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Forward osmosis: Definition and evaluation of FO water transmission coefficient
Journal of Water Process Engineering 20 (2017) 106–112
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Forward osmosis: Definition and evaluation of FO water transmission coefficient
MARK
⁎
Kang Ronga, , Tian C. Zhanga, Tian Lib a b
Civil Engineering Department, University of Nebraska-Lincoln at Omaha campus, Omaha, NE, 68182-0178, United States Department of Plant Protection, Southwest University, 400715, PR China
A R T I C L E I N F O
A B S T R A C T
Keywords: Forward osmosis Transmission coefficient Osmotic reflection coefficient Osmotic pressure difference Water permeability coefficient
Forward Osmosis (FO) usually has a measured water flux (Jw,exp) much smaller than its theoretical water flux (Jw,theoretical); the discrepancy between Jw,exp and Jw,th increases at a higher theoretical osmotic pressure difference (Δπtheoretical). Such discrepancy has been explained by concentration polarization (CP) and membrane resistance, together with an osmotic reflection coefficient (σ). However, it is not clear how to link the discrepancy or σ with FO performance and process optimization in different FO systems. In this study, a FO water transmission coefficient was defined as ηWT = Jw,exp/Jw,theoretical. The procedure was developed for determining ηWT and A (water permeability coefficient) with a static FO system. Results showed the relationship between ηWT and bulk solution concentration difference as per log ηWT = a•log(CDB − CFB) + b for different FO systems. This study also evaluated the difference between σ and ηWT.
1. Introduction The forward osmosis (FO) process happens spontaneously, with the driving force being provided by the osmotic pressure difference (Δπ) between a draw solution (DS) and feed solution (FS). It has been found that FO usually has an experimentally measured FO water flux, Jw,exp much smaller than the theoretical FO water flux, Jw,theoretical. For most FO processes, Jw,exp/Jw,theoretcial is about 5–90% at a water flux of 2 gal/ ft2 d (3.4 L/m2 h) and 0.5–10% at 200 gal/ft2 d (340 L/m2 h, an economically viable flux) [1]. Many studies showed a non-linear dependence of Jw,exp on the theoretical Δπ ( = ΔπTheoretical) [1–6]; the discrepancy between Jw,exp and Jw,theoretcial appears to increase at a higher ΔπTheoretical, indicating a symptom of “self-limiting flux behaviour” [3]. Historically, the discrepancy between Jw,exp and Jw,theoretical has been explained by the departure of the FO membrane from perfect semipermeability [2,5,7–12], membrane-induced concentration polarization (CP) [13–16,6,17,1], reverse solute flux [2], and FO membrane resistance [4,18]. The current understanding is that, in the FO process, CP reduces the solute concentration difference across the membrane, thereby lowering ΔπTheoretical to effective Δπ (i.e., Δπeff) [3,16,15,6,17,1]. Usually, internal CP (ICP) is believed to be the major reason for the significant reduction of ΔπTheoretical, while external CP (ECP) is a minor reason for such reduction [19,5]. Models have been developed to describe osmotic flow through porous membranes [9,11,20–24] and to predict FO
⁎
performance (e.g., water flux and reverse salt flux) by using parameters (e.g., A and B–respective water and solute permeability coefficient, S−the membrane structural parameter) of the FO membrane and draw solution diffusivity of different FO systems [25,19,26,5]. Recently, it was reported that the effects of CP are not enough to explain the low water fluxes generated by some solutes (e.g., urea and ethylene glycol) [2]; incorporating a reflection coefficient σ into the calculation of the coupling effects between the water and solute fluxes within the active layer of the membrane is needed [2,4]. Ref. [4] showed that the low Δπeff in FO processes resulted from a serious leakage of draw solutes from DS to FS due to the membrane sublayer structure, which is the origin of CP in the FO mode. Ref. [18] reported that the low Jw,exp mainly stems from the FO membrane resistance–the low A value. Despite these studies, a knowledge gap exists, i.e., it is essentially unknown how to evaluate the discrepancy between Jw,exp and Jw,theoretical with respect to the performance of FO processes operating at different FO configurations and conditions. Therefore, there is a need to establish a new parameter for one to look into FO system performance in terms of osmotic efficiency and its calculation. This study was conducted to fill this knowledge gap. In this study, the authors first defined a FO water transmission coefficient ηWT ( = Jw,exp/Jw,theoretical), and then conducted the study to: 1) find the relationship between ηWT and solute concentration in different FO systems via experiments and an analysis of data previously reported; 2) predict (with the relationship developed) FO water flux and FO
Corresponding author at: Civil Engineering Department, University of Nebraska-Lincoln at Omaha campus, Omaha, NE, 68182-0178, United States. E-mail addresses: [email protected] (K. Rong), [email protected] (T.C. Zhang), [email protected] (T. Li).
http://dx.doi.org/10.1016/j.jwpe.2017.10.003 Received 19 June 2017; Received in revised form 3 October 2017; Accepted 7 October 2017 2214-7144/ © 2017 Elsevier Ltd. All rights reserved.
Journal of Water Process Engineering 20 (2017) 106–112
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Here, ηWT has a physical meaning similar to the transmission coefficient defined in physics and electrical engineering [28]. ηWT is the ratio of actual FO flux (mass) passing through the FO membrane (Jw,exp) to the maximum possible water flux (mass) (Jw,theoretical) passing through the membrane in an imaginary membrane system that has no FO effects at all (i.e., the differences of chemical potential between DS and FS, Δμ = 0) but with an applied ΔP ( = Δπtheoretical). While introducing ηWT may have several additional implications (see discussions below), results of this study demonstrate that we can use Eqs. (4–6) to evaluate ηWT–the discrepancy between Jw,exp and Jw,theoretical–in different FO systems under different configurations and operating conditions.
performance in different FO systems under different conditions; and 3) evaluate the difference between ηWT and σ as well as the related implications. 2. Materials and methods 2.1. Definition of σ and ηWT By convention, FO flux is given by Eq. (1) [12]:
JW = A•(σΔπ − ΔP)
(1)
where Jw = the FO water flux, L/m2 h (LMH); A = membrane water permeability coefficient, m/s-pa; σ = osmotic (or Staverman) reflection coefficient, unitless; ΔP = applied hydraulic pressure, Pa. Δπ = the osmotic pressure difference between DS and FS. It is important to remember that when Staverman defined σ in Eq. (1), he assumed that the fluid on either side of the membrane is completely mixed so that the pressure, potential, and composition (or anything) of the liquid is uniform. In other words, no CP was considered by [12]. As a result, Δπ = πDB − πFB = πDM − πFM with πDB (πFB) being π of the bulk of draw solution (feed solution) and πDM (πFM) being π at the solutionactive layer interface of the DS (FS) side. In this study, we defined Δπtheoretical = πDB − πFB, which is different from Δπeff = πDM − πFM [1]. Δπtheoretical, also called thermostatic Δπ by Ref. [12], can be calculated with Van’t Hoff osmotic pressure equation [27,13,5,1]. Up to now, there have been two major ways to define σ. Way 1 is to define σ as per Eq. (1) and such σ is named as σ1 in this study thereafter to avoid the possible confusion. With way 1, one can find σ1 via σ1 = Jw,exp/AΔπtheoretical at ΔP = 0 with Jw,exp = the experimental measured FO water flux [10,20] or σ1 = ΔP/Δπtheoretical at Jw = 0 [9]. Because CP always exists in the membrane systems and the actual driving force is always lower than the theoretical one, the concept of Δπeff = πDM − πFM was introduced [1] and was used widely in the literature to define σ (called σ2 thereafter)–Way 2, that is, σ2 = Δπexp/ Δπeff with Δπexp = the experimentally measured Δπ [1] or σ2 = Jw,exp/ A(πDM − πFM) [2]. In this way, we have [1,2,5]:
2.2. FO system and measurement of FO flux and water head In this study, the authors chose a static FO system, i.e., without mixing in both the FS and DS chamber, and operated it with both the pressure-retarded osmosis (PRO) and FO mode (i.e., the PRO mode is DS facing the active layer while the FO mode is DS facing the supporting layer). The reasons for using a static FO system in this study are: 1) under dynamic conditions it is hard to acquire the real driving force (Δπexp), not Δπeff, if a countercurrent FO system is used, while it can be easily observed in a static FO system through the measurement of water head. Water head is a necessary parameter for determining the water transmission coefficient. Thus, the static configuration offers an intrinsic advantage over cross-flow design; 2) it is easy to actually measure water flux in a static FO system under different conditions (e.g., DS, FS) and orientations of FO membrane; and 3) it is easier to develop a standard testing procedure, based on the static FO system, for testing the important parameters (e.g., A and ηWT, see below) of different FO membranes for comparative purposes. In this study, the static FO system (reactor) is made of two transparent plexiglass chambers (Fig. 1), with an effective inner diameter of 70 mm. In the middle of the two chambers lies a semi-permeable membrane (area = ∼38.5 cm2). The upper chamber (depth adjustable but fixed as 25.4 mm in this study) was filled with FS. The FS was either deionized water (DI) or a low salt concentration solution. The lower chamber (67 mm in depth) was filled with DS. CaCl2 and NaCl were used as DSs, respectively, with a concentration of 0.1, 0.5, 1.0 and 2.0 M. The overflow port and DS outlet are necessary to keep the membrane at the same position. By linking the DS outlet pipe with a monometer (i.e., a vertical glass tube, diameter = 3 mm) and considering the water level at the overflow port of the FS chamber to be the datum, we can measure the water head difference (ΔHexp) between the two chambers as a function of time or at the steady-state condition (SSC). In this study, if the difference between the two FO water volumes
Jw,exp = AΔπexp = Aσ2Δπeff = Aσ2(πDM − πFM) (2) To use Eq. (2), one needs to correct Δπeff from Δπtheoretical with a mass transfer coefficient, k and Jw,exp. For example, in a rectangular channel [5]:
k=
Sh × D Re•Sc•dh 0.33 , Sh = 1.85 × ( ) (laminar flow)or Sh dh L
= 0.04Re 0.75Sc0.33 (turbulent flow)
(3)
Where Re = the Reynolds number; Sc = the Schmidt number; D = the solute diffusion coefficient; dh = the hydraulic diameter; and L = the length of the channel. These parameters are case specific and are very difficult to obtain for different FO systems or for the same FO system but operated at different conditions (e.g., Re changes with flow velocity). Obviously, the current challenges are that Eq. (2) is valid only if complete mixing exists in the two chambers (i.e., Δπtheoretical = Δπeff), and Eq. (2) is not easy to use for different FO systems. Thus, in this study, we officially define a new coefficient–FO water transmission coefficient, ηWT:
ηWT = JW, exp/JW, theoretical
(4)
and further define:
JW, theoretical = AΔπtheoretical at ηWT = 1
Fig. 1. The schematic diagram of the FO system. The FO system is similar to Ref. [7] and the same as Refs. [1] and [3] but without impeller or magnetic mixing. A burette with a 50 mL volume (not shown) can be used to measure water flux (Jw,exp). A vertical glass tube connected to draw solution outlet can be used to measured water head difference (ΔHexp). Note that two such systems are needed to measure both Jw,exp and ΔHexp at the same time.
(5)
We then have:
JW, exp = AΔπ exp = AηWT Δπtheoretical and ηWT =
Δπexp Δπtheoretical
(6) 107
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collected in a 1 h period is less than 0.5 mL, we considered the FO system reached SSC, while pseudo-SSC means the system is very close to SSC. Usually, it would take ∼30 min to reach pseudo-SSC, but we waited ∼10 h for collecting data at SSC. The observed water head difference can be used to calculate the osmotic pressure difference ( = Δπexp) between the two chambers (ΔHexp (m) = 10.1972Δπexp (bar)) [29]. In this study, we defined Δπexp as the Δπ drives the measured FO flux in the FO system, which was measured at the precision of ± 0.5 mm under different tests conditions. By collecting the FO flow rate drained from the DS outlet with a titration burette, we can measure the actual FO water flux, Jw,exp at the precision of ± 0.5 mL/has a function of time and different test conditions. Experiments were conducted in both the PRO and FO mode. The FO membrane used in this study was provided by Hydration Technologies, Inc. (HTI) (Albany, OR), and it is a cartridge membrane (thickness = ∼30−50 μm) made of cellulose triacetate with an embedded polyester screen mesh. FO membranes were soaked in DI water before used. Different concentrations of DSs were prepared in advance and stored in room temperature (∼ 24 °C). To do the test, the FO membrane was put into the reactor; then DS was added into the lower chamber; then FS (DI water or DI water + salt with a lower concentration) was added into the upper chamber to the level of the overflow port. The time courses of Jw,exp or ΔHexp were then measured. After 10 h reached SSC, and then, Jw,exp or ΔHexp were measured every 1 h. Δπexp was then calculated with ΔHexp (m) = 10.1972Δπexp (bar). It should be noticed that, in a static FO system, water flux and water head cannot be measured at the same time in one single static FO system, because water head cannot be measured when water flux is being measured. In order to gain water flux and the corresponding water head, two parallel experiments were conducted under the same operation conditions: one reactor was for the measurement of water flux and the other one for water head measurement. Because of this setup, the reactor for measuring FO water flux always had a zero applied hydraulic pressure (i.e., ΔP = 0 in Eq. (1)). In addition, the measured ΔHexp of the static FO system at SSC in all of the tests conducted in this study (8 sets total) were between 0.14 and < 1 m (except one ΔHexp = 1.24 m, see Table S1 in Supplementary Materials (SM)); the corresponding FO water volumes were between 9.9 × 10−7 and 7.1 × 10−6 m3 (except one = 8.8 × 10−6 m3), which is only 0.38−2.7% (except one = 3.4%) of the volume of the draw solution chamber (=2.6 × 10−4 m3), indicating that the concentration of the draw solution during the tests was essentially a constant. Therefore, the steady state equation (Eq. (2)) can be used for calculation of A via Jw,exp and ΔHexp obtained under SSC.
Fig. 2. Δπexp vs. Jw,exp, both measured with the static FO system. Test conditions shown in Table S1: membrane orientations = either the PRO or FO mode; DS = 0.1, 0.5, 1 and 2 M CaCl2 or NaCl; FS = DI water or 0.1 M CaCl2 or NaCl.
logηWT vs. log(CDB – CFB); and ηWT, CDB and CFB are defined as before. Eq. (7) is confirmed with data from previous studies obtained from dynamic FO systems with different configurations, e.g., countercurrent (flat-sheet membrane) FO systems (tests 9–17 in Table S2) or completely-stirred tank reactor (CSTR) FO systems with mixing or intensive stirring (test 18 in Table S2) and from FO systems with HTI (Tables S1 and S2) or other non-HTI FO membranes (Table S3). As the average R2 of tests 9–18 is 0.972, the relationship between logηWT and log(CDB – CFB) holds as Eq. (7) for different solutes and experimental conditions, even though parameters a and b may change (see Fig. 4). Eq. (7) is a new relationship found in this study. The Van’t Hoff equation is shown in Eq. (8) [27,13,5,1]:
Δπ = i•Φ•R•T•ΔC
(8)
where i = number of ions produced during dissociation of solute, unitless; Φ = osmotic coefficient, 1, unitless (Van’t Hoff equation is suitable for use when DS and FS concentration are low, Φ then is 1); ΔC = concentration difference, mol/L; R = universal gas constant, 0.083145 L%bar/(moles·K); and T = absolute temperature, K. Van’t Hoff equation is used in our study, because for a relatively dilute solutions the osmotic pressure is proportional to solution concentration [5]. As indicated by Eq. (8), parameter a in Eq. (7) is linked with DS and FS concentration for sure, but it may also reflect the FO membrane’s nature to absorb solute and the associated solute-solvent interaction within the FO membrane (Yuan and Zhang 2017), which deserves more studies in the future. Parameter b corresponds to logηWT when the DS concentration is 1 M; b is higher when there is mixing (Fig. 4 vs. Fig. 3) or the FO is operated in the PRO mode (tests 1, 3, 5 7 vs. 2, 4, 6, 8 in Fig. 3 and Table S1). However, it cannot prove statistically (i.e. t-test failed) that b is lower when the draw solute is metal ions of a higher valence (Fig. 3c vs. b). Thus, FO performance can be evaluated by Eq. (7), which is associated with ηWT. For example, when using the same FO membrane and draw solution, the higher b is, the more efficient the FO system (the higher ηWT) is (as shown in Tables S1, S2 and S3). The static FO system is easy to use for determining A, ηWT or other parameters (e.g., B–the solute permeability coefficient–as per method reported by Ref. [31]). In previous studies, A was calculated through A = JW/ΔP, and the experiment was conducted under RO conditions [32]. An applied pressure (ΔP) was added at the DS chamber until the permeate rate reached a steady state, and the permeation rate then was normalized by the effective membrane area to yield the water flux, Jw,exp. In our study, however, we calculated A through the spontaneous FO process without extra pressure added on the DS side. The advantage of this method is that A can be obtained under the influence of the real
3. Results and discussions 3.1. Determination of a and relationship of ηWT and CDB – CFB, and their implications Table S1 in SM shows the 8 sets of test conditions and data obtained with the static FO system shown in Fig. 1. Using the data in Table S1, the average A value was found to be 0.88 LMH/bar (Fig. 2), which is very similar to the value ( = 0.8) reported previously [30]. In the following analysis, we consider A = 0.88 LMH/bar for the HTI membrane used. Fig. 3 shows the relationship between ηWT and solute concentration in the DS/FS chamber. Fig. 3a shows that ηWT decreases with an increase in DS concentration in either the PRO or FO mode, and the trend is the same when the FS concentration is 0.1 M of NaCl or CaCl2. For the first time, we found that logηWT and log(CDB – CFB) have a linear relationship as shown in Figs. 3 and 4 and Tables S2 and S3: log ηWT = a•log(CDB − CFB) + b (7) where a and b are the slope and intercept of the straight line, i.e., 108
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Fig. 4. Confirmation of a straight-line relationship between ηWT and (CDB – CFB) with data obtained from countercurrent (tests 9–17) or CSTR FO systems (test 18) as shown in Table S2.
corresponding ηWT, which would provide the information on dynamic nature of the FO system. Fig. S1 (in SM) shows that ηWT reduces with time during the non-SSC period, indicating the CP (both ECP and ICP) effects may take time to be stabilized. Therefore, the efficiency of a FO system could be better understood during the whole procedure by evaluating ηWT. 3.2. Effects of mixing on ηWT In dynamic FO systems like CSTR or countercurrent FO systems (see Table S2), Δπexp can be calculated according to Eq. (2) (Jw,exp = AΔπexp, A = 0.88 LMH/bar). Since Δπtheoretical is available for most of the solute, it is possible to evaluate the effects of mixing or stirring on ηWT ( = Δπexp/Δπtheoretical). Fig. 5 shows that ηWT increases with an increase in mixing intensity (rpm in Fig. 5a and water flow velocity in Fig. 5b), which means Mixing improves FO performance [3,34,5]. It is interesting to compare the ηWT obtained in the static FO system (Table S1) with that obtained from the same FO system but with mixing (the CSTR FO system, Table S4). In the static FO system, test 1 (DS = 0.5 M NaCl) of Table S1 gives ηWT = 0.25%, while that in the CSTR FO system, tests (DS = 0.31 M NaCl but stirring intensity changes) of Table S4 gives ηWT = 32.4% at 200 rpm to 46.3% at 600 rpm. The corresponding Jw,exp is 0.04 LMH in the static FO system as compared with that of 4.0–5.7 LMH (column 2 in Table S4) in the CSTR FO system (> 100 × increase). Similar improvement on ηWT can be observed from Fig. 5b where ηWT changed from 32.3% to 33% when the draw solution concentration is 2.0 M, 52.2% to 54% when the draw solution concentration is 1.0 M, 74.5% to 75.8% when the draw solution concentration is 0.5 M These results indicate that mixing would improve ηWT, Δπexp and thus Jw,exp in different FO systems. We should note that without mixing, ηWT would be very small (e.g. 0.25% shown in Table S1), because the water flux would be very limited without mixing according to our experiment. It is well known that changing stirring or mixing intensity would compress the thickness of the liquid film and the concentration boundary layer, reduce the effect of ECP and thus, improve Jw,exp, leading to a better FO performance at a certain degree. Fig. 5a and b indicate that an increase in mixing or water flow velocity can reduce the CP (mainly ECPs) in a CSTR or countercurrent FO systems. Nevertheless, Fig. 5 also indicates that the increase in ηWT would be level off with an increase in mixing intensity (Fig. 5a) or water flow velocity (Fig. 5b). Beyond a certain mixing intensity or water flow velocity ηWT would reach its maximum value ηWTmax; so does Jw,exp (or the efficiency) of FO system. In other words, under dynamic conditions (i.e. countercurrent system), ECP impact can be reduced by mixing, but such improvement has a limitation as ηWTmax exists, which is a parameter
Fig. 3. Relationship between FO water transmission coefficient, ηWT and draw solute concentration. In general, ηWT decreases with (CDB – CFB) (a) and a relationship of a straight line exists between the two: logηWT = a·log(CDB – CFB) + b for either NaCl (b) or CaCl2 (c) as draw solute (DS) under different conditions (as shown in Table S1). Tests 1–4 used NaCl as DS (0.1–2 M), while tests 5–8 used CaCl2 as DS (0.1–2 M). Tests 1, 2, 5, 6 used DI water as feed solution (FS), while Tests 3, 4 used 0.1 M NaCl and tests 7, 8 used 0.1 M CaCl2 as FS. Tests 1, 3, 5, 7 used the PRO mode, while tests 2, 4, 6, 8 used the FO mode.
driving force (Δπexp) and salt resistance, which both naturally occur under FO process. The FO membrane would have a tendency to absorb the solute within the FO membrane, which otherwise will not be counted by the RO-based method (Yuan and Zhang, 2017). Actually, Fig. 2, in turn, reflects the correctness of Eq. (6), that is, the method of using the static FO system to measure A is feasible and correct, and is much easier to follow. It is interesting to know our static FO system can measure extremely low ηWT (e.g., 0.04% to 0.44% at SSC), which is much lower than 8%, an implied ηWT (but reported as σ1) value of a solute of the size of water extrapolated by Ref. [33]. In fact, one can use the static FO systems to measure both Jw,exp and Δπexp precisely. Moreover, because at the beginning 25–30 min the static FO system is at non-SSC, the static FO system can also be used to study the time courses of Jw,exp and the 109
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large solutes like Albumin, but is non-zero even for very small solutes (e.g., NaCl) [39]. A few studies showed σ1 was concentration-dependent [7,20]. It is not completely clear whether these reported σ1 involved ICP/ECP or other interactions, but it is highly possible they did as eliminating these effects in the FO system is extremely difficult (if not impossible). Thus, these σ1 (or at least some of them) are actually ηWT as per our definition. Since the 1970s, σ1 was determined in synthetic membranes or FO systems to link σ with solute properties [7,8]. Most studies treat σ1 as 1 for self-rejecting membranes (e.g., FO and reverse osmosis, RO) [29,18,5,1]. Modifying Δπtheoretical ( = πDB − πFB) with Δπeff ( = πDM − πFM) to correct ECP and ICP effects is a significant advance in membrane science because it allows one to consider CP effects in FO modeling; models based on σ2 usually can fit the experimental data well (i.e., Jw,exp ≈ Jw,model). Many studies treat σ2 ≈ 1, which may be true for some solutes (e.g., in Test 15 of Table S2, σ2 = 105% for NaCl and = 93% for glucose), but may not be true for others (σ2 = 67% for urea and = 69% for ethylene glycol) [2]. Despite the improvement by introducing σ2 and Δπeff, the difficulty inherited from the concept of σ remains. For example, Δπeff can be significantly different from Δπtheoretical even in the same FO system but operated at different conditions. It is difficult to link the aforementioned discrepancy and σ2 with different FO systems because the related parameters (e.g., those in Eq. (3)) are case specific and difficult to find. In this study, ηWT is proposed for the first time as the ratio of Δπexp/ Δπtheoretical (even though Δπexp/Δπeff has been used widely before). We remark that ηWT ( = Δπexp/Δπtheoretical) ≠ σ2 (=Δπexp/Δπeff) as Δπtheoretical ≠ Δπeff; even though ηWT and σ1 look the same mathematically, ηWT ≠ σ1 because ηWT deals with real world situations (i.e., it includes all factors and conditions of the FO system) while σ1 is only valid under completely mixed conditions. In other words, using Δπexp/ Δπtheoretical may or may not find σ1; rather it always gives ηWT because ICE/ECP and interactions among solute, solvent, and membrane always exist in the FO system. Results of this study indicate that ηWT is much easier to use for different configurations and operating conditions. It is interesting to notice that even though countercurrent FO systems were used in most of the previous studies (Table S2–S4), the actual ηWT of these systems were about 2–78% as compared to the currently consensus understanding (σ ≈ 1). With these results in mind, one should not be surprised to find that in the static FO systems without mixing, ηWTwas about 0.04–0.44% because the effects of ECP and ICP in a static FO system could be much more serious than in a CSTR FO system. With the concept of ηWT, one could see more clearly how much contribution the real driving force Δπexp would make to FO performance. Table S1 shows that ηWT decreases with an increase in DS concentration even though the corresponding Jw,exp increases with an increase in DS concentration. Fig. 5b also indicates that changing the operating condition (e.g., countercurrent velocity within the FO chamber) of an FO system with a higher DS concentration (or a higher CDB – CFB) would have a less improvement in ηWT than that with a lower DS concentration (or a lower CDB – CFB). Results of this study can be used to explain why the discrepancy between Jw,exp and Jw,th increases at a higher Δπtheoretical. Combining Eqs. (6–8), we have:
Fig. 5. Effects of mixing intensity and operating mode on FO water transmission coefficient ηWT. (a) ηWT as a function of mixing intensity (data from Ref. [3]) and are shown in Table S4. Test conditions: DS = 0.31 M NaCl and FS = DI water. (b) ηWT as a function of water flow velocity (22.2–66.7 cm/s) within a countercurrent FO reactor (chamber size: 250, 30, 2 mm for length, width and height) operated with the PRO mode, DS = 0.5, 1.0, 2.0 M NaCl and FS = DI water (data from Ref. [34]).
determining the highest efficiency of a FO system under certain experimental conditions. The high ηWT value ( = ∼78%) shown in Fig. 5b (at 0.5 M NaCl) seems to indicate the concept of ηWTmax is right. On the other hand, the (1 – ηWT) value obtained at SSC may indicate the maximum possible impact of CP (including both ICP and ECP), while the corresponding initial time (e.g., 25–30 min) to reach pseudo-SSC is the time needed for CP effects to build up (see Fig. S1). Therefore, results shown in Fig. 5 indicate it is possible to evaluate ICP and ECP effects with the introduction of ηWT for different FO systems, which warrants future studies. 3.3. Discussion For the first time, we defined ηWT with Eq. (4) and systematically discussed it. Eqs. (4–6) allow us to understand more about ηWT and to link ηWT, Jw,exp ( = FO performance), Jw,theoretical with the conditions of the FO system. The difference between ηWT and σ as well as the related implications deserve more discussions. 3.3.1. Difference between ηWT, σ1 and σ2 In the literature, σ (as in Eq. (1)) has been used to quantify the magnitude of the FO water flux or how “tight” or “leaky” the membrane is to the solutes [12]. Historically (e.g., before 1981), many studies showed the measurement and prediction of σ1 in a biological system and/or environment [21], such as microvascular fluid exchange with the solute being total plasma protein [35], cell membranes [36,37], capillary walls [38]. In these studies, σ1 was used to infer the solute size effects [38] and membrane properties (e.g., the pore size, salt rejection) [20,38]. Based on these σ1 measurements, σ1 was in the range of 0.05–1, and increased as a function of solute size and approaches 1.0 for
Jw,exp =
A•10b•(Δπtheoretical)1 +a (i•Φ•R•T)a
(9)
Using the data shown in Table S2, we have Fig. 6 below. Because a usually is negative (Tables S1–S4), (1 + a) < 1. Therefore, Eq. (9) indicates the non-leaner nature of Jw,exp as a function of Δπtheoretical, which explains why the discrepancy between Jw,exp and Jw,theoretical appears to increase at a higher ΔπTheoretical as shown in Fig. 6. Moreover, Table S2–S4 indicate that for countercurrent FO systems, ηWT is relatively high (e.g., 2–78%), but the values of Jw,exp are consistently 110
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Fig. 6. Relationship between Δπtheoretical and Jw,exp or Jw,theoretical as per Eq. (9) and data in Table S2. Note: For the data from Table S1, the Jw,exp is too small compared to Jw,theoretical. Thus, all the Jw,exp is completely on the x-axis, while Jw,theoretical is still along the line of Jw,theoretical vs. Δπtheoretical. Therefore, no results from Table S1 are shown here.
procedure for determining ηWT and A with a static FO system, and found a linear relationship between logηWT and log (CDB – CFB) for FO systems operating at different configurations and conditions. Because all measured FO water fluxes reported in the literature belong to Jw,exp, and such a Jw,exp is driven by the real driving force Δπexp, not Δπeff as most studies indicated, the method developed in this study allows one to link together the real measured water flux (Jw,exp), real driving force (Δπexp), theoretical driving force (ΔπTheoretical), FO water transmission coefficient ηWT, concentrations of the bulk of DS and FS, and the membrane water permeability coefficient, A. It allows people to understand and compare the efficiency of different FO systems based on ηWT. In addition, one can predict FO water flux and FO performance in different FO systems under different conditions using logηWT = alog (CDB – CFB) + b and to evaluate the impacts of different experimental conditions on ηWT and implications related to ηWT. One should treat ηWT as an indicator of the departure of the FO system from its perfectibility instead of from FO membrane’s perfect semipermeability alone.
low, meaning that the low Jw,exp mainly stems from the FO membrane resistance–the low A value (as Jw,exp = AηWTΔπtheoretical), which confirms the previous report [18]. However, water flux with a higher ηWT is greater than water flux with a lower ηWT. 3.3.2. Significance and implications Theoretically, one may not be able to determine the exact σ1 experimentally because of the requirement of completely mixing as Staverman assumed in his work. σ2 and Eq. (2) are not easy to use for different FO systems [13,2,5,1]; in order to get σ2, the solution concentration at the membrane surface needs to be known, which is always changing with time. Overall, results of this study (together with previous studies) demonstrate that in the FO process ηWT is more convenient to use as ηWT is a function of the FO system (i.e., configuration and operating conditions), time, DS concentration, molecular size/ shape/charge, and FO membrane properties. Results of this study indicate that ηWT reflects the efficiency of the FO system, and thus, should be viewed as an indicator−a FO water transmission coefficient–to quantify the departure of the FO system from its perfectibility (i.e., Jw,theoretical = A•Δπtheoretical). Therefore, in the future one should always report ηWT with the information on the FO system and experimental conditions. Introducing ηWT potentially brings several advantages to FO study such as: 1) ηWT can be determined for all FO systems; 2) ηWT can link the major FO parameters together, and can be used to evaluate the effectiveness of changing a specific parameter (e.g., FO membrane porosity, thickness) or operation condition (e.g., CDB, CFB, countercurrent velocity) on the performance or the efficiency of the FO system; 3) it is possible to utilize the concepts of ηWT, Δπtheoretical, Δπexp, and σ2 together for detailed studies, e.g., evaluation of the contributions of ICP and ECP to the reduction of FO efficiency and finding Δπeff or σ2 via the experiments with two or more solutes being involved as Δπexp = ηWTΔπtheoretical (Eq. (4)) = σ2Δπeff (definition of σ2). Rong and Zhang (2017) developed a new set of ηWT-based FO models to evaluate ECP, ICP and ηWT changes under different FO systems and experimental conditions, demonstrating the fundamental value of ηWT in membrane science.
Acknowledgements The authors appreciate Dr. Edward G. Beaudry of HTI Inc. for providing the FO membrane used in this study. The authors would like to than Drs. Zhou and Luo of Huazhong University of Science and Technology, China and Mr. Yuan of UNL for providing technical support and useful discussion in this research. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.jwpe.2017.10.003. References [1] K.L. Lee, R.W. Baker, H.K. Lonsdale, Membranes for power generation by pressureretarded osmosis, J. Membr. Sci. 8 (1981) 141–171. [2] J.S. Yong, W.A. Phillip, M. Elimelech, Coupled reverse draw solute permeation and water flux in forward osmosis with neutral draw solutes, J. Membr. Sci. 392–393 (2012) 9–17. [3] A. Zhou, T.C. Zhang, Y. Yuan, Performance of Forward Osmosis Processes under Different Operating Conditions and Draw Solutes, World Environ. Water Resour. Congr. (2012) 808–817. American Society of Civil Engineers, 2012, http:// ascelibrary.org/doi/abs/10.1061/9780784412312.083 . (Accessed November 7, 2016).
4. Conclusions For the first time, we defined ηWT as Δπexp/Δπtheoretical, proposed the 111
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membranes to non-electrolytes, Biochim. Biophys. Acta 27 (1958) 229–246. [23] P.M. Ray, On the theory of osmotic water movement 1, Plant Physiol. 35 (1960) 783–795. [24] K.S. Spiegler, Transport processes in ionic membranes, Trans. Faraday Soc. 54 (1958) 1408–1428. [25] T. Zhang, R. Surampalli, S. Vigneswaran, R. Tyagi, S. Leong Ong, C. Kao, Membrane Technology and Environmental Applications, American Society of Civil Engineers, 2012. [26] A. Achilli, T.Y. Cath, A.E. Childress, Selection of inorganic-based draw solutions for forward osmosis applications, J. Membr. Sci. 364 (2010) 233–241. [27] Y. Wang, M. Zhang, Y. Liu, Q. Xiao, S. Xu, Quantitative evaluation of concentration polarization under different operating conditions for forward osmosis process, Desalination 398 (2016) 106–113. [28] D.J. Griffiths, Introduction to Quantum Mechanics, 2nd ed., Pearson Prentice Hall, 2004. [29] H.K. Shon, S. Phuntsho, T.C. Zhang, R.Y. Surampalli, Forward Osmosis: Fundamentals and Applications, ASCE Reston, Virginia, 2015. [30] T.Y. Cath, M. Elimelech, J.R. McCutcheon, R.L. McGinnis, A. Achilli, D. Anastasio, A.R. Brady, A.E. Childress, I.V. Farr, N.T. Hancock, J. Lampi, L.D. Nghiem, M. Xie, N.Y. Yip, Standard methodology for evaluating membrane performance in osmotically driven membrane processes, Desalination 312 (2013) 31–38, http://dx.doi. org/10.1016/j.desal.2012.07.005. [31] W.A. Phillip, J.S. Yong, M. Elimelech, Reverse draw solute permeation in forward osmosis: modeling and experiments, Environ. Sci. Technol. 44 (2010) 5170–5176. [32] H.K. Lonsdale, B.P. Cross, F.M. Graber, C.E. Milstead, Permeability of cellulose acetate membranes to selected solutes, J. Macromol. Sci. Part B 5 (1971) 167–187. [33] F.-R.E. Curry, C.C. Michel, A fiber matrix model of capillary permeability, Microvasc. Res. 20 (1980) 96–99. [34] C.H. Tan, H.Y. Ng, Modified models to predict flux behavior in forward osmosis in consideration of external and internal concentration polarizations, J. Membr. Sci. 324 (2008) 209–219. [35] E.H. Starling, On the adsorbtion of fluid from interstitial spaces, J. Physiol. (1896) 312–326. [36] A.E. Hill, Osmotic flow in membrane pores, in: K.W.J, J. Jarvik (Eds.), International Review of Cytology, Academic Press, 1995, pp. 1–42. [37] D.A. Goldstein, A.K. Solomon, Determination of equivalent pore radius for human red cells by osmotic pressure measurement, J. Gen. Physiol. 44 (1960) 1–18. [38] F.E. Curry, C.C. Michel, J.C. Mason, Osmotic reflextion coefficients of capillary walls to low molecular weight hydrophilic solutes measured in single perfused capillaries of the frog mesentery, J. Physiol. 261 (1976) 319–336. [39] M.R. Kellen, A Model for Microcirculatory Fluid and Solute Exchange in the Heart Thesis, Thesis, (2002).
[4] J. Su, T.-S. Chung, Sublayer structure and reflection coefficient and their effects on concentration polarization and membrane performance in FO processes, J. Membr. Sci. 376 (2011) 214–224. [5] J.R. McCutcheon, M. Elimelech, Influence of concentrative and dilutive internal concentration polarization on flux behavior in forward osmosis, J. Membr. Sci. 284 (2006) 237–247. [6] G.T. Gray, J.R. McCutcheon, M. Elimelech, Internal concentration polarization in forward osmosis: role of membrane orientation, Desalination 197 (2006) 1–8. [7] W.S. Opong, A.L. Zydney, Effect of membrane structure and protein concentration on the osmotic reflection coefficient, J. Membr. Sci. 72 (1992) 277–292. [8] J.S. Schultz, R. Valentine, C.Y. Choi, Reflection coefficients of homopore membranes: effect of molecular size and configuration, J. Gen. Physiol. 73 (1979) 49–60. [9] J.L. Anderson, D.M. Malone, Mechanism of osmotic flow in porous membranes, Biophys. J. 14 (1974) 957–982. [10] A. Mauro, Some properties of ionic and nonionic semipermeable membranes, Circulation 21 (1960) 845–854. [11] A. Mauro, Nature of solvent transfer in osmosis, Science 126 (1957) 252–253. [12] A.J. Staverman, The theory of measurement of osmotic pressure, Recl. Trav. Chim. Pays-Bas. 70 (1951) 344–352. [13] N.-N. Bui, J.T. Arena, J.R. McCutcheon, Proper accounting of mass transfer resistances in forward osmosis: improving the accuracy of model predictions of structural parameter, J. Membr. Sci. 492 (2015) 289–302. [14] B.S. Chanukya, S. Patil, N.K. Rastogi, Influence of concentration polarization on flux behavior in forward osmosis during desalination using ammonium bicarbonate, Desalination 312 (2013) 39–44. [15] C.Y. Tang, Q. She, W.C.L. Lay, R. Wang, A.G. Fane, Coupled effects of internal concentration polarization and fouling on flux behavior of forward osmosis membranes during humic acid filtration, J. Membr. Sci. 354 (2010) 123–133. [16] Y. Xu, X. Peng, C.Y. Tang, Q.S. Fu, S. Nie, Effect of draw solution concentration and operating conditions on forward osmosis and pressure retarded osmosis performance in a spiral wound module, J. Membr. Sci. 348 (2010) 298–309. [17] J.R. McCutcheon, R.L. McGinnis, M. Elimelech, A novel ammonia—carbon dioxide forward (direct) osmosis desalination process, Desalination 174 (2005) 1–11. [18] J. Su, T.-S. Chung, B.J. Helmer, J.S. de Wit, Understanding of low osmotic efficiency in forward osmosis: experiments and modeling, Desalination 313 (2013) 156–165. [19] S. Zhao, L. Zou, D. Mulcahy, Effects of membrane orientation on process performance in forward osmosis applications, J. Membr. Sci. 382 (2011) 308–315. [20] R.P. Adamski, J.L. Anderson, Solute concentration effect on osmotic reflection coefficient, Biophys. J. 44 (1983) 79–90. [21] G. Bhalla, Osmotic Reflection Coefficient, Thesis, Massachusetts Institute of Technology, 2009 http://dspace.mit.edu/handle/1721.1/51614 . (Accessed November 7 2016). [22] O. Kedem, A. Katchalsky, Thermodynamic analysis of the permeability of biological
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Forward osmosis: Definition and evaluation of FO water transmission coefficient
MARK
⁎
Kang Ronga, , Tian C. Zhanga, Tian Lib a b
Civil Engineering Department, University of Nebraska-Lincoln at Omaha campus, Omaha, NE, 68182-0178, United States Department of Plant Protection, Southwest University, 400715, PR China
A R T I C L E I N F O
A B S T R A C T
Keywords: Forward osmosis Transmission coefficient Osmotic reflection coefficient Osmotic pressure difference Water permeability coefficient
Forward Osmosis (FO) usually has a measured water flux (Jw,exp) much smaller than its theoretical water flux (Jw,theoretical); the discrepancy between Jw,exp and Jw,th increases at a higher theoretical osmotic pressure difference (Δπtheoretical). Such discrepancy has been explained by concentration polarization (CP) and membrane resistance, together with an osmotic reflection coefficient (σ). However, it is not clear how to link the discrepancy or σ with FO performance and process optimization in different FO systems. In this study, a FO water transmission coefficient was defined as ηWT = Jw,exp/Jw,theoretical. The procedure was developed for determining ηWT and A (water permeability coefficient) with a static FO system. Results showed the relationship between ηWT and bulk solution concentration difference as per log ηWT = a•log(CDB − CFB) + b for different FO systems. This study also evaluated the difference between σ and ηWT.
1. Introduction The forward osmosis (FO) process happens spontaneously, with the driving force being provided by the osmotic pressure difference (Δπ) between a draw solution (DS) and feed solution (FS). It has been found that FO usually has an experimentally measured FO water flux, Jw,exp much smaller than the theoretical FO water flux, Jw,theoretical. For most FO processes, Jw,exp/Jw,theoretcial is about 5–90% at a water flux of 2 gal/ ft2 d (3.4 L/m2 h) and 0.5–10% at 200 gal/ft2 d (340 L/m2 h, an economically viable flux) [1]. Many studies showed a non-linear dependence of Jw,exp on the theoretical Δπ ( = ΔπTheoretical) [1–6]; the discrepancy between Jw,exp and Jw,theoretcial appears to increase at a higher ΔπTheoretical, indicating a symptom of “self-limiting flux behaviour” [3]. Historically, the discrepancy between Jw,exp and Jw,theoretical has been explained by the departure of the FO membrane from perfect semipermeability [2,5,7–12], membrane-induced concentration polarization (CP) [13–16,6,17,1], reverse solute flux [2], and FO membrane resistance [4,18]. The current understanding is that, in the FO process, CP reduces the solute concentration difference across the membrane, thereby lowering ΔπTheoretical to effective Δπ (i.e., Δπeff) [3,16,15,6,17,1]. Usually, internal CP (ICP) is believed to be the major reason for the significant reduction of ΔπTheoretical, while external CP (ECP) is a minor reason for such reduction [19,5]. Models have been developed to describe osmotic flow through porous membranes [9,11,20–24] and to predict FO
⁎
performance (e.g., water flux and reverse salt flux) by using parameters (e.g., A and B–respective water and solute permeability coefficient, S−the membrane structural parameter) of the FO membrane and draw solution diffusivity of different FO systems [25,19,26,5]. Recently, it was reported that the effects of CP are not enough to explain the low water fluxes generated by some solutes (e.g., urea and ethylene glycol) [2]; incorporating a reflection coefficient σ into the calculation of the coupling effects between the water and solute fluxes within the active layer of the membrane is needed [2,4]. Ref. [4] showed that the low Δπeff in FO processes resulted from a serious leakage of draw solutes from DS to FS due to the membrane sublayer structure, which is the origin of CP in the FO mode. Ref. [18] reported that the low Jw,exp mainly stems from the FO membrane resistance–the low A value. Despite these studies, a knowledge gap exists, i.e., it is essentially unknown how to evaluate the discrepancy between Jw,exp and Jw,theoretical with respect to the performance of FO processes operating at different FO configurations and conditions. Therefore, there is a need to establish a new parameter for one to look into FO system performance in terms of osmotic efficiency and its calculation. This study was conducted to fill this knowledge gap. In this study, the authors first defined a FO water transmission coefficient ηWT ( = Jw,exp/Jw,theoretical), and then conducted the study to: 1) find the relationship between ηWT and solute concentration in different FO systems via experiments and an analysis of data previously reported; 2) predict (with the relationship developed) FO water flux and FO
Corresponding author at: Civil Engineering Department, University of Nebraska-Lincoln at Omaha campus, Omaha, NE, 68182-0178, United States. E-mail addresses: [email protected] (K. Rong), [email protected] (T.C. Zhang), [email protected] (T. Li).
http://dx.doi.org/10.1016/j.jwpe.2017.10.003 Received 19 June 2017; Received in revised form 3 October 2017; Accepted 7 October 2017 2214-7144/ © 2017 Elsevier Ltd. All rights reserved.
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Here, ηWT has a physical meaning similar to the transmission coefficient defined in physics and electrical engineering [28]. ηWT is the ratio of actual FO flux (mass) passing through the FO membrane (Jw,exp) to the maximum possible water flux (mass) (Jw,theoretical) passing through the membrane in an imaginary membrane system that has no FO effects at all (i.e., the differences of chemical potential between DS and FS, Δμ = 0) but with an applied ΔP ( = Δπtheoretical). While introducing ηWT may have several additional implications (see discussions below), results of this study demonstrate that we can use Eqs. (4–6) to evaluate ηWT–the discrepancy between Jw,exp and Jw,theoretical–in different FO systems under different configurations and operating conditions.
performance in different FO systems under different conditions; and 3) evaluate the difference between ηWT and σ as well as the related implications. 2. Materials and methods 2.1. Definition of σ and ηWT By convention, FO flux is given by Eq. (1) [12]:
JW = A•(σΔπ − ΔP)
(1)
where Jw = the FO water flux, L/m2 h (LMH); A = membrane water permeability coefficient, m/s-pa; σ = osmotic (or Staverman) reflection coefficient, unitless; ΔP = applied hydraulic pressure, Pa. Δπ = the osmotic pressure difference between DS and FS. It is important to remember that when Staverman defined σ in Eq. (1), he assumed that the fluid on either side of the membrane is completely mixed so that the pressure, potential, and composition (or anything) of the liquid is uniform. In other words, no CP was considered by [12]. As a result, Δπ = πDB − πFB = πDM − πFM with πDB (πFB) being π of the bulk of draw solution (feed solution) and πDM (πFM) being π at the solutionactive layer interface of the DS (FS) side. In this study, we defined Δπtheoretical = πDB − πFB, which is different from Δπeff = πDM − πFM [1]. Δπtheoretical, also called thermostatic Δπ by Ref. [12], can be calculated with Van’t Hoff osmotic pressure equation [27,13,5,1]. Up to now, there have been two major ways to define σ. Way 1 is to define σ as per Eq. (1) and such σ is named as σ1 in this study thereafter to avoid the possible confusion. With way 1, one can find σ1 via σ1 = Jw,exp/AΔπtheoretical at ΔP = 0 with Jw,exp = the experimental measured FO water flux [10,20] or σ1 = ΔP/Δπtheoretical at Jw = 0 [9]. Because CP always exists in the membrane systems and the actual driving force is always lower than the theoretical one, the concept of Δπeff = πDM − πFM was introduced [1] and was used widely in the literature to define σ (called σ2 thereafter)–Way 2, that is, σ2 = Δπexp/ Δπeff with Δπexp = the experimentally measured Δπ [1] or σ2 = Jw,exp/ A(πDM − πFM) [2]. In this way, we have [1,2,5]:
2.2. FO system and measurement of FO flux and water head In this study, the authors chose a static FO system, i.e., without mixing in both the FS and DS chamber, and operated it with both the pressure-retarded osmosis (PRO) and FO mode (i.e., the PRO mode is DS facing the active layer while the FO mode is DS facing the supporting layer). The reasons for using a static FO system in this study are: 1) under dynamic conditions it is hard to acquire the real driving force (Δπexp), not Δπeff, if a countercurrent FO system is used, while it can be easily observed in a static FO system through the measurement of water head. Water head is a necessary parameter for determining the water transmission coefficient. Thus, the static configuration offers an intrinsic advantage over cross-flow design; 2) it is easy to actually measure water flux in a static FO system under different conditions (e.g., DS, FS) and orientations of FO membrane; and 3) it is easier to develop a standard testing procedure, based on the static FO system, for testing the important parameters (e.g., A and ηWT, see below) of different FO membranes for comparative purposes. In this study, the static FO system (reactor) is made of two transparent plexiglass chambers (Fig. 1), with an effective inner diameter of 70 mm. In the middle of the two chambers lies a semi-permeable membrane (area = ∼38.5 cm2). The upper chamber (depth adjustable but fixed as 25.4 mm in this study) was filled with FS. The FS was either deionized water (DI) or a low salt concentration solution. The lower chamber (67 mm in depth) was filled with DS. CaCl2 and NaCl were used as DSs, respectively, with a concentration of 0.1, 0.5, 1.0 and 2.0 M. The overflow port and DS outlet are necessary to keep the membrane at the same position. By linking the DS outlet pipe with a monometer (i.e., a vertical glass tube, diameter = 3 mm) and considering the water level at the overflow port of the FS chamber to be the datum, we can measure the water head difference (ΔHexp) between the two chambers as a function of time or at the steady-state condition (SSC). In this study, if the difference between the two FO water volumes
Jw,exp = AΔπexp = Aσ2Δπeff = Aσ2(πDM − πFM) (2) To use Eq. (2), one needs to correct Δπeff from Δπtheoretical with a mass transfer coefficient, k and Jw,exp. For example, in a rectangular channel [5]:
k=
Sh × D Re•Sc•dh 0.33 , Sh = 1.85 × ( ) (laminar flow)or Sh dh L
= 0.04Re 0.75Sc0.33 (turbulent flow)
(3)
Where Re = the Reynolds number; Sc = the Schmidt number; D = the solute diffusion coefficient; dh = the hydraulic diameter; and L = the length of the channel. These parameters are case specific and are very difficult to obtain for different FO systems or for the same FO system but operated at different conditions (e.g., Re changes with flow velocity). Obviously, the current challenges are that Eq. (2) is valid only if complete mixing exists in the two chambers (i.e., Δπtheoretical = Δπeff), and Eq. (2) is not easy to use for different FO systems. Thus, in this study, we officially define a new coefficient–FO water transmission coefficient, ηWT:
ηWT = JW, exp/JW, theoretical
(4)
and further define:
JW, theoretical = AΔπtheoretical at ηWT = 1
Fig. 1. The schematic diagram of the FO system. The FO system is similar to Ref. [7] and the same as Refs. [1] and [3] but without impeller or magnetic mixing. A burette with a 50 mL volume (not shown) can be used to measure water flux (Jw,exp). A vertical glass tube connected to draw solution outlet can be used to measured water head difference (ΔHexp). Note that two such systems are needed to measure both Jw,exp and ΔHexp at the same time.
(5)
We then have:
JW, exp = AΔπ exp = AηWT Δπtheoretical and ηWT =
Δπexp Δπtheoretical
(6) 107
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collected in a 1 h period is less than 0.5 mL, we considered the FO system reached SSC, while pseudo-SSC means the system is very close to SSC. Usually, it would take ∼30 min to reach pseudo-SSC, but we waited ∼10 h for collecting data at SSC. The observed water head difference can be used to calculate the osmotic pressure difference ( = Δπexp) between the two chambers (ΔHexp (m) = 10.1972Δπexp (bar)) [29]. In this study, we defined Δπexp as the Δπ drives the measured FO flux in the FO system, which was measured at the precision of ± 0.5 mm under different tests conditions. By collecting the FO flow rate drained from the DS outlet with a titration burette, we can measure the actual FO water flux, Jw,exp at the precision of ± 0.5 mL/has a function of time and different test conditions. Experiments were conducted in both the PRO and FO mode. The FO membrane used in this study was provided by Hydration Technologies, Inc. (HTI) (Albany, OR), and it is a cartridge membrane (thickness = ∼30−50 μm) made of cellulose triacetate with an embedded polyester screen mesh. FO membranes were soaked in DI water before used. Different concentrations of DSs were prepared in advance and stored in room temperature (∼ 24 °C). To do the test, the FO membrane was put into the reactor; then DS was added into the lower chamber; then FS (DI water or DI water + salt with a lower concentration) was added into the upper chamber to the level of the overflow port. The time courses of Jw,exp or ΔHexp were then measured. After 10 h reached SSC, and then, Jw,exp or ΔHexp were measured every 1 h. Δπexp was then calculated with ΔHexp (m) = 10.1972Δπexp (bar). It should be noticed that, in a static FO system, water flux and water head cannot be measured at the same time in one single static FO system, because water head cannot be measured when water flux is being measured. In order to gain water flux and the corresponding water head, two parallel experiments were conducted under the same operation conditions: one reactor was for the measurement of water flux and the other one for water head measurement. Because of this setup, the reactor for measuring FO water flux always had a zero applied hydraulic pressure (i.e., ΔP = 0 in Eq. (1)). In addition, the measured ΔHexp of the static FO system at SSC in all of the tests conducted in this study (8 sets total) were between 0.14 and < 1 m (except one ΔHexp = 1.24 m, see Table S1 in Supplementary Materials (SM)); the corresponding FO water volumes were between 9.9 × 10−7 and 7.1 × 10−6 m3 (except one = 8.8 × 10−6 m3), which is only 0.38−2.7% (except one = 3.4%) of the volume of the draw solution chamber (=2.6 × 10−4 m3), indicating that the concentration of the draw solution during the tests was essentially a constant. Therefore, the steady state equation (Eq. (2)) can be used for calculation of A via Jw,exp and ΔHexp obtained under SSC.
Fig. 2. Δπexp vs. Jw,exp, both measured with the static FO system. Test conditions shown in Table S1: membrane orientations = either the PRO or FO mode; DS = 0.1, 0.5, 1 and 2 M CaCl2 or NaCl; FS = DI water or 0.1 M CaCl2 or NaCl.
logηWT vs. log(CDB – CFB); and ηWT, CDB and CFB are defined as before. Eq. (7) is confirmed with data from previous studies obtained from dynamic FO systems with different configurations, e.g., countercurrent (flat-sheet membrane) FO systems (tests 9–17 in Table S2) or completely-stirred tank reactor (CSTR) FO systems with mixing or intensive stirring (test 18 in Table S2) and from FO systems with HTI (Tables S1 and S2) or other non-HTI FO membranes (Table S3). As the average R2 of tests 9–18 is 0.972, the relationship between logηWT and log(CDB – CFB) holds as Eq. (7) for different solutes and experimental conditions, even though parameters a and b may change (see Fig. 4). Eq. (7) is a new relationship found in this study. The Van’t Hoff equation is shown in Eq. (8) [27,13,5,1]:
Δπ = i•Φ•R•T•ΔC
(8)
where i = number of ions produced during dissociation of solute, unitless; Φ = osmotic coefficient, 1, unitless (Van’t Hoff equation is suitable for use when DS and FS concentration are low, Φ then is 1); ΔC = concentration difference, mol/L; R = universal gas constant, 0.083145 L%bar/(moles·K); and T = absolute temperature, K. Van’t Hoff equation is used in our study, because for a relatively dilute solutions the osmotic pressure is proportional to solution concentration [5]. As indicated by Eq. (8), parameter a in Eq. (7) is linked with DS and FS concentration for sure, but it may also reflect the FO membrane’s nature to absorb solute and the associated solute-solvent interaction within the FO membrane (Yuan and Zhang 2017), which deserves more studies in the future. Parameter b corresponds to logηWT when the DS concentration is 1 M; b is higher when there is mixing (Fig. 4 vs. Fig. 3) or the FO is operated in the PRO mode (tests 1, 3, 5 7 vs. 2, 4, 6, 8 in Fig. 3 and Table S1). However, it cannot prove statistically (i.e. t-test failed) that b is lower when the draw solute is metal ions of a higher valence (Fig. 3c vs. b). Thus, FO performance can be evaluated by Eq. (7), which is associated with ηWT. For example, when using the same FO membrane and draw solution, the higher b is, the more efficient the FO system (the higher ηWT) is (as shown in Tables S1, S2 and S3). The static FO system is easy to use for determining A, ηWT or other parameters (e.g., B–the solute permeability coefficient–as per method reported by Ref. [31]). In previous studies, A was calculated through A = JW/ΔP, and the experiment was conducted under RO conditions [32]. An applied pressure (ΔP) was added at the DS chamber until the permeate rate reached a steady state, and the permeation rate then was normalized by the effective membrane area to yield the water flux, Jw,exp. In our study, however, we calculated A through the spontaneous FO process without extra pressure added on the DS side. The advantage of this method is that A can be obtained under the influence of the real
3. Results and discussions 3.1. Determination of a and relationship of ηWT and CDB – CFB, and their implications Table S1 in SM shows the 8 sets of test conditions and data obtained with the static FO system shown in Fig. 1. Using the data in Table S1, the average A value was found to be 0.88 LMH/bar (Fig. 2), which is very similar to the value ( = 0.8) reported previously [30]. In the following analysis, we consider A = 0.88 LMH/bar for the HTI membrane used. Fig. 3 shows the relationship between ηWT and solute concentration in the DS/FS chamber. Fig. 3a shows that ηWT decreases with an increase in DS concentration in either the PRO or FO mode, and the trend is the same when the FS concentration is 0.1 M of NaCl or CaCl2. For the first time, we found that logηWT and log(CDB – CFB) have a linear relationship as shown in Figs. 3 and 4 and Tables S2 and S3: log ηWT = a•log(CDB − CFB) + b (7) where a and b are the slope and intercept of the straight line, i.e., 108
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Fig. 4. Confirmation of a straight-line relationship between ηWT and (CDB – CFB) with data obtained from countercurrent (tests 9–17) or CSTR FO systems (test 18) as shown in Table S2.
corresponding ηWT, which would provide the information on dynamic nature of the FO system. Fig. S1 (in SM) shows that ηWT reduces with time during the non-SSC period, indicating the CP (both ECP and ICP) effects may take time to be stabilized. Therefore, the efficiency of a FO system could be better understood during the whole procedure by evaluating ηWT. 3.2. Effects of mixing on ηWT In dynamic FO systems like CSTR or countercurrent FO systems (see Table S2), Δπexp can be calculated according to Eq. (2) (Jw,exp = AΔπexp, A = 0.88 LMH/bar). Since Δπtheoretical is available for most of the solute, it is possible to evaluate the effects of mixing or stirring on ηWT ( = Δπexp/Δπtheoretical). Fig. 5 shows that ηWT increases with an increase in mixing intensity (rpm in Fig. 5a and water flow velocity in Fig. 5b), which means Mixing improves FO performance [3,34,5]. It is interesting to compare the ηWT obtained in the static FO system (Table S1) with that obtained from the same FO system but with mixing (the CSTR FO system, Table S4). In the static FO system, test 1 (DS = 0.5 M NaCl) of Table S1 gives ηWT = 0.25%, while that in the CSTR FO system, tests (DS = 0.31 M NaCl but stirring intensity changes) of Table S4 gives ηWT = 32.4% at 200 rpm to 46.3% at 600 rpm. The corresponding Jw,exp is 0.04 LMH in the static FO system as compared with that of 4.0–5.7 LMH (column 2 in Table S4) in the CSTR FO system (> 100 × increase). Similar improvement on ηWT can be observed from Fig. 5b where ηWT changed from 32.3% to 33% when the draw solution concentration is 2.0 M, 52.2% to 54% when the draw solution concentration is 1.0 M, 74.5% to 75.8% when the draw solution concentration is 0.5 M These results indicate that mixing would improve ηWT, Δπexp and thus Jw,exp in different FO systems. We should note that without mixing, ηWT would be very small (e.g. 0.25% shown in Table S1), because the water flux would be very limited without mixing according to our experiment. It is well known that changing stirring or mixing intensity would compress the thickness of the liquid film and the concentration boundary layer, reduce the effect of ECP and thus, improve Jw,exp, leading to a better FO performance at a certain degree. Fig. 5a and b indicate that an increase in mixing or water flow velocity can reduce the CP (mainly ECPs) in a CSTR or countercurrent FO systems. Nevertheless, Fig. 5 also indicates that the increase in ηWT would be level off with an increase in mixing intensity (Fig. 5a) or water flow velocity (Fig. 5b). Beyond a certain mixing intensity or water flow velocity ηWT would reach its maximum value ηWTmax; so does Jw,exp (or the efficiency) of FO system. In other words, under dynamic conditions (i.e. countercurrent system), ECP impact can be reduced by mixing, but such improvement has a limitation as ηWTmax exists, which is a parameter
Fig. 3. Relationship between FO water transmission coefficient, ηWT and draw solute concentration. In general, ηWT decreases with (CDB – CFB) (a) and a relationship of a straight line exists between the two: logηWT = a·log(CDB – CFB) + b for either NaCl (b) or CaCl2 (c) as draw solute (DS) under different conditions (as shown in Table S1). Tests 1–4 used NaCl as DS (0.1–2 M), while tests 5–8 used CaCl2 as DS (0.1–2 M). Tests 1, 2, 5, 6 used DI water as feed solution (FS), while Tests 3, 4 used 0.1 M NaCl and tests 7, 8 used 0.1 M CaCl2 as FS. Tests 1, 3, 5, 7 used the PRO mode, while tests 2, 4, 6, 8 used the FO mode.
driving force (Δπexp) and salt resistance, which both naturally occur under FO process. The FO membrane would have a tendency to absorb the solute within the FO membrane, which otherwise will not be counted by the RO-based method (Yuan and Zhang, 2017). Actually, Fig. 2, in turn, reflects the correctness of Eq. (6), that is, the method of using the static FO system to measure A is feasible and correct, and is much easier to follow. It is interesting to know our static FO system can measure extremely low ηWT (e.g., 0.04% to 0.44% at SSC), which is much lower than 8%, an implied ηWT (but reported as σ1) value of a solute of the size of water extrapolated by Ref. [33]. In fact, one can use the static FO systems to measure both Jw,exp and Δπexp precisely. Moreover, because at the beginning 25–30 min the static FO system is at non-SSC, the static FO system can also be used to study the time courses of Jw,exp and the 109
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large solutes like Albumin, but is non-zero even for very small solutes (e.g., NaCl) [39]. A few studies showed σ1 was concentration-dependent [7,20]. It is not completely clear whether these reported σ1 involved ICP/ECP or other interactions, but it is highly possible they did as eliminating these effects in the FO system is extremely difficult (if not impossible). Thus, these σ1 (or at least some of them) are actually ηWT as per our definition. Since the 1970s, σ1 was determined in synthetic membranes or FO systems to link σ with solute properties [7,8]. Most studies treat σ1 as 1 for self-rejecting membranes (e.g., FO and reverse osmosis, RO) [29,18,5,1]. Modifying Δπtheoretical ( = πDB − πFB) with Δπeff ( = πDM − πFM) to correct ECP and ICP effects is a significant advance in membrane science because it allows one to consider CP effects in FO modeling; models based on σ2 usually can fit the experimental data well (i.e., Jw,exp ≈ Jw,model). Many studies treat σ2 ≈ 1, which may be true for some solutes (e.g., in Test 15 of Table S2, σ2 = 105% for NaCl and = 93% for glucose), but may not be true for others (σ2 = 67% for urea and = 69% for ethylene glycol) [2]. Despite the improvement by introducing σ2 and Δπeff, the difficulty inherited from the concept of σ remains. For example, Δπeff can be significantly different from Δπtheoretical even in the same FO system but operated at different conditions. It is difficult to link the aforementioned discrepancy and σ2 with different FO systems because the related parameters (e.g., those in Eq. (3)) are case specific and difficult to find. In this study, ηWT is proposed for the first time as the ratio of Δπexp/ Δπtheoretical (even though Δπexp/Δπeff has been used widely before). We remark that ηWT ( = Δπexp/Δπtheoretical) ≠ σ2 (=Δπexp/Δπeff) as Δπtheoretical ≠ Δπeff; even though ηWT and σ1 look the same mathematically, ηWT ≠ σ1 because ηWT deals with real world situations (i.e., it includes all factors and conditions of the FO system) while σ1 is only valid under completely mixed conditions. In other words, using Δπexp/ Δπtheoretical may or may not find σ1; rather it always gives ηWT because ICE/ECP and interactions among solute, solvent, and membrane always exist in the FO system. Results of this study indicate that ηWT is much easier to use for different configurations and operating conditions. It is interesting to notice that even though countercurrent FO systems were used in most of the previous studies (Table S2–S4), the actual ηWT of these systems were about 2–78% as compared to the currently consensus understanding (σ ≈ 1). With these results in mind, one should not be surprised to find that in the static FO systems without mixing, ηWTwas about 0.04–0.44% because the effects of ECP and ICP in a static FO system could be much more serious than in a CSTR FO system. With the concept of ηWT, one could see more clearly how much contribution the real driving force Δπexp would make to FO performance. Table S1 shows that ηWT decreases with an increase in DS concentration even though the corresponding Jw,exp increases with an increase in DS concentration. Fig. 5b also indicates that changing the operating condition (e.g., countercurrent velocity within the FO chamber) of an FO system with a higher DS concentration (or a higher CDB – CFB) would have a less improvement in ηWT than that with a lower DS concentration (or a lower CDB – CFB). Results of this study can be used to explain why the discrepancy between Jw,exp and Jw,th increases at a higher Δπtheoretical. Combining Eqs. (6–8), we have:
Fig. 5. Effects of mixing intensity and operating mode on FO water transmission coefficient ηWT. (a) ηWT as a function of mixing intensity (data from Ref. [3]) and are shown in Table S4. Test conditions: DS = 0.31 M NaCl and FS = DI water. (b) ηWT as a function of water flow velocity (22.2–66.7 cm/s) within a countercurrent FO reactor (chamber size: 250, 30, 2 mm for length, width and height) operated with the PRO mode, DS = 0.5, 1.0, 2.0 M NaCl and FS = DI water (data from Ref. [34]).
determining the highest efficiency of a FO system under certain experimental conditions. The high ηWT value ( = ∼78%) shown in Fig. 5b (at 0.5 M NaCl) seems to indicate the concept of ηWTmax is right. On the other hand, the (1 – ηWT) value obtained at SSC may indicate the maximum possible impact of CP (including both ICP and ECP), while the corresponding initial time (e.g., 25–30 min) to reach pseudo-SSC is the time needed for CP effects to build up (see Fig. S1). Therefore, results shown in Fig. 5 indicate it is possible to evaluate ICP and ECP effects with the introduction of ηWT for different FO systems, which warrants future studies. 3.3. Discussion For the first time, we defined ηWT with Eq. (4) and systematically discussed it. Eqs. (4–6) allow us to understand more about ηWT and to link ηWT, Jw,exp ( = FO performance), Jw,theoretical with the conditions of the FO system. The difference between ηWT and σ as well as the related implications deserve more discussions. 3.3.1. Difference between ηWT, σ1 and σ2 In the literature, σ (as in Eq. (1)) has been used to quantify the magnitude of the FO water flux or how “tight” or “leaky” the membrane is to the solutes [12]. Historically (e.g., before 1981), many studies showed the measurement and prediction of σ1 in a biological system and/or environment [21], such as microvascular fluid exchange with the solute being total plasma protein [35], cell membranes [36,37], capillary walls [38]. In these studies, σ1 was used to infer the solute size effects [38] and membrane properties (e.g., the pore size, salt rejection) [20,38]. Based on these σ1 measurements, σ1 was in the range of 0.05–1, and increased as a function of solute size and approaches 1.0 for
Jw,exp =
A•10b•(Δπtheoretical)1 +a (i•Φ•R•T)a
(9)
Using the data shown in Table S2, we have Fig. 6 below. Because a usually is negative (Tables S1–S4), (1 + a) < 1. Therefore, Eq. (9) indicates the non-leaner nature of Jw,exp as a function of Δπtheoretical, which explains why the discrepancy between Jw,exp and Jw,theoretical appears to increase at a higher ΔπTheoretical as shown in Fig. 6. Moreover, Table S2–S4 indicate that for countercurrent FO systems, ηWT is relatively high (e.g., 2–78%), but the values of Jw,exp are consistently 110
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Fig. 6. Relationship between Δπtheoretical and Jw,exp or Jw,theoretical as per Eq. (9) and data in Table S2. Note: For the data from Table S1, the Jw,exp is too small compared to Jw,theoretical. Thus, all the Jw,exp is completely on the x-axis, while Jw,theoretical is still along the line of Jw,theoretical vs. Δπtheoretical. Therefore, no results from Table S1 are shown here.
procedure for determining ηWT and A with a static FO system, and found a linear relationship between logηWT and log (CDB – CFB) for FO systems operating at different configurations and conditions. Because all measured FO water fluxes reported in the literature belong to Jw,exp, and such a Jw,exp is driven by the real driving force Δπexp, not Δπeff as most studies indicated, the method developed in this study allows one to link together the real measured water flux (Jw,exp), real driving force (Δπexp), theoretical driving force (ΔπTheoretical), FO water transmission coefficient ηWT, concentrations of the bulk of DS and FS, and the membrane water permeability coefficient, A. It allows people to understand and compare the efficiency of different FO systems based on ηWT. In addition, one can predict FO water flux and FO performance in different FO systems under different conditions using logηWT = alog (CDB – CFB) + b and to evaluate the impacts of different experimental conditions on ηWT and implications related to ηWT. One should treat ηWT as an indicator of the departure of the FO system from its perfectibility instead of from FO membrane’s perfect semipermeability alone.
low, meaning that the low Jw,exp mainly stems from the FO membrane resistance–the low A value (as Jw,exp = AηWTΔπtheoretical), which confirms the previous report [18]. However, water flux with a higher ηWT is greater than water flux with a lower ηWT. 3.3.2. Significance and implications Theoretically, one may not be able to determine the exact σ1 experimentally because of the requirement of completely mixing as Staverman assumed in his work. σ2 and Eq. (2) are not easy to use for different FO systems [13,2,5,1]; in order to get σ2, the solution concentration at the membrane surface needs to be known, which is always changing with time. Overall, results of this study (together with previous studies) demonstrate that in the FO process ηWT is more convenient to use as ηWT is a function of the FO system (i.e., configuration and operating conditions), time, DS concentration, molecular size/ shape/charge, and FO membrane properties. Results of this study indicate that ηWT reflects the efficiency of the FO system, and thus, should be viewed as an indicator−a FO water transmission coefficient–to quantify the departure of the FO system from its perfectibility (i.e., Jw,theoretical = A•Δπtheoretical). Therefore, in the future one should always report ηWT with the information on the FO system and experimental conditions. Introducing ηWT potentially brings several advantages to FO study such as: 1) ηWT can be determined for all FO systems; 2) ηWT can link the major FO parameters together, and can be used to evaluate the effectiveness of changing a specific parameter (e.g., FO membrane porosity, thickness) or operation condition (e.g., CDB, CFB, countercurrent velocity) on the performance or the efficiency of the FO system; 3) it is possible to utilize the concepts of ηWT, Δπtheoretical, Δπexp, and σ2 together for detailed studies, e.g., evaluation of the contributions of ICP and ECP to the reduction of FO efficiency and finding Δπeff or σ2 via the experiments with two or more solutes being involved as Δπexp = ηWTΔπtheoretical (Eq. (4)) = σ2Δπeff (definition of σ2). Rong and Zhang (2017) developed a new set of ηWT-based FO models to evaluate ECP, ICP and ηWT changes under different FO systems and experimental conditions, demonstrating the fundamental value of ηWT in membrane science.
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4. Conclusions For the first time, we defined ηWT as Δπexp/Δπtheoretical, proposed the 111
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