Effect of Molecular Weight of Draw Solute on Water Permeation in

Article pubs.acs.org/IECR

Effect of Molecular Weight of Draw Solute on Water Permeation in Forward Osmosis Process Masahiro Yasukawa, Yasuhiro Tanaka, Tomoki Takahashi, Masafumi Shibuya, Shoji Mishima, and Hideto Matsuyama* Center for Membrane and Film Technology, Department of Chemical Science and Engineering, Kobe University, 1-1 Rokkodaicho, Nada-ku, Kobe 657-8501, Japan S Supporting Information *

ABSTRACT: To realize the application of forward osmosis (FO) membranes to industrial-level water treatment, the correct selection of the draw solute (DS) and good membrane performance is necessary. In this study, the FO flux behavior was investigated using draw solutes of inorganic salt (NaCl) and neutral polymers (PEGs) with molecular weights of 200−8300. The FO flux dramatically decreased with increasing molecular weight of the DS. Severe internal concentration polarization originated from the lower diffusivity of the larger DS molecules, which brought about the flux reduction. The experimental data were analyzed with a model developed using a virial expansion equation for osmotic pressure in the case of the polymeric draw solutions. The analyzed results fit well with the experimental data, which allowed us to predict a relation between FO performance and the molecular weights of the draw solutes for different FO membranes. nanofiltration (NF) membrane processes.26,27 In general, RO and NF membranes show water permeabilities (A) of approximately less than 8.3 and 14.4 L m−2 h−1 bar−1 (LMH/ bar), respectively,28,29 whereas commercial and developing FO membranes show an osmotic pressure difference-based pseudowater permeability (AFO) of approximately less than 1.5 LMH/ bar when the active layer is facing the FS (AL-FS mode).30,31 When applying an FO membrane to water treatment using actual water as the FS, the AL-FS mode is usually used because the active layer has a lower fouling propensity than the support layer.32,33 However, in the case of the AL-FS mode, the effective osmotic driving force tends to be lower than that expected from the bulk osmotic pressure difference, owing to internal concentration polarization (ICP), in which the permeate water flux enhances the dilution of the draw solute within the porous support layer of the FO membrane.26 To reduce the ICP effect, the porous support layers should be very thin, highly porous, and have small tortuosity in order to enhance DS diffusivity in the porous support.34 Therefore, the ICP depends on both the characteristics of the FO membrane and the DS diffusivity. Theoretical understanding of FO performance with different DSs is one of the most important issues in designing an FO process. However, although various types of DSs have been proposed and their FO performance has been investigated, there have been few reports on the theoretical analysis of the flux behavior when using different types of DSs. In this study, FO flux behaviors were investigated by using model draw solutes of inorganic salt (NaCl) and neutral polymers (PEGs) with a wide variety of molecular weights (200−8300). The experimental data were analyzed with a model developed using the virial expansion

1. INTRODUCTION Forward osmosis (FO) membrane processes have attracted much research interest because of their versatile potential application in water treatment.1−3 Water transport in the FO process can be driven by the osmotic pressure difference across the semipermeable membrane. FO enables spontaneous transport of water molecules through a selective membrane from a lower-concentration solution (feed solution: FS) to a higherconcentration solution (draw solution: DS) by an osmotic pressure gradient. FO is regarded as a low-energy-cost process because it utilizes other energy such as low-grade waste heat, and it is a promising emerging technology in wastewater reclamation and seawater desalination.4,5 However, there are still technical barriers to large-scale commercial application of the FO process. One is the development of a draw solute that is suitable and specified for the FO process. To obtain clean water by the FO process, lowenergy and low-cost production of pure water from the diluted DS is required.3,6,7 DS regeneration is therefore indispensable for water purification and desalination using FO technology.6,8 Since a pioneering work in 20059 using ammonium bicarbonate as the draw solute, which could be regenerated by distillation at approximately 60 °C, there have been numerous efforts to develop DS. Various types of DS such as volatile solvents,10 glycol ethers,11 amines with a lower critical solution temperature (LCST),12 switchable polarity solvents,13 zwitterions,14 surfactants,15,16 thermoresponsive polymers,17,18 stimuli-responsive hydrogels,19 carbon quantum dots,20 switchable dual-responsive polymers,21 magnetic nanoparticles,22 and dendrimers23 have been proposed with a wide variety of recovery technologies. Another critical issue in FO is the development of FO membranes. Various FO membranes, including flat sheets and hollow fibers, have been prepared.1,24,25 However, the water flux is still low as compared to conventional pressure-driven membrane processes such as reverse osmosis (RO) and © XXXX American Chemical Society

Received: May 28, 2015 Revised: July 13, 2015 Accepted: July 28, 2015

A

DOI: 10.1021/acs.iecr.5b01960 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

Article

Industrial & Engineering Chemistry Research

Figure 1. Schematic of FO system.

2.3. FO Flux Measurement. The FO flux behavior was evaluated by a laboratory-scale cross-flow FO system with an effective membrane area of 139 cm2. A schematic of the system is shown in Figure 1. Before the experiments, both the DS and FS were stored in a water bath at 25 ± 1 °C. Both the DS and FS were introduced to a custom-made acrylic FO cell (Kokugo Co., Ltd., Japan) with a counter-flow pattern, and then continuously recirculated to the respective receiving tanks (DS, 500 mL, and FS, 1000 mL) by circular pumps (FTU-1, Membrane Soltech Co., Japan) at a constant flow rate (DS, 500 mL min−1, and FS, 1000 mL min−1). To eliminate the contribution of the external concentration polarization (ECP) effect, mesh spacers were inserted in both the DS and FS side channels to enhance the turbulence of the feed flows. The inlet pressures of the DS and FS were carefully adjusted to same pressure (PDS‑in = PFS‑in) by pressure control valves. The tests were carried out in AL-FS mode. The water flux (JwFO, LMH) was obtained in 1 min intervals by recording the FS volume reduction using a real-time data logging system connected to a personal computer. In the FO experiment, a preliminary time interval is usually required in order to form a uniform concentration polarization layer.25 Therefore, we conducted a prior operation for at least 30 min, and then the average water flux over 30 min was calculated. To judge the uniform ICP formation, we also checked the deviation of the average flux every 1 min. When the deviation dropped below 2% and continued at least for 10 min, the flux data was assumed to have reached a steady state. After the flux measurements, the osmotic pressure of the DS was measured by the vapor osmometer, as described above. The measured osmotic pressure was used as the osmotic driving force for theoretical analysis.

equation for osmotic pressure expression. From the viewpoint of easy regeneration and lower DS leakage, studies have recently focused on higher-molecular-weight DSs. Therefore, we also theoretically simulated the relation between DS molecular weight and FO performance.

2. EXPERIMENTAL SECTION 2.1. Materials and Chemicals. Sodium chloride (Wako Pure Chemical Co., Osaka, Japan) and polyethylene glycol (PEG; Mn = 100, 200, 600, 2000, 3000, and 8300; Wako Pure Chemical Co., Osaka, Japan) were used as model draw solutes. To investigate FO membrane performance, commercially available FO membranes (CTA-NW and CTA-ES) made from cellulose triacetate (CTA) were purchased from Hydration Technologies, Inc. (HTI, Albany, OR, USA). Prior to the experiment, the HTI FO membranes were washed by soaking them in ultrapure water overnight to remove the glycerin coating. Ultrapure water was supplied from a Milli-Q ultrapure water system (Millipore, Bedford, MA, USA). All chemicals used in this study were of analytical grade and used without further purification. 2.2. Osmotic Pressure Measurement. To investigate the relationship between the osmotic pressure and FO flux, we measured the osmolality, m, of the prepared solutions by using a Wescor 5600 vapor pressure osmometer (Wescor Inc., Logan, UT, USA). This instrument measures dew point temperature depression of a solution in vapor equilibrium in a closed chamber and has an advantage over freezing point depression methodology for analysis of high viscous polymer solution.35 All measurements were carried out on fresh solutions at 25 ± 1 °C within 1 h after solution preparation to reduce water evaporation. The detailed protocol was described in a previous report.36 The osmometer was frequently recalibrated using a NaCl standard solution (Wescor Inc., Logan, UT, USA) during the experiments. The osmolality of each solution was measured repeatedly at least three times, and then we obtained the average value. We converted the values of the obtained osmolalities to the osmotic pressure by using the following equation:36,37 π = mρRT

3. RESULTS AND DISCUSSION 3.1. Osmotic Pressure Measurement. Figure 2 shows the relationships between π/C and the concentration, C, of NaCl and PEG (Mn = 106, 200, 600, 2000, 3000, and 8300). In the case of NaCl, a constant linear relation was obtained, as expected from the following van’t Hoff equation:

(1)

π iRT = C Msalt

where π is the osmotic pressure for the driving force in FO, m is the osmolality measured by a vapor pressure osmometer, ρ is the density of water, and R and T are the ideal gas constant and absolute temperature, respectively.

(2)

where Msalt is the molecular weight of salt, R and T are the ideal gas constant and absolute temperature, respectively, and i is the B


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Figure 4. Concentration dependence on DPEG with different molecular weights. Data were provided from the literature.42

Figure 2. Relation between π/C and C. Theoretical lines were drawn by using eqs 2 and 3.

Table 2. Fitting Parameters α and β for the Calculation of DPEG Using Equation 11

Table 1. Virial Coefficients for Various PEG Cases Mpolymer (g/mol)

RT/Mpolymer (bar L/g)

RTA2 (bar L2/g2)

RTA3 (bar L3/g3)

R

106 200 600 2000 3000 8300

2.33 × 10−1 1.24 × 10−1 4.13 × 10−2 1.24 × 10−2 8.26 × 10−3 2.98 × 10−3

1.35 × 10−4 1.11 × 10−4 5.86 × 10−5 4.00 × 10−5 3.45 × 10−5 3.37 × 10−5

7.99 × 10−7 6.01 × 10−7 5.66 × 10−7 4.73 × 10−7 4.77 × 10−7 4.51 × 10−7

0.993 0.990 0.987 0.997 0.995 0.994

2

D0 (m2 h−1)

α (m2 h−1 wt %−1)

β (m2 h−1 wt %−2)

200 300 400 600 1000 1500 2000 3400 10000

2.23 × 10−6 1.82 × 10−6 1.57 × 10−6 1.26 × 10−6 9.77 × 10−7 7.90 × 10−7 6.60 × 10−7 4.97 × 10−7 2.50 × 10−7

−1.67 × 10−8 −1.33 × 10−8 −6.29 × 10−9 −5.33 × 10−9 6.03 × 10−9 7.31 × 10−9 1.24 × 10−8 1.82 × 10−8 3.55 × 10−8

−7.09 × 10−11 −3.10 × 10−11 −1.16 × 10−10 −4.86 × 10−12 −2.68 × 10−11 −1.18 × 10−10 −1.69 × 10−10 −2.38 × 10−10 −7.62 × 10−10

consider molecular weight dependence on osmotic pressure, the fitting lines in Figure 2 were drawn using eq 3, in which virial coefficients higher than the third one were assumed to be zero.38 The point at which a line intersected a coordinate axis was first determined as RT/Mpolymer, and then the second and the third virial coefficients were fitted. The dotted fitting lines agree well with the experimental data for PEG, with the determination coefficient R2 exceeding 0.987. The second and third virial coefficients obtained in this study for the different molecular weights of PEG are summarized in Table 1. In this table, the determination coefficients in the respective cases are also included. Considering the molecular weight dependence on the virial coefficients, the second virial coefficient decreased with increasing molecular weight of PEG; the third virial coefficient also decreased slightly with increasing molecular weight. These trends agree well with previous reports.38,40 3.2. FO Flux Measurement. In the case of an osmoticdriven membrane, the water flux (JwFO) depends on both the membrane characteristics and the solution chemicals.1 Because an FO membrane generally consists of two layers (a thin active layer and a porous support layer), the existence of a porous support layer affects the diffusivity of the draw solute in the porous support layer, resulting in a reduction in performance caused by concentration polarization in the support layer (ICP).26 In the case of hydraulic-pressure-driven membranes such as RO and NF membranes, the water flux JwRO increases linearly with increasing hydraulic driving force. In the current case, however, JwFO did not increase linearly with increasing osmotic pressure because the higher FO flux resulted in severe ICP and a subsequent severe flux reduction.26 The JwFO in AL-FS

Figure 3. DS concentration profile in the forward osmosis membrane operated in AL-FS mode.

van’t Hoff coefficient. Therefore, the value of π/C should be constant in the NaCl case. In contrast, in the case of PEG, it is well-known from previous reports36 that there is not a linear relationship between osmotic pressure and concentration, owing to its divergence from ideality. With increasing molecular weight of PEG, the osmotic pressure decreases because the osmotic pressure depends on colligative properties. The osmotic pressures of polymer solutions are often described as follows:38,39 ⎛ 1 ⎞ π = RT ⎜⎜ + A 2 C + A3C 2 ···⎟⎟ C ⎝ M polymer ⎠

MPEG (g/mol)

(3)

where Mpolymer is the molecular weight of the polymer and A2 and A3 are the second and third virial coefficients, respectively. To C


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are the water permeability and DS permeability of the active layer, respectively. The S value theoretically includes the thickness t (μm), tortuosity τ, and porosity ε of the support layer, as described in eq 5. However, in the case of using a polymer as the DS, the osmotic pressure cannot be expressed by a linear correlation (van’t Hoff equation) as shown in Figure 2; therefore, JwFO cannot be expressed by using eq 4. To express JwFO in the polymer DS case, we derived a modified flux equation with three assumptions. The first assumption was that draw solute permeability through the active layer (the B value for the polymer) was zero because HTI’s CTA FO membrane has an RO-membrane-like skin layer with over 95% rejection, even for NaCl.1 The second assumption was that the osmotic pressure of FS could be regarded as zero (πFS,b = 0 and πFS,m = 0 in Figure 3), owing to the negligible DS leakage from DS to FS. Here, πFS,b and πFS,m are the osmotic pressures in bulk and at the active layer surface, respectively. The third assumption was that the ECP effect on the DS side was negligible (CDS,s = CDS,b in Figure 3) because the ICP effect should have a greater impact than the ECP effect in AL-FS operation. Here, CDS,s and CDS,b are the DS concentrations at the support membrane surface and in bulk DS, respectively. According to these assumptions, water flux and salt flux can be written respectively as41 Jw FO = A(πDS,m − πFS,m) ≈ AπDS,m

(6)

Js = B(C DS,m − C FS,m) ≈ 0

(7)

As shown in Figure 3, CDS,m and πDS,m are the DS concentration and the osmotic pressure at the active layer surface of the support layer side, respectively, and CFS,m and πFS,m are the FS concentration and osmotic pressure at the active layer, respectively. However, the salt flux across the membrane can be also expressed as follows:41 −Js = −Dε

C DS,m C DS,s

Table 3. Intrinsic Membrane Characteristics of the FO Membrane Used in This Studya FO membrane CTA-ES CTA-NW

A (L m

−1

h

−1

bar )

0.27 0.33

B (L m

−2

0.07 0.10

−1

h )

S (μm)

(9)

⎛ S ⎞ Jw FO = ARTC DS,s exp⎜ −Jw FO ⎟ DPEG ⎠ ⎝

238 978

These parameters were obtained from FO and RO tests and used for the analysis of all FO flux data.

⎧ ⎛ 1 S ⎞ ⎨ + A 2 C DS,s exp⎜ −Jw FO ⎟ ⎪M DPEG ⎠ ⎝ ⎩ polymer ⎪

mode is expressed by a classical solution diffusion model taking ICP into account as follows:1,41 ⎞ B + AπDS D ⎛⎜ ⎟ ln⎜ FO ⎟ S ⎝ AπFS + B + Jw ⎠

⎛ S⎞ = exp⎜ −Jw FO ⎟ ⎝ D⎠

where S is the structure parameter as described in eq 5. Equations 3, 6, and 9 can be combined to give

a

Jw FO =

(8)

where ε is the porosity of the support layer and D is the diffusion coefficient of DS. With the boundary conditions of C(x) = CDS,s at x = τt and C(x) = CDS,m at x = 0 and the first assumption (Js = 0), eq 8 can be converted as follows:

Figure 5. Effect of DS molecular weight on the FO flux behavior when using (a) CTA-ES and (b) CTA-NW FO membranes. The dotted and solid lines are theoretical predictions by eqs 4 and 10, respectively.

−2

d(C(x)) + Jw FO C(x) dx

2⎫ ⎛ ⎛ ⎞⎞ ⎪ FO S + A3⎜⎜C DS,s exp⎜ −Jw ⎟⎟⎟ ⎬ DPEG ⎠⎠ ⎪ ⎝ ⎝ ⎭

(4)

(10)

As described above, virial coefficients higher than the third one were assumed to be zero. We used eqs 4 and 10 for the theoretical analysis of the FO flux data in the NaCl and PEG cases, respectively. In eqs 4 and 10, the diffusion coefficient and S value were important parameters. Theoretically, the S value is an intrinsic membrane parameter and should be regarded as a

τt S= (5) ε where D is the DS diffusion coefficient in the bulk, πDS and πFS are the osmotic pressure of the DS and FS, respectively, and A and B D


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Figure 6. Calculation protocol for the prediction of FO flux data using PEG as the DS. The JwFO and DPEG values were decided after the loop calculation.

almost constant in the range of 0.1−1.2 mol L−1.43,44 Likewise, the DPEG value depended on the PEG concentration. DPEG in eq 9 is described by the following approximation:45

Table 4. DS Values Reported in Literature and Their Respective Diffusion Coefficients DS chemicals dimethyl ether NaCl glycine diethylbutylamine dimethylbutylamine triethylamine 1-ethylpiperidine methyldipropylamine L-proline glycine betaine L-valine N,N-dimethyl cyclohexylamine 1-butylpyrrolidine dimethylhexylamine propylene glycol n-butyl ether dimethylbenzylamine methyldibutylamine L-glutamine di(propylene glycol) n-propyl ether di(ethylene glycol) n-hexyl ether PEG 200 cetylpyridinium chloride nBu-TAEA Triton X-100 PEG 3000 PEG 8300 a

M (g/mol)

D (m2/h) −6

46 58 75 87 101 101 113 115 115 117 117 127 127 129 132 135 143 146 176

4.79 × 10 5.30 × 10−6 a 3.80 × 10−6 a 2.39 × 10−6 2.79 × 10−6 2.78 × 10−6 2.78 × 10−6 2.56 × 10−6 3.16 × 10−6 a 3.24 × 10−6 a 2.78 × 10−6 a 2.56 × 10−6 2.55 × 10−6 2.26 × 10−6 2.48 × 10−6 2.56 × 10−6 2.22 × 10−6 2.74 × 10−6 a 2.12 × 10−6

190 200 340 356 647 3000 8300

2.02 × 10−6 2.41 × 10−6 1.39 × 10−6 1.37 × 10−6 9.32 × 10−7 2.61 × 10−7 8.97 × 10−8

DS ref.

DPEG = D0 + αC DS + βC DS2

10 29−33 14 47 47 47 47 47 14 14 14 13 47 47 11 47 47 14 11

(11)

where DPEG and D0 are the diffusion coefficients at the DS concentration of CDS and at infinite dilution (CDS ≈ 0), respectively. The concentration dependences on DPEG are shown in Figure 4. The DPEG data were obtained from the literature. The fitted lines using eq 11 are included in Figure 4, and the detailed fitting parameters, α and β, are summarized in Table 2. For the analysis of the fluxes in the case of PEG 3000 and PEG 8300, we used the diffusion coefficient data of PEG 3400 and 10 000, respectively, because of the lack of concentration dependence data for PEG 3000 and PEG 8300. In the cases of the other molecular weights of PEG, the concentration dependence data shown in Figure 4 were used. Figure 5 shows JwFO operated in AL-FS mode against osmotic pressure when NaCl and PEG were used as draw solutes with CTA-ES and CTA-NW FO membranes. When using NaCl, JwFO was much higher than it was when using PEG, even at the same osmotic pressure. Moreover, in the case of PEG, the FO flux decreased with increasing molecular weight of PEG. The higher molecular weight of DS led to lower diffusivity, resulting in severe ICP. To investigate the effect of the DS diffusivity on JwFO more quantitatively, we attempted to illustrate the theoretical lines calculated from eqs 4 (NaCl case) and 10 (PEG cases) by using diffusion coefficients and osmotic pressure data as described above. First, to obtain the S value of the FO membrane, the theoretical calculation was fitted to the JwFO of NaCl by using A and B values measured by preliminary reverse osmosis experiments for each FO membrane. The obtained S values were then used for the theoretical analysis of the PEG data. The obtained S values were 238 and 978 μm for CTA-ES and CTANW, respectively. These S values were higher than the respective membrane thicknesses (about 50 μm for CTA-ES and about 100 μm for CTA-NW).2 The intrinsic membrane characteristics of the FO membranes are summarized in Table 3. The detailed RO experimental data are shown in the Supporting Information. Here, the B value for the calculation of PEG data was assumed to

11 this study 16 12 16 this study this study

The data were obtained from the literature.14,42

constant. However, the diffusion coefficient depends on both the molecular weight and the concentration.40 Therefore, their concentration dependences on the diffusion coefficients of NaCl (DNaCl) and PEG (DPEG) were obtained from the literature.42,43 In the case of NaCl, the DNaCl at 298 K varied from 5.30 × 10−6 to 5.77 × 10−6 m2 h−1 when the NaCl concentration changed from 0.0001 to 5.4 mol L−1.43 Here, we used 5.30 × 10−6 m2 h−1 as the DNaCl value in all concentration cases because DNaCl seemed to be E


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obtained using CDS,m. The calculation protocol is shown in Figure 6. In this way, the calculation was repeated until the deviations of both JwFO and DPEG at the CDS,m became less than 0.1%. The calculated results from eq 4 obtained from the van’t Hoff equation and from eq 10 from the virial expansion equation are shown in Figure 5. The calculated results for NaCl from eq 4 agreed with the experimental data because the S values were fitted. The results calculated using eq 10 and the obtained S value without fitting parameters were also in good agreement for the different molecular weights of PEG. Therefore, although the DS types were different, the FO fluxes can be expressed by using the same intrinsic parameters of the FO membrane. The FO flux data agreed with the calculation data in two membrane cases (Figure 5a,b). This agreement suggests that ICP mainly depends on the diffusivity in the porous membrane, and the behavior can be estimated by careful consideration of the osmotic pressure and diffusion coefficient at the active layer surface. The theoretical agreements allowed us to predict the relationship between the molecular weights of the DS and FO performance quantitatively. Recently, there have been numerous reports about DSs with different molecular weights for FO applications. Different types of DSs recently reported in the literature10−14,16,47 are summarized in Table 4. The diffusion coefficients were obtained from the literature14,43 or estimated by using the Wilke−Chang equation,48 in which the molar volume of DS was calculated by additive group contribution methods.49 In this table, the concentration dependence on the DDS was not considered for simplicity. To determine the effect of the DS molecular weight on the FO flux, FO fluxes for DSs with PEG molecular weights of 200, 600, 3000, and 8300 were predicted by using a virial expansion equation. The calculations were done for FO flux behavior operating in AL-FS mode with an osmotic driving force of 30 bar. Recent developments25,50−55 for FO membranes have achieved higher active layer characteristics (A values, 0.25−3.9 LMH/bar) and lower support layer characteristics (S values, 107−789 μm). However, there is still a lack of knowledge about the target membrane characteristics for novel DSs. The simulated results with different FO membrane characteristics are shown in Figure 7. Figure 7a,b shows the A and S value dependences on the FO flux, respectively. The FO flux increased with increasing A value and decreasing S value. The FO flux dramatically decreased with increasing molecular weight of PEG. When using PEG 200 as the DS, the A value and S value dependences on FO flux are relatively high, whereas when using PEG 2000 as the DS, the A value and S value dependences on the FO flux decreased. Therefore, to improve the FO membrane performance when using highmolecular-weight DSs, improvement of the A values and S values is not very effective. To achieve high FO performance for polymeric DSs, additional research on FO membranes is required. A doubleactive-layer FO membrane56 or a wholly active layer FO membrane57 would be suitable research directions for FO desalination technology using novel DSs. These analytical calculations are promising as a useful index to designing not only FO membrane characteristics but also various types of DSs.

Figure 7. Predicted FO flux when using different molecular weight of PEGs. (a) Effect of A value on FO flux with same S value of 978 μm. (b) Effect of S value on FO flux with same A value of 4.0 LMH/bar. The osmotic driving force for the calculation was 30 bar.

be zero, as mentioned above. However, the smaller organic molecules such as PEG 200, one would have reverse diffusion. To justify this assumption, we also measured the reverse diffusion of PEG 200, the smallest molecule in the FO flux measurement, by FO test. The experimental details were shown in the Supporting Information. The reverse diffusion of PEG 200 was about 6 g−2 h−1 ,and this value was similar to that of NaCl (2.8 g−2 h−1).46 In addition, the PEG 200 leakage from DS to FS was less than 0.1% after FO test for 30 min. This result also supported the idea that the PEG leakage could be negligible in this study. However, if we measure the FO flux in AL-DS orientation, then we should consider the reverse diffusion more carefully for the theoretical calculation of FO flux. To obtain JwFO for the PEGs, we used a convergent calculation method. The DPEG at the support layer surface [CDS,s (= CDS,b)] was first inserted into eq 10, and then the obtained JwFO was subsequently used for the calculation of DPEG at the CDS,m using eq 11. After that, JwFO was again calculated by using the DPEG

4. CONCLUSIONS In this study, we investigated the effect of DS molecular weight on FO performance by using NaCl and PEGs with different molecular weights as model DSs. The FO tests revealed that the FO flux dramatically decreased with increasing molecular weight of the DS. This flux reduction was due to severe ICP, which F


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Industrial & Engineering Chemistry Research Greek Letters

originated from the lower diffusivity of the DS molecules. A reliable flux analysis method based on the virial expansion equation was conducted for the calculation of FO flux specifically for the polymeric DSs. The calculated results agreed well with the experimental results obtained using the same intrinsic membrane parameters, which allowed us to predict the dependence of DS molecular weight on FO performance more quantitatively. To clarify the effects of the A and S values of the FO membrane, the relationship between FO flux and the molecular weight of DS was calculated for different FO membrane characteristics. The calculated results are promising as a useful index for designing FO membranes and estimating the FO process when using novel DSs.

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α = parameter in eq 11 for the calculation of D, m2 h−1 wt %−1 β = parameter in eq 11 for the calculation of D, m2 h−1 wt %−2 ε = porosity of the support layer τ = tortuosity of the support layer π = osmotic pressure, bar Subscripts

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ASSOCIATED CONTENT

REFERENCES

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S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.iecr.5b01960. Water permeability and salt permeability of the FO membranes used in this study as measured by RO tests. (PDF)

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DS = draw solution side FS = feed solution side b = at bulk s = at surface

AUTHOR INFORMATION

Corresponding Author

*Tel./Fax: +81-78-803-6180. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This research was funded by a grant from the Ministry of Education, Culture, Sports, Science and Technology (MEXT) for the Regional Innovation Strategy Support Program of JAPAN, and partly supported by Grants-In-Aid from the Special Coordination Funds for Promoting Science and Technology, Creating of Innovation Centers for Advanced Interdisciplinary Research Areas (Innovative Bioproduction, Kobe) from the Ministry of Education, Culture, Sports, Science and Technology, Japan.

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NOMENCLATURE A = water permeability, L m−2 h−1 bar−1 A2 = second virial coefficient, bar L2 g−2 A3 = third virial coefficient, bar L3 g−3 B = DS permeability of the active layer, L m−2 h−1 C = concentration of DS, g L−1 D = mutual diffusion coefficient of DS, m2 h−1 D0 = diffusion coefficient at infinite dilution, m2 h−1 i = van’t Hoff coefficient Js = permeate flux of DS, g m−2 h−1 JwFO = water flux in FO, L m−2 h−1 m = osmolality, mol kg−1 Msalt = molecular weight of salt, g mol−1 Mpolymer = molecular weight of polymer, g mol−1 PDS‑in = inlet pressure of DS, bar PFS‑in = inlet pressure of FS, bar R = gas constant, L bar K−1 mol−1 R2 = determination coefficient S = structure parameter of the support layer, μm T = thickness of the support layer, μm T = temperature, K G


Article

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