The Heat and Mass Transfer Phenomena in Vacuum Membrane Distillation for Desalination

Transcription

1 International Journal o Chemical and Biological Engineering 4:1 211 The Heat and Mass Transer Phenomena in Vacuum Membrane Distillation or Desalination Bhausaheb L. Pangarkar, M. G. Sane, Saroj B. Parjane, Rajendra M. Abhang, Mahendra Guddad Abstract Vacuum membrane distillation (VMD) process can be used or water puriication or the desalination o salt water. The process simply consists o a lat sheet hydrophobic micro porous PTFE membrane and diaphragm vacuum pump without a condenser or the water recovery or trap. The eed was used aqueous NaCl solution. The VMD experiments were perormed to evaluate the heat and mass transer coeicient o the boundary layer in a membrane module. The only operating parameters are eed inlet temperature, and eed low rate were investigated. The permeate lux was strongly aected by the eed inlet temperature, eed low rate, and boundary layer heat transer coeicient. Since lowering the temperature polarization coeicient is essential enhance the process perormance considerable and maximizing the heat transer coeicient or maximizes the mass lux o distillate water. In this paper, the results o VMD experiments are used to measure the boundary layer heat transer coeicient, and the experimental results are used to reevaluate the empirical constants in the Dittus- Boelter equation. Keywords Desalination, heat and mass transer coeicient, temperature polarization, membrane distillation I. INTRODUCTION EMBRANE distillation (MD) is a hybrid o thermal M distillation and membrane process. The possible application o MD or desalination has been examined by some researchers [1]-[5]. MD oers various advantages in comparison to the traditional distillation and pressure driven membrane processes [6]. MD or water desalination is a membrane technique or separating water vapor rom a liquid saline aqueous solution by transporting through the pores o hydrophobic membranes, made mainly o polypropylene (PP), polytetraluoroethelyne (PTFE), polyvinylideneluoride (PVDF) and polyethylene (PP). Various types o methods may be employed to impose a vapor pressure dierence across the membrane to drive a lux. The permeate side may be a cold liquid in direct contact with the membrane, called direct contact membrane distillation (DCMD) or a condensing surace separated rom the membrane by an air gap called air gap membrane distillation (AGMD) or a sweep gas blown across the membrane called sweep gas membrane distillation (SGMD) or vacuumed called vacuum membrane distillation (VMD). Because AGMD and DCMD do not need an external condenser, they are best suited or applications where water is B.L. Pangarkar, S.B. Parjane, R.M. Abhang and M. Guddad are Assistant Proessors with Chemical Engineering Department o Sir Visvesvaraya Institute o Technology, Nashik, At. Post - Chincholi, Taluka Sinnar, District Nashik (Ailiated to University o Pune), India. Phone: ; ax: ; pbl_1978@yahoo.com. M.G. Sane is Ex. Scientist o National Chemical Laboratory, Pune (India) the permeating lux. SGMD and VMD are typically used to remove volatile organic or dissolved gas rom an aqueous solution [5], [7]-[1].VMD is a kind o MD process; it is an evaporative process and in recent years, it has received attention as a means or eicient removing trace amount o volatile organic contaminants rom water [7], [8]. VMD can be characterized by the ollowing steps: vaporization o the more volatile compounds at the liquid-vapor interace and diusion o the vapor through the membrane pores according to Knudsen mechanism [8]-[12]. VMD is also useul tool or measuring the boundary layer eects with in a membrane module. In this paper, the results o VMD experiments or desalination process are used to measure the boundary layer heat transer coeicient within the membrane module, and experimental results are used to evaluate the empirical constants o the heat transer correlation. Then, using a heatmass transer analogy, the boundary layer mass transer coeicient are calculated and used along with the complete VMD model to predict the perormance o VMD o salt water eed [8]-[12]. An examination o the literature permits to assert that the DCMD has been the coniguration more studied, as apposed with VMD, which has deserved less attention. II. THEORY In MD processes mass transport and heat transport are coupled. This study proposes VMD process, in which a eed solution is brought into contact with one side o a micro porous membrane and vacuum is pulled on the opposite side. In these conditions, a transmembrane water vapor pressure dierence is created. The driving orce or mass transer in MD systems is the dierence in the partial pressure o water vapor across micro porous hydrophobic membrane. The recognized transport mechanisms or mass transer across the membrane are usually molecular diusion and Knudsen diusion and, sometimes, viscous low. Molecular diusion has a partial pressure dierence as driving orce and nonidentical molecules that are in the way orm the resistance to mass transer. The driving orce or Knudsen diusion is also a partial pressure dierence, but in this case molecules bounces into the membrane matrix, which orm the resistance to mass transer. Knudsen diusion is thus important or small pores and / or low pressure. Finally, viscous low has a total pressure dierence as driving orce, and the membrane matrix orms the resistance against it [8]-[12]. In a VMD coniguration, the molecular diusion is not adequate due to the very low value o the partial pressure o the air inside the 7

2 International Journal o Chemical and Biological Engineering 4:1 211 pores. Consequently, the Knudsen and viscous low diusion should be a chosen as more appropriated [13]-[15]. The model suggests a linear relationship between the water lux, N, and the water vapor pressure dierence between evaporating and condensing surace. N = K Δ P = K ( P P ) (1) M V M V Where K m is called MD coeicient, P is the pressure in the vacuum side and P v is the water vapor pressure in the membrane surace at the temperature T w. Coeicient K m depends on temperature as well as on some geometric characteristics o the membrane. Based on the Kinetic Theory o Gases or the Dusty Gas Model, suggest that there is a Knudsen type diusion o water molecules through the membrane pores and the permeation lux, N, was written [13], [15], [16]: N 1 2 r ε M Δ PV = τ RT δ Where r is the pore size, ε is the ractional void volume o the membrane, δ is the membrane thickness, τ is the pore tortuosity, M is the water molecular mass and R is the gas constant. As it is well known, the water vapor pressure at liquid vapor interace (in Pa) may be related with the temperature (in K), by using the Antoine s equation [12]: P V (2) = exp( ) (3) T VMD is a thermally driven process, heat and mass transer are involved simultaneously and boundary layers are ormed near the membrane surace. Consequently, there is a decrease o the driving orce due to polarization eects o both temperature and concentrations [6]. When a molecular mixture is brought to the membrane surace by the driving orce action, some molecules will permeate through the membrane whilst others will be retained. This leads to an accumulation o the retained components and a depletion o the more permeating components in the boundary layer adjacent to the membrane surace. This phenomenon is reerred to as concentration polarization. In VMD process, there is a heat transer occurs by two major mechanisms: (i) the latent heat transer accompanying the transmembrane vapor lux, and (ii) heat transerred by conduction through the membrane matrix [13], [15]. Consequently, there is rather complex relationship between both heat and mass transer. This is related and involved with the presence o an unstirred boundary layer that adjoins the membrane at the eed side. The temperature at the membrane surace is lower than the corresponding value at the bulk phase. This creates temperature gradients in the liquid ilm adjoining the membrane. This phenomenon is called temperature polarization [13]-[15], [17], [18]. Heat transer across the boundary layers in a MD module is oten the rate limiting step or mass transer, because such a large quantity o heat must be supplied to the vapor liquid interace to vaporize the liquid. The heat transer coeicient o the VMD eed side boundary layer, h, is deined by [8]: Q = h Δ T (4) Where Q is the rate o heat transer across the boundary layer and T is the temperature drop across the boundary layer. In VMD, the conductive heat transer across the membrane is negligible because o the low pressure on the permeate side o the membrane [8], [13]; thereore, the heat transerred through the liquid boundary layer and the energy transported through the membrane or VMD [8], [12]: h Δ T = N Δ H (5) V where H v is the latent heat o vaporization o water. The empirical correlation like a Dittus-Boelter equation gives the value o h or turbulent liquid low written in the simpliied orm [8]: hd b c T = Nu = a Re Pr (6) k Where d is the eective tube diameter, k T is the thermal conductivity o the water, Nu, Re and Pr are the Nusselt, Reynolds and Prandtl numbers respectively, and a, b and c are characteristic constants o the module design and liquid low regimes. The viscosity correction actor normally associated with the Dittus-Boelter equation (μ / μ wall ).14, is negligible or MD application [8]. When both heat and mass transer are occurring simultaneously, the mass and heat transer coeicients may be related by the Reynolds analogy [19]. h k Sc = ρ C P Pr Where k is the mass transer coeicient o boundary layer, ρ is the density o water, C p is the speciic heat, and Sc is the Schmitt number. From (7), the mass transer coeicient can be calculated once the heat transer coeicient is known III. EXPERIMENTAL Experiments were perormed using a micro porous hydrophobic PTFE lat membrane (Millipore). The typical characteristics o the membrane are summarized in Table I. In all experiments, the aqueous eed solution o about 25 to 35 mg/l NaCl in pure water was prepared and continuously circulated through the membrane module rom the vessel by a eed low pump. A low rate o eed water was 2 3 (7) 8

3 International Journal o Chemical and Biological Engineering 4:1 211 measured by the Rotameter connected in between the pump and module. A vacuum pump was connected to the permeate side o the membrane module to remove the water vapor lux. Cold trap was used to condense and recover the water permeating vapor. The condensed pure water was collected to calculate the distillate lux. Calibrated vacuum gauge was used to measure the pressure at the permeate side o the module. A schematic view o the setup is presented in Fig. 1. The eed temperature and eed low rate was varied respectively between 4 and 6 C, and 3 and 54 l/h. The vacuum pressure was kept 3 kpa in all the experiment. The process was allowed to run or approximately 1 to 2 h. TABLE I MEMBRANE CHARECTRISTICS Material Hydrophobic PTFE Pore size, µm.22 Porosity, % 7 Thickness, µm 175 Membrane area, cm During the experiment, the level in the eed tank was maintained by adding measured amounts o eed water to the eed tank every 15 to 2 min. The lux was calculated by plotting the cumulative volume added to the eed versus time, and taking the slope. The membrane wetting or ouling was not observed during the experiment, because the volume versus time data did not all on a straight line. The total volume o water added to the eed tank was compared to the volume o permeate collected at the end o experiment. Apparatus leaks or excessive evaporation rom the eed tank did not seem to a problem with this experimental setup. experimental values o the MD lux as unction o the water low rate, with the water inlet temperature as parameter. The eed low rate was varied between 3 and 54 l/h or each one o the ollowing water inlet temperature: 313, 323 and 333 K. The Reynolds s numbers range rom to In this case, the MD lux increases with the eed low rate because o increased Re and decreased boundary layer resistances. At higher Re, high heat transers rom the bulk eed to the membrane surace approaches to the corresponding temperature in the bulk phases leading to grater MD lux. Pearmeate lux (Kg/m 2 h) T = 313 K T = 323 K T = 333 K Feed low rate (l/h) Fig. 2 Eect o eed low rate at eed salt conc. = 3 mg/l, and permeate pressure = 3 kpa. Fig. 3 shows the experimental values o MD lux as unction o the water inlet temperature, with eed low rate as a parameter. Again the MD lux increases with both the eed low rate and water inlet temperature. This eect can be attributed to the higher water vapor pressure sensitivity at higher temperatures. The eed temperature was varied between 313 and 333 K at 54 l/h eed low rate and 3 kpa vacuum pressure at permeate side to give Pr ranging rom 3.71 to Pearmeate lux (Kg/m 2 h) l/h 42 l/h 54 l/h Temperature (K) Fig. 1 Experimental setup IV. RESULTS AND DISCUSSION In this work, the MD lux has been measured or dierent values o the eed low rate and temperature o the eed at the inlet o the membrane module. This was measured at constant vacuum pressure in the permeate side. Fig. 2 show the Fig. 3 Eect o eed temperature at eed salt conc. = 3 mg/l, and permeate Pressure = 3 kpa. According to (4), the values o heat transer coeicient o water eed boundary layer was calculated. It was observed that an increase in the water eed low rate is accompanied by an increase in the MD lux and corresponding increase in the heat transer coeicient. This can be attributed to a reduction in the 9

4 International Journal o Chemical and Biological Engineering 4:1 211 temperature polarization eect. As the heat transer coeicient increases, the temperature at the membrane surace approaches to the bulk temperature and the vapor pressure driving orce increases. log (Nu) K 323 K 333 K log (Re) Fig. 4 log (Nu) versus log (Re) at constant eed inlet temperature, eed low rate = 54 l/h, Permeate pressure = 3 kpa, and eed salt conc. = 3 mg/l. The heat transer coeicient associate with each o the data points was measured and the dimensionless Re and Nu were calculated rom the solution properties. Fig. 4 shows the results as a log-log plot o Nu Versus Re is made to estimate the dependence o the heat transer coeicient on the Re, that is, on the water eed low rate. These results were used to evaluate the empirical constants b in the heat transer correlation (6). This plot is made or each water inlet temperature, so the inluence o the Pr will be small. The best it line slope is which agrees with the Dittus- Boelter value o.8. Thus, in the VMD experiments, the Dittus Boelter value o b =.8 is applicable to this work Nu =.23Re Pr (8) h (W / m 2 K) h = T Bulk eed temeprature ( C) Fig. 6 Heat transer coeicient, h, is a unction o bulk eed temperature at eed low rate = 54 l/h The (8) was simpliied and calculated the heat transer coeicient is a linear unction o eed temperature. Fig. 6 shows a graph o the heat transer coeicient over a to 1 C temperature range at 54 l/h eed low rate and or 3 mg/l o salt concentration in eed water. Additionally, the simpliied mass transer coeicient, k, equation was developed by using the heat-mass transer analogy as shown in Fig. 7. The ollowing simpliied equations (9), (1) o heat and mass transer are ormed, which are used requently or VMD system (T is in C): k h = T (9) = T (1) log (Nu / Re.8 ) log (pr) Fig. 5 log (Nu /Re.8 ) versus log (Pr) In the Fig. 5, a plot o log (Nu / Re b ) versus log (Pr) was made on to estimated the empirical constant a and c o (6). The best it line slope is and the intercept gives a value o which corresponds well with the Dittus-Boelter value o a =.23 and c =.33. Hence, the experimentally determined empirical constants did not deviate signiicantly rom their Dittus-Boelter values. Thus, (6) can be re-written as: k (m/s) k = T Bulk eed temperature ( C) Fig.7. Mass transer coeicient, k, is a unction o bulk eed temperature at eed low rate = 54 l/h Attention would be better ocused on designing VMD module to provide high heat transer coeicient practically, i VMD has been used or desalination, it will be operated at low pressures with good membrane permeability to maximize the lux. Thereore, the process will be heat transer limited. So 1

5 International Journal o Chemical and Biological Engineering 4:1 211 maximizing the heat transer coeicient by a good module design maximizes the mass lux. The eect o boundary layer heat transer resistance relative to the total heat transer resistance o the system is given by the (11) o temperature polarization coeicient, θ: ( T T m ) ( T TV ) θ = (11) where T is the bulk eed temperature, T m is the eed side membrane surace temperature, and T v is the vacuum side temperature. The concept o the temperature polarization actor will be used as a tool or evaluating the eect o the input parameters on maximizing the mass lux. When, the value o θ approaches zero or systems, T T m and the process is limited by mass transer through the membrane and resistance in the liquid phase is negligible. When θ 1, T m T v so the resistance in the membrane is negligible and the process is limited by heat transer to the membrane surace [18]. The calculated value o θ as a unction o eed bulk temperature is shown in Fig. 8. The results indicate that θ increases by increasing bulk eed temperature. Since increasing the bulk eed temperature increases the mass lux that requires suicient heat o vaporization providing such a heat increases the dierence between the T and T m, and in turn the polarization actor. It is important to keep θ as small as possible. temperature polarization coeicient, (θ) Bulk eed temperature ( C) Fig. 8 Temperature polarization coeicient at eed salt concentration = 3 mg/l, and permeate pressure = 3 kpa V. CONCLUSIONS An experimental study o VMD process was reported or water puriication or the desalination o salt water in a lat sheet membrane module coniguration. The eect o water eed low rate and eed inlet temperature on MD lux has been discussed and presented a method to estimate the eed boundary layer heat and mass transer coeicient rom the Dittus- Boelter equation and its mass transer analogy. The experimental heat transer coeicients were used to test the applicability o Dittus-Boelter equation to VMD process. The role o heat transer resistance in the liquid phase and mass transer resistance in the membrane matrix are more important in the transport mechanism. So in the module design to provide the high heat transer coeicient or maximize the mass lux o distilled water. MD lux is strongly dependent on the water eed low rate and eed inlet temperature. An increase in the water eed low rate and temperature is a accompanied by an increase in the MD lux and corresponding increase in the heat transer coeicient in the water eed boundary layer. This can be attributed reduction in the temperature polarization eect. Also, the study undertaken o the eect o bulk eed temperature on the temperature polarization actor and ound it increase with increase in bulk eed temperature. Hence, the polarization actor is a major tool or VMD process behavior. ACKNOWLEDGMENT We are deeply indebted to University o Pune, Pune or the inancial support or this research work and also the aculty o Chemical Engineering Department and management o Sir Visvesvaraya Institute o Technology, Nashik, or the constant support during the work. We are especially thankul to Pro. S.G. Wakchaure or his support during the abrication o experimental setup. 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