Coupled reverse draw solute permeation and water flux in forward osmosis with neutral draw solutes

Journal of Membrane Science 392–393 (2012) 9–17

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Coupled reverse draw solute permeation and water flux in forward osmosis with neutral draw solutes Jui Shan Yong a , William A. Phillip b,∗ , Menachem Elimelech a a b

Department of Chemical and Environmental Engineering, P.O. Box 208286, Yale University, New Haven, CT 06520-8286, USA Department of Chemical and Biomolecular Engineering, 182 Fitzpatrick Hall, University of Notre Dame, Notre Dame, IN 46556-5637, USA

a r t i c l e

i n f o

Article history: Received 5 October 2011 Received in revised form 5 November 2011 Accepted 9 November 2011 Available online 8 December 2011 Keywords: Forward osmosis Reverse draw solute permeation Reflection coefficient Reverse flux selectivity Coupled diffusion

a b s t r a c t Understanding the simultaneous forward water flux and reverse draw solute flux in osmotically driven membrane processes is essential to the development of these emerging technologies. In this work, we investigate the reverse fluxes of three neutral draw solutes-urea, ethylene glycol, and glucose-across an asymmetric forward osmosis membrane. Our experiments reveal that for the rapidly permeating draw solutes (urea and ethylene glycol), an additional resistance to mass transfer develops due to external concentration polarization on the feed side of the membrane. A model to predict the reverse flux for these highly permeable solutes is derived and then validated using independently determined transport parameters. The experimentally measured water fluxes generated by these solutes are consistently lower than those predicted by theories for calculating the water flux in osmotically driven membrane processeseven when the effects of external concentration polarization are taken into account. These results are indicative of a coupling between the forward water flux and reverse solute flux, and a reflection coefficient is introduced to account for the solute–solvent coupling. Interestingly, our experiments demonstrate that solute–solvent coupling does not significantly impact the reverse flux of draw solute. The effect of this solute–solvent coupling on the reverse flux selectivity (i.e., the ratio of the forward water flux to the reverse solute flux) is demonstrated. © 2011 Elsevier B.V. All rights reserved.

1. Introduction Osmotically driven membrane processes (ODMP), including forward osmosis (FO) and pressure retarded osmosis (PRO), have gained renewed interest in recent years because of their potential applications in separation processes as well as power generation [1,2]. The viability of these technologies has been demonstrated in a variety of applications including desalination [3–6], wastewater reclamation [7,8], industrial wastewater treatment [9], brine concentration [10], osmotic membrane bioreactors [11], biofuels production [12], liquid food processing [13], protein concentration [14], and power generation from salinity gradients [15–17]. To date, much of the research on osmotically driven membrane processes has focused on the phenomenon of internal concentration polarization (ICP) [17–21] and the fabrication of membranes which reduce the deleterious effects of ICP [20–22]. One area of research that received significantly less attention is the systematic

Abbreviations: ECP, external concentration polarization; FO, forward osmosis; ICP, internal concentration polarization; ODMP, osmotically driven membrane process; PRO, pressure retarded osmosis; RO, reverse osmosis. ∗ Corresponding author. Tel.: +1 574 631 2708. E-mail address: [email protected] (W.A. Phillip). 0376-7388/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.memsci.2011.11.020

understanding of the reverse permeation of draw solutes from the draw solution into the feed [23–26]. Reverse permeation of draw solutes in osmotically driven membrane processes is a direct result of the solute concentration difference across the membrane, which is necessary to generate the driving force for water permeation. This reverse flux of solute reduces the effective osmotic pressure difference across the membrane, and thus the efficiency of both the FO and PRO systems. Recent research efforts have attempted to address this problem by developing draw solutions comprising hydrophilic nanoparticles, which cannot cross the membrane active layer [27–29]. However, nanoparticle-based draw solutions have not been shown to generate sufficiently high osmotic pressures for applications involving seawater desalination, and efficient separation and recycling methods for such draw solutions need to be developed. In a previous paper, we developed a model to predict the reverse flux of a strong electrolyte (sodium chloride) draw solution, and identified the reverse flux selectivity (i.e., the ratio of the forward water flux to the reverse solute flux) as an important design parameter for osmotically driven membrane processes [25]. Furthermore, the reverse flux selectivity was shown to be related solely to the membrane active layer transport properties, namely the solute and solvent (water) permeability coefficients. Other studies have focused on the bidirectional permeation of feed and draw solutes

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J.S. Yong et al. / Journal of Membrane Science 392–393 (2012) 9–17

in FO operations [23,24]. Experimental work with a variety of dissolved solutes demonstrated that solutes diffuse at different rates based primarily on ion solvation and hydrodynamic size [23,26], while other modeling efforts focused on predicting the rejection of boron by FO [24]. An area of reverse solute permeation that remains to be explored is the potential coupling between solvent (water) and solute fluxes within the membrane active layer. Recent experimental results demonstrated the need to use a reflection coefficient to accurately predict the water flux generated by an NaCl draw solution when using leaky membranes [30], thus suggesting that frictional coupling between the solute and solvent (water) molecules is occurring as the two species diffuse across the active layer. This coupling reduces the attainable water flux, which further decreases the efficiency of FO and PRO operations. Neutral draw solutes, which are not rejected as effectively as strong electrolytes by an FO membrane, provide a means for studying the potential coupling of solute and solvent (water) fluxes in osmotically driven membrane processes. Understanding the coupling between solute and solvent fluxes in ODMPs is critical to the development of these processes, because coupling of fluxes will have a negative impact on the achievable water flux and solute rejection for a variety of proposed FO operations. A better understanding of these effects will allow for the development of systems that compensate for the deleterious impacts of reverse solute permeation. Additionally, the fundamental knowledge gained from these studies can be used to guide the development of membranes for PRO processes, where more permeable membranes may have advantages over more selective membranes [31]. In this paper, we examine the rapid reverse permeation of neutral draw solutes across an FO membrane through a combination of experiments and modeling. We also study the effect of using a draw solute that is rapidly transported across the membrane active layer on the predicted water flux, thus exploring the impact of coupled solute and water fluxes. The implications of these results for the design of FO and PRO systems are discussed. 2. Theory A schematic of an asymmetric membrane operating in FO mode is shown in Fig. 1. To leak into the feed solution, a draw solute first diffuses through the support layer in the opposite direction of the convective flow of solvent (water). At the interface between the support layer and the active layer, the solute partitions into the active layer before diffusing across it. The rapid transport of highly permeable solutes across the active layer results in a boundary layer forming adjacent to the membrane active layer on the feed solution side. Beyond the boundary layer, in the bulk feed solution, there is negligible concentration of the draw solute. By considering the mass transfer through the support layer and the active layer in series, as described in our earlier publication [25], followed by mass transfer through the feed side boundary layer, the transport of highly permeable draw solutes can be described. 2.1. Draw solute flux in the support layer Assuming operation at steady-state, a mass balance can be written on a differential volume in the support layer and solved using boundary conditions described in our earlier publication [25] to yield JsS =



Jw exp(Pes ) − 1



m (exp(Pes )cD − cD )

(1)

where Pes = Jw

ts  S = Jw εD D

(2)

Fig. 1. A schematic of a highly permeable draw solute leaking into the feed solution in an FO mode operation. The high concentration of the solute in the draw solution, cD , creates a chemical potential gradient which drives both the water flux, Jw , and the reverse flux of the solute, Js . For the draw solute to permeate across the asymmetric membrane into the bulk feed solution where its concentration, cF , is negligible, it first must be transported across the support layer of thickness, ts , followed by the active layer of thickness, tA , and finally through an external boundary layer of thickness, ı. cDm and cFm represent the draw solute concentration in solution at the active-layer-solution-interface on the support layer side and the boundary layer side, respectively. For a system operating in PRO mode, the membrane orientation would be switched, so that the support layer is in contact with the feed solution and the external boundary layer would form on the draw solution side of the membrane.

Here JsS is the total flux of draw solute across the support layer, Jw m is the draw solute concentration is the superficial fluid velocity, cD at the interface of the active and support layer of the membrane, cD is the bulk draw solute concentration, and Pes is the Peclet number in the support layer. In Eq. (2), D is the binary diffusion coefficient for the solute and water and ts , ε, and  are the thickness, porosity, and tortuosity of the support layer, respectively. The thickness, porosity, and tortuosity, which are independent of the draw solute used, can be combined to define S, the membrane structural parameter (S = ts /ε). The structural parameter characterizes the effective distance a solute molecule must travel through the support layer when going from the bulk draw solution to the active layer.

2.2. Draw solute flux in the active layer By assuming that only a diffusive flux contributes to total flux in the active layer, the following equation for the solute flux is obtained: JsA = −

DA H m m (cD − cFm ) = −B(cD − cFm ) tA

(3)

Here, JsA is the total flux of draw solute across the active layer, DA is the draw solute diffusion coefficient in the active layer, H is the partition coefficient describing the relative solute concentration in active layer and solution phases, tA is the active layer thickness, cFm is the draw solute concentration at the interface of the active layer of the membrane with the boundary layer in the feed, and B is the draw solute membrane permeability coefficient of the active layer.

J.S. Yong et al. / Journal of Membrane Science 392–393 (2012) 9–17

2.3. Draw solute flux across the feed-side boundary layer Next, a third mass balance is carried out on the feed side boundary layer that results from the rapid permeation of the draw solute. Assuming steady-state and taking into account both the diffusive and convective flux, a mass balance can be written on a differential volume: dJsı d2 c dc = −D 2 + Jw =0 dz dz dz

(4)

where JSı is the total flux of draw solute across the boundary layer. Integrating Eq. (4) with the following boundary conditions: z = −ı c = cF = 0 z=0 c=

(5a)

cFm



Jw exp(Peı ) − 1



(exp(Peı )cF − cFm )

(6)

where Peı =

Jw k

(7)

Here Peı is the Peclet number of the boundary layer and k is the feed side mass transfer coefficient, which can be estimated from a correlation for the rectangular cell geometry and given operating conditions [32]. In our previous work with less permeable solutes, cFm could reasonably be approximated as being equal to zero. Here, however, because of the rapid solute permeation it must be included as a finite, non-zero value. This is important for accurately predicting the reverse flux of highly permeable draw solutes, and is critical for accurately determining the reflection coefficient of these solutes (vide infra). 2.4. Expression for the reverse draw solute flux The solute flux across the three layers is equal because no solute is accumulating or reacting at the support layer-active layer interface (z = 0) or at the boundary layer-active layer interface (z = −tA ): JsA = JsS = Jsı

(8)

This relationship allows us to use Eqs. (1), (3) and (6) and solve m and c m . Substitution of the expresfor the unknown variables cD F m and c m into any one of the three expressions for reverse sions for cD F solute flux (i.e., Eqs. (1), (3), or (6)) and rearranging yields: Js =

3.1.1. Urea Urea (Fischer Scientific) was used as a draw solute to study the reverse permeation behavior of neutral solutes because, based on RO experiments, its reverse permeation is expected to be rapid [33]. The binary diffusion coefficient for urea and water was assumed constant at a value of 1.38 × 10−9 m2 /s [34]. Draw solutions with concentrations ranging from 1 to 4 M were used for the reverse permeation experiments. The concentration of urea in the feed solution was determined by a spectrophotometric method, which is based on the yellow-green color produced when p-dimethylaminobenzaldehyde is added to urea in a dilute hydrochloric acid solution [35]. The UV absorbance at 420 nm of the resulting solution is directly proportional to urea concentration [35].

(5b)

where ı is the thickness of the feed side boundary layer and cF is the concentration of the draw solute in bulk feed solution, yields: Jsı =

11

Jw B(cF exp(Pes + Peı ) − cD ) (B exp(Peı ) + Jw ) exp(Pes ) − B

(9)

Eq. (9) expresses the reverse flux of solute in terms of experimentally accessible quantities. 3. Materials and methods 3.1. Model neutral draw solutes and their analytical quantification Analytical grade urea, glucose, and ethylene glycol were used as model neutral draw solutes. Deionized (DI) water, obtained from a Milli-Q ultrapure water purification system (Millipore, Billerica, MA), was used to prepare the draw solutions. The osmotic pressures of the various draw solutions were calculated using a software package from OLI Systems, Inc. (Morris Plains, NJ). The characteristics of the draw solutes in solution and their analytical quantification methods are described in the following subsections.

3.1.2. Glucose Glucose (J.T. Baker) was selected as a neutral draw solute whose reverse permeation is not expected to be rapid due to its relatively high molecular weight of 180 g/mol [36]. Glucose was dissolved in DI water at concentrations of 0.5 and 1 M. The concentration of glucose was kept low due to the relatively high viscosity of more concentrated solutions. The binary diffusion coefficient for glucose and water was assumed constant at a value of 6.7 × 10−10 m2 /s [34]. The glucose concentration was determined by measuring the total organic carbon (TOC) with a total carbon analyzer (Shimazdu). 3.1.3. Ethylene glycol For reverse permeation experiments, concentrated ethylene glycol (J.T. Baker) was dissolved in DI water at concentrations ranging from 1 to 3 M. Results based on RO experiments suggest that the rate of ethylene glycol permeation will be between the rate of urea and glucose permeation [37]. The binary diffusion coefficient for ethylene glycol and water was assumed constant at a value of 9 × 10−10 m2 /s [38]. Ethylene glycol concentration in the feed was determined by measuring the total organic carbon (TOC) with a total carbon analyzer (Shimazdu). 3.2. Forward osmosis membrane A commercial asymmetric cellulose triacetate (CTA) membrane (Hydration Technology Inc., Albany, OR) was used for the reverse permeation experiments. This proprietary membrane, which has been used extensively in prior research exploring osmotically driven membrane processes [18,19,39], consists of a dense asymmetric polymer layer embedded within a woven fabric mesh. 3.3. Experimental setup 3.3.1. Forward osmosis crossflow unit The experimental cross flow system employed is similar to that described in our previous studies. 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 [18,19,39]. No mesh feed spacers were used and the feed and draw solutions were pumped co-currently 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. 3.3.2. Diaphragm cell test unit A diaphragm cell test unit was used to determine the solute permeability coefficient, B. The cell involved a slight modification to the experimental crossflow system described above. In this testing unit, the draw solution volume was kept constant at 2.25 L. The original draw solution vessel was modified to have a watertight cover and flow connections to prevent the permeation of water. In

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J.S. Yong et al. / Journal of Membrane Science 392–393 (2012) 9–17

this configuration, only solute flux from the draw to the feed could occur. All other aspects of the set up and testing conditions were unchanged.

membrane structural parameter S was previously determined in FO mode operation using a 1 M NaCl draw solution and DI water feed. The S parameter used in our calculations is 481 ␮m [25].

3.4. Measurement of water flux and reverse solute flux

3.5.2. Membrane solute permeability of neutral draw solutes The active layer solute permeability coefficients, B, for the three draw solutes were determined from diaphragm cell experiments [34]. A draw concentration of 0.5 M was used with a DI water feed for these experiments. Monitoring the concentration of dissolved solute in the feed as a function of time and taking the draw solution concentration to be constant allows B to be calculated from [34]:

The water flux, Jw , across the membrane was determined by measuring the change in mass of the draw solution reservoir, which rested on a balance (Ohaus, Pine Brook, NJ), as a function of time. Details are given in our previous publications [25,39]. We note that this experimental method measures the mass flux (or volume flux when assuming constant solution density) across the membrane, which is not exactly equal to the water flux. However, when using draw solutes that are highly rejected (e.g., NaCl), the difference between the water flux and mass flux is insignificant. Even when highly permeable draw solutes are used the difference between the water flux and mass flux is found to be less than 6%. The reverse solute flux, Js , of the various draw solutes was determined using the protocol described in our previous study [25]. The CTA membrane was placed in the custom built crossflow cell. By switching the orientation of the membrane, both FO and PRO mode tests were run, depending on the purpose of the experiments. FO mode experiments were carried out to test the model for rapid reverse solute permeation, while PRO mode experiments were run to measure the solute permeability coefficient, B. Once the water flux stabilized after 20–30 min, the system was assumed to be at steady-state. The concentration in the feed was monitored by withdrawing samples from the feed at 20-min time intervals. Two milliliters were withdrawn for urea concentration testing and 7 mL for ethylene glycol and glucose. The data collected was used to calculate the experimental reverse draw solute flux. Because the initial draw solute concentration in the feed is zero, a species mass balance yields: cF (VF0 − Jw Am t) = Js Am t

(10)

where cF is the draw solute 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. The experimental draw solute flux, Js , can be calculated from the slope of a plot of the number of moles of solute in the feed per unit membrane area vs. time. 3.5. Determination of membrane transport properties 3.5.1. Pure water permeability and membrane structural parameter The pure water permeability coefficient, A, of the CTA membranes had been previously determined in our earlier study using a laboratory-scale crossflow reverse osmosis (RO) test unit [25]. For our calculations, we used an average value of 0.44 ± 0.12 L m−2 h−1 bar−1 (1.23 ± 0.33 × 10−12 m s−1 Pa−1 ). The



1 ln B= Am t((1/Vdraw ) + (1/Vfeed ))

0 0 cdraw − cfeed



(11)

t t cdraw − cfeed

0 0 where cdraw and cfeed are the concentrations of the solute in the t t and cfeed draw and feed at t = 0, cdraw are the concentrations of the solute in the draw and feed at time t, Am is the membrane area, and Vdraw and Vfeed are the volume of the draw and the feed of the diaphragm cell, respectively. The CTA membrane was tested in both orientations, with the active layer facing the draw (PRO mode) and the active layer facing the feed (FO mode). Once the diaphragm cell experiment was started, samples from the feed were withdrawn at 10-min intervals, and the concentration of solute in the feed was determined. The draw solution was placed on a balance (Ohaus, Pine Brook, NJ) and monitored every 10 min to ensure no water permeation occurred from the feed into the draw. The assumption that the draw solute concentration is constant was checked by measuring the draw solute concentration at the beginning and end of each experiment, which lasted for 100 min. The active layer solute permeability coefficients, B, were also determined from PRO mode experiments using DI water as the feed solution. Draw solution concentrations of 0.5 and 1 M were used to determine B for all the draw solutes. For each experiment, the solute permeability coefficient, B, is calculated by dividing the measured solute flux, Js , by the difference in draw solute concentration across the membrane active layer:

B=

m (cD

JsA Js Jw exp(Pes ) = m − cF ) Js (1 − exp(Peı + Pes )) + Jw cD

(12)

Eq. (12) is obtained by rearranging an equation analogous to Eq. (9) for the PRO mode orientation. The derivation exactly follows the derivation of Eq. (9) except that ICP now occurs on the feed side of the active layer and ECP occurs on the draw side. We further note that in Eq. (12), the draw solute concentration on both sides of the active layer needs to be considered because of the rapid permeation of some neutral draw solutes and the subsequent development of ICP on the feed side. In our previous publication using NaCl as a

Table 1 Membrane solute permeability coefficients, B, solute-water binary diffusion coefficients, D, feed side mass transfer coefficients, k, and reflection coefficients, , for urea, ethylene glycol, glucose, and sodium chloride. The B values were determined from both the diaphragm cell and PRO mode experiments, using Eqs. (11) and (12), respectively. Draw solution concentrations of 0.5 M were used for both types of experiments. The diffusion coefficients were compiled from various sources [34,38]. The mass transfer coefficients were calculated using a correlation developed for the specific flow cell geometry used in this study [32]. Reflection coefficients, , were calculated from Eq. (13) using the experimental FO data. To convert from units of L m−2 h−1 to m s−1 , multiply by 2.78 × 10−7 . Solute

Molecular weight (g/mol)

Urea Ethylene glycol Glucose NaCl

60.06 62.07 180.00 58.84

Solute permeability coefficient, B (L m−2 h−1 ) PRO mode

Diaphragm cell

6.650 2.852 0.022 0.240

6.356 2.768 0.026 0.217

Solute–water diffusion coefficient, D (m2 /s)

Feed side mass transfer coefficient, k (L m−2 h−1 )

Reflection coefficient, 

1.37 × 10−9 9.00 × 10−10 6.70 × 10−10 1.61 × 10−9

58.4 42.0 34.5 62.0

0.67 0.69 0.93 1.06

J.S. Yong et al. / Journal of Membrane Science 392–393 (2012) 9–17

10

(b)

Urea Ethylene Glycol Glucose NaCl

8 6

Water Flux (L m-2h-1)

-2 -1

Solute Flux (mol m h )

(a)

4 2

13

Urea Ethylene Glycol Glucose NaCl

20 15 10 5

0 0

1

2

3

4

0

0

1

Draw Concentration (M)

2

3

4

Draw Concentration (M)

4. Results and discussion 4.1. Solute permeability coefficients of neutral draw solutes Solute permeability coefficients for the various draw solutes across the CTA FO membrane were determined using diaphragm cell experiments, where Jw = 0, and PRO mode tests, where Jw = / 0. The measured values (Table 1) demonstrate that the B values are comparable for both methods, which indicates that the presence of a water flux does not impact the solute flux across the active layer of the membrane. We obtained average B values of 6.50, 2.80, and 0.024 L m−2 h−1 for urea, ethylene glycol, and glucose, respectively, which are used later in our calculations. In addition to solute permeability coefficients, Table 1 presents the solute reflection coefficients that will be discussed later in the paper. We also include the solute permeability (0.23 L m−2 h−1 ) and reflection coefficients for sodium chloride, a well characterized strong electrolyte used in our previous study [25], for comparison. The solute permeability coefficients of urea and ethylene glycol are higher than that of sodium chloride. The solute permeability of urea might be higher than that of ethylene glycol due to its compact tetrahedral shape. Conversely, glucose, which is larger, has a smaller permeability [33]. 4.2. Reverse draw solute flux and water flux as a function of draw concentration FO mode experiments were carried out using draw solutions with solute concentrations ranging from 0.5 to 4 M. The measured solute and water fluxes from these experiments are presented in Fig. 2a and b, respectively. For all solutes used, as the draw solute concentration increases, the reverse draw solute flux and water flux increase. Consistent with the trend observed in the solute permeability coefficients, urea permeation was the most rapid, followed by ethylene glycol, while glucose leaked most slowly into the feed solution. Water fluxes obtained using a sodium chloride draw solution are higher than the water fluxes obtained when using the neutral solute draw solutions at similar molar concentrations (Fig. 2b). This is primarily the result of the sodium chloride solutions generating a higher osmotic driving force. Sodium chloride dissociates to form two ions when dissolved in solution, whereas the neutral draw solutes do not. For example, the measured water fluxes for the glucose system are about one half the water fluxes measured for the sodium chloride system, which reflects the difference in osmotic

-1

100

Urea Ethylene Glycol Glucose NaCl

-2

draw solute and DI water as a feed [25], ICP was negligible in PRO mode and cFm was set to zero.

Predicted Solute Flux (mol m h )

Fig. 2. (a) Experimental reverse draw solute fluxes for urea, ethylene glycol, glucose, and sodium chloride as a function of draw concentration. (b) Experimental water fluxes generated when using urea, ethylene glycol, glucose, and sodium chloride as draw solutes. The reverse draw solute fluxes and water fluxes were measured from experiments using DI water as a feed solution and draw solutions of varying concentrations.

10 1 0.1 0.01 0.01

0.1

1

10

100 -2

-1

Experimental Solute Flux (mol m h ) Fig. 3. A comparison of model predictions and experimental results for the reverse draw solute flux of urea, ethylene glycol, glucose, and sodium chloride. The predicted solute fluxes are calculated from Eq. (9), using the corresponding water fluxes presented in Fig. 2b and the membrane permeability coefficients from Table 1. The experimental draw solute fluxes are those presented in Fig. 2a. The solid line (slope = 1) represents prefect agreement between model predictions and experimental data.

pressure between the two solutions. The measured water fluxes for the urea and ethylene glycol systems are even lower. Possible causes for this further reduction in water flux, namely coupled diffusion effects and the feed side boundary layer, are discussed later in Section 4.4. 4.3. Comparison of experimental solute fluxes to model predictions The measured ethylene glycol, urea, glucose, and NaCl fluxes are compared to the solute fluxes predicted by the model in Fig. 3. The solute flux data lie near the solid line (slope = 1), which represents perfect agreement between the predicted and experimental values, thereby demonstrating very good agreement between the model predictions and experiments over three orders of magnitude of solute flux. The average B values presented in Table 1 and the experimentally measured water fluxes shown in Fig. 2b were used in Eq. (9) to predict the draw solute fluxes in Fig. 3. We found that it is necessary to include the additional feed side boundary layer in the model derivation to accurately predict the flux of rapidly permeating draw solutes (ethylene glycol and urea). This boundary layer increases the draw solute concentration on the feed side of the active layer (i.e., cFm = / 0) and decreases the driving force for m − c m ). If the additional resistance reverse solute permeation (i.e., cD F

14

J.S. Yong et al. / Journal of Membrane Science 392–393 (2012) 9–17

-2 -1

Water Flux, Jw (Lm h )

25

we determined  experimentally by taking the ratio of the experimental water flux to the predicted water flux:

Urea Ethylene Glycol Glucose NaCl

20

=

15

10

5

0

0

1

2

3

4

5

Draw Concentration (M) Fig. 4. Comparison of the experimental and predicted water fluxes for urea, ethylene glycol, glucose, and sodium chloride draw solutions. Experimental water fluxes as a function of draw solution concentration are plotted as discrete points. Predicted water fluxes from an existing theory that incorporates external concentration polarization (ECP), but not coupled diffusion effects are shown as dashed lines. Water flux calculations that incorporate coupled diffusion effects through the use of the reflection coefficients reported in Table 1 along with ECP are represented by solid lines.

to mass transfer of this layer was excluded, the solute fluxes were over predicted.

4.4. Comparison of experimental water fluxes to model predictions Given the need to include the feed side boundary layer to accurately predict the reverse flux of rapidly permeating draw solutes, we compared the experimental water fluxes generated by these solutes to an existing model for predicting water flux in ODMPs [17]. The experimental water fluxes as a function of the draw solution concentration are presented in Fig. 4. These data are compared to two predictions. The first prediction accounts for ECP but not interactions between solute and solvent molecules as they permeate across the membrane active layer (i.e., coupled diffusion effects), and is plotted as a dashed line. The second prediction, which is plotted as a solid line, includes the effects of ECP and uses a reflection coefficient to quantify any coupled diffusion effects. For draw solutes that are well-rejected by the CTA membrane, i.e., glucose and NaCl, good agreement is observed between the experimental water flux data and the predictions that account for ECP, but not coupled diffusion effects (dashed lines). In these cases, any frictional coupling between the solvent and solute fluxes is negligible. On the other hand, the experimental data for urea and ethylene glycol are consistently lower than the predicted fluxes represented by the dashed lines, which have accounted for the / 0, sugincreased osmotic pressure on the feed side because cFm = gesting a coupling of the solute and solvent fluxes within the membrane active layer. One common way to account for this coupling is to incorporate a reflection coefficient in the water flux calculations [40,41]. The reflection coefficient, , is a parameter that characterizes the ability of a membrane active layer to preferentially allow solvent permeation over solute permeation [42]. For example, a perfectly selective membrane that does not allow for solute permeation but allows for solvent to pass freely would have a reflection coefficient of 1. On the other hand, a non-selective membrane that transports solute and solvent at equal rates would have  = 0. Because there is not a reliable method to predict the reflection coefficient a priori,

Jw,exp Jw,exp = m − m ) Jw,pred A(D F

(13)

m and  m are the draw solution and feed solution osmotic where D F pressures adjacent to the active layer, respectively [17]. The difference between these osmotic pressures can be calculated by assuming that the osmotic pressure is proportional to the solute concentration (i.e., by using the van’t Hoff equation with the values m and c m ). for cD F The reflection coefficients for the various draw solutes, determined from Eq. (13), are listed in Table 1. As expected,  values for NaCl and glucose are ∼1, consistent with their low solute permeability coefficients. The reflection coefficients for urea and ethylene glycol were lower than 1, and equal to 0.67 and 0.69, respectively. Using these values for , the predicted water fluxes (solid lines) for urea and ethylene glycol show better agreement with the experimental data.

4.5. Reverse flux selectivity as a function of draw concentration for neutral draw solutes The reverse flux selectivity, defined in our previous publication [25] as the ratio of the forward water flux to the reverse solute flux, can be regarded as the volume of water produced per the moles (or mass) of draw solute lost. Additionally, our work demonstrated the reverse flux selectivity is independent of the support layer structural parameter S as well as the bulk draw solution concentration [25]. A similar result is derived here, but we note that when predicting the reverse flux selectivity for highly permeable draw solutes, the reflection coefficient, , has to be incorporated to account for the coupling between solute and solvent. Incorporating this additional term yields the following expression for the reverse flux selectivity: AnRg T Jw = Js B

(14)

where n is the number of dissolved species created by the draw solute (n is 2 for NaCl and 1 for the neutral draw solutes), Rg is the ideal gas constant, and T is the absolute temperature. Using the reflection coefficients, , and solute permeability coefficients, B, for the three neutral solutes reported in Table 1, along with A = 0.44 L m−2 h−1 bar−1 , n = 1, Rg = 8.3145 × 10−2 bar L mol−1 K−1 , and T = 293 K, the theoretical reverse flux selectivities for the neutral draw solutes were calculated. These predictions are plotted in Fig. 5 as solid horizontal lines and the discrete points represent the experimental data. The good agreement between the predicted and experimental values demonstrates that the reverse flux selectivities for highly permeable draw solutes vary little with the draw solute concentration. That the reverse flux selectivity does not vary dramatically with solute concentration suggests that that the coupled diffusion effects we report are not strongly influenced by membrane plasticization [43]. 4.6. On the coupled transport of solute and solvent in osmotically driven membrane processes Based on the difference between the measured and predicted water fluxes, a reflection coefficient, , was needed to accurately predict the water flux generated by highly permeable draw solutes. However, a similar factor was not needed to calculate the reverse flux of these same draw solutes. This is an interesting result because the theoretical development that incorporates the reflection

(a) 1.5 1.0 0.5 0.0 0

1

2

3

4

Urea Draw Conc. (M)

5

(b) 3 2 1 0 0

1

2

3

4

Reverse Flux Selectivity (L/mol)

2.0

Reverse Flux Selectivity (L/mol)

Reverse Flux Selectivity (L/mol)

J.S. Yong et al. / Journal of Membrane Science 392–393 (2012) 9–17

15

(c) 600 400 200 0 0.0

Ethylene Glycol Draw Conc. (M)

0.5

1.0

1.5

Glucose Draw Conc. (M)

Fig. 5. Experimental and theoretical reverse flux selectivities as a function of draw solution concentrations for: (a) urea, (b) ethylene glycol, and (c) glucose. The experimental reverse flux selectivities, which are presented as discrete points, were determined using the experimental water and reverse solute fluxes depicted in Fig. 2. The theoretical reverse flux selectivities, which are shown as solid lines, were calculated using Eq. (14) with A = 0.44 L m−2 h−1 bar−1 and the solute permeability coefficients, B, and reflection coefficients, , reported in Table 1.

coefficient into the expression for Jw also produces a term containing  in the expression for Js [40,41]: Js = Bc + (1 − )¯c Jw

(15)

where c¯ is an average solute concentration across the membrane. Furthermore, this derivation relies on the assumption of the Onsager reciprocal relationship, which states that  for the volume (water) and solute fluxes is equivalent [41]. Our experimental results appear to contradict this assumption. We can suggest several potential explanations for these results, but cannot conclusively state why the reflection coefficient must be included in the calculation of the water flux but not the solute flux. It is likely that the second term on the right hand side of Eq. (15), which closely resembles a convective contribution to the solute flux, does not contribute significantly to the total flux of solute. In other words, the high permeability of these solutes results in the diffusive flux of solute being the dominant mode of transport. The relative contributions of the convective and diffusive fluxes can be estimated using the reported values for , B, and Jw in conjunction with Eq. (15). These order of magnitude calculations demonstrate that at lower draw solution concentration, where the water fluxes are small, the convective term contributes about 5% to the overall solute flux. However, for higher draw solution concentrations the convective transport of solute contributes more than 15% to the total solute flux. No systematic deviations exist in our data of reverse solute flux with increasing draw solution concentration to suggest this is the case. Confusion may arise from the nomenclature used in Eq. (15). Specifically, how should c¯ be calculated? The use of a reflection coefficient to quantify solute–solvent coupling in membrane systems was originally implemented for porous membranes [40]. However, the “dense” cellulose membranes used here do not contain pores and operate by the solution-diffusion transport mechanism. This requires that the solute and solvent partition into the active layer phase before diffusing across it. The coupled diffusion effects discussed here arise within the active layer of the membrane, so the average solute concentration in Eq. (15) should be the average concentration in the active layer phase. Therefore, to accurately calculate c¯ , the solute concentration in solution needs to be multiplied by the solute partition coefficient, H [44]. For urea partitioning between an aqueous solution and a dense cellulose membrane, the partition coefficient is around 0.3 [37]. Including this additional factor reduces the contribution from the convective term in Eq. (15)-even at higher draw solution concentrationsand may explain why solute–solvent coupling does not appear to impact the solute flux, but does impact the solvent flux. The convective contribution to the total solute flux would also become small if  for solute transport were close to 1. For this to

occur, the Onsager reciprocal relationship would have to fail for the transport of highly permeable solutes across dense cellulose membranes. The failure of the Onsager relationship has been reported for the diffusion of gases across polymeric membranes [45]. However, to our knowledge, this topic has not been explored extensively for the diffusion of solutes across membranes used in RO or ODMPs. Going forward, a more fundamental understanding of when solute–solvent coupling will affect the water flux, and possibly the solute flux, in FO and PRO operations is necessary for the continued development of osmotically driven membrane processes. One practical example that demonstrates this need is a recent work exploring the impact of a permeability-selectivity tradeoff for a thin-film composite PRO membrane on the peak power density that the membrane could potentially produce [17]. It was shown that because the goal of a PRO process is power generation and not a chemical separation, using membranes that were more permeable but less selective could increase the peak power density. However, if the membrane selectivity were decreased too much in an attempt to increase permeability, and the draw solute permeated rapidly across the active layer, a reflection coefficient would need to be included in the calculations. Knowing when such a factor needs to be incorporated would be beneficial to the design of better membranes for the PRO process.

5. Concluding remarks This work investigates the phenomena of forward water flux and reverse draw solute flux in FO. We demonstrate that the rapid permeation of urea and ethylene glycol results in external concentration polarization on the feed side of the membrane. Accounting for this concentration polarization is essential for the accurate prediction of the reverse flux of rapidly permeating draw solutes. However, the effects of concentration polarization are not enough to explain the low water fluxes generated by these solutes. This observation is indicative of a coupling between the water and solute fluxes within the active layer of the membrane. Here, this solute–solvent coupling was adequately quantified by incorporating a reflection coefficient into the calculation of the water flux.

Acknowledgements 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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J.S. Yong et al. / Journal of Membrane Science 392–393 (2012) 9–17

Nomenclature A Am B cD cF m cD

cFm D DA H JS Jw k n PeS Peı Rg S t tA tS T VF0 Vdraw Vfeed z

water permeability coefficient membrane area solute permeability coefficient molar concentration of solute in the bulk draw solution molar concentration of solute in the bulk feed solution molar concentration of solute at the active layersupport layer interface molar concentration of solute at the active layerboundary layer interface binary diffusion coefficient of draw solute and water diffusion coefficient of draw solute in active layer solute partition coefficient total flux of draw solute water flux mass transfer coefficient of the draw solute on the feed side number of dissolved species created by draw solute Peclet number in support layer Peclet number in the external boundary layer ideal gas constant membrane structural parameter Time active layer thickness support layer thickness absolute temperature initial feed solution volume volume of the draw in the diaphragm cell volume of the feed in the diaphragm cell coordinate system

Greek letters ı external boundary layer thickness ε porosity of support layer osmotic pressure of the draw solution D F osmotic pressure of the feed solution  reflection coefficient tortuosity of support layer 

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