Water and solute transport in pervaporation hydrophilic membranes to reclaim contaminated water for micro-irrigation

Journal of Membrane Science 252 (2005) 19–28

Water and solute transport in pervaporation hydrophilic membranes to reclaim contaminated water for micro-irrigation Edgar Qui˜nones-Bola˜nos a,b , Hongde Zhou a,∗ , Ranganathan Soundararajan c , Lambert Otten a b

a School of Engineering, University of Guelph, Guelph, Ont., Canada N1G 2W1 Facultad de Ciencias e Ingenieria, Universidad de Cartagena, Cartagena de Indias, Colombia c DuPont Canada, R&BD Centre, Kingston, Ont., Canada K7L 5A5

Received 3 June 2004; received in revised form 15 October 2004; accepted 26 October 2004 Available online 11 March 2005

Abstract The suitability of a homogeneous hydrophilic dense membrane for reusing brackish and/or contaminated waters was investigated. Its performance was evaluated in terms of water permeate flux and membrane enrichment factors using borate, selenate, sodium chloride and glucose as model contaminants. A series of experiments were conducted using a sweeping air pervaporation unit to examine the effects of membrane configuration (hollow fiber membranes (HFM) and corrugated sheet membranes (CSM)), sweeping air velocity, feed temperature, pressure and contaminant concentration. The collected data were then modelled to determine the individual mass transfer coefficients. The results showed that water fluxes ranged from 2.9 to 4.4 and 2.0 to 3.7 kg/(m2 day) for HFM and CSM, respectively. Air velocity and feed pressure were identified as the controlling factors for water flux. In all the cases, the average enrichment factors for glucose, selenate, borate and sodium chloride were 0.18, 0.08, 0.20 and 0.23, respectively. Thus, it was concluded that this membrane has the promise to provide an innovative treatment alternative for reusing brackish groundwater and residential wastewater in agriculture micro-irrigation. © 2004 Elsevier B.V. All rights reserved. Keywords: Pervaporation; Diffusion; Desalination; Water treatment; Agricultural irrigation

1. Introduction Over the last two decades, membrane pervaporation has emerged as a promising separation process in biotechnology, chemical and environmental engineering because of its excellent separation efficiency and low energy requirement. About 100 pervaporation units are currently in operation worldwide [27,7]. Applications include water desalination [12,11], removal of volatile organic compounds from water [13,24,25,28,4,20], dehydration of alcohol–water streams [6] and separation of close boiling point mixtures such as the removal of aromatic compounds from gasoline [19,7]. Nevertheless, little information has been reported on membrane pervaporation in treating contaminated water for crop irrigation. ∗ Corresponding author. Tel.: +1 519 824 4120x56990; fax: +1 519 836 0227. E-mail address: [email protected] (H. Zhou).

0376-7388/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.memsci.2004.10.038

Water-reuse for agricultural irrigation has been practiced over a long period in Europe, Asia and North America [23]. However, a major concern in reusing brackish groundwater and residential wastewater is the presence of high concentrations of phytotoxic substances such as borate (BO3 − ), selenates (SeO3 2− , SeO4 2− ), sodium ions (Na+ ) and chloride (Cl− ). They are difficult to remove with conventional wastewater treatment processes because of high water solubility, chemical and biological stability [5,10,9,17]. At present, treatment options commonly suggested include ion exchange, chemical precipitation, catalytic reduction, nanofiltration and reverse osmosis. These processes are often either costly due to the consumption of materials and/or high energy consumption or too low removal efficiency [9,17]. As agricultural irrigation represents more than 60% of the world’s water demand, the purpose of these sweeping air pervaporation tests is to examine the suitability of pervaporation membranes that are intended to be installed directly in the soil to reuse brackish groundwater or municipal wastewater

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in agricultural micro-irrigation. The specific objectives are: • to characterize the hydrophilic dense membrane in terms of permeate flux, mass transfer resistances and enrichment factors for various selected inorganic and organic compounds, • to develop a mathematical model to determine the relative permeate fluxes of water to solutes under different operating conditions and membrane configurations, and • to assess whether the water supplied by the test membrane pervaporation systems can meet the requirements for agri cultural micro-irrigation.

Table 1 Experimental conditions Membrane configuration Hollow fiber module (36 fibers) Corrugated sheet (32 channels) Surface area of HFM = 2070 cm2 Surface area of CSM = 2020 cm2 CSM and HFM length = 60 cm Feed solutions Milli-Q® -water (12 M) 0.08–2.0% NaCl 37–2300 mg/L glucose 3.30–98.0 mg/L boron 0.056–0.154 mg/L selenium Operating conditions Feed flow rate: 500 mL/min Feed pressure: 15–100 kPa Feed temperature: 22.0–28.7 ◦ C

2. Methods 2.1. Sweeping air pervaporation testing Fig. 1 shows two membrane configurations tested in this study: hollow fiber and corrugated sheet. HFM modules were arranged in a 36-fiber bundle while CSM modules were made in a 32-channel flat sheet. The membrane used in both configurations is a homogeneous, hydrophilic, dense membrane developed by E.I. DuPont de Nemours and Company. The membrane polymer falls under the category of thermoplastic copolyether esters elastomers. The advantages of using this type of membrane compared to others are its good chemical resistance and high mechanical strength. Fig. 2 shows a schematic of the laboratory air sweeping testing apparatus used for this study. It consists of a 1000-mL graduate cylinder serving as a feed tank and a membrane module with a length of 0.60 m. The test membrane modules were cased in a cylindrical CPVC tube with a diameter of 8.0 and 20.0 cm for HFM and CSM modules, respectively. Feed solutions were pumped into the module and the retentate was recycled back from the other end to the feed tank with the flow rate being measured by an in-line rotameter. The feed pressure of the solution was controlled by a back pressure valve along with a pressure gauge placed on the retentate recycle line. Sweeping air was introduced into the cylindrical case of the module to continuously remove water vapor from the membrane surface. The permeate water activity was determined by measuring the permeate relative humidity with an in-line hygrometer probe. Water permeate fluxes were monitored continuously by measuring the initial

Air-Re: 0–2200 Incoming air temperature: 22 ◦ C

and final volume of the water in the feed tank over a period of time. Note that the permeate flux was measured only after the first hour because of the interference caused by membrane swelling. Table 1 summarizes the experimental conditions to determine the enrichment factor and the water permeate flux. Four chemical solutions were selected to represent typical inorganic and organic contaminants present in brackish groundwater and residential wastewater, namely sodium chloride, sodium selenate, sodium borate and glucose solutions. All these feed solutions were prepared using reagent grade chemicals with Milli-Q® water (≈12 M cm). Their permeation rates were determined by monitoring their initial and final concentrations in the feed tank. NaCl concentrations were determined using the conductivity method, glucose concentrations with a TOC-V total organic carbon analyzer and selenium and boron concentrations using the inductively coupled plasma-atomic absorption method according to the [21] standard methods (1998). 2.2. Permeate flux model The pervaporation process is based on the selective dissolution of liquid compound into the membrane, followed by releasing it as vapor to the other side of the membrane. It is usually evaluated based on two parameters: permeate flux

Fig. 1. Tested membrane configurations (no scale).

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Fig. 2. Scheme of the sweeping air pervaporation process.

and enrichment factor. Permeate flux is defined as the amount of mass or moles (M) of a compound i permeating through the membrane per unit of time (t) per unit area (A), Ji =

Mi At

(1)

In dilute solutions, the enrichment factor is a ratio between the concentration of the compound in the permeate (cp,i ) to that in the feed (cf,i ). Mathematically, it can be expressed as βi =

cp,i cf,i

(2)

The driving force for pervaporation is the chemical potential gradient across the membrane. Thus, the flux Ji of a component i can be described by [26]: Ji = −Li

dµi dx

(3)

where Li is the proportionality coefficient. The chemical potential is related to temperature (T), pressure (p) and chemical activity (ai ) as dµi = T d ln(ai ) + vi dpi

(4)

Substituting Eq. (4) into Eq. (3) and assuming linear variation of ai and pi in the direction of the flux within the membrane leads to Ji =

pi −TLi ai − L i vi ai x x

(5)

where ai , and p represent the activity and pressure difference of component i between permeate and feed side, respectively, while x is the membrane thickness difference. Replacing x by the membrane thickness lM because of its thin film and recognizing the transport resistance consist of two terms Rc and Rd which are lM /Li vi and ai lM /TLi , re-

spectively, the flux Ji can be expressed as Ji = −

ai pi − Rd Rc

(6)

In cases that the pressure difference becomes negligible, it can be reduced to Ji =

1 (af,i − ap,i ) Rd

or in terms of concentration
 γp,i γf,i Ji = cf,i − cp,i γf,i Rd

(7)

(8)

The term γ i /Rd is normally referred to as the overall mass transfer coefficient kov,i . Depending on the nature of the solvent and membrane material, kov,i can be estimated based on the well-known resistance-in-series model as 1 kov,i

=

1 1 1 + + kf,i sf,i kM,i kp,i [sf,i /sp,i ]

(9)

For the hydrophilic membrane pervaporation experiments, the feed side mass transfer coefficient kf,i of a specie i can be neglected because of the low fluxes (<120 kg/(m2 day)) [16]. The local mass transfer resistance (sp,i /sf,i kp,i ) in the permeate-gas film is also negligible due to the high airflow maintained on the permeate side (e.g. Re > 2300), therefore, the overall mass transfer coefficient kov,i can be reduced to the local mass transfer coefficient within the membrane sf,i kM,i . Furthermore, the permeate activity may be considered negligible because a rapid sweeping air is maintaining on the permeate side. Consequently, the permeate flux defined by Eq. (8) can be reduced to Ji = kov,i (cf,i )

(10)

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Fig. 3. Schematic representation of transport through a pervaporation membrane.

2.3. Solute transport model In order to determine the enrichment factors and overall mass transfer resistances for the test membranes, a solute transport model was developed based on the mass balance for a specific compound. It was assumed that the feed solution flows longitudinally through a membrane module as plugflow. Additional assumptions include: • constant feed pressure along the membrane as the mea surements showed that the pressure drop between inlet and outlet of the membrane modules is less than 1% and • uniform solvent flux along the membrane because the feed solution was recirculated rapidly. Under steady-state condition, the mass balance around an arbitrary differential membrane element (see Fig. 3) leads to d(Qcf,i ) = −2πRJi dz

(11)

After combining with Eq. (10) for Ji , an integration of Eq. (11) from the membrane inlet concentration (ci ,inp ) to the concentration at exit of the membrane unit (ci ,out ) leads to
 Qp {(Akov,i /Qp )−1} (12) ci,out = ci,inp 1 − Qinp where A is the effective area of the membrane (=πdHFM L for HFM and =2WL for CSM). Similarly, a solute mass balance around the feed reservoir leads to d(Vci,inp ) (13) = [(Qinp − Qp )ci,out − Qinp ci,inp ] dt Combined with Eq. (12), the solute concentration decline in the feed reservoir can be expressed as
[(Qinp −Qp )/Qp ]{1−(1−Qp /Qinp )(kov,i A/Qp )−1 } V0 ci,inp = ci,0 V0 − Qp t (14) With knowing the solute concentration (ci,inp ) at specific time (t), the initial feed concentration ci,0 , the water permeate flow Qp and the initial volume of the solution in the feed reservoir V0 , the mass transfer coefficient (kov,i = sf,i kM,i ) can be determined by using nonlinear regression.

3. Results and discussion A series of sweeping air membrane pervaporation experiments were conducted by varying sweeping air velocity, feed

Fig. 4. Typical initial transient regime from sweeping air tests.

temperature and pressure and solute concentration. Because of its hydrophilic nature, the test membrane swelled initially, resulting in an initial transient increase in permeate flux. Fig. 4 presents a typical membrane swelling trend over time. The membrane swelling ratio was defined by the ratio of the length increase to the dry length of the membrane. Depending on the feed-membrane system and the starting membrane conditions (dry or pre-swollen), the membrane swelling usually lasted from 20 min to 1 h. At the end of the transient period, the swollen membrane was around 10% longer than the dry membrane. As a result, only data obtained after the initial transient period were used to evaluate the membrane performance. 3.1. Effects of sweeping air velocity on water flux To examine the effects of sweeping air velocity on water flux, pervaporation tests were conducted by varying the airRe from 0 to 2200 and using Milli-Q® water (≈12 M cm) as feed solution while keeping other process parameters constant. The resultant Reynolds numbers on the permeate side were calculated with the hydraulic diameter (dh ) as defined below: HFM :

dh =

2 2 − NHFM dHFM dmod dmod + NHFM dHFM

(15)

CSM :

dh =

2 πdmod πdmod + 2dmod

(16)

Fig. 5 shows the typical variation of the water flux against variation of the sweeping air-Re. The water flux increased with the increase in sweeping air-Re values till 1200 for HFM and 2000 for CSM, whereas above these values the water flux was almost constant in both cases. In similar manner, the relative humidity (RH) decreased as the air-Re increased. This was in agreement with the visual observations that the numbers of drops varied from a thin-film layer of water at Re = 0 to very few at high Re (Re > 2000). Similar findings have been reported by Korin et al. [11] for water desalination and Strathman and Gudernatsch [22] for dehydration of ethanol–water

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Fig. 5. Variation of the permeate flux with the relative humidity and Reynolds number.

Fig. 7. Effect of feed pressure on water permeate flux.

solution by sweeping air pervaporation with HFM. To ensure that the mass transfer resistance in the sweeping air film is negligible, sweeping air-Re greater than 1200 for HFM and 2000 for CSM modules were used, for all the subsequent experiments described hereafter.

energy for water according to the Arrhenius relationship:
 E Ji = A0 exp − (17) T

3.2. Effects of feed temperature on water flux In order to examine the effects of the feed temperature on pure water flux, the pervaporation experiments were carried out by varying the feed temperature from 22.0 to 28.7 ◦ C while maintaining CSM at a constant air-Re (2200), sweeping air temperature at 22 ◦ C, feed pressure at 25 kPa and feed flow at 300 mL/min. As shown in Fig. 6, the total water flux increased from 2.47 to 3.67 kg/(m2 day) when the feed temperature was increased. This can be attributed to the increase in molecular diffusivity and the reduction in flow viscosity at the higher temperature. Similar observations have been reported by Jiraratananon et al. [6] and Chan et al. [3]. To better quantify the dependence of the mass transfer resistance on temperature, the collected permeate flux data at different temperatures were used to calculate the activation

The resultant activation energy was 44.3 kJ/mol, consistent with the occurrence of a physical mass transfer process. This also fell within the interval of 16–92 kJ/mol reported in the literature for pure compounds in membrane pervaporation [15]. 3.3. Effects of feed pressure on water flux Fig. 7 shows a typical variation of the water flux with feed pressure for pure water using CSM modules. Consistent with the prediction from Eq. (5), the water flux increased linearly with the feed pressure. The rate of water flux changes with pressure as represented by the slope of this plot was found to be 0.0155 kg/(m2 day kPa). This value corresponds to a water permeability (Lw ) of 1.9 × 10−12 mol/(m s Pa), using a molar volume of water of 18 cm3 /mol and a membrane thickness of 18 mm. Similarly, a membrane permeability of 3.2 × 10−13 mol/(m s Pa) was obtained for the HFM. These values also fell within the range reported for other pervaporation membranes [11,8,1]. 3.4. Effects of solute concentration on water flux

Fig. 6. Effect of feed temperature on water flux.

Fig. 8 shows a typical plot of water flux as a function of glucose and sodium chloride concentration. In general, the water permeate flux decreased slightly as the solute concentration increased. Similar observation was reported by Ravindra et al. [18], who used chitosan membranes for desalting a variety of aqueous solutions by the pervaporation method. This decrease in the water flux with an increase in solute concentration was attributed to the occurrence of increased concentration polarization adjacent to membrane surface. It is also interesting to note that the rate of water flux decline for glucose (−9 × 10−4 kg L/(mg m2 day) is almost an order of

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Fig. 8. Effect of solute concentration on water flux.

magnitude higher than those obtained with sodium chloride (−7 × 10−5 and −4 × 10−5 kg L/(mg m2 day) for HFM and CSM, respectively). One probable explanation is the different molecular sizes. The kinetic diameters for glucose and sodium chloride are 0.86 and 0.35 nm, respectively, as computed using DS ViewerPro 5.0, Accelrys, Inc. Thus, it is easier for glucose molecules than for sodium chloride molecules to block the passage of water through the membrane, thereby reducing the water flux. Additional examinations were made using scanning electron microscopy (SEM) images in an attempt to reveal whether any salts would be accumulated on the membrane surfaces. As illustrated in Fig. 9(a), there exist some white crystal-like materials on the inner surface of the membrane after being used for 96 h in sodium chloride membrane selectivity tests, indicating the possibility of sodium chloride accumulation during the test. This could also be the cause of the water flux decline since the greater the salt accumulation is, the greater the blockage to the passage of water

molecules through the membrane. On the outer surface of the membrane, however, was little salt deposition after 96 h of operation. This could be due to the application of sweeping airflow on the outer surface of the membrane (see Fig. 9(b)). 3.5. Solute transport Fig. 10 shows the typical variation of borate concentration in the feed solution during a pervaporation test. Similar trends were obtained for other solutes at different pervaporation conditions. In general, the solute concentration in the feed increased over time because the concentrated retentate was continuously recycled to the feed tank. This also resulted in an increase in solute concentrations in the permeate. Nevertheless, the enrichment factor represented by the ratio of solute concentration in the permeate to that in the feed solution varied very slightly, being from 0.19 to 0.21 for borate concentrations from 14.3 to 34.5 mg/L. Table 2 summarizes the average membrane enrichment factors with their

Fig. 9. SEM diagrams of the cross-section of hollow fiber membranes after they have been tested for selectivity to sodium chloride.

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Fig. 10. Temporal variation of the feed and permeate concentration and selectivity for boron.

respective standard deviation error. It can be seen that average membrane enrichment factors have little dependence on the type of membrane configurations and solute concentrations in the feed. It is interesting to note that even though the membrane used in this study is dense, hydrophilic and homogeneous, there were still small amounts of solutes passing through it. One possibility is the solute transport through fine micropores within the membranes. Similar to the mass transport in pressure driven membrane processes such as microfiltration and ultrafiltration, this pathway would result in the water permeate flux as a function of feed pressure, as observed during the pervaporation tests (see Fig. 7). An examination was made using a scanning electronic microscopic examination at a nominal magnification of 10 000× to detect any micropores within the membranes. No micropores were detected at this magnification. Unfortunately, due to the limitations of the SEM equipment, SEM images at magnifications greater than 10 000× were not possible. Consequently, the hypothesis of solutes transporting through micropores within the membrane could not be entirely ruled out.

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Fig. 11. Diffusion of NaCl through the membrane.

Another possible cause for the transport of solutes through the membrane is that the solutes can be partitioned into the membrane, thereby released into the permeate side through molecular diffusion. This transport can be further facilitated if there are some molecules embedded in the polymer structure that are widening the interspaces between the polymer chains. To evaluate this hypothesis, a test with 4500 mg/L NaCl solution was conducted by immersing the test membrane in pure water to eliminate the convection of NaCl with the water permeate flow. The transmembrane pressure was adjusted so lowly that the permeate flux could be considered insignificant during the entire test. As shown in Fig. 11, even though the volume of feed solution was constant throughout the experiment (no water permeate flux), NaCl concentration in the feed solution decreased over time, suggesting the occurrence of NaCl diffusion through the membrane. 3.6. Solute mass transfer coefficients With the collected permeate flux and the solute concentration in the feed tank over time, the overall mass

Table 2 Summary of membrane enrichment factors for different contaminants Numbera

Enrichment factorb

kov × 10−5 (cm/min)c

Water flux (kg/(m2 day))

0.13 ± 0.01 0.18 ± 0.03

4.0 ± 0.6 3.7 ± 0.6

4.2 ± 0.3 2.7 ± 0.2

37–280 1050–2300

10–30 25–30

± ± ± ± ± ±

3200–5200 9900–18000 20000–30000 850–1400 2900–4300 6800–16800

15–20 15–20 15–20 20–25 20–25 30–35

Feed concentration (mg/L)

Feed pressure (kPa)

Glucose

HFM CSM

7 8

Sodium chloride

HFM HFM HFM CSM CSM CSM

22 17 3 4 3 13

Borate

CSM HFM

6 9

0.19 ± 0.01 0.22 ± 0.01

3.6 ± 0.8 6.4 ± 0.2

2.9 ± 0.1 4.3 ± 0.1

14.0–36.0 3.30–98.0

20–25 20–25

Selenate

CSM

7

0.08 ± 0.06

2.1 ± 1.1

2.9 ± 0.2

0.056–0.154

20–25

a b c

Total number of samples per case. Determined by Eq. (2). Determined by Eq. (14).

0.22 0.22 0.22 0.23 0.23 0.23

± ± ± ± ± ±

0.02 0.02 0.02 0.03 0.03 0.02

5.6 4.8 3.8 4.1 3.2 3.6

± ± ± ± ± ±

0.5 0.6 1.2 0.3 0.2 0.5

3.5 3.1 2.9 2.6 2.0 2.3

0.4 0.3 0.5 0.2 0.1 0.4

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Fig. 12. Comparison between the experimental measurements and the model predictions.

transfer coefficients (kov = sf,i kM ) for glucose, borate, selenate and sodium chloride were estimated using Eq. (14). The resultant kov values are summarized in Table 2. Fig. 12 shows a comparison between the experimental measurements and model predictions based on the estimated overall mass transfer coefficients. An excellent agreement is evident as over 95% of the results of cpre falls within the interval cexp ± 10%cexp , even though the data were obtained at different membrane configurations and experimental conditions. 3.7. Engineering significance The investigated pervaporation membrane modules are intended to be used, by burying them directly into the root plant zone in the soil, to reuse of brackish groundwater or residential wastewater for agricultural micro-irrigation. Thus, an assessment was made to determine whether the water supplied by the current membrane modules could meet the water requirements in quality and quantity for crop growth. In doing so, the water permeate flux was used as an indicator of the amount of water available for irrigation and the membrane enrichment factor as indicator of the quality of the irrigated water. Only the CSM module was evaluated further because of its high mechanical strength and simple placement into the soil. Based on the results obtained above, the water permeate fluxes ranged from 2.0 to 3.7 × 10−3 m3 /(m2 day) or in terms of water flow from 3.9 to 7.4 × 10−4 m3 /day. Considering the irrigation area (0.096 m2 ) for each membrane module, the average water supplied is then 0.006 m3 /(m2 day). Table 3 compares the achievable amount of water supplied by the tested CSM with the water requirements for selected crops under greenhouse irrigation condition. It can be seen that the average water supply meets the water requirements for the selected crops, indicating the good potential for this membrane pervaporation system to be used for agricultural micro-irrigation. However, it should be mentioned that the water supply was calculated based on the permeate flux obtained from sweep-air membrane

Table 3 Crop water requirements in m3 /(m2 day) Tomato

Pepper

Cucumber

Water requirementa

Maximum Minimum

0.005 0.0008

0.005 0.0008

0.003 0.002

Water supplied

Maximum Average Minimum

0.008 0.006 0.004

0.008 0.006 0.004

0.008 0.006 0.004

a

Calculated from [2].

pervaporation tests. Additional mass transfer resistance for water to transports from the membrane outer surface to the plant roots may exist, thereby, reducing the amount of water supply. To compensate for this concern, it is suggested that thinner membrane materials be installed for future applications. In terms of water quality, the tested membrane pervaporation system can consistently achieve enrichment factors of 0.20 or even less for glucose, borate, selenate and sodium chloride. Considering the fact that according to USEPA guidelines [14], the maximum contamination levels of Se and boron for irrigation water is 20 ␮g/L and 0.5 mg/L, respectively. Therefore, the treated water with membrane pervaporation will also comply with water quality criteria for crop irrigation when raw contains less than 2.5 mg/L and 250 ␮g/L, boron and selenium concentrations, respectively.

4. Conclusions Based on the above results, it can be concluded that the application of membrane pervaporation processes as an alternative to reuse brackish or residential waters for crop irrigation is promising for the following reasons: • the homogeneous hydrophilic membranes might provide a maximum water supply between 2.0 × 10−3 and 4.4 × 10−3 m3 /(m2 day) to the soil, depending on the choice of membrane configuration and operating conditions,

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• the removal of total organic carbon (glucose) and phytotoxic substances such as borate, selenate and sodium chloride was over 80% from highly contaminated waters, • the membrane enrichment factors and the mass transfer coefficients were independent of solute concentration in the feed solution and membrane configuration, and • the treated water with membrane pervaporation complies with water quality criteria for crop irrigation when raw water contains less than 2.5 mg/L and 250 ␮g/L, boron and selenium concentrations, respectively. In addition, the mathematical model developed to predict feed and permeate solute concentrations could be used to aid in further optimization of the membrane thickness and configuration in terms of the water flux and membrane enrichment factor.

Nomenclature List of symbols a chemical activity A active area of the membrane (m2 ) A0 Arrhenius pre-exponential parameter (kg/m2 day) c concentrations (mg/L) d diameter (m) E overall activation energy (kJ/mol) J permeate flux (kg/m2 day) k mass transfer coefficients (m/s) l membrane thickness (m) L chemical gradient proportionality constant (kg2 /Nm2 day); membrane length (m) M amount of target compound (kg) N number of hollow fiber membranes p pressure (Pa) Q flow rate (m3 /s) R transport resistance (kg/m2 s); hollow fiber membrane radius (m)  universal gas constant (kJ/kmol K) Re Reynolds number s partition coefficient t time (s) T temperature (K) v molar volume (m3 /mol) V volume (m3 ) W CSM width (m) x direction in the membrane thickness (m) z longitudinal direction along the membrane (m) Greek letters β membrane enrichment factor γ activity coefficient µ chemical potential (N m/kg)

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Subscripts c convection d diffusion dry dry condition exp experimental data f feed h hydraulic HFM hollow fiber membranes i solute or target compound inp inlet or input M membrane mod module out outlet or output ov overall p permeate pre predicted data w water 0 initial condition t = 0

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