Reverse Draw Solute Permeation in Forward Osmosis: Modeling and

Jun 7, 2010 - A model was developed that describes the reverse permeation of draw solution across an asymmetric membrane in forward osmosis operation...
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Environ. Sci. Technol. 2010, 44, 5170–5176

Reverse Draw Solute Permeation in Forward Osmosis: Modeling and Experiments WILLIAM A. PHILLIP, JUI SHAN YONG, AND MENACHEM ELIMELECH* Department of Chemical Engineering, Environmental Engineering Program, P.O. Box 208286, Yale University, New Haven, Connecticut 06520-8286

Received March 20, 2010. Revised manuscript received May 19, 2010. Accepted May 21, 2010.

Osmotically driven membrane processes are an emerging set of technologies that show promise in water and wastewater treatment, desalination, and power generation. The effective operation of these systems requires that the reverse flux of draw solute from the draw solution into the feed solution be minimized. A model was developed that describes the reverse permeation of draw solution across an asymmetric membrane in forward osmosis operation. Experiments were carried out to validate the model predictions with a highly soluble salt (NaCl) as a draw solution and a cellulose acetate membrane designed for forward osmosis. Using independently determined membrane transport coefficients, strong agreement between the model predictions and experimental results was observed. Further analysis shows that the reverse flux selectivity, the ratio of the forward water flux to the reverse solute flux, is a key parameter in the design of osmotically driven membrane processes. The model predictions and experiments demonstrate that this parameter is independent of the draw solution concentration and the structure of the membrane support layer. The value of the reverse flux selectivity is determined solely by the selectivity of the membrane active layer.

Introduction Forward osmosis (FO) and pressure retarded osmosis (PRO) are two emerging technologies that fall under the classification of osmotically driven membrane processes (1, 2). These technologies take advantage of the osmotic pressure difference that is generated when a semipermeable membrane separates two solutions of differing concentrations. By using the osmotic pressure difference to drive the permeation of water across the semipermeable membrane, osmotically driven membrane processes may be capable of addressing several of the shortcomings of hydraulically driven membrane processes, such as reverse osmosis (RO). Unlike RO, FO does not require a high applied hydraulic pressure, thereby decreasing capital and energy costs (3). Furthermore, recent investigations have demonstrated a lower fouling propensity with FO (1, 4-6), implying lower operating costs. Several studies have taken advantage of these benefits and demonstrated the use of osmotically driven membrane processes to desalinate seawater and brackish water (1, 7-9), treat wastewater (4, 10), and reclaim wastewater using an osmotic membrane bioreactor (11). * Corresponding author phone: (203)432-2789; e-mail: menachem. [email protected]. 5170

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A significant portion of the efforts to improve FO and PRO operations has focused on tailoring the membrane structure to decrease the effects of internal concentration polarization (ICP) (12-19) or on developing new draw solutions (20) that are capable of generating large osmotic pressures, but are still relatively easy to separate from water. Further developments in these areas are still needed for successful commercialization of these technologies. However, one area of research that has received limited attention, but could be a significant impediment to the viability of osmotically driven membrane processes, is the reverse permeation of draw solute from the draw solution into the feed solution (11, 21). An ideal semipermeable membrane would prevent any dissolved draw solute from permeating into the feed solution. However, no membrane is a perfect barrier, and a small amount of dissolved solute will be transported across the membrane. If an expensive draw solute is used, the cost of replenishing the draw solute lost to the feed solution could make the process less economical. Alternatively, if the draw solute was detrimental to the aquatic environment, an additional treatment step of the feed solution concentrate would be required prior to discharge. Therefore, a thorough understanding of the phenomenon of reverse solute permeation is critical to the effective development of osmotically driven membrane technologies. The objectives of this paper are (i) to formulate a model that describes the reverse permeation of a single draw solute across an asymmetric membrane in a forward osmosis operation, (ii) to validate the model through laboratory experiments with a well characterized forward osmosis membrane and draw solution, and (iii) to use the model to gain insights into the processes that govern draw solute permeation in forward osmosis. In our model, the draw solute reverse flux is described in terms of experimentally accessible quantities and common transport parameters. The implications of our results for the future development of forward osmosis are further evaluated and discussed.

Theory A schematic of an asymmetric membrane operating in FO mode (i.e., with the selective layer facing the feed solution) is shown in Figure 1. For the draw solute to leak into the feed solution, it must first diffuse through the support layer, where its diffusion is opposed by the convective flow of solvent, until it reaches the interface between the support layer and the active layer. Once there, the draw solute partitions into the active layer before diffusing across it. After diffusing across the active layer, the draw solute partitions into the feed solution, which has a negligible concentration of draw solute. This process can be described by considering the mass transfer through the support layer and then the active layer in series. Draw Solute Mass Balance in the Support Layer. For the support layer, a steady-state mass balance can be written on a differential volume dJsS d2c dc ) -DS 2 + Jw )0 dz dz dz

(1)

where JsS is the total flux of draw solute, c is the solute concentration, DS is the solute diffusion coefficient in the support layer, and Jw is the superficial fluid velocity, which is equivalent to the solvent permeate flux. This mass balance is, in principle, the same as that used to describe the 10.1021/es100901n

 2010 American Chemical Society

Published on Web 06/07/2010

General Solution for Draw Solute Concentration Profile and Flux in the Support Layer. Integrating eq 1 twice and using boundary conditions 3a-3b give the following expression for the draw solute concentration profile in the support layer exp c)

(

)

( )

JwtSτ z JwtSτ s (c - cis) + exp c - cD Dε tS D Dε i JwtSτ exp -1 Dε

( )

(4)

The concentration profile can then be used to find an expression for the total draw solute flux by taking the sum of the diffusive and convective components of the flux JsS ) -DS

dc + Jwc dz

(5)

Substituting eq 4 for c in eq 5 yields an expression for the solute flux into the feed solution

JsS

FIGURE 1. A schematic of draw solute leaking into the feed solution. The high concentration of solute in the draw solution, cD, creates a chemical potential gradient that drives both the forward water flux, Jw, and the reverse flux of solute, Js. For the draw solute to permeate across the asymmetric membrane into the feed solution, where its concentration cF is negligible, it must be transported across the support layer of thickness tS, and the active layer of thickness tA. ciS and ciA represent the draw solute concentrations on the support layer side and active layer side of the support layer-active layer interface, respectively. phenomenonofinternalconcentrationpolarization(12,14,22). We also note that eq 1 implies that DS, JsS, and Jw are independent of z and are constant across the entire support layer. Implicitly, we assume that the draw solute is a single entity, even though it may consist of several chemical species that are strongly associated, as is the case with strong electrolytes (23). Also, the diffusion coefficient in this equation DS is an effective diffusion coefficient, which can be related to the bulk diffusion coefficient D by accounting for the porosity, ε, and tortuosity, τ, of the support layer (24) DS )

Dε τ

(2)

The porosity accounts for the fact that the experimental measurements are based on the total membrane area and not the cross-sectional area of the pores, while the tortuosity accounts for the additional distance a solute molecule must travel relative to the support layer thickness. Because the coordinate system z points into the support layer, eq 1 is subject to the following boundary conditions z ) 0 c ) ciS

(3a)

z ) tS c ) cD

(3b)

Here, ciS is the draw solute concentration on the support layer side of the support layer-active layer interface, cD is the bulk draw solute concentration, and tS is the support layer thickness.

)

( ( ) ( )

)

JwtSτ s c - cD Dε i JwtSτ exp -1 Dε

Jw exp

(6)

This expression is not readily compared to experiments because the draw solute concentration at the interface, ciS, cannot be measured. However, we do know ciS has a finite value because the osmotically driven water flux, Jw, is not zero. Draw Solute Flux Across the Active Layer. In order to express the reverse flux in terms of experimentally accessible quantities, we begin by considering the flux of draw solute across the active layer. This flux, JsA, can be written as JsA ) -

DA A (c - 0) tA i

(7)

where DA is the draw solute diffusion coefficient in the active layer, tA is the active layer thickness, and ciA is the draw solute concentration on the active layer side of the support layeractive layer interface. An ideal draw solute should not permeate the active layer (i.e., the reflection coefficient should be equal to 1); therefore, we have ignored any multicomponent diffusion effects in writing eq 7 (25, 26). An additional term accounting for the influence of the water flux on the salt flux would need to be included in eq 7 only if multicomponent diffusion effects were important (25). Analytical Expression for the Reverse Flux of Draw Solute. The flux across the active layer, JsA, can be related to the flux across the support layer by examining the interface (z ) 0) between the two layers. Because no draw solute is accumulating or reacting at the interface, a mass balance yields z ) 0 JsA ) JsS

(8)

Additionally, the draw solute concentration on the active layer side of the interface can be related to the concentration on the support layer side by assuming that the chemical potential is equal across the interface ciA ) HciS

(9)

where H is the partition coefficient describing the relative concentration in each phase. Equating eqs 6 and 7 and substituting eq 9 for ciA, the reverse draw solute flux is expressed in terms of the experimentally accessible bulk draw solution concentration cD VOL. 44, NO. 13, 2010 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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Js )

(

JwcD JwtA

) ( )

JwtSτ exp 1- 1+ A Dε D H

)

JwcD Jw JwS exp 1- 1+ B D (10)

(

) ( )

Note that the derived equation for the draw solute flux contains two important transport parameters S)

B)

tSτ ε

(11)

DAH tA

(12)

The first term is the membrane structural parameter, S, characterizing the average distance a solute molecule must travel through the support layer when going from the bulk draw solution to the active layer. The structural parameter, S, can be determined from FO and RO experiments as described elsewhere (14, 19). The second parameter, B, is the active layer salt permeability coefficient (3, 26). This parameter can be determined from RO or PRO experiments as described later in this paper. Written in this form, eq 10 can be used to predict the draw solute reverse flux and compared with FO mode experiments.

Materials and Methods Model Draw Solute. ACS reagent sodium chloride (NaCl crystals, J.T. Baker) was used as a draw solute because it is highly soluble in water and its properties in solution are well-characterized. For reverse permeation experiments, NaCl was dissolved in deionized water (DI) obtained from a Milli-Q ultrapure water purification system (Millipore, Billerica, MA) at concentrations ranging from 0.5 to 4 M. The osmotic pressures of these solutions were calculated using a software package from OLI Systems, Inc. (Morris Plains, NJ), and the binary diffusion coefficient for sodium chloride and water was assumed constant at a value of 1.61 × 10-9 m2/s (27, 28). NaCl concentration in the feed solution was measured using a calibrated conductivity meter (Oakton Instruments, Vernon Hills, IL). Forward Osmosis Membrane and Crossflow Setup. A commercial asymmetric cellulose triacetate (HTI-CTA) membrane (Hydration Technology Innovations, Albany, OR) was used for the reverse permeation experiments. This proprietary membrane consists of a woven fabric mesh embedded within a continuous polymer layer. The HTI-CTA membrane has been used extensively in prior research exploring osmotically driven membrane processes (20, 29). The experimental crossflow FO system employed is similar to that described in our previous studies (14, 20, 29). The unit was custom built with channel dimensions measuring 77 mm long, 26 mm wide, and 3 mm deep on both sides of the membrane. Variable speed gear pumps (Cole-Parmer, Vernon Hills, IL) were used to pump the feed and draw solutions cocurrently. No mesh feed spacers were used, and the solutes were pumped in closed loops at 1.0 L/min, corresponding to a crossflow velocity of 21.4 cm/s. A water bath (Neslab, Newington, NH) maintained the temperature of both the feed and draw solutions at 20 ( 0.5 °C. The draw solution reservoir rested upon a balance from Ohaus (Pine Brook, NJ), and the change in mass as a function of time was used to determine the water flux across the membrane. Measurement of Membrane Properties in Reverse Osmosis. The pure water permeability coefficient, A, and NaCl permeability coefficient, B, of the HTI-CTA membranes were evaluated in a laboratory-scale crossflow reverse osmosis test unit. The effective membrane area was 20.02 cm2, and the crossflow velocity was fixed at 21.4 cm/s. During 5172

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experiments, the temperature was kept constant at 20 ( 0.5 °C. Initially, the membrane was equilibrated with DI at an applied pressure, ∆P, of 27.6 bar (400 psi) until the permeate flux reached a steady value (after about 10 min). After equilibration, the volumetric permeate rate was measured at applied pressures ranging from 6.9 to 27.6 bar (100 to 400 psi) in 6.9 bar (100 psi) increments. The water flux, Jw, at each pressure drop was calculated by dividing the volumetric permeate rate by the membrane area. The water permeability coefficient, A, was obtained from the slope of water flux plotted versus pressure drop. NaCl rejection, R, was also determined at applied pressures ranging from 6.9 to 27.6 bar (100 to 400 psi) in 6.9 bar (100 psi) increments. Using a 50-mM NaCl feed solution, the observed rejection was determined from the difference in bulk feed (cb) and permeate (cp) salt concentrations, R ) 1 - cp/cb. The NaCl permeability coefficient was determined after correcting for concentration polarization using (3, 30)

( 1 -R R ) exp(- k ) Jw

B ) Jw

(13)

where k, the crossflow cell mass transfer coefficient of NaCl, was calculated from correlations for rectangular cell geometry (14, 31). In this equation, Jw and R correspond to the permeate flux and NaCl rejection observed at each applied pressure. Measurement of Reverse Draw Solute Permeation in Forward Osmosis. The reverse NaCl flux, Js, was determined using the following protocol. An HTI-CTA membrane was placed in the custom built cross-flow cell. Both FO and PRO mode tests were run, depending on the purpose of the experiments. FO mode tests were carried out to test our newly developed model for reverse solute permeation, while PRO mode tests were run to verify the accuracy of the salt permeability coefficient, B, determined from RO experiments. After loading the membrane, both the feed and draw solution reservoirs were filled with DI. The inlet and outlet to the cross-flow cell were closed, isolating the membrane from feed and draw solutions, and the draw solution reservoir was dosed with the proper amount of NaCl stock solution. The draw solution was then mixed by pumping the solution in a closed loop for 10 min. After the draw solution was mixed, the membrane was exposed to the feed and draw solutions, and data recording was initiated. The mass of the draw solution was monitored as a function of time to determine the water flux, and the NaCl concentration in the feed was monitored by submerging the conductivity meter probe at 20-min time intervals. It usually took about 20 to 30 min for the water flux to stabilize; once this occurred, the reverse solute flux was assumed to be at a steady-state. The data collected after the water flux had stabilized was used to calculate the experimental reverse draw solute flux. Because the initial NaCl concentration in the feed is zero, a species mass balance yields cF(VF0 - JwAmt) ) JsAmt

(14)

where cF is the NaCl concentration in the feed, VF0 is the initial volume of feed solution, Jw is the measured water flux, Am is the membrane area, and t is time. This equation can be linearized such that the slope of a plot of 1/cF versus 1/t is equal to VF0/(JsAm), allowing the experimental draw solute flux, Js, to be calculated VF0 1 Jw 1 ) cF JsAm t Js

()

(15)

The active layer salt permeability coefficient B was also determined from PRO mode experiments using DI water as a feed on the support layer side and NaCl (0.5, 1.0, and 2.0

M) as a draw solution on the membrane active layer side. The salt permeability coefficient B is calculated by dividing the measured salt flux Js by the draw solute concentration at the membrane active layer surface. The latter is obtained after correcting for dilutive external concentration polarization (14), yielding Js

B)

( )

cD exp -

Jw k

(16)

where k is the mass transfer coefficient calculated for a rectangular cell (31).

Results and Discussion Membrane Performance Parameters. Five samples of the HTI-CTA membranes were used to determine the performance parameters A and B. The water flux for a pure DI feed was measured at four different applied pressures in RO operation. Linear regression was then used to determine the water permeability coefficient A from a plot of water flux versus applied pressure, giving a value for A of 0.44 ( 0.12 L m-2 h-1 bar-1 (1.23 ( 0.33 × 10-12 m s-1 Pa-1). The relatively large standard deviation is attributed to cutting smaller samples from a large nonuniform flat sheet membrane. For our calculations, we use the average A value of 0.44 L m-2h-1 bar-1. The salt permeability coefficient B was also determined in RO operation. The observed salt rejection was used to determine B after correcting for external concentration polarization using eq 13. The experiments yielded observed percent rejections that ranged from 89.1% to 96.1%. The value of B determined from these measurements was 0.261 ( 0.061 L m-2 h-1 (7.25 ( 1.69 × 10-8 m s-1). PRO mode was also used to determine the B parameter to ensure that the value determined from RO operation (i.e., high applied pressure) accurately reflected the value in FO operation (i.e., no applied pressure). The B parameter for a single membrane was calculated from eq 16 to be 0.269 ( 0.020 L m-2 h-1 (7.47 ( 0.55 × 10-8 m s-1), in good agreement with the RO experiments. The average of the B values obtained in RO and PRO modes, 0.265 L m-2h-1, was used for our calculations. Membrane Structural Parameter. The membrane structural parameter S was calculated from (12, 14, 15, 19-22) S)

()

B + AπDb D ln Jw B + Jw

(17)

where πDb is the osmotic pressure in the bulk draw solution. The experimentally determined A and B values were used along with the bulk osmotic pressure for the 1 M NaCl draw solution (47.3 bar or 686.3 psi), and the water flux was determined in FO mode with a 1 M NaCl draw solution and DI water as the feed. Higher concentration draw solutions were not used for this calculation because the osmotic pressure deviated from the ideal van’t Hoff behavior, an assumption underlying the model to calculate S. The nonideality of these solutions was observed as a deviation of the osmotic pressure calculated using the OLI software from that calculated using the van’t Hoff equation. The S parameter determined from the 1 M data was 481 µm. Reverse Draw Solute Flux as a Function of Draw Solution Concentration. As the concentration of the draw solution increases, the measured water flux and reverse draw solute flux should both increase. Experiments were run using NaCl draw solutions ranging in concentration from 1 to 4 M to examine the dependency of water flux and reverse NaCl flux on NaCl concentration. The results of these experiments, plotted in Figure 2, show that, as anticipated, both the water flux and reverse NaCl flux increase with increasing NaCl

FIGURE 2. Experimental water flux and reverse flux of NaCl as a function of NaCl draw solution concentration. The water flux and reverse solute flux were measured from experiments using DI water as a feed solution and draw solutions of varying concentration as indicated. The experiments were conducted with a crossflow velocity of 21.4 cm/s, a constant temperature of 20 °C, and an ambient (unadjusted) solution pH of 5.7. The osmotic pressures of the 1, 2, 3, and 4 M NaCl draw solutions are 47.3, 105.3, 172.3, and 246.2 bar, respectively. The draw solution osmotic pressure was calculated using a software package from OLI Systems, Inc. (Morris Plains, NJ).

FIGURE 3. A comparison of experimental results and model predictions for the reverse draw solute flux. The measured solute fluxes are those presented in Figure 2, and the predicted solute fluxes are calculated using eq 10, using the corresponding water fluxes, Jw, presented in Figure 2. Values for the transport parameters in eq 10 were as follows: A ) 0.44 L m-2 h-1 bar-1, B ) 0.265 L m-2 h-1, S ) 481 µm, and DNaCl ) 1.61 × 10-9 m2/s. The solid line (slope ) 1) represents perfect agreement between experimental data and predictions. concentration. This is consistent with prior experimental (14, 15, 29) and modeling efforts (12, 14, 22) that have investigated the relationship between measured water flux and draw solution concentration. The reverse flux of draw solute has only recently been explored through experiments (21). However, this phenomenon has not yet been modeled, which motivated our efforts to develop the model described above. The values of the predicted and measured NaCl fluxes are compared on a linear-linear plot in Figure 3. The agreement between the model and experiments is strong, as demonstrated by the experimental data, located near the solid line (slope ) 1), that represents perfect agreement between experimental data and model predictions. The predicted values in Figure 3 were calculated using the B and S values determined in the preceding sections and the experimentally measured water fluxes. The experimental water fluxes were VOL. 44, NO. 13, 2010 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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FIGURE 4. Experimental salt flux as a function of the draw solute concentration at the interface between the support and active layers of the membrane. The experimental conditions for measuring the solute flux are presented in Figure 2. The draw solute concentration at the active layer surface was calculated using eq 18, using the experimental water fluxes from Figure 2, a value of A ) 0.44 L m-2 h-1 bar-1, and T ) 293 K. used instead of attempting to predict Jw a priori because of the nonideal behavior observed at higher draw solution concentration. Future, more complex models can account for the nonideal behavior at higher concentrations, but here we continue using the experimental value because of the physical insights our model can provide. Reverse Draw Solute Flux as a Function of Interfacial Concentration. It is interesting to explore what form NaCl takes when permeating the active layer of the asymmetric HTI-CTA membrane. To do this, we compare how the measured reverse salt flux varies with the NaCl concentration at the surface of the active layer, ciS. The osmotic pressure difference across the active layer can be calculated using the experimental water flux and the water permeability coefficient. Because the feed is DI, the osmotic pressure difference is equal to the draw side osmotic pressure at the support layer-active layer interface. We use the van’t Hoff equation to calculate the NaCl concentration at the active layer surface πDi )

Jw ) nRgTciS A

(18)

where πDi is the osmotic pressure of the draw solution at the active layer surface, n is the number of dissolved species created by the draw solute (2 for NaCl), Rg is the ideal gas constant, and T is the absolute temperature. The measured NaCl flux is plotted versus the concentration calculated from eq 18 in Figure 4. When these data are fit using linear regression, the slope equals 0.251 L m-2 h-1 (6.97 × 10-8 m s-1)sa value close to the salt permeability coefficient determined from RO and PRO experiments (0.265 L m-2 h-1 or 7.36 × 10-8 m s-1). The fact that this inferred B value is consistent with that measured in PRO mode indicates that there is no significant change in membrane structure when it is exposed to high NaCl concentrations. Therefore, the nonlinear dependence of flux on osmotic pressure observed in FO mode is primarily a result of internal concentration polarization, not osmotic deswelling (32). The linear relationship between the NaCl flux and the NaCl concentration at the surface of the active layer, cSi , further indicates that individual ions, not ion pairs, are permeating the active layer. If the ions were to form ion pairs before diffusing across the active layer, the flux would depend on the NaCl concentration squared (33). It is intriguing that even though the ions permeate the active layer as two separate entities, the process can be described by the single transport coefficient B. Prior experimental work examined this aspect 5174

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of salt transport by quantifying the flux of individual ions (21). For NaCl, it was found that the flux of Na+ and Cl- ions were nearly equimolar, which explains why a single transport coefficient can be used to describe the flux of NaCl. In order to maintain electroneutrality, the ion that permeates the active layer more quickly drags a counterion across the membrane. Implications for FO Membrane Design and System Performance. The model developed in this work can help in selecting a membrane that minimizes the loss of draw solute into the feed solution, thereby reducing operating costs. A previous publication has defined the ratio of the reverse solute flux to the forward water flux as the specific reverse salt flux (21). Because the ratio has units of concentration rather than flux, we suggest that a more appropriate quantity is the inverse of this ratiosa value analogous to the membrane selectivity (3). This ratio of the water flux to the reverse solute flux, which we term the reverse flux selectivity, can be regarded as the volume of water produced per the moles (or mass) of draw solute lost. An expression for the reverse flux selectivity is developed using our model. First, the water flux is expressed as a function of the osmotic pressure of the bulk draw solution, πDb. The nonlinear relationship between water flux and the bulk osmotic pressure, a result of internal concentration polarization, is given for a DI feed by (14)

( )

Jw ) AπDb exp -

( )

JwS JwS ) AnRgTcD exp D D

(19)

where the bulk osmotic pressure has been written using the van’t Hoff equation. Next, the reverse flux selectivity is calculated by taking the ratio of eq 19 to eq 10 to give

[ ( ) (

AnRgT JwS Jw Jw ) exp - 1+ Js Jw D B

)]

(20)

While valid, eq 20 is not immediately useful because it does not explicitly express the ratio Jw/Js. Examining the term in brackets allows the equation to be significantly simplified. The water flux can range from 0 to infinity; however, the term, exp(-JwS/D) - 1, will always fall between 0 and -1, respectively. Therefore, the -Jw/B term dominates, and the absolute value of the reverse flux selectivity reduces to Jw A ≈ nR T Js B g

(21)

This is an insightful result. It states that the reverse flux selectivity is independent of the support layer structural parameter S as well as the bulk draw solution concentration. The second implication of eq 21 can be tested experimentally. This is done in Figure 5, which plots the reverse flux selectivity versus the bulk NaCl concentration. As predicted, the experimental data do not vary with concentrationsan observation consistent with another recent study (21). Furthermore, as shown by the solid line in Figure 5, eq 21 accurately predicts the reverse flux selectivity using only the measured values of A and B. The reverse flux selectivity is determined solely by the selectivity of the active layer A/B and the ability of the draw solute to generate an osmotic pressure, nRgT. That the reverse flux selectivity is independent of the membrane structural parameter is consistent with our physical understanding of the system. A high concentration of draw solute at the support layer - active layer interface is necessary to generate a large osmotic gradient, which drives a high water flux. However, this higher concentration of draw solute also increases the concentration gradient across the active layer, which increases the reverse salt flux. For an ideal solution, the osmotic

DS

FIGURE 5. Reverse flux selectivity as a function of draw solute concentration. The experimental values were determined using the measured water fluxes and reverse solute fluxes depicted in Figure 2. The theoretical prediction was calculated using eq 21, with A ) 0.44 L m-2 h-1 bar-1, B ) 0.265 L m-2 h-1, n ) 2, T ) 293 K, and Rg ) 8.3145 × 10-2 L bar K-1 mol-1. gradient is proportional to the concentration gradient, and, therefore, the ratio of the two quantities remains constant (34). The analysis above highlights the need to select a membrane with a highly selective active layer (i.e., high A and low B) and a draw solute capable of generating a large osmotic pressure, but it does not diminish the importance of reducing the structural parameter S of forward osmosis membranes. An FO process needs to achieve high water fluxes at low draw solution concentrations to minimize the energy required to separate fresh water from the diluted draw solution and reconcentrate/recycle the draw solution. Reducing this energy can only be realized by having FO membranes with small S so that the effects of ICP are minimized. Effectively operating an osmotically driven membrane process requires selecting a membrane and draw solute pair to maximize the forward water flux, minimize the reverse draw solute flux, and achieve an efficient and effective separation of the product water from the draw solution among other considerations. The model developed in this work provides a simple basis (eq 21) for selecting a membrane and draw solute system that maximizes the water flux while minimizing the loss of draw solute. In the future, this criterion can be used in concert with other design heuristics to help optimize a forward osmosis process.

NOMENCLATURE A Am B c cD cF ciA ciS D DA

water permeability coefficient membrane area draw solute permeability coefficient molar concentration of draw solute molar concentration of draw solute in the bulk draw solution molar concentration of draw solute in the bulk feed solution molar concentration of draw solute on the active layer side of the interface between the support layer and active layer molar concentration of draw solute on the support layer side of the interface between the support layer and active layer bulk diffusion coefficient of draw solute in water diffusion coefficient of draw solute in active layer

H Js Jw n R Rg S t T tA tS VF z ε π τ

effective diffusion coefficient of the draw solute in support layer solute partition coefficient total draw solute flux water flux number of dissolved species created by draw solute solute rejection ideal gas constant membrane structural parameter time absolute temperature thickness of active layer thickness of support layer feed solution volume coordinate system porosity of support layer osmotic pressure tortuosity of support layer

Acknowledgments The work was supported by the WaterCAMPWS, a Science and Technology Center of Advanced Materials for the Purification of Water with Systems under the National Science Foundation Grant CTS-0120978; and Oasys Water Inc.

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