Control of Calcium Sulfate (Gypsum) Scale in Nanofiltration of Saline Agricultural Drainage Water

Transcription

1 ENVIRONMENTAL ENGINEERING SCIENCE Volume 19, Number 6, 2002 Mary Ann Liebert, Inc. Control of Calcium Sulfate (Gypsum) Scale in Nanofiltration of Saline Agricultural Drainage Water Yann A. Le Gouellec 1 and Menachem Elimelech 2, * 1 Environmental Engineering and Technology Newport News, VA Department of Chemical Engineering Environmental Engineering Program Yale University New Haven, CT ABSTRACT A methodology for calcium sulfate (gypsum) scale control in nanofiltration of saline waters is presented. The methodology involves the use of both theoretically and experimentally determined parameters. Pitzer s thermodynamic equations for electrolytes are used to determine the gypsum scaling potential of the feed water based on its ionic composition, whereas the extent of concentration polarization at the membrane surface is determined from the film model. A proportionality factor that relates the kinetic difference between the saturation predicted by the gypsum solubility model and the actual crystallization is determined using data from glassware crystallization experiments. The last step involves an experimentally developed parabolic equation relating antiscalant (polyacrylic acid) dose to the normalized concentration factors of the saline solution. These parameters are combined into a single model for predicting the required antiscalant dose to control calcium sulfate scale in nanofiltration membranes for any given saline solution. The model is tested by nanofiltration membrane experiments utilizing model solutions simulating saline agricultural drainage waters. Key words: scaling; calcium sulfate; gypsum, nanofiltration; agricultural drainage water; scale control; antiscalant INTRODUCTION MANY AGRICULTURAL PARTS OF THE WORLD, especially the arid and semiarid regions, suffer from adverse effects of irrigation, such as waterlogging and soil salinity. Concurrently, fresh-water resources continue to dwindle either from excessive use or from deterioration of water quality due to contamination. Because irrigation requires vast amount of water, affected regions are considering or already embarking on programs that exploit brackish aquifers or reuse agricultural drainage water for irrigating crops (Sorour et al., 1992). Since the early 1970s, serious consideration has been given to membrane technology for reclamation and reuse *Corresponding author: Department of Chemical Engineering, Environmental Engineering Program, P.O. Box , Yale University, New Haven, CT Phone: ; Fax: ; menachem.elimelech@yale.edu 387

2 388 LE GOUELLEC AND ELIMELECH of agricultural drainage water in one of the largest agricultural centers of the world, the San Joaquin Valley, CA. Agricultural drainage water reclamation would reduce the quantity of imported water and minimize drainage water volume. However, high levels of calcium and sulfate ions in the agricultural drainage water could potentially form scale on the membrane surface as their concentrations increase due to water recovery and concentration polarization effects. In our recent paper (Le Gouellec and Elimelech, 2002), the conditions for gypsum scale formation on nanofiltration (NF) membrane surfaces were systematically studied for the reclamation of agricultural drainage water. The work involved glassware experiments to observe basic characteristics of gypsum crystallization, and experimental studies of gypsum scale formation on a highperformance NF membrane with actual samples and model solutions of the agricultural drainage water. Scaling occurred at low-water recoveries, and was mostly due to calcium sulfate (gypsum) formation at the membrane surface. Additives inhibiting precipitation of calcium sulfate and calcium carbonate scales can economically increase the recovery of desalting membrane systems. The overall goal of this article is to develop a methodology for control of membrane scaling by gypsum (CaSO 4? 2H 2 O) during nanofiltration of agricultural drainage water. More specifically, the work involves a study of the impact of hydrodynamics and antiscalant dosage on inhibition of gypsum scaling in nanofiltration of model agricultural drainage water that accurately reflected the ionic composition of actual samples from the Joaquin Valley. A predictive model correlating drainage water scaling potential with membrane operating parameters is also presented. EXPERIMENTAL PROTOCOLS Model drainage water Model solutions simulating ionic composition of the drainage water were made up from deionized (DI) water and reagent grade salts, and were based on the analysis of drainage water sampled at the Adams Avenue and Tulare Lake sites in the San Joaquin Valley (Table 1). Nanofiltration scaling experiments with these drainage waters were reported in our recent publication (Le Gouellec and Elimelech, 2002). Nitrate was simulated as chloride, because it has no effect on membrane scaling and performance. Ambient ionic composition of the Adams Avenue drainage water was simulated by M CaCl 2? 2H 2 O, M MgSO 4? 7H 2 O, M Na 2 SO 4, M NaCl, and M NaHCO 3 ; drainage water ionic composition of the Tulare Lake location was simulated by M CaCl 2? 2H 2 O, M MgCl 2? 6H 2 O, M Na 2 SO 4, M NaCl, and M NaHCO 3. Alkalinity was assumed to be essentially due to bicarbonate because ph was less than 8.3. Replacing NaHCO 3 with NaCl in model solutions simulated acidification of drainage water (to prevent calcium carbonate scaling), so that the overall ionic strength was kept almost identical. Nanofiltration membrane and membrane test unit A low-pressure, fully aromatic polyamide NF membrane (NF-90, FilmTec, Dow Chemical, Midland, MI) was used for drainage water nanofiltration. The membrane was available in spiral-wound elements that were cut open. The membrane sheets were thoroughly rinsed with deionized water and stored at 5 C in a closed plastic bottle filled to the rim with deionized water. Table 1. Composition of drainage water from the Adams Avenue and Tulare Lake sites, San Joaquin Valley, California. Adams Avenue Tulare Lake Constituent (mg/l) (mm) (mg/l) (mm) Total dissolved solids 7,760 5,810 Alkalinity (as CaCO 3 ) ph [7.7] [7.9] Total organic carbon 6 21 Calcium Magnesium Sodium 1, , Sulfate 3, , Chloride 1, , Nitrate Discussion of the measurements is given in Le Gouellec and Elimelech (2002). These data were used to prepare the corresponding model solutions used in this article.

3 CONTROL OF GYPSUM SCALE IN NANOFILTRATION OF SALINE WATER 389 Membrane experiments were conducted in a small plate-and-frame laboratory recirculation unit, having two rectangular test cells, each with a membrane area of 20 cm 2 (7.7 by 2.6 cm) and a channel height of 3 mm. The magnetically stirred polyethylene reservoir (Nalgene) was designed to accommodate a feed solution of up to 18 L. Feed water temperature was maintained at 20 C by a chiller (Model 625, Fisher Scientific, Pittsburgh, PA). A positive displacement pump (Hydracell, Wanner Engineering, Minneapolis, MN) delivered 2.1 liter per minute of water to each cell. This flow rate resulted in a crossflow velocity of 0.4 m/s and a Reynolds number (with the channel hydraulic diameter as a characteristic length) of 2,176. A back-pressure regulator (U.S. Paraplate, Auburn, CA) controlled the applied pressure. Flux and cumulated permeate volume were continuously monitored by a digital flow meter (Model 1000, Fisher Scientific, Pittsburgh, PA) interfaced with a personal computer. Membrane was stabilized overnight prior to each run. Stabilization served the dual purpose of membrane compaction and conditioning. The membrane was stabilized at the planned initial flux (most runs at 7.1 mm/s or 15 gfd) with all salts present, except CaCl 2? 2H 2 O, which was added at the onset of the scaling experiment. Nanofiltration membrane experiments included permeate disposal runs (permeate disposed and concentrate recycled) to simulate water recovery and its effect on the onset of scaling (Le Gouellec and Elimelech, 2002), and feedwater recirculation runs (permeate and concentrate recycled) at a fixed concentration factor to establish performance change over time. When each run was completed, usually over a course of 48 h, the membranes were taken out of the cells and replaced with wastable membranes, following which the unit was cleaned by recirculation of a basic solution (ph 10) containing detergent and EDTA, and then thoroughly flushed with deionized water. Gypsum precipitation in glassware experiments A multiposition magnetic stirrer (Cole Parmer, Chicago, IL) allowed the simultaneous observation of five glassware experiments. Such experiments were conducted in open 500 ml beakers, when calcium monitoring was performed, or Erlenmeyer flasks with stoppers when simple observation was required. In the calcium electrode experiments, it was difficult to maintain a constant temperature and the temperature ranged from 17 to 23 C. For visual determination experiments, however, the glassware was immersed in a water-filled acrylic open bath, which was placed on top of the five-position magnetic stirrer. An immersion circulator (Isotemp model 71, Fisher Scientific) controlled the temperature of the bath. A calcium half-cell electrode (model 93-20, Orion, Beverly, MA) and a single junction reference electrode (model 90-01, Orion) were connected to a ph/mv meter (Accumet, model 15, Fisher Scientific, Pittsburgh, PA). Measurement of calcium concentration by calcium selective electrode is simple and fast compared to other traditional methods such as atomic absorption or titration by EDTA. When the electrode is in contact with a calcium solution, a potential, which depends on the free calcium ion activity in solution, develops across the gelled organophilic membrane and is measured against a constant reference potential. If the background ionic strength is high and constant relative to the calcium ion concentration, then the solution activity coefficient is constant and the calcium ion activity is directly proportional to the free calcium ion concentration. A decrease in voltage with time indicates that free calcium ion concentration decreases because of calcium sulfate dihydrate (gypsum) precipitation (Kalyanaraman et al., 1973). Details on the calcium electrode calibration are given in Le Gouellec and Elimelech (2002). A batch of five simultaneous tests could be run for glassware experiments with visual qualitative determination of scaling. Each Erlenmeyer flask was filled with a freshly prepared drainage water model solution at a specific concentration factor (relative to the base model solution set at CF 5 1). Each batch was observed by the naked eye over a period of 24 h, and precipitation was deemed to have occurred if the solution became slightly turbid when compared to its initial clarity. The process was iterated until the concentration factor (CF) at which gypsum precipitated was narrowed down to CF Concentration factor and water recovery increase simulation in the NF unit Because the membrane surface area in the plate-andframe NF unit was very small (20 cm 2 per cell), it was not possible to directly study the effect of water recovery on gypsum scaling. The small surface area of the membrane coupon would produce permeate water in quantities too small to reasonably assess recovery variations. To circumvent this difficulty, the permeate was disposed rather than recycled back to the feed tank, thus allowing the feed tank salt concentration to increase continuously with time. The concentration factor (CF) obtained in such way was related to the recovery of a real membrane module, Y, when salt rejection, R, is known at each recovery via (Le Gouellec and Elimelech, 2002): Antiscalant CF 2 1 Y 5 }} (1) CF 2 (1 2 R) Flocon 100 (obtained from FMC, Princeton, NJ) is an antiscalant additive for controlling calcium carbonate and ENVIRON ENG SCI, VOL. 19, NO. 6, 2002

4 390 LE GOUELLEC AND ELIMELECH calcium sulfate scales in waters with high precipitate fouling potential. Although the formula is proprietary, Amjad (1985) characterized it as a polyacrylic acid (PAA) with a molecular weight in the range of 3,500 g/mol. The pale yellow liquid sample, with specific gravity of 1.17 at 25 C, was diluted in stock solutions of 10,000 mg/l. RESULTS AND DISCUSSION Scale formation and control in glassware experiments Figure 1 illustrates the effect of polyacrylic acid (PAA) on scaling in the model drainage water solution from the Adams Avenue site at CF 2.0 (i.e., at twice the ionic concentration of the model drainage water). Gypsum precipitation, indicated by a decrease in free calcium ion concentration, takes place in absence of antiscalant after a short induction time, with the initial plateau (at M Ca 21 ) lasting about 4 h. Gypsum incipient nuclei are formed during the induction time, which is dependent on initial concentration and temperature (Le Gouellec and Elimelech, 2002). Note that the added calcium concentration was M, which means that M of free Ca 21 was used for the formation of gypsum incipient nuclei. If the antiscalant mode of action was to sequester the initial calcium ions, the formation of incipient nuclei would be inhibited. However, in the presence of antiscalant, the initial concentration of free Ca 21 is the same as in absence of antiscalant, i.e., M. Furthermore, the concentration of the antiscalant introduced (10 mg/l polyacrylic acid) is very small compared to the M Ca 21 used for the formation of incipient nuclei, thereby making calcium ion sequestration unlikely. Rather, polyacrylic acid inhibited, if not retarded, the gypsum crystallization phase (Amjad, 1985). Impact of concentration polarization modulus on scale formation Glassware experiments with visual observation of gypsum precipitation were conducted for different concentration factors of model solutions, which simulated drainage water from the Adams Avenue and Tulare Lake sites. By trial and error, a threshold precipitation CF was determined for each type of drainage water. Membrane recirculation experiments were then conducted to determine the threshold scaling CF at which crystals first appear on the membrane at a specific flux. The fouled membrane surface was scanned with a 203 magnifier to detect the crystals. Flux decline was only observed for CF values significantly higher than the threshold scaling CF. The ratio of threshold precipitation CF (glassware experiments) to threshold scaling CF (membrane experiments) is directly related to the concentration polarization modulus (i.e., the ratio of membrane surface salt concentration to the bulk salt concentration) at the specific flux, as described later in this section. For model solution based on acidified (ph 5.3 to prevent calcium carbonate scaling) Adams Avenue drainage water, glassware experiments yielded precipitation CF 1.5, whereas from membrane experiments (Fig. 2) gypsum crystals started to appear on the membrane at a Figure 1. Effect of 10 mg/l polyacrylic acid (PAA) in Adams Avenue model solution at CF 2.0 on calcium sulfate precipitation during glassware experiments.

5 CONTROL OF GYPSUM SCALE IN NANOFILTRATION OF SALINE WATER 391 Figure 2. Recirculation of Adams Avenue and Tulare Lake model solutions, without bicarbonate, at CF 1.1 and CF 3.4, respectively. Gypsum crystals start to appear on the membrane surface at these CFs. Experimental conditions: ph 5.7, initial permeate flux 7.1 mm/s, crossflow 0.4 m/s, and temperature 20 C. threshold scaling CF 1.1. As shown in Fig. 2, no significant flux decline was observed because only a very small portion of the membrane surface area (approximately less than 5%) was covered with these permeation-obstructing crystals. Based on the above CF values, one can suggest that the increase in membrane surface concentration due to concentration polarization is by a factor of 1.5/1.1, i.e., a concentration polarization modulus (CPM) value of For the model solution based on Tulare Lake drainage water without CaCO 3 (s) scaling potential, glassware experiments resulted in precipitation CF 4.45, and membrane experiments in a threshold scaling CF 3.4 (Fig. 2), so that the CPM is Recirculation experiments at initial fluxes of 4.7, 7.1, and 9.4 mm/s (10, 15, and 20 gfd) were conducted with model solutions based on Adams Avenue drainage water at ambient ph, which started to precipitate at precipitation CF 1.9 in glassware experiments. For membrane experiments, threshold scaling CF s were 1.6, 1.45, and 1.3 for 4.7, 7.1, and 9.4 mm/s (10, 15, and 20 gfd), respectively, which yielded CPM 1.19, 1.31, and 1.46 for the corresponding permeate fluxes. CF values obtained from glassware experiments need to be compared with saturation values predicted using Pitzer s thermodynamic equations for electrolytes at 20 C (Pitzer, 1973, 1975; Pitzer and Mayorga, 1973, 1974; Pitzer and Kim, 1974). This ion-specific interaction model provides accurate values for the mean activity coefficient of an electrolyte as well as for the activity of water. The activity coefficient expressions are parameterized using binary and ternary system solubility and osmotic data. Derivatives of the virial expansion of the excess free energy are arranged into terms directly accessible for determination by a fitting procedure with experimental data. Extensive details on the solubility model were given elsewhere (Le Gouellec de Schwarz, 1998). The predicted saturation CF values for the model solutions based on Adams Avenue and Tulare Lake drainage waters, were 1.01 and 2.98, respectively, [without CaCO 3 (s) scaling potential]. These predicted saturation CF values are below the threshold precipitation CF values obtained in glassware experiments. Precipitation CFs from glassware experiments actually correspond to a crystallization value (i.e,. first appearance of crystals) within a fixed time frame (24 h), whereas the solubility model predicts the thermodynamic saturation value. The proportionality factor between experimental (glassware) and predicted (solubility model) CF values for both model drainage water solutions is 1.5. Note that this proportionality factor seems to be independent of ionic composition, because it is the same for the Adams Avenue and Tulare Lake model solutions, which vastly differ in ionic composition. This factor represents the kinetic discrepancy between saturation and actual crystallization. Based on this finding, crystallization CF (CF cryst ) values can be obtained for our predictive scale control model (developed below) without experiments by simply using the saturation CF (CF sat ) value predicted by the gypsum solubility model and multiplying it by the kinetic proportionality factor (1.5). Although no specific experiments were made to test the time dependence of this kinetic crystallization factor, one may expect its value to decrease with increasing experimental time frame. ENVIRON ENG SCI, VOL. 19, NO. 6, 2002

6 392 LE GOUELLEC AND ELIMELECH Determination of concentration polarization modulus by the film model Experimental CPM values need to be compared with values predicted by the classic film model for concentration polarization (Mulder, 1991): CPM 5 5 exp 1 2 (2) Here, C m, C b, and C p are the solute concentrations at the membrane surface, in the brine (bulk), and in the permeate, respectively, J w is the water flux, and k is the mass transfer coefficient. The latter is determined by using (Cussler, 1997) k Re 1/3 Sc 1/ /3 (3) for laminar flow, and C m 2 C p } Cb 2 C p D } dh D k Re 0.8 Sc 1/3 (4) } dh for turbulent flow. In these equations, the hydraulic diameter, d h, the Reynolds number, Re, and the Schmidt number, Sc, are defined as channel cross section area d h }}} 2 (5) channel wetted perimeter ud h Re 5 } (6) v v Sc 5 } (7) D where D is the diffusion coefficient, u is the feed crossflow velocity, and n is the kinematic viscosity. Ion concentrations and diffusion coefficients were combined in a weighted average to determine the model solution diffusivity, D. Values for ion diffusion coefficients and ion J w } k d h } L concentrations used in the calculations of D are shown in Table 2 (Cussler, 1997). Equation (3) describes mass transfer in laminar flow whereas Equation (4) is for turbulent flow. Under the conditions employed in the experiments, the flow in each rectangular membrane channel cell is in the transition region between laminar and turbulent (Re 5 2,176). Hence, predicted CPM values in laminar and turbulent conditions should be averaged for comparison with experimental CPM results. Predicted CPM values are presented in Table 3 for each model solution and at various fluxes. As shown, a good agreement between calculated values and experimental results is obtained. This important finding will be utilized later when we present our model for scale control. Scale control in membrane experiments Initial membrane experiments for gypsum scale control were conducted at various concentrations of polyacrylic acid (PAA). Figure 3 shows flux behavior when the Adams Avenue model solution at CF 3.1 is recirculated over 24 h with 5, 15, and 45 mg/l PAA initially present. The various salts were directly introduced at 3.1 times the ionic concentration of the model drainage water in deionized water initially containing 5, 15, and 45 mg/l PAA. Based on Equation (1), CF 3.1 simulates an equivalent 70% water recovery (i.e., Y 5 0.7). Antiscalant dosage is crucial, and if it is insufficient, membrane fouling occurs as seen by the sharp flux declines for 5 and 15 mg/l PAA. The results also demonstrate that PAA is able to prevent both calcium carbonate and calcium sulfate scales if there is enough antiscalant in solution (i.e., 45 mg/l for Adams Avenue model solution at CF 3.1). Presented in Fig. 4 are scanning electron microscopy (SEM) images of the membrane surface when the model solution at CF 3.1 is recirculated with 45 mg/l PAA and 5 mg/l PAA (see flux curves in Fig. 3). As Table 2. Ion diffusion coefficients and concentrations from Adams Avenue and Tulare Lake, which are needed for the calculation of the overall diffusion coefficient of the solution. Diffusion Concentration (M) Concentration (M) Species coefficients (cm 2 /s) Adams Avenue Tulare Lake H a a Na Ca Mg CO a a SO Cl a Because the diffusion coefficient of HCO 3 2 was not available, bicarbonate was assumed to be H 1 1 CO In the absence of calcium carbonate scaling potential, concentrations of H 1 and CO 3 22 were considered negligible.

7 CONTROL OF GYPSUM SCALE IN NANOFILTRATION OF SALINE WATER 393 Table 3. Experimental and predicted concentration polarization modulus (CPM) values for different model solutions and at various fluxes. Adams solution Tulare solution (NaHCO 3 replaced (NaHCO 3 replaced Adams solution by NaCl) by NaCl) (with NaHCO 3 ) Diffusivity cm 2 /s cm 2 /s cm 2 /s k (laminar) k (turbulent) k (transition) CPM cal (4.7 mm/s) CPM cal (7.1 mm/s) CPM cal (9.4 mm/s) CPM exp (4.7 mm/s) 1.19 CPM exp (7.1 mm/s) CPM exp (9.4 mm/s) 1.46 seen from the SEM images, the membrane surface is clean, smooth, and void of any crystals at an optimal dose, but a fouling layer is present when the antiscalant is underdosed. To confirm the above findings, an Adams Avenue model solution with initially 15 mg/l of PAA was concentrated to CF 3.1 by successive permeate disposal experiments and subsequently recirculated for 24 h. The curve (solid line) is comparable to the recirculation of a feed solution directly prepared at CF 3.1 with 45 mg/l initially present (Fig. 3). Whether concentration of the model solution was performed by successive permeate disposal experiments or direct salt introduction, the same PAA dosage to prevent scaling during recirculation was obtained (i.e., 3.1 times 15 mg/l < 45 mg/l). The fact this PAA dosage was obtained through two distinct methods validates the above assertion. Glassware experiments with visualization of precipitation onset were conducted for different CFs of the model solution based on Adams Avenue drainage water at ambient ph (i.e., ph 7.7) to determine the required PAA dosage. Results are presented in Fig. 5, where a parabolic-type curve fits the data rather well. The graph also shows that 45 mg/l is required at CF 4.0. This is compatible with the above CF 3.1 result in membrane experiments, because CF 3.1 multiplied by the CPM value at 7.1 mm/s (i.e., CPM ) is equal to CF 4.0. Similar glassware experiments were run for model solutions based on Adams Avenue and Tulare Lake drainage waters but without calcium carbonate scaling potential. Figure 3. Recirculation at 7.1 mm/s (15 gfd) of the model solution based on Adams Avenue drainage water (at initially ph amb 5 7.7) for CF 3.1, with various polyacrylic acid (PAA) dosages. Experimental conditions: crossflow 0.4 m/s, temperature 20 C. ENVIRON ENG SCI, VOL. 19, NO. 6, 2002

8 394 LE GOUELLEC AND ELIMELECH Figure 4. SEM images of the cross-section of the membrane after recirculation of Adams Avenue model solution (at initially ph amb 5 7.7) for CF 3.1 (70% recovery) with (a) 5 mg/l and (b) 45 mg/l polyacrylic acid, respectively (corresponding to runs of Fig. 3). Figure 5. Polyacrylic acid (PAA) dosage required to prevent the onset of precipitation at different concentration factors (CFs) of the model solution based on Adams Avenue drainage water (ph amb 5 7.7) (glassware experiments at 20 C). Glassware experiments demonstrated that 5 mg/l PAA was required to prevent gypsum precipitation when solutions were set at their CF cryst multiplied by CPM at 7.1 mm/s (i.e., CF 1.9 for Adams Avenue and CF 5.9 for Tulare Lake). To confirm these findings, the Tulare Lake solution with 5 mg/l PAA was recirculated in the NF system at CF 4.45 (80% water recovery) and 7.1 mm/s (Fig. 6). SEM images, similar to those presented in Fig. 4, demonstrated that the membrane was clear at optimal dose. The membrane surface is clean, and no flux decline was observed, which confirms the validity of accounting for CPM in evaluating PAA dosage from glassware experiments. Similarly, 25 mg/l PAA was required to prevent precipitation of the Adams Avenue model solution (without calcium carbonate scaling potential) at CF 3.1 in glassware experiments. Recirculation of the Adams Avenue solution (with gypsum scaling potential only) at CF 2.35 and 7.1 mm/s (i.e., CF CPMCF 3.1) revealed no flux decline when 25 mg/l of antiscalant were introduced in solution (Fig. 6). With corresponding operating pressures of 15.3 and 22.4 bars (225 and 330 psi) and recoveries of 60 and 80% for Adams Avenue and Tulare Lake, respectively, there is considerable improvement in performance compared to earlier attempts at drainage water reclamation by reverse osmosis membranes (McCutchan et al., ; Mariñas and Selleck, 1987). Table 4 shows the rejection levels of each ion under these physico-chemical conditions. The overall TDS rejection level provided by the membrane is about 94% for both waters, and is calculated as the weighted average of the ion rejection percentages based on their concentration in the permeate. As expected, divalent cations are much better rejected than monovalent ions (Rautenbach and Gröschl, 1990; Yaroshchuk and Staude, 1992; Seidel et al., 2001). Parameter correlation Glassware experiments were conducted to determine the minimum PAA dosage required to prevent gypsum crystallization at different normalized concentration factors (CF norm ) of Adams Avenue and Tulare Lake model solutions (with no calcium carbonate scaling potential). Figure 7 plots PAA dosage vs. normalized concentration factors (CF/CF cryst ) of both model solutions. CF cryst corresponds here to the threshold precipitation CF obtained in glassware experiments for each solution (discussed earlier). At CF norm 1.3 and 2.1, the required PAA dosage

9 CONTROL OF GYPSUM SCALE IN NANOFILTRATION OF SALINE WATER 395 Figure 6. Recirculation experiment of Adams Avenue and Tulare Lake model solutions (without calcium carbonate scaling potential) made directly at the planned CF with their required PAA dosage. Experimental conditions: ph 5.7, initial permeate flux 7.1 mm/s, crossflow 0.4 m/s, and temperature 20 C. is identical for Tulare Lake and Adams Avenue. This demonstrates that the required PAA dosage depends only on the gypsum supersaturation level of each solution. This finding is important because both types of water have very different ionic composition. In other words, if the level of supersaturation is the same for both solutions, then the minimum PAA dosage required to prevent gypsum crystallization will also be the same. PAA dosage follows a parabolic (i.e., second order) curve with CF norm, as seen in Fig. 7, and therefore indicates that PAA dosage does not simply vary with the number of formed nuclei as in a linear (first order) dependence, but rather prevents crystal growth by other, more complex mode of action. This suggestion is supported by the work of Weijnen et al. (1987), and especially their reference to the model of Cabrera and Vermileya (1958), which showed that growth inhibition was accomplished through a stockade of adsorbed antiscalant on the surface of nascent crystals (i.e., nuclei). Calcium sulfate scale control can be modeled without having to conduct specific and systematic laboratory experiments for each type of drainage water. Optimization of operating conditions for all types of water with gypsum scaling potential can now be generalized by correlating planned water recovery (i.e., CF), desired permeate flux, saturation level of feed solution at the designed recovery, and required PAA dosage. First, permeate quality must meet the desired standard, TDS perm (depends on the application of the reclaimed water). As feedwater flows across the membrane module, the salinity of the brine and permeate increases. Thus, the feed solution can only be concentrated to a factor that ensures a permeate salinity below the desired standard. This feed solution maximum CF Table 4. Ion rejection levels by the NF membrane for the recirculation at 7.1 mm/s (15 gfd) of Adams Avenue and Tulare Lake model solutions at CF 2.35 and 4.45, respectively. Adams Avenue at CF 2.35 Tulare Lake at CF 4.45 Feed Permeate Feed Permeate Ion (mg/l) (mg/l) Rejection (mg/l) (mg/l) Rejection Ca 21 1, % % Mg % % Na 1 3, % 7, % 22 SO 4 9, % 9, % Cl 2 2, % 5, % Other experimental conditions are given in the caption of Fig. 6. ENVIRON ENG SCI, VOL. 19, NO. 6, 2002

10 396 LE GOUELLEC AND ELIMELECH Figure 7. Determination from glassware experiments (20 C) of required polyacrylic acid (PAA) dosage at various normalized concentration factors (CF/CF cryst ) of model solutions based on drainage water composition from Adams Avenue and Tulare Lake sites (both without calcium carbonate scaling potential). (CF max ) can be evaluated knowing the TDS rejection level provided by the NF membrane, R: TDS perm CF max 5 }} (8) (1 2 R)TDSfeed Then, depending on the desired flux, CF max is increased by the concentration polarization modulus, CPM, using Equation (2). The concentrations corresponding to CPM 3 CF max are entered in the solubility model (discussed earlier), which predicts saturation CF (CF sat ) of the solution at the membrane surface. This value needs to be multiplied by the kinetic related proportionality factor to obtain CF cryst (discussed earlier). Finally, the required PAA dosage for the normalized concentration factor CF norm 5 (CPM 3 CF max )/CF cryst is evaluated based on the dosage versus CF norm curve from Fig. 7. Note that in real membrane plants, this optimal PAA dosage, when added in the feed, would be divided by CF max, because feed concentration (i.e., recovery) occurs in membrane modules. A flowchart of these steps is presented in Fig. 8. CONCLUDING REMARKS A novel predictive model for physico-chemical control of gypsum scale in nanofiltration membranes was developed based on a rigorous gypsum solubility model and a correlation between concentration polarization Figure 8. Flow chart describing the steps to determine the required polyacrylic dosage to prevent gypsum scaling, based on planned quality of effluent. modulus, permeate flux, and initial scale formation. A proportionality factor, which appeared independent of the saline solution ionic composition, linked the saturation CF (CF sat ) calculated by the solubility model to a crystallization value for use in the PAA dosage parabolic curve. The model parameters (i.e., intended permeate salinity, planned flux that directly affects recovery, and PAA dosage) are dependent on each other so that setting one parameter directly affects the value of the other parameters. This interdependence may result in economic tradeoffs, such as favoring operating cost savings (e.g., low flux or antiscalant dosage) over permeate quality. This gypsum scale control model is applicable to any given saline solution. ACKNOWLEDGMENTS The authors thank the California Department of Water Resources for their financial support during this study.

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