Boric Acid Permeation in Forward Osmosis Membrane Processes

ARTICLE pubs.acs.org/est

Boric Acid Permeation in Forward Osmosis Membrane Processes: Modeling, Experiments, and Implications Xue Jin,†,‡ Chuyang Y. Tang,*,†,‡ Yangshuo Gu,†,‡ Qianhong She,†,‡ and Saren Qi†,‡ †

School of Civil and Environmental Engineering and ‡Singapore Membrane Technology Center, Nanyang Technological University, Singapore, 639798

bS Supporting Information ABSTRACT: Forward osmosis (FO) is attracting increasing interest for its potential applications in desalination. In FO, permeation of contaminants from feed solution into draw solution through the semipermeable membrane can take place simultaneously with water diffusion. Understanding the contaminants transport through and rejection by FO membrane has significant technical implications in the way to separate clean water from the diluted draw solution. In this study, a model was developed to predict boron flux in FO operation. A strong agreement between modeling results and experimental data indicates that the model developed in this study can accurately predict the boron transport through FO membranes. Furthermore, the model can guide the fabrication of improved FO membranes with decreased boron permeability and structural parameter to minimize boron flux. Both theoretical model and experimental results demonstrated that when membrane active layer was facing draw solution, boron flux was substantially greater compared to the other membrane orientation due to more severe internal concentration polarization. In this investigation, for the first time, rejection of contaminants was defined in FO processes. This is critical to compare the membrane performance between different membranes and experimental conditions.

’ INTRODUCTION Forward osmosis (FO), as an emerging water treatment technology, has gained increasing interest in recent years. FO is defined as the net movement of water across a semipermeable membrane from a feed solution of lower osmotic pressure to a draw solution of higher osmotic pressure. Consequently, the draw solution is being diluted which may be further treated to extract for freshwater.1 Using FO in water treatment can be highly attractive due to its lower fouling potential, simplicity, and higher recovery,2 although energy consumption could be high if draw solution regeneration is required. Potential applications of FO include seawater desalination,3 wastewater reclamation,4 liquid food processing,5 and electricity generation via a derivative pressure retarded osmosis process.6 Previous research has focused on the effects of internal concentration polarization (ICP) on solvent (water) and major solute (NaCl) transport through FO membranes,3,7,8 manufacturing high-performance FO membranes,9,10 and developing easily separable draw solutions with a high osmotic pressure.11 Further research efforts are needed for better understanding FO process. For instance, there lacks a systematic mechanistic understanding of the permeation of trace contaminants from the feed solution into the draw solution. This is critical to the viability of this technology, especially when it is used to purify dirty water for direct potable consumption.12 Boron is a contaminant of interest in the desalination field. Boron concentrations in seawater range from 4 to 6 mg/L.13 r 2011 American Chemical Society

However, concentrations up to 100 mg/L have been found in groundwater as a result of wastewater discharge.14,15 Oral exposure to excess boron can adversely affect cardiovascular, nervous, and alimentary systems of humans.16 Consequently, the World Health Organization guideline for drinking water quality sets a limit of 0.5 mg/L for boron.15 At the natural pH level of seawater, size exclusion is proposed as the primary mechanism for boron removal by reverse osmosis (RO) membranes as boron will mainly exist as neutrally charged boric acid with a pKa value of 9.25.13 Consequently, this uncharged species can diffuse readily through membranes due to its small diameter of 0.4 nm.17 In general, boron removal of 40-90% could be achieved by RO membranes in neutral pH condition.18 When evaluating FO as a treatment process for seawater desalination, it is important to ensure that trace contaminants such as boron are removed from the treated water. Thus, a fundamental understanding of boron transport in FO membrane processes is critical to the effective development of FO membrane technology. Despite the importance of this aspect, very few studies on the removal of trace contaminants by FO have been reported in the literature.19-21 However, this phenomenon has not yet been modeled. As a result, the fundamental mechanisms governing boron Received: November 9, 2010 Accepted: January 21, 2011 Revised: January 20, 2011 Published: February 17, 2011 2323

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transport through and removal by FO membranes are not well understood. The objectives of this study were (1) to formulate a model that describes the transport of boron across an asymmetric membrane in FO operation, (2) to validate the model through well controlled laboratory experiments, and (3) to define the removal efficiency of contaminants in FO operation, which was used to compare the boron removal between FO and RO. The model and definition developed in this study can be extended to gain insights into the behaviors of other trace contaminants in FO, and thus have further-reaching implications for seawater desalination and wastewater reclamation using FO technology.

’ THEORY AND MODELING OF BORON TRANSPORT IN FO PROCESS Water and Solute Permeability. According to the classical solution-diffusion model,1,6 water flux, Jw, through an FO membrane is proportional to the osmotic pressure difference across the active layer of membrane, Δπ, and described by

Jw ¼ AΔπ

ð1Þ

where A is the water permeability of the membrane. The driving force for solute permeation through the membrane is largely based on the solute concentration gradient across the active layer of membrane, Δc. The solute flux through the membrane, Js, is expressed as ð2Þ Js ¼ BΔc where B is the solute permeability of the membrane. Internal Concentration Polarization (ICP). Compared to pressure-driven membrane processes, FO process suffers from severe ICP in the porous support layer of FO membranes.1,22,23 Consequently, the effective driving force is much smaller than the apparent osmotic pressure difference between the draw and feed solutions.1,23 Considering the effect of ICP, water flux in FO can be expressed as7 ! Aπdraw þ Bs Jw ¼ Km, s ln Aπfeed þ Jw þ Bs ðactive layer facing feed solutionÞ ! Aπdraw - Jw þ Bs Jw ¼ Km, s ln Aπfeed þ Bs

ð3Þ

ðactive layer facing draw solutionÞ

ð4Þ

where Bs is salt permeability of FO membrane, and πdraw and πfeed are the osmotic pressure of the bulk draw solution and feed solution, respectively. Km,s is the mass transfer coefficient of salt within membrane porous support layer, which is given by the ratio of salt diffusion coefficient (Ds) over the membrane structural parameter (S): Ds ð5Þ Km , s ¼ S Here S is a property of FO membrane support layer structure (S = (tτ)/ε) where t, τ, and ε are the thickness, tortuosity, and porosity of the support layer, respectively). Similar to the mass transfer coefficient (k) for external concentration polarization (ECP), Km can be used to determine the influence of ICP on

Figure 1. Schematic of boron transport into draw solution in the FO process: (A) active layer is facing feed solution and (B) active layer is facing draw solution.

water and solute flux.24 Also, analogous to the boundary layer thickness (δ) for ECP, S provides a length scale of ICP in the support layer.22 In this study, ECP was minimized by using a high cross-flow velocity and spacers for both feed and draw solutions. Previous studies showed that ECP effect was not significant compared to ICP effect under such conditions.25 Boron Transport through FO Membrane. A schematic of boron transport into draw solution in the FO process is shown in Figure 1. When the feed solution is against the active layer (Figure 1a), boron flux (JB) through FO membrane is expressed as26 JB ¼ BB ðcf , B - ci, B Þ ð6Þ where BB is the boron permeability coefficient, cf,B is boron concentration in feed solution, and ci,B is boron concentration at the interface of FO support layer and active layer. Equation 6, which assumes that the boron transport through the dense membrane active layer is uncoupled from the water transport, has been commonly used for modeling boron transport in RO membranes.27 In the active layer facing feedwater (AL-FW) orientation, once boron permeates through the active layer, it is carried away from the membrane support layer by the water 2324

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Environmental Science & Technology flux. Thus, boron does not experience ICP in this orientation. JB and Jw are related via the boron concentration transported across the FO membrane: JB ð7Þ ci, B ¼ Jw Substituting eq 7 for ci,B in eq 6 yields an expression for the boron flux into the draw solution: BB c ðAL-FWÞ ð8Þ JB ¼ BB f , B 1þ Jw All the parameters necessary to calculate JB are readily determined from RO and FO experiments. Equation 8 suggests the JB increases with higher Jw. This is because ci,B becomes more dilute at higher water flux, which enhances the driving force for boron transport across the membrane active layer. When active layer is facing the draw solution (AL-DS), JB through FO membrane is expressed as26 JB ¼ BB ðci, B - cd, B Þ ð9Þ where cd,B is the effective boron concentration in draw solution arising from the boron flux (cd,B = (JB)/(Jw)). Boron in the feed freely enters the porous support layer as it is transported into this layer by convective water flow as well as diffusion. Due to the retention of boron by the active layer, boron concentration at the support layer-active layer interface (ci,B) is higher than that in bulk feed solution (cf,B). This is the concentrative ICP of boron inside the porous support layer, in a way similar to the ICP of major solutes such as NaCl. ci,B can be derived from film theory28 and described as follows: ! ci, B - cd, B Jw ¼ exp ð10Þ cf , B - cd, B Km , B where Km,B is mass transfer coefficient of boron within the membrane porous support layer, which is given by the ratio of boron diffusion coefficient (DB) over the membrane structural parameter (S): DB Km , B ¼ ð11Þ S By substituting eq 10 into eq 9, boron flux through an asymmetric FO membrane in the AL-DS orientation can be predicted from BB expðJw =Km, B Þ JB ¼ c ðAL-DSÞ ð12Þ BB expðJw =Km, B Þ f , B 1þ Jw Unknown parameter Km,B was estimated as follows. First, Km,s was determined according to eq 4, where A and Bs were determined from RO experiments; Jw was determined from FO experiments; πdraw and πfeed were calculated using OLI Stream Analyzer 3.1 (Morris Plains, NJ). Since the structural characteristics of membrane support layer t, τ, and ε should be constant for membranes that are mechanically and chemically stable under the chosen experimental conditions,22 Km,B was estimated from the measured Km,s using the following relationship by assuming equal S value: Km , B DB ¼ ð13Þ Km , s Ds DB and Ds were calculated using OLI Stream Analyzer 3.1.

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Boron Rejection by FO Membranes. Rejection of a pressuredriven membrane is typically defined as 1 minus the ratio of permeate concentration over feed concentration, where the permeate concentration is given by the ratio of permeate solute flux over the water flux.29 Consistent to this definition, the rejection of contaminants in FO processes is defined as cd, B JB ¼ 1ð14Þ R ¼ 1cf , B Jw 3 cf , B

By substituting eqs 8 and 12 into eq 14, rejection of boron by an FO membrane is expressed as follows: BB ðAL-FWÞ ð15Þ R ¼ 1BB þ Jw R ¼ 1-

BB expðJw =Km, B Þ ðAL-DSÞ BB expðJw =Km, B Þ þ Jw

ð16Þ

’ MATERIALS AND METHODS Chemicals and Solution Chemistry. The feed solution was either deionzied water or 0.5 M NaCl, which simulated seawater. Unless otherwise specified, the draw solution was composed 2 M NaCl to produce permeate flux comparable to that of RO desalination plants. The pH of all solutions was 5.9 ( 0.2. Boric acid was used as the source of boron and was spiked in the feed solution at 5 or 10 mg/L as boron. FO Membranes. Two commercial FO membranes (CTAHW and CTA-W) used in this study were provided by Hydration Technologies, Inc. (Albany, OR). Both membranes have asymmetric structure and are made of cellulose triacetate (CTA) supported by embedded polyester screen mesh. The pure water permeability coefficient, A, NaCl permeability coefficient, Bs, and boron permeability coefficient, BB, of the FO membranes were evaluated in a pressurized crossflow filtration test unit (i.e., under RO testing mode). The effective membrane area was 42 cm2, and crossflow velocity was fixed at 23.2 cm/s. Feed water temperature was maintained at 24 ( 0.5 °C. The A value was determined by measuring the water flux over a range of applied pressures (60-260 psi). Using a 10 mM NaCl feed solution, NaCl rejection was determined based on feed and permeate conductivity measurements (Ultrameter II, Myron L Company, Carlsbad, CA). Similarly, boron rejection was determined using a feed solution containing 5 mg B/L based on boron concentration measurements by an inductively coupled plasma atomic emission spectrometer (ICP-AES, Perkin-Elmer Optima 2000). BNaCl or Bboron value was determined based on classical solution-diffusion theory:7 1 ð17Þ R ¼ B 1þ AðΔP - ΔπÞ

where ΔP and Δπ are the hydraulic pressure difference and osmotic pressure difference across the membrane, respectively; R is NaCl or boron rejection. FO Filtration Experiments. The bench-scale FO system employed is similar to that described in our previous studies.7 Briefly, a membrane coupon with an effective area of 60 cm2 was housed in a cross-flow membrane cell. Diamond-patterned spacers were placed on both sides of the membrane to improve support of the membrane as well as promote mass transfer.7,22 2325

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Table 1. Membrane Performance Parameters selectivity (Kpa) membrane

water permeability A, (m/s 3 Pa) -12

CTA-HW

2.55 ( 0.11  10

CTA-W

1.07 ( 0.12  10-12

NaCl permeability Bs, (m/s) -7

boron permeability BB, (m/s) -6

Bs/A

BB/A

2.72 ( 0.31  10

5.02 ( 0.87  10

107

1969

6.45 ( 0.53  10-8

1.95 ( 0.52  10-6

60

1822

Co-current flow was used with cross-flow rate on both sides of membrane controlled by a variable-speed peristaltic pump (ColeParmer, Vernon Hills, IL). The cross-flow velocities (calculated based on the ratio of cross-flow rate to cross-section area of flow channel) for both feed and draw solutions were maintained at 23.2 cm/s during all experiments. The feed solution tank was placed on a digital scale (Mettler Toledo, Germany) and weight changes as a function of time were utilized to determine permeate water flux. Both membrane orientations, AL-FW and AL-DS, were tested. The duration of each FO membrane test was 2 h. Samples from feed tank and draw solution tank were taken at specified time intervals for boron, conductivity, pH, and temperature measurements. Because the initial boron concentration in the draw solution was zero, a mass balance yields ð18Þ cBðtÞ ðVd0 þ Jw Am tÞ ¼ JB Am t where cB(t) is the experimentally measured boron concentration in draw solution at time t, Vd0 is the initial volume of draw solution, Jw is the measured water flux, Am is the membrane surface area, and t is time. The experimental boron flux, JB, was obtained from the slope of plotted (cB(t)(Vd0þJwAmt))/(Am) versus t.

’ RESULTS AND DISCUSSION Membrane Performance Parameters. The performance parameters (A, Bs, and BB) of FO membranes are reported in Table 1. Consistent with previous research,7,30,31 the A values were on the same order of magnitude as those of seawater RO membranes. The NaCl rejections yielded in RO experiments ranged 89-91% for CTA-HW membrane and 94-95% for CTA-W membrane, which are comparable to the values of brackish RO membranes.31,32 The values of Bs determined by these measurements were 2.72 ( 0.31  10-7 m/s for CTA-HW membrane and 6.45 ( 0.53  10-8 m/s for CTA-W membrane. CTA-HW membrane had higher BB value, indicating that it had lower retention against boron. Model Prediction of Boron flux in FO Processes. Data presented in Figure 2 describe the model predictions of boron flux as a function of water flux for CTA-HW and CTA-W membranes. According to eqs 8 and 12, JB shall be proportional to the boron concentration in feed solution Cf. Here, JB values reported on the y-axis are normalized by Cf. BB was determined independently from RO experiments (Table 1). Thus the determination of normalized boron flux (JB/Cf) for AL-FW orientation does not require any additional parameters. To predict JB/Cf for AL-DS orientation, eq 12 requires that we know BB and Km,B. According to eq 13, Km,s (2.73  10-6 m/s for CTA-HW and 1.94  10-6 m/s for CTA-W, respectively), DB (1.46  10-9m2/s), and Ds (1.57  10-9m2/s) were used to calculate Km,B.

Figure 2. Model predictions for CTA-HW and CTA-W forward osmosis membranes. Normalized boron flux (JB/Cf) is plotted against water flux (Jw).

As presented in Figure 2, JB/Cf increases with increasing Jw in all cases. The increment in JB/Cf with Jw is much more severe for AL-DS orientation, especially at higher water flux. This indicates that boron transport through FO membranes is more sensitive to permeate flux for the AL-DS orientation and can be attributed to concentrative ICP. In this operation mode, boric acid molecules in the feedwater enter the porous support layer of membrane. This causes a concentration build-up in the membrane support layer, which elevates the boron concentration difference across the active layer and thus enhances boron passage (Figure 1b). According to eq 10, the magnitude of ICP increases exponentially with permeate flux, which explains why the differences in boron flux between two operation modes (AL-FW versus ALDS) become more significant at greater water flux levels. For the AL-FW orientation, at the same water flux, CTA-HW membrane exhibits greater boron flux due to its larger boron permeability coefficient BB. In contrast, for the AL-DS orientation, normalized boron fluxes are similar for both membranes. Explanations for this trend can be provided using our model. Normalized boron flux is predicted from JB ¼ cf , B

BB expðJw =Km, B Þ 1 ¼ 1 1 ð19Þ BB expðJw =Km, B Þ þ 1þ BB expðJw =Km, B Þ Jw Jw

Examination of the term BBexp(Jw/Km,B) allows the equation to be simplified. The BB values of the selected membranes in this study are in the same order of magnitude with Jw; however, the term exp(Jw/Km,B) increases exponentially with Jw. Therefore, 1/Jw dominates and the normalized boron flux reduces to (JB)/ (cf,B) ≈ Jw. As presented in Figure 2, JB/Cf is nearly linear with respect to Jw, as a result, almost no boron rejection is achieved (Figure 4), especially at higher water flux level. This is an insightful result which suggests that boron transport through 2326

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Figure 3. Experimental water flux with (A) CTA-HW and (B) CTA-W membranes and boron flux with (C) CTA-HW and (D) CTA-W membranes. All experiments were conducted with 2 M NaCl as draw solution.

FO membranes is dominated by boron concentration in bulk feed solution and water flux in the AL-DS orientation. In this orientation, boron permeability coefficient BB and support layer structural parameter S (which influences Km,B) have minor effects on boron transport behavior for commercially available FO membranes. Experimental Water and Boron Fluxes. The experimental water fluxes through CTA-HW and CTA-W are presented in Figure 3a and 3b, respectively. Generally, the water flux was not influenced by the boron concentration in feed solution (either 5 or 10 mg B/L), indicating that the presence of boron does not change the intrinsic separation properties and structure of FO membranes. The higher water fluxes observed for CTA-HW membrane confirm that this membrane is more permeable compared to the CTA-W membrane. When feedwater was composed of 0.5 M NaCl, water flux was lower than that when DI water was used as feed. This is due to the higher osmotic pressure in 0.5 M NaCl feed solution and related greater concentrative ICP of NaCl (for the AL-DS orientation) in membrane support layer, both of which result in lower osmotic driving force across the FO membranes. Compared to the AL-DS orientation, the AL-FW orientation experienced more severe ICP and thus exhibited lower water flux. Figure 3c and 3d present the measured boron flux through CTA-HW and CTA-W, respectively. Boron passage through FO membranes with 10 mg B/L in feed solution was approximately double that with 5 mg B/L in feed solution. This is consistent with our modeling predictions that boron flux is proportional to the boron concentration in feed solution. As the NaCl concentration of the feed solutions increased (DI versus 0.5 M NaCl),

Figure 4. Observed and predicted boron rejection by CTA-HW membrane as a function of water flux with various operation modes. The feed solution contained 5 mg B/L in DI water. Other experimental conditions were as follows: cross-flow velocity = 23.2 cm/s, pH ≈ 6, and temperature = 24 °C. The permeate flux was varied by changing the applied pressure (60-260 psi) for RO operation and by changing NaCl concentration (0.1-5 M) in draw solution.

the measured boron flux was reduced. This was likely due to the reduced water flux (Figure 3a and 3b), as boron flux increases with increasing water flux (Figure 2). At the same experimental conditions, the AL-DS orientation always exhibited greater boron flux than the AL-FW orientation. The faster boron passage for the AL-DS orientation arises from the combined influence of (1) concentrative ICP of boron in support layer as well as (2) the higher water flux in this orientation (Figure 3a and 3b). In all the 2327

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Figure 5. Influence of boron permeability (BB) and membrane structural parameter (S) on predicted (A) boron flux and (B) rejection.

cases investigated, CTA-HW membrane showed a higher boron flux compared with CTA-W membrane. This phenomenon can be attributed to the higher water flux through CTA-HW membrane for both membrane orientations. Moreover, for the AL-FW orientation, the greater BB of CTA-HW membrane is also contributing to the higher boron passage. In general, there is a strong agreement between experimental results and model prediction for boron flux (Figure S5, Supporting Information). This indicates that the model developed in this study, which incorporates both operating parameters (orientation and water flux) and membrane characteristics, can be used as a reliable predicator for boron transport during FO processes. Experimental and Predicted Boron Rejection. In this section, boron rejection achieved by FO experiments is compared to that by RO membrane process. To the authors’ best knowledge, this is the first study to compare the performance of FO and RO for boron removal. Experimental and predicted boron rejections by CTA-HW membrane as a function of water flux are illustrated in Figure 4. The experimental data follow closely with the model results. For the AL-FW orientation, boron rejection increased with increasing permeate flux. Experimental results revealed that boron rejection by CTA-HW membrane ranged from 29% to 62% when water fluxes of 2.6-6.9 μm/s were achieved. These observed rejections are comparable to the values (38-65%) reported for commercial brackish RO membranes.33 Since the removal mechanisms of FO membrane in AL-FW orientation are similar to those of RO,20 the boron rejection determined from RO experiments using CTA-HW can also be modeled by the solid line. However, when applied hydraulic pressure was over 200 psi (Jw = 3.5 μm/s), the RO rejection was slightly lower compared to the model prediction.

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One possible explanation is that the high hydraulic pressure may damage the commercial FO membrane which is designed for low or no pressure conditions. From the model prediction for the AL-DS orientation, boron rejection increased initially with increasing water flux due to the dilution effect. However, further increase in water flux resulted in reduced rejection due to significant ICP of boron. The experimental data agreed well with the model, with an observed boron rejection of merely 2.4% at a water flux of 10.5 μm/s. Based on the model predictions, the maximum boron rejection by CTA-HW membrane in the AL-DS orientation is only 15.5%, much lower compared to the AL-FW orientation. Implications for FO Membrane in Seawater Desalination. The above results indicate that boron permeation through the commercially available FO membranes into draw solution is fast, especially for the AL-DS orientation. This has important technical implications in the way to separate clean water from the diluted draw solution and thus the potential use of FO membrane processes in seawater desalination. The model developed in this study can guide process design and fabrication of improved FO membranes, with decreased BB and S, preferred to minimize the transport of boron. Figure 5 illustrates the effect of changing BB and S on the normalized boron flux and boron rejection based on eqs 8, 12, 15, and 16. The lines labeled with “BB, S” represent the performance of CTA-HW membrane. BB was then decreased by 10 times to represent the typical boron permeability of a high boron rejection SWRO membrane13 or a BWRO membrane when operating at pH of 10.5.34 S was reduced to half of the value of CTA-HW membrane to simulate a membrane with less thickness, higher porosity, and lower tortuosity. For the ALFW orientation, reducing BB can significantly decrease the boron flux (Figure 5a) and enhance the boron rejection up to 97% (Figure 5b). For the alternative orientation, reducing BB value can result in lower predicted boron flux. Decreasing S value, which reduces ICP, can further reduce the boron flux. The reduction effect is more significant at higher water flux. Moreover, water flux and boron concentration in feed solution are important factors that must be considered. Higher water flux and feed concentration result in higher boron flux. In this investigation, for the first time, rejection of trace contaminants is defined in FO processes. This is critical to compare the membrane performance between different membranes and experimental conditions. It is worth noting that based on current FO membrane technology, the AL-DS orientation is not preferred due to its higher fouling potential7 and lower removal efficiency of contaminants. Finally, previous studies reported that boron rejection by RO membranes was influenced by pH, temperature, and membrane fouling.27 The effect of these parameters on boron rejection by FO membranes will be investigated in our further studies.

’ ASSOCIATED CONTENT

bS

Supporting Information. S1, Speciation of boric acid; S2, FO membrane structure and surface characteristics; S3, calculation of experimental boron rejection in FO operation; S4, experimental results and model predictions for water flux; S5, a comparison between experimental results and model predictions for boron flux; S6, experimental and predicted boron rejection by CTA-W membrane. This material is available free of charge via the Internet at http://pubs.acs.org.

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’ AUTHOR INFORMATION Corresponding Author

*Address: Nanyang Technological University, N1-1B-35, 50 Nanyang Avenue; Singapore, 639798; tel: (65) 67905267; fax: (65) 67910676; e-mail: [email protected].

’ ACKNOWLEDGMENT We thank the Environment and Water Industry Programme Office (EWI) under the National Research Foundation of Singapore (grant MEWR C651/06/173) for the financial support of the work. The Singapore Membrane Technology Center is supported by both EWI and Nanyang Technological University. We also thank HTI for supplying membrane samples. ’ NOMENCLATURE A water permeability of membrane membrane surface area Am boron permeability of membrane BB salt permeability of membrane Bs experimentally measured boron concentration in draw cB(t) solution at time t effective boron concentration arising from the boron cd,B flux (= JB/Jw) boron concentration in feed cf,B boron concentration at membrane support layer ci,B active layer interface boron diffusivity DB salt diffusivity Ds boron flux JB salt flux Js water flux Jw boron mass transfer coefficient within membrane porKm,B ous support layer salt mass transfer coefficient within membrane porous Km,s support layer R rejection S membrane structural parameter t time thickness of membrane support layer ts initial volume of draw solution Vd0 Greek letters

ε Δp πdraw πfeed Δπ τ

porosity of membrane support layer hydraulic pressure osmotic pressure in draw solution osmotic pressure in feed solution trans-membrane osmotic pressure tortuosity of membrane support layer

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