Accurate and self-consistent procedure for determining pH in seawater desalination brines and its manifestation in reverse osmosis modeling

Accepted Manuscript

Accurate and self-consistent procedure for determining pH in seawater desalinationbrines and its manifestation in reverse osmosis modeling

Oded Nir, Esra Marvin, Ori Lahav

PII: S0043-1354(14)00498-9

DOI: 10.1016/j.watres.2014.07.006

Reference: WR 10765

To appear in: Water Research

Received Date: 24 March 2014

Revised Date: 24 June 2014

Accepted Date: 2 July 2014

Please cite this article as: Nir, O., Marvin, E., Lahav, O., Accurate and self-consistent procedure fordetermining pH in seawater desalination brines and its manifestation in reverse osmosis modeling,Water Research (2014), doi: 10.1016/j.watres.2014.07.006.

This is a PDF file of an unedited manuscript that has been accepted for publication. As a service toour customers we are providing this early version of the manuscript. The manuscript will undergocopyediting, typesetting, and review of the resulting proof before it is published in its final form. Pleasenote that during the production process errors may be discovered which could affect the content, and alllegal disclaimers that apply to the journal pertain.

MANUSCRIP

T

ACCEPTED

ACCEPTED MANUSCRIPT

MANUSCRIP

T

ACCEPTED

ACCEPTED MANUSCRIPT

Accurate and self-consistent procedure for determining pH in seawater desalination 1

brines and its manifestation in reverse osmosis modeling 2

Oded Nira*, Esra Marvinb and Ori Lahava 3

a Faculty of Civil and Environmental Engineering, Technion – ITT, Haifa, 32000, Israel; 4

b Faculty of Environmental Engineering, Helsinki Metropolia University of Applied 5

Sciences, Finland; 6

*corresponding author, E-mail: [email protected] 7

8

Abstract 9

Measuring and modeling pH in concentrated aqueous solutions in an accurate and 10

consistent manner is of paramount importance to many R&D and industrial applications, 11

including RO desalination. Nevertheless, unified definitions and standard procedures 12

have yet to be developed for solutions with ionic strength higher than ~0.7 M, and 13

implementation of conventional pH determination approaches may lead to significant 14

errors. In this work a systematic yet simple methodology for measuring pH in 15

concentrated solutions (dominated by Na+/Cl-) was developed and evaluated, with the 16

aim of achieving consistency with the Pitzer ion-interaction approach. Results indicate 17

that the addition of 0.75 M of NaCl to NIST buffers, followed by assigning a new 18

standard pH (calculated based on the Pitzer approach), enabled reducing measured errors 19

to below 0.03 pH units in seawater RO brines (ionic strength up to 2 M). To facilitate its 20

use, the method was developed to be both conceptually and practically analogous to the 21

conventional pH measurement procedure. The method was used to measure the pH of 22

MANUSCRIP

T

ACCEPTED

ACCEPTED MANUSCRIPT

seawater RO retentates obtained at varying recovery ratios. The results matched better the 23

pH values predicted by an accurate RO transport model. Calibrating the model by the 24

measured pH values enabled better boron transport prediction. A Donnan-induced 25

phenomenon, affecting pH in both retentate and permeate streams, was identified and 26

quantified. 27

Key Words: pH, brine, Pitzer, Phreeqc, reverse-osmosis 28

29

30

31

MANUSCRIP

T

ACCEPTED

ACCEPTED MANUSCRIPT

1. Introduction 32

The pH value is a parameter of major significance in reverse osmosis (RO) applications. 33

Most significantly, it affects the permeation rate of potentially toxic weak-acid elements, 34

e.g. boron (Tu et al., 2010), NH3 (Hurtado and Cancino-Madariaga, 2014) and arsenic 35

(Teychene et al., 2013) and at the same time controls the development of chemical 36

scaling of minerals e.g. calcite and brucite (Nir et al., 2012). Additionally, the pH affects 37

the membrane’s lifespan (Donose et al., 2013) and may induce a change in its physical 38

properties and thereby in its performance (Wang et al., 2014). Despite this, an accurate 39

measurement procedure and a reliable predictive model for pH in desalination brines are 40

currently lacking in the literature. Regarding the measurement procedure, the knowledge 41

gap is associated with theoretical and practical difficulties arising from standardization of 42

pH in high ionic strength (I) solutions (Buck et al., 2002). Regarding modeling, the gap is 43

attributed to the high complexity of transport and reaction processes, affecting the 44

evolution of pH in seawater-brines in full-scale RO operations (Nir and Lahav, 2013). 45

To date, a widely accepted definition and a measurement procedure are available for both 46

dilute solutions (I < 0.1 mol kg-1) and seawater, but not for seawater desalination brines 47

(approximately twice SW concentration). In practice, pH is regularly measured in 48

desalination feeds and brines by a combined glass electrode, calibrated by standard NIST 49

buffers (NIST stands for U.S. National Institute of Standards, which develops and 50

maintains pH standards; the value measured by this procedure is termed pHNIST). 51

However, this concept, which was developed for dilute solutions (see brief discussion in 52

the supporting material file), encompasses two assumptions which are theoretically 53

invalid for concentrated solutions: (1) In the process of assigning primary pH standards, 54

MANUSCRIP

T

ACCEPTED

ACCEPTED MANUSCRIPT

the activity coefficient of chloride ions can be estimated by the Bates-Guggenheim 55

convention; (2) The liquid junction potential term, appearing in the process of measuring 56

pH using the glass electrode arrangement, is practically cancelled out as a result of the 57

calibration procedure (Buck et al. 2002). As a result of relying on these erroneous 58

assumptions, measuring pHNIST in concentrated solutions invariably leads to considerable 59

errors. 60

Extensive work has been dedicated to measurement, interpretation and standardization of 61

pH in seawater (see brief discussion in the supporting material file). Although high 62

precision pH measurements have been shown feasible by potentiometric and 63

spectrometric methods, interpretation and standardization are still under debate (Marion 64

et al. 2011). Overall, the seawater pH scale approach is based on the relatively constant 65

composition of seawater and therefore cannot be readily extended to desalination brines 66

of varying compositions, nor to seawater brines at salinity >45‰ or pH values 67

significantly different from 8.1 (Millero et al., 2009). 68

The Pitzer approach, has been long recognized as a potential framework within which the 69

definition and traceability of pH values could be soundly extended to higher ionic 70

strengths (Covington, 1997; Ferra, 2009; Millero 2009). Based on statistical mechanics 71

approach, the Pitzer equations for ion activity coefficients take into account both long-72

range interactions, represented by the Debye-Huckel term, and short-range specific 73

interactions between dissolved species (Pitzer 1973). Since the establishment of a new 74

pH reference system requires extensive and precise analytical work (which, ultimately, 75

will have to be conducted in institutions responsible for standards) and extensive 76

uncertainty analysis (Spitzer et al., 2011), the progress in this direction is slow. 77

MANUSCRIP

T

ACCEPTED

ACCEPTED MANUSCRIPT

Meanwhile, industries such as desalination or oil&gas are in urgent need for a practical 78

solution, which will allow for improved modeling and better process monitoring and 79

design. Different approaches introduced for pH measurement in NaCl brines include the 80

use of a liquid-junction free cell coupled with ion selective electrode (Knauss et al., 81

1990), calibration techniques involving acid/base titrations (Mesmer, 1991) and 82

spectroscopic methods (Millero et al. 2009). These procedures were, by and large, not 83

adopted by desalination professionals, probably due to the relatively large disparity 84

between them and the conventional NIST concept in terms of both measurement 85

complexity and the pH scale employed. 86

The problem of consistency between the measured pH and the applied thermodynamic 87

model was already recognized by Harvie et al. (1984) whose Pitzer-based model formed 88

the basis for many studies on thermodynamic properties of desalination brines. In their 89

work, this issue was addressed by adopting the extended Macinnes convention (i.e. the 90

chloride ion activity coefficient is equal to the mean activity coefficient of a KCl solution 91

of the same ionic strength) for the representation of activity coefficients. The Macinnes 92

scale was set as a default in the implementation of the Pitzer model in the geochemical 93

program PHREEQC (Plummer et al., 1988). Although not considered superior from the 94

thermodynamic standpoint, the extended Macinnes convention is acknowledged the most 95

appropriate due to its higher compatibility with the NIST scale at high ionic strengths, as 96

compared with other conventions (e.g. Bates-Guggenheim) (Harvie et al., 1984). 97

However model-measurement discrepancies resulting from liquid junction potential are 98

still apparent in determining pH of concentrated solutions (Plummer et al., 1988). 99

MANUSCRIP

T

ACCEPTED

ACCEPTED MANUSCRIPT

The Pitzer model has been increasingly applied to desalination brines mainly for the 100

assessment of scaling tendency (Azaroual et al., 2004; Huff, 2004; Schausberger et al., 101

2009; Radu et al. 2014; Sousa et al. 2014) and energy requirements (Mistry et al., 2013). 102

In a previous work the writers developed a computer simulation code for predicting the 103

transport and equilibrium state of weak acid-base species within SWRO streams (Nir and 104

Lahav, 2013; Nir and Lahav, 2014). The simulation was based on a reactive-transport 105

approach, i.e. membrane transport equations (solution-diffusion-film model) coupled 106

with elaborated thermodynamic and chemical-equilibrium calculations, facilitated by the 107

use of the Pitzer concept, as implemented in PHREEQC. By performing a full species 108

distribution analysis at each numerical brine recovery step the simulation code enabled 109

the prediction of the pH evolution in the rejected solution as it flowed through a full-scale 110

membrane train. This approach was shown to improve the modeling predictions of boron 111

permeation (Nir and Lahav, 2013), compared to the approach applied in most of the 112

works published thus far on boron membrane transport, in which the hypothesis is that 113

the pH of the reject remains constant from the raw seawater to the brine produced at the 114

outlet of the SWRO step (e.g. Taniguchi et al., 2001; Sagiv and Semiat, 2004; Mane et 115

al., 2009). However, considerable differences in pH values were measured at the feed and 116

brine in many SWRO applications (Waly et al., 2011; Andrews et al., 2008). 117

Being a key parameter in acid-base equilibria, the exact knowledge of the pH value 118

throughout the retentate path within the membrane train is imperative in any predictive 119

model, both as an input parameter and throughout the membrane train path, as means of 120

calibrating and assessing model predictions. However, little attention has been thus far 121

given to errors associated with the measured pH in the context of desalination brines. In 122

MANUSCRIP

T

ACCEPTED

ACCEPTED MANUSCRIPT

the current work a heuristic measurement procedure for desalination brines dominated by 123

Na+/Cl- was developed and evaluated. Similarly to Nordstrom et al. (1999), a computer 124

program implementing the Pitzer approach was used to assign pH values to non-standard 125

buffer solutions according to the Macinnes convention. Subsequently, the significance of 126

the new measurement procedure to SWRO modeling was demonstrated by comparing 127

simulated and experimental pH values. 128

129

2. Material and Methods 130

2.1 Experimental 131

pH measurements were made using the Metrohm Aquatrode Plus (6.0257.600) combined 132

glass electrode with integrated Pt 1000 temperature sensor and a Metrohm780 pH meter. 133

Temperature was kept constant at 25±0.6⁰C with a MRC BL-30 circulating bath. Sample 134

measurements and calibrations were carried out in mixed 25 ml beakers. Certified 135

secondary standard buffers phthalate (pH=4.01), equimolal phosphate (pH=6.86), and 136

carbonate (pH=10.01) from Merck were used for calibration when the pH was measured 137

in the NIST scale (see results in Fig.1 and part of the results in Fig.3). For the NaCl-138

buffers: the abovementioned NIST buffers were prepared in the lab using analytical grade 139

chemicals. Prior to NaCl addition, the mV of the prepared buffers were compared with 140

the certified value (margin of error ∆mV<0.2). Chemicals used in the preparation of 141

samples and standards were oven-dried at 60-100⁰C for a minimum of one hour and 142

stored in a desiccator before weighing. Sodium carbonate was dried at 250⁰C for a 143

minimum of two hours and stored in a desiccator over CaCl2 salt. Sample and calibration 144

buffers were prepared on a volume (molar) basis and modeled accordingly. Accurate 145

MANUSCRIP

T

ACCEPTED

ACCEPTED MANUSCRIPT

compositions and pH values of the three buffers used are available in the SM files. In the 146

experimental set whose results are shown in Fig. 1, synthetic SW salts were weighed and 147

added cumulatively to sample solutions, while in the other experimental sets samples and 148

calibration standards were prepared from stock solutions. Synthetic seawater was 149

prepared according to a typical seawater composition (35g/kg). CaCl2 was not added to 150

high pH carbonate-containing samples to avoid CaCO3(s)/CaSO4(s) precipitation. Model 151

calculations always followed the exact composition of the prepared samples. The test 152

solutions (Fig. 4) consisted of 0.0025M carbonate, 0.001M borax, synthetic sea-water 153

ranging from 0 to 2.5xSW and HCl ranging from 0M to 0.01M. HCl was added to 154

samples using Metrohm 775 Dosimat automatic pipette. All samples were prepared 155

separately in a systematic order: synthetic-SW was added first, then Borax, HCl, dilution 156

with decarbonized water to about 80 ml and then CaCl2 (for low pH samples). Carbonate 157

addition and filling to 100ml with decarbonized water was carried out immediately before 158

measurement of each sample to minimize atmospheric CO2(g) exchange. 159

RO experiments were performed using a pilot-scale system, supporting a 4” diameter 40” 160

long spiral wound module (Dow SW304040-HRLE). 100 l of real Mediterranean 161

seawater was used as feed. To avoid CaCO3 scaling at high pH and recovery, the 162

seawater pH was first adjusted to pH4 using HCl. Air was bubbled subsequently for ~1h 163

for reducing the inorganic carbon concentration to ~0.05M (estimated from base dose 164

required to raise pH back to 7.8). The pH was then raised to pH 9.08 using NaOH. For 165

each recovery ratio, the system operated in a full recirculation mode for ~20 min before 166

sampling. Operating pressure, temperature and cross-flow velocity were maintained at 167

65±1 bar, 25±10C and 0.17±0.1 respectively. pHNIST was measured in the brine and 168

MANUSCRIP

T

ACCEPTED

ACCEPTED MANUSCRIPT

permeate solutions using Orion-Ross 8102BN combination electrode with Eutech 169

Instruments pH1500 pH meter. When calibrated by the same buffers, deviations between 170

the two electrodes (Orion-Ross & Metrohm) were <0.005 pH units. Permeate alkalinity 171

was measured by a standard Gran titration (R2>0.999). Concentrations of boron and 172

seawater major ions were measured using ICP-AES 173

2.2 Software and modeling 174

Theoretical pH calculations, based on charge balance, were performed using PHREEQC 175

(Parkhurst and Appelo, 1999), a software package developed by the USGS (United States 176

Geological Survey) for modeling hydrogeochemical systems. For speciation of aqueous 177

species PHREEQC offers various thermodynamic data sets and theoretical approaches. In 178

this work the database pitzer.dat was mainly used. This database implements the Pitzer 179

approach and retrieves thermodynamic data mostly from Harvie et al. (1984). The results 180

of implementing pitzer.dat were compared in this work (Fig. 1) with results emanating 181

from the use of two other database files: (1) minteqV4.dat - implementing an extended 182

Debye-Huckel approach and thermodynamic data compiled by the U.S environmental 183

protection agency; and sit.dat - which implements the Bronsted-Gugenheim approach and 184

uses thermodynamic data compiled by the European nuclear energy agency. The pH of 185

the NaCl buffers used for calibration was also calculated by PHREEQC, using the 186

Pitzer.dat database. Missing Pitzer interaction coefficients (i.e. phthalic acid (Chan et al., 187

1995; Ferra et al., 2009) and phosphoric acid (Covington and Ferra, 1994)) were added 188

manually. Ion transference numbers used in Eq. 1 for generating Fig. 2 were adopted 189

from the literature (Della Monica et al., 1979; Poisson et al. 1979; Panopoulos et al., 190

1986). Our SWRO computer model coupled the solution-diffusion-film model (Python 191

MANUSCRIP

T

ACCEPTED

ACCEPTED MANUSCRIPT

code) and the Pitzer approach, implemented within PHREEQC_COM object (Charlton 192

and Parkhurst, 2011). For detailed model description see Nir and Lahav (2013) and Nir 193

and Lahav (2014). Membrane permeabilities for water (4.18*10-7 m/s/bar), salt (1.66*10-8 194

m/s) and boric-acid (6.3*10-7 m/s) were determined from independent RO experiments 195

using distilled water and seawater at pH7. The correlation for Sherwood’s number 196

(Sh=ARebSc0.25) was used for calculating the mass transfer coefficient used within the 197

film concentration-polarization model (Schock and Miquel, 1987). A and b were 198

estimated from independent experiments to be 0.079 and 0.73, respectively. The 199

measured composition of the seawater feed, which was used as input to the simulation, is 200

given in Table 1. 201

Table 1

202

3. Results and Discussion 203

3.1 Measuring and modeling pH in highly concentrated solutions 204

The pH measurement approach applied in this work was to minimize liquid junction 205

potential errors by adding NaCl to standard NIST buffers and assigning new pH values to 206

the newly-generated saline buffers using the Pitzer approach. The combined glass 207

electrode was then calibrated with the assigned pH values. 208

This procedure was tested systematically in light of the following criteria: (1) The new 209

measurement technique should be almost identical to the conventional one (i.e. three-210

point calibration), with the aim of facilitating adoptability by both industry and academia; 211

(2) wide range of salinities and pH values should be covered; (3) The pH calculated by 212

the thermodynamic model used for assigning pH values to the calibration buffers (pHcalc) 213

MANUSCRIP

T

ACCEPTED

ACCEPTED MANUSCRIPT

should be highly consistent with the pH assigned by NIST to standard reference buffer 214

solutions (pHS,NIST) in order to maintain continuum pH scale from low to high ionic 215

strengths; (4) The differences between pH values measured on the NIST scale (pHX,NIST) 216

and pHcalc should be as small as possible even at high ionic strengths in order to retain 217

meaningfulness of the pHNIST (which will most likely remain the most widely use 218

method) and allow practitioners to maintain their intuition for pH, thereby encouraging 219

them to practice the new method; (5) The pH measured by the new method, pHX,PM, (PM: 220

Pitzer-Macinnes) should be consistent with pHcalc. 221

The three chosen standard buffer solutions (see Experimental section) resembled the pH4, 222

pH7 and pH10 three-point calibration system, which is both widely-used and also covers 223

the pH range required in desalination applications (in compliance with the first two 224

criteria). The choice of the buffer weak-acid systems was also induced by the reliability 225

and availability of Pitzer's coefficients characterizing the interactions of the weak acid 226

species with NaCl. Pitzer coefficients absent from the PHREEQC database were adopted 227

from the literature and incorporated manually into the database. As a prerequisite step, 228

the equilibrium model was tested for consistency with standard NIST pH values and 229

compared against other databases embedded in the software, analogously to the 230

theoretical analysis made by Camoes et al. (1997). The pH values reported by NIST were 231

generally the closest to those calculated by the Pitzer model for almost all the temperature 232

range considered (see Fig. 1A on supporting material file), implying high consistency of 233

the Pitzer model and database with the dilute NIST buffers, in compliance with criterion 234

(3). 235

MANUSCRIP

T

ACCEPTED

ACCEPTED MANUSCRIPT

Criterion (4) was tested by adding seawater salts to borate and carbonate NIST buffers, 236

measuring pHX,NIST and comparing the results to the theoretical pH values obtained by 237

different thermodynamic models. As shown in Fig. 1, the differences between calculated 238

and measured pH values significantly increased in all the models except for the Pitzer-239

Macinnes model, for which the difference remained relatively constant. A one-tail, 240

unequal variance T-test was performed to compare the average absolute difference, 241

(∆pH= |pHX,NIST – pHcalc|) for this model with each of the other three models. The Pitzer-242

Macinnes model was found to be significantly closer to the average pH-NIST value. The 243

average error was 0.063 pH units as compared to 0.22 (p=0.011) pH units for 244

MinteqV.4.dat, 0.18 pH units (p=0.00038) for SIT.dat and 0.12 pH units (p=0.0011) for 245

unscaled Pitzer. The lower average ∆pH obtained with Pitzer.dat compared with SIT.dat 246

and MinteqV4.dat was attributed to both the inherent inaccuracy of the latter models at 247

high ionic strength and liquid junction potential. However, the lower average ∆pH 248

obtained for the Macinnes-Pitzer model, as compared with the unscaled Pitzer model was 249

a direct result of the Macinnes activity convention, which was assumed to decrease the 250

absolute value of the liquid junction potential term appearing in Eq. 1. 251

Figure 1

252

This relation was examined by calculating the theoretical ∆pH resulting from an ideal 253

liquid junction potential for both Macinnes and unscaled activity conventions using Eq. 1 254

(Harvie et al. 1984) 255

(3 ) (3 )

ln ln

ln(10) / ln(10)

KCl M KCl Mc ck kk k

k kk kX S

t td a d a

z zLJPpH

RT F

−∆∆ = =

∑ ∑∫ ∫ (1) 256

MANUSCRIP

T

ACCEPTED

ACCEPTED MANUSCRIPT

Where: tk is the ion transference number of ion k (i.e. the fraction of electrical current 257

carried by each ion when the solution is subject to an electromagnetic field); akC is the 258

conventional activity of ion k. The first integral in Eq. 3 refers to the potential of the 259

liquid junction between the measured solution X and the 3M KCl reference filling 260

solution, while the second integral refers to the liquid junction potential forming when the 261

electrode is dipped in a standard solution S (represented here by a 0.1M NaCl solution). 262

The results of this calculation for seawater and NaCl solutions of different salinities and 263

25 0C are presented in Fig. 2. Although, as expected, Eq. 1 did not provide accurate 264

predictions of the experimental ∆pH (liquid junction potential), the trends appearing in 265

Fig. 2 followed the empirical results, i.e. using the unscaled Pitzer model resulted in 266

increased ∆pH as a function of ionic strength, while using the Macinnes convention 267

maintained it relatively constant. Another observation obtained from Fig. 2 is the high 268

similarity between ∆pH for NaCl and ∆pH for seawater when the Macinnes convention 269

was used. These theoretical considerations suggest that a buffer system containing single 270

NaCl concentration is sufficient for a wide ionic strength range and varying ion 271

compositions when the Macinnes scale is used, thereby corroborating the approach used 272

in this work. 273

Figure 2

274

Figure 3

275

The amount of NaCl needed to be added to the NIST buffers was determined according 276

to criterion (5). The glass electrode was calibrated using three NIST+NaCl buffers at 277

varying NaCl concentration and then used to measure the pH of borax and carbonate 278

MANUSCRIP

T

ACCEPTED

ACCEPTED MANUSCRIPT

buffers in seawater-based solutions of varying concentrations (i.e. SW⋅1.5, SW⋅2, etc.). 279

The measurements were compared to the calculated pH in the ionic strength range 0.5-280

2.0M, adequate for most desalination applications. Since ∆pH~0.03 was estimated as the 281

uncertainty associated with the NIST procedure (Buck et al., 2002) it was selected as the 282

accuracy limit of the current measurement approach. As shown in Fig. 3, the difference 283

between measured and modelled pH (∆pH) amounted to 0.09 when the standard NIST 284

buffers were used, while calibration with 0.75M NaCl buffer resulted in ∆pH<0.03, with 285

almost all standard deviations inside this range, represented by the dotted lines in Fig. 3. 286

Calibrations with 0.5M and 1M added NaCl (not shown) produced very similar, but 287

slightly less consistent results. 288

Standard phtalate, phosphate and carbonate buffers comprising additional 0.75M NaCl 289

were chosen as the three-point calibration buffer system for measuring pH in desalination 290

brine streams. The new procedure was tested by measuring the pH of a borate/carbonate 291

mixture in synthetic seawater media (SSW) at four different concentrations (SSW⋅1, 292

SSW⋅1.5, SSW⋅2 and SSW⋅2.5). ∆pH<0.02 was obtained for all SSW concentrations 293

used, indicating high consistency between the model and the chosen measurement 294

procedure. Subsequently, the pH of borate-carbonate-HCl in SSW was measured and 295

compared to the model to evaluate the consistency over a wide pH range. As shown in 296

Fig. 4, the titration curve was reasonably well predicted by the model at all SSW 297

concentrations. Most importantly, at the high pH range (pH8-9), which is the most critical 298

for both boron rejection by RO and CaCO3 solubility, ∆pH<0.03 was obtained for all 299

SSW concentrations examined. At the pH range of 6-7 ∆pH was in the range of 0.03-0.09 300

while in the low range of 3-5 0.07<∆pH<0.19 was observed. The increasing error at the 301

MANUSCRIP

T

ACCEPTED

ACCEPTED MANUSCRIPT

low pH range was likely due to both atmospheric CO2 dissolution and experimental 302

errors stemming from the acid dosage. 303

Figure 4

304

3.2 High pH SWRO operation: empirical vs. simulated results 305

RO filtration experiments, closely simulating the decrease in permeate flux and the 306

increase in the retentate concentration, as encountered in actual SWRO applications, were 307

performed using real seawater feed. Simulated pH values were compared to empirical 308

results obtained by both the conventional pH measurement procedure and the method 309

developed in this work. The model used for simulating the acid-base properties of the 310

SWRO brine was first evaluated for its capability to predict trans-membrane water flux 311

and permeate salt (mainly NaCl) concentrations at different recovery ratios. As shown in 312

Fig. 5, the model predicted both parameters reasonably well, demonstrating the ability of 313

the solution-diffusion-film model to account for flux and concentration-polarization 314

effects on the transport of all solutes, including acid-base species whose transport and 315

chemical equilibrium processes relate to the pH of the brine and permeate streams. 316

Figure 5

317

The measured seawater feed pH value was 9.08 on the Pitzer-Macinnes scale 318

(pHPM=9.08) and 9.02 on the conventional scale (pHNIST=9.02). The brine pH gradually 319

decreased, arriving at pHPM=8.80 and pHNIST=8.60 at the highest-applied recovery ratio 320

of 50%. As depicted in Fig.6, when the pH was measured on the Pitzer-Macinnes scale, 321

the values matched the modeled results better. The measured pHNIST was lower than the 322

MANUSCRIP

T

ACCEPTED

ACCEPTED MANUSCRIPT

measured and modeled pHPM and this gap increased with increased ionic-strength in 323

accordance with the results shown in Fig. 2. 324

Figure 6

325

Overall, the trend in the pH values developing in the brine as measured on the new scale 326

was in par with the model. Having said this, the encountered 0.06-0.08 pH units 327

differences between measured and modeled pHPM values at the high recovery range were 328

higher than the previously estimated (∆pH~0.03 measurement) error. This extended error 329

was accompanied by a surprisingly high pH values on the permeate side (Fig. 7), higher 330

than the brine pH at all the recovery ratios applied. These observations go against the 331

common conception that RO permeate pH should be lower than that of the brine, 332

stemming from the logic that almost only acidic species (e.g. CO2, B(OH)3) pass the 333

membrane. Andrews et al. (2008) already observed this phenomenon in the results of a 334

full scale SWRO plant, however no explanation was provided. Combined, the lower-335

than-expected brine pH and the higher-than-expected permeate pH implied strongly to a 336

small transfer of alkalinity-species mass from the brine stream to the permeate stream. In 337

the current work it was hypothesized that this phenomenon was induced by a Donnan 338

effect, i.e. sodium cations diffusing through the membrane at a higher rate compared to 339

chloride anions, mainly due to the membrane’s negative charge at the working pH range, 340

inducing a small potential difference. This potential drives hydroxide ions from the brine 341

to the permeate side and/or hydronium ions in the opposite way, to maintain electro-342

neutrality. Ultimately, this transport phenomenon results in the addition of alkalinity to 343

the permeate side and loss of alkalinity (or addition of acidity) to the brine. 344

MANUSCRIP

T

ACCEPTED

ACCEPTED MANUSCRIPT

Figure 7

345

In an attempt to assess the magnitude of this alkalinity transfer under the experimental 346

conditions tested in this work, a similar RO filtration experiment was performed using a 347

synthetic solution with major ion composition resembling that of seawater, but without 348

addition of carbonic- and boric acids. The feed pH was maintained at pHPM=9 while 349

permeate pH values were again higher by 0.3-0.5 pH units, corroborating the 350

hydroxide/hydronium transfer hypothesis. Alkalinity values measured (by the Gran 351

titration) in the permeate solution at the initial (→0%) and final (50%) recovery ratios 352

were 23µeq/l and 33µeq/l, respectively. Additional filtration experiments performed with 353

distilled water and NaCl (results not shown) revealed complex relation between the 354

permeate pH value and quite a few operational parameters i.e. water flux, cross-flow 355

velocity, feed pH and NaCl concentration. Detailed understanding of this Donnan-356

inspired alkalinity transfer requires an in-depth study which was beyond the scope of this 357

work. Having said this, the trend-like effect of this phenomenon on model predictions 358

was assessed in this work by its inclusion in the model once as an empirical observation 359

and once as means of model calibration. As a first approximation, it was assumed that the 360

addition of alkalinity to the permeate side was constant throughout the process. As seen 361

in Fig. 6, when the average measured alkalinity value (28µeq/l) was used, the modeled 362

retentate pH was ~0.02-0.03 lower than the model run which did not include the Donnan 363

alkalinity transfer, resulting in a small (yet apparent) improvement in the prediction of the 364

measured pHPM. At the same time, the prediction trend as manifested by the permeate pH 365

values improved significantly when the transferred alkalinity was set to 28µeq/l. 366

Conversely, when the pH was measured on the NIST scale, only a negligible progress 367

MANUSCRIP

T

ACCEPTED

ACCEPTED MANUSCRIPT

towards the measured pHNIST (right hand side of Fig. 6) was observed. Matching the 368

modeled retentate pH to the measured pHPM at high recovery ratios required setting the 369

transferred alkalinity to 66µeq/l. This resulted in excellent predictions of the permeate pH 370

at recovery ratio >40%. At the lower recovery range the modeled permeate pH was ~0.1-371

0.15 pH units above the measured one; however the accuracy of the pH measurement in 372

these highly-diluted poorly-buffered waters is questionable. In order to absolutely match 373

the modeled pH to the measured pHNIST, the transferred alkalinity had to be set to 374

180µeq/l, resulting in an unrealistically high values of modeled permeate pH. A similar 375

trend can be seen in Fig. 8, which illustrates measured and modeled boron permeate 376

concentration. When the empirical transferred alkalinity (28µeq/l) was used, the model 377

showed better boron rejection prediction at both pH scales. However, when the 378

transferred alkalinity was calibrated according to pHNIST (i.e. transferred alkalinity set to 379

180µeq/l), modeled boron concentration results were significantly higher than the 380

empirical results. Conversely, when the transferred alkalinity was calibrated according to 381

the measured pHPM (i.e. transferred alkalinity set to 66µeq/l) a small improvement in 382

model prediction was observed. 383

Figure 8

384

It remains unclear why the empirical transferred alkalinity, measured in boron/carbonate 385

free solution, was lower than the calibrated value. A possible explanation could be that 386

the low buffering capacity of the synthetic solution resulted in local pH changes (e.g. in 387

the concentration polarization layer), thus creating hydroxide/hydronium concentration 388

gradients which acted as a counter force to their Donnan-inspired electromigration. 389

MANUSCRIP

T

ACCEPTED

ACCEPTED MANUSCRIPT

4. Conclusions 390

A reliable methodology for measuring pH in seawater desalination brines was developed 391

in this work. The method is consistent with the best available thermodynamic model (i.e. 392

Pitzer). Improvement over the conventional NIST method was most significant at high 393

pH and high ionic-strength conditions, which, fortunately, are the most important 394

conditions with respect to pH depended chemical scaling tendency. The potential of the 395

new methodology for improving reactive transport desalination models by utilizing the 396

Pitzer approach and the Macinnes scale was evaluated and compared to the conventional 397

(pHNIST) approach. It was found that although seawater pHNIST measurements could be 398

used as input (since the inconsistency is of the order of ~0.05 pH units), higher salinity 399

retentates, important for model calibration and evaluation, as well as for process 400

monitoring, require the use of a specialized method, such as the one suggested in this 401

work. In the current study, the added accuracy in the pH value allowed to fine-tune the 402

simulation model to attain better pH predictions in both brine and permeate streams and 403

more accurate prediction of boron permeate concentrations. 404

405

References 406

Andrews, B., Davé, B., López-Serrano, P., Tsai, S., Frank, R., Wilf, M., Koutsakos, E. 407

2008. Effective scale control for seawater RO operating with high feed water pH and 408

temperature. Desalination 220 (1-3), 295-304. 409

Azaroual, M., Kervévan, C., Durance, M. N., Durst, P. 2004. SCALE2000: reaction-410

transport software dedicated to thermokinetic prediction and quantification of scales 411

applicability to desalination problems. Desalination 165, 409-419. 412

Buck, R. P., Rondinini, S., Covington, A. K., Baucke, F. G. K., Brett, C. M. A., 413

Camões, M. F., Milton, M. J. T., Mussini, T., Naumann, R., Pratt, K. W., Spitzer, P., 414

Wilson, G. S. 2002. Measurement of pH. Definition, standards, and procedures (IUPAC 415

Recommendations 2002). Pure and Applied Chemistry 74 (11), 2169-2200. 416

MANUSCRIP

T

ACCEPTED

ACCEPTED MANUSCRIPT

Camões, M. F., Guiomar, L. M., Ferra, M. I. A., Covington, A. K. 1997. Consistency 417

of pH standard values with the corresponding thermodynamic acid dissociation constants. 418

69, 6, 1325-1333. 419

Chan, C., Eng, Y., Eu, K. 1995. Pitzer Single-Ion Activity Coefficients and pH for 420

Aqueous Solutions of Potassium Hydrogen Phthalate in Mixtures with KCl and with 421

NaCl at 298.15 K. Journal of Chemical & Engineering Data 40 (3), 685-691. 422

Charlton, S. R. and Parkhurst, D. L. 2011. Modules based on the geochemical model 423

PHREEQC for use in scripting and programming languages. Computers and Geosciences 424

37 (10), 1653-1663. 425

Covington, A. K. 1997. The quantity ‘pH’. Talanta 44 (11), 2161-2164. 426

Covington, A. K. and Ferra, M. I. A. 1994. A pitzer mixed electrolyte solution theory 427

approach to assignment of pH to standard buffer solutions. 23 (1), 1-10. 428

Della Monica, M., Petrella, G., Sacco, A., Bu̇ fo, S. 1979. Transference numbers in 429

concentrated sodium chloride solutions. Electrochimica Acta 24 (9), 1013-1017. 430

Donose, B. C., Sukumar, S., Pidou, M., Poussade, Y., Keller, J., Gernjak, W. 2013. 431

Effect of pH on the ageing of reverse osmosis membranes upon exposure to hypochlorite. 432

Desalination 309, 97-105. 433

Ferra, M. I. A., Graca, J. R., Marques, A. M. M. 2009. Application of the Pitzer Model 434

to Assignment of pH to Phthalate Standard Buffer Solutions. 38 (11), 1433-1448. 435

Harvie, C. E., Møller, N., Weare, J. H. 1984. The prediction of mineral solubilities in 436

natural waters: The Na-K-Mg-Ca-H-Cl-SO4-OH-HCO3-CO3-CO2-H2O system to high 437

ionic strengths at 25°C. Geochimica et Cosmochimica Acta 48 (4), 723-751. 438

Huff, G. F. 2004. Use of simulated evaporation to assess the potential for scale 439

formation during reverse osmosis desalination. Desalination 160 (3), 285-292. 440

Hurtado, C. F. and Cancino-Madariaga, B. 2014. Ammonia retention capacity of 441

nanofiltration and reverse osmosis membranes in a non steady state system, to be use in 442

recirculation aquaculture systems (RAS). Aquacultural Engineering 58, 29-34. 443

Knauss, K. G., Wolery, T. J., Jackson, K. J. 1990. A new approach to measuring pH in 444

brines and other concentrated electrolytes. Geochimica et Cosmochimica Acta 54 (5), 445

1519-1523. 446

Mane, P. P., Park, P., Hyung, H., Brown, J. C., Kim, J. 2009. Modeling boron 447

rejection in pilot- and full-scale reverse osmosis desalination processes. Journal of 448

Membrane Science 338 (1–2), 119-127. 449

MANUSCRIP

T

ACCEPTED

ACCEPTED MANUSCRIPT

Marion, G. M., Millero, F. J., Camões, M. F., Spitzer, P., Feistel, R., Chen, C. -. A. 450

2011. pH of seawater. Marine Chemistry 126 (1-4), 89-96. 451

Mesmer, R. E. 1991. Comments on “a new approach to measuring pH in brines and 452

other concentrated electrolytes” by K.G. Knauss T.J. Wolery, K.J. Jackson. Geochimica 453

et Cosmochimica Acta 55 (4), 1175-1176. 454

Millero, F. J. 2009. Use of the pitzer equations to examine the dissociation of TRIS in 455

NaCl solutions. Journal of Chemical and Engineering Data 54 (2), 342-344. 456

Millero, F. J., DiTrolio, B., Suarez, A. F., Lando, G. 2009. Spectroscopic 457

measurements of the pH in NaCl brines. Geochimica et Cosmochimica Acta 73 (11), 458

3109-3114. 459

Mistry, K. H., Hunter, H. A., Lienhard V, J. H. 2013. Effect of composition and 460

nonideal solution behavior on desalination calculations for mixed electrolyte solutions 461

with comparison to seawater. Desalination 318, 34-47. 462

Nir, O. and Lahav, O. 2013. Coupling mass transport and chemical equilibrium 463

models for improving the prediction of SWRO permeate boron concentrations. 464

Desalination 310, 87-92. 465

Nir, O., Herzberg, M., Sweity, A., Birnhack, L., Lahav, O. 2012. A novel approach for 466

SWRO desalination plants operation, comprising single pass boron removal and reuse of 467

CO2 in the post treatment step. Chemical Engineering Journal 187, 275-282. 468

Nir, O. and Lahav, O. 2014. Modeling weak acids' reactive transport in reverse 469

osmosis processes: A general framework and case studies for SWRO. Desalination, 343, 470

147-153. 471

Nordstrom, D. K., Alpers, C. N., Ptacek, C. J., Blowes, D. W. 1999. Negative pH and 472

Extremely Acidic Mine Waters from Iron Mountain, California. Environmental Science 473

& Technology 34 (2), 254-258. 474

Panopoulos, D., Kaneko, H., Spiro, M. 1986. Transference numbers of sodium 475

chloride in concentrated aqueous solutions and chloride conductances in several 476

concentrated electrolyte solutions. 15 (3), 243-252. 477

Park, P., Lee, S., Cho, J., Kim, J. 2012. Full-scale simulation of seawater reverse 478

osmosis desalination processes for boron removal: Effect of membrane fouling. Water 479

research 46 (12), 3796-3804. 480

Parkhurst, D. L. and Appelo, C. 1999. User's guide to PHREEQC (Version 2): A 481

computer program for speciation, batch-reaction, one-dimensional transport, and inverse 482

geochemical calculations. 483

MANUSCRIP

T

ACCEPTED

ACCEPTED MANUSCRIPT

Pitzer, K. S. 1973. Thermodynamics of electrolytes. I. Theoretical basis and general 484

equations. Journal of Physical Chemistry 77 (2), 268-277. 485

Plummer, L. N., Parkhurst, D. L., Flemming, G. W., Dunkle, S. A. 1988. A computer 486

program incorporating Pitzer’s equations for calculation of geochemical reactions in 487

brines. 88-4153. 488

Poisson, A., Perie, M., Perie, J., Chemla, M. 1979. Individual equivalent conductances 489

of the major ions in seawater. 8 (5), 377-394. 490

Radu, A. I., Bergwerff, L., van Loosdrecht, M. C. M., Picioreanu, C. 2014. A two-491

dimensional mechanistic model for scaling in spiral wound membrane systems. Chemical 492

Engineering Journal 241, 77-91. 493

Sagiv, A. and Semiat, R. 2004. Analysis of parameters affecting boron permeation 494

through reverse osmosis membranes. Journal of Membrane Science 243 (1–2), 79-87. 495

Schausberger, P., Mustafa, G. M., Leslie, G., Friedl, A. 2009. Scaling prediction based 496

on thermodynamic equilibrium calculation — scopes and limitations. Desalination 244 497

(1–3), 31-47. 498

Schock, G. and Miquel, A. 1987. Mass transfer and pressure loss in spiral wound 499

modules. Desalination 64, 339-352. 500

Sousa, M. F. B. and Bertran, C. A. 2014. New methodology based on static light 501

scattering measurements for evaluation of inhibitors for in bulk CaCO3 crystallization. 502

Journal of colloid and interface science 420, 57-64. 503

Spitzer, P., Fisicaro, P., Meinrath, G., Stoica, D. 2011. pH buffer assessment and 504

Pitzer's equations. Accreditation and Quality Assurance 16 (4-5), 191-198. 505

Taniguchi, M., Kurihara, M., Kimura, S. 2001. Boron reduction performance of 506

reverse osmosis seawater desalination process. Journal of Membrane Science 183 (2), 507

259-267. 508

Teychene, B., Collet, G., Gallard, H., Croue, J. 2013. A comparative study of boron 509

and arsenic (III) rejection from brackish water by reverse osmosis membranes. 510

Desalination 310, 109-114. 511

Tu, K. L., Nghiem, L. D., Chivas, A. R. 2010. Boron removal by reverse osmosis 512

membranes in seawater desalination applications. Separation and Purification 513

Technology 75 (2), 87-101. 514

MANUSCRIP

T

ACCEPTED

ACCEPTED MANUSCRIPT

Waly, T., Kennedy, M. D., Witkamp, G., Amy, G., Schippers, J. C. 2011. Predicting 515

and measurement of pH of seawater reverse osmosis concentrates. Desalination 280 (1–516

3), 27-32. 517

Wang, J., Mo, Y., Mahendra, S., Hoek, E. M. V. 2014. Effects of water chemistry on 518

structure and performance of polyamide composite membranes. Journal of Membrane 519

Science 452, 415-425. 520

MANUSCRIP

T

ACCEPTED

ACCEPTED MANUSCRIPT

List of Figures 521

522

Figure 1. Average measured pHX,NIST values of the borax and carbonate standard buffers 523

(n=3),compared to pH values calculated in PHREEQC using different databases / species 524

activity models, as a function of ionic strength resulting from the addition of seawater 525

salts. 526

527

Figure 2. ∆pH resulting from theoretical liquid junction potential considerations as 528

function of ionic strength upon calibration with I=0.1M buffers at T=250C. Seawater and 529

NaCl solutions were measured. Theoretical calculations were carried out using Pitzer's 530

ion activity model with/without Macinnes convention application 531

532

Figure 3. The difference between the calculated (Pitzer-Macinnes) and the average (n=3) 533

measured pH using four different sets of calibration buffers, as a function of ionic 534

strength 535

536

Figure 4. Measured (markers) and calculated pH for HCl+0.0025M Na2CO3 +0.0025M 537

NaHCO3+ 0.001M Na2B4O7:10H2O in synthetic seawater at: SSWx1 (a), SSWx1.5(b), 538

SSWx2(c) and SSWx2.5(d) 539

540

Figure 5. Model results (dashed lines) versus experimental results of permeate flux and 541

permeate salt concentration as a function of recovery ratio 542

543

Figure 6. Model results (dashed lines) Vs. experimental results of retentate pH, measured 544

on the new Pitzer-Macinnes scale (left hand side graph) and on the NIST scale, as a 545

function of recovery ratio. Trans_Alk stands for assumed passage of alkalinity mass due 546

to the electromigration of H+/OH- ions. 547

548

Figure 7. Model results (dashed lines) Vs. experimental results of permeate pH, 549

measured on the NIST scale, as a function of recovery ratio. Trans_Alk stands for 550

assumed passage of alkalinity mass due to the electromigration of H+/OH- ions. 551

552

Figure 8. Model results (dashed lines) Vs. experimental results of permeate boron 553

concentration as a function of recovery ratio: A comparison between the NIST pH scale 554

and the Pitzer-Macinnes pH scale developed in this work. Trans_Alk stands for assumed 555

passage of alkalinity mass due to the electromigration of H+/OH- ions. 556

557

558

MANUSCRIP

T

ACCEPTED

ACCEPTED MANUSCRIPT

Cl- Na+ Mg2+ SO42- K+ Ca2+ BT (mg/l as B) CT (mg/l as CO2)

22011 12282 1423 3202 501 467 4.54 2.20

Table 1. Seawater feed major ions and weak acid species concentrations (mg/l)

MANUSCRIP

T

ACCEPTED

ACCEPTED MANUSCRIPT

MANUSCRIP

T

ACCEPTED

ACCEPTED MANUSCRIPT

MANUSCRIP

T

ACCEPTED

ACCEPTED MANUSCRIPT

MANUSCRIP

T

ACCEPTED

ACCEPTED MANUSCRIPT

MANUSCRIP

T

ACCEPTED

ACCEPTED MANUSCRIPT

MANUSCRIP

T

ACCEPTED

ACCEPTED MANUSCRIPT

MANUSCRIP

T

ACCEPTED

ACCEPTED MANUSCRIPT

MANUSCRIP

T

ACCEPTED

ACCEPTED MANUSCRIPT

MANUSCRIP

T

ACCEPTED

ACCEPTED MANUSCRIPT

Highlights

• An accurate method for determining pH in SW desalination brines was developed

• NIST + 0.75M NaCl buffers, to which new standard pH is assigned by Pitzer, are

used

• The method shows improved consistency and accuracy over standard pH

measurement

• A set of three modified buffer standards covers wide pH and salinity ranges

• The new procedure enabled better calibration of a SWRO reactive-transport

model

MANUSCRIP

T

ACCEPTED

ACCEPTED MANUSCRIPT

Supporting material for the paper

A short description of the NIST definition and measurement procedure for pH

For dilute solutions, pH is defined as the activity of the free proton and is most

frequently measured by using an electrochemical cell comprising the proton responsive

glass electrode and a reference electrode. While the glass electrode is in direct contact

with the measured solution (or standard), the reference electrode is in contact with the

reference electrolyte (commonly 3M-4.2M KCl), separated by a porous medium – the

liquid junction. This electrode arrangement can be merged into a single probe, producing

the highly employed pH combination electrode. The e.m.f of this cell is attributed to the

sum of the potential induced by the glass response to H+ and the liquid junction potential

(LJP) resulting from unequal diffusion rates of opposite charged ions across the junction.

Calibrating the pH electrode using standard solutions provide the quantitative relation

between e.m.f (E) and pH and allows for the elimination of the LJP term from Eq. A1

which is the working equation for pH measurement using the glass electrode and one

point calibration buffer.

( , ) ( , )

ln(10) / ln(10) /X s

X

E E LJP KCl X LJP KCl SpH

RT F RT F

− −= + (A1)

The embedded assumption is that the difference between liquid junction potential (LJP)

developed between the reference electrolyte and the standard solution - LJP(KCl,S), is

very similar to the LJP between the measured solution and the reference electrolyte –

LJP(KCl,X). Standard solutions can be traced back to primary pH measurements

executed in institutions such as NIST (U.S National Institute of Standards and

Technology) and DIN (the German Institute for Standardization). Primary measurements

of pH involve a different electrochemical setting, comprising of a standard hydrogen

MANUSCRIP

T

ACCEPTED

ACCEPTED MANUSCRIPT

electrode and a silver/silver-chloride reference electrode. Both electrodes are placed in

direct contact with the buffer solution (i.e. no liquid junction), to which a small amount of

KCl or NaCl was added. The e.m.f of the cell is related to the mean activity of the

chloride and proton by Nernst’s equation, which can be written as follows:

0

0

( )( ) log( / )

ln(10) /cell

H Cl Cl

E Ep a m m

RT Fγ −= + (A2)

The activity coefficient of the chloride, which is the only unknown in Eq. A2 apart from

the pH, is determined via the Bates-Guggenheim convention. It is important to note that

the activity (or activity coefficient) of a single ion cannot be measured in a

thermodynamic valid method and therefore requires a convention. The standard pH value

is obtained by repeating this process several times with different concentrations of

chloride followed by an extrapolation to zero chloride concentration. A comprehensive

description of the definitions, procedures, mathematical expressions, assumptions and

uncertainties associated with the pH of dilute solutions, is provided in the latest IUPAC

guidelines (Buck et al, 2002).

A short description of the seawater pH standardization

The most up-to-date accepted approach for seawater pH standardization involves

specialized seawater buffers with a pKa* (apparent pKa in seawater) value close to the

natural pH of seawater. pH values were carefully assigned to these buffers via

measurements in liquid-junction free electrochemical cells (DelValls and Dickson, 1998)

at temperature and salinity ranges relevant for seawater. The assigned pH provided a

measure for the concentration of protons (rather than activity), thereby including

additional proton complexes, depending on the pH scale used (Dickson, 1984). pKa*

values for carbonic and boric acids in seawater were also determined based on the

MANUSCRIP

T

ACCEPTED

ACCEPTED MANUSCRIPT

concentration scale (Dickson, 1990); Millero et al., 2006) thus, for example, using these

pKa* values for determining weak-acid species concentrations requires the pH

measurements to be on a similar scale, otherwise significant errors arise. Overall, the

seawater pH scale approach relies on the relatively constant composition of seawater and

therefore cannot be easily extended to desalination brines of varying compositions, nor to

seawater brines at salinity >45‰ nor to pH values significantly different from 8.1Millero et

al. (2009)

Key equations of the RO weak-acid transport simulation

The Solution-Diffusion-Film is used as the membrane transport model in the simulation.

The key equations for this model are:

( )V wJ P P= ∆ − ∆Π (1)

( )v p s m pJ C P C C= − (2)

/( ) vJ km p b pC C C C e− = −

(3)

JV – permeate flux

Pw, Ps – Water and salt permeability constants respectively

∆P = Trans-membrane hydraulic pressure difference

∆Π = Trans-membrane hydraulic pressure difference

Cp = Permeate concentration

Cb = Bulk concentration

Cm = Concentration near membrane surface

k = Mass transfer coefficient

The osmotic pressure difference is given by:

MANUSCRIP

T

ACCEPTED

ACCEPTED MANUSCRIPT

( )m m p pC C RT∆Π = Φ − Φ

Φ is the osmotic coefficient, which is determined from the Pitzer equations for a given water composition (typically Φ =0.91 for seawater and Φ =0.97 for the permeate).

For total concentrations of weak acid species (AT) and for alkalinity (Alk), an average mass transfer coefficient is used for modeling concentration polarization, yielding:

exp( / )T

Tm TpV A

Tb Tp

A AJ k

A A

−=

−

exp( / )m pV Alk

b p

Alk AlkJ k

Alk Alk

−=

−

Further description of the algorithm and assumptions of the coupled simulation modeled can be found in Nir and Lahav (2014)

REFERENCES

Buck, R. P., Rondinini, S., Covington, A. K., Baucke, F. G. K., Brett, C. M. A., Camões, M. F., Milton, M. J. T., Mussini, T., Naumann, R., Pratt, K. W., Spitzer, P., Wilson, G. S. 2002. Measurement of pH. Definition, standards, and procedures (IUPAC Recommendations 2002). Pure and Applied Chemistry 74 (11), 2169-2200.

DelValls, T. A. and Dickson, A. G. 1998. The pH of buffers based on 2-amino-2-hydroxymethyl-1,3-propanediol (‘tris’) in synthetic sea water. Deep Sea Research Part I: Oceanographic Research Papers 45 (9), 1541-1554.

Dickson, A. G. 1990. Thermodynamics of the dissociation of boric acid in synthetic seawater from 273.15 to 318.15 K. Deep Sea Research Part A, Oceanographic Research Papers 37 (5), 755-766.

Dickson, A. G. 1984. pH scales and proton-transfer reactions in saline media such as sea water. Geochimica et Cosmochimica Acta 48 (11), 2299-2308.

(5)

(6)

(4)

MANUSCRIP

T

ACCEPTED

ACCEPTED MANUSCRIPT

Millero, F. J., DiTrolio, B., Suarez, A. F., Lando, G. 2009. Spectroscopic measurements of the pH in NaCl brines. Geochimica et Cosmochimica Acta 73 (11), 3109-3114.

Millero, F. J., Graham, T. B., Huang, F., Bustos-Serrano, H., Pierrot, D. 2006. Dissociation constants of carbonic acid in seawater as a function of salinity and temperature. Marine Chemistry 100 (1–2), 80-94.

Nir, O. and Lahav, O. 2014. Modeling weak acids' reactive transport in reverse osmosis processes: A general framework and case studies for SWRO. Desalination, 343, 147-153.

Table 1A. Compositions and pH values of the buffers used

MANUSCRIP

T

ACCEPTED

ACCEPTED MANUSCRIPT

Figure 1A. The pH value of four standard NIST buffers (Buck et al. 2002), compared to

pH values calculated in PHREEQC by using three databases/species activity models, as a

function of temperature