Modeling and CFD Simulation of Water Desalination Using

Article pubs.acs.org/IECR

Modeling and CFD Simulation of Water Desalination Using Nanoporous Membrane Contactors Mehdi Ghadiri,† Safoora Fakhri,‡ and Saeed Shirazian*,§ †

Research Lab for Advanced Separation Processes, Department of Chemical Engineering, Iran University of Science and Technology, Narmak, Tehran 16846-13114, Iran ‡ Maxan Management of Renewable Energy Projects (MORECO), RAMPCO Group, Zafaranieh, Tehran, Iran § Institute of Chemical Technologies, Iranian Research Organization for Science & Technology (IROST), Tehran 3353136846, Iran ABSTRACT: A two-dimensional comprehensive model was developed to predict the transport of water in the nanoporous membrane contactors. The considered membrane distillation device was a counter-current flat-sheet membrane contactor for production of pure water from saline water. The developed model formulates the fundamental transport equations of heat, mass, and momentum in the membrane contactor. The computational fluid dynamics techniques were applied for numerical simulation of model equations. The simulation results were compared with experimental data obtained from literature and showed great agreement with the measured values. A combination of the Knudsen flow and Poiseuille flow was used in the model for estimation of diffusion inside the membrane pores and increased the accuracy of the model. Simulation results revealed that, in the regions adjacent to the membrane wall, the temperature difference is significant. This could be attributed to the fact that a temperature boundary layer is formed near the membrane wall and causes a high temperature decline in this region.

1. INTRODUCTION Membrane distillation (MD) is a separation process which is widely used for separation of water from aqueous solutions. MD is being investigated as a low cost and energy saving alternative to conventional separation processes such as reverse osmosis and distillation.1 The membranes used in MD must be porous and hydrophobic, and the driving force is the vapor pressure gradient across the membrane. Mostly, the vapor pressure gradient is created by a temperature difference across the membrane.2 Various methods can be implemented to create lower vapor pressure on the permeate side including directcontact membrane distillation (DCMD),3 sweeping-gas membrane distillation (SGMD),4 air-gap membrane distillation (AGMD),5 and vacuum membrane distillation (VMD).6 Among various types of MD, the DCMD has been investigated extensively by different researchers which have used commercially hydrophobic flat-sheet membranes of polytetrafluoroethylene (PTFE), polypropylene (PP), and polyvinylidene fluoride (PVDF). DCMD provides low-cost membrane distillation compared to other types of MD. It also avoids common problems encountered in conventional contactors such as flooding, foaming, and entraining.7−11 Most studies on DCMD have focused on experimental works, and there is a shortage of DCMD modeling which is necessary for design and optimization of this process. Simulation and modeling of heat and mass transfer in porous membranes has been investigated by some researchers. A series of CFD simulations have been carried out for single-fiber modules using simplified 2D heat-transfer models.12 In this method, the equations of change are derived and solved by appropriate numerical procedure based on computational fluid dynamics (CFD). Recently, some researchers13−17 utilized this method to simulate gas permeation and solvent extraction © 2013 American Chemical Society

carried out in hollow-fiber membrane contactors (HFMCs). Their results show good agreement with the experimental data. Another method which has been used in simulation of DCMD is development of transport models based on resistance-in-series theory. The latter method reveals the impacts of key parameters that affect the performance of direct-contact membrane distillation.18,19 Furthermore, the Monte Carlo simulation model has been developed to study vapor flux through hydrophobic membranes used DCMD.20 The current study presents a new procedure for modeling of simultaneous heat and mass transfer in direct-contact membrane distillation (DCMD) in a flat-sheet module. The equations of change including mass, momentum, and heat transfer are derived and solved using finite element analysis. The aim of simulation was to predict the profiles of temperature, pressure, and velocity in the contactor.

2. MODEL DEVELOPMENT A comprehensive 2D mathematical model is developed for prediction of water transport in the desalination of water through a flat-sheet membrane contactor used in DCMD. Three transport phenomena are considered in the model. The transport equations include energy convection and conduction for all three layers of contactor, momentum transport for the feed and the permeate channel, and mass transport for the membrane pores. The model is developed using the following assumptions:21,22 (1) Steady state operation. (2) Laminar flow for two phases in the membrane contactor. Received: Revised: Accepted: Published: 3490

January 17, 2013 February 2, 2013 February 7, 2013 February 7, 2013 dx.doi.org/10.1021/ie400188q | Ind. Eng. Chem. Res. 2013, 52, 3490−3498

Industrial & Engineering Chemistry Research

Article

Figure 1. Schematic of the model domain used in simulation of DCMD in 2D (counter-current).

Table 1. Parameters Used in the Simulation of DCMD parameter

value

Tc0 (K)9 Th0 (K)9 Qfeed (m3/s)9 Qpermeate (m3/s)9 kh (W/m K)25 km (W/m K) (calculated by eq 4) kc (W/m K)25 ks (W/m K)24 a (m)9 b (m)9 c (m)9 L (m)9

293 333 7.5 × 10−5 7.5 × 10−5 0.64 0.04 0.6 0.178 0.001 0.0011 0.0021 0.4

(3) Heat loss to the environment is negligible. (4) No chemical reaction takes place. (5) The concentration polarization of NaCl solution is ignored. 2.1. Calculation of Physical and Transport Properties. Physical and transport properties are required for simulation of the DCMD process. Diffusion of water through the porous membrane is modeled by combination of the Knudsen and Poiseuille equations.23 Di,m for the description of water transport in pores of membrane is obtained from the following equations:24 Di,m

⎛ 1 ⎞−1 1 ⎟ = ⎜⎜ + Dp ⎟⎠ ⎝ Dk

(1)

Figure 2. Flowchart of the procedure for numerical simulation. 3491

dx.doi.org/10.1021/ie400188q | Ind. Eng. Chem. Res. 2013, 52, 3490−3498


Article

where Ti is the temperature in °C. The effect of nonvolatile solute on the water vapor pressure must be taken into account for accurate estimation of vapor pressure. For nonideal binary mixtures, the partial pressure can be estimated as25 P1sat = yw P = x wa w Pwsat

(7)

a w = 1 − 0.5x NaCl − 10x NaCl 2

(8)

where yw denotes the vapor mole fraction of water, xw the liquid mole fraction of water, aw the water activity in NaCl solution, and xNaCl the mole fraction of NaCl in the saline solution. 2.2. Model Equations. Figure 1 shows a schematic diagram of the parallel-flow membrane contactor used in the DCMD system. The contactor is a flat-sheet porous membrane with a counter-current flow pattern. As seen, the open conduit is divided by inserting a porous membrane into two parts. The hot feed is flown from the feed channel of the membrane contactor, whereas the cold water is passed in the permeate channel counter currently. The temperature difference between two phases provides the driving force of the process. This causes the evaporation of water at the feed−membrane interface. The water then is condensed at the permeate side by contacting with the cold water. 2.2.1. Equations of Feed Side. In the feed channel, an aqueous solution containing water and NaCl salt is flown. The feed is hot to create a temperature gradient for distillation. The energy balance equation including convection and conduction for feed flow in the feed channel is derived as Figure 3. Model domain and meshes used for numerical simulation of DCMD. The three domains from left to right are feed channel, membrane, and permeate channel, respectively.

D k = 9.7 × 103

Dp =

dp 2

T M

(3)

Dk and Dp are the Knudsen and Poiseuille diffusion coefficients, respectively. Membrane thermal conductivity (km) can be written as9 k m = εkg + (1 − ε)ks

(4)

(10)

∂VY (h)

− ∇ × η(∇VY (h) + (∇VY (h))T(h)) ∂t + ρ(VY (h)·∇)VY (h) + ∇p = f

∇·VY (h) = 0

(11)

where ρh denotes the density of the fluid (kg/m ), VY(h) the velocity vector in the Y direction (m/s), η the dynamic viscosity (kg/m·s), p the pressure (Pa), and f the external force (N). The boundary conditions considered for the feed channel are as follows: 3

kg(Tm) = 0.0144 − 2.16 × 10−5(Tm + 273.15)

@x = 0: ∂Th = 0 (Thermal insulation), No slip condition ∂x

(5)

where Tm is the mean temperature in the membrane. sat Psat 1 and P2 are the saturated pressure of water on the hot and cold solution−membrane interface, respectively. These pressures are estimated using the Antoine equation:25 Pisat = 133.322 × 10(8.10765 − (1450.286/(Ti + 235)))

⎡ ∂ 2T ∂ 2Th ⎤ ∂T ⎥ = ρh CphVY (h) h k h⎢ 2h + 2 ∂y ∂y ⎦ ⎣ ∂x

ρh

where ε is the membrane porosity and kg and ks refer to the thermal conductivity coefficients of vapor within the membrane pores and the solid membrane, respectively. The thermal conductivity of the gas phase in the pores of membrane can be written as25

+ 1.32 × 10−7(Tm + 273.15)2

(9)

where ρh is the liquid density, Cph is the specific heat capacity at constant pressure, kh is the liquid thermal conductivity (w/m K), VY(h) is the velocity vector (m/s), and Th is the temperature of hot solution (K). The Navier−Stokes equations for laminar flow in the feed channel can be expressed as follows:

(2)

P × d p2 16 × μ

ρh CphVY (h)·∇Th − ∇·(k h∇Th) = 0

(12)

@x = a: Th = Tmembrane , No slip condition

(13)

@y = 0: i = 1, 2

Th = Th0 , VY (h) = V0h (inlet boundary)

(6) 3492

(14)



Article

Table 2. Comparison of the Temperature Profile for Both Experimental and Modeling Results (Hot Side Inlet Temperature of 60 °C, Cold Side Inlet Temperature of 20 °C, NaCl Concentration 1%, Counter-Current) hot outlet temperature (°C)

cold outlet temperature (°C)

velocity (m/s)

experimental9

modeling

error (%)

experimental9

modeling

error (%)

0.17 0.28 0.39 0.5 0.55

50.1 52.3 53.9 55.1 55.3

49.82 52.54 53.99 54.9 55.25

0.56 0.46 0.16 0.36 0.09

29.1 27.4 26.3 25.8 25.4

29.05 26.45 25.15 24.33 24.05

0.17 3.4 4.3 5.6 4.2

where ρc is the cold liquid density, Cpc is the specific heat capacity at constant pressure, kc is the liquid thermal conductivity (w/m K), VY(c) is the velocity vector (m/s), and Tc is the temperature of cold solution (K). The Navier−Stokes equations for laminar flow in the permeate channel of the membrane contactor can be expressed as follows:

@y = L: Convective flux, p = patm (outlet boundary)

(15)

2.2.2. Membrane Equations. The conduction equation was used for the energy balance in the membrane, which considers heat transfer through membrane pores and solid: ∇·(k m∇Tm) = 0

⎡ ∂ 2T ∂ 2Tm ⎤ ⎥=0 k m⎢ 2m + ∂y 2 ⎦ ⎣ ∂x

(16)

ρc (17)

(18)

⎡ ∂ 2C ∂ 2C i,m ⎤ i,m ⎥=0 Di,m⎢ + ⎢⎣ ∂x 2 ∂y 2 ⎥⎦

(19)

where ρc denotes the density of the fluid (kg/m ), VY(c) the velocity vector in the Y direction (m/s), η the dynamic viscosity (kg/m·s), p the pressure (Pa), and f the external force (N). The boundary conditions considered for the permeate channel are as follows: @x = b: Tc = Tm , No slip condition

(27)

@x = c: ∂Tc = 0 (Thermal insulation), No slip condition ∂x

(28)

@y = 0:

@x = a:

Convective flux, p = patm (outlet boundary)

(20)

(29)

@y = L:

@x = b: Tm = Tc , C = Cc

(26) 3

where Ci,m denotes the concentration of water (mol/m3) and Di,m denotes its diffusion coefficient (m2/s). The boundary conditions considered for the water concentration in the membrane pores are as follows:

Tm = Th , C = C h

− ∇ × η(∇VY (c) + (∇VY (c))T(c)) ∂t + ρ(VY (c)·∇)VY (c) + ∇p = f

∇·VY (c) = 0

where km is the membrane thermal conductivity (w/m K) and Tm is the temperature inside the membrane (K). The steady-state mass transfer equation for transport of water vapor inside the membrane pores, which is considered to be due to diffusion alone, may be expressed as ∇·(Di,m∇Cw,m) = 0

∂VY (c)

Tc = Tc0 , VY (c) = V0c (inlet boundary)

(21)

The parameters used in the simulations are listed in Table 1. 2.3. Numerical Solution of Model Equations. The model equations related to feed channel, membrane, and permeate channel with the boundary conditions were solved using COMSOL Multiphysics version 3.5 software. The latter uses finite element method analysis for numerical solution of the governing equations developed in this work. The numerical solver of UMFPACK version 4.2 was applied as a direct solver. The latter is appropriate for numerical solution of stiff and nonstiff nonlinear boundary value problems. The accuracy, applicability, and robustness of this method for simulation of membrane contactors have been proved by some researchers.26,27 The flowchart of numerical simulation is shown in Figure 2. Figure 3 shows a segment of the mesh used to simulate the water transport in DCMD. Adaptive mesh refinement in COMSOL, which generates the best and minimal meshes, was selected to mesh the DCMD geometry. A scaling factor of 120 has been applied in the y direction because of the large difference between x and y. A system with the

@y = 0: ∂Th ∂Cm = 0 (Thermal insulation), = 0 (insulation) ∂x ∂r (22)

@y = L: ∂Th ∂Cm = 0 (Thermal insulation), = 0 (insulation) ∂x ∂r (23)

2.2.3. Equations of Permeate Side. The temperature distribution in the permeate side is calculated by solving the convection and conduction equations: ρc CpcVY (c)·∇Tc − ∇·(kc∇Tc) = 0

(24)

⎡ ∂ 2T ∂ 2Tc ⎤ ∂T ⎥ = ρc CpcVY (c) c kc⎢ 2c + 2 ∂y ∂y ⎦ ⎣ ∂x

(25)

(30)

3493



Article

Figure 4. Velocity field in the feed and permeate channels of membrane distillation.

specifications of Intel Core i5CPU M 460 @ 2.53 GHz and 6 GB RAM was used to solve the governing equations.

3. RESULTS AND DISCUSSION 3.1. Model Validation. The modeling findings were compared with the experimental data obtained from references to verify the model accuracy developed here for DCMD. Different velocities of feed and permeate channels were taken into account. Table 2 lists the experimental and simulation results for hot side and cold side outlet temperatures. As it can be seen from Table 2, for low outlet temperatures, modeling results show great agreement with the experimental values. For the cold outlet temperatures, a maximum deviation of 5.6% between the model and experimental data is observed when the velocity of either phase is 0.50 m/s. Generally, the simulation results show a good agreement with the experiment results, with an average deviation of less than 5.0%. It confirms that the two-dimensional model developed here for DCMD based on the momentum, energy, and mass transfer is accurate in prediction of DCMD operation. 3.2. Velocity Field in DCMD. The velocity field and profile in the feed and permeate channels of the DCMD are illustrated in Figures 4 and 5. The velocity field in the DCMD is simulated by numerical solution of the Navier−Stokes equations. The velocity distribution in the feed and permeate channels is shown in Figure 4, while the velocity profile at different module

Figure 5. Velocity profile in the feed channel.

lengths is shown in Figure 5. It is observed that the velocity profile in the flat-sheet membrane contactor is almost parabolic with a mean velocity which increases with the module length. It 3494



Article

Figure 6. Temperature distribution in direct-contact membrane distillation.

Figure 8. Temperature profile in the x direction at three sides of membrane distillation. Figure 7. Temperature profile in the feed side.

temperature distribution in the DCMD is of great importance for theoretical consideration of DCMD. The two-dimensional model developed in this work is capable of obtaining the temperature distribution in three sides of a membrane contactor. Owing to finding the exact temperature distributions on both membrane surfaces, Figure 6 shows the temperature distribution in the feed channel, membrane, and permeate channel of a membrane contactor. Figure 7 also presents the temperature profile in x directions at different lengths in the feed channel.

confirms that, after a short distance from the inlet of the membrane module, the velocity becomes fully developed. Figures 4 and 5 also reveal that the model developed for DCMD considers the inlet effects on the hydrodynamics of fluid flow in the contactor which would increase the accuracy of the model. 3.3. Temperature Distribution in the DCMD. Since the driving force in the membrane distillation process is the temperature difference between two contacting phases, the 3495



Article

Figure 9. Partial pressure distribution and total mass transfer flux of water vapor inside the membrane.

temperature of Tc,0 flows in the permeate channel counter currently. The liquid water evaporates at the feed−membrane interface due to the temperature difference across the membrane and causes the temperature decline in the feed channel. Then, water vapor is transported through the membrane pores due to the partial pressure gradient (equivalent to vapor concentration) across the membrane. Eventually, the water vapor is liquefied at the permeate side with cold temperature. It should be pointed out that the hydrophobicity of membrane effectively prevents penetration of liquid water inside the membrane pores which might block the membrane pores and reduce evaporation flux. The temperature profile in the feed channel of the DCMD is also shown in Figure 7 where the brine solution is flown. Figure 7 indicates that, with increasing height from z = 0 to z = L, the temperature gradient increases in the feed channel of the membrane contactor in the x direction. 3.4. Temperature Profile in x Direction of Membrane Distillation. To further investigate the temperature decline in the membrane distillation, the temperature profile in the x direction of the membrane contactor is shown in Figure 8. As observed, an overall temperature decline exists in the membrane contactor from feed channel to permeate side. It should be noted that the energy required for evaporation of water in DCMD is supplied by the hot feed solution. In both channels, i.e., feed and permeate channels, a temperature

Figure 10. Profile of partial pressure inside the membrane.

As shown, a counter-current flow is considered in the membrane module to minimize heat loss. Hot water with a temperature of Th,0 is entered in the feed channel where the hottest region is shown in Figure 6. The cold water with 3496



■

decline is observed in the region near the membrane wall. This phenomenon, called temperature polarization, would reduce the evaporation flux mainly due to decrement of pressure gradient, since the saturation pressure depends exponentially on the temperature.3,9,19,20 It is also observed that, in the regions adjacent to the membrane wall, the temperature difference along the module length is significant. This could be attributed to the fact that a temperature boundary layer is formed near the membrane wall and causes high temperature changes in this region. Furthermore, a high contribution of convective heat transfer causes lower temperature changes in the region far from the membrane wall. Furthermore, in the DCMD process, simultaneous heat and mass transfers occur. The temperatures at the feed−membrane interfaces differ from the temperatures at the bulk of the feed due to the temperature polarization effect, as shown in Figure 8. The transport of water occurs through the pores of the hydrophobic membrane. The heat transfer within the membrane involves the latent heat needed for evaporation of the water and the heat transferred by conduction across both the vapor-filled pores and solid membrane material. 3.5. Partial Pressure Distribution Inside the Membrane. Figure 9 presents the vectors of diffusive fluxes of vapor water inside the hydrophobic porous membrane. It also presents the pressure distribution (colored surface) of vapor water inside the pores of membrane. As it can be seen, diffusive flux of water vapor decreases along the module length. This is due to decreases of partial pressure difference from Y = 0 to Y = L. Consequently, it causes decline of driving force for mass transfer of vapor water through the membrane pores. The pressure profile of vapor water in the x direction inside the microporous membrane is also presented in Figure 10. It is indicated that, as the brine solution (feed solution) flows through the feed channel, the pressure difference of water vapor drops down because the temperature of the solution decreases along the membrane module.

NOMENCLATURE Cpc = cold side specific heat capacity at constant pressure (J/ (kg·K)) Cph = hot side specific heat capacity at constant pressure (J/ (kg·K)) Cpm = specific heat capacity of the membrane at constant pressure (J/(kg·K)) k = thermal conductivity (W/m K) kc = cold side liquid thermal conductivity (W/m K) kh = hot side liquid thermal conductivity (W/m K) km = liquid thermal conductivity of the membrane (W/m K) kg = vapor thermal conductivity of the membrane (W/m K) ks = solid thermal conductivity of the membrane (W/m K) L = module length (m) M = molecular weight of water (kg/mol) p = pressure (Pa) Psat 1 = saturated vapor pressure on the hot side membrane surface (Pa) Psat 2 = saturated vapor pressure on the cold membrane surface (Pa) pc = cold side pressure (Pa) ph = hot side pressure (Pa) dp = average membrane pore size (m) R = gas constant (J/mol·K) Tc = cold side temperature (K) Tci = cold side inlet temperature (K) Tc,o = cold side outlet temperature (K) Th = hot side temperature (K) Th,i = hot side inlet temperature (K) Th,o = hot side outlet temperature (K) Tm = membrane temperature (K) Vc = cold side flow velocity (m/s) Vh = hot side flow velocity (m/s) Vc,I = cold side inlet flow velocity (Y direction) Vh,I = hot side inlet flow velocity (Y direction) X = X direction Y = Y direction

Greek Letters

4. CONCLUSIONS A two-dimensional mathematical model is developed to predict the desalination of water using a flat-sheet membrane contactor used as direct-contact membrane distillation (DCMD). The process has been designed for production of pure water in membrane distillation. A novel model is developed by coupling momentum, mass, and heat transfers. The modeling findings are then validated with experimental results for a countercurrent configuration. The results confirmed the accuracy of the model. The result reveals that, at the inlet regions in the feed side, the velocity is not developed. After a short distance from the inlet, the velocity profile is fully developed. As the brine solution flows through the feed channel, the pressure difference of water vapor drops down because the temperature of water decreases along the membrane module.

■

Article

■

ε = membrane porosity

REFERENCES

(1) Lawson, K. W.; Lloyd, D. R. Membrane distillation. J. Membr. Sci. 1997, 124 (1), 1−25. (2) Izquierdo-Gil, M. A.; Fernández-Pineda, C.; Lorenz, M. G. Flow rate influence on direct contact membrane distillation experiments: Different empirical correlations for Nusselt number. J. Membr. Sci. 2008, 321 (2), 356−363. (3) Cath, T. Y.; Adams, V. D.; Childress, A. E. Experimental study of desalination using direct contact membrane distillation: a new approach to flux enhancement. J. Membr. Sci. 2004, 228 (1), 5−16. (4) Khayet, M.; Godino, P.; Mengual, J. I. Nature of flow on sweeping gas membrane distillation. J. Membr. Sci. 2000, 170 (2), 243−255. (5) Guillén-Burrieza, E.; Blanco, J.; Zaragoza, G.; Alarcón, D.-C.; Palenzuela, P.; Ibarra, M.; Gernjak, W. Experimental analysis of an air gap membrane distillation solar desalination pilot system. J. Membr. Sci. 2011, 379 (1−2), 386−396. (6) Lawson, K. W.; Lloyd, D. R. Membrane distillation. I. Module design and performance evaluation using vacuum membrane distillation. J. Membr. Sci. 1996, 120 (1), 111−121. (7) Dumée, L. F.; Sears, K.; Schütz, J.; Finn, N.; Huynh, C.; Hawkins, S.; Duke, M.; Gray, S. Characterization and evaluation of carbon nanotube Bucky-Paper membranes for direct contact membrane distillation. J. Membr. Sci. 2010, 351 (1−2), 36−43.

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel.: +98 21 77240496. Fax: +98 21 77240495. Notes

The authors declare no competing financial interest. 3497



Article

(8) Qtaishat, M.; Rana, D.; Khayet, M.; Matsuura, T. Preparation and characterization of novel hydrophobic/hydrophilic polyetherimide composite membranes for desalination by direct contact membrane distillation. J. Membr. Sci. 2009, 327 (1−2), 264−273. (9) Hwang, H. J.; He, K.; Gray, S.; Zhang, J.; Moon, I. S. Direct contact membrane distillation (DCMD): Experimental study on the commercial PTFE membrane and modeling. J. Membr. Sci. 2011, 371 (1−2), 90−98. (10) Qtaishat, M.; Matsuura, T.; Kruczek, B.; Khayet, M. Heat and mass transfer analysis in direct contact membrane distillation. Desalination 2008, 219 (1−3), 272−292. (11) Qu, D.; Wang, J.; Hou, D.; Luan, Z.; Fan, B.; Zhao, C. Experimental study of arsenic removal by direct contact membrane distillation. J. Hazard. Mater. 2009, 163 (2−3), 874−879. (12) Yu, H.; Yang, X.; Wang, R.; Fane, A. G. Analysis of heat and mass transfer by CFD for performance enhancement in direct contact membrane distillation. J. Membr. Sci. 2012, 405−406 (0), 38−47. (13) Abdullah, N. S.; Das, D. B. Modelling nutrient transport in hollow fibre membrane bioreactor for growing bone tissue with consideration of multi-component interactions. Chem. Eng. Sci. 2007, 62 (21), 5821−5839. (14) Al-Marzouqi, M. H.; El-Naas, M. H.; Marzouk, S. A. M.; AlZarooni, M. A.; Abdullatif, N.; Faiz, R. Modeling of CO2 absorption in membrane contactors. Sep. Purif. Technol. 2008, 59 (3), 286−293. (15) Shirazian, S.; Ashrafizadeh, S. N. Mass Transfer Simulation of Caffeine Extraction by Subcritical CO2 in a Hollow-Fiber Membrane Contactor. Solvent Extr. Ion Exch. 2010, 28 (2), 267−286. (16) Shirazian, S.; Ashrafizadeh, S. N. Mass Transfer Simulation of Carbon Dioxide Absorption in a Hollow-Fiber Membrane Contactor. Sep. Sci. Technol. 2010, 45 (4), 515−524. (17) Shirazian, S.; Moghadassi, A.; Moradi, S. Numerical simulation of mass transfer in gas−liquid hollow fiber membrane contactors for laminar flow conditions. Simul. Modell. Practice Theory 2009, 17 (4), 708−718. (18) Martínez, L.; Rodríguez-Maroto, J. M. Membrane thickness reduction effects on direct contact membrane distillation performance. J. Membr. Sci. 2008, 312 (1−2), 143−156. (19) Martínez, L.; Rodríguez-Maroto, J. M. On transport resistances in direct contact membrane distillation. J. Membr. Sci. 2007, 295 (1− 2), 28−39. (20) Imdakm, A. O.; Matsuura, T. Simulation of heat and mass transfer in direct contact membrane distillation (MD): The effect of membrane physical properties. J. Membr. Sci. 2005, 262 (1−2), 117− 128. (21) Ghadiri, M.; Marjani, A.; Shirazian, S. Mathematical modeling and simulation of CO2 stripping from monoethanolamine solution using nano porous membrane contactors. Int. J. Greenhouse Gas Control 2013, 13 (0), 1−8. (22) Ghadiri, M.; Shirazian, S.; Ashrafizadeh, S. N. Mass Transfer Simulation of Gold Extraction in Membrane Extractors. Chem. Eng. Technol. 2012, 35 (12), 2177−2182. (23) Chiang, H. L.; Chiang, P. C.; Chiang, Y. C.; Chang, E. E. Diffusivity of microporous carbon for benzene and methyl-ethyl ketone adsorption. Chemosphere 1999, 38 (12), 2733−2746. (24) Xu, J.; Li, R.; Wang, L.; Li, J.; Sun, X. Removal of benzene from nitrogen by using polypropylene hollow fiber gas−liquid membrane contactor. Sep. Purif. Technol. 2009, 68 (1), 75−82. (25) Chen, T.-C.; Ho, C.-D.; Yeh, H.-M. Theoretical modeling and experimental analysis of direct contact membrane distillation. J. Membr. Sci. 2009, 330 (1−2), 279−287. (26) Shirazian, S.; Rezakazemi, M.; Marjani, A.; Moradi, S. Hydrodynamics and mass transfer simulation of wastewater treatment in membrane reactors. Desalination 2012, 286 (0), 290−295. (27) Marjani, A.; Shirazian, S. Simulation of heavy metal extraction in membrane contactors using computational fluid dynamics. Desalination 2011, 281 (0), 422−428.

3498


Modeling and CFD Simulation of Water Desalination Using

Recommend Documents