Experimental study on the kinetics of silica polymerization during cooling of the Bouillante geothermal fluid (Guadeloupe, French West Indies)

    Experimental study on the kinetics of silica polymerization during cooling of the Bouillante geothermal fluid (Guadeloupe, French West Indies) Christelle Dixit, Marie-Lise Bernard, Bernard Sanjuan, Laurent Andr´e, Sarra Gaspard PII: DOI: Reference:

S0009-2541(16)30408-9 doi: 10.1016/j.chemgeo.2016.08.031 CHEMGE 18045

To appear in:

Chemical Geology

Received date: Revised date: Accepted date:

8 June 2016 19 August 2016 23 August 2016

Please cite this article as: Dixit, Christelle, Bernard, Marie-Lise, Sanjuan, Bernard, Andr´e, Laurent, Gaspard, Sarra, Experimental study on the kinetics of silica polymerization during cooling of the Bouillante geothermal fluid (Guadeloupe, French West Indies), Chemical Geology (2016), doi: 10.1016/j.chemgeo.2016.08.031

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ACCEPTED MANUSCRIPT Experimental study on the kinetics of silica polymerization during cooling

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of the Bouillante geothermal fluid (Guadeloupe, French West Indies)

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Christelle Dixita, Marie-Lise Bernarda, Bernard Sanjuanb,*, Laurent Andréb, Sarra Gaspardc

LaRGE, University of Antilles, 97159 Pointe-à-Pitre, Guadeloupe, France ([email protected],

[email protected])

BRGM, 3 Av. Claude Guillemin, 45060 Orléans Cedex 02, France ([email protected],

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b

[email protected])

COVACHIMM, University of Antilles, 97159 Pointe-à-Pitre, Guadeloupe, France (sgaspard@univ-

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ag.fr)

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* Corresponding author address: BRGM, Georesource Division, Department of

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Geothermal Energy, 3 - Avenue Claude Guillemin, BP36009, 45060 Orléans Cedex 02,

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France, phone: +33(0)238643420, e-mail: [email protected]

ABSTRACT

Despite many studies, our understanding of silica precipitation from natural waters remains limited, in particular for geothermal waters. Here we present a detailed study on the kinetics of silica polymerization as a function of fluid temperature and pH using high-temperature (250°C) seawater-derived geothermal fluids as those discharged from the Bouillante geothermal site. We monitored the on-site decrease in monomeric silica concentration (initial SiO2 concentration of about 600 mg l-1) with time using the molybdenum blue spectrophotometric method on samples of separated water collected from the high-pressure separator at 167 °C

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ACCEPTED MANUSCRIPT and cooled to 25, 50, 75, and 90 °C and for pH values ranging from 5 to 8. During all these experiments, only silica polymerization was observed, with the formation of colloidal particles in

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suspension in the solutions. No scaling of amorphous silica was formed. The collected data were

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after modeled in order to determine the useful kinetic parameters for predicting and preventing

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amorphous silica precipitation in the production wells during fluid exploitation in the specific context of Bouillante. Results under the investigated experimental conditions show that the

kinetics of silica precipitation is affected more strongly by pH than by temperature change.

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The reaction in the acidic Bouillante solution begins with a transition period that significantly

decreases the kinetics of silica polymerization. Modeling the experimental data indicates that

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the silica polymerization up to the state of equilibrium is characterized by a 2nd-order kinetic law relative to dissolved silica; this could indicate that the polymerization is controlled mainly

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by the formation of dimers. However, the first hour of the experiments is better characterized

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by a 4th-order kinetic law, suggesting more complex polymerization reactions in the initial

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stage with the formation of nanocolloidal particles containing 3 to 4 monomers. In both cases, the corresponding kinetics rate constant k is linearly dependent on pH for pH between 5 and 7.

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The activation energy Ea for the overall reaction, calculated using the Arrhenius equation under the considered pH and temperature conditions, ranges between 41 ± 9.8 and 54 ± 9.6 kJ mol-1. To complete this work, the colloid particles formed at the end of the kinetics experiments were extracted and analyzed by SEM and TEM microscopy, X-Ray Diffraction and the BET method. Results show that the size of the colloids increase and their specific surface decrease

with increasing pH and are thus dependent on pH. Globally, our work provides a reliable database for understanding silica polymerization kinetics in natural geothermal brines or geologic waters characterized by a near neutral pH and moderate dissolved silica concentrations.

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ACCEPTED MANUSCRIPT Key words: kinetics, amorphous silica, geothermal fluids, Bouillante power plant,

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polymerization, cooling

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ACCEPTED MANUSCRIPT 1. INTRODUCTION

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Scale formation, and more particularly silica deposition, is a common problem observed and

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studied in many geothermal plants around the world (Makrides et al., 1978; Gallup, 1997 and

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2002; Potapov et al., 2001; Gunnarsson and Arnórsson, 2003, 2005; Padilla et al., 2005; Potapov and Zhuravlev, 2005). This arises because the extraction of geothermal fluids is accompanied by a decrease in both temperature and pressure, resulting in supersaturation with

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respect to amorphous silica. The degassing and cooling of the geothermal fluid may then lead

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either to precipitation of dissolved silica directly onto a solid surface (silica scaling), or to polymerization of the silica into larger molecules that eventually coalesce to form silica colloids, also called silica gel (White et al., 1956; Baumann, 1959; Iler, 1979; Rothbaum and

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Rohde, 1979; Makrides et al., 1980; Chan, 1989; Sanjuan et al., 2005; Gunnarsson and Arnórsson, 2005, 2008; Bergna and Roberts, 2006; Gunnarsson et al., 2010; Alekseyev et al.,

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2010; Amjad, 2010; Guerra and Jacobo, 2012; Dixit, 2014; Kley et al., 2014; De Guzman et al., 2015; Noguera et al., 2015). Polymeric silica has fewer tendencies to precipitate from

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solution than monomeric silica and can remain suspended in the solution for long periods of time (Gunnarsson and Arnorsson, 2005), but it can also become a scale deposit. The direct scaling depends on the interaction of siloxane bonds of the silicic acid to the metal surface. This reaction is known to usually occur at high pH levels (pH > 8) and is catalyzed by hydroxyl ions (De Guzman et al., 2015). This produces a hard, dense and vitreous layer. On the other hand, colloidal formation occurs via a condensation-polymerization mechanism from silicic acid due to increasing silica saturation/supersaturation. This formation pathway forms small molecular weight dimers and trimers prior to forming rings of various sizes, and cross-linked polymeric chains, and ultimately a complex and amorphous product as discussed by Amjad (2010). Recent detailed studies on the silica polymerization from supersaturated

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ACCEPTED MANUSCRIPT aqueous solutions were performed by Bergna and Roberts (2006), Amjad (2010), Kley et al. (2014) and Noguera et al. (2015) and will be used for discussion in the next sections.

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According to the study carried out by Gunnarsson et al. (2010), which process takes place in

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spent high-temperature geothermal waters can also depend to some extent on the water

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environment. If the waters are in turbulent flow where there is surface available for monomeric deposition onto the surface, silica scaling is likely to take place, but if the waters are placed in quiet environment, silica polymerization is the favorable process.

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Studies of silica precipitation in high-temperature geothermal energy operations have mainly

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been aimed at preventing it (Rothbaum and Anderton, 1975; Rothbaum and Rohde, 1979; Hibara et al., 1989; Abe, 1997; Gallup, 1997, 2002; Kato et al., 2003; Ueda et al., 2003; Gallup et al., 2003; Park et al., 2006; Gunnarsson et al., 2010). These have shown that the

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efficiency of the proposed silica removal method greatly depends on a good knowledge of the fluid characteristics and the kinetics of the scale formation. However, little has been published

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concerning kinetic experiments on geothermal waters, or on solutions simulating natural geothermal fluids, in order to obtain kinetic parameters on silica precipitation (Owen, 1975;

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Makrides et al., 1978, 1980; Mroczek, 1994; Carroll et al., 1998; Gunnarsson and Arnórsson, 2005; Sanjuan et al., 2005; Park et al., 2006; Conrad et al., 2007; Tobler et al., 2009; Gunnarsson et al., 2010; Tobler and Benning, 2013). Silica precipitation has been studied mainly in the laboratory on aqueous silica solutions that are generally a simple mixture of pure water and industrial silica gel (Alexander, 1954; Goto, 1956; Krauskopf, 1956; Kitahara, 1960; Rothbaum and Rhode, 1979; Iler, 1979; Bohlmann et al., 1980; Rimstidt and Barnes, 1980; Crerar et al., 1981; Weres et al., 1981; Cary et al., 1982; Shimono et al., 1983; Jamieson,1984; Fleming, 1986; Tarutani, 1989; Icopini et al., 2005). Moreover, the precipitation of silica polymorphs has been more widely studied than that of amorphous silica, even though the latter is the most common form of silica observed in

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ACCEPTED MANUSCRIPT high-enthalpy geothermal fields (Iler, 1979). Among the few studies into amorphous silica precipitation, some have been in the laboratory on aqueous solutions of silicic acid (Makrides

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et al., 1980; Weres et al., 1981; Jamieson, 1984) and others in the field on natural geothermal

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waters (Mroczek, 1994; Carroll et al., 1998; Gunnarsson and Arnórsson, 2005; Gunnarsson et

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al., 2010).

Differences in the experimental conditions (e.g. solution composition, ionic strength, pH, temperature, etc.), in the analytical procedures, or in the kinetic models (as a function of the

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Gibbs free energy or the amorphous silica solubility) may contribute to the variety of results

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reported in the literature, particularly on the effect of pH and on the reaction order of the kinetic law used to model the silica precipitation, the first-, second-, and fourth-order reactions being more commonly adopted in the literature (Alexander, 1954; Goto, 1956;

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Kitahara, 1960; Owen, 1975; Iler, 1979; Rothbaum and Rohde, 1979; Bohlmann et al., 1980; Rimstidt and Barnes, 1980; Makrides et al., 1980; Weres et al., 1981; Chan, 1989; Mroczek,

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1994; Carroll et al., 1998; Icopini et al., 2005; Sanjuan et al., 2005; Conrad et al., 2007; Tobler et al., 2009). Nevertheless, despite the discrepancies that exist between these studies,

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several similar observations on amorphous silica precipitation have been reported. For example, the dominant parameters influencing this precipitation are the solution’s chemical composition, its degree of supersaturation with respect to amorphous silica, its pH and temperature, and its ionic strength (or salinity). It is also well established that the precipitation rate of amorphous silica increases with increasing degree of fluid supersaturation, increasing ionic strength (higher salinity) of the solution, and decreasing temperature. In brief, most of the studies indicate that, despite abundant experimental data, the kinetics and mechanisms involved in amorphous silica precipitation are still poorly understood and depend highly on the fluid characteristics. For natural waters, silica scaling currently remains a significant geochemical problem. Moreover, our current knowledge on the kinetics of silica

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ACCEPTED MANUSCRIPT precipitation is based largely on well-controlled laboratory experiments and to a lesser extent on field experiments. As synthetic solutions involve no chemical impurities that can affect the

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kinetics of the silica precipitation, a reliable understanding of the kinetics of silica reactions in

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more complex field environments requires specific on-site experiments conducted on natural

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geothermal fluids. Such experiments are not only a central issue for better predicting and preventing silica precipitation in geothermal plants, but are also very useful with regard to the

fluids by controlled precipitation processes.

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increasing interest on the industrial value of minerals that can been extracted from geothermal

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Here we present a detailed study on the kinetics of silica polymerization carried out during the cooling of high-temperature seawater-derived waters as those discharged from the wells of the Bouillante geothermal field (Guadeloupe, French West Indies) because only the formation of

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nanocolloidal gels was observed and no scaling of amorphous silica was formed during our experiments. However, during exploitation, the geothermal fluid at Bouillante flashes and

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cools from 250-260 °C to 167 °C in a high-pressure (HP) steam-liquid separator, with part of the fluid also being separated close to 110 °C in a low-pressure (LP) phase separator. The

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dissolved species such as silica and metal ions contained in these geothermal waters (Traineau et al., 1997, 2015; Sanjuan et al., 2000, 2001, 2010; Mas et al., 2006; Dixit, 2014) can precipitate in this temperature range to form troublesome scale deposits like amorphous silica or poly-metallic sulfides. Deposits of hard adherent silica are indeed regularly observed on low-temperature surface installations at Bouillante, consistently bringing production to a standstill in order to remove them (Serra et al., 2004; Sanjuan et al., 2005; Azaroual et al., 2005; Dixit, 2014); the abundance of these deposits and the difficulty in removing them also represent an additional expenditure for the operator. An operation under consideration at Bouillante is total or partial underground reinjection of the production fluids after cooling in order to both sustain the reservoir pressure and reduce the environmental impact. But here

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ACCEPTED MANUSCRIPT again, silica scaling in the injection wells can be problematic (Itoi et al., 1987; Stefànsson, 1997; Kaya et al., 2011).

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Our experimental study was carried out on site, inside the Bouillante geothermal energy plant,

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on samples of HP-separated (initial SiO2 concentration of about 600 mg l-1) waters collected,

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after cooling, at temperatures of 25, 50, 75, and 90 °C and at a pH ranging from 5 to 8. This enabled us to investigate the effect of temperature and pH on silica precipitation in the Bouillante context in which the pH value of the geothermal fluid is close to 5.3 at 250-260 °C

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in the reservoir, and close to 7 after steam separation at 165 °C. We also carried out experiments at lower and higher pH values (4 and 9, 10, 12, respectively; Dixit, 2014) that are

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not presented in this study. At elevated pH (> 9), silicic acid (H4SiO4) is dissociated as H+, H3SiO4- and H2SiO42- and consequently, the solubility of amorphous silica is increased (Dixit,

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2014). We found that there was no silica removal from the solution at pH 4, whilst at pH 10 and 12, the concentrations of dissolved silica were very quickly close to zero and other white

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deposits, such as calcium silicate (CaH2SiO4) or calcium carbonate (CaCO3), co-precipitated with amorphous silica (Dixit, 2014).

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The collected experimental data were modeled using the PHREEQC geochemical code (Parkhurst and Appelo, 1999) in order to estimate the kinetic parameters useful for predicting and preventing, in the specific context of Bouillante, silica precipitation during fluid exploitation, particularly at temperatures lower than 160 °C, or during reinjection. These kinetic parameters are also necessary for studying the possibility of improving the value of the Bouillante geothermal fluids. Moreover, using the Arrhenius equation, we used the rate constants estimated at the different working temperatures to compute the activation energy of the reaction of silica precipitation for each working pH.

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ACCEPTED MANUSCRIPT 2. BOUILLANTE GEOTHERMAL FIELD

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2.1. Present exploitation

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The Bouillante high-temperature (250-260 °C) geothermal field is located on the west coast of the volcanic island of Guadeloupe (Fig. 1a), which belongs to the Lesser Antilles island arc. This geothermal area is associated with fissured-volcanic activity, which is probably related to

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the major regional Montserrat/Marie-Galante fault system (Traineau et al., 1997; Lachassagne

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et al., 2009; Thinon et al., 2010; Bouchot et al., 2010; Calcagno et al., 2012). The first geothermal exploration in the area occurred in the 1960s-1970s and is summarized, along with the history of France’s unique Bouillante geothermal field’s exploitation, by several

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authors such as Sanjuan and Traineau (2008). The present geothermal power station has, since 2005, a total capacity of 15 MWe produced

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by two turbines (4 + 11 MWe), which represents about 600 tons h-1 of discharged fluid and 120 tons h-1 of steam for electricity production (6-7% of the island’s annual electricity needs).

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Between 2005 and 2010, the station was supplied with geothermal water from wells BO-4, BO-5, and BO-6 (Fig. 1b). As of 2011, only BO-5 and BO-6 remain as production wells and BO-4 has become an observation well. The high pressure (HP) steam-water separator separates the extracted geothermal fluid, at 167 °C and 6-7 bars, into approximately 20% steam and 80% water that is termed separated water. Part of the fluid is also separated at close to 110 °C in a low-pressure (LP) phase separator. Currently the separated geothermal water is cooled to below 40 °C through mixing with seawater (used as cooling fluid) before being discharged into Bouillante Bay. Since 2014, however, partial underground reinjection of this separated water (about 100 tons h-1 at

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ACCEPTED MANUSCRIPT about 160 °C) through the old production well BO-2 has been tested in order to both maintain

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reservoir pressure and limit the impacts of the exploitation on the environment.

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2.2. Geochemical composition of the geothermal fluid

Regular geochemical monitoring of Bouillante fluids carried out by BRGM in collaboration with CFG services since 1996, and several geochemical and mineralogical studies (Sanjuan et

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al., 2000, 2001, 2010 and 2013; Correia et al., 2000; Patrier et al., 2003; Mas et al., 2006;

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Guisseau et al., 2007; Millot et al., 2010; Sanjuan and Brach, 2015; Traineau et al., 2015) have provided us with a rather good understanding of the geochemistry of the Bouillante geothermal fluids. Samples of separated water, steam and incondensable gases, representative

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of the fluids discharged from the production wells (BO-2 before 2003, BO-4, BO-5 and BO-6 between 2003 and 2010, and BO-5 and BO-6 since 2011), are regularly collected in order to

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monitor the fluid chemistry and the gas/stream ratio (GSR). The chemical and isotopic analyses are performed in the BRGM laboratories using classic analytical methods; these are

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described in detail, including the analytical uncertainties, by Sanjuan et al. (2005), Millot et al. (2010) and Dixit (2014). It is thus well established that the deep geothermal fluid collected from wells BO-2, BO-4, BO-5 and BO-6 is a Na-Cl brine (TDS = 20 g.l-1) comprising 58% seawater and 42% freshwater that has attained a chemical equilibrium at 250-260 °C. Following the phase separation, the salinity of the separated geothermal waters is close to 25 g l-1. A compilation of the data collected between 2005 and 2011 shows that the chemical composition of the geothermal fluids discharged at each production well remains stable over time, despite variations in the production rate. This accords with the observations of Sanjuan et al. (2010, 2013), Sanjuan and Brach (2015), Dixit (2014), and Traineau et al. (2015). Moreover, the

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ACCEPTED MANUSCRIPT chemical homogeneity of the water samples collected at each production well suggests a common deep origin of the geothermal fluids discharged by the different wells.

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The chemical homogeneity and stability of the Bouillante fluid observed over a long period of

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exploitation ensure that the on-site kinetic experiments proposed in this study will be

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reproducible and representative. Indeed, the separated waters on which we conducted our kinetics experiments came from a mixture of the geothermal fluids discharged by the production wells in activity since 2005 (BO-4, BO-5 and BO-6 before 2010, and only BO-5

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and BO-6 after this date). We were therefore able to compute an average chemical

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composition for these separated waters (Table 1) through applying a statistical method on the geochemical data obtained for 15 samples collected between 2005 to 2011 following their high-pressure separation. We then used this average chemical composition in the

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experimental data modeling presented in Section 4. Table 1 shows that the water collected following the phase separation is characterized by a

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TDS close to 25 g l-1, a near neutral pH of 6.8, and a SiO2 concentration of about 600 mg l-1; average characteristics that are consistent with previously reported data (Mas et al., 2006;

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Sanjuan et al., 2010, 2013; Dixit, 2014; Traineau et al., 2015). According to the thermodynamic data on the solubility of amorphous silica as a function of temperature (Fournier and Rowe, 1977; Marshall and Warakomski, 1980), the Bouillante geothermal fluid becomes supersaturated with respect to dissolved silica at temperatures close to 150 °C. Silica precipitation is then possible at temperatures below 160 °C and, consequently, over the temperature range (90 to 25 °C) used in this study to investigate the kinetics of silica precipitation.

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ACCEPTED MANUSCRIPT 3. MATERIALS AND EXPERIMENTAL METHODS

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3.1. Sampling and sample preparation

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The separated water for the kinetic experiments was sampled in 250 ml polyethylene bottles from a fixed fluid sampling point located after the HP separator phase. The samples were obtained directly at the relevant working temperatures (25, 50, 75, and 90 °C) using a suitable

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cooling system composed of a tank with a small submerged streamer (Fig. 2). One end of the

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streamer is connected directly to the power plant pipe through which the separated water circulates at 167 °C and where a sluice can be activated to divert a fraction of this hot water flow toward the cooling system. The tank itself is continuously renewed with cold water to

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cool down the hot fluid through heat exchange. Thus, by adjusting the flow of the hot separated water diverted into the streamer (5 to 80 ml s-1), the sample can be collected at the

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streamer outlet at the desired working temperature of 90, 75, 50, or 25 °C. Once sampled, the separated water (250 ml) was rapidly stored in a thermostatic water bath to

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maintain its working temperature (±1 °C) for the entire duration of the kinetic experiment (about 9 hours). The natural pH of the separated water was 7.1. To study the effect of pH on the reaction rate, each sample’s pH was adjusted within the first minutes following collection to a working value of 8, 7, 6, or 5 by the addition of few milliliters of 1N NaOH or 0.1N HCl solution under magnetic stirring. Any variations in pH during the kinetic experiments were limited to 0.2 units, the pH values being measured at room temperature (22 °C) with a pHmeter. No HCl readjustment of the pH was made in basic solutions, and no NaOH readjustment of the pH was made in acidic solutions. To monitor the change in dissolved silica concentration over time, a few milliliters of the sample stored in the thermostatic water bath was taken with a syringe, filtered at 0.45 µm, and

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ACCEPTED MANUSCRIPT then diluted at least 100 times by weight with milli-Q water to avoid silica polymerization, following which the SiO2 concentration was measured using the method described in Section

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3.2.1. Including the time necessary to collect the sample on site and adjust its pH, the first

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SiO2 measurement on each sample fraction was made 5 minutes after sampling. The SiO2

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measurement was then repeated every 10 minutes during the first hour, every 20 minutes during the second hour, and finally every hour up to 9 h (= 540 min.). Each experiment was repeated three times for each pH and temperature condition in order to obtain a reliable

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dataset. However, since the measurements were not always reiterated at exactly the same

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times, the experimental dataset for a given (pH, T) condition consists of all three subsets. With a selection of the experimental conditions (pH 7 for all the temperature values and 25 °C for all the pH values), the particle suspensions (silica gel) in solution were recovered at the

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end of the experimental runs by filtering under vacuum. These suspensions were analyzed by X-ray diffraction (XRD), scanning and transmission electron microscopy (SEM and TEM),

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and BET gas adsorption to detect any change in crystallinity, morphology/chemical composition, and surface area, respectively. The sample preparation is described in Section

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3.2.2.

3.2. Analytical procedures

3.2.1. Analysis of the dissolved silica The decrease in dissolved silica concentration with time was monitored by spectrophotometry using the molybdenum blue method. With this method, the sample reacts with ammonium molybdate over 10 min to give a blue complex species (silicomolybdic acid) whose absorbance is measured at 650 nm using a MERCK spectrophotometer. The uncertainty with this method is typically about 5%.

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ACCEPTED MANUSCRIPT In principle, only low-molecular-weight silica polymers, including monomers, dimers, trimers, and longer chained polymers, can be complexed with molybdate. But the real species

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measured with this method are still not well defined (Alexander, 1954; Iler, 1979; Rothbaum

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and Rohde, 1979; Icopini et al., 2005). For the present study, we assumed that the measured

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molybdate-reactive silica concentration included only monomers. Consequently, it is referred hereafter as “monomeric silica”, or “molybdate-reactive silica”, represented by [H4SiO4]. This assumption is based on the fact that the polymers (dimers, trimers, tetramers) must de-

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polymerized before reacting with the molybdate reagent and that this step, under our

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experiment conditions, is probably too slow to influence the measurements (Makrides et al., 1980; Carroll et al., 1998). The assumption is also validated by the speciation modeling done under our experiment conditions (see Section 4.1), which is in agreement with the fact that

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only monomeric silica significantly contributes to SiO2 concentration in solution.

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3.2.2. Measurement of the specific surface area The specific surface area of the colloidal silica at the end of each experimental run was

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determined at 25 °C (for all pHs) and at pH 7 (for all temperatures) in order to evaluate potential changes in this parameter under the investigated temperature and pH conditions, as observed in other studies (Iler, 1979; Carroll et al., 1998). The silica colloids were extracted by filtration under vacuum and dried in a high-temperature oven for 24 hours at 105 °C to obtain a powder on which the specific surface area (or total surface area), noted SBET, was measured from the BET N2 gas adsorption isotherm. These powder samples were also used for XRD, TEM and SEM analysis (see Section 5.2). In order to obtain sufficient amount of powder for all these analyses, samples of 1-2 liters of separated water were used and renewed as many times as necessary.

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ACCEPTED MANUSCRIPT 4. NUMERICAL METHODS

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The geochemical code PHREEQC (Parkhurst and Appelo, 1999) and the associated LLNL

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(Lawrence Livermore National Laboratory) thermodynamic chemical database were used for

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all the calculations made in this study. The code offers the possibility of taking into account both the chemical species in solution (as monomeric and polymeric silica, complexes, etc.) and the solubility of minerals at different temperatures, as well as of using a specific kinetic

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law. We chose, however, to replace the standard equation for amorphous silica equilibrium constant as a function of temperature by that provided by Gunnarsson and Arnórsson (2000):

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log 𝐾𝑒 = − 8.476 − 485.24 ∗ 𝑇 −1 − 2.268 ∗ 10−6 ∗ 𝑇 2 + 3.068 ∗ log 𝑇

(1)

where Ke is the equilibrium constant for amorphous silica and T is the absolute temperature

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(K). This equation, fitted to a large experimental dataset, gives great precision up to 350 °C.

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4.1. Silica speciation in solution

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The dissolution or precipitation of silica in an acidic/neutral aqueous phase can be described by the following reaction: 𝑆𝑖𝑂2 (𝑎𝑚)

(𝑠)

+ 2𝐻2 𝑂(𝑙) ↔ 𝐻4 𝑆𝑖𝑂4 (𝑎𝑞)

(2)

In most geothermal reservoir waters (with T < 350 °C, pH < 8), the dissolved silica consists mainly of monomeric silica (monosilicic acid), noted H4SiO4 (Zotov and Keppler, 2002). With higher pH (pH > 8), however, the monomeric silica H4SiO4 is not the only species in solution because the monosilicic acid dissociates according to the equations: 𝐻4 𝑆𝑖𝑂4 = 𝐻 + + 𝐻3 𝑆𝑖𝑂4−

(3)

𝐻3 𝑆𝑖𝑂4− = 𝐻 + + 𝐻2 𝑆𝑖𝑂42−

(4)

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al., 1982). An estimation of the distribution of silica species at pH 8 was calculated up to

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100 °C using the geochemical code PHREEQC and the approach proposed by Kashutina et al.

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(2009) and Potapov et al. (2014). The numerical results show that, at pH 8 and for -

experimental temperatures lower than 100 °C, only H4SiO4 and H3SiO4 species are present in solution, the fraction of other species (dimer or trimer) being negligible.

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Finally, the addition of NaOH in experiments at pH 8 has shown that Na-Si complex species

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could exist in solution according to the following reaction (Crerar and Anderson, 1971; Applin, 1987):

𝑁𝑎+ + 𝐻3 𝑆𝑖𝑂4− ⇔ 𝑁𝑎𝐻3 𝑆𝑖𝑂4

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(5)

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We also undertook speciation calculations in this study, both with and without considering the

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NaH3SiO4 complex aqueous species, in order to determine the effects of the complex on the calculated silica solubility. Our results show that the concentration of the NaH3SiO4 complex is negligible, and so we have considered the concentration of dissolved silica in solution (Ct -

for pH 8.

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term in Eq.6, see next section) to be equal to [H4SiO4] for pH 5-7 and ([H4SiO4] + [H3SiO4 ])

4.2. Kinetic modeling

The rate of silica precipitation r (mol l-1 s-1) was calculated using the generalized equation derived from the Transition State Theory (TST) developed by Lasaga (1981): 𝑟=−

𝑑𝐶𝑆𝑖𝑂2(𝑎𝑚) 𝑑𝑡

𝐶

𝑛

= − 𝑘 ∙ 𝐴𝑠 ∙ (1 − 𝐶 𝑡 ) 𝑒𝑞

(6)

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ACCEPTED MANUSCRIPT where k is the rate constant (mol m-2 s-1), n is the kinetic reaction order (which is an integer), Ct is the concentration of dissolved silica at a given time t (mol l-1), Ceq is the amorphous

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silica solubility at a given temperature T (mol l-1), and As is the surface area of silica particles

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(m² l-1).

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Ceq was calculated under four-temperature and four-pH conditions using the PHREEQC code for a fluid representative of the Bouillante separated water with a TDS close to 25 g l-1 and an initial dissolved silica concentration of 595 mg l-1 (Table 2). The results highlight the need to

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consider both temperature and pH in order to calculate the correct amorphous silica solubility.

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We found that the silica solubility at all the pH values is affected mainly by the temperature increase from 25 to 90 °C, whilst the effect of pH increase is greater between pH 7 and 8 (soft alkaline solutions) for temperatures over 75 °C. Thus the solubility at 25 °C increases by

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D

about 2% between pH 7 and 8, but increases by about 10% at 90 °C. Between pH 5 and 7, the solubility appears to be independent of pH regardless of the temperature.

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As was estimated from the measured specific surface area, SBET (in m2 g-1), using: 𝐴𝑆 = 𝑆𝐵𝐸𝑇 ∗ (𝐶𝑖 − 𝐶𝑒𝑞 ) 𝑇 ∗ 60.0848

(7)

AC

where Ci and Ceq are respectively the initial concentration of dissolved silica (mol l-1) and the amorphous silica solubility (mol l-1) at a given temperature T. In order to estimate an As value for each investigated temperature and pH, the specific surface areas measured at 25 °C for the different pHs were also used at the other temperatures. Equation 6 was coded in PHREEQC with both the Ceq and As parameters for each kinetic simulation being fixed to the appropriate values given in Table 2 according to the temperature and pH conditions. The n and k parameters for each experimental T and pH condition were adjusted progressively to fit the three sets of measured SiO2 concentrations as a function of time. The adjusted n and k values minimize the gap ε between the experimental SiO2

17

ACCEPTED MANUSCRIPT concentrations, Cexp, and the theoretical SiO2 concentrations, Ccal, computed with the code PHREEQC. The parameter is an estimation of the error on the model, computed using the

∑𝑁 𝑖=1(𝐶𝑒𝑥𝑝 −𝐶𝑐𝑎𝑙 ) ∑𝑁 𝑖=1(𝐶𝑒𝑥𝑝 )

2

2

(8)

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𝜀=√

IP

T

following relation:

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not converge and is therefore not suitable.

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We considered the model to be valid if is lower than 10%. Above this limit, the model does

D

5. EXPERIMENTAL DATA

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5.1. Fluid data

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Figure 3 shows the evolution of the measured silica concentrations as a function of time in the Bouillante separated water at pH ~ 7 for each of the four experimental temperatures (25, 50,

AC

75, and 90 °C). Each experimental dataset is composed of three subsets since each experiment was repeated three times (see Section 3.1). The difference between the three replicates remains generally close to the experimental error (5%). With all the temperatures, the concentration of monomeric silica rapidly decreases as a function of time and tends toward the amorphous silica solubility corresponding to the relevant working temperature. At 50, 75, and 90 °C, the solubility is reached after about 6 hours whereas at 25 °C, the solution did not reach equilibrium by the end of the experiment (3 days are necessary). The experimental data issued from all the kinetic experiments under the four pH (5, 6, 7, and 8) and temperature (25, 50, 75, and 90 °C) conditions are presented in Figure 4 (a, b, c, d).

18

ACCEPTED MANUSCRIPT With the experiments in an acidic solution (pH 5 and 6), we observed a transition period (termed induction period), lasting from a few minutes at 25 °C to 3 hours at 90 °C, during

T

which the concentration of monomeric silica does not significantly vary. At pH 5, following

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the induction period, the monomeric silica concentration decreases very slowly and no

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equilibrium is reached after 9 hours. In this case the differences between replicates could be high (up to 15%), which may be due to the difficulty in maintaining the pH exactly equal to 5 during the experiment. At pH 6, following the induction period, the SiO2 concentration

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decreases rapidly to come close to the solubility of amorphous silica at the end of the

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experiment.

At pH 7 and 8, the concentration of dissolved silica rapidly decreases without an induction period. Here the final SiO2 concentrations are close to the amorphous silica solubility, apart

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D

from the experiment carried out at pH 8 and 75 °C. Thus increasing temperature seems to decrease the time needed to reach the equilibrium solubility (faster reaction), except at pH 8

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for which it is difficult to conclude. We did, however, obtain good repeatability with the specific experimental condition of pH 8 and 75 °C, which eliminates possible experimental

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error; moreover, the final experimental SiO2 concentration was confirmed by ICP-AES measurements where a difference of less than 5% was observed with the molybdate-reactive silica concentration. Consequently, further investigations are necessary to understand this 75 °C result for basic pH. To summarize, all the experiments show the concentration of monomeric silica to decrease over time, although with an induction period at low pH (5-6). As the reaction rate varies according to the pH and temperature conditions, amorphous silica solubility is reached more or less quickly.

19

ACCEPTED MANUSCRIPT 5.2. Characterization of the silica gel

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The resultant colloidal silica was recovered at the end of each experiment for physico-

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chemical analysis (XRD, SEM and TEM) at 25 °C for each pH (except pH 5) and at pH 7 for

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each temperature.

The chemical elemental analysis (SEM) and XRD analysis of the precipitates recovered at 25 °C show that, for pH 6 and 7, these contain only amorphous silica (Fig. 5a). At pH 8,

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where NaOH was added for pH adjustment, a co-precipitation of calcite with amorphous

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silica phase, which strongly reduces the bump characteristic of amorphous silica present at pH 6 and 7, can be observed in Figure 5b. This result is consistent with previous observations on silica removal with CaO in alkaline solutions (Rothbaum and Anderton, 1975; Gallup et al.,

TE

D

2003). The presence of Ca in the precipitated phase could explain the difficulty of reaching the computed amorphous solubility in the solution at pH 8, as shown in Figure 4, since the

silica phase.

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thermodynamic equilibrium may not only depend on the precipitation of pure amorphous

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At 90 °C, for pH 6 and 7, the XRD patterns (Fig. 5c) still indicate a dominant phase of amorphous silica ( 95 wt.%), but there is also a sodium chloride phase (NaCl) in the precipitate ( 5 wt.%), which is probably a residual phase precipitated during the drying of the samples at 105°C. The SEM analysis of all the samples shows that the surface morphology of the silica gel has a roughness with granular and friable aspects (Fig. 6a), whereas the TEM images show complex structures with varied sizes of near-spherical aggregated and agglomerated particles (Fig. 6b, c, d). The silica particles obtained at 25 °C and pH 7 (the pH representative of the natural untreated geothermal water) are small near-spherical particles with an average diameter of about 10 nm that form a homogeneous cluster (Fig. 6b). Small particles (~ 25 nm) are also

20

ACCEPTED MANUSCRIPT observed at 25 °C and pH 8 (Fig. 6c), but they surround larger particles (~ 150 nm) that have an almost smooth surface and, unlike the small particles which seem to be closely

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agglomerated, they are juxtaposed or superimposed but do not seem to be clumped.

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At 90 °C and pH 7 (Fig. 6d), the silica particles present similar surface aspects and

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arrangements as at 25 °C and pH 7. Their size, however, seems to increase with temperature, showing a mean of about 25 nm at 90 °C.

Most of the particle sizes observed in this study are higher than those observed by Iler (1979)

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and Carroll et al. (1998) or, more recently, by Tobler and Benning (2013) who report particle

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diameters ranging from 3 to 7 nm. Conrad et al. (2007), however, also observed larger particles with diameters of 30 to 40 nm that they interpret as aggregates of 3 nm primary nanocolloids and not as the result of continued growth of the primary particles. They also

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conclude that such observations are evidence that aggregation is the primary growth mechanism of silica nanocolloids once the primary particles have been formed.

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The TEM images also give the BET surface areas (SBET) measured on the corresponding samples, which have been used to calculate the As values in Table 2. For the experiments

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conducted at 25 °C, the specific surface areas obtained by the BET method at pH 6, 7, and 8 are 278, 206, and 72 m2 g-1 respectively, in agreement with the results previously reported by Potapov and Zhuravlev (2005) for colloidal silica under similar temperature and pH conditions (300 - 30 m2 g-1). Few colloids being precipitated at pH 5, the specific surface area is not measurable. The previously observed increase in particle size with pH or temperature seems to correlate with a decrease in specific surface area. For example, the SBET at pH 7 is equal to 206 m2 g-1 at 25 °C and decreases to 105 m2 g-1 when the temperature rises to 90 °C. Similarly, the amorphous silica phase obtained at pH 8 (25 °C) is characterized by a lower specific surface area (72 m2 g-1) and a larger particle size (~ 100-150 nm). Similar

21

ACCEPTED MANUSCRIPT observations were made by Goto (1956), Iler (1979), and Carroll et al. (1998), who reported that larger particles associated with lower BET surface areas are formed at higher pH.

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To summarize, the silica gel that formed in the acidic-neutral solutions under our

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experimental conditions is mainly amorphous silica. Amorphous silica is still the dominant

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phase in basic solutions, although with traces of calcite. The silica particles are nearly spherical and their size is dependent on the pH. The effect of temperature on the

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characteristics of the silica particles is more limited.

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6. DATA INTERPRETATION AND DISCUSSION

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6.1. Silica polymerization mechanisms

If we don’t consider biogenic deposition which is not a major concern for geothermal

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applications, two kinds of process can lead to remove silica in a supersaturated amorphous silica solution (Gunnarson and Arnorsson, 2005; De Guzman et al., 2015): amorphous silica

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can precipitate to form silica scales onto an available surface, or silica can polymerize and form colloidal particles that may remain suspended in the solution for a long period of time. In all the experiments reported in this paper, silica removal was characterized by a polymerization process with the formation of a colloidal gel in the solutions. We did not observe any scaling of silica in the solutions, even after several days/months. Despite many studies on silica precipitation, silica polymerization is not fully understood and there is no unified theory or thorough understanding of the mechanisms involved in this reaction. However, it is largely admitted that silica polymerization in supersaturated aqueous solutions follows a general three-stage process (Weres et al., 1981; Tobler et al., 2009): (1) silica polymerization leading to silica nanoparticle formation (stable nuclei of a critical size); 22

ACCEPTED MANUSCRIPT (2) nanoparticle growth and ripening (growth of the supercritical particles by further molecular

deposition

of

silicic

acid

on

their

surfaces),

and

(3)

aggregation

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(coagulation/flocculation) and cementation of colloidal particles to form a gel. In the first

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step, silica monomers polymerize via dimers and trimers to cyclic oligomers, which form

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condensed 3D nanoparticles (Perry and Keeling-Tucker, 2000; Tossell, 2005; Trinh et al., 2006; Tobler et al., 2009; Malani et al., 2010; Hunt et al., 2011).

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6.2. Kinetic modeling

6.2.1. Rate of the overall silica polymerization reaction a) Determination of the reaction order and the rate constant

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The numerical simulations using PHREEQC show that the 9-hour kinetic data on silica precipitation measured on the Bouillante geothermal waters can be well modeled with a

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second-order reaction (Eq. 9) because lower  values are obtained for n = 2 (Fig.4).

𝐶

2

𝑟 = −𝑘2 ∙ 𝐴𝑠 ∙ (1 − 𝐶 𝑡 )

(9)

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𝑒𝑞

The rate constant k2 (in mol m-2 s-1) is introduced in Eq. 9 to refer to the 2nd-order law used to compute it; the computed values are given in Table 2, along with the parameters used to validate the kinetic models. Note that for the data at pH 5 and 6, the model adjustment begins at the end of the induction period. Over the entire dataset, the rate constant k2 ranges from 6.0 10-11 to 6.7 10-7 mol m-2 s-1. Our second-order model (Eq. 9), which characterizes “the overall” three-stage reaction mentioned in the previous section, is in good agreement with that obtained in several other studies (Alexander, 1954; Okamoto et al., 1957; Kitahara, 1960; Bishop and Bear, 1972;

23

ACCEPTED MANUSCRIPT Bohlmann et al., 1980). It is also consistent with the assumption that the polymerization process is controlled by the formation of silica dimers as long as the solution is

T

supersaturated. These dimers are formed by the condensation of monomeric silica, which

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forms high molecular weight polymers (Tossell, 2005; Trinh et al., 2006; Malani et al., 2010;

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Hunt et al., 2011).

On purely theoretical considerations, Rimstidt and Barnes (1980) derived a differential rate equation for silica-water reactions from 0 to 300 °C based on stoichiometry and activities of

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the reactants according to Eq.2. They established that the rate constant k for the precipitation

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of all silica phases in solution can be determined using the relationship: log 𝑘 = −0.707 −

2598 𝑇

(10)

D

where T is the absolute temperature (in K) and k is given in s-1 based on a standard system of 1

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m2 of surface area and 1 kg of solution in order to produce absolute rate constants that are comparable from one experiment to another. Dove and Crerar (1990) argue that the unit of the

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rate constant k according to the Rimstidt and Barnes (1980) convention is equivalent to mol m-2 s-1 since the choice of the units does not affect the numerical values of reaction rates and

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rate constants. Equation 10 provides theoretical k values that increase with temperature, varying from 0.4 10-9 mol m-2 s-1 at 25 °C to 13.7 10-9 mol m-2 s-1 at 90 °C. Comparing them to our experimental k2 values (Table 2), we note that they are comparable to those obtained at pH 6 (0.5 10-9 mol m-2 s-1 at 25 °C to 17.5 10-9 mol m-2 s-1 at 90 °C). Since Rimstidt and Barnes (1980) based their equation on precipitation in silica-water solutions with a pH close to 6, we can conclude a good consistency of our results with those of Rimstidt and Barnes (1980). Few studies exist on the kinetics of silica polymerization reactions in natural geothermal waters and even less that are usable under our experimental conditions for direct comparison with our study-derived kinetic constant rates, n and k2, characterizing the overall reaction. 24

ACCEPTED MANUSCRIPT Using a first-order reaction, Carroll et al. (1998) found k values of about 10-11-10-10 mol m-2 s1

from laboratory experiments on the Wairakei geothermal waters (New Zealand) for

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temperatures between 80 and 120 °C with pH  7. In the present study, the k value computed

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for a 2nd-order reaction (k2) is equal to 1.94 10-7 mol m-2 s-1 at pH 7 and 90 °C; i.e. a difference

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of 3 to 4 orders of magnitude. An explanation for this difference is that the Wairakei geothermal waters are characterized by a low degree of supersaturation (about 1.3; Si  234 ppm) and a moderate ionic strength (about 0.13 M), which can result in a slower precipitation

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reaction. Moreover, the precipitation experiments were performed over a longer period (10

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days) and so the effect of the more rapid decrease observed at the initial phase is attenuated,

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leading to lower k values.

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b) Induction period

The induction period, which was only observed at the beginning of our experiments under

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acidic conditions (pH 4-6) (Fig. 4), has been noted by numerous authors in the literature (White et al., 1956; Baumann, 1959; Rothbaum and Rodhe, 1979; Makrides et al., 1980;

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Bourret et al., 1991; Gunnarsson and Arnórsson. 2000; Icopini et al., 2005; Tobler and Benning, 2013; Guerra and Jacobo, 2012; Kley et al., 2014; Noguera et al., 2015 ). The induction period tends to increase with increasing temperature (Rothbaum and Rohde, 1979) or decreasing degree of supersaturation (White et al., 1956; Baumann, 1959; Rothbaum and Rodhe, 1979; Icopini et al., 2005), ionic strength (salinity) (Makrides et al., 1980), and pH value (Tarutani, 1989). Following this induction period, which can be from a few minutes to several hours, the SiO2 concentration decreases towards equilibrium solubility. From our experimental data in acidic solutions (pH 5 and 6), we could not get accurate estimates of the induction period. Nevertheless, the induction period is clearly higher at low pH (acidic solutions) and, in agreement with other studies, seems to increase with 25

ACCEPTED MANUSCRIPT temperature. A maximal duration of about 3 hours is reached at 90 °C and pH 5. Makrides et al. (1980) reported an induction time of 2 hours under similar experimental conditions ([SiO2]

T

= 740 ppm; 95 °C and pH 5.5) and indicated that the duration of the induction period

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increases with decreasing initial SiO2 concentration and decreases by approximately a factor

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10 for each pH unit increase in the pH range of 4.50-6.50. Since the initial SiO2 concentration in the Bouillante waters is  600 ppm, we can conclude that our observations are consistent with their results.

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Little is known about the origin of the induction period, but since the first step of the

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polymerization is an “instantaneous and homogeneous” nucleation of stable critical nuclei of 1-2 nm in diameter (White et al., 1956; Makrides et al., 1978; Rothbaum and Rohde. 1979;

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Weres et al., 1981; Shimono et al., 1983; Tobler et al., 2009), the induction time could reflect

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a delay within this first step. This period may thus represent the time necessary to form critical nuclei of silica (polymers) that do not react with the molybdate complex. So, Makrides

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et al. (1978), who focused for the first time on the nucleation of the silica polymerization and obtained a linear trend of the induction period with the inverse of silica supersaturation,

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postulated that the predominant number of nuclei was formed during the induction period. Moreover, Tobler and Benning (2013) observed the presence of larger critical nuclei in the experiments with an induction period, in agreement with this last hypothesis. Noguera et al. (2015) discard the hypothesis of an induction period as an explanation for the plateaus observed in the saturation curves relying on Kaishev’s theory of non-stationary nucleation, and conclude that the latter result from a competition between nucleation, growth, and dissolution of particles which take place simultaneously. These authors also studied the characteristics of the particle population and shown that they were much more complex than generally assumed by simple models of precipitation and strongly dependent on how supersaturation is reached.

26

ACCEPTED MANUSCRIPT We can thus conclude, from the induction period results of our experiments, that silica polymerization can be delayed by several hours in the Bouillante geothermal waters by

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ensuring that the fluids are under acidic conditions (pH 5 or 6) and at temperatures higher

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than 90 °C.

c) pH dependence of the rate constant

In our experiments, with each temperature value, the rate constant k2 increases with increasing

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pH (Fig. 7), indicating a faster removal rate of dissolved silica at pH 7 and 8.

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The pH effect generally is observed in the literature, and as an approximate rule, lowering the solution pH slows kinetics by a factor 10 for every pH unit (Rothbaum et al., 1979; Hirowatari and Yamaguchi, 1990; Klein, 1995). Several other studies have reported a more

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detailed dependence of the rate constant k on the pH. First, Goto (1956) found a linear increase of k with pH ranging from 7 to 10 plotted on a logarithmic scale. More recently,

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similar conclusions were reported by Carroll et al. (1998) and Conrad et al. (2007) for pH values ranging from 3 to 9. However, there are other studies (Kitahara, 1960; Owen, 1975;

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Iler, 1979; Rothbaum and Rodhe, 1979; Tarutani, 1989) that report the existence of a pH range in which the maximum polymerization rate occurs mainly around pH 6 to 9.

d) Temperature dependence of the rate constant and estimation of the activation energy The rate constant for each pH value clearly increases with increasing temperature (Fig. 8), indicating a faster precipitation of silica at high temperature. Although this tendency is generally true for pH 8, we noted that the computed k2 is oddly smaller at 75 °C than at 50 °C, although the decrease is not observed at 90 °C. The k2 values obtained at 75 and 90 °C are very close and very different from those found at 25 and 50 °C. Figures 7 and 8 clearly indicate that the rate constant values are dependent on both temperature and pH.

27

ACCEPTED MANUSCRIPT The temperature dependence of the rate constant k can be described by the Arrhenius equation: 𝐸𝑎⁄ 𝑅𝑇)

(12)

T

𝑘 = 𝐴 ∙ 𝑒 −(

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or

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𝐸𝑎 1 log 𝑘 = log 𝐴 − ( )∙( ) 2.303 𝑅 𝑇

(13)

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where A is a pre-exponential factor (mol m-2 s-1), Ea is the activation energy (J mol-1), R (J K-1 mol-1) is the gas constant, and T the absolute temperature (K).

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The activation energy for amorphous silica precipitation in the temperature range of 25 to 90 °C was calculated for each investigated pH using Eq. 13 and the computed k2 given in

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Table 2. More exactly, log k2 was plotted as a function of 1000/T (for a given pH) and Ea was

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computed from the slope of the straight line fitting the data. Results of these linear regressions

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are shown in Figure 8 and the corresponding Ea values are given in Table 3. The fits are generally good according to the high correlation coefficients (R2) reported in Table 3. This may indicate a consistency of the k2 values estimated in this study using a 2nd-order reaction.

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Note that the rate constant computed at 75 °C for pH 8 was not used since this value appears to be inconsistent with the other data, as observed above. At pH 7 (close to the natural pH of the production fluids at Bouillante), the results show the activation energy of the silica precipitation reaction Ea to be about 52 kJ mol-1. Considering the higher standard errors observed at pH 5 and 8, these Ea values remain relatively close and it is difficult to conclude on a pH effect. Nevertheless, Ea seems to be slightly lower at pH 8, which may imply that the amorphous silica polymerization is favored in basic solutions, and slightly higher at pH 5, indicating a slower precipitation reaction under acid conditions. The activation energies involved in amorphous silica precipitation obtained in this study are consistent with the values reported in previous studies for aqueous silica solutions: 49.8 kJ 28

ACCEPTED MANUSCRIPT mol-1 at pH  6 (Rimstidt and Barnes, 1980), 54.8 kJ mol-1 at pH 4-8 (Fleming, 1986) and 611 kJ mol-1 at pH  3-7 (Carroll et al., 1998). Carroll et al. (1998) also report an activation

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energy of 503 kJ mol-1in good agreement with our results for the Wairakei geothermal

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waters, characterized by a pH7 and an initial silica concentration of 234 ppm.

6.2.2. Initial polymerization rate (corresponding to the initial fast decrease of dissolved silica

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with time)

Even though modeling the experimental data with a second-order kinetic rate gives accurate

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results, we propose to further refine our results by considering the first minutes of the precipitation mechanism. Few authors, in fact, have paid attention to the kinetics of the initial

D

stage of polymerization and especially to the formation of silica nanoparticles -i.e. particles

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about 3 nm in diameter at the beginning of the reaction (Iler, 1979; Crerar et al., 1981; Icopini et al., 2005; Conrad et al., 2007; Tobler et al., 2009; Tobler and Benning, 2013). Even so, it is

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thought that silica monomers initially combine to form small oligomers, which in turn react with monomers to form larger oligomers (Perry and Keeling-Tucker, 2000; Trinh et al., 2006;

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Malani et al., 2010; Hunt et al., 2011). Tobler et al. (2009) showed that the initial fast decrease of monomeric silica concentration must correspond to a 3D growth of the silica nanoparticles. This condensation is thought to lead to the formation of stable nanocolloids with 3 to 6 silica units, i.e. Si(OH)4 monomers. Icopini et al. (2005) found that the initial polymerization rate of monomeric silica was better described as a 4th-order function: 𝑟𝑎𝑡𝑒 = −

𝑑[𝐻4 𝑆𝑖𝑂4 ] 𝑑𝑡

= 𝑘4 ∗ [𝐻4 𝑆𝑖𝑂4 ]4

(14)

In practice, they determined the corresponding rate constant, noted k4, in assuming that the polymerization reaction was initially controlled by the rate of monomer [H4SiO4] removal and

29

ACCEPTED MANUSCRIPT by using a subset of their experimental kinetic data corresponding to the first reaction stage. A 4th-order reaction is consistent with a critical nucleus of 4 monomers (cyclic tetramers) in the

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formation of nanocolloidal particles, and is supported by theoretical studies (West and Hench,

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1994, 1995).

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In this study, following the analytical method proposed by Icopini et al. (2005), we used Eq. 14, successively considering 2nd-order, 4th-order and 6th-order reactions (n = 2, 4, and 6) to model a subset of our experimental data corresponding to the first hour of the kinetic

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experiments. Examples of the rate function versus time (as defined by Eq. 5 in Icopini et al.,

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2005) used to estimate k4 in considering a 4th-order reaction are given in Figure 9. The determined kn values for n = 2, 4, and 6 are plotted versus pH in Figure 10 for comparison. The data obtained by Icopini et al. (2005) under similar conditions (25 °C, ionic strength 

TE

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0.24 M, and initial SiO2 concentration ~ 750 mg l-1or 12.5 mmolal) are also shown in Figure 10. It appears that their data are in good agreement with our results at 25° C, which seems to

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confirm that the initial reaction rate of silica polymerization corresponds to a 4th-order reaction, at least at low temperatures. The results using the 4th-order reaction are also

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preferred at the other temperatures, if we consider the linear fits used to quantify the dependence on pH under acidic conditions. The best fits generally correspond to n = 4, but n = 6 (corresponding to a nanoparticle composed of 6 monomers) seems to be equally suitable, especially at the higher temperatures (75 and 90 °C). A growth law of order 6 was used by Noguera et al. (2015) and allowed reproducing experimental results taking into account at the same time for the plateau lengths and maximum reaction rates, without being correlated to the presence of silica oligomers in the aqueous solution. Figure 10 also indicates that the choice of the rate order n does not impact on the rate constant kn dependence on pH, since the linear fits present similar slopes. The dependence of k4 on pH and temperature is analyzed in Section 6.2.3.

30

ACCEPTED MANUSCRIPT In conclusion, the 4th-order reaction gives fairly accurate fits over the 1st hour of the precipitation reaction. However, data modeling shows that when we consider the entire

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reaction, i.e. the decrease of monomeric silica concentration until the equilibrium state (9

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hours of data), then the kinetics of the successive stages involved in silica polymerization are

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not necessarily described by the 4th-order rate. The different values of the reaction orders proposed for describing the different steps of silica polymerization in our experiments show that the polymerization rates change over the reaction time. Consequently, one must consider

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the coexistence of different species of oligomers in solution in any attempt to describe the process and kinetics of silica polymerization. At the beginning of the process, fast silica

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precipitation follows a 4th-order reaction law, probably due to the formation of large oligomers (silica tetramers). Thereafter, with a lower silica supersaturation, the monomers

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react to form smaller oligomers (dimers) in great quantity. These remain in solution or

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contribute to polymer growth.

6.2.3. pH and temperature effects on the rate constant for the initial polymerization reaction

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For pH ranging from 3 to 7, Icopini et al. (2005) proposed the following linear relation between log k4 and the pH: 𝑙𝑜𝑔 𝑘4 = 𝑚 𝑝𝐻 + 𝑙𝑜𝑔 𝑘0 (15)

where k0 is the rate constant extrapolated to pH 0 and m is the apparent reaction order with respect to the activity of aqueous H+. This relation implies that the rate constant is proportional to [H+]-m. For an initial SiO2 concentration of  750 ppm and a pH ranging from 3 to 6, they found m = 0.92 ( 0.28) and log k0 = -12.3, with a high correlation coefficient (R2 = 0.97). Table 4 shows our results using Eq. (15) for 2nd-order, 4th-order and 6th-order reactions. We limited the linear fits to acidic solutions since we observed a change in pH dependence at pH 31

ACCEPTED MANUSCRIPT 8. Results for the 4th-order reaction at 25 °C are consistent with the results of Icopini et al. (2005) since we found m = 0.83  0.1 and log k0 = -11.7  0.6, with R2 = 0.986. Moreover, the

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m values for k2 and k4 are comparable and the reaction order seems to have a low effect on the

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relationship between the rate constant and the pH. Indeed, the slopes of the straight lines used

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to fit the constant rates (k2 and k4) under acidic conditions (pH 5 - 7) are relatively constant regardless of the temperature, thus indicating a low temperature effect on the dependence of the rate constant on pH, at least under the investigated temperature range (25 to 90 °C).

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The calculated rate constants k4 at pH 8 are clearly lower than the extrapolated values that we

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will get using these linear fits (except at 25 °C), which may indicate a change in the kinetics of the initial step of the polymerization reaction in basic solutions, not clearly observed from

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k2 parameter.

6.2.4. Comparison of rate constants for overall and initial reactions

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Figure 11 shows the rate constant of the initial polymerization k4 and the rate constant for the overall reaction k2 versus pH. The constant k4 ranges between 10-5 and 10-8 mmol-3 s-1 (note

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that k2 and k4 units are different). The magnitude of k4 is generally higher than k2 (except at 90 °C), as expected since the decrease in SiO2 concentration is faster at the beginning of the reaction. The difference, which reaches about 2 orders of magnitude at 25 °C, decreases with increasing temperature (Fig. 11). As previously observed for k2, k4 increases with increasing pH but, above 25 °C, there is a change in its dependence on pH at pH 8 (basic solutions); this change is more pronounced than with k2. Figure 11 also shows that k4 is relatively insensitive to temperature contrary to k2. This observation suggests that the beginning of the polymerization process (formation of stable nanocolloids with 4 silica units) is lowly dependent on temperature and depends more strongly on pH. The following steps (formation of dimers) depend more on temperature.

32

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7. CONCLUSION

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The aim of our study was to investigate the kinetics of amorphous silica precipitation during

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the cooling of high-temperature seawater-derived geothermal fluids as those collected from

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the wells of the Bouillante power plant in Guadeloupe (FWI). This Na-Cl fluid (20 g l-1), produced from a geothermal reservoir at 250-260 °C, separated from its steam and incondensable gases at 160-170 °C, and with an initial SiO2 concentration close to 600 mg l,was sampled at surface temperatures of 90, 75, 50, and 25 °C, using a cooling system.

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1

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Experiments were then conducted on each temperature fraction at pH values of 5, 6, 7, and 8. All the experiments only revealed silica polymerization in the form of colloidal silica gel. The on-site measurements on the evolution of silica concentration versus time in the separated

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geothermal water, along with the modeling of the experimental data, have enabled us to determine the kinetic parameters of the colloidal silica gel formation under the specific

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conditions at Bouillante. In agreement with earlier studies, we found that the formation kinetics of this phase depends on several parameters, such as the degree of fluid

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supersaturation with respect to amorphous silica, the pH, and the temperature. In the present study, as in several previous studies, the formation of colloidal silica gel was characterized by a second-order kinetic law (n = 2) relative to monomeric silica concentration. This order is consistent with the assumption that the polymerization process is controlled by the formation of silica dimers as long as the solution is in supersaturation. Dimers are formed by the condensation of monomeric silica, which combines to form high molecular weight polymers. Our results indicate that the activation energy for the formation of colloidal silica gel, under the specific exploitation conditions of Bouillante, is close to 52 ± 3 kJ mol-1, except at pH 8 where it is lower (41 ± 10 kJ mol-1). We also found that the initial polymerization stages of

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ACCEPTED MANUSCRIPT nanocolloidal silica gel formation could be characterized by a fourth-order reaction (formation of silica tetramers), as cited in the recent literature.

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Although scales of amorphous silica was never observed in our experiments, even after

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several months of observation, our results are still useful for providing recommendations

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regarding the optimal conditions to prevent or reduce the risk of silica scaling at Bouillante and, more generally, at other geothermal fields with similar exploitation conditions. For example, the existence of significant induction periods at pH < 5-6 suggests that it could be

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preferable to operate at this pH range during the cooling of the Bouillante geothermal fluid in

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order to avoid silica precipitation. Our work can thus contribute to an assessment of the best operating conditions to optimize the long-term exploitation management of the Bouillante geothermal reservoir, even though additional pilot-site experiments will be necessary to

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validate the approach.

Studies about the silica polymerization rate help to develop methods to control silica

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precipitation from the cooling of high-temperature geothermal fluids. Among the main methods, we can quote (Guerra and Jacobo, 2012): (1) lowering the pH by acidification using

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concentrated commercial acids (H2SO4, HCl, etc.), or by retaining acid gases such as H2S or CO2 in the geothermal fluids (or by injecting them), (2) fluid aging to convert monomeric silica to colloid silica and remove silica excess from fluids, (3) use of inhibitors to prevent or reduce silica scaling, (4) precipitation of silica with lime or other reactants, (5) mixing separated water with steam condensate, (6) removal of colloidal silica by coagulation and (7) settling and controlling separator pressure to maintain the fluid temperature above that of silica supersaturation. As it has been known for decades that the kinetics of silica polymerization is retarded when the pH of an aqueous solution is decreased, pH modification technologies continues to develop as one of the best and more acceptable solutions to controlling siliceous scaling from geothermal fluids. They are commonly recommended and

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ACCEPTED MANUSCRIPT have been deployed today at a number of geothermal fields around the world (Gallup, 2011). By acidifying fluids to pH  4.5 (at ambient conditions), both scaling and corrosion are

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minimized. Price comparison of different silica inhibitors indicates that the pH modification

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technology using sulfuric acid is probably the least expensive option for silica control. For

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example, the treatment of 295 kg/s of fluid in the Berlin geothermal field, in Salvador, requires an intake of 7500 kg per month of concentrated sulfuric acid to decrease pH values in the range of 5.5-5.6, which represents about 3,000 $ of monthly cost (Guerra and Jacobo,

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2012). Another possible approach could be to reduce silica oversaturation with controlled

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silica precipitation using lime or other reactants, but this approach produces large quantities of waste silica that has to be regularly removed and transported.

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One of the main objectives still to be attained is to determine whether amorphous silica scales

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can be formed (and at what rate) during the cooling of the Bouillante geothermal fluid. If such is the case, it will then be necessary to determine under what specific conditions and through

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which mechanisms the colloidal silica gel observed in our experiments can be transformed into amorphous silica scales. In a wider perspective, all the knowledge and experience

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acquired in the context of Bouillante field can be used for the development other hightemperature geothermal fields in volcanic islands. Our work also provides a reliable database for understanding silica polymerization kinetics in natural geothermal brines or geologic waters characterized by a near neutral pH and moderate dissolved silica concentrations.

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ACCEPTED MANUSCRIPT ACKNOWLEDGEMENTS

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This work was co-funded by ADEME (French Environment and Energy Management

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Agency) and BRGM through the GEO3BOU and ORBOU R&D projects and a PhD.

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fellowship for C. Dixit. We gratefully thank Géothermie Bouillante and its staff for access to the Bouillante power plants and technical support in making the on-site experiments possible. We also thank M. Brach (BRGM) for his help in the field work, H. Traineau (CFG Services)

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for his technical support in monitoring the exploitation, and J-L. Mansot and P. Thomas for their assistance in characterizing the silica deposits through MEB, TEM, and DRX analysis at

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the C3MAG laboratory (Antilles University). P. Rose (EGI, Utah University, USA), U. Jauregui-Haza (Havana University, Cuba) and B. Fritz (Strasbourg University, France) are

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also acknowledged for fruitful discussions that helped improve the earlier draft of this paper. We would like to particularly thank the two anonymous reviewers for their valuable

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contribution which greatly improved the quality of this manuscript.

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ACCEPTED MANUSCRIPT List of captions

Figure 1

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(a) Map of the regional framework of the Guadeloupe archipelago (from Thinon et al., 2010

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and modified from Feuillet et al., 2001). Box: kinematics of the Lesser Antilles arc.

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(b) Simplified map of the Bouillante geothermal field with the location of the wells (from Traineau et al., 2015 and adapted from Bouchot et al., 2010). The old BO-2 and BO-4 wells

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are used as injection and observation wells, respectively.

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Figure 2

Cooling system used for sampling separated water directly from the HP separator at

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temperatures of 25, 50, 75, and 90 °C.

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Figure 3

Evolution of the monomeric silica concentration as a function of time for the original Bouillante fluid (with pH ~ 7) at the different temperatures. Dashed lines correspond to the

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amorphous silica solubility computed for the different experimental conditions (see Table 2).

Figure 4 Evolution of the experimental (symbols) and calculated (dashed black curves) silica concentrations with time for the different pH and temperature conditions. Dashed gray lines correspond to computed amorphous silica solubility for pH 5 and 8 (see Table 2).

Figure 5 Examples of XRD patterns of polymerized silica extracted at (a) 25 °C and pH 6 and 7; (b) 25 °C and pH 8; (c) 90 °C and pH 6 and 7. 48

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Figure 6

(c) TEM images at 25 °C and pH 8; (d) TEM images at 90 °C and pH 7.

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pH 7;

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Examples of (a) SEM images of silica gel at 25 °C and pH 7; (b) TEM images at 25 °C and

Figure 7

Plot of log k2 vs. pH at 25, 50, 75, and 90 °C. The k2 values are computed from Eq. 9 and

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using the geochemical code PHREEQC (Parkhurst and Appelo, 1999).

Figure 8

Plot of log k2 vs. 1000/T based on Arrhenius law (under Eq. 13 form) for different pH

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conditions.

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Figure 9

Example of rate functions vs. time (defined by Eq. 5 in Icopini et al., 2005) for monomeric

Figure 10

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silica precipitation. The rate constant k4 is defined as the slope of the linear fit.

Plot of log kn vs. pH. The rate constants kn are computed using the analytical method proposed by Icopini et al. (2005) for n = 2, 4, and 6. The solid lines represent the linear fits obtained for our experimental data for the pH range 5-8 at 25 °C, and pH 5-7 at the other temperatures. The dotted lines represent the linear fits derived by Icopini et al. (2005) from their experiment at 25 °C with an initial SiO2 concentration of ~ 750 mg l-1 and an ionic strength of 0.24 M.

Figure 11

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ACCEPTED MANUSCRIPT Comparison of the rate constant k2 and k4, for the overall and the initial reactions respectively,

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T

and their dependence on pH at the different temperatures.

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ACCEPTED MANUSCRIPT Figure 1

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T

a)

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b)

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Figure 2

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Figure 3

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Figure 3

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Figure 4

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ACCEPTED MANUSCRIPT Figure 5

T

Amorphous SiO2

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NaCl

20

30

40

50

90 C, pH 6 and 7 (c) 25 C, pH 8 (b)

25 C, pH 6 and 7 (a)

60

70

80

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°2Theta

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10

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Intensity

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Calcite

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Figure 6

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Figure 7

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Figure 8

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Figure 9

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Figure 9

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Figure 10

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Figure 11

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ACCEPTED MANUSCRIPT List of tables

Table 1

T

Physical characteristics and average chemical compositions of the separated water collected

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following the 160 °C phase separation at the Bouillante power plant, computed from

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statistical analysis of the geochemical data collected by BRGM between 2005 and 2011. The concentrations are given in mg l-1.

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Table 2

The rate constants k2 characterizing the kinetics of amorphous silica precipitation for the

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Bouillante geothermal waters computed using PHREEQC and a 2nd order reaction (Eq. 9). As is the surface area computed using Eq. 6, ε is an estimation of the error on the model

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computed using Eq. 8 and Ceq (mg l-1) is the solubility of amorphous silica in a fluid

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representative of the Bouillante separated water computed with the geochemical code

conditions. Table 3

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PHREEQC (Parkhurst and Appelo, 1999) under different experimental temperature and pH

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The activation energy Ea at the different pHs, estimated for the temperature range of 25 90 °C using the Arrhenius law (Eq. 12) and k2 values. The standard errors and the correlation coefficient R2 are also provided. Table 4 Values of m and log k0 from Eq. 13 with standard errors and correlation coefficient R2 for 2nd order, 4th order and 6th order reactions in the pH range 5 - 7.

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Well BO-5

Well BO-6

pH (at 25 °C)

6.29 ± 0.91

6.41 ± 0.86

Eha

- 201 ± 47

- 182 ± 60

TDS (g.l )

23.8 ±1.4

24.0 ± 1.1

Cl

14008 ± 769

14150 ± 665

14561 ± 355

Na

6093 ± 295

6087 ± 251

6331 ± 186

Ca

2146 ± 159

2150 ± 105

2217 ± 108

K

918 ± 61

906 ± 50

944 ± 33

SiO2

579 ± 55

591 ± 37

595 ± 34

Br

49.0 ± 4.5

49.4 ± 4.2

51.0 ± 3.9

HCO3

25.6 ± 3.0

SO4

19.7 ± 3.9

Sr

17.9 ± 0.9

B

14.2 ± 1.1

Ba Mn

Mg F H 2S a

T

6.78 ± 0.31

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- 220 ± 37 24.6 ± 0.6

24.7 ± 4.4

25.3 ± 6.1

21.3 ± 2.8

21.3 ± 2.2

17.8 ± 0.9

18.1 ± 1.5

14.1 ± 1.1

14.6 ± 1.1

7.6 ± 0.7

7.5 ± 0.5

7.7 ± 0.6

5.5 ± 0.4

5.3 ± 0.3

5.2 ± 0.3

4.7 ± 0.2

4.7 ± 0.3

4.9 ± 0.4

1.7 ± 0.4

1.6 ± 0.5

1.9 ± 0.7

1.3 ± 0.4

1.3 ± 0.3

1.3 ± 0.5

0.38 ± 0.19

0.89 ± 0.19

0.68 ± 0.45

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Li

-1

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b

D

(mV)

Separated water

Eh is the redox potential; bTDS is the total dissolved solids (salinity)

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5

136

0.06

5

6

136

0.50

5

7

104

4.6

8

34

37.1

5

125

0.15

6

123

2.4

7

93

8

30

5

110

6

104

7

77

8

26

25

Ceq (mg l-1)

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5

117 117 117

5

119

4

184

7

184

28.6

6

185

70.4

8

191

1.7

4

272

11.2

7

272

112.6

7

274

51.9

6

291

90

2.3

4

334

90

17.5

6

335

7

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194.6

4

338

8

21

674.5

3

367

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6

TE

5

D

75

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90

ε (%)

As

T

k2*10-9 (mol m-2 s-1)

pH

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T (°C)

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8

41  9.8

0.946

7

52  2.6

0.995

6

51  2.0

0.994

5

54  9.6

0.942

A (mol m-2 s-1) 0.699

T

R2

2.416

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Ea (kJ mol-1)

0.658 0.413

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pH

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ACCEPTED MANUSCRIPT Table 4 T (°C)

k4*

k6*

logk0

R2

m

logk0

R2

m

logk0

R2

0.94  0.01 1.14 0.03 0.91 0.05 0.97 0.05

-14.9 0.1 -15.5 0.2 -13.4 0.3 -13.5 0.3

0.9998 0.9992 0.9969 0.9978

0.83 0.1 1.26 0.02 0.78 0.02 0.73 0.02

-11.7 0.6 -14.6 0.1 -11.7 0.9 -11.6 0.1

0.9856 0.9997 0.9638 0.9995

1.15 0.3 1.61 0.1 1.03 0.1 0.91 0.1

-15.4 1.6 -18.40.7 -15.0 0.4 -14.6 0.3

0.950 0.996 0.995 0.997

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T

m

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25 50 75 90

k2

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* Initial rate constants obtained following the analytical method of Icopini et al. (2005).

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