The effect of pH on the formation of a gypsum scale in the presence of a phosphonate antiscalant

Desalination 284 (2012) 207–220

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The effect of pH on the formation of a gypsum scale in the presence of a phosphonate antiscalant Yoav O. Rosenberg a,⁎, Itay J. Reznik a, Sharon Zmora-Nahum b, Jiwchar Ganor a a b

Department of Geological and Environmental Sciences, Ben-Gurion University of the Negev, P.O.B. 653, Beer Sheva 84105, Israel Mekorot, Israel National Water Company, Ashkelon, Israel

a r t i c l e

i n f o

Article history: Received 2 June 2011 Received in revised form 29 August 2011 Accepted 30 August 2011 Available online 27 October 2011 Keywords: Gypsum Adsorption Scaling Rate law Antiscalant pH

a b s t r a c t A massive gypsum scale in a discharge pipe of a desalination plant occurred despite the presence of an antiscalant (PermaTreat, PC-191). The scaling occurred following a sharp drop in the reject-brine pH when an acidic effluent (pH b 2) was introduced. Batch experiments revealed that the antiscalant is effective in postponing nucleation and hindering the crystal growth kinetics of gypsum in the supersaturated brine (Ωgypsum N 2) at neutral pH. However, as pH decreases both nucleation and crystal growth accelerate. A single general rate law that consistently described the crystal growth of gypsum as a function of pH in the batch experiments was found to be: Rate ¼ SBET




10
2  1=2 1=2 ; k1 ⋅ Ω −1 þ k2 ⋅ Ω −1

where ki is the pH-dependant rate coefficient (mol m − 2 s− 1) and SBET is the BET surface area of gypsum (m 2). The dependence of the rate coefficients on pH is described quantitatively by an adsorption model which considers the protonation of the antiscalant functional groups. Finally, the precipitation rate of gypsum in the pipe was investigated with the laboratory rate law and adsorption model. It is shown that gypsum precipitation in the pipe occurs even in the absence of the acidic effluent and despite the fact that it could not be analytically detected. © 2011 Elsevier B.V. All rights reserved.

1. Introduction Calcium sulfate minerals (i.e., gypsum, anhydrite and hemi-hydrate) are common scale-deposit minerals in water treatment plants [1–4] and oil and gas industry [5]. Commercial scale inhibitors (henceforth, antiscalants) are widely used for preventing scale-deposits in pipes, heat exchangers and desalination facilities [5]. As reactive constituents, these antiscalants interact with their surroundings and alter the course and/or progress of different mineral precipitation [6]. Usually, the specific chemical formula and structure of the antiscalants are not revealed by the manufacturers and numerous studies were conducted in order to describe the physicochemical conditions for optimal antiscalant performance [7, and references therein]. One of the most important and widely used group of antiscalants is phosphonic acid derivatives [8 and references therein, 9]. Such antiscalants contain phosphonates as functional groups (C-PO(OH)2), which were reported as efficient precipitation inhibitors for sulfate minerals such as gypsum [10–12] and barite (BaSO4) [10,13,14].

⁎ Corresponding author. E-mail address: [email protected] (Y.O. Rosenberg). 0011-9164/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.desal.2011.08.061

Antiscalants are considered to inhibit the growth of crystals by adsorbing to reactive surface sites [8,14–16], and thus the antiscalants effect on mineral precipitation is often described in terms of an adsorption model [17,18]. For phosphonate based antiscalants, Weijnen and Van Rosmalen [12] have argued that both the protonated phosphonate groups, PO3H −, and fully dissociated groups, PO32−, are essential in the adsorption process to gypsum surface. The latter is able to penetrate the hydration layer which coats the gypsum surface while the former adsorbs more strongly to the reactive surface sites. Phosphonate additives have a profound effect on the structure and morphology of gypsum crystals. For example, Akyol et al. [19] have shown that the presence of phosphonate additives in a supersaturated solution of gypsum resulted in the precipitation of less elongated needle and plate-like crystals compared to a similar solution in the absence of additives. The arithmetic and geometric mean diameters of gypsum crystals were lowered with all additives than in the absence of these additives. On the molecular scale Bosbach and Hochella [8] have shown that the step morphology changes when exposed to a phosphonate additive. The [101] steps on the (010) surface become jagged while [001] remain virtually unaffected and steps with a new crystallographic direction parallel [100] are established.

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The role of the phosphonate functional groups in adsorbing to the crystal surface indicates that pH should affect the inhibition performance of phosphonate compounds [16], and thus may alter the precipitation kinetics of minerals that are not directly pH dependent (e.g., gypsum). Weijnen et al. [11] and Weijnen and van Rosmalen [12] studied the adsorption of two phosphonate compounds (HEDP and amino-methane-disphosphonic acid, AMDP) to gypsum surfaces and their inhibition effect on gypsum crystal growth. Weijnen et al. [11] have shown that the rate of gypsum crystal growth in the presence of hydroxyethylene diphosphonic acid (HEDP) increases as pH decreased from 7 to 3.5. Weijnen and Van Rosmalen [12] have shown that the amount of HEDP adsorbed to gypsum surface decreased as pH decreased from 7 to 5. Many of the studies on scale-deposit minerals were performed in the laboratory or in small scale pilot systems. The present study combines both laboratory and field based research in order to quantitatively describe the growth of a gypsum scale-deposit in a reject pipe of a regional desalination plant. Through this combination the present study aims to better understand the kinetics of gypsum precipitation and its interactions with phosphonate inhibitors on a larger scale than the laboratory. It is shown in the paper that the scale-deposit grew despite the presence of a phosphonate antiscalant due to low pH conditions of the reject brine. We first performed a comprehensive laboratory study on the effects of pH and antiscalant concentration on the gypsum precipitation kinetics. Detailed models of pH dependent crystal growth and antiscalant adsorption were then applied to the field study in order to quantitatively describe the growth of the gypsum scale. 1.1. Description of the case study The Ketziot desalination plant (KDP), situated in the Negev desert in Israel, desalinizes saline groundwater (~ 3.7 ∙ 10 6 m 3 year − 1) by reverse osmosis (RO) in order to provide fresh water to the surrounding villages. The plant usually works at a high recovery ratio, yielding ~ 88% of the feed water as product water. The remaining reject brine, (~ 4.4 ∙ 10 5 m 3 year − 1, henceforth, KDP concentrate) which is supersaturated with respect to gypsum (CaSO4∙2(H2O), Table 1), is conveyed through an 8 inch pipe, 6.5 km long, to 6 sequential evaporation ponds. A phosphonate antiscalant PermaTreat 191 (henceforth, PC-191) is added to the feed water at initial concentration of ~ 5.5 ppm to prevent scale formation on the RO membranes. Since the antiscalant does not pass through the RO membranes, it remains in the KDP concentrate after the RO process, at concentrations up to ~ 45 ppm. Due to the high concentration of the antiscalant in the KDP concentrate, it is expected that scale formation will be prevented as the concentrate flows through the discharge pipe (b6 h). However, during a period of 2 years, a massive gypsum scale formed inside the discharge pipe. In some cases, the gypsum clogged extensive parts of the pipe diameter causing a considerable pressure increase (Fig. 1a). Since the product water serves for agriculture, it is further treated with anionic exchange columns in order to remove boron which is not filtered by the RO membranes (Rohm and Haas AMBERPACK boron removal system packed with AMBERLITE IRA743 resin). Replenishment of the column adsorption sites is performed by washing the columns repeatedly with NaOH and H2SO4. The resultant acidic effluent (AE, pH 1.8 Table 1) was periodically released into the KDP concentrate stream at the head of the discharge pipe. The average weight fraction of the AE from the whole mix was ~5%, reducing the concentrate pH from 7.3 to 2.8. The KDP case study presents an opportunity to study the formation of a massive scale-deposit. The effects of PC-191, AE mixing, and pH on the kinetics of gypsum nucleation and crystal growth were initially studied in laboratory batch experiments. The results of these experiments were then utilized to quantitatively describe the growth of the gypsum scale along the KDP discharge pipe.

Table 1 Chemical compositions of the Ketziot desalination plant concentrate (KDP), synthetic −1 concentrate (Syn) and acidic effluent (AE). Compositions are in mmol kgH2O . Cl−

SO42−

Na+

K+

Ca2+

Mg2+

B3+

pH

Ptotal

Ωgypsum

KDP Synb

424 437

65 55

380 370

8 6.6

54 50

41 40

bdla 0

7.3 7.0

0.20 0.0035c 0.22d

2.23 1.82

AE

bdla

88

120

0.4

bdla

bdla

20

1.8

a

bdl — below detection limit. b Based on the mass balance of the synthetic salts which were added except SO42− which was analyzed. c Corresponds to synthetic concentrate with 0 ppm antiscalant. d Corresponds to synthetic concentrate with 45 ppm antiscalant, similar to the expected concentration in the plant concentrate.

2. Methods 2.1. Laboratory experiments KDP concentrate for batch experiments was collected immediately after exiting the RO membranes of the plant (Table 1). AE was collected immediately after exiting the boron exchange columns (Table 1). Batch experiments were conducted in 250 ml polyethylene bottles (Kartell company) shaken in a thermostatic water bath. Most of the experiments were conducted at 25 °C except one series which was conducted at 30 °C. The experiments were sampled periodically and were immediately filtered through a 0.45 μm Millipore filter and diluted using double distilled water (DDW). To examine the effect of antiscalant concentration, PC-191 was added at various concentrations to a synthetic concentrate which was prepared by dissolving Na2SO4, CaCl2, KCl, MgCl2 and NaCl in DDW. Na2SO4 was dissolved in a separate vessel in order to avoid the attainment of supersaturation with respect to gypsum. Each experiment was initialize by mixing the two end-member solutions. The effect of AE on the nucleation and crystal growth of gypsum was studied by mixing it with either KDP or synthetic concentrates at a weight fraction of 4.8%. The effect of pH on crystal growth was studied by adding trace amounts of ultra-pure nitric acid (70%, Fluka) to the KDP concentrate. The latter set of experiments was conducted at 30 °C in order to simulate the temperature in the KDP discharge pipe. All solutions (KDP concentrate and the two end-members solutions of the synthetic concentrate) were filtered through a 0.45 μm filter prior to the beginning of the experiments. In crystal growth experiments, 2 g of gypsum seeds were added. The crystallization seeds were prepared from gypsum crystals (selenite) collected from Machtesh Ramon, Israel. The crystals were ground using an agate pestle and mortar and then sieved to obtain a crystal diameter of between 0.053 and 0.149 mm. X-ray diffraction (XRD) and Inductively Coupled Plasma (ICP) analysis of the gypsum seeds revealed that the sample was clean and contained only trace amounts of Cl (580 ppm), Na (22 ppm), K (7 ppm) and Mg (4 ppm). Table 2 summarizes all the laboratory batch experiments performed in the present study. 2.2. Field test Gypsum precipitation in the discharge pipe was measured by sampling the flowing concentrate using taps which are located along the 6.5 km pipe. Gypsum precipitation was measured during the flow of: (1) KDP–AE mixture, and (2) KDP concentrate only. The samples were filtered using a 0.22 μm filter and diluted by weight immediately in the field in order to bring the solution to be undersaturated with respect to gypsum. SO42− and Cl − were measured for each sample, while full chemical composition was determined for representative samples.

Y.O. Rosenberg et al. / Desalination 284 (2012) 207–220

a

209

b

5cm

5cm

Fig. 1. Gypsum scale in the desalination plant discharge pipe which conveys the concentrate to the evaporation ponds. About 25% of the pipe diameter is clogged by the scale (a). Following the results of the present study the scale was dissolved (b) — see Section 3.5 for discussion.

increases in the studied temperature range (K°sp,gypsum = 10− 4.581 and 10− 4.583) at 25 and 30 °C, respectively [24].

2.3. Analytical work The following methods and their associated uncertainties (one standard deviation) were used for chemical analyses of the solution samples: pH by semi-micro 83-01 Orion Ross combination electrode, ±0.02 pH units; SO42− and Cl− by ion chromatograph (Dionex, DX5000), ±2%; Na, K, Ca, Mg and total boron by ICP-AES (Vista-Prom Varian) with uncertainties better than ±5%; phosphorous (Ptotal) by ICP-MS (Agilent 7500cx), ±10%. Specific surface area of the gypsum seeds was measured by the Brunauer–Emmett–Teller (BET) method [20], using 5-points of N2 adsorption isotherms, with a Micromeritics Gemini II-2375 surface area analyzer. BET surface area was determined after degassing for 10 days at 40 °C. The relatively low temperature for the degassing procedure was selected in order to avoid dehydration of gypsum and transformation into bassanite or anhydrite [21,22]. The BET-determined initial specific surface area of the gypsum seeds is 0.41 ± 0.06 m2 g− 1. Thermodynamic calculations were performed with the ion interaction model of Pitzer (1991) using the USGS geochemical speciation software Phreeqc [23]. Gypsum supersaturation degree, Ωgypsum, is defined as (aSO42− ∙ aCa2+ ∙ a 2H2O)/K°sp,gypsum, where ai is the activity of component i and K°sp,gypsum is the solubility product constant of gypsum. Gypsum solubility product constant only slightly Table 2 Summary of laboratory batch experiments performed in the present study.

a

Reactiona

Experiment Solution compositionb name

Nucleation, antiscalant effect

12Kz−A 12Kz−B 12Kz−C

Synthetic concentrate + 0 ppm antiscalant, pH = 7.7 Synthetic concentrate + 22 ppm antiscalant, pH = 7.7 Synthetic concentrate + 45 ppm antiscalant, pH = 7.7

Nucleation, AE mixing effect

12Kz−E 12Kz−F

AE-synthetic concentrate mixture + 45 ppm antiscalant, pH = 2.8 AE-KDP concentrate mixture, pH=2.8

Nucleation, pH effect 20Kz−C

Neutralized AE-KDP concentrate mixture, pH = 7.3

Crystal growth, antiscalant effect

12KZ−H 12Kz−I

Synthetic concentrate + 0 ppm antiscalant, pH = 7.7 Synthetic concentrate + 45 ppm antiscalant, pH = 7.7

Crystal growth, AE mixing effect

12Kz−J 12Kz−G

KDP concentrate, pH=7.2 AE-KDP concentrate mixture, pH=2.7

Crystal growth, pH effect

20Kz−A 20Kz−B

Neutralized AE-KDP concentrate mixture, pH = 2.8 Neutralized AE-KDP concentrate mixture, pH = 7.3

Crystal growth, gradual pH effectc

17Kz−A to 17Kz−J

KDP concentrate acidified by nitric acid, see Table 3

All KDP concentrate contained ~45 ppm antiscalant that originated from the desalination process. b All crystal growth experiments contained 2 g of gypsum seeds. c Performed at 30 °C to simulate the temperature at the KDP pipe.

3. Results Chemical composition of the KDP concentrate, synthetic concentrate and AE are presented in Table 1. SO42− measurements as a function of time for all the experimental data are provided in the Electronic Annex (EA – 1). The serial number of each experiment appears both in the figure captions and the EA. The preparation of the synthetic concentrate was based on a previous chemical analysis of the KDP concentrate (Table 1). The deviation between the concentrations of the major ions in the synthetic concentrate and the KDP concentrate did not exceed 15%, and is probably due to changes in the recovery ratio of the plant; due to the high recovery ratio of the plant (88%), even 1% change may lead to 8% change in the concentrate composition. The concentration of Ptotal in −1 the synthetic concentrate (0.22 mmol kgH2O ) and the plant concen−1 trate (0.2 mmol kgH2O), both with ~45 ppm of the PC-191 antiscalant, is very comparable. Ptotal in the synthetic concentrate with no antisca−1 lant (0.0035 mmol kgH2O ) is significantly lower, indicating that the main source of Ptotal is from the antiscalant. 3.1. Nucleation In the absence of crystallization seeds, some time elapses between the establishment of a supersaturated solution and a new phase detection in a system. This time is known as the “induction period” or “induction time” [25]. Induction time, tind, for nucleation is determined here as the median time (±1 standard deviation) of two consecutive points between which a significant decrease in SO42− concentrations (N2%) is observed. The induction time in the synthetic concentrate without antiscalant was 18 ± 5 h (Fig. 2). Both the synthetic concentrate (containing 45 ppm of PC-191 antiscalant) and KDP concentrate (containing antiscalant originating in the RO process) did not show any significant change in SO42− concentration within the 600 h of the experiment (Figs. 2 and 3, respectively), demonstrating the antiscalant's ability to inhibit gypsum nucleation for relatively long periods. Additional experiment with half of the antiscalant concentration (22 ppm) and the synthetic concentrate also did not show any significant change in SO42− concentration within the 600 h of the experiment (AE-1, Experiment 12Kz-B). However, upon mixing the AE with both the above solutions, tind for nucleation was similar to the experiment without antiscalant and ranged

210

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60

55

55

seed seeds +antiscalant

SO4 (mmol kg-1)

50

2-

2-

50

45

SO

4

-1

(mmol kg )

55 50

45 0

2

4

6

8

10

45

antiscalant

40 antiscalant + AE

40

no antiscalant

35 0.01

0.1

1

10

100

0

1000

50

100

Fig. 2. Gypsum nucleation experiments with a synthetic concentrate containing: (●) 45 ppm of antiscalant (Experiment 12Kz-C); (▲) 45 ppm of antiscalant + 4.8% weight fraction of AE (Exp. 12Kz-E); (□) no antiscalant (Exp. 12Kz-A).

between 29 ± 5 and 17 ± 8 h for the synthetic and KDP concentrates, respectively (Figs. 2 and 3). As gypsum nucleation precedes the measured tind, the short tind in the concentrate–AE mixture experiments indicates that gypsum nuclei probably formed over the duration of the mixture flow in the discharge pipe (~ 6 h). Thus, the relatively short tind upon mixing the AE with the KDP concentrate demonstrates the significant role of the AE in promoting gypsum nucleation. Neutralizing the AE to pH 7.3 before mixing it with KDP concentrate postponed gypsum nucleation to tind greater than the experiment duration (200 h, Fig. 3). This observation indicates that the decrease in pH, caused by the mixing of AE, accelerated gypsum nucleation. 3.2. Crystal growth The change in SO42− concentration with time in a synthetic concentrate containing 45 ppm of antiscalant was significantly slower compared to concentrate containing no antiscalant (Fig. 4). Notice that both experiments were initiated with the same SO42− concentration and that a significant difference between the curves

250

300

350

400

occurs after less than 10 min (inset of Fig. 4). Similarly, gypsum crystal growth from the KDP concentrate (pH 7.2) was significantly slower in the absence than in the presence of AE (pH 2.7, Fig. 5). Neutralizing the AE before mixing it with the KDP concentrate significantly diminished this effect and slowed the precipitation rate of gypsum (Fig. 5). 3.3. Gypsum crystal growth dependence on pH Table 3 presents the initial pH, nitrate concentrations and initial saturation degree (Ωgypsum) in the 10 experiments that were conducted with nitric acid using the antiscalant bearing KDP concentrate. The rest of the chemical composition was the same as presented in Table 1. As pH decreased significantly, the initial Ωgypsum also decreased as the result of the formation of HSO4− which lowers the concentration of SO42− (Table 3). Gypsum precipitation rate (i.e., decrease in SO42− concentration with time) initially increased as pH decreased from 7.4 to 2.7 (Fig. 6). As pH continued to decrease, this trend was reversed and the change in SO42− concentration became gradually slower. To demonstrate this, the total amount of precipitated gypsum during the first 6.5 h and the first 40 h was calculated as the difference in

seeds seeds + AE seeds

65

+ AE pH 7

SO4 (mmol kg-1)

65

2-

200

Fig. 4. Gypsum crystal growth experiments with synthetic concentrate containing: (■) gypsum seeds (Exp. 12Kz-H); (●) gypsum seeds + 45 ppm of antiscalant (Exp. 12Kz-I).

70

60

64

60

60 56

52

55

0

2

4

6

8

10

2-

SO4 (mmol kg-1)

150

Elapsed time (hour)

Elapsed time (hour)

55

50 50

antiscalant antiscalant + AE antiscalant + neutralized AE

45 0.01

45 0

0.1

1

10

100

1000

50

100

150

200

250

300

350

400

Elapsed time (hour)

Elapsed time (hour) Fig. 3. Gypsum nucleation experiments with KDP concentrate containing: (●) antiscalant; (▲) 4.8% weight fraction of AE (Exp. 12Kz-F); (⧅) 4.8% weight fraction of neutralized AE (Exp 20Kz-C, pH 7.3). Antiscalant originated from the desalination process is present in all experiments.

Fig. 5. Gypsum crystal growth experiments with KDP concentrate containing: (⧅) gypsum seeds (Exp. 12Kz-J, pH 7.2); (●) gypsum seeds + 4.8% weight fraction of AE (Exp. 12Kz-G, pH 2.7); (▲) gypsum seeds + 4.8% weight fraction of neutralized AE (Exp. 20Kz-B, pH 7.3). Antiscalant originated from the RO process is present in all experiments. Error bars are omitted from the inset for clarity.

Y.O. Rosenberg et al. / Desalination 284 (2012) 207–220

4.5

Table 3 Initial conditions for crystal growth experiments with the Ketziot desalination plant concentrate acidified by nitric acid (30 °C).

17Kz-A 17Kz-B 17Kz-C 17Kz-D 17Kz-E 17Kz-F 17Kz-G 17Kz-H 17Kz-I 17Kz-J a b

Initial pH

HNO3a

7.36 6.55 6.09 5.05 4.39 3.55 2.98 2.68 2.35 1.96

2.3 2.6 3.0 3.2 3.4 4.1 5.7 8.2 14.2 27.8

SO42−

Ωgypsum

Fractionb 2.23 2.23 2.23 2.23 2.23 2.22 2.20 2.17 2.11 1.94

1.00 1.00 1.00 1.00 1.00 0.99 0.98 0.96 0.93 0.84

~6.5 h

4

Gypsum (mmol kg-1)

Experiment

211

~40 h

3.5 3 2.5 2 1.5 1

−1 mmol kgH2O . Initial fraction of free sulfate calculated as [SO42−]/[Stotal].

0.5 1

2

3

4

5

6

7

8

Initial pH SO42− concentration between time 0 (t0) and time n (tn, ~6.5 and ~40 h, Fig. 7). Fig. 7 demonstrates that the overall precipitation rate of gypsum increased with the decrease in pH from N7 to b2, despite the fact that the acidification caused the solution to be slightly closer to equilibrium with respect to gypsum (Table 3). 3.4. Gypsum precipitation in the plant discharge pipe The two field tests examined gypsum precipitation from the concentrate along the discharge pipe in the presence and the absence of the AE. Each of these field tests was conducted when the flowing conditions were stable for a long period of time (the order of a few months). Therefore, it is reasonable to assume that a quasi-steady state at time exists for each tap that was sampled (i.e., not along the pipe). During the flow of the KDP concentrate–AE mixture (first field test) 5 taps were sampled along the discharge pipe: 1. Exit of the concentrate from the RO membranes (distance 0 m from the KDP); 2. After the formation of the concentrate–AE mixture (adjacent to tap 1, distance 0 m from the KDP); 3. At a distance of 1 km from the KDP; 4. At a distance of 3.3 km from the KDP; 5. At the outflow of the solution to the evaporation ponds (6.5 km from the KDP). The flow rates of the KDP concentrate and the AE were 47.5 and 2.3 m 3 h − 1, respectively. During the flow of the KDP concentrate without AE (second field test), only taps 1 and 5 were sampled. The temperature of the solution in the discharge pipe in both field tests was similar and 65 62

2-

SO4 (mmol kg-1)

60

60

Fig. 7. The amount of gypsum precipitated as a function of pH in crystal growth experiments after ~ 6.5 and ~ 40 h. The KDP concentrate was acidified by nitric acid (Table 3, Series 17Kz).

stable along the flow (32.7 ± 0.8 C°). Table 4 summarizes the results of the two field tests. Fig. 8 shows the change in SO42− concentrations along the discharge pipe for the two field tests (symbols). The lines represent a forward model which will be discussed below (Section 4.4). During the flow of the KDP concentrate–AE mixture, a nearly constant decrease in SO42− concentrations was observed with the distance of the flow. Initial Ca2+ concentration was measured (i.e., tap 1), while Ca2+ concentrations in taps 2–5 where calculated by the change in SO42− concentrations. Ωgypsum (Table 4) was then calculated assuming that the rest of the major ions concentrations are as in Table 1. The relative precipitation potential (% ppt) was calculated according to: h

h i 2− − SO4 %ppt ¼  2−  0  2−  n ; SO4 0 − SO4 eq 2−

SO4

i

ð1Þ

where the subscripts 0, n and eq represent the initial, sampling point ‘n’ along the discharge pipe and equilibrium SO42− concentration, respectively ([SO42−] = 42 mmol kg − 1 for the KDP concentrate–AE mixture). The %ppt (Table 4) demonstrates that over a third of the precipitation potential was exploited along the pipe during the flow of the KDP concentrate–AE mixture. During the flow of the concentrate alone, no detectable change in SO42− concentration could be observed. Measurement of Ca 2+ concentrations showed the same results. However, as will be discussed below, it is reasonable to assume that gypsum does precipitate but at quantities which are below the detection limits.

58

3.5. Operational solutions

55 56 0

0.5

1

1.5

2

50

45

pH 7.36

pH 2.68

pH 1.96

40 0

50

100

150

200

250

Elapsed time (h) Fig. 6. Gypsum crystal growth experiments with the KDP concentrate (gypsum seeds) at different pH values. The KDP concentrate was acidified with nitric acid (Table 3, Series 17Kz).

Both laboratory experiments and field tests have shown that the drop in pH due to the mixing of the acidic effluent has lowered the efficiency of the PC-191 antiscalant and accelerated the scaling. Therefore, as an immediate operational solution the mixing of the AE with the reject brine was ceased and the AE was transferred independently to the ponds by a sewage tanker. About 50% of the pipe length was replaced by a new pipe in order to ease the pressure and to allow steady operation of the plant. On the long term it was hypothesized that the pure AE can dissolve the gypsum scale. Despite its high SO42− concentration it contains no Ca 2+ and its high ionic strength and acidity can lead to substantial dissolution of gypsum (Table 1). This hypothesis was examined in the lab by dissolving in AE a gypsum sample taken from

212

Y.O. Rosenberg et al. / Desalination 284 (2012) 207–220

Table 4 −1 Field tests data, SO42− and Ca2+ concentrations (mmol kgH2O ), supersaturation degree and precipitation potential in the plant discharge pipe for two field tests. pH

density

T(°C)

SO42−

Ca2+

Ωgypsum

Precipitation potential (%)

07 August 2008 — KDP concentrate–AE mixture Membrane exit 0 Concentrate–AE mixing point 0 1Km 1 3.3Km 3.3 End of pipe 6.5

6.64 2.90 2.91 2.87 2.86

1.022 1.02 1.02 1.02 1.02

32.1 33.2 33.2 33.5 33.2

66.5 66.1 64.5 60.4 58.0

56.0 55.5a 54.0a 49.9a 47.5a

2.3 2.2 2.1 1.9 1.8

0% 7% 25% 36%

14 February 2010 — KDP concentrate only Membrane exit 0 End of pipe 6.5

6.54 6.32

1.021 1.021

31 29

67.5 68.2

50.9 50.1

2.2 2.2

0% ~ 0%

Location

a

Distance from plant (km)

Calculated according to the change in SO42− concentrations.

4. Discussion

Experiments in which the pH was decreased by the addition of HNO3 acid showed that the acceleration effect of gypsum crystal growth is gradual, even at circum neutral pH values. The maximum around pH 2.7 in the amount of gypsum that precipitated can be explained as a competition between two opposite effects of the pH: 1. lowering of the Ωgypsum, and 2. lowering of the antiscalant effectiveness (Fig. 7). In the following, the rate law for gypsum precipitation is examined, in order to quantify the effects of the antiscalant and pH on this reaction.

4.1. The effect of pH on gypsum precipitation

4.2. Empirical rate law for gypsum crystal growth

Experiments with the synthetic concentrate showed that trace amount of the antiscalant PC-191 (45 ppm) can postpone gypsum nucleation for long time periods (N600 h) and to significantly slow down gypsum crystal growth despite the initial supersaturation degree of the solution (Ωgypsum N 2). As the pH of the KDP concentrate decreased by mixing it with the AE, both processes were accelerated. Neutralizing the pH of the AE prior to the mixing significantly diminished this effect.

At constant temperature and antiscalant concentration, the rate of gypsum crystal growth depends on the gypsum reactive surface area and the distance from equilibrium. A common dependency of the rate on the distance from equilibrium is given by the rate law [26]:

the scale at a ratio of 2 g solid to 100 g solution. Fig. 9 shows the increase in SO42− concentration due to gypsum dissolution. The partially clogged parts of the pipe which were taken out were then used as a new line to convey the AE to the ponds separately from the reject brine. Under this operation the AE line was examined a year later and revealed that the gypsum scale became softer and dissolved almost completely (Fig. 1b).

ð2Þ

where SA is the reactive surface area (m 2), k is the rate coefficient (mol m − 2 s − 1), Ω is the saturation degree, ν is the number of ions in the mineral formula (2 for gypsum), n is the reaction order with respect to the distance from equilibrium and Rate is the precipitation rate (mol m − 2 s − 1). The concept of “reactive surface area” [27] is consistent with the theories of surface controlled reaction kinetics. In practice, this concept is difficult to implement and the common practice is to use BET surface area [20] of the dry powder as a proxy for the reactive surface

70

65 -1

(mmol kg )


n Rate 1=v ¼ k· Ω −1 ; SA

105

SO

24

60

(mmol kg-1)

100 55

concentrate + acidic effluent

95

50 0

1

2

3

4

5

6

7

X (km)

SO4

2-

only concentrate

90

SO42−

Fig. 8. concentration along the plant discharge pipe during the flow of the KDP concentrate–AE mixture (●), and during the flow of the KDP concentrate alone (◊). Lines represent two forward models for gypsum precipitation in the plant pipe as discussed in Section 4.4: 1. During the flow of a KDP concentrate–AE mixture (gray lines), and 2. During the flow of the KDP concentrate alone (black line). For the flow of the mixture the effective surface area of the scale, S′s (Eq. (19)), was fitted. The dashed lines represent the uncertainty on S′s. Using the median of S′s the precipitation of gypsum during the flow of the KDP concentrate alone was predicted. This prediction demonstrates that gypsum precipitation cannot be detected by measuring SO42− concentrations.

85 0

200

400

600

800

1000

1200

1400

Elapsed time (hour) Fig. 9. A gypsum sample taken from the scale dissolved in the acidic effluent of the plant. Dissolution was performed in a batch type experiment similar to the precipitation experiments in a ratio of 2 g of solid to 100 g of solution.

Y.O. Rosenberg et al. / Desalination 284 (2012) 207–220

area. In the present study, as well as in most studies that utilized batch experiments, only the initial BET surface area can be measured. The increase in BET surface area (SBET) following dissolution or precipitation may be empirically related to the initial surface area by [28–31]: !p ;

ð3Þ 1

where SBET and M are the BET surface area (m 2) and mass (g) of the mineral, respectively, the subscripts i and t refer to the initial time and any other time point of the experiment, respectively, and p is a coefficient which depends on the crystal morphology and the relative growth of its different faces. Different studies [29] proposed the value p = 0.5 for gypsum growth, since its growth is principally two dimensional. Linearization of Eq. (2) in the form of:

log

Rate SBET;t

!


 1=2 ¼ logðkÞ þ n· log Ω −1 ;

ð4Þ

permits the fitting of the parameters k and n. The rate normalized to the surface area (Rate/SBET,t) will hence be written as RateS. Different studies show that close to equilibrium it is possible to describe gypsum growth with the rate law of Eq. (2) and n = 2 (parabolic rate law) [29,32–36]. Other studies [e.g., 37,38], as well as the present study, found that the reaction order is not constant with the distance from equilibrium, and that further from equilibrium a higher reaction order is observed which most likely represent a change in precipitation mechanism. In such cases the introducing of a second term into the rate law is necessary [28]:
n
n 1 2 1=2 1=2 Rates ¼ k1 · Ω −1 þ k2 · Ω −1 :

Experiment A pH=7.36 RateS (mmol h-1 m-2)

Mt MðiÞ

conducted. Fig. 10 shows the change in the normalized precipitation rate for these three experiments. The error bars are the standard error for the slope of SO42− concentration versus time in each 4 consecutive time points. It can be seen that the precipitation rate increases as pH drops below 3, and a small decrease is also evident as pH continues to drop (Fig. 10b and c, respectively).

ð5Þ

The existence of two terms in the rate law (Eq. (8)) may be interpreted by the existence of two distinguished growth mechanisms that acts in parallel. This hypothesis is further discussed below, in Section 4.3. An initial approximation of the reaction orders (n1 and n2) and the rate coefficients (k1 and k2) were found in this study by the non-linear regression of Eq. (5):

Δt

⋅msol ;

ð7Þ

where msol is the solution mass (kg) and the time point t refers to the second time point of each quartet. This calculation introduces a certain error as it assumes that the precipitation rate within each 4 consecutive time point is constant. However, this calculation serves as an initial approximation for the fitting of the rate law parameters, which will be verified by a forward model in the discussion that follows. In the following, three representative experiments (pH of 7.4, 2.7 and 2.0) are presented out of the ten experiments which were

0.001

100

200

300

400

500

600

700

Elapsed time (h) 10

Experiment H pH=2.68

1

0.1

0.01

0.001

0.0001 0

100

200

300

400

500

600

700

800

Elapsed time (h) 10

Experiment J pH=1.96

1

RateS (mmol h-1 m-2)

Ratet ¼

h i 2− Δ SO4

0.01

0

  1=2 1=2 logk þn · log Ω −1ÞÞ logk þn ·log Ω −1ÞÞ logðRateS Þ ¼ log 10ð 1 1 ð þ 10ð 2 2 ð ð6Þ 4.2.1. Fitting the rate law for the experimental data The rate law for gypsum crystal growth was fitted to the series of 10 experiments acidified by HNO3 acid. Gypsum growth rate for each time point in these experiments (Ratet) was calculated by the slope of the changing SO42− concentrations with time for each 4 consecutive points as:

0.1

0.0001

RateS (mmol h-1 m-2)

SBET;t ¼ SBET;i ·

213

0.1

0.01

0.001

0.0001 0

100

200

300

400

500

600

700

800

Elapsed time (h) Fig. 10. Three representative experiments showing the change in the normalized crystal growth rate of gypsum from the KDP concentrate acidified with nitric acid (Table 3, Series 17Kz). Notice the higher rates as pH decrease below 3.

214

Y.O. Rosenberg et al. / Desalination 284 (2012) 207–220

Initially, the data was fitted to a rate law with only one dependency on the distance from equilibrium (Eq. (2)) using its linearized form (Eq. (4)). This rate did not yield an adequate fitting to all of the experiments using a constant reaction order (n in Eq. (2)). Using n as an additional fitting parameter (i.e., n is not constant) showed no clear trend between it and the experiments pH. As a result of these trials, no consistent rate law could be fitted in order to describe the dependency of gypsum precipitation with pH. This was further verified by a forward model as discussed below. Therefore, it was decided to include another term in the rate law (Eq. (5)) and to fit it by applying Eq. (6) as suggested by Reznik et al. [38]. After an initial fitting of Eq. (6) to all the 10 experiments, and a comparison to the work of Reznik et al. [38], the following rate law was determined:  RateS ¼


10
2  1=2 1=2 k1 · Ω −1 þ k2 · Ω −1 :

ð8Þ

The importance of the empirical rate law presented in Eq. (8) is that it adequately describes the effect of deviation from equilibrium on the rate of gypsum crystal growth in all of the experiments with the same dependencies (i.e., for all the experiments n1 = 10 and n2 = 2). Moreover, the same empirical equation (with the same reaction orders) was used by Reznik et al. [38] to describe the dependence of gypsum precipitation from Dead Sea brines and mixtures of seawater and Dead Sea brines. As was noted by Reznik et al. [38], the two terms of this rate law may indicate that two parallel mechanisms control the heterogeneous precipitation rate: under further-fromequilibrium conditions the rate is dominated by the first term of Eq. (8) (apparent 10th order reaction), whereas under closer-toequilibrium conditions it is dominated by the second term of the equation (2nd order reaction). In the absence of a growth inhibitor, the only indirect effect that pH bares on gypsum precipitation is through the formation of HSO4− and lowering Ωgypsum. Therefore, the effect of pH on the rate coefficients (k1 and k2), which are independent of the degree of saturation, is attributed to changes in the antiscalant effectiveness (i.e., an indirect effect of pH on precipitation rate). In order to confirm the rate law of Eq. (8) and to minimize the error evoked by calculating constant rates for each 4 consecutive points (Eq. (7)), a forward model was used for all 10 experiments. The forward model was written and run with the Phreeqc software [23]. The initial solution concentrations of each experiment (Tables 1 and 3), solution mass and gypsum seeds mass were fed to the forward model, which then calculated gypsum precipitation rates according to the rate law of Eq. (8). The model was run with time increments that increased with the reaction progress so that the change in SO42− concentration due to gypsum precipitation did not exceed 0.15%. At the end of each increment the increase in gypsum mass and decrease in SO42− and Ca 2+ concentrations were recorded. The changes in SBET,t and Ωgypsum were then calculated by the model according to Eq. (3) and the Pitzer formalism [39], respectively, before calculating the precipitation rate of the next increment. Using this forward model the rate coefficients (k1 and k2) were altered until achieving the best possible fit between the measured and predicted SO42− concentrations. The forward model was also used to quantify the uncertainty of the rate coefficients. As a criterion for the best fit values, the rate coefficients were changed until 95% of the experiments results were within two standards deviation (4%) from the model prediction. To evaluate the uncertainty of the rate coefficients, their best fit values were independently changed until the above criterion was not met, yielding the rate coefficient maximum and minimum values. As the first term and the second term in Eq. (8) dominate the rate further from equilibrium and closer to equilibrium, respectively, changes in the value of k1 influenced the change

in SO42− with time from the onset of the experiment while changes in k2 start to affect SO42− concentration at a much later stage. Fig. 11 shows the model results for the three representative experiments, while Table 5 summarizes the rate coefficients values (best fit, minimum and maximum) for all of the 10 experiments. The solid lines in Fig. 11a–c correspond to the best fit values of the rate coefficients, while the broken lines are the uncertainty envelopes calculated with the minimum and maximum values of the rate coefficients. In each of the figures, the uncertainty envelop of k1 is plotted in the inset (first few tens or hundreds of hours when the reaction is far from equilibrium), while the uncertainty envelop of k2 is plotted in the main figure. Fig. 12 shows the quality of the fit of the rate law by plotting the predicted SO42− concentrations against the measured values for all the 10 experiments. The solid line corresponds to the concord line (1:1), while the dashed lines represent ±4% deviation from this line along the X axis. 99% of the predicted values agree with the observations within 2 standard deviations (±4%). 4.2.2. The antiscalant effect on the rate coefficients In order to evaluate the effect of the antiscalant on the rate coefficients, an additional experiment for gypsum crystal growth was conducted in a synthetic concentrate and without the addition of the antiscalant. The rate law of Eq. (8) was fitted to the results of this experiment using the forward model, yielding the rate coefficients: k1 = 1 ± 0.75, k2 = (1 ± 0.5) · 10 − 6 mol m − 2 s − 1. The values of these rate coefficients are significantly higher than the corresponding values of an experiment at similar pH that contained the antiscalant (k1 = (5 ± 5) · 10 − 5, k2 = (5 ± 2) · 10 − 8 mol m − 2 s − 1, Table 5). Assuming that the rate coefficient in the absence of the antiscalant corresponds to their maximum values (i.e., k1,max and k2,max), it is possible to estimate the remnant effect of the antiscalant as a function of pH by normalizing the rate coefficients at each pH by the maximum values. This normalization may also represent the effectiveness of the antiscalant as growth inhibitor at a constant saturation degree [11,12]. The maximum value of the rate coefficients was fitted to an experiment at 25 °C, while the rate law (Eq. (8)) was fitted to experiments at 30 °C. However, as will be shown below the temperature effect on the rate coefficients at this temperature range is probably negligible. Fig. 13 shows the normalizations of the two rate coefficients; the large error bars are a consequence of error propagation on both the maximum and pH-dependent values of the rate coefficients. The k2,(pH)/k2,max ratio approaches 1 as pH decrease; this suggests that at close to equilibrium conditions under low pH values the antiscalant is barely effective. On the other hand, the k1,(pH)/k1,max ratio exhibits a value of ~ 100 even at the most acidic experiment, which means that the antiscalant is capable of retarding crystal growth of gypsum under far from equilibrium and acidic conditions. 4.3. The effect of pH on gypsum crystal growth in the presence of a phosphonate antiscalant 4.3.1. Conceptual model for the antiscalant adsorption to the crystal surface As discussed above, antiscalants are considered to inhibit crystal growth by adsorbing to its reactive surface sites [8,14–16]. The functional groups of the tested PC-191 antiscalant are phosphonates (i.e., C-PO(OH)2), which protonate as the pH decrease. Therefore, it is likely that the protonation of these functional groups lowers the antiscalant adsorption to the reactive surface sites which, in turn, results in an increase in the rate of crystal growth. A simplified Langmuir model for the adsorption of the antiscalant to the gypsum surface is studied below. Since characterizing the PC191 chemical structure and affinity is beyond the scope of this study, the model intends to conceptualize the above hypothesis, rather than to suggest a mechanistic rigorous description. In the model it

Y.O. Rosenberg et al. / Desalination 284 (2012) 207–220 Table 5 Rate coefficients valuesa (k1 and k2, Eq. (8)) fitted by the forward modelb.

65

65

215

Experiment

Initial pH

k1 min

k1 best fit

k1 max

k2 min

k2 best fit

k2 max

A B C D E F G H I J

7.36 6.55 6.09 5.05 4.39 3.55 2.98 2.68 2.35 1.96

2.5E-06 6.1E-06 1.5E-05 3.0E-05 2.5E-05 2.5E-04 2.5E-04 7.5E-04 2.0E-03 2.0E-03

5.1E-05 6.1E-05 8.4E-05 3.0E-04 2.5E-04 1.8E-03 1.5E-03 5.0E-03 6.8E-03 1.0E-02

9.9E-05 2.0E-04 4.0E-04 8.0E-04 7.0E-04 4.7E-03 4.5E-03 1.3E-02 3.0E-02 5.0E-02

3.0E-08 3.5E-08 4.0E-08 7.5E-08 1.0E-07 2.0E-07 2.1E-07 2.0E-07 2.0E-07 1.8E-07

5.0E-08 5.3E-08 6.0E-08 1.3E-07 1.4E-07 3.5E-07 3.5E-07 3.5E-07 3.5E-07 3.5E-07

7.0E-08 7.0E-08 9.0E-08 1.8E-07 2.1E-07 5.3E-07 6.5E-07 8.0E-07 8.0E-07 6.5E-07

60

55

55

50

2-

SO4 (mmol kg-1)

60

0

50

100

150

200

250

50

Rate coefficients units are mol m− 2 s− 1. Forward model was run with the Phreeqc software, and the Pitzer thermodynamic database. a

b

45

Experiment A pH=7.36 0

100

200

300

400

500

600

700

800

Elapsed time (h)

is assumed that the two rate coefficients, ki,pH, in the presence of a constant antiscalant concentration depend on the fraction of free reactive sites on the gypsum surface: ki;pH ¼ ki; max ·ð1−θÞ;

65

65

60

55

55 50

2-

SO4 (mmol kg-1)

60

45

50

0

10

20

30

40

45

−

0

100

200

300

400

500

600

700

800

Elapsed time (h)

65

65

60

þ

Kdis ¼

aHþ ·½An−  ; ½AnH 

−

≡Si þ An ↔≡Si −An;

55

55

50

0

20

40

60

80

100

50

Experiment J, pH=2.0

45 0

100

200

300

400

500

Elapsed time (h)

600

700

800

ð10Þ

where Kdis is a conditional dissociation constant (dimensionless), and aj and [j] are the activities (dimensionless) and concentrations (mol kg− 1) of species j, respectively. The use of the concentrations of the An species, rather than their activities, is legitimate by the use of a conditional dissociation constant (i.e., the activity coefficients of An− and AnH adsorb into Kdis). The deprotonated functional group, An −, can adsorb to the reactive surface sites, ≡ Si, according to the reaction:

60

2-

SO4 (mmol kg-1)

where θ is the fraction of surface sites filled by the antiscalant; the subscript i (=1, and 2) refer to the two terms of the rate law (Eq. (8)). In the absence of the antiscalant all the surface sites are free and the rate coefficients equal their maximum values which were already evaluated (Section 4.2.2). As pointed out by Weijnen and Van Rosmalen [12], both the protonated phosphonate groups, PO3H−, and fully dissociated groups, PO32−, are essential in the adsorption process of phosphonate inhibitors to gypsum surface. As a simplified model, it is assumed in the present study that the above two stages adsorption process of the antiscalant is represented by an apparent functional group, designated as An, which can protonate and deprotonate only once according to the reaction: AnH↔An þ H ;

Experiment H, pH=2.68

ð9Þ

Kads;i ¼

½≡Si −An ; ½≡Si ·½An− 

ð11Þ

where [≡ Si] and [≡Si-An] are the concentrations of free and occupied reactive surface sites normalized by the solution mass (mol kg − 1), and Kads,i is an apparent adsorption coefficient (kg mol − 1). As discussed above, the occurrence of the two terms in the rate law (Eq. (8)) is interpreted as two distinguish growth mechanisms. This interpretation is considered in the present conceptual model as representing two types of reactive adsorption sites, each with a respective adsorption coefficient (i = 1 and 2). Fig. 11. Forward model (lines) predicting the change in SO42− concentration with time according to Eq. (8). The solid line is the best fit for which the rate coefficients were changed to fit 95% of the experimental data (symbols). The uncertainty envelops of the rate coefficients (minimum and maximum values) are shown by the dashed lines: in the inset of each figure only k1 was changed, while in the main figure only k2 was changed.

216

Y.O. Rosenberg et al. / Desalination 284 (2012) 207–220

By studying the adsorption isotherm of HEDP to gypsum, Weijnen and Van Rosmalen [12] concluded that gypsum exhibits two distinctive adsorption sites, namely kinks and micro-steps. However, this conclusion was based on the assumption that spiral pattern dominant the growth of gypsum. Recent studies could not find evidence for dominant spiral growth on gypsum surface [5,40]. Bosbach and Hochella [8] have studied the effect of HEDP and ethylene diaminetetra (methylenephosphonic acid) (ENTMP) on the growth of the (010) gypsum surface using scanning force microscopy. They concluded that on the (010) face the steps on the [101] direction are more reactive than steps on the [001] direction, and that the [101] steps were, therefore, more affected by the phosphonates inhibitors. Though the nature of these studies is more microscopic, the existence of distinguish adsorption sites on the gypsum surface may still have an expression in the macroscopic scale as suggested in the present study. The two mass balance (mol) equations for the antiscalant and reactive surface sites are:

60

55

50

2-

SO4 predicted (mmol kg-1)

65

45

45

50

55

60

65

2-

SO4 observed (mmol kg-1)

−

Fig. 12. Predicted vs. observed SO42− concentrations for the experiments acidified by nitric acid (Table 3). The rate coefficients (Eq. (8)) were changed to fit 95% of the experimental data. The solid line represents the agreement line (1:1), while the dashed lines represent ± 3% deviation from this line along the x axis.

Antotal ¼ An þ AnH þ ≡Si −An

ð12Þ

and ≡Si;total ¼≡Si þ ≡Si −An;

ð13Þ

respectively. Using Eqs. (9)–(13), and defining θ = [ ≡ Si − An]/[≡Si,total], the following conceptual model can be written:

k1,(pH)/k1,max

10

10

5

ki; max ki;pH ¼
 1 þ Kdis ·Kads;i ·ð½Antotal −½≡Si −AnÞ= aHþ þKdis Þ :

4

1000

100

a 10 2

1

3

4

5

6

7

8

pH 35 30 25

k2,(pH)/k2,max

ð14Þ

20 15 10 5

b

ki; max ki;pH ¼
 ′ 1 þ Kdis ⋅K ads;i = aHþ þKdis Þ ;

0 1

The full derivation of Eq. (14) is described in EA-2. Eq. (14) cannot be fitted to the experimental data without prior knowledge regarding the concentration of [Antotal] and [ ≡ Si − An] and their possible change with time. It is known that organic molecule which adsorb to mineral surfaces may then be incorporated into the lattice by the overgrown mineral [6,41,42]. This may thus affect significantly [Antotal] when fitting k2 with Eq. (14) (i.e., when a significant amount of gypsum precipitated). To estimate this effect Ptotal concentration may serve as a proxy for the antiscalant concentration. [Ptotal] was measured in the less acidic experiment (pH = 7.4) where the antiscalant adsorption to the gypsum surface should be the most extensive. Fig. 14 shows the amount of Ptotal (mol) which was removed from the solution as a function of the amount of precipitated gypsum (calculated by the change in [SO42−]). The amount of Ptotal removed by gypsum precipitation increases until it reaches a maximum of 1.6 ± 0.1 ∙ 10 − 5 mmol. This amounts to a maximum decrease of ~ 80% in [Ptotal]. Though this change is significant, Eq. (14) is mainly affected by the change in pH. That is, the change in the ratio ([Antotal] − [ ≡ Si − An])/(aH+ − Kdis) is mostly driven by the denominator, as it is changes by more than 2 orders of magnitude. On the other hand, the change of the nominator with pH (i.e., between the experiments) is probably much less than an order of magnitude. Therefore, as an approximation, the phrase Kads,i · ([Antotal] − [ ≡ Si − An]) is regarded as constant, and Eq. (14) is written as:

2

3

4

5

6

7

ð15Þ

8

pH Fig. 13. The ratio between the rate coefficients at different pH values to their maximum value. The maximum values of the rate coefficients were fitted from experiments of synthetic concentrate in the absence of the antiscalant (Exp. 12Kz-H). The proximity of the ratio k2/k2,max to unity (gray dashed line) suggests that its corresponding growth mechanism is no longer inhibited in pH values b 4.

where K′ads,i = Kads,i · ([Antotal] − [ ≡ Si − An]). 4.3.2. Fitting the adsorption model to the experimental data The model was fitted to the determined values of ki,pH (i = 1 and 2) as a function of pH (Table 5). The value of k1,max was taken from the fitting of the crystal growth experiment in the absence of the antiscalant.

Y.O. Rosenberg et al. / Desalination 284 (2012) 207–220

217

-1 -5

Log(k1) (mol sec-1 m-2)

Ptotal precipitated (mmol)

2 10

-5

1.5 10

1 10

-5

-2

-3

-4

-5 5 10

a

-6

-6 1

2

3

4

5

6

7

8

5

6

7

8

pH 0 0

0.5

1

1.5

2

2.5

3

3.5

4

-7

6 10

Gypsum precipitated (mmol)

Since k2,pH reaches saturation at pHb 4, k2,max was re-evaluated as the average between its values below pH of 4 (5 determinations) and its value in the absence of the antiscalant. Therefore, the free parameters in the model are K′ads,1 and K′ads,2 to each of the rate coefficients and a singular Kdis to both rate coefficients (i.e., 1.5 degrees of freedom). Fig. 15a–b shows the fitting of Eq. (15) to the two rate coefficients. The best fit was derived by changing Kdis, K′ads,1 and K′ads,2 to minimize the residual sum of squares between the observed values of the rate coefficients (Table 5) and their predicted values by Eq. (15). The values of the adsorption model parameters are summarized in Table 6. Despite the simplification of the adsorption model, it conceptualizes the effect that pH has on the adsorption of the phosphonate antiscalant and, therefore, on the rate coefficients. When the pH value equal to pKdis (=4.6) half of the antiscalant is deprotonated (Eq. (10)). Below this pH value the decrease in both rate coefficients is more intense as evident by the experimental results (Fig. 15a–b). Therefore, the effectiveness of the antiscalant PC-191 in preventing crystal growth of gypsum decreases considerably at pH b 4.6. This value is expected to vary for solutions of different composition and ionic strength (i.e., different activity coefficients of the antiscalant species). 4.3.3. Prediction of gypsum growth from a KDP concentrate–AE mixture at 25 °C The rate law for gypsum crystal growth and the antiscalant adsorption model, that were constructed using experiment acidified by HNO3 at 30 °C, were extrapolated to experiments conducted with KDP concentrate–AE mixtures at 25 °C. Using Eq. (15) and the parameters in Table 6 the values of the rate coefficients were calculated as a function of pH for these experiments. Table 7 presents the pH and rate coefficients values calculated for these experiments. Fig. 16a–d presents the model prediction for the 4 experiments. The agreement between the model prediction (solid line) and experiments observations (symbols) is good. It is important to emphasize that the model predictions were not fitted to the observations and all the parameters were determined from independent experiments that were conducted with HNO3 acid-KDP concentrate mixtures. These results emphasis that the increase in gypsum growth rate in the KDP concentrate is a consequence of the decrease in pH followed by mixing the AE. Since the experiments conducted at 25 °C were predicted by the rate coefficient of 30 °C, it can be assumed that

-7

5 10

k2 (mol sec-1 m-2)

Fig. 14. The amount of Ptotal removed by gypsum precipitation in crystal growth experiment at pH = 7.4. Ptotal serves as a proxy for the antiscalant concentration which remained in the solution during crystal growth of gypsum.

-7

4 10

-7

3 10

-7

2 10

-7

1 10

b 0 1

2

3

4

pH Fig. 15. The fit of the adsorption model (solid line, Eq. (14)) to the two rate coefficients as a function of pH evaluated from the crystal growth experiments (symbols). Error bars were depicted by the maximum and minimum values of the rate coefficients (Table 5). The best fit parameters of the adsorption model were evaluated by minimizing the residual sum of squares between the evaluated values and the model, and are presented in Table 6.

the effect of temperature within this range on the rate coefficient is insignificant, and that the precipitation of gypsum in the plant discharge pipe is not considerably affected by small temperature variations around 30 ± 3 °C. 4.4. Gypsum precipitation in the plant discharge pipe The field test results demonstrate that gypsum precipitation in the discharge pipe commenced relatively fast when the KDP concentrate– AE mixture was discharged to the pipe, whereas the precipitation could not be detected when the KDP concentrate was discharged alone (Fig. 8). These qualitative observations are supported by the laboratory findings.

Table 6 Parameters used in the adsorption model for the antiscalant to the gypsum surface.

−2

−1

ki,max (mol m s K′ads,i (kg mol− 1) Kdis

)

i=1

i=2

1.0 3.6E + 08 2.5E-05

5E-07a 8.2

a Average between k2,pH values below pH of 4 (5 determinations) and k2 value in the absence of the antiscalant.

218

Y.O. Rosenberg et al. / Desalination 284 (2012) 207–220

Table 7 Measured pH values and calculated rate coefficients of 4 crystal growth experiments. Solution

Experiment

pH

k 1a

k2a

KDP KDP KDP KDP

12KzJ 12KzG 20KzB 20KzA

7.15 2.71 7.35 2.82

2.8E-05 2.2E-03 2.8E-05 1.7E-03

5.6E-08 4.5E-07 5.6E-08 4.4E-07

concentrate concentrate + AE concentrate + neutralized AE concentrate + AE

a Rate coefficients (mol m− 2 s− 1) for Eq. (8) were calculated with Eq. (14) and the parameters in Table 6.

In the following, a simplistic model for the crystal growth of gypsum in the discharge pipe is described, in order to compare it to the laboratory results and to deduce a quantitative understanding of the scale growth kinetics. The model follows the linear flow of 1 liter volumetric unit of concentrate (≈1 kg of concentrate); i.e., dispersion and diffusion are neglected. The volumetric unit precipitates gypsum along the flow in the discharge pipe on a gypsum layer which is already present, whose surface area is unknown. It is further assumed that the scale of gypsum is uniformly spread along the discharge pipe; hence, both the scale surface area and the pipe diameter are constant along the pipe. The length unit of the pipe (l) which is filled by the volumetric unit of the concentrate (V) is given by: l ¼ V=Apipe

where Apipe is the inner area of the (partly) clogged pipe (m 2), and l and V are in metric units. Since Apipe is constant, the flow time of the volumetric unit (s) is related to the distance of the flow (x) according to: time ¼ x·Apipe =F;

ð17Þ

where F is the flow rate of the solution in the discharge pipe as controlled by the desalination plant operators (50 m 3/h = 0.0139 m 3/s). The constant surface area of the gypsum scale which is in contact with the volumetric unit of the concentrate can be expressed as: ′

′

St ¼ S s ·l ¼ S s ·V=Apipe ;

ð18Þ

where S′s is the effective surface area of the gypsum per length unit of the discharge pipe (m 2gypsum/mpipe). Introducing Eqs. (17) and (18) into Eq. (8), the gradient of SO42− concentration along the discharge pipe can be derived as:

Gradient ¼

h i d SO2− 4

 dx
10
2  S′ ·V 1=2 1=2 þ k2 · Ω −1 · s : ¼ k1 · Ω −1 F

ð16Þ

ð19Þ

65 65 64

55 56 0

50

5

10

15

20

25

60

55 56

2-

60

-1 SO4 (mmol kg )

60

60

2-

SO4 (mmol kg-1)

64

0

10

20

30

40

50 45

c (20KzB, pH=7.35)

a (12KzJ, pH=7.36) 45

40 0

100

200

300

400

500

600

0

100

Elapsed time (h) 65

65

60

55

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Fig. 16. A forward model predicting gypsum precipitation (solid line) from different mixes of the concentrate at 25 °C: a. KDP concentrate; b. KDP concentrate + 4.8% weight fraction of AE; c. KDP concentrate + 4.8% weight fraction of neutralized AE; and d. KDP concentrate + 4.8% weight fraction of AE (as in b). The model predicts gypsum precipitation according to the measured initial concentrations and the rate coefficients calculated by Eq. (14) and the parameters in Table 6.

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At a constant flow rate the flow velocity will increase due to continuous blockage of the discharge pipe by gypsum. However, Eq. (19) shows that as long as the flow rate is constant, the change in SO42− concentration along the discharge pipe depends only on the effective surface area of the scale and not on the flow velocity. Therefore, Eq. (19) allows to calculate the amount of gypsum that precipitates in the pipe without dependency on the scale thickness (i.e., without knowing Apipe). A forward model for the precipitation of gypsum in the discharge pipe was written using Eq. (19). Fig. 8 shows the agreement between the model (lines) and the field results (symbols) of the SO42− concentrations along the pipe. S′s was the only parameter fitted to predict gypsum precipitation during the flow of the mixture (gray line). The two rate coefficients were calculated by Eq. (14) and the parameters in Table 6. The dashed lines represent the uncertainty envelope in fitting S′s, while the solid gray line represents the median value of the uncertainty envelop for S′s. The median value of S′s that matched the field observations is: S′s = 70 ± 35 m 2gypsum/mpipe. This BET based surface area of the gypsum scale is much higher than the maximum geometrical surface area of an unclogged pipe (0.61 m 2/mpipe), suggesting an extensive roughness for the scale surface. A comparison between the reactivity of the gypsum in the discharge pipe and in the batch experiments is possible only after the ratios between the gypsum surface area to the solution volume in both cases are weighed against each other. In the batch experiments the ratio of the BET surface area to the solution volume is 3.3 m 2gypsum L − 1. Since the effective surface area, S′s, in the discharge pipe was fitted using the rate law of the batch experiments, it is equivalent to the BET surface area. The ratio between S′s to the solution volume depends on the inner surface of the clogged pipe (Apipe, Eq (18)). A similar ratio of 3.3± 1.6 m2gypsum L − 1 is attained for a pipe which on the average ~16% of its diameter is clogged. This thickness of scaling is reasonable with the field observation. For a pipe with a thin scale covering its interior, the reactivity of the gypsum in the pipe is only 40% higher. These calculations demonstrate that the reactivity of the gypsum in the discharge pipe is very similar to that used in the batch experiments. Therefore, it is concluded that it is possible to upscale the batch experiments, and use their rate law in order to evaluate the precipitation of gypsum in the discharge pipe at different pH values. Using the effective surface area of gypsum in the discharge pipe it is now possible to predict the precipitation of gypsum during the flow of the concentrate alone (black line, Fig. 8). This prediction assumes that S′s did not change much between the two field tests. In practice, about 54% of the pipe length was replaced by a new pipe. The model predicts a decrease of 1.3 mmol kg − 1 in SO42− concentration when the KDP concentrate exits the pipe. This decrease is well within the analytical error in measuring SO42− and therefore undetectable. Such precipitation will eventually lead to a renewed increase in gypsum precipitate and a blockage of the pipe. 5. Summary Within the framework of this study the following points are concluded: 1. Antiscalant performance: Though this work did not systematically studied the PC-191 antiscalant effectiveness, it can be concluded that this additive hinders gypsum nucleation and significantly slows down its crystal growth at relatively high saturation degrees (Ωgypsum N 2). However as pH decreases, the effectiveness of PC191 decreases and the precipitation rate of gypsum significantly increases, both in laboratory and field tests. In the desalination plant this effect was induced by mixing small amounts of acidic effluent (AE, pH b 2) with the plant concentrate. 2. Rate law for gypsum crystal growth: The precipitation rate of gypsum in laboratory batch experiments could not be consistently

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predicted with a rate law having a singular dependency on the distance from equilibrium. Therefore, another term for the dependency on the distance from equilibrium was introduced, and the following rate law was found to describe the experimental data satisfactorily:  Rate ¼


10
2  1=2 1=2 k1 · Ω −1 þ k2 · Ω −1 ·St ;

where ki and St are the rate coefficients (mol m − 2 s − 1) and the BET surface area of gypsum (m 2), respectively. This is in agreement with the experimental work of Reznik et al. [38] for gypsum crystal growth in Dead Sea brines and Dead Sea- seawater mixtures. 3. The effect of pH on the antiscalant PC-191: It is suggested that the increase in the precipitation rate of gypsum with pH decrease is the result of protonation of the antiscalant functional group. This protonation reduced the adsorption efficiency of the antiscalant to the reactive surface sites of gypsum, and therefore the precipitation rate increases. Using a simplified adsorption model the effect of pH on the rate coefficients could be adequately described and gypsum precipitation from mixtures between the KDP concentrate and the AE could be well predicted. 4. Gypsum scaling in the discharge pipe: By fitting only the surface area of the scale it was possible to upscale the laboratory rate law and adsorption model to the plant discharge pipe. Such upscaling procedure allows inferring quantitatively geochemical reaction in the industry level. In the present case study, the precipitation of gypsum in the discharge pipe in the presence and absence of the acidic effluent was quantitatively described. Thus, it was possible to predict gypsum precipitation in the absence of the AE, despite the fact that no changes in SO42− concentration could by analytically detected. Acknowledgments This study was supported by Mekorot, the Israel National Water Company. We wish to express our gratitude to the operators of the Ketziot desalination plant and to S. Ross and I. Bar-Or for their technical assistance. Y.O. Rosenberg is supported by the Adams Fellowship Program of the Israel Academy of Sciences and Humanities, and is also grateful to the Rieger Foundation — JNF Program for Environmental Studies and to the Water Authority of Israel for their generous support. I. J Reznik expresses his gratitude to the Levi Eshkol scholarship fund at the Israeli Ministry of Science, Rieger Foundation — JNF Program for Environmental Studies and Water Authority of Israel for their generous support. Appendix A. Supplementary data Supplementary data to this article can be found online at doi:10. 1016/j.desal.2011.08.061. References [1] D.H. Kim, B.M. Jenkins, J.H. Oh, Gypsum scale reduction and collection from drainage water in solar concentration, Desalination 265 (2011) 140–147. [2] H.A. El Dahan, H.S. Hegazy, Gypsum scale control by phosphate ester, Desalination 127 (2000) 111–118. [3] S.K. Hamdona, O.A. Al Hadad, Influence of additives on the precipitation of gypsum in sodium chloride solutions, Desalination 228 (2008) 277–286. [4] M. Uchymiak, E. Lyster, J. Glater, Y. Cohen, Kinetics of gypsum crystal growth on a reverse osmosis membrane, J. Membr. Sci. 314 (2008) 163–172. [5] D. Bosbach, J.L. Junta-Rosso, U. Becker, M.F. Hochella, Gypsum growth in the presence of background electrolytes studied by scanning force microscopy, Geochim. Cosmochim. Acta 60 (1996) 3295–3304. [6] J. Ganor, I.J. Reznik, Y.O. Rosenberg, Organics in water–rock interactions, in: J. Schott, E. Oelkers (Eds.), Thermodynamics and Kinetics of Fluid–Rock Interaction, 2009, pp. 259–369.

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