Solubility of FeCO 3 in aqueous NaCl, and aqueous HCl

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Introduction
FeCO 3 is present in many industries, and its solubility governs processes ranging from carbon storage to sweet corrosion.Carbon capture and storage (CCS) has an immense potential of reducing the anthropogenic CO 2 in the atmosphere (Neerup et al., 2022), steel corrosion has an annual global cost of 2.5 trillion dollars (GlobalSpec, 2016).CO 2 can be stored in geological formations, (Blondes et al., 2018) but concerns exist about the risk of leakage.Mineralization is a permanent storage method (Kakooei et al., 2017), where CO 2 is injected into subsurface reservoirs, subsequently reacting with Mg 2+ , Ca 2+ , and Fe 2+ forming stable carbonates (MgCO 3 , CaCO 3 , FeCO 3 ) ( Schmitt and Hörstmeier, 2006;Kahyarian et al., 2017b).The solubility and precipitation dynamics of these carbonates are therefore crucial for designing injection schemes and estimating the rate of mineralization.In corrosion, FeCO 3 exists as a corrosion product.Corrosion is initiated as a steel surface is exposed to dissolved CO 2 , where the ions electrochemically react with the steel surface releasing Fe 2+ .Once the solubility of Fe 2+ and CO 3 2-, is exceeded FeCO 3 precipitates on the steel surface, forming a protective layer (Stumm and Lee, 1961;Salmon et al., 2006;Kahyarian et al., 2017a;Schmitt and Hörstmeier, 2006;Farida, 2012;Garg et al., 2007;Hernandez, Munoz and Genesca, 2012;Kakooei et al., 2017).FeCO 3 creates a barrier, retarding further corrosion.
Whether FeCO 3 is considered as mineralization or as a corrosion product, detailed knowledge of its solubility is important in the prediction of CO 2 corrosion and CO 2 storage.Industrial systems consisting of high ionic-strength waters are often complex as they contain multiple electrolytes such as chlorides, sulphates, and magnesium (Dong et al., 2008).Under storage conditions, if CO 2 is dissolved in seawater for injection, there is a large amount of NaCl, which will significantly influence the FeCO 3 solubility.For corrosion processes, when CO 2 reacts with water and dissociates to H + , HCl is present.
Fosbøl et al. (Fosbøl, Thomsen and Stenby, 2010) presented a literature review on FeCO 3 solubility in different systems from pure water to systems containing different salts.Based on Fosbøl et al.'s discussion, we here summarise the challenges with existing solubility data of FeCO 3 .Ehlert and Hempel (Ehlert and Hempel, 1912) studied the equilibrium concentrations of FeCO 3 in aqueous NaCl solutions (50 to 351.2 g NaCl/ kg water), but they did not report the equilibrium temperature.Bardy and Péré (Bardy and Péré, 1976) measured FeCO 3 solubility in aqueous solutions with a NaCl concentration of 0.01-0.4mol/L at 20 • C. The solubility was also studied under the influence of CO 2 pressure, however, the partial pressure was not given (Bardy and Péré, 1976).Ptacek (Ptacek, 1992) studied FeCO 3 solubility at 25 • C in an aqueous solution containing 0-6 molal NaCl and 0-0.004 molal NaHCO 3 .The FeCO 3 concentration was analysed after an equilibrium time of 2 months.
Ptacek observed an increase in the solubility as a function of increased NaCl concentration, which gradually decreased as NaCl saturation was approached.Silva et al. (Silva, Liu and Millero, 2002) measured the impact of CO 2 on the solubility of FeCO 3 at 25 • C in solutions containing 0.1-5.5 m NaCl solutions as a function of ionic strength.Unfortunately, it is not apparent, which ions are added to the solutions to change pH.Bénézeth et al. (Bénézeth, Dandurand and Harrichoury, 2009) measured the solubility in 0.1 mol kg − 1 NaCl in a temperature range from 25 to 250 • C. Bénézeth et al. (Bénézeth, Dandurand and Harrichoury, 2009) extracted siderite from rock samples.Therefore, there is a likelihood of the solubility data being biased by oxidation.Based on the previous discussion there is a gap in the literature on 1) equilibrium time and temperature, 2) ions present in the solution, and 3) CO 2 partial pressure.The FeCO 3 solubility in aqueous NaCl solution has been studied by several authors (Ehlert and Hempel, 1912;Bardy and Péré, 1976;Ptacek, 1992;Silva, Liu and Millero, 2002;Bénézeth, Dandurand and Harrichoury, 2009) but to the authors' knowledge, the solubility has not been studied in systems containing aqueous solutions of HCl.
We expand on our previous work (Neerup et al., 2023a), which showed FeCO 3 solubility in H 2 O.In the present work, we focus on the solubility of FeCO 3 in the binary systems NaCl-H 2 O, and HCl-H 2 O without gaseous CO 2 present.The aim is to analyse the solubility in more complex systems than water and to mimic ions, which could be present in relevant brines in the CO 2 value chain, e.g. during storage.The experimental data are measured in a broad chloride concentration range at temperatures 25-80 • C. Equilibrium time is presented for all systems.
The purpose of this study is to create new fundamental knowledge of FeCO 3 solubility.This is crucial for future understanding, and process  , 1990).b Previous work (Neerup et al., 2023a).

Table 3
Binary interaction parameters u o ij (K) for the species presented in this work.Parameters are obtained from Iliuta et al. (Iliuta, Thomsen and Rasmussen, 2002), and Thomsen and Rasmussen (Thomsen and Rasmussen, 1999).

Table 4
Binary interaction parameters u T ij (K) for the species presented in this work.Parameters are obtained from Iliuta et al. (Iliuta, Thomsen and Rasmussen, 2002), and Thomsen and Rasmussen (Thomsen and Rasmussen, 1999).simulation of systems dealing with CCS, especially within CO 2 corrosion, storage, and CO 2 mineralization.

Extended UNIQUAC model
The experimental solubility data of FeCO 3 in the binary systems NaCl-H 2 O, and HCl-H 2 O was validated using the Extended UNIQUAC model (Thomsen, Rasmussen and Gani, 1996), which has an extended Debye-Hückel term, that is applicable for electrolyte systems.The Extended UNIQUAC model consists of three terms, which are a combinatorial (entropic), a residual (enthalpic), and an electrostatic term, with G E being the excess Gibbs energy (J/mol).R is the gas constant (J/mol K − 1 ), and T is the temperature (K).
The combinatorial term accounts for the size and volume of the chemical species.In term of the adjustable parameters are volume, r, and surface area, q.The combinatorial term is defined by:  (

G E RT
) z is the coordination number describing the interacting molecules surrounding the central molecule.A coordination number of 10 was applied in this study as this was previously proposed by Abrams and Prausnitz (Abrams and Prausnitz, 1975).ϕ and θ are the volume and the surface area fraction.x is the mole fraction and i represents the components in the solution.The volume and the surface area fractions are: The residual term expresses the difference in energy between molecules: the parameter ψ ji is given as: The adjustable parameters u jj and u ji are, respectively, the interaction across a binary pair of the same component and the interaction across a binary pair of different components.They are calculated using a linear temperature relation:

Speciation reactions
The following equilibria are considered in the Extended UNIQUAC: Vapour-liquid equilibrium (VLE): Solid-liquid equilibrium (SLE): Speciation equilibria: The electrochemical CO 2 corrosion model, which was shown in our previous work (Neerup et al., 2023a), is not included in the Extended UNIQUAC model.

Standard state properties and model parameters
The standard state properties are relevant for the determination of equilibrium constants to define the Gibbs energy of reaction and enthalpies of the above speciation scheme.In this study, the properties are used for the determination of FeCO 3 solubility in NaCl-H 2 O, and HCl-H 2 O.The Gibbs free energy of formation, Δ f G, enthalpy of formation, Δ f H, and heat capacities, Cp, were collected from the NIST database (NIST, 1990).Δ f G and Δ f H of FeCO 3 were determined in our previous work (Neerup et al., 2023a).The standard state properties for all species are presented in Table 1.
The volume (r) and surface area (q) parameters were previously adjusted by Thomsen (Thomsen, 1997), and Thomsen and Rasmussen (Thomsen and Rasmussen, 1999) and are outlined in Table 2.
The interaction parameters u 0 ij and u T ij were previously fitted by Iliuta et al. (Iliuta, Thomsen and Rasmussen, 2002), and Thomsen and Rasmussen (Thomsen and Rasmussen, 1999).The interaction parameters are presented in Table 3 and Table 4.The meaning of low and negative u 0 ij value and the reason for anchoring the ion parameters to H + was explained previously by the authors (Neerup et al., 2023a).For values of 10 9 no interactions between the ions are considered.The interaction between Fe 2+ -H + is set to 10 9 .The reason for doing this is to anchor ion parameters to H + in order to prevent an infinite number of interaction parameters the same system [4].For the interaction parameters set to zero it is to prevent an infinite number of parameter sets.

Materials
Aqueous solutions of FeCl 2 ⋅4H 2 O, NaHCO 3 , and Na 2 CO 3 were used to synthesise FeCO 3 .The solubility of FeCO 3 was measured in aqueous NaCl, and HCl solutions.See Table 5 for supplier and purity.The purchased HCl was standardised using Na 2 CO 3 .Na 2 CO 3 was dried for 24 h to evaporate water.Na 2 CO 3 was titrated with the HCl using a Titrando 888 (Metrohm).The HCl solution was diluted to the desired concentration using degassed Milli-Q water.Silicone oil was added to the samples to hinder evaporation and intrusion of oxygen.Degassed ultrapure Milli-Q water with a conductivity of 18.2 μS cm − 1 was used to mix the solutions.

FeCO 3 synthesis
FeCO 3 was synthesized as described by Neerup et al. (Neerup et al., 2023b).The FeCO 3 synthesis was prepared in a glovebox (MBRaun) with an atmosphere of less than 0.01 ppm oxygen.Ultra-pure milli-Q water was degassed with nitrogen to prevent oxidation of FeCO 3 .Aqueous solutions of FeCl 2 ⋅4H 2 O and NaHCO 3 /Na 2 CO 3 were loaded into a titanium piston cylinder.The cylinder was transferred outside the glovebox and pressurized to 10 bar.The cylinder was then placed in a furnace at 130 • C for 24 h.The synthesis was terminated by cooling the cylinder to room temperature.After cooling, the cylinder was transferred to the glove box.FeCO 3 was washed several times with degassed milli-Q water and let to dry.The synthesis product was confirmed by X-ray powder diffraction (XRPD).

FeCO 3 solubility
Solubility measurements were conducted in the temperature range of 25-80 • C and at ambient pressure.The setup and method have previously been described elsewhere (Fosbøl, Thomsen and Stenby, 2009;Fosbøl, Pedersen and Thomsen, 2011).To avoid oxidation of FeCO 3 , samples were prepared in a glovebox.pH was deliberately not measured, because this would ruin the atmosphere around the sample and also pollute the sample with salts from the pH probe.
A stirring bar, 15 mg of FeCO 3 , and 22 g of a saline solution prepared with degassed Milli-Q water were added to a blue-cap flask and 5-10 mL of silicone oil was transferred on top of the sample solution.Adding silicone oil to the solution prevents the intrusion of air into the sample.
The equilibrium setup had up to five cells that were connected in parallel to a heating bath (Julabo).Each cell was filled with silicon oil.The solutions were immersed in the cell and set to equilibrate over a period of several days.Samples were filtered using 0.22 μm PVDF membrane (Merck Millipore Ltd.).The membrane filter, syringe, and filtration unit were heated to obtain the temperature equivalent to the sample.The iron concentration was determined spectrophotometrically (Hach Lange, DR 3900) using iron test kits (Hach Lange: LCK321, LCK320).The total iron content was determined in the FeCO 3 -NaCl-H 2 O system whereas the system FeCO 3 -HCl-H 2 O was analysed for Fe 2+ and Fe 3+ .
The evaporated CO 2 amount from the sample is expected to play no role in the analysis of solubility.The sample was not exposed to an artificial high pressure of CO 2 .The headspace of the sample container is typically 10 mL and the liquid content is typically 10 mL.The calculated pH of the solution is in the order of 8⋅10 -10 .This results in a CO 2 partial pressure of 1-100 Pa.This constitutes up to 0.0004 % of the total carbon dissolved in the liquid.This CO 2 amount is small and has little impact on the final solubility of FeCO 3 .

Results and discussion
The experimentally measured solubility of FeCO 3 in aqueous NaCl solutions, and aqueous HCl solutions is described in the following sections.The oxidation of FeCO 3 in aqueous HCl solutions, the dissolution rate of FeCO 3 in aqueous NaCl solutions and in aqueous HCl solutions, together with the Extended UNIQUAC model prediction of these systems are presented.
The time required to reach equilibrium is presented for each system.Equilibrium time in solubility measurements often varies from system to system and can take from less than a couple of hours (Fosbøl, Thomsen and Stenby, 2009) to several months (Jensen et al., 2002) depending on the dissolution rate of the solid phase.The FeCO 3 solubility equilibrium was obtained when the iron concentration no longer changed significantly, which is visually determined often in the range of ± 3 days.

Solubility of FeCO 3 in aqueous NaCl
The experimental solubility data of FeCO 3 in aqueous NaCl solutions at 25-80 • C and at atmospheric pressure are presented in Table 6-9.The concentration is presented in molality with corresponding standard deviations of the FeCO 3 concentration.The solubility of FeCO 3 in aqueous NaCl solutions (0.5-20 wt% NaCl) at 25-80 • C as a function of time is shown in Fig. 1.The solubility of FeCO 3 in 0.5-2 wt% NaCl was only measured at 25 • C to study the solubility trend at low salt concentrations.Minor outliers are seen in all the systems.These outliers are to our understanding caused by oxidation of FeCO 3 .Each measurement was run from beginning to end without opening the containers before sampling, to minimize oxidation.The solubility concentrations reported in Table 6-9 are an average of three measurements.In some cases, the concentration is reported as a single measurement due to analysis failure.
In general, as seen in Fig. 1, for all the systems at 25-80 • C the FeCO solubility is increasing from an initial Fe concentration of approximately 30⋅10 -6 mol Fe 2+ /kg solvent at day 1 to a final concentration above 200⋅10 -6 mol Fe/kg solvent.The solubility is increasing almost linearly   in the beginning before it gradually slows down and the final Fe concentration is obtained.The equilibrium kinetics seem to be influenced by the temperature.The dissolution kinetics will be further characterized in Section 4.6.At 25 • C, the equilibrium concentration is obtained after approximately 11 days.
Increasing the temperature to 40 • C and above the equilibrium concentration is obtained after 7 and 5 days for the solubility at 40 • C and 60-80 • C respectively.
The FeCO 3 equilibrium solubility is presented in Fig. 2 as a function of the NaCl concentration.The solubility is increasing fast and almost linearly in solutions from 0 to 3 wt% NaCl.Hereafter the solubility has reached a maximum level at 283⋅10 -6 mol Fe 2+ /kg solvent (Fig. 2).The solubility gradually decreases at NaCl concentrations between 3 and 7 wt%.At NaCl concentrations above 7 wt%, the FeCO 3 solubility stagnates to a concentration level of around 227⋅10 -6 mol Fe 2+ /kg solvent.This trend is dominating at 40 • C (green circles) and 80 • C (black circles).The trend at 60 • C (red circles) deviates from the observed trends at 25, 40, and 80 • C.Here the solubility is decreasing gradually.Ptacek (Ptacek, 1992) observed the same phenomenon at 25 • C.She observed that the FeCO 3 solubility was increasing with NaCl concentrations and decreasing gradually when the halite saturation was approached.Dong et al. (Dong et al., 2008) reported the stability and solubility of MgCO 3 ⋅3H 2 O in solutions containing NaCl, KCl, MgCl 2 , and NH 4 Cl.They R. Neerup et al. observed that the MgCO 3 ⋅3H 2 O solubility increased reaching a maximum and then decreased with NaCl concentrations.

Oxidation of FeCO 3
FeCO 3 is known to oxidize to Fe 2 O 3 in the presence of minute amounts of oxygen (Pan et al., 2000;Dongun Kim et al., 2013;Bachan and Kump, 2015) and it is during the analysis of solubility, quite important to prevent oxidation.Any oxidation will create Fe 3+ ions from Fe 2+ .The solubility of most Fe 3+ components is low, much lower than FeCO 3 (Tremaine and LeBlanc, 1980).This means if the Fe 2+ is oxidized to Fe 3+ , then the results no longer express FeCO 3 solubility.The concentration of both Fe 2+ and Fe 3+ was measured for the FeCO 3 -HCl-H 2 O system to confirm if the iron was oxidized.
The equilibrium concentrations of FeCO 3 in HCl solutions were measured by monitoring the Fe 2+ concentration using the method described in the previous section.Oxidation of FeCO 3 was measured by observing the Fe 3+ concentration as a function of time, discussed in   10-11.The percentage of oxidation versus the Fe 2+ concentration in aqueous HCl solutions is shown in Fig. 3.The average oxidation for FeCO 3 in HCl solutions is 2 % and does not exceed 10 %.Most of the oxidation occurred prior to the system reaching equilibrium, reflected in a Log b Fe2+ of − 3 to 4 mol Fe 2+ /kg water (Fig. 3) with oxidation of more than 20 %.

Solubility of FeCO 3 in aqueous HCl
The solubility and oxidation of FeCO 3 represented by Fe 2+ (mol Fe 2+ /kg HCl) and Fe 3+ (mol Fe 3+ /kg HCl), respectively are listed in Table 10-11.The solubility was measured at 25-80 • C in solutions containing 0.005 mol/kg, 0.01 mol/kg, 0.02 mol/kg, and 0.04 mol/kg HCl .The solubility of Fe 2+ and Fe 3+ in solutions containing 0.005 mol/kg HCl to 0.04 mol/kg HCl at 25-80 • C are shown in Fig. 4 as a function of equilibrium time.
The equilibrium kinetics of Fe 2+ in aqueous HCl solutions (Fig. 4) seem not only to be influenced by the temperature but also by the HCl concentration or the solution pH.The equilibrium solubility of Fe 2+ is obtained much faster with higher HCl concentrations.From 2 to 3 days for 0.005 mol/kg HCl and less than 1 day for 0.04 mol/kg HCl.The temperature does not seem to have an effect on the equilibrium kinetics as the equilibrium solubility at all temperatures is obtained more or less at the same time.
Most of the Fe 3+ is below 100⋅10 -6 mol Fe 3+ /kg solvent.The reasons for the higher Fe 3+ concentration was explained in the previous section.Another explanation could also be the equilibrium kinetics of Fe 3+ is much slower than Fe 2+ .The Fe 2+ solubility data point for 0.005 mol/kg HCl at day 3 (25 • C), Fig. 4, is most likely biased by oxidation as the Fe 3+ content is similar to the Fe 2+ concentration.For all systems on the first day, the Fe 2+ has likewise similar concentration as Fe 3+ .
The FeCO 3 solubility (Fig. 5) is increasing with higher HCl concentrations.The increased solubility in higher concentrations of HCl is expected due to the low pH which increases the H + ions present in the solutions and thereby raising the solubility.It seems that the FeCO 3 solubility is approaching a maximum of 0.04 mol/kg HCl and above.

Influence of temperature on the FeCO 3 solubility
The impact of temperature on the FeCO 3 solubility in aqueous solutions of NaCl, and HCl is shown in Fig. 6.The FeCO 3 solubility in NaCl solutions is also compared to literature values at 25-90 • C measured by Bénézeth et al. (Bénézeth, Dandurand and Harrichoury, 2009).
The temperature influence on the FeCO 3 solubility in NaCl solutions is insignificant even though it seems to be a slight decrease with temperature.The FeCO 3 solubility in NaCl solutions presented in this work shows the identical temperature trend as in the findings by Bénézeth et al. (Bénézeth, Dandurand and Harrichoury, 2009)      solvent in the work by Bénézeth et al. (Bénézeth, Dandurand and Harrichoury, 2009).The difference might be caused by NaCl concentration or the starting material of FeCO 3 .In this work we synthesised FeCO 3 whereas it was extracted from rock material in the work by Bénézeth et al. (Bénézeth, Dandurand and Harrichoury, 2009).The temperature has a minute impact on the FeCO 3 solubility in the HCl-H 2 O systems.The solubility is increasing with temperature with the highest increase in solubility being from 25 to 40 • C. The FeCO 3 solubility seems to approach a maximum level of around 80 • C.
The FeCO 3 solubility is strongly affected by the HCl concentration from − 2.5 to − 1.7 mol Fe 2+ /kg solvent as seen in Fig. 6.Furthermore, the FeCO 3 solubility is approximately 10 times more soluble in HCl compared to solutions containing NaCl.This means that it is more difficult to precipitate FeCO 3 and create a protective barrier against corrosion in a more acidic system.

Kinetics of FeCO 3 dissolution
The kinetics of FeCO 3 dissolution is an important parameter in relation to carbon dioxide storage, as it is related to permanent underground mineralization.The dissolution kinetics of FeCO 3 in the presence of NaCl, and HCl can readily be determined from the presented data.To  investigate the observed kinetic trends, a simple kinetic model was developed based on the Fe 2+ solubility results.The dissolution of FeCO 3 is described by: We assume that the rate of dissolution is proportional to the remaining solute concentration where r Fe 2+ (mol Fe 2+ /kg water) is the reaction rate of Fe 2+ , b eq (mol Fe 2+ /kg water) is the averaged equilibrium concentration, b t (mol Fe 2+ / kg water) is the concentration of Fe 2+ in the solution at time t (day) and n is the reaction order.From our previous work (Neerup et al., 2023), the reaction order was determined to be first-order.A first-order reaction leads to the following expression: where k d (day − 1 ) is the reaction rate constant.The solution was stirred at 400 rpm, which allowed us to assume ideal mixing.An integrated rate equation was obtained by assuming an excess of solvent: The rate constant is thereby a measure of how rapidly the dissolution occurs, e.g., large k d represents quick dissolution, while lower k d values indicate a slow dissolution.
The rate constant is tabulated for the various experimental conditions in Table 12 and plotted as a function of foreign salt concentration in Fig. 7.For NaCl, the dissolution tends to be slower at high NaCl concentrations (Fig. 7.a) and quicker at higher temperatures.
Lastly, the dissolution of FeCO 3 in HCl (Fig. 7.b) does not show a clear trend as a function of salt concentration, and only a weak correlation between concentration and dissolution rate can be observed.However, the dissolution rate constant is much larger for dissolution in HCl compared to dissolution in NaCl solutions.The Extended UNIQUAC was in our previous study shown capable of calculating the binary system FeCO 3 -H 2 O by only changing the standard state properties of FeCO 3 .
The model parameters have already been fitted to the literature data of systems containing Cl -, and Na + (Thomsen and Rasmussen, 1999;Iliuta, Thomsen and Rasmussen, 2002).The standard state properties, the volume and surface parameters, and the interaction parameters are presented in Table 1-3.These parameters were validated towards the experimental solubility of FeCO 3 in aqueous NaCl solutions and in aqueous HCl solutions.The model was validated for the temperature range 25-80 • C at atmospheric pressure.It was expected that interaction parameters, u 0 and u T had an insignificant effect on the standard state properties, since the concentration of the ions present in the solution is very low.The number of applied experimental data for the ternary systems FeCO 3 -NaCl-H 2 O and FeCO 3 -HCl-H 2 O are shown in Table 13.
The results from the calculation using the Extended UNIQUAC model and the experimental FeCO 3 solubility in aqueous HCl (0.005-0.04 mol/ kg) solutions are shown in Fig. 8. Fig. 8 also includes the solubility of FeCO 3 in water (Neerup et al., 2023a), which shows that the model is capable of calculating the FeCO 3 solubility in water.For the system FeCO 3 -HCl-H 2 O the Extended UNIQUAC model resembles the experimental data fairly well.The model tends to overpredict the FeCO 3 solubility especially at 25 and 40 • C.
The calculated FeCO 3 solubility in the binary system NaCl-H 2 O was likewise compared to the experimental results (Fig. 9) and in this case, the model does not perform as well.The largest discrepancy is again observed between 25 and 40 • C. The calculated solubilities have a downward going trend with the FeCO 3 solubility being less soluble in 3 wt% NaCl.The upper set is seen in the experimental data having the FeCO 3 solubility being more soluble in 3 wt% NaCl and less in 20 wt% NaCl.Furthermore, the experimental data shows that the FeCO 3 solubility in 20 wt% NaCl is approaching a maximum.
To improve the model calculation more experimental data is needed for the systems FeCO 3 -NaCl-H 2 O and FeCO 3 -HCl-H 2 O.
A residual plot of the Log 10 b Fe2+ predicted and measured solubility values is shown in Fig. 10.The residuals for the system FeCO 3 -H 2 O is very close to zero with only one data point at 5 • C deviating more than others.For the two other systems FeCO 3 -NaCl-H 2 O, and FeCO 3 -HCl-H 2 O the residuals are mostly below zero indicating that the Extended UNI-QUAC is tending to over predict the measured values, which is also seen in the Fig. 8 and Fig. 9.There is no clear reason for the deviation and it could be related both to the model parameterization and the uncertainty of the data.
Calculated equilibrium pH in aqueous solutions of FeCO 3 , FeCO 3 -HCl, and FeCO 3 -NaCl are presented in Fig. 11 and Fig. 12, and in Table 14, and Table 15.pH is relatively stable at NaCl concentrations from 0 to 20 wt%, It increases 0.3 independent of temperature, see Fig. 11.pH decreases as function of temperatures from approximately pH 10 to 8.6 in the range from 25 to 80 • C.This could explain why there of is a higher corrosion rate at higher temperatures (Fosbøl, 2007), since a low pH increases corrosion rate.
In the aqueous FeCO 3 -HCl system, pH is expected to decrease as function of HCl concentration.However, pH seems to have reached a steady level at a concentration of 0.04 m HCl, see Fig. 12.Similar to the NaCl solutions, elevated temperature and HCl concentration results in lower pH, which both contribute to increased corrosion.

Conclusion
The solid-liquid phase equilibrium of FeCO 3 in the binary systems NaCl-H 2 O, and HCl-H 2 O has been studied in this work.The FeCO 3 solubility was measured at 25-80 • C, at atmospheric pressure and in the absence of a CO 2 partial pressure.We presented 136 new data points on FeCO 3 solubility in aqueous NaCl (0.5-20 wt%) solutions, and 53 data points on the solubility in aqueous HCl (0.005-0.01 mol/kg) solutions.Solubility data were supplemented with iron oxidation, producing Fe 3+ from FeCO 3, which was measured in solutions containing HCl.The obtained FeCO 3 results showed that less than 10 % was oxidized.
The equilibrium time to obtain a constant Fe 2+ concentration is 7-10 days for solutions containing NaCl.Equilibrium was obtained approximately after two days in aqueous HCl solutions.The temperature had a minor impact on the FeCO 3 solubility in the systems containing aqueous NaCl and aqueous HCl.In HCl, FeCO 3 solubility is 10 times more soluble compared to NaCl, and the solubility increases with HCl concentrations.
The rate constant for FeCO 3 dissolution in aqueous solutions of NaCl, and HCl was estimated based on the experimental data.The rate constant was observed to be slower with high NaCl concentrations and faster with increased temperature.The dissolution rate of FeCO 3 in HCl did not show a clear trend as a function of concentration.Although the dissolution rate constant is much larger for dissolution in HCl compared to dissolution in NaCl.
The extended UNIQUAC model showed very good results in calculating the FeCO 3 solubility in HCl-H 2 O.The deviation between the model and the experimental results for the system FeCO 3 -NaCl-H 2 O was larger at 25-40 • C. Further validation of the model parameters is needed at a higher temperature range.
The presented solubility data is suitable for future understanding and prediction of CO 2 corrosion and mineralization.

Contributions
The manuscript was written through the contributions of all authors.All authors have approved the final version of the manuscript.

Funding Sources
This work received funding from DTU Offshore through the project CO 2 impact on corrosion product (FeCO 3 ) solubility (CTR.2D.15, LR_21) and the Technical University of Denmark, Department of Chemical Engineering.

Fig. 1 .
Fig. 1.FeCO 3 solubility in NaCl-H 2 O as a function of equilibrium time.Vertical lines indicate equilibrium.

a
b Fe 2+ and b Fe 3+ correspond to the average of three measurements.b u(b) is the standard deviation.

Fig. 4 .
Fig. 4. FeCO 3 solubility in aqueous HCl as a function of equilibrium time.Horizontal lines indicate equilibrium.
. The solubility measured in their work is showing an almost constant solubility in the temperature range of 25-90 • C. The solubility (Log b Fe ) measured in our work is in the order − 3.5 mol Fe/kg solvent towards − 3.2 mol Fe/kg

Fig. 11 .
Fig. 11.Calculated pH using the extended UNIQUAC model as function of NaCl concentration.

Fig. 12 .
Fig. 12. Calculated pH using the Extended UNIQUAC model, as function of HCl concentration.

Table 1
Standard state properties.
a Standard state properties obtained from the NIST database (NIST

Table 5
Chemicals used for the FeCO 3 synthesis and solubility determination.

Table 6
Solubility data of FeCO 3 in aqueous NaCl solutions versus equilibrium time measured at 25 • C, and atmospheric pressure, p = 0.1 MPa.Fe corresponds to the average of three measurements.
a b b u(b) is the standard deviation.

Table 7
Solubility data of FeCO 3 in aqueous NaCl solutions versus equilibrium time measured at 40 • C, and atmospheric pressure, p = 0.1 MPa.

Table 8
Solubility data of FeCO 3 in aqueous NaCl solutions versus equilibrium time measured at 60 • C, and atmospheric pressure, p = 0.1 MPa.Fe corresponds to the average of three measurements.
a b b u(b) is the standard deviation.

Table 9
Solubility data of FeCO 3 in aqueous NaCl solutions versus equilibrium time measured at 80 • C, and atmospheric pressure, p = 0.1 MPa.
a b Fe corresponds to the average of three measurements.b u(b) is the standard deviation.

Table 12
Rate constants for dissolution of FeCO 3 in NaCl, and HCl at 25-80 • C.

Table 14
Calculated equilibrium pH in the FeCO 3 -NaCl-H 2 O system, using the Extended UNIQUAC model.

Table 15
Calculated equilibrium pH in the FeCO 3 -HCl-H 2 O system, using the Extended UNIQUAC model.

Table 16
Solubility of FeCO 3 in 0.02 ± 0.03 mol/kg HCl versus equilibrium time measured at 25-80 • C, and at atmospheric pressure, p = 0.1 MPa.Fe 2+ and b Fe 3+ correspond to the average of three measurements.
a b b u(b) is the standard deviation.4.6.Modelling of FeCO 3 solubility in NaCl-H 2 O, and HCl-H 2 O Fe 2+ and b Fe 3+ correspond to the average of three measurements.
a b b u(b) is the standard deviation.R.Neerup et al.