 0.007

20

Width, Y (m)

Fig. 12. Temperature variation across the entire module domain for permeate side.

70

50

Predicted outlet temperature (°C)

Surface Temperature (°C)

45

40

35

30

60

50

40

30

25 20 20

20 0.0000

0.0548

0.1096

0.1644

0.2192

0.2740

Length, X direction (m) Fig. 13. Membrane surface temperature along the length of the module.

Therefore, the drop in flux may influence of concentration on viscosity that affect the polarization phenomena and transport coefficients in the feed side and also vapor pressure reduction due to the presence of chromium salt. When salts are present in the feed solution at high concentration, an additional boundary layer develops next to the membrane interface which is parallel to the temperature and velocity boundary layers. This concentration boundary layer, together with the temperature boundary layer further reduces the driving force for evaporation finally reducing flux in the permeate side. 4.5. Temperature distribution profile Fig. 9 shows the temperature distribution profile across the width at 0.165 m of the module length at inlet temperature of feed and permeate as 50 1C and 20 1C respectively, and flow rates of feed and permeate were maintained at 75 and 50 LPH respectively. The profile shows the existence of thermal boundary layers on both side of feed and permeate channel and there is no temperature variations near the wall of module along longitudinal coordinate. Moreover, the variation in boundary layer thickness along the length of each channel is evident which is shown in Fig. 10 by the generation

30

40

50

60

70

Experimental outlet temperature (°C)

Fig. 14. Pareto plot for experimental and predicted values of both feed and permeate outlet temperature.

of contour temperature profiles for every particular point of length of the membrane module along transversal coordinate. Clearly it can be noticeable from Fig. 11 in a three dimensional temperature variation profile of inside the feed channel. The thickness of temperature boundary layer increases as does the membrane surface temperature along the direction of flow through the channel. This is expected to have a notable effect on the mass transfer driving force which may be compromised due to temperature polarization phenomenon. Similar observations can be made from Fig. 12 for the permeate channel. However, due to counter current mode of operation, the feed side temperature boundary layer is formed opposite to the permeate side temperature boundary layer along the length of the module. Furthermore, the transmembrane pressure affected by the temperature gradient between both membrane surfaces taper along the flow direction, resulting in decreasing the water productivity per unit area of membrane. 4.6. Membrane surface temperatures The model is also instrumental in predicting the membrane surface temperatures for both the feed and the permeate contact

M. Bhattacharya et al. / Journal of Membrane Science 450 (2014) 447–456

surfaces of the membrane. This is demonstrated in Fig. 13. It reflects a significant idea about the variation of temperature driving force along the length of the module. It can be seen that highest driving force is achieved at the two ends of the module. This is expected since at the channel inlets, the thermal boundary layers are not fully developed and temperature polarization and concentration polarization effects are negligible. However, half way between the channels, due to fully developed thermal boundary layers, the temperature difference between feed and permeate, and consequently, the temperature driving force, is minimum for countercurrent flow which reflects on the membrane performance. Finally, the validity of the model equations can be tested by comparing experimental with predicted flux and temperature (using model parameters). Accordingly, such a 5.0

Predicted Flux (L/m2. h)

4.5 4.0 3.5 3.0 2.5 2.0 2.0

2.5

3.0

3.5

4.0

4.5

5.0

Experimental Flux (L/m2. h) Fig. 15. Pareto plot for experimental and predicted permeate flux.

comparison is shown in Figs. 14 and 15. From this figures, it is obvious that outlet temperatures and water fluxes match quite well and it is a pictorial verification of the model derived for predicting flux. In turn, such verifications also justify the obtained experimental results.

5. Conclusions The removal of toxic, heavy chromium (VI) metal through DCMD process served the purpose exceedingly well towards the generation of clear water for repeated using. Applications of this emerging membrane method in near future will have a good prospect for the treatment of ground water by removing heavy metals in industrial scale which will greatly improve the ecological situation. A comparative study among PTFE/PET and PTFE/PP membranes concluded that PTFE/PET membrane is much more efficient with respect of normalized flux obtained for chromium (VI) removal. The effect of feed temperature and flow rate are found to be greatly influenced on flux by increasing order. The validation of theoretical model depicts that there lies a good agreement between the predicted and experimental results. Temperature polarization effects increased as one moves towards the center of the module from both of its ends. The variation of temperature driving force is predicted through calculating membrane surface temperature along the length of the module by computational study. The highest driving force is observed at the two ends of the module. The temperature distribution profiles showed the existence of thermal boundary layers on both in the feed and the permeate channels. The variation in boundary layer thickness along the length of each channel is evident. Thereby it can be proved that the two dimensional model developed for this present study is worthy enough.

APPENDIX A: Flowchart of Theoretical Calculation START Insert module dimensions and other input parameters

Calculate: flux and new grid point temperatures

Calculate: 1. Tortuosity factor 2. Feed and permeate velocity 3. membrane thermal conductivity

Assign initially values to feed and permeate channel grid point temperatures Iteration= Iteration +1

455

Calculate Error

No

Error < 10-8

Iteration = 0 Yes STOP

Update the grid point temperatures

Specify: velocity, density, specific heat, thermal conductivity and viscosity of feed and permeate as temperature function Fig. A1 .

456

M. Bhattacharya et al. / Journal of Membrane Science 450 (2014) 447–456

Appendix A. Flowchart of theoretical calculation See appendix Fig. A1.

Nomenclature A effective membrane area (m2) A(T) and B(T) Knudsen diffusion model and Poiseuille flow model contribution respectively Cp permeate concentration (ppb) Cf feed concentration (ppb) Cm membrane coefficient cpa heat capacity either hot feed or cold feed solution respectively (J/kg 1C) d height of the feed channel (m) g gravity force (m/s2) J permeate flux (L/m2 h) ka thermal conductivity either hot feed or cold feed solution respectively (J/m 1C s) km thermal conductivity of the porous membrane (J/ m 1C s) M molecular weight of water (g/mol) N″ mass flux (L/m2 h) P 1 sat ; P 2 sat saturated vapor pressure of water on the hot feed and cold feed (kPa) respectively Pm mean saturated pressure in membrane (kPa) r pore radius (m) R gas constant (J/mol K) Rb rejection t operating time (h) Tm mean temperature in membrane (1C) Tf ; Tp hot feed and cold permeate stream temperature respectively (1C) v mean stream velocity (m/s) vf ; vp hot feed and cold feed stream velocity respectively (m/s) V′ volume of permeate sample (m3) W width of channel (m) X geometric factor Greek symbols Θ s δm ε λ μf ; μp τ ρf ; ρp

liquid–solid contact angle liquid surface tension (N m  1) thickness of membrane (m) membrane porosity latent heat of water (J/kg) viscosity of hot feed and cold permeate stream respectively (N s/m2) membrane tortuosity factor fluid density of hot feed cold permeate and solution respectively (kg/m3)

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