Parametric Sensitivity Analysis of Vacuum Membrane Distillation for Desalination Process

Transcription

1 International Conference on Chemical, Ecology and Environmental Sciences (ICCEES'11 Pattaya Dec. 11 Parametric Sensitivity Analysis of Vacuum Membrane Distillation for Desalination Process Sushant Upadhyaya*, Kailash Singh, S.P. Chaurasia, Madhu Agarwal, Rajeev Kumar Dohare Abstract Membrane distillation is a thermally driven process in which only vapor molecules pass through a hydrophobic membrane. The liquid feed to be treated by membrane distillation should be in direct contact with one side of the membrane and should not penetrate inside the dry pores of the membrane. It differs from other membrane technologies in terms of driving force for desalination being the difference in vapor pressure of water across the membrane rather than pressure. Vacuum membrane distillation is one of the several methods available for desalination processes. In this process, vacuum is applied on the permeate side to drive the evaporation of water. To increase the performance of vacuum membrane distillation, various parameters have been studied. The sensitivity analysis was carried out to study the effects of parameters on mass flux for the desalination process. The parameters studied are membrane pore size, membrane characteristics, permeate-side pressure, and feed temperature. Sensitivity of mass flux increases with membrane poresize. The process sensitivity is not much affected by changing membrane characteristics parameter and membrane pore diameter, however mass flux increase linearly with membrane characteristics and pore diameter both. The process is much sensitive below feed temperature of 5 o C and is always positive. The process was also found to be sensitive with respect to permeate-side pressure; it is always negative and therefore on increasing permeate-side pressure, the mass flux decreases. Keywords Vacuum membrane distillation, sensitivity analysis, desalination, mathematical model, Knudsen-diffusion. M I. INTRODUCTION embrane distillation (MD is a thermally driven process, in which only vapor molecules are transported through porous hydrophobic membranes. The liquid feed to be treated by MD must be in direct contact with one side of the membrane and does not penetrate inside the dry pores of the membranes. The MD driving force is the trans-membrane vapor pressure difference that may be maintained in the permeate side of the membrane [1]. MD is an emerging technology for desalination. It differs from the other membrane technologies in that the driving force for desalination is the difference in vapor pressure of water across the membrane, rather than total pressure. An increasing number of areas on our planet will suffer more in the near future because of rapid depletion of ground water and surface water []. Mohammadi and Safavi [3] applied Taguchi method *Corresponding author, sushant.cipet@gmail.com, Ph in optimization of desalination by vacuum membrane distillation (VMD. In VMD, the feed solution directly contacts with the membrane surface and is kept at pressure lower than the minimum entry pressure (LEP; at the other side of the membrane, the permeate pressure is often mentioned below the equilibrium vapor pressure by a vacuum pump. The vapor permeated is taken out by vacuum and is condensed in an external condenser. VMD configuration is as shown in Fig. 1. The total pressure difference between the two sides of the membrane causes a convective mass flow through the pores that contributes to the total mass transfer of VMD. There is only the diffusive flux of volatile component within the membrane pores, therefore, mass flux of VMD is generally larger than that of other MD configurations. Another advantage of VMD comes from the negligible heat conduction through membrane. Banat et al. [4] studies the sensitivity of the mass flux to the process operating parameters including downstream pressure, feed temperature, feed flow rate, and membrane permeability. Many researchers only concentrated on the sensitivity of mass flux to variation in the mass and heat transfer coefficients and did not discuss the sensitivity of mass flux to process operating parameters like membrane pore size, membrane characteristics, permeate side pressure, feed side membrane temperature, feed bulk temperature as well as salt concentration. A micro-porous membrane is generally characterized by four parameters, i.e., the thickness δ (m, mean pore size, diameter d or radius r (m, porosity ε and the tortuosity τ (defined as the ratio of pore length to membrane thickness. Each of the parameter influences the permeability of the membrane. The permeability is proportional to r a ξ/τδ, where a may be equal to 1 or, depending on the predominant mass transfer mechanism within the membrane pores [5]. The membranes used in MD exhibit pores sizes ranging from 1 nm to 1μm and it is admitted that the MD flux increases with the increase of the pore size. The increase in trans-membrane flux with increasing membrane pore size may be related to the enhanced mass transport process from being more likely Knudsen diffusion controlled for membranes having very small pore sizes to Knudsen-viscous transition for membranes exhibiting larger pore size. The effect of the feed temperature on permeate flux has been widely investigated in the different cited MD configurations. The feed temperature has been varied from to 8 C (below the boiling point of the feed solution maintaining all other MD parameters constant. 447

2 International Conference on Chemical, Ecology and Environmental Sciences (ICCEES'11 Pattaya Dec. 11 Generally it is agreed up on that in all MD configurations, there is an exponential increase of the MD flux with the increase of the feed temperature. This is due to the exponential increase of the vapor pressure of the feed solution with temperature, which increases the trans-membrane vapor pressure. The main objective of this work is to deepen the knowledge and explore the sensitivity analysis on the mass flux with respect to the controlling parameters of the VMD process such as membrane pore size, membrane characteristics, permeate side pressure, etc. At steady state these heat fluxes are equal, i.e, q f =q m =q p. By solving the equations, we get, N H+ T ( hf + hm + hh m f hp ht m p = hf ( 1+ hm hp (5 These model equations can be used to predict the mass flux of water vapor through VMD for desalination of water by taking the values of the parameters given in Table 1. Therefore for a given membrane characteristics the performance of VMD can be found by simulating the above equations. Membrane Feed in Vacuum Condenser TABLE I NOMINAL VALUES OF PARAMETERS USED FOR DESALINATION OF WATER Parameter Value Feed out Permeate Fig. 1 Configuration of VMD II. MATHEMATICAL MODEL OF VMD In VMD, the process is driven by both the temperature difference and the total pressure difference between two sides of the membrane. The total pressure difference arises from the vacuum pulled by a vacuum pump in the cold chamber of membrane module. The permeated vapor is sucked out of the cold chamber by the vacuum pump and condensed in an external heat exchanger. The mass transfer in MD consists of two steps: one is across the boundary layer at the feed side; the other is across the membrane. The mass flux is given by [6], N 1 = ε 1 y + 3 πm ( P P A A, M K -P pm τδ RT DAB 4d RT + εr PM ( P τδ 8η RT (1 The heat energy needed for the water to vaporize into the membrane pores is provided by the heat transfer through the boundary layer at the feed side. The heat flux is, qf = hf ( T ( Assuming the contribution of both evaporation and conduction, the total heat flux transferred through the membrane is, qm = N H + hm ( T Tpm (3 The heat flux at the thermal boundary layer at permeate side is given by, qp = hp ( Tpm Tp (4 P pm 7.3 kpa P 13.5 kpa T f 33 K T 34.9 K R m Ε.5 Τ. δ m λ s.8 W/m K λ g.1w/m K h m 519 W/m K h p W/m K D AB at 34.9 K m /s (water-air system η (water vapour kg/m s at 34.9 K h f W/m K [3] M 18 kg/kmol R 8314 J/kmol K 1-y A (mole fraction of air III. SENSITIVITY ANALYSIS To study the sensitivity of various parameters to the mass flux, the following sensitivity factors were derived from the mathematical model given in [6]. Sensitivity factor of mass flux to the membrane characteristics is ln N S N, ε = = 1 τδ ε ln τδ (6 Sensitivity factor of mass flux to the membrane pore diameter (d is, 448

3 International Conference on Chemical, Ecology and Environmental Sciences (ICCEES'11 Pattaya Dec. 11 ln N 4dc fd bd c SN, d ln d 4d fd bd c bd c (7 where 1 ya 3 M PM a, b, c, ep, f T D 4 RT 8 AB Sensitivity factor of mass flux to the permeate side membrane pressure is given by, SN, P (8 Sensitivity factor of mass flux to the feed side membrane temperature: T N SN, T N T (9 N ae c 1 ace a 1 xmp b T c T d c RT db T b d d ad ef ad f 1 x MP P e 4T 4P RT (1 The Claussius-Clapeyron equation including activity coefficient is given by, dp 1 x MP dt RT (11 P 1x P where and saturation pressure is given by the well known Antoine equation for water: ln P T (1 The activity coefficient for saline water is [5] 1.5x 1x (13 Sensitivity factor of mass flux to the feed bulk temperature is given by ln N N SN, ln N (14 N 38.7T 519tp N N T T where f T and, or N N 519t p T 38.7 (15 T 1 N (16 N N T N 1 N T T 38.7 (17 Sensitivity factor of mass flux to the salt concentration: S N, x 3x 19x 1.5x P 3 3 1x 9.5x 1.5x1 P P pm IV. RESULTS AND DISCUSSION (18 A. Sensitivity of Mass Flux to Membrane Characteristics The effect of membrane characteristic / τ δ on transmembrane flux and its sensitivity is shown in Fig.. There is a remarkable variation in mass flux on changing the membrane characteristic / τ δ from to 1. The behavior shows that trans-membrane flux is proportional to /τδ. However, the sensitivity remains constant because of the linear change in the mass flux, which is also clear from equation (6. N (Kg/m hr / τ δ (m -1 (a / τ δ (m -1 Fig. (a Response of S(N, ε/τδ to the membrane characteristics effect of / τ δ on trans-membrane flux B. Sensitivity of Mass Flux to Membrane Pore Diameter The effect of membrane pore size on mass flux was estimated as shown in Fig. 3. There is a significant change in mass flux on changing the pore diameter from. to.5 microns. The behavior shows that trans-membrane flux is proportional to d, indicating that Knudsen diffusion prevails as compared to Poiseuille flow. The Knudsen number K n (=mean free path/pore diameter in this case has been estimated to be 1.66, which also confirms that the contribution of Knudsen diffusion predominates. 449

4 International Conference on Chemical, Ecology and Environmental Sciences (ICCEES'11 Pattaya Dec. 11 Normalized Sensitivity Factor S (N, (kpa d(μm (a -1.6 (a N (Kg/m hr N(Kg/m hr d(μm Fig. 3 (a Response of S(N, d to the membrane pore diameter effect of membrane pore diameter on flux C. Sensitivity of Mass Flux to Permeate-Side Membrane Pressure Fig. 4 shows the effect of permeate-side membrane pressure. The mass flux decreases linearly with permeate-side membrane pressure (or increases on increasing the degree of vacuum. This indicates that vacuum increases the driving force linearly for Knudsen-molecule transition and Poiseuille flow. It may be noted that sensitivity is negative indicating the opposite change in mass flux with respect to the permeate-side membrane pressure. This behavior agrees well with Pangarkar et al. [7][8]. D. Sensitivity of Mass Flux to Feed Bulk Temperature The flux and its sensitivity to the feed bulk temperature are shown in Fig. 5. On increasing the feed temperature, the mass flux also increases because of the corresponding increase in vapor pressure of water. This increment may be due to additional convective flow (Poiseuille caused by the total pressure difference. The normalized sensitivity of the mass flux to the feed bulk temperature remains positive although decreasing trend indicating that the mass flux will increase in increasing the feed bulk temperature. This is in agreement with Pangarkar et al. [7]. Fig. 4 (a Response of S(N, P pm to the of permeate-side pressure the effect of permeate-side pressure on mass flux Normalized Sensitivity Factor S (N, N(Kg/m T ( C f (a Fig. 5 (a Response of S(N, T f to the feed bulk temperature effect of feed side temperature on mass flux V. CONCLUSIONS Sensitivity of vacuum membrane distillation process was determined with respect to several parameters such as membrane characteristics, pore diameter, permeate-side pressure and feed bulk temperature. The normalized 45

5 International Conference on Chemical, Ecology and Environmental Sciences (ICCEES'11 Pattaya Dec. 11 sensitivity was found to be positive in all these cases except permeate-side pressure in which it is negative. This study is useful in parametric effects on the yield of permeate in desalination process. Nomenclature d Membrane pore diameter (m D AB Diffusivity of A in B (m /s, where A is water vapour, and B is air ΔH Latent heat of vaporization of water, J/kmol h m Membrane heat transfer coefficient (W/m K h p Permeate side heat transfer coefficient (W/m K h f Feed side heat transfer coefficient (W/m K M Molecular weight of water (kg/kmol N A,M-K-P Total trans-membrane flux (kmol/m s N A,P Flux due to Poiseullie flow(kmol/m s N A,K Knudsen diffusion (kmol/m s N A,M Molecular diffusion (kmol/m s P pm Permeate side membrane pressure(kpa P Feed side membrane pressure (kpa R Universal gas constant (J/kmol K r Membrane pore radius (m T f Feed temperature (K T Feed side membrane temperature (K T pm Permeate side membrane temperature (K T p Permeate side pressure (kpa Mole fraction of water vapour y A Greek letters δ Membrane thickness (m ε Membrane porosity λ s Thermal conductivity of PTFE membrane (W/m K λ g Thermal conductivity of water vapour (W/m K η Viscosity of water vapour (kg/m s τ Membrane tortuosity [5] K.W. Lawson and D.R. Lloyd, Membrane distillation, Journal of Membrane Science, vol. 14, pp. 1-5, [6] S. Upadhyaya, K. Singh, S.P. Chaurasia, and C.K. Jha, Modeling and Simulation of Vacuum Membrane Distillation for Desalination, in 1 Proc. CHEMCON Conf., Annamalaianagar. [7] B.L. Pangarkar, S.B. Parjane, R.M. Abhang. and M. Guddad, The Heat and Mass Transfer Phenomena in Vacuum Membrane Distillation for Desalination, International Journal of Chemical and Biomolecular Engineering, vol. 3, pp , 1 [8] B. L. Pangarkar, M. G. S., S.B. Parjane, and M. Guddad, Vacuum Membrane Distillation for Desalination of Ground Water by using Flat Sheet Membrane, World Academy of Science, Engineering and Technology, pp , 11. Sushant Upadhyaya is currently working as Assistant Professor in the Department of Chemical Engineering at Malaviya National Institute of Technology Jaipur. He is B.Tech. in Chemical Engineering from RBS Engineering College, Agra and M.Tech. in Plastics Engineering and Technology from CIPET Lucknow. He is currently pursuing his Ph.D. on vacuum membrane distillation from MNIT Jaipur. His areas of interest are membrane separation, polymer testing & processing, and transport phenomena. Kailash Singh is working as Reader in the Department of Chemical Engineering at Malaviya National Institute of Technology Jaipur. He is B.Tech. in Chemical Engineering from University of Roorkee (now known as IIT Roorkee and M.Tech. from IIT Kanpur. He is doctorate from Curtin University of Technology, Australia. His areas of interest are modeling and simulation, and process control. S.P. Chaurasia is B.Tech. and M.Tech. in Chemical Engineering from HBTI Kanpur. He is Ph.D. from IIT Bombay. Now he is working as Professor in the Department of Chemical Engineering, Malaviya National Institute of Technology Jaipur. His areas of interest are membrane separation, biofuels, Oil/ Fat Processing, Bioprocess Engineering, and Environmental Engineering. Madhu Agarwal is B. Tech. and M.Tech. from Calcutta University (India in 1996 and 1998 respectively, with first class. Now she is working as Assistant Professor in the Department of Chemical Engineering at Malaviya National Institute of Technology Jaipur. She has completed her Ph.D. on the topic Studies on preparation and characterization of Biodiesel from the same institute in February 11. Her Research areas/interests are process modeling and simulation, biofuels, adsorption, catalysis, fluid mechanics, and processes optimization. Rajeev Kumar Dohare is B.E from NIT Surat in and M.Tech from Aligarh Muslim University, Aligarh, in 6. Now he is working as Assistant Professor in the Department of Chemical Engineering at Malaviya National Institute of Technology Jaipur. He is also currently pursuing Ph.D. on Dividing wall Column from the same institute. His Research areas are process modeling, simulation and control, solid waste management, fluid mechanics, and processes optimization. REFERENCES [1] M. S. El-Bourawi, Z. MDING, R. Ma, and M. Khayet, A framework for better understanding membrane distillation separation process, Journal of Membrane Science, vol. 85, pp. 4-9, 6. [] G.W. Meindersma, C.M. Guijt, and A.B. De Haan, Desalination and water recycling by air gap membrane distillation, Desalination,vol. 187, pp , 6. [3] T. Mohammadi, and M.A. Safavi, Application of Taguchi method in optimization of desalination by vacuum membrane distillation, Desalination,vol. 49, pp , 9. [4] F. Banat, F.A. Al-Rub, and K. Bani-Melhem, Desalination by vacuum membrane distillation: sensitivity analysis, Separation and Purification Technology, vol. 33, pp ,