Measurements and modelling of FeCO 3 solubility in water relevant to corrosion and CO 2 mineralization

(cid:1) FeCO 3 solubility data allow for deeper understanding and prediction of CO 2 corrosion and CO 2 mineralization. (cid:1) Limited temperature dependency on FeCO 3 solubility. (cid:1) Extended UNIQUAC cable of describing FeCO 3 solubility in water. (cid:1) New calculated Gibbs energy and enthalpy of formation for FeCO 3. (cid:1) Activation energy for FeCO 3 dissolution in water.


Introduction
Carbon capture and storage (CCS) technologies are vital to combat anthropogenic greenhouse gas emissions and mitigate the consequences associated with global temperature increase.However, successful implementation is currently impeded by high operational costs and uncertainty in storage facilities (Steeneveldt et al., 2006;Zhang et al., 2019;Neerup, 2022).Surprisingly, a single mineral is present throughout the CCS value chain, namely FeCO 3 .During capture and transport, FeCO 3 is a major component in corrosion processes, which increases the capital costs, and, in storage, FeCO 3 acts as a mineral responsible for permanent storage.Currently, limited experimental solubility data exist for FeCO 3. By increasing the current understanding of FeCO 3 solubility behaviour, costs associated with capture and transport can be lowered, and storage capacity can be improved.
CO 2 corrosion is present both in the capture facility, in the transport pipes, on ships, and downhole in the injection equipment and is the cause for a major capital expenditure as more expensive corrosion resistant materials must be used.The corrosion process is initiated as CO 2 is absorbed into an aqueous liquid phase.CO 2 dissolves readily in a minute amount of water, and subsequently hydrolysed to form bicarbonate and hydrogen ions (Glezakou et al., 2009;Fosbøl, 2007).Depending on the pH, HCO 3 -, H 2 O or H + diffuses to the steel surface, where it is reduced (Nesic ´et al., 1997).Steel is oxidised, releasing Fe 2+ into the liquid.The released Fe 2+ reacts with carbonate and forms FeCO 3 as a solid precipitate, which creates a protective layer on the steel surface (Farida https://doi.org/10.1016/j.ces.2023.1185490009-2509/Ó 2023 The Authors.Published by Elsevier Ltd.This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).Abbreviations: AARD, average absolute deviation; CCS, carbon capture and storage; PCC, post combustion capture; PRV, pressure reaction vessels; SLE, solidliquid equilibrium; XRPD, X-ray powder diffraction.
For storage purposes, FeCO 3 is present in anthropogenic mineral carbonation (Stumm and Lee, 1961).Carbon mineralisation is performed by injecting almost pure CO 2 into reactive geological formations, such as basaltic rock (Blondes et al., 2018).CO 2 reacts with divalent metal ions leading to the formation of carbonates (Matter et al., 2009(Matter et al., , 2011;;Razote et al., 2019), resulting in mineral carbonation.CO 2 can be directly injected into porous geological formations.However, the reaction of CO 2 into carbonate is slow as it relies on natural weathering (Razote et al., 2019).Therefore, FeCO 3 solubility is a crucial parameter in understanding capacities and sequestration rates for the mineralization process.With an increased understanding of FeCO 3 solubility, CO 2 storage can be optimized (Matter et al., 2009(Matter et al., , 2011)).
Therefore, accurate models of FeCO 3 solubility are vital to predict CO 2 corrosion and CO 2 storage, as corrosion is controlled by the amount of dissolved FeCO 3 in the solution.At the same time, the rate of mineralization is governed by species solubility (Nesic ét al., 1997).However, these systems are complex to model due to the reactions taking place in the solution and the formation of new ions and molecules.Therefore, predictive models must be based on reliable experimental solid-liquid equilibria (SLE) data.However, currently a comprehensive databank for FeCO 3 solubility data does not exist, and this limits the applicability of existing models.
The existing thermodynamic data on FeCO 3 are incomplete, as concluded in an extensive literature review by Fosbøl et al. (Fosbøl et al., 2010) due to missing information on equilibrium temperatures, equilibrium time, uncertainties with the used method, and the purity of FeCO 3 due to oxygen contamination.In most cases the solubility data were collected at ambient conditions and with fixed ionic strength without distinction between different chemical systems and use of buffer (Fosbøl et al., 2010).Sampling under such conditions limits the applicability of the data from a modelling perspective as the activity coefficients change in different systems (Fosbøl et al., 2010).Furthermore, there is an absence on information on equilibrium time (Baylis, 1926;Ehlert and Hempel, 1912).Few authors (Baylis, 1926;Ehlert and Hempel, 1912;Murcia, 2018) have measured the solubility of FeCO 3 in water without the addition of a buffer, or gaseous CO 2 .However, equilibrium temperature was not mentioned in work from Ehlert and Hempel (Ehlert and Hempel, 1912) and Baylis (Baylis, 1926).Murcia (Murcia, 2018) studied the solubility of FeCO 3 in water at 25-80 °C, which revealed that the FeCO 3 solubility was decreasing with temperature.
The aim of this work is to present a comprehensive experimental investigation of the solid-liquid equilibria of the binary system FeCO 3 -H 2 O, which will simultaneously solve corrosion and CO 2 storage.This work presents FeCO 3 solubility data, and data of equilibrium time in the temperature range 5-120 °C.Furthermore, the Extended UNIQUAC model (Thomsen et al., 1996) will be applied for representing FeCO 3 in a corroding system and in the mineralization process.This is crucial for future understanding, and process simulation of systems dealing with CCS, especially for CO 2 corrosion and CO 2 mineralization.

Theory
The implementation of the Extended UNIQUAC model and the used parameters, is presented in this section.

Extended UNIQUAC model
The Extended UNIQUAC model (Thomsen et al., 1996) is, in this work, applied to describe the solid-liquid behaviour of FeCO 3 in water.The model has an extended Debye-Hückel term, which allows the model to be used for electrolyte systems.The Extended UNIQUAC is an activity coefficient model that consists of three terms: 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 À1 ), and T is the temperature (K).The electrostatic term has no adjustable parameters.Adjustable parameters are only present in the combinatorial and the residual term, and these are the surface area, and the volume parameters, and the energy interaction parameters.
The combinatorial term is dependent on the size and shape of the species and is defined by: z is the coordination number describing the interacting molecules surrounding the central molecule.In this study, the coordination number is 10, which is an average value between z ¼ 6 and z ¼ 12 (Abrams and Prausnitz, 1975;Bruin et al., 1971).A coordination number of 10 was previously proposed by Bruin and Prausnitz (Bruin et al., 1971) and the value z ¼ 10 has since then been used./ and h are, respectively, 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: r and q are volume and surface area parameters.Both parameters are adjustable in the Extended UNIQUAC model.
The residual term is temperature dependent and it expresses the difference in energy between molecules: the parameter w ji given as: Where u jj is the interaction across a binary pair of the same component and u ji represents the interaction across a binary pair of different components.They are calculated using a linear temperature relation: The adjustable parameters are, in this work, determined by fitting experimental solid-liquid equilibrium (SLE) data but can be fitted to a wider range of thermodynamic properties like vapour liquid equilibrium, enthalpy of reaction, heat capacity, excess properties and osmotic coefficients.
The dissociation of water is included with the following reaction The solid formation is covered by the mass action law equation for FeCO 3 in water: The electrochemical CO 2 corrosion model assumes that CO 2 (aq) reacts cathodically with the iron surface producing HCO 3 -and H 2 (aq), (Eq.( 12) and Eq. ( 13)) (Zhang et al., 2019).The anodic reaction is the dissolution of Fe, (Eq.( 14)).
The Extended UNIQUAC model is used for determining composition and activities in the liquid phase, the model does not include the electrochemical reactions.These are only relevant for the analysis of the surface reactivity on the steel-liquid interface.

Standard state properties
The standard state properties are used as a basis for calculating phase equilibrium conditions.They are especially relevant for determination of equilibrium constants to determine 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 this study the majority of properties for Gibbs free energy of formation, enthalpy of formation, and heat capacities, were obtained from the NIST data base (NIST, 1990).The standard state properties for all species are listed in Table 1.The standard state properties for FeCO 3 were adjusted with the Extended UNIQUAC to fit the experimental SLE data.The fitted values for the Gibbs energy and the enthalpy of formation are in bold in Table 1.
In this work FeCO 3 formation standard state properties were obtained by fitting to the measured solubility data.There exists no consensus on the standard state properties for FeCO 3 , as shown in Table 2.The conclusion from Table 2 is that FeCO 3 formation Gibbs energy, D f G FeCO3 , is within À665.16 to À740.57kJ mol À1 and À724.78 to À775.71 kJ mol À1 for D f H FeCO3 , a very large scatter.According to the review by Fosbøl et al. (Fosbøl et al., 2010), the deviation is related to properties of Fe 2+ .The determined equilibrium constant of reaction, (Eq.( 11)), dictates the D r G from Fe 2+ + CO 3 2-to FeCO 3 (s).If the Fe 2+ properties are difficult to determine, then FeCO 3 (s) properties will be similarly difficult, if the same D r G is used for FeCO 3 (s) formation.From (Fosbøl et al., 2010) it is also clear that the equilibrium constant or the D r G for reaction, Eq. ( 11), is similarly ill-defined due to lack of data, so the combination of ill-defined Fe 2+ properties and D r G gives the observed scatter in the D f G values of FeCO 3 .Standard state formation properties of Fe 2+ are presented in Table 3.Here it is seen that D f G 0 is varying quite significantly.Robie et al. (Robie et al., 1978) use a D f G 0 of À78.87 kJ mol À1 for Fe 2+ and obtain a D f G 0 of À666.698 kJ mol À1 for FeCO 3 whereas Robie et al. (Robie et al., 1984) in another study report D f G 0 of À680.03 kJ mol À1 for FeCO 3 , using a D f G 0 of À96.3 kJ mol À1 for Fe 2+ .This clearly shows the importance of Fe 2+ .The standard state formation properties of CO 3 2-are welldefined in the literature as stated in the review by Fosbøl et al. (Fosbøl et al., 2010).
The standard formation enthalpy of FeCO 3 (s) similarly depends on the Fe 2+ and CO 3 2-properties.A large deviation in reported enthalpy is likely caused by few experimental data points being available on the solubility of FeCO 3 (s) as function of temperature, while the large uncertainty in the enthalpy reflected in the availability of measured data at high temperature.

Model parameters
The volume (r) and surface area (q) parameters for the systems were previously adjusted by Thomsen (Thomsen, 1997), and Thomsen and Rasmussen (Thomsen and Rasmussen, 1999).The volume parameters were used as input for the modelling work.The r and q parameters are listed in Table 4.
The interaction parameters u 0 ij and u T ij were previously fitted by Iliuta et al. (Iliuta et al., 2002), and Thomsen and Rasmussen (Thomsen and Rasmussen, 1999).Normally the interaction parameters are fitted to experimental data for ion pairs considered to be in the solutions.The interaction parameters are presented in Table 5 and 6.Low and negative u 0 ij values indicate strong interaction between the molecular pairs.The u 0 ij of Fe 2+ -CO 2 and Fe 2+ -HCO 3 -are set to 10 9 which is aligned with the meaning no  À724.78(Murcia, 2018) interaction between the ions.These interactions are difficult to determine because the three components are rarely present in any mixture at the same time.Only at very high pressure will Fe 2+ and CO 2 be present.But, this type of data is not available and for this reason the interaction parameter cannot be determined.The Fe 2+ -H + interaction is also set equal to 10 9 but for another reason.This relates to the thermodynamic consistency ofDl H þ ¼ 0. The reason of making this assumption is to anchor the ion parameters to H + otherwise an infinite number of interaction parameters could be found for the same system and most likely many of these parameter spaces would not be thermodynamic consistent (Fosbøl, 2007).Interaction between Cl --Cl -is therefore relative to the data from the aqueous HCl system and Fe 2+ -Fe 2+ is relative set equal to zero in a similar way to H + , preventing singularity in the parameter space which would results in infinite number of parameter sets.
The average absolute relative deviation (AARD) was used as an objective function to fit between experimental and calculated data.AARD is defined as: With u representing corresponding measured and predicted values.n exp is the number of experimental data points.

Materials
Solutions of FeCl 2 Á4H 2 O and NaHCO 3 /Na 2 CO 3 with a Fe/CO 2 mole ratio of 1:4 were prepared in a glovebox (MBRAUN).The used chemicals are shown in Table 7.For solubility measurements, silicone oil purchased from Sigma-Aldrich was used to prevent inlet of oxygen and evaporation of the sample.Degassed ultra-pure water was used to mix the solutions.Nitrogen with a purity of 99.9999 % (AGA) was used to pressurize the sample mixture at 100 and 120 °C.

FeCO 3 synthesis
FeCO 3 is not commercially available and was synthesized as described by Murcia (Murcia, 2018) and Neerup et al. (Neerup et al., 2023).To prevent oxidation of FeCO 3 the synthesis was prepared in a glovebox (MBRAUN) with an inside atmosphere containing less than 0.01 ppm O 2 .Degassed ultra-pure milli-Q water was used to dilute and prepare the solutions.The prepared FeCl 2 Á4H 2 O and NaHCO 3 /Na 2 CO 3 solutions were loaded into a titanium piston cylinder inside the glovebox.The cylinder was pressurized to 10 bar outside the glovebox and placed in a furnace at 130 °C for 24 h.The precipitated FeCO 3 was washed several times with degassed milli-Q water in the glovebox.The obtained product was light beige.
The synthesised FeCO 3 was analysed using X-ray powder diffraction (XRPD) to identify the crystal structure.The crystal pattern (black) of the synthesised product is shown in Fig. 1 together with the reference spectrum (red).It can be concluded that the produced iron carbonate product has an XRPD spectrum very sim-  a Thomsen (Thomsen, 1997); b Thomsen and Rasmussen (Thomsen and Rasmussen, 1999).

Table 5
Binary interaction parameters u o ij parameters for the species presented in this work.Parameters are obtained from Iliuta et al. (Iliuta et al., 2002), and Thomsen and Rasmussen (Thomsen and Rasmussen, 1999).Binary interaction parameters u T ij parameters for the species presented in this work.Parameters are obtained from Iliuta et al. (Iliuta et al., 2002), and Thomsen and Rasmussen (Thomsen and Rasmussen, 1999).ilar to the pure FeCO 3 reference spectrum, see Fig. 1.This product was used for FeCO 3 solubility determination, without further purification.

FeCO 3 solubility
Solubility measurements were conducted in two different setups, an ambient pressure setup and a high-pressure setup.The following two subsections explain the experimental methods and the setups.

Solubility setup at ambient pressure
Solubility measurements in the temperature range 25-80 °C and at ambient pressure were performed using a setup similar to the setup described by Fosbøl et al. (Fosbøl et al., 2009).The setup consists of 5 cells connected in parallel to a heating/cooling circulation bath (Julabo).Each cell is filled with silicon oil.Approximately 15 mg of FeCO 3 and 22 g of degassed Milli-Q water were added to a 25 mL blue-cap bottle.5-10 mL of silicon oil was transferred to the blue-cap bottle in order to prevent inlet of oxygen and evaporation of the sample solution.The solutions were immersed in the cell and set to equilibrate.The solubility was analysed as a function of time up to 35 days.After sampling the equilibrium cell was discarded and was not used any further solubility analyses.Any repetition of experiments was carried out from scratch every time.Each sample was filtrated using a 0.22 lm PVDF membrane (Merck Millipore ltd.).Membrane filter, syringe, and filtration unit were heated to obtain the temperature equivalent to the sample, to prevent disturbance of equilibrium during sampling.

The high-pressure solubility setup
Pressure reaction vessels (PRV) (Andrews Glass) were used for solubility measurements at 100 °C and 120 °C.The PRV tolerates pressure up to 10 bar.The PRV setup is shown in Fig. 2. It consists of six PRV connected in parallel (a).A monometer (b) is attached to the lid (c) of each PRV.All PRVs are connected with stainless steel pipes and valves (d).Approximately 15 mg of FeCO 3 and 22 g of degassed Milli-Q water are transferred to the PRV in the glove box.A stirring bar is added to each of the PRV.The lids are screwed on and the setup is transported out of the glove box.To prevent boiling of water the setup is pressurized to approximately 3 bar using nitrogen.Afterwards the setup was left in an oven at the tar-geted temperature.The samples were mixed using a magnetic stirrer (2mag emagnetic motion: MIXdrive 6, MIXcontrol 40).

FeCO 3 analysis
The concentration of Fe 2+ , Fe 3+ , and total Fe, were determined spectrophotometrically (Hach Lange, DR 3900) using iron test kits from Hach Lange (LCK321, LCK320).The test kit concentration determination was validated using know iron samples.The uncertainty on the spectrophotometer was determined to be 3 % by analysing solutions containing a known amount of FeCl 2 Á4H 2 O.

Results and discussion
The following sections present and discuss the solubility and the oxidation of FeCO 3 in water.The dissolution rate, and derived activation energy of FeCO 3 in water together with the Extended UNIQUAC model prediction of FeCO 3 -H 2 O are presented.

Effect of equilibrium time on the FeCO 3 solubility
The equilibrium time is defined as the time required to obtain a saturated solution.This work defines the equilibrium time as the time passed until the iron concentration no longer significantly changes.This is determined visually often in the range of ± 3 days.
Solubility data with equilibrium time and standard deviation are listed in Table 8 and Table 9 for 5-80 °C and 100-120 °C, respectively.The data are given as an average of three measurements.In general, minor outliers are seen for all systems and could be caused by oxidation.Each measurement was run from beginning to end, and to minimize oxidation the containers were not opened before sampling.
The FeCO 3 equilibrium concentration was typically obtained after approximately 7-12 days, as indicated with the vertical lines in Fig. 3.This means that the temperature had no significant influence on the equilibrium kinetics.The equilibrium Fe 2+ concentration at 100 °C and 120 °C (see Fig. 3) was reached after approximately 10 days.In the work by Murcia (Murcia, 2018), equilibrium was obtained after 3-7 days at temperatures !40 °C.Equilibrium at 25 °C was not reached after 7 days.
For all solubility measurements (5 to 120 °C), the general trend is that the iron concentration is increasing linearly on a logarithmic scale until the equilibrium concentration is reached.The temperature seems to have an influence on the kinetics as the equilibrium solubility is obtained faster with temperature.
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 reaction Eq. ( 11), section 2.2.
The rate of dissolution was assumed to be proportional to the remaining solute concentration Where r Fe 2þ (mol Fe 2+ /kg water) is the reaction rate of Fe 2+ , b eq (mol Fe 2+ /kg water) is the averaged equilibrium concentration (Table 8-9).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.The reaction order was determined by comparing the goodness of fit for different reaction orders.The best fit was obtained with a first order, which leads to the following expression: where k d (day À1 ) is the reaction rate constant.The solution is not assumed to be limited by mass transfer of ions to the crystalline surfaces, since the mixtures were stirred at an rpm of 400.Slower dissolution kinetics due to mass transfer limitation were observed in samples discarded due to malfunctioning stirrer.In these samples equilibrium was not obtained.
An integrated rate equation was obtained by assuming an excess of solvent: The integrated rate law for FeCO 3 dissolution as function of time at the temperatures from 5 to 120 °C is displayed in Fig. 4. The rate constants for FeCO 3 dissolution at 5-120 °C are visualized in Fig. 5.The rate constant increases with temperature.The rate constants at 80 °C and 120 °C deviate from the increasing trend compared   to the constants at 5-60 °C and at 100 °C, see Fig. 5.These outliers are most likely related to the equilibrium concentration, which is an average of the solubility data at equilibrium.The activation energy for the reaction was obtained by fitting the extracted rate constants to the Arrhenius equation (Fogler, 2012): A is the frequency factor (day À1 ), E a (kJ/mol) is the activation energy for the reaction, R is the gas constant, and T (K) is the temperature.The activation energy is the minimum energy needed to initiate the reaction.lnðkÞ as a function of 1=T is shown in Fig. 6.Based on the slope of the linear regression line the activation energy was calculated.This fit yielded an activation energy of 1.55 kJ mol À1 .
Golubev et al. (Golubev et al., 2009) measured the activation energy of siderite dissolution in aqueous NaCl solutions with varying pH.They saw that the activation energy decreased from 61 kJ mol À1 at pH = 2 to 48 kJ mol À1 at pH = 4.This indicates that the activation energy is pH dependent.pH measured in this work is approximately 7, which according to Golubev et al. (Golubev et al., 2009) should give an even lower activation energy.The activation energy estimated in this work cannot be directly compared to the work of Golubev et al. (Golubev et al., 2009) due to the use of different solvents and the origin of FeCO 3 .Golubev et al. (Golubev et al., 2009) measured the dissolution of polycrystalline siderite planes in solutions of 0.1 M mixture of NaOH and HCl.In this work FeCO 3 was synthesized from aqueous solutions of FeCl 2 Á4H 2 O and NaHCO 3 /Na 2 CO 3 .Golubev et al. (Golubev et al., 2009) extracted the FeCO 3 from rock samples from Peyrebrune, France (Bénézeth et al., 2009) and from Ivigtut, Greenland.It is assumed that these samples contain impurities such as Mn, Na, Mg (Golubev et al., 2009).Testemale et al. (Testemale et al., 2009) did also measured the activation energy of crystals of siderite (mineralogical collection, University of Paris) in aqueous solution mixtures of HCl and NaCl at 300 bar.The derived activation energy was 73 kJ mol À1 .
Little literature exit on the activation energy of FeCO 3 (Golubev et al., 2009;Testemale et al., 2009;Greenberg and Tomson, 1992) and mainly under acidic conditions at atmospheric pressure and temperatures from 25 to 100 °C.The activation energy of FeCO 3 dissolution has, to the authors knowledge, not been derived from pure water solutions.

Effect of equilibrium temperature on the FeCO 3 solubility
Fig. 7 presents the equilibrium concentration as a function of the equilibrium temperature plotted alongside the FeCO 3 solubility data from Murcia (Murcia, 2018) and CaCO 3 solubility data by Coto et al. (Coto et al., 2012).The solubility measured in this work shows a small temperature impact on the FeCO 3 solubility, with FeCO 3 being less soluble as the temperature increases.The temperature dependency is more pronounced in the work from Murcia (Murcia, 2018).However, the data point at 25 °C measured by Murcia (Murcia, 2018) has not reached equilibrium.The solubility data by Murcia (Murcia, 2018) also show a decreasing FeCO 3 solubility trend with temperature.The solubility of CaCO 3 , determined by Coto et al. (Coto et al., 2012) (see Fig. 7), shows the same decreasing trend as for FeCO 3 observed in this work.Other carbonate systems such as BaCO 3 -H 2 O, and SrCO 3 -H 2 O also show a decreasing solubility trend with increasing temperature (García et al., 2006).
The aqueous CO 2 system is complicated by the dissociation of CO 2 into HCO 3 -and CO 3 2-.The basic chemical effect is the CO 2 partial pressure which controls the FeCO 3 chemistry.There are basicallytwo ways of maintaining chemical condition for the system containing CO 2 -FeCO 3 -H 2 O: 1. Constant CO 2 partial pressure 2. Constant total dissolved CO 2 When the temperature is varied, the CO 2 solubility decreases resulting in a lower CO 2 content in the liquid phase.As CO 2 is an acid, the dissociation results in a higher pH and HCO 3 -dissociates to CO 3 2-.
If the CO 2 pressure instead is increased to maintain a constant total CO 2 content in the liquid phase -while increasing the temperature, then the acid content is maintained and the relative amount of HCO 3 and CO 3 2-is kept constant in the solution and there is no overall dissociation.The effect of this is a constant FeCO 3 solubility.
The experiments carried out in this work is maintained at a constant pressure at increasing temperature, corresponding to case 1 above.The results of such action is a decreasing total CO 2 content in the liquid and therefore an increasing CO 3 2-content.This may sound counterintuitive, but it is not.When the CO 2 pressure is maintained constant, the liquid ''looses" a minute amount of CO 2 and pH increases resulting in HCO 3 -dissociating to CO 3 2-.Despite the total carbon content in the liquid decreases, the CO 3 2-content increases.The observed effect on the FeCO 3 solubility is a decrease in the Fe content and a decrease in the FeCO 3 solubility.The reason is simple: the equilibrium constant isK ¼ a Fe 2þ a CO 2À

3
. If a CO 2À 3 increases then a Fe 2þ must decrease to obtain a constantK.K may not be completely constant as function of temperature, but close to.
If the experiment instead was performed by increasing the CO 2 pressure and increasing the temperature, a constant FeCO 3 solubility would probably have been observed.This type of experiment is difficult to perform, because the CO 2 pressure to use is unknown.It is much more straight forward to maintain constant CO 2 pressure.
It could also be oxidation of Fe 2+ and precipitation of iron oxide which has a much smaller solubility than FeCO 3 .The FeCO 3 solubility data obtained by Murcia (Murcia, 2018) have a larger temperature dependency than the ones measured in this work, as seen in Fig. 7.The concentration profiles obtained in this work and by Murcia (Murcia, 2018) declines linearly, on a logarithmic scale, with temperature.The iron concentration of Murcia (Murcia, 2018) is two orders of magnitude lower than the solubility data measured in this study.A reasonable explanation for this deviation is that the samples have been contaminated with oxygen during the iron analysis resulting in oxidation of Fe 2+ to Fe 3+ forming e.g.iron oxide and/or iron hydroxide.Solubility data for Fe 3 O 4 in alkaline solutions at 25 °C are in the range À6 < log(b) (mol/ kg) < -7 (Tremaine and LeBlanc, 1980).

Oxidation of FeCO 3 over time
To identify the observed difference between the results obtained in this study and the data by Murcia (Murcia, 2018), the Fe 2+ and the Fe 3+ concentrations in a sample mixture were measured shortly after filtration and over a period of three days after filtration.The concentration of Fe 2+ , and Fe 3+ over time are presented in Table 10.It is also displayed in Figure 8, which shows the iron concentration as a function of time.The Fe 2+ concentration was approximately constant for the first two hours.After two hours, the Fe 2+ concentration decreased linearly at the logarithmic scale.The opposite occurred for the Fe 3+ concentration.A Fe 3+ intermediate was formed as more oxygen was dissolved from the atmosphere into the solution.The first 30 min the Fe 3+ concentration increased exponentially until the concentration reaches a plateau.This concentration was constant for two days.Subsequently, iron precipitated as iron oxides, lowering the Fe 3+ concentration in the solution.The precipitation of Fe 3+ was observed visually, indicated by orange to red precipitated particles.Figure 9 shows the solution after filtration (A) and after three days (B).The solution   is clearly influenced by oxygen (see Figure 9B).This suggests that the difference in the observed concentrations between this work and the study by Murcia (Murcia, 2018) (see Fig. 7) is due to oxidation.Murcia (Murcia, 2018) obtained at 25 °C and 80 °C concentrations of 12.6 mol Fe kg À1 water and 4.9 mol Fe kg À1 water respectively, which is similar to the Fe 3+ concentration obtained in Table 10 and the reported solubility values of Fe 3 O 4 by Tremaine and LeBlanc (Tremaine and LeBlanc, 1980).

Modelling of FeCO 3 solubility in water
The FeCO 3 solubility in water was calculated for the temperature range 5-120 °C by fitting the experimental SLE data to the Gibbs energy and the enthalpy of formation for FeCO 3 using the Extended UNIQUAC model.The adjusted standard state properties are presented in Table 11.
D f G FeCO3 and D f H FeCO3 were fitted to the equilibrium data at 5-120 °C (seen in Table 2) and the overall average deviation (AARD) was 0.08.The interaction parameters, u 0 and u T were not adjusted as they had an insignificant effect on the standard state properties, since the concentration of the ions present in the solution is very low.
The calculated and experimental SLE of FeCO 3 in water versus the temperature are shown in Fig. 10.There is a decrease in solu-b Fig. 7. FeCO 3 solubility in water as function of temperature.The black circles represent the data obtained from Murcia (Murcia, 2018).Blue circles denote the solubility data of CaCO 3 by Coto et al. (Coto et al., 2012).(For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)bility as function of temperature.This trend resembles the observed behaviour for CaCO 3 solubility, but orders of magnitude lower, as seen in Fig. 7.The results are presented as Fe 2+ .The Extended UNIQUAC model describes the experimental SLE data quite accurately except at 5 °C, which has an AARD of 0.05.The model performance can be improved by more experimental SLE data.

Conclusion
The solubility of FeCO 3 in water was measured at temperatures from 5 to 120 °C.In total 78 new solubility data points for the system FeCO 3 -H 2 O and 27 oxidation data points are presented in this study.
The FeCO 3 equilibrium concentration was obtained much faster upon increasing the temperature; 12 days were required to obtain equilibrium at 5-80 °C and 14 days for the 100-120 °C range.However, even though the temperature affected the equilibrium kinetics, it had an insignificant influence on the solubility.
We present the first ever measured activation energy of FeCO 3 dissolution in water, which was found to be 1.55 kJ mol À1 .
The Extended UNIQUAC model was applied to calculate the FeCO 3 solubility in water.The model was improved with the experimental FeCO 3 solubility data by adjusting the standard state formation properties of FeCO 3 .The model showed a fairly good result in representing the solubility in the temperature range 5-120 °C.The AARD was found to be 0.08.Gibbs energy and enthalpy of formation for FeCO 3 was estimated to be À653.27kJÁmol À1 and À710.01 kJÁmol À1 , respectively.The values are comparable to data found in the literature.
Oxidation of Fe 2+ were studied and the results revealed that Fe 2+ is stable for nearly 2 h.Hereafter Fe 2+ oxidizes.An intermediate Fe 3+ form as the oxygen concentration present in the solution increases.The Fe 3+ concentration increased exponentially until a constant level.Solid Fe 3+ was observed after three days.These observations signify the importance of maintaining an oxygen free environment when studying the FeCO 3 solubility.These results are important as oxygen can influence the solubility measurements.
The data generated in this study contribute to the fundamental understanding of CO 2 corrosion and CO 2 storage through the route of the FeCO 3 solubility.

Funding sources
This work received funding from the Danish Offshore Technology Centre through the project ''CO 2 impact on corrosion product (FeCO 3 ) solubility" (CTR.2D.15, LR_21).

CRediT authorship contribution statement
Chemical Engineering Science 270 (2023) 118549 Contents lists available at ScienceDirect Chemical Engineering Science j o u r n a l h o m e p a g e : w w w .e l s e v i e r .c o m / l o c a t e / c e s

ab
Fe corresponds to the average of three measurements, b u(b) is the standard deviation, c The coefficient of variance (CV) is calculated by dividing the standard deviation ðrÞ of data at equilibrium by average solubilityðgÞ, at equilibrium:CV ¼ r=g.CV 100 C ¼ 0:47,CV 120 C ¼ 0:78.FeCO 3 solubility in water as a function of equilibrium time.The vertical lines indicate equilibrium.

Fig. 6 .
Fig. 6.Activation energy for FeCO 3 dissolution.Dashed line is the trend, and circles are the experimental data.

Fig. 9 .
Fig. 9. Solubility and oxidation of FeCO 3 in water.A: Solution shortly after filtration, B: Solution 3 days after filtration and oxidation.

Table 1
Standard state properties.D f G and D f H for FeCO 3 obtained from the Extended UNIQUAC.
a Standard state properties obtained from the NIST data base (NIST, 1990).

Table 2
Standard state formation properties of FeCO 3 at 298.15 K and at 1 bar.

Table 3
Standard state formation properties of Fe 2+ at 298.15 K and at 1 bar.
a N/A: not available.

Table 4
Volume (r) and surface (q) parameters for the Extended UNIQUAC model.

Table 7
Chemicals used for the FeCO 3 synthesis.

Table 8
Solubility data of FeCO 3 in water versus equilibrium time measured at 5-80 °C and at atmospheric pressure.

Table 9
Solubility data of FeCO 3 in water at 100 and 120 °C versus equilibrium time measured and at 3 bar.

Table 10
Oxidation data a and corresponding standard deviations b for FeCO 3 as a function of time at atmospheric pressure.
a b Fe 2þ , and b Fe 3þ correspond to the average of three measurements.b u(b) is the standard deviation.

Table 11
Regression results of the SLE of FeCO 3 -H 2 O. Extended UNIQUAC model fitted to experimental data for the FeCO 3 -H 2 O system.