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Scale formation in reverse osmosis desalination: model development
Desalination 238 (2009) 333–346
Scale formation in reverse osmosis desalination: model development Hyun-Je Oha, Youn-Kyoo Chounga, Sangho Leeb*, June-Seok Choib, Tae-Mun Hwangb, Joon Ha Kimc a
School of Civil and Environmental Engineering, Yonsei University, Seoul 120-749, Korea Environmental Research Division, Korea Institute of Construction Technology, Gyeonggi-Do 411-712, Korea Tel. +82 (31) 910-0320; Fax: +82 (31) 910-0291; email: [email protected] c Department of Environmental Science and Engineering, Gwangju Institute of Science and Technology (GIST), Gwangju 500-712, Korea b
Received 20 May 2008; Accepted 16 October 2008
Abstract Scale formation of soluble salts is one of the major factors limiting the performance of reverse osmosis (RO) membranes for desalination. In this study, a dynamic model based on the crystallization theory was developed to analyze the effect of CaSO4 scale formation on RO desalination process. Taking into consideration two mechanisms in scale formation including surface and bulk crystallization, the performance of RO filtration was predicted as a function of crossflow velocity, transmembrane pressure, permeate recovery, and operation mode. The model results indicated that RO fouling due to surface crystallization is important in batch filtration whereas both surface and bulk crystallization is important in crossflow filtration. This is because concentration polarization is directly related to surface crystallization. RO fouling due to bulk crystallization appeared to increase with increasing crossflow velocity and permeate recovery. The effects of background organic matters and antiscalant on scale formation were quantified using the model. The effect of operating parameters on RO fouling and concentration polarization was explored based on the model analysis. Keywords: Eesalination; Reverse osmosis; Scale formation; Fouling; Model; Crystallization mechanisms
1. Introduction As water resources become more limited, desalination of seawater and brackish water is *Corresponding author.
becoming important [1–3]. Recently, reverse osmosis (RO) membrane processing has been considered a promising technology for desalination. RO membrane processing removes ions and organic chemicals, and its treatment effi-
Presented at the IWA Efficient 2007, May 20–23, 2007, Jeju, Korea. 0011-9164/09/$– See front matter © 2009 Published by Elsevier B.V. doi:10.1016/j.desal.2008.10.005
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ciency and performance are stable and predictable. RO has been shown to be adequate for producing water for potable and industrial uses from seawater for reasonable costs [4–7]. However, one of the major problems in the application of RO for desalination is membrane fouling due to the formation of inorganic salt scale on the membrane surface. Scales are hard mineral deposits that precipitate from the feed stream onto the membrane surface. The salts that cause scale formation are ubiquitous in most water environments. They include calcium sulfate (CaSO4), calcium carbonate (CaCO3), and silica (SiO2). Scale formation is a complex process in which both crystallization and hydrodynamic transport mechanisms are involved. Two pathways for crystallization have been identified [8, 9]: surface (heterogeneous) crystallization and bulk (homogeneous) crystallization. In surface crystallization, flux decline results from the blockage of the membrane surface by lateral growth of the scale deposit on the membrane. In bulk crystallization, crystals formed in the bulk solution sediment on the membrane surface leading to a flux decline. Concentration polarization plays an important role in scale formation in membrane systems [9,10]. As concentration polarization increases, scale formation occurs more through surface crystallization. However, other factors affect the crystallization process including pH [11], temperature [12], and the presence of other metal ions [13]. Scale formation has always been recognized as a serious constraint in designing and operating RO systems because since scale formation not only lowers the flux and rejection of RO permeate but also shortens the membrane life. Many studies have been attempted to reduce scale formation in RO membrane system by increasing the fluid velocity [10], adding antiscalants [14, 15], performing chemical pretreatments [16], using ion exchange prior to RO [16], combining a crystallizer with RO [17–19], and applying an online microfilter [9].
In this paper, we developed a dynamic model based on the crystallization theory to explore the effect of CaSO4 scale formation on the RO desalination process. Using the model, we analyzed the performance of RO filtration as a function of crossflow velocity, transmembrane pressure, permeate recovery, and operation mode. We also investigate the effect of background organic matters and additives on RO membrane fouling due to scale formation based on the model analysis.
2. Theory 2.1. Mechanisms for scale formation Scale formation is a complex process in which both crystallization and hydrodynamic transport mechanisms are involved. Two pathways for crystallization have been identified [8–10]: surface (heterogeneous) crystallization and bulk (homogeneous) crystallization. In surface crystallization, flux decline results from the blockage of the membrane surface by lateral growth of the scale deposit on the membrane. In bulk crystallization, crystals formed in the bulk solution sediment on the membrane surface leading to a flux decline. Fig. 1 illustrates the two different schemes of scale formations in RO system. In this study, we have applied the resistancein-series model modified with the concentration polarization theory and crystallization kinetics to analyze RO fouling due to scale formation over a wide range of conditions. Unlike previous works, we included both surface crystallization and bulk crystallization in our model. Thus, the permeate flux is given by combining the surface blockage and cake filtration models:
J Lv (P )
A Ab P Rm Rc A
where Lv is the solvent transport parameter; ΔP is
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Fig. 1. Scale formation mechanisms in RO system.
the transmembrane pressure; π is the osmotic pressure, η is the permeate viscosity, Rm is the membrane resistance, Rc is the resistance due to cake formation, A is the membrane area, and Ab is the membrane area occupied by surface crystals. Since the thickness of crystal layer formed on the membrane surface is almost constant [20], the Ab could be defined as follows:
Ab
ms A
mc
cw c p
e
J k
(5)
where k is the mass transfer coefficient for the back diffusion of the solute from the membrane to the bulk solution on high pressure side of membrane. In a stirred cell, the growth of the concentration boundary layer is limited by stirring according to the mass transfer coefficient [21]: 2 D r k 0.104 r
A
where is the specific cake resistance and mc is the accumulated weight of precipitated scale. Based on the solution–diffusion model, the solute flux, Js , through the membrane is:
J s Ls (cw c p )
The difference between cw and cb (the bulk concentration of solute) results from the concentration polarization phenomenon. On the basis of the film model theory and from Fick’s law for diffusion, the concentration profile near the membrane surface is:
cb c p
where β is the area occupied per unit mass and ms is the weight of scale formed directly on the membrane surface. Assuming that the crystal slurry is incompressible, cake resistance Rc can be calculated based on Darcy’s law:
Rc
2.2. Estimation of wall concentration
(4)
where Ls is the solute transport parameters, cw is the wall concentration near membrane surface, and cp is the permeate concentration.
2/3
1/ 3
Dsw
(6)
where r is the stirring radius, ω is the stirring speed, ρ is the solution density, and D is the diffusion coefficient of solute. In a crossflow filtration system, the mass transfer coefficients are [22]: C laminar flow
uD 2 k 1.86 dh L
0.33
(7)
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C turbulent flow
u 0.8 D 0.67 k 0.023 0.2 0.47 dh
(8)
where k is the mass transport coefficient, u is the flow velocity, D is the diffusion coefficient of salts, dh is the hydraulic diameter for channel flow, L is the channel length, and ν is the kinematic viscosity of feed. Rearranging Eq. (5), the solute concentration at the membrane surface can be estimated from the solute concentration of bulk phase. 2.3. Induction time and crystal growth rate Although the solution is supersaturated, scale formation may not immediately occur without sufficient nucleation. Thus, induction time, which is defined as time to induce formation of detectable crystals, is important in scale formation of RO membrane. Assuming that the induction time is proportional to the nucleation rate, the induction time, τ, is:
0e
C 3 T 3 ln( Sw ) 2
(9)
where τ0 is a constant related to frequency factor, C is a constant embodying physical properties; σ is the crystal surface energy, T is the absolute temperature, and Sw is the supersaturation ratio. The surface crystal growth rate of scaleforming salt can be written as:
d ms n k s A Ab cw cS dt n m k s A 1 s cw cs A
(10)
where ks is the rate constant of surface crystallization, cs is the saturation concentration, and n is the order of reaction rate.
On the other hand, assuming that bulk crystallization occurs on the surface of suspended crystal particles, the mass of cake crystals can be also expressed as:
d mc m m kc s p cb cs kb cb cs dt
(11)
where kc is the rate constant of bulk crystallization, sp is surface area of active sites on bulk crystals, cb is the bulk phase concentration, ψ is the deposition probability of crystal particles, m is the order of reaction rate, and kc is the apparent rate constant of bulk crystallization (=kcspψ). The major difference between Eqs. (10) and (11) is the driving force for the crystallization. In surface crystallization, the concentration difference between cw and cs is the driving force for crystallization whereas in bulk crystallization, the term (cb!cs) is the driving force. This implies the concentration polarization is important only in the surface crystallization. Moreover, the induction time for surface crystallization and bulk crystallization may be different. 2.4. Solution method In batch filtration (both stirred cell and crossflow system), J, cb, and cp are not constant because the volume of concentrate (Vc) changes continuously. The time rate of change of cb and vc for a membrane of area A is given by
d cbVc d mc d ms JAc p dt dt dt d Vc JA dt
(12) (13)
with the initial conditions cb = cf and Vc = Vf at t = 0 where cf and Vf are the initial feed concentration of solute and feed volume, respectively. All parameters used in this study are summarized in Table 1, and the procedures of solving the model equations are shown in Fig. 2. α, β, ks
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Table 1 Parameters and assumptions used in this study Items
Definition
Values
Refs.
C σ n m
Constant embodying physical properties Crystal surface energy (without additives) Reaction order for surface crystallization Reaction order for bulk crystallization
90,700 m6 K3 (MJ)!3 9.4×10!3 J/m2 1 1
[23] [23] [24] [24]
Fig. 2. Flow chart for the solution method of the model.
and kb were experimentally determined from a separate set of batch tests and then used in the model calculation.
3. Experimental A commercially available RO membrane (Filmtec, USA) was used in this study. The membrane was of the thin film composite (TFC) type. The experiments were performed using a stirred cell as well as a crossflow filtration module as shown in Fig. 3.
The stirred cell was made of aluminum and coated with Teflon to improve chemical stability. The diameter of the stirred cell was 54 mm and the working volume was 100 ml. A magnetic stirrer (Stirrer assembly 8200, Millipore, USA) was positioned just above the membrane. The length of the stirring bar was 52 mm. The working pressure was controlled by a high pressure nitrogen cylinder and by a gas pressure regulator. The stirring speed was controlled by a magnetic stirrer plate. The temperature of the feed solution was adjusted to 20–25EC and the effect of temperature on viscosity and density was corrected. Since the experiment was performed in a short time (normally less than 30 min), the variations of the temperature during an experiment were smaller than ±1EC. The experimental apparatus for a crossflow RO consisted of a feed tank with a total working volume of 20 L and a membrane module. Raw water was stored in a 5 L feed tank and then entered a recirculation loop, where a diaphragm pump sustained the recirculation flow rate. A back-pressure valve was located in the recirculation loop to adjust the transmembrane pressure. The permeate, which was collected in a reservoir on the electronic balance to measure the flux, was either returned into the feed tank for total recycle or discharged for concentration operation. The water in the recirculation loop was maintained at 25EC by a water jacket. The RO module was a plate and frame configuration with the channel height of 3 mm. The total surface area of the membrane used was 27.4 cm2.
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(a)
(b)
Fig. 3. Schematic diagram of experimental set-up. (a) Stirred cell RO device. (b) Crossflow RO filtration equipment.
In both systems, the permeate flux was expressed in terms of concentration factor (VCF). The concentration factor, defined as a ratio of the feed volume to concentrate volume, indicates the extent of concentration:
VCF
Vf Vc
1
Vp Vc
(14)
where Vf, Vc, and Vp are defined as the volume of feed, concentrate, and permeate, respectively. VCF is proportional to permeate recovery. A saturated solution of CaSO4 (2000 mg/L) was used as a model feed solution. Prior to the filtration test, the solution was prefiltered using a 0.45 µm filter. The concentrations of CaSO4 were determined by an ion chromatography (Dionex 4000I, USA) and by a conductivity meter (Model 170, Orion, USA). The turbidity measurement for the feed and retentate was made on a turbidimeter (HF, DRT-100B, USA).
4. Results and discussion 4.1. Determination of model parameters To apply the model for analyzing RO filtration system, it is necessary to determine the model
parameters such as α, β, ks and kb. Fig. 4(a) shows the flux and the normalized solute concentration, cb/cf, in batch cell filtration of a CaSO4 saturated solution as a function of VCF. The transmembrane pressure was 1000 kPa, and the stirring speed ω was 0 rpm. Under this condition, RO fouling occurs only by surface crystallization due to high concentration polarization [9], allowing an accurate determination of β from experimental data. Using the mass balance for CaSO4, ms/A was calculated and correlated with surface coverage (φ=Ab/A). Without bulk crystallization, φ=1!J/Ji where Ji is the initial flux. As shown in Fig. 4(b), a linear relationship between ms/A and φ was found and β was estimated to be 2.83104 m2/kg. Fig. 5(a) shows the flux and the normalized solute concentrations in crossflow filtration of a supersaturated solution (4800 mg/L of CaSO4) under total recycle mode to estimate α. According to a previous study [10], this condition is favorable for bulk crystallization rather than surface crystallization. Based on the mass balance and resistance analysis, a linear relationship between mc/A and Rc was obtained as depicted in Fig. 5(b). The α was calculated at 4.151014 m/kg. The rate constants for surface crystallization and bulk crystallization were also estimated using batch crystallization data and Eqs. (10) and (11).
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(a)
339
(b)
Fig. 4. Determination of surface coverage constant (ß) using unstirred cell device. (Operating conditions: ΔP = 1000 kPa; ω = 300 rpm; —, model calculation; ! experimental data).
(a)
(b)
Fig. 5. Determination of specific cake resistance (α) using crossflow RO filtration. (Operating conditions: ΔP = 1000 kPa; v = 2 m/s; —, model calculation; ! experimental data). (a) Flux and bulk concentration. (b) Felationship between bulk crystal formation and cake resistance.
Differential and integral methods were used for solving surface and bulk crystallization equations, respectively. Through linear regressions of the data in Fig. 6, ks was determined as 0.75×10!5 m/s and kc was determined as 8.52×10!9 m3/s. These parameters were used in the model for the remainder of this paper. 4.2. Model calculations for stirred cell system As shown in Fig. 7, the model calculation was compared with experimental data for RO filtra-
tion in a stirred cell. The transmembrane pressure was 1000 kPa, and the stirring speed ω was 300 rpm. The flux remains almost constant until the VCF reaches about 4.2. Above this VCF, the flux abruptly decreases. These results suggest that crystallization is delayed until a VCF above 4 is reached. Then the CaSO4 in solution crystallizes and the crystals foul the membrane, rapidly reducing the permeate flux. Although there are some differences, the model correctly predicts the trends of the experimental data. The flux decline below the VCF of
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(a)
(b)
Fig. 6. Determination of the rate constant for bulk crystallization through batch crystallization experiment.
crystallization appears to be negligible because of high concentration polarization. As shown in Fig. 8(b), cw is initially 1.6 times high than cb, resulting in a faster nucleation and crystal growth at RO membrane surface. The difference between cw and cb decreases as flux is reduced by surface crystallization. Considering that the concentration polarization is substantial for most stirred cell tests, it is likely that the scale formation due to bulk crystallization is negligible in batch cell filtration. 4.3. Effect of background organics and additives Fig. 7. Comparison of model calculation with experimental data from stirred cell. (Operating conditions: ΔP = 1000 kPa; ω = 300 rpm).
4 is attributed to an increase in osmotic pressure. At VCF = 4, the induction period ends, leading to a rapid crystallization and membrane fouling. The induction time for this test was calculated as 2949 s. Fig. 8(a) illustrates how the scale formation occurs during the RO filtration. Based on the model calculation, scale formation due to surface crystallization starts above VCF = 4. At the end of the test, approximately 16% of total CaSO4 was precipitated. Scale formation due to bulk
In RO filtration, a small amount of organic matters and additives may exist in the feed solution. Especially, antiscalants such as sodium hexametaphosphate (SHMP) are commonly used for most RO plants to retard scale formation. Here, the effect of organic matters was examined in both experimental and theoretical ways. Figs. 9(a) and (b) shows the flux as a function of VCF for stirred cell filtration of the CaSO4 saturated solution in the presence of background organics. The concentrations for bovine serum albumin (BSA) and dextran were 2 mg/L. It is evident that BSA and dextran did not affect the flux decline due to scale formation. On the contrary, an addition of tannin or SHMP at 2 mg/L was effective to retard scale formation as illus-
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(a)
341
(b)
Fig. 8. Model calculation of scale formation and concentration profiles. (Operating conditions: ΔP = 1000 kPa; ω = 300 rpm). (a) Scale formation. (b) Bulk concentration (Cb) and wall concentration (Cw).
Fig. 9. Model calculation and experimental data for permeate flux in in crossflow RO filtration with various additives. (Operating conditions: ΔP = 1000 kPa; ω = 300 rpm; —, model calculation; ! experimental data).
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Fig. 10. Comparison of model calculation with experimental data for permeate flux and solute concentration in crossflow RO. (Operating conditions: ΔP = 1000 kPa; ω = 300 rpm; —, model calculation; ! experimental data). (a) Permeate flux. (b) Bulk concentration (Cb).
trated in Figs. 9(c) and (d). This is because these organics may adsorb or affect the active sites of crystal growth, leading to a reduced rate of nucleation and crystal growth. To quantify the effect of organics on scale formation, the model was fitted with the experimental data in Fig. 9 by changing the induction time. Then the surface energy σ was calculated from the induction time. As expected, σ values for BSA and dextran were same as that without any organics or additives (9.4×10!3 J/m2), σ values for tannin and SHMP were 9.6810!3 J/m2 and 9.5910!3 J/m2, respectively, which are slightly higher. It is likely that that the model may be used to quantify the impact of background organics or effectiveness of antiscalant on scale formation in RO process.
Fig. 11. Model calculation of scale formation from bulk crystallization and surface crystallization in crossflow RO filtration. (Operating conditions: ΔP = 1000 kPa; v = 0.6 m/s; —, surface scale formation; - -, bulk scale formation).
4.4. Model calculations for crossflow system While it is helpful to consider dead-end batch filtration using the stirred cell, a RO system will more likely operate in crossflow operation mode. Fig. 10 shows the flux and the normalized solute concentration in crossflow filtration as a function of VCF. The transmembrane pressure was 1000 kPa, and the crossflow velocity v was
0.6 m/s. In crossflow filtration, a longer time is required to reach the same VCF than in batch filtration and thus the induction time for crossflow filtration is different from that for batch filtration. Nevertheless, the model matches the experimental flux and bulk concentration well by adjusting the induction time.
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Fig. 12. Model calculation and experimental data for permeate flux in crossflow RO filtration at various crossflow velocities. (Operating conditions: ΔP = 100 kPa).
Based on the model calculation, the scale formation rates were compared as a function of VCF as shown in Fig. 11. Unlike batch filtration, the scale formation by bulk crystallization becomes important at high VCF in crossflow filtration. This is attributed to relatively low concentration polarization ratio in crossflow filtration. The maximum value for concentration polarization ration in batch filtration (ΔP = 1000 kP, ω = 300 rpm) was 1.6 whereas that in crossflow filtration (ΔP =1000 kPa, v = 0.6 m/s) was less than 1.1. Thus, it is necessary to consider
bulk crystallization as well as surface crystallization in crossflow filtration. Since the concentration polarization is sensitive to hydrodynamics in the RO system, the crossflow velocity is an important factor affecting the scale formation. Fig. 12 illustrates the effect of crossflow velocity on flux decline due to scale formation. As expected, an increase in crossflow velocity from 0.35 to 4 m/s substantially improved the flux as well as the maximum VCF without scale formation. In all cases, model matches experiments well without changing any
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Fig. 13. Model calculation and experimental data for scale formation in crossflow RO filtration at various crossflow velocities. (Operating conditions: ΔP = 100 kPa; —, surface scale formation; - -, bulk scale formation).
parameters. Fig. 13 compares the scale formation by surface and bulk crystallization. As crossflow velocity increases, the VCF for the start of scale formation increases as well. Fig. 14 shows the dependence of concentration polarization ratio on crossflow velocity, which is calculated using the model. Compared with batch filtration, the concentration polarization ratio is smaller in crossflow filtration and decreases with increasing crossflow velocity.
Nevertheless, an additional benefit on permeate flux by increasing crossflow velocity over 1 m/s seems to be negligible because high crossflow velocity requires high energy consumption. This result suggests that an optimization of operating condition for RO filtration is required for better control of scale formation in a cost-effective way.
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References
Fig. 14. Model calculation of concentration polarization ratio in crossflow RO filtration at various crossflow velocities.
5. Conclusions In this work, scale formation in RO membrane system was investigated using a transient model based on the crystallization theory and resistancein-series model. The following conclusions can be drawn from this work: 1. In batch stirred cell filtration, surface crystallization was the dominant scale formation mechanism due to high ratio of concentration polarization. The measured flux from the experiments matches the model results quite well. 2. The model has potential as a method to quantify the effect of organics and additives on scale formation phenomena in RO filtration. 3. In crossflow filtration, both surface crystallization and bulk crystallization were important. As crossflow velocity increases, the concentration polarization ratio decreases, leading to a decreased rate of surface crystallization. The model was also useful for analyzing the flux and concentration in crossflow RO filtration. Acknowledgements This research was supported by a research grant (no. 2008-0206-49-1) from the Korea Institute of Construction Technology (KICT).
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Scale formation in reverse osmosis desalination: model development Hyun-Je Oha, Youn-Kyoo Chounga, Sangho Leeb*, June-Seok Choib, Tae-Mun Hwangb, Joon Ha Kimc a
School of Civil and Environmental Engineering, Yonsei University, Seoul 120-749, Korea Environmental Research Division, Korea Institute of Construction Technology, Gyeonggi-Do 411-712, Korea Tel. +82 (31) 910-0320; Fax: +82 (31) 910-0291; email: [email protected] c Department of Environmental Science and Engineering, Gwangju Institute of Science and Technology (GIST), Gwangju 500-712, Korea b
Received 20 May 2008; Accepted 16 October 2008
Abstract Scale formation of soluble salts is one of the major factors limiting the performance of reverse osmosis (RO) membranes for desalination. In this study, a dynamic model based on the crystallization theory was developed to analyze the effect of CaSO4 scale formation on RO desalination process. Taking into consideration two mechanisms in scale formation including surface and bulk crystallization, the performance of RO filtration was predicted as a function of crossflow velocity, transmembrane pressure, permeate recovery, and operation mode. The model results indicated that RO fouling due to surface crystallization is important in batch filtration whereas both surface and bulk crystallization is important in crossflow filtration. This is because concentration polarization is directly related to surface crystallization. RO fouling due to bulk crystallization appeared to increase with increasing crossflow velocity and permeate recovery. The effects of background organic matters and antiscalant on scale formation were quantified using the model. The effect of operating parameters on RO fouling and concentration polarization was explored based on the model analysis. Keywords: Eesalination; Reverse osmosis; Scale formation; Fouling; Model; Crystallization mechanisms
1. Introduction As water resources become more limited, desalination of seawater and brackish water is *Corresponding author.
becoming important [1–3]. Recently, reverse osmosis (RO) membrane processing has been considered a promising technology for desalination. RO membrane processing removes ions and organic chemicals, and its treatment effi-
Presented at the IWA Efficient 2007, May 20–23, 2007, Jeju, Korea. 0011-9164/09/$– See front matter © 2009 Published by Elsevier B.V. doi:10.1016/j.desal.2008.10.005
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H.-J. Oh et al. / Desalination 238 (2009) 333–346
ciency and performance are stable and predictable. RO has been shown to be adequate for producing water for potable and industrial uses from seawater for reasonable costs [4–7]. However, one of the major problems in the application of RO for desalination is membrane fouling due to the formation of inorganic salt scale on the membrane surface. Scales are hard mineral deposits that precipitate from the feed stream onto the membrane surface. The salts that cause scale formation are ubiquitous in most water environments. They include calcium sulfate (CaSO4), calcium carbonate (CaCO3), and silica (SiO2). Scale formation is a complex process in which both crystallization and hydrodynamic transport mechanisms are involved. Two pathways for crystallization have been identified [8, 9]: surface (heterogeneous) crystallization and bulk (homogeneous) crystallization. In surface crystallization, flux decline results from the blockage of the membrane surface by lateral growth of the scale deposit on the membrane. In bulk crystallization, crystals formed in the bulk solution sediment on the membrane surface leading to a flux decline. Concentration polarization plays an important role in scale formation in membrane systems [9,10]. As concentration polarization increases, scale formation occurs more through surface crystallization. However, other factors affect the crystallization process including pH [11], temperature [12], and the presence of other metal ions [13]. Scale formation has always been recognized as a serious constraint in designing and operating RO systems because since scale formation not only lowers the flux and rejection of RO permeate but also shortens the membrane life. Many studies have been attempted to reduce scale formation in RO membrane system by increasing the fluid velocity [10], adding antiscalants [14, 15], performing chemical pretreatments [16], using ion exchange prior to RO [16], combining a crystallizer with RO [17–19], and applying an online microfilter [9].
In this paper, we developed a dynamic model based on the crystallization theory to explore the effect of CaSO4 scale formation on the RO desalination process. Using the model, we analyzed the performance of RO filtration as a function of crossflow velocity, transmembrane pressure, permeate recovery, and operation mode. We also investigate the effect of background organic matters and additives on RO membrane fouling due to scale formation based on the model analysis.
2. Theory 2.1. Mechanisms for scale formation Scale formation is a complex process in which both crystallization and hydrodynamic transport mechanisms are involved. Two pathways for crystallization have been identified [8–10]: surface (heterogeneous) crystallization and bulk (homogeneous) crystallization. In surface crystallization, flux decline results from the blockage of the membrane surface by lateral growth of the scale deposit on the membrane. In bulk crystallization, crystals formed in the bulk solution sediment on the membrane surface leading to a flux decline. Fig. 1 illustrates the two different schemes of scale formations in RO system. In this study, we have applied the resistancein-series model modified with the concentration polarization theory and crystallization kinetics to analyze RO fouling due to scale formation over a wide range of conditions. Unlike previous works, we included both surface crystallization and bulk crystallization in our model. Thus, the permeate flux is given by combining the surface blockage and cake filtration models:
J Lv (P )
A Ab P Rm Rc A
where Lv is the solvent transport parameter; ΔP is
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Fig. 1. Scale formation mechanisms in RO system.
the transmembrane pressure; π is the osmotic pressure, η is the permeate viscosity, Rm is the membrane resistance, Rc is the resistance due to cake formation, A is the membrane area, and Ab is the membrane area occupied by surface crystals. Since the thickness of crystal layer formed on the membrane surface is almost constant [20], the Ab could be defined as follows:
Ab
ms A
mc
cw c p
e
J k
(5)
where k is the mass transfer coefficient for the back diffusion of the solute from the membrane to the bulk solution on high pressure side of membrane. In a stirred cell, the growth of the concentration boundary layer is limited by stirring according to the mass transfer coefficient [21]: 2 D r k 0.104 r
A
where is the specific cake resistance and mc is the accumulated weight of precipitated scale. Based on the solution–diffusion model, the solute flux, Js , through the membrane is:
J s Ls (cw c p )
The difference between cw and cb (the bulk concentration of solute) results from the concentration polarization phenomenon. On the basis of the film model theory and from Fick’s law for diffusion, the concentration profile near the membrane surface is:
cb c p
where β is the area occupied per unit mass and ms is the weight of scale formed directly on the membrane surface. Assuming that the crystal slurry is incompressible, cake resistance Rc can be calculated based on Darcy’s law:
Rc
2.2. Estimation of wall concentration
(4)
where Ls is the solute transport parameters, cw is the wall concentration near membrane surface, and cp is the permeate concentration.
2/3
1/ 3
Dsw
(6)
where r is the stirring radius, ω is the stirring speed, ρ is the solution density, and D is the diffusion coefficient of solute. In a crossflow filtration system, the mass transfer coefficients are [22]: C laminar flow
uD 2 k 1.86 dh L
0.33
(7)
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C turbulent flow
u 0.8 D 0.67 k 0.023 0.2 0.47 dh
(8)
where k is the mass transport coefficient, u is the flow velocity, D is the diffusion coefficient of salts, dh is the hydraulic diameter for channel flow, L is the channel length, and ν is the kinematic viscosity of feed. Rearranging Eq. (5), the solute concentration at the membrane surface can be estimated from the solute concentration of bulk phase. 2.3. Induction time and crystal growth rate Although the solution is supersaturated, scale formation may not immediately occur without sufficient nucleation. Thus, induction time, which is defined as time to induce formation of detectable crystals, is important in scale formation of RO membrane. Assuming that the induction time is proportional to the nucleation rate, the induction time, τ, is:
0e
C 3 T 3 ln( Sw ) 2
(9)
where τ0 is a constant related to frequency factor, C is a constant embodying physical properties; σ is the crystal surface energy, T is the absolute temperature, and Sw is the supersaturation ratio. The surface crystal growth rate of scaleforming salt can be written as:
d ms n k s A Ab cw cS dt n m k s A 1 s cw cs A
(10)
where ks is the rate constant of surface crystallization, cs is the saturation concentration, and n is the order of reaction rate.
On the other hand, assuming that bulk crystallization occurs on the surface of suspended crystal particles, the mass of cake crystals can be also expressed as:
d mc m m kc s p cb cs kb cb cs dt
(11)
where kc is the rate constant of bulk crystallization, sp is surface area of active sites on bulk crystals, cb is the bulk phase concentration, ψ is the deposition probability of crystal particles, m is the order of reaction rate, and kc is the apparent rate constant of bulk crystallization (=kcspψ). The major difference between Eqs. (10) and (11) is the driving force for the crystallization. In surface crystallization, the concentration difference between cw and cs is the driving force for crystallization whereas in bulk crystallization, the term (cb!cs) is the driving force. This implies the concentration polarization is important only in the surface crystallization. Moreover, the induction time for surface crystallization and bulk crystallization may be different. 2.4. Solution method In batch filtration (both stirred cell and crossflow system), J, cb, and cp are not constant because the volume of concentrate (Vc) changes continuously. The time rate of change of cb and vc for a membrane of area A is given by
d cbVc d mc d ms JAc p dt dt dt d Vc JA dt
(12) (13)
with the initial conditions cb = cf and Vc = Vf at t = 0 where cf and Vf are the initial feed concentration of solute and feed volume, respectively. All parameters used in this study are summarized in Table 1, and the procedures of solving the model equations are shown in Fig. 2. α, β, ks
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Table 1 Parameters and assumptions used in this study Items
Definition
Values
Refs.
C σ n m
Constant embodying physical properties Crystal surface energy (without additives) Reaction order for surface crystallization Reaction order for bulk crystallization
90,700 m6 K3 (MJ)!3 9.4×10!3 J/m2 1 1
[23] [23] [24] [24]
Fig. 2. Flow chart for the solution method of the model.
and kb were experimentally determined from a separate set of batch tests and then used in the model calculation.
3. Experimental A commercially available RO membrane (Filmtec, USA) was used in this study. The membrane was of the thin film composite (TFC) type. The experiments were performed using a stirred cell as well as a crossflow filtration module as shown in Fig. 3.
The stirred cell was made of aluminum and coated with Teflon to improve chemical stability. The diameter of the stirred cell was 54 mm and the working volume was 100 ml. A magnetic stirrer (Stirrer assembly 8200, Millipore, USA) was positioned just above the membrane. The length of the stirring bar was 52 mm. The working pressure was controlled by a high pressure nitrogen cylinder and by a gas pressure regulator. The stirring speed was controlled by a magnetic stirrer plate. The temperature of the feed solution was adjusted to 20–25EC and the effect of temperature on viscosity and density was corrected. Since the experiment was performed in a short time (normally less than 30 min), the variations of the temperature during an experiment were smaller than ±1EC. The experimental apparatus for a crossflow RO consisted of a feed tank with a total working volume of 20 L and a membrane module. Raw water was stored in a 5 L feed tank and then entered a recirculation loop, where a diaphragm pump sustained the recirculation flow rate. A back-pressure valve was located in the recirculation loop to adjust the transmembrane pressure. The permeate, which was collected in a reservoir on the electronic balance to measure the flux, was either returned into the feed tank for total recycle or discharged for concentration operation. The water in the recirculation loop was maintained at 25EC by a water jacket. The RO module was a plate and frame configuration with the channel height of 3 mm. The total surface area of the membrane used was 27.4 cm2.
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(a)
(b)
Fig. 3. Schematic diagram of experimental set-up. (a) Stirred cell RO device. (b) Crossflow RO filtration equipment.
In both systems, the permeate flux was expressed in terms of concentration factor (VCF). The concentration factor, defined as a ratio of the feed volume to concentrate volume, indicates the extent of concentration:
VCF
Vf Vc
1
Vp Vc
(14)
where Vf, Vc, and Vp are defined as the volume of feed, concentrate, and permeate, respectively. VCF is proportional to permeate recovery. A saturated solution of CaSO4 (2000 mg/L) was used as a model feed solution. Prior to the filtration test, the solution was prefiltered using a 0.45 µm filter. The concentrations of CaSO4 were determined by an ion chromatography (Dionex 4000I, USA) and by a conductivity meter (Model 170, Orion, USA). The turbidity measurement for the feed and retentate was made on a turbidimeter (HF, DRT-100B, USA).
4. Results and discussion 4.1. Determination of model parameters To apply the model for analyzing RO filtration system, it is necessary to determine the model
parameters such as α, β, ks and kb. Fig. 4(a) shows the flux and the normalized solute concentration, cb/cf, in batch cell filtration of a CaSO4 saturated solution as a function of VCF. The transmembrane pressure was 1000 kPa, and the stirring speed ω was 0 rpm. Under this condition, RO fouling occurs only by surface crystallization due to high concentration polarization [9], allowing an accurate determination of β from experimental data. Using the mass balance for CaSO4, ms/A was calculated and correlated with surface coverage (φ=Ab/A). Without bulk crystallization, φ=1!J/Ji where Ji is the initial flux. As shown in Fig. 4(b), a linear relationship between ms/A and φ was found and β was estimated to be 2.83104 m2/kg. Fig. 5(a) shows the flux and the normalized solute concentrations in crossflow filtration of a supersaturated solution (4800 mg/L of CaSO4) under total recycle mode to estimate α. According to a previous study [10], this condition is favorable for bulk crystallization rather than surface crystallization. Based on the mass balance and resistance analysis, a linear relationship between mc/A and Rc was obtained as depicted in Fig. 5(b). The α was calculated at 4.151014 m/kg. The rate constants for surface crystallization and bulk crystallization were also estimated using batch crystallization data and Eqs. (10) and (11).
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(a)
339
(b)
Fig. 4. Determination of surface coverage constant (ß) using unstirred cell device. (Operating conditions: ΔP = 1000 kPa; ω = 300 rpm; —, model calculation; ! experimental data).
(a)
(b)
Fig. 5. Determination of specific cake resistance (α) using crossflow RO filtration. (Operating conditions: ΔP = 1000 kPa; v = 2 m/s; —, model calculation; ! experimental data). (a) Flux and bulk concentration. (b) Felationship between bulk crystal formation and cake resistance.
Differential and integral methods were used for solving surface and bulk crystallization equations, respectively. Through linear regressions of the data in Fig. 6, ks was determined as 0.75×10!5 m/s and kc was determined as 8.52×10!9 m3/s. These parameters were used in the model for the remainder of this paper. 4.2. Model calculations for stirred cell system As shown in Fig. 7, the model calculation was compared with experimental data for RO filtra-
tion in a stirred cell. The transmembrane pressure was 1000 kPa, and the stirring speed ω was 300 rpm. The flux remains almost constant until the VCF reaches about 4.2. Above this VCF, the flux abruptly decreases. These results suggest that crystallization is delayed until a VCF above 4 is reached. Then the CaSO4 in solution crystallizes and the crystals foul the membrane, rapidly reducing the permeate flux. Although there are some differences, the model correctly predicts the trends of the experimental data. The flux decline below the VCF of
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(a)
(b)
Fig. 6. Determination of the rate constant for bulk crystallization through batch crystallization experiment.
crystallization appears to be negligible because of high concentration polarization. As shown in Fig. 8(b), cw is initially 1.6 times high than cb, resulting in a faster nucleation and crystal growth at RO membrane surface. The difference between cw and cb decreases as flux is reduced by surface crystallization. Considering that the concentration polarization is substantial for most stirred cell tests, it is likely that the scale formation due to bulk crystallization is negligible in batch cell filtration. 4.3. Effect of background organics and additives Fig. 7. Comparison of model calculation with experimental data from stirred cell. (Operating conditions: ΔP = 1000 kPa; ω = 300 rpm).
4 is attributed to an increase in osmotic pressure. At VCF = 4, the induction period ends, leading to a rapid crystallization and membrane fouling. The induction time for this test was calculated as 2949 s. Fig. 8(a) illustrates how the scale formation occurs during the RO filtration. Based on the model calculation, scale formation due to surface crystallization starts above VCF = 4. At the end of the test, approximately 16% of total CaSO4 was precipitated. Scale formation due to bulk
In RO filtration, a small amount of organic matters and additives may exist in the feed solution. Especially, antiscalants such as sodium hexametaphosphate (SHMP) are commonly used for most RO plants to retard scale formation. Here, the effect of organic matters was examined in both experimental and theoretical ways. Figs. 9(a) and (b) shows the flux as a function of VCF for stirred cell filtration of the CaSO4 saturated solution in the presence of background organics. The concentrations for bovine serum albumin (BSA) and dextran were 2 mg/L. It is evident that BSA and dextran did not affect the flux decline due to scale formation. On the contrary, an addition of tannin or SHMP at 2 mg/L was effective to retard scale formation as illus-
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(a)
341
(b)
Fig. 8. Model calculation of scale formation and concentration profiles. (Operating conditions: ΔP = 1000 kPa; ω = 300 rpm). (a) Scale formation. (b) Bulk concentration (Cb) and wall concentration (Cw).
Fig. 9. Model calculation and experimental data for permeate flux in in crossflow RO filtration with various additives. (Operating conditions: ΔP = 1000 kPa; ω = 300 rpm; —, model calculation; ! experimental data).
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Fig. 10. Comparison of model calculation with experimental data for permeate flux and solute concentration in crossflow RO. (Operating conditions: ΔP = 1000 kPa; ω = 300 rpm; —, model calculation; ! experimental data). (a) Permeate flux. (b) Bulk concentration (Cb).
trated in Figs. 9(c) and (d). This is because these organics may adsorb or affect the active sites of crystal growth, leading to a reduced rate of nucleation and crystal growth. To quantify the effect of organics on scale formation, the model was fitted with the experimental data in Fig. 9 by changing the induction time. Then the surface energy σ was calculated from the induction time. As expected, σ values for BSA and dextran were same as that without any organics or additives (9.4×10!3 J/m2), σ values for tannin and SHMP were 9.6810!3 J/m2 and 9.5910!3 J/m2, respectively, which are slightly higher. It is likely that that the model may be used to quantify the impact of background organics or effectiveness of antiscalant on scale formation in RO process.
Fig. 11. Model calculation of scale formation from bulk crystallization and surface crystallization in crossflow RO filtration. (Operating conditions: ΔP = 1000 kPa; v = 0.6 m/s; —, surface scale formation; - -, bulk scale formation).
4.4. Model calculations for crossflow system While it is helpful to consider dead-end batch filtration using the stirred cell, a RO system will more likely operate in crossflow operation mode. Fig. 10 shows the flux and the normalized solute concentration in crossflow filtration as a function of VCF. The transmembrane pressure was 1000 kPa, and the crossflow velocity v was
0.6 m/s. In crossflow filtration, a longer time is required to reach the same VCF than in batch filtration and thus the induction time for crossflow filtration is different from that for batch filtration. Nevertheless, the model matches the experimental flux and bulk concentration well by adjusting the induction time.
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Fig. 12. Model calculation and experimental data for permeate flux in crossflow RO filtration at various crossflow velocities. (Operating conditions: ΔP = 100 kPa).
Based on the model calculation, the scale formation rates were compared as a function of VCF as shown in Fig. 11. Unlike batch filtration, the scale formation by bulk crystallization becomes important at high VCF in crossflow filtration. This is attributed to relatively low concentration polarization ratio in crossflow filtration. The maximum value for concentration polarization ration in batch filtration (ΔP = 1000 kP, ω = 300 rpm) was 1.6 whereas that in crossflow filtration (ΔP =1000 kPa, v = 0.6 m/s) was less than 1.1. Thus, it is necessary to consider
bulk crystallization as well as surface crystallization in crossflow filtration. Since the concentration polarization is sensitive to hydrodynamics in the RO system, the crossflow velocity is an important factor affecting the scale formation. Fig. 12 illustrates the effect of crossflow velocity on flux decline due to scale formation. As expected, an increase in crossflow velocity from 0.35 to 4 m/s substantially improved the flux as well as the maximum VCF without scale formation. In all cases, model matches experiments well without changing any
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Fig. 13. Model calculation and experimental data for scale formation in crossflow RO filtration at various crossflow velocities. (Operating conditions: ΔP = 100 kPa; —, surface scale formation; - -, bulk scale formation).
parameters. Fig. 13 compares the scale formation by surface and bulk crystallization. As crossflow velocity increases, the VCF for the start of scale formation increases as well. Fig. 14 shows the dependence of concentration polarization ratio on crossflow velocity, which is calculated using the model. Compared with batch filtration, the concentration polarization ratio is smaller in crossflow filtration and decreases with increasing crossflow velocity.
Nevertheless, an additional benefit on permeate flux by increasing crossflow velocity over 1 m/s seems to be negligible because high crossflow velocity requires high energy consumption. This result suggests that an optimization of operating condition for RO filtration is required for better control of scale formation in a cost-effective way.
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References
Fig. 14. Model calculation of concentration polarization ratio in crossflow RO filtration at various crossflow velocities.
5. Conclusions In this work, scale formation in RO membrane system was investigated using a transient model based on the crystallization theory and resistancein-series model. The following conclusions can be drawn from this work: 1. In batch stirred cell filtration, surface crystallization was the dominant scale formation mechanism due to high ratio of concentration polarization. The measured flux from the experiments matches the model results quite well. 2. The model has potential as a method to quantify the effect of organics and additives on scale formation phenomena in RO filtration. 3. In crossflow filtration, both surface crystallization and bulk crystallization were important. As crossflow velocity increases, the concentration polarization ratio decreases, leading to a decreased rate of surface crystallization. The model was also useful for analyzing the flux and concentration in crossflow RO filtration. Acknowledgements This research was supported by a research grant (no. 2008-0206-49-1) from the Korea Institute of Construction Technology (KICT).
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