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Experimental Measurement of CO2 Solubility in Aqueous NaCl Solution at Temperature from 323.15 to 423.15 K and Pressure of up to 20 MPa Hamdi Messabeb,*,† François Contamine,*,† Pierre Cézac,† Jean Paul Serin,† and Eric C. Gaucher‡ †

Laboratoire de Thermique, Energétique et Procédés (LaTEP), Institut Carnot ISIFoR, Université de Pau et des Pays de l’Adour, Rue Jules Ferry, BP 7511 Pau Cedex, France ‡ TOTAL, CSTJF, Avenue Larribau, F-64018 Pau Cedex, France ABSTRACT: Interest in CO2 solubility in brine at high pressure and high temperature has grown in the last few decades. Solubility data are especially important in petroleum geology, carbon capture and geological storage, and geothermal reservoir engineering. Nevertheless, for the CO2 + NaCl + H2O system there are fewer solubility data available in literature, particularly at high salt molality. A high-pressure experimental device was designed to perform measurements for carbon dioxide solubility in a complex aqueous solution. The apparatus was first validated from experiment on the CO2−pure water system at 323.15 K by comparison with literature data. Thirty-six new experimental solubility data point were obtained in the pressure range between 5 and 20 MPa at three temperatures (323.15, 373.15, and 423.15 K) and at three molalities of NaCl (1, 3, and 6 moles per kilogram of water). Solubility measurements were obtained by potentiometric titration after sample trapping in a sodium hydroxide solution. The experimental solubility data generated in this work were consistent with literature data, and four original isotherms were obtained at high salinity.

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INTRODUCTION CO2 solubility in salty aqueous solutions at high pressure and temperature is of huge interest in many environmental fields such as carbon dioxide capture and storage in deep saline aquifers1 and in depleted hydrocarbon reservoirs.2,3 A good knowledge of phase composition is essential to the estimation of the storage potential4 and to the description of interactions that could exist between the fluid phase and the sedimentary rock in the long run.5 CO2 solubility under these conditions is also very important in several industrial applications such as CO2-enhanced oil and gas recovery6 and the simulation of petroleum reservoirs. In this case, phase composition is fundamentally needed to design and optimize chemical process and separation operations.7 Researchers in the field of natural hydrothermal fluids are also waiting for precise solubility data for economic or scientific applications.8 The number of studies on this topic is still increasing, but CO2 solubility data, particularly at high pressure and high salinity, are quite scarce. Therefore, there is a need to obtain data under these conditions. This article presents a description of the apparatus and analytic method developed for determining CO2 solubility data in NaCl solution. The CO2 + pure water system at 323.15 K is first used to validate the experimental equipment, operating procedure, and analysis method; therefore, the data obtained are compared to published literature data. Then we report solubility data obtained © XXXX American Chemical Society

over a wide range of pressure (5−20 MPa), temperature (323.15−423.15 K), and molality of NaCl (1, 3, and 6 mol/kg).

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LITERATURE REVIEW CO2 + H2O System. The CO2 solubility in pure water has been investigated over a wide range of temperature and pressure. The CO2−H2O system is well described, and abundant literature data exist. During the last two decades, several reviews have been published by Diamond and Akinfiev,9 Spycher et al.,5 Chapoy et al.,10 and Ji et al.11 The works of Springer et al.12 and Mao et al.13 also include an extensive summary of experimental data available in the literature. Studies with experimental data in the temperature and pressure ranges of interest are listed in the Table 1, which enumerates for each study the pressure and temperature ranges. Most of the data are consistent with each other at pressures up to 10 MPa. At 323 K and 10 MPa, there is a gap of 0.1 mol/kg between the maximum and minimum literature values. The highest and lowest values are respectively 1.2114 and 1.11 mol/ kg,4 and at 15 MPa, a difference of 0.07 mol/kg can be observed Received: June 17, 2016 Accepted: September 22, 2016

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DOI: 10.1021/acs.jced.6b00505 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Table 1. Literature Experimental Data for the CO2−H2O System authors

temp/K

pressure/MPa

Sander Zel’venskii44 Wiebe and Gaddy26 Prutton and Savage50 Ellis51 Tödheide and Franck45 Takenouchi and Kennedy26 Matous et al.52 Malinin and Saveleva31 Malinin and Kurovskaya32 Shagiakhmetov and Tarzimanov43 Zawisza and Malesinska53 Drummond48 Cramer33 Gillepsie and Wilson54 Briones et al.15 D’Souza et al.46 Müller et al.55 Nighswander et al.34 Sako et al.17 King et al.56 Dohrn et al.47 Rumpf et al.20 Bamberger et al.38 Kiepe et al.23 Bando et al.4 Chapoy et al.10 Valtz et al.18 Bermejo et al.57 Koschel et al.24 Han et al.58 Siqueira Campos et al.59 Ferrentino et al.21 Liu et al.22 Yan et al.14 Savary et al.30 Lucile et al.16 Hou et al.19 Tong et al.60 Guo et al.61 Carvalho et al.35 Mohammadian et al.27 Zhao et al.28

293.15 to 375.15 273 to 373 285 to 373 374.15 to 393.15 387.15 to 621.15 323.15 to 373.15 383.15 to 623.15 303.15 to 353.15 298.15 to 358.15 298.15 to 358.15 323.15 to 423.15 323.15 to 473.15 303 to 564 306.15 to 486.25 288.75 to 366.45 323.15 323.15 to 348.15 373.15 to 473.15 352.85 to 471.25 348.15 288 to 398.15 323.15 323.17 323 to 353 313.2 to 393.2 303.15 to 333.15 283.38 to 351.31 273.2 to 318.2 296.7 to 369.7 323.1 to 373.1 313.2 to 343.2 313.2 to 343.2 308.15 to 323.15 308.15 to 328.15 323.15 to 413.15 393.15 298.15 to 393.15 298.15 to 448.15 374 273.15 to 573.15 283 to 363 333.15 to 373.15 323.15 to 423.15

2.45 to 14.71 1.07 to 9.4 2.5 to 70 2.33 to 70.31 0.50 to 16.4 20 10 to 20 1 to 3.88 4.795 4.795 10 to 20 0.237 to 5.3 3.8 to 16.9 0.8 to 5.8 0.7 to 20.27 6.82 to 17.68 10.13 to 15.2 0.325 to 8.11 2.04 to 10.2 10.34 to 15.31 6.08 to 20.27 10.1 to 20.1 1.059 to 5.798 4.05 to 14.11 0.01 to 9.257 10 to 20 0.287 to 5.216 0.5 to 8 1.55 to 8.34 2.06 to 20.2 4.33 to 18.34 0.5 to 5 7.58 to 13.1 2.08 to 15.99 5 to 40 11.3 to 33.7 0.54 to 5.14 1 to 18 7.21 to 27.26 10 to 120 0.3 to 12.08 0.1 to 21.3 15

49

Kiepe et al.23 made solubility measurement by the mass balance method. Results were obtained from an accurate knowledge of the amount loaded, the experimental parameters (temperature and pressure), and the density of the aqueous phase under equilibrium conditions. CO2 + H2O + NaCl System. By comparison with the CO2− H2O system, solubility data for the CO2−NaCl−H2O system are scarce, especially at high salt molality (6 mol/kg), high pressure (20 MPa), and high temperature (423 K). Koschel et al.24 determined the solubility of CO2 in NaCl solution by a calorimetric technique through the measurement of mixture enthalpy. Guo et al.25 used a Raman spectroscopy method to obtain CO2 solubility data in NaCl solution. The calibration step involves the knowledge of the molar volume of carbon dioxide and the brine density. Takenouchi and Kennedy26 trapped a sample in a sodium hydroxide solution and analyzed it by colorimetric titration using colored indicators. Mohammadian et al.27 used the same trapping method but analyzed their samples with potentiometric titration. Yan et al.14 measured the CO2 solubility using a volumetric approach. This approach is based on the determination of three volumes. The first one is the volume of CO2 released after degassing a sample. This value is obtained by weighing the sampling cylinder before and after degassing. The second volume corresponds to the volume of CO2 in the gas phase in the sampling cylinder. The third volume corresponds to the remaining volume of CO2 in the aqueous phase at atmospheric pressure, and this volume is estimated from Henry’s law. The Henry’s law constant is calculated from a correlation. Zhao et al.28 also obtained solubility data thanks to a volumetric approach by taking a sample and degassing it in a pressure cell. The mass of CO2 released into the pressure cell after sample expansion is calculated by an equation of state developed by Span and Wagner.29 The trapping method was also used by Savary et al.30 to perform a solubility measurement; in this study, samples were analyzed by alkalinity titration. Another type of trapping method, without a titration step, was developed and utilized by Malinin and Saveleva31 and Malinin and Kurovskaya32 to determine the CO2 solubility. It requires a sample to pass through an absorption train of potassium hydroxide. In this case, the amount of CO2 is determined from the weight gain of the absorption train. The volumetric technique was used by Cramer,33 who estimated the solubility by means of the ideal gas law and Henry’s law to determine the amount of CO2 released and the quantity of carbon dioxide that remained in the liquid phase after saturated sample depressurization in a buret, respectively. Nighswander et al.34 obtained solubility data by measuring through a volumetric U-tube the volume of CO2 released after the depressurization and bubbling of the saturated sample in a H2SO4 solution. Carvalho et al.35 obtained solubility data using bubble-point detection. Hou et al.36 used a gas chromatography to analyze the liquid phase. Studies providing experimental data in the temperature and pressure ranges of interest are listed in Table 2.

between literature data. The highest and the lowest results are respectively 1.2515 and 1.18 mol/kg.4 These experimental data were obtained using different methods. Lucile et al.16 analyzed the liquid phase by ion chromatography. Sako et al.,17 Valtz et al.,18 and Hou et al.19 used a gas chromatograph to determine the CO2 solubility. Rumpf et al.20 obtained solubility data through a bubble point method from the exact amount of component injected into the system. Several authors determined the solubility by the volumetric analysis of liquid samples. Ferrentino et al.21 measured the amount of gas desorbed from a degassed sample by a mass flow meter or by volume and CO2 density. Liu et al.22 produced solubility data by measuring the amount of gas released after degassing the sample into a pressure cell.

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EXPERIMENTAL SECTION Chemicals. Carbon dioxide was provided by Air Liquid with a certified purity of 99.7% (CAS registry no. 124-38-9). Water was purified by a Barnstead Easypure RoDi with a resistivity of 18.2

B



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Table 2. Literature Experimental Data for the CO2−H2O− NaCl System pressure/MPa

mNaCl/mol·kg−1

423.15 to 723.15

10 to 138

1.1 to 4.3

298.15 to 348.15

4.795

0.4 to 4.9

298.15 to 423.15

4.795

1 to 6.8

292.85 to 673.15 296.75 to 511.75 353.15 to 473.65 313.15 to 433.15 313.15 to 353.15 303.15 to 333.15 323.15 to 373.15 318.15 323.15 to 413.15 393.15 323.15 to 423.15 293.15 to 353.15 333.15 to 373.15 323.15−423.15 273.15 to 473.15

3.5 to 39 0.8 to 6 2 to 10 0.5 to 9.5 0.1 to 10 10 to 20 5 to 20 2.1 to 15.83 5 to 40 12.5 to 34.1 0.28 to 18.08 1.02 to 12.25 0.1 to 21.3 15 10 to 40

1 to 6.5 0.5 to 2 0.17 4 to 6 0.5 to 4.3 0.15 to 0.55 1 to 3 1.93 to 1.98 1 to 5 2 2.5 to 4 0.25 to 2 0.017 to 0.256 1 to 6 1 to 5

authors

temp/K

Takenouchi and Kennedy26 Malinin and Saveleva31 Malinin and Kurovskaya32 Drummond48 Cramer33 Nighswander et al.34 Rumpf et al.20 Kiepe et al.23 Bando et al.4 Koschel et al.24 Liu et al.22 Yan et al.14 Savary et al.30 Hou et al.36 Carvalho et al.35 Mohammadian et al.27 Zhao et al.28 Guo et al.25

A high-pressure, thermostated volumetric pump (Top Industrie PMHP 200−200) of about 200 cm3 allows us to load liquid or gas carbon dioxide. The cell and pump are connected by a high-pressure three-port manual valve; this configuration gives us the possibility to operate in pressure-regulation mode by piston displacement. The cell and pump are both fitted with a pressure transducer (PA 33X) from Keller with an accuracy of ±0.15% of full scale. The cell and pump are protected by two rupture discs. The sampling system consists of a high-pressure two-way valve located in the bottom of the cell and connected to the sampling syringe by a short tube in PEEK. Operating Procedure. The equilibrium cell and lines were first evacuated to a pressure of 0.01 MPa using a vacuum pump prior to introducing about 700 cm3 of aqueous solution. Then, temperature was fixed at the desired value. After reaching this temperature, the carbon dioxide was pumped into the preheated cell until the wanted pressure was reached. Afterward, efficient stirring was started, 800 rpm is sufficient to increase the contact surfaces between the two phases. Pressure was stabilized within a few minutes, but stirring was kept during 2 h to make sure that equilibrium state was reached before sampling and analysis.16 Once equilibrium was achieved, an aqueous-phase sample was withdrawn by opening valve V2. This valve is connected to a sampling syringe containing a trapping solution of NaOH. (The sodium hydroxide solution must be free of carbonate; it was analyzed by ion chromatography to check the purity and to make sure the solution does not contain any trace of carbonate.) Therefore, CO2 in the aqueous-phase sample is absorbed. NaOH must be present in excess in order to convert all CO2 and HCO3− to CO32−, in accordance with the following reactions:27,37

MΩ·cm. Sodium hydroxide (CAS registry no. 1310-73-2) was provided by VWR with a certified purity of 99%. Sodium chloride (CAS registry no. 7647-14-5) was supplied by Acros Organics with a certified purity of 99.5%. Hydrochloric acid (0.1 mol/L ± 0.2%) was provided by VWR (CAS registry no. 7647-01-0). The source and purity of materials are outlined in Table 3. Table 3. Sample Description Table chemical name

formula

carbon dioxide sodium chloride sodium hydroxide hydrochloric acid water

CO2 NaCl

Air Liquide Acros Organics

0.997a 0.995a

NaOH

VWR

0.990a

HCl

VWR

H2O

Barnstead Easypure RoDi filtering system

between 0.998 and 1.002a 18.2 MΩ·cm

a

source

purity

CO2 + 2OH− ↔ CO32 − + H 2O

(1)

HCO3− + OH− ↔ CO32 − + H 2O

(2)

During the sampling process, valve V1 was opened to allow pressure compensation so that the pressure remains constant in the equilibrium cell by pump piston displacement (Figure 2). The molalities mentioned in this article are those of the feed brine. Depending on the pressure and temperature conditions, a small amount of water might be transferred from the aqueous solution to the gas phase, which could increase the molality. On the basis of sensitivity of CO2 solubility with respect to the salt molality, this change can be considered to be negligible.36 A simulation carried out with PHREEQC software, using the PITZER.DAT database, demonstrates that the molality increases by 0.007 mol/kg under equilibrium conditions of 423.15 K, 5 MPa, and 6 mol/kg of salt. Analysis. Potentiometric Titration. An automatic titrator (Titroline alpha plus TA 20) from SCHOTT Instruments and 0.1 M HCl solution were used to determine the composition of the aqueous phase by potentiometric titration method (pH versus added titrant volume). The titration curve obtained includes three main parts: The first end point was reached when the excess OH− was neutralized (reaction 3), and the volume was recorded as v1.

Mass fraction purity stated by the supplier.

Apparatus. Solubility measurements were performed with an apparatus through a static analytical method with aqueous phase sampling. The device used in this work (Figure 1) is based on a highpressure equilibrium cell that is made of a C276 alloy. The volume of the cell is approximately 1000 cm3 and can be operated up to 20 MPa from (293.15 to 423.15) K. The autoclave is thermostatically controlled by circulating a heat carrier fluid through a double jacket, and the temperature is strictly controlled and regulated by a thermostated bath (Lauda Proline RP 845 C). Four heating resistors are inserted into the lid to minimize the thermal gradient between the top and the bottom of the cell. Furthermore, the apparatus is provided with four probes (PT100) to measure temperature at three locations in the cell and also in the lid. The stirrer, a Rushton turbine in the liquid phase, and a fourblade impeller in the gas phase ensure the homogeneity of the two phases.

OH− + H+ ↔ H 2O

(3)

The second end point was obtained when all CO32− was converted to HCO3− (reaction 4), and the volume was recorded as v2. CO32 − + H+ ↔ HCO3− C

(4) DOI: 10.1021/acs.jced.6b00505 J. Chem. Eng. Data XXXX, XXX, XXX−XXX


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Figure 1. Photograph of the experimental apparatus.

uncertainty of the temperature measurement was less than 0.06 K. The pressure measurement uncertainty was estimated to be within 0.01 MPa. The overall standard uncertainty in the brine molality was evaluated to be 0.3%, including all steps of solution preparation and salt purity. Errors driven by pressure, temperature, and salt molality are small, and their effects on solubility data can be considered to be insignificant. Therefore, calculations of uncertainties including uncertainty due to the experimental setup and uncertainty due to the analysis were performed using the ANOVA method. These calculations are based on the reproducibility and repeatability of experiments. Repeatability corresponds to results obtained for the experiment with several samplings whereas reproducibility corresponds to results obtained for distinct experiments carried out under the same conditions. These calculations are performed on four experiments at 373.15 K, 10 MPa, and 1 mol/kg NaCl. Each experiment was conducted with 13 titrations. The relative standard deviation of these 52 analyses is 2%. The experimental average uncertainty calculated by the ANOVA method is about 3.5%, with the coverage factor chosen to obtain a level of confidence of 95%.

Figure 2. Scheme of the experimental apparatus.

The last end point was detected when HCO3− was neutralized and transformed to carbonic acid, and the volume was recorded as v3. HCO3− + H+ ↔ H 2CO3

(5)

Finally, the concentration of total CO2 was calculated and checked by the following equation: C HCl(v 2 − v1) = C HCO3− v′ C (v3 − v 2) = HCl v′

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RESULTS AND DISCUSSION First, the CO2 solubility in pure water at 323.15 K and in the pressure range between 5 and 20 MPa was studied in order to validate both the apparatus and experimental procedure, through comparison with a large amount of literature data available from different references. Solubility data are plotted in Figure 3 with the literature data available under the same temperature and pressure conditions. Experimental results are presented with an uncertainty of 4%. The graph shows good agreement between our results and the literature data at pressure below 10 MPa and at 20 MPa. At 10 MPa, our results are especially consistent with data from Bamberger et al.,38 Hou et al.,19 and Zhao et al.28 At 15 MPa, our results are particularly in agreement with data by Weibe and Gaddy39 and Zhao et al.28

CCO2 = CCO32− =

(6)

with v′ being the volume of the sample. The density of the sample was measured with a DM 40 density meter from Mettler Toledo. By knowing the mass fraction of the saturated solution in the titrated sample (mixture of a saturated aqueous phase and a NaOH solution), the carbon dioxide molality in the aqueous-phase solution could be determined. The results reported in this work are the means of three successive titrations performed under each set of equilibrium conditions. Experimental Uncertainty. The platinum probes were calibrated by the Laboratoire National d’Essais (Paris), and the D



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Figure 3. Solubility of carbon dioxide in pure water at 323.15 K up to 20 MPa: ○, This study; ▲, Zhao et al.;28 ■, Koschel et al.;24 △, Yan et al.;14 ◊, Bamberger et al.;38 □, Bando et al.;4 × , Liu et al.;22 *, Lucile et al.;16 gray fill ◊, Rumpf et al.;20 +, Wiebe and Gaddy;39 gray fill, black outline □, Shagiakhmetov and Tarzimanov;43 ●, Zel’venskii;44 gray fill, black outline ◊, Tödheide and Franck;45 gray fill □, Briones et al.;15 gray fill ○, D’Souza et al.;46 ◆, Dohrn et al.;47 gray fill △, Ferrentino et al.;21 −, Hou et al.19

Figure 4. Solubility of carbon dioxide in a 1 mol/kg NaCl solution at T = 323.15 and 373.15 K up to 20 MPa: ●, This study at 323.15 K; ■, Koschel et al.24 at 323.15 K; ◆, Yan et al.14 at 323.15 K.; ▲, Zhao et al.28 at 323.15 K; gray fill, black outline ○, this study at 373.15 K; gray fill □, Koschel et al.24 at 373.15 K; gray fill ◊, Yan et al.14 at 373.15 K.; and gray fill △, Zhao et al.28 at 373.15 K.

The first three graphs (Figures 4, 5, and 6) show that results obtained in this work are consistent with solubility data in the literature. At 423.15 K and 3 mol/kg and for all studied isotherms at a NaCl molality of 6 mol/kg, only one point was available in the literature28 (Figures 7 and 8). Our results are especially consistent with the data of Zhao et al.28 within a maximum gap of 4.65% at 373.15 K, 15 MPa, and 6 mol/kg and a minimum gap of 0.5% at 423.15 K, 15 MPa, and 1 mol/kg. Data obtained in this work are also coherent with the data of Yan et al.14 with a percentage deviation between 0.3% and 2.65% except for the point measured at 323.15 K, 5 MPa, and 1

Consequently, the apparatus is adapted to solubility measurements, and the operating procedure and potentiometric titration are validated. Then the CO2 solubility in sodium chloride solution at molalities of 1 and 3 mol/kg in the pressure range between 5 and 20 MPa at 323.15, 373.15 and 423.15 K was investigated. Finally, three isotherms at a NaCl molality of 6 mol/kg were investigated under previous conditions of temperature and pressure. The results are shown in comparison with literature data in Figures 3 to 8. The numerical values for CO2 solubility in pure water and NaCl solutions are given in Table 4. E



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Figure 5. Solubility of carbon dioxide in 1 mol/kg NaCl solution at T = 423.15 K up to 20 MPa: ○, This study; Kurovskaya;32 −, Drummond;48 and ◊, Takenouchi and Kennedy.26

△,

Zhao et al.;28 *, Malinin and

Figure 6. Solubility of carbon dioxide in a 3 mol/kg NaCl solution at T = 323.15 and 373.15 K up to 20 MPa: ●, This study at 323.15 K; ■, Koschel et al.24 at 323.15 K; ▲, Zhao et al.28 at 323.15 K; gray fill, black outline ○, this study at 373.15 K; gray fill □, Koschel et al.24 at 373.15 K; gray fill △, Zhao et al.28 at 373.15 K; and gray fill ◊, Guo et al.25 373.15 K.

mol/kg. Under these conditions, our result is more than 9% higher than the data of Koschel et al.24 and more than 13% below the result of Yan et al.14 The rise in pressure leads to a significant increase in CO2 solubility (at 323.15 K and 1 mol/kg, the solubility increases from 0.650 mol/kg at 5.03 MPa to 0.965 at 10.02 MPa); nevertheless, the pressure effect decreases as the pressure increases. (Under the same conditions of temperature and molality, the solubility increases from 1.042 mol/kg at 15.06 MPa to 1.081 mol/kg at 20.01 MPa.) The rise in temperature leads to a decrease in CO2 solubility (at 15 MPa and 1 mol/kg, the solubility drops from 1.042 mol/kg

at 323.15 K to 0.850 mol/kg at 373.15 K), even though the temperature dependence diminishes at higher temperature (under the same conditions of pressure and molality, the solubility increase by 0.046 mol/kg between 373.15 and 423.15 K). The increase in salt molality clearly reduces the CO2 solubility (at 323.15 K and 10 MPa, the solubility decreases from 0.965 mol/kg at 1 mol/kg of NaCl to 0.676 mol/kg at 3 mol/kg of NaCl and 0.438 mol/kg at 6 mol/kg of NaCl). F



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Figure 7. Solubility of carbon dioxide in a 3 mol/kg NaCl solution at T = 423.15 K up to 20 MPa: ○, This study; △, Zhao et al.28

Figure 8. Solubility of carbon dioxide in a 6 mol/kg NaCl solution at T = 323.15, 373.15 and 423.15 K up to 20 MPa: ●, This study at 323.15 K; ▲, Zhao et al.28 at 323.15 K; gray fill, black outline ○, this study at 373.15 K; gray fill △, Zhao et al.28 at 373.15 K; ○, this study at 423.15 K; and △, Zhao et al.28 at 423.15 K.

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MATHEMATICAL CORRELATION

Assuming that the partial molar volume does not depend on pressure and composition, in a γ/Φ approach we have40

This section consists merely of proposing a simple mathematical tool to approximate the solubility of CO2 in a NaCl−H2O system with temperature, pressure, and salinity. The vapor/aqueous phase equilibrium for CO2 implies that the pressure, temperature, and fugacity are identical in both phases:40 f iaq (T , P , xi) = fiV (T , P , yi )

∞ ⎡ V CO (P − Pws(T )) ⎤ 2 ⎥ ′ HCO2(T , Pws(T )) exp⎢ mCO2γCO 2 ⎢⎣ ⎥⎦ RT v (T , P , yCO )P = yCO ΦCO 2 2

2

(8)

This equation requires a knowledge of thermodynamic models such as the activity coefficients of all species, Henry’s constant, the solvent vapor pressure (Psw), the partial molar volume of carbon dioxide V∞ CO2, and the fugacity coefficient in the gas phase

(7)

If the asymmetric convention is used, then the standard state for the ionic solute and CO2 is the infinitely dilute aqueous solution. G



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Table 4. Experimental and Calculated Data of CO2 Solubility at 323.15, 373.15, and 423.15 Ka mNaCl/mol·kg−1b

temp/K

pressure/MPa

mCO2 (exp)/mol/kgb

mCO2 (cal)/mol/kgb

RSD %c

0

323.15 323.15 323.15 323.15 323.15 323.15 323.15 323.15 323.15 323.15 323.15 323.15 323.15 323.15 323.15 323.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 423.15 423.15 423.15 423.15 423.15 423.15 423.15 423.15 423.15 423.15 423.15 423.15

5.01 10.03 15.04 20 5.03 10.02 15.06 20.01 4.99 10.06 14.97 19.96 5.05 10.09 14.99 20.04 5.01 10.08 15.02 19.96 5.08 10.07 15.01 20.16 5.08 10.07 15.01 20.16 5.03 10.04 15.05 20.01 5.06 10.1 14.96 20.23 5.04 10.1 14.96 20.21

0.791 1.164 1.234 1.308 0.650 0.965 1.042 1.081 0.452 0.676 0.713 0.779 0.291 0.438 0.484 0.509 0.376 0.668 0.850 0.942 0.289 0.492 0.609 0.727 0.196 0.331 0.408 0.471 0.305 0.577 0.804 0.960 0.245 0.425 0.570 0.717 0.162 0.285 0.379 0.463

0.788 1.163 1.302 1.296 0.664 0.992 1.115 1.113 0.478 0.723 0.816 0.821 0.296 0.450 0.498 0.514 0.369 0.625 0.788 0.886 0.280 0.468 0.587 0.659 0.183 0.316 0.377 0.420 0.316 0.584 0.810 0.996 0.246 0.445 0.608 0.746 0.167 0.299 0.398 0.478

1.51 0.08 5.51 0.84 2.15 2.79 7.00 3.05 5.75 7.10 14.58 5.51 2.06 2.96 5.78 2.16 1.86 6.43 7.17 5.83 2.76 4.87 3.61 9.35 6.63 8.45 7.59 10.61 3.93 1.38 0.74 3.85 0.81 4.70 6.66 4.18 3.08 5.26 5.01 3.23

1

3

6

1

3

6

1

3

6

a

Standard uncertainties u are u(T) = 0.06 K, u(P) = 30 kPa, ur(m(NaCl)) = 0.003, and ur(m(CO2)) = 0.035 bMolalities are expressed in moles per kilogram of water cRSD = |(mCO2(exp) − mCO2(cal))/mCO2(exp)| × 100.

⎛ 7258.2 ⎞ ⎟ − 7.3037 ln(T /K) ln(Pws /Pa) = 73.649 − ⎜ ⎝ T /K ⎠

(Φ). We choose to simplify it to obtain a simple but physically consistent correlation. Therefore, we propose the simplified relation

+ 4.1653 × 10−6(T /K)2

P

mCO2 = SF(T , P , mNaCl )HCO2(T ,

Pws(T ))

s ∞ (P − Pw (T )) ⎤ ⎡ VCO exp⎢ 2 RT ⎣ ⎦⎥

Thanks to this formulation, we calculated from our experimental data the value of the parameters that we called the solubility factor (SF) term, defined by

(9)

Henry’s constant for the carbon dioxide solubility in water is obtained from Rumpf and Maurer41 ⎛ 9624.4 ⎞ ⎟ + 0.01441(T /K) ln(HCO2/MPa·kg·mol−1) = 192.876 − ⎜ ⎝ T /K ⎠ − 28.749 ln(T /K)

(11)

P

SF(T , P , mNaCl ) = mCO2HCO2(T ,

(10)

The vapor pressure is calculated with the equation from Chapoy:42

Pws(T ))

∞ (P − Pws(T )) ⎤ ⎡ VCO exp⎢ 2 RT ⎣ ⎦⎥ (12)

Then, we fitted it according to the following polynomial

H



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Figure 9. Calculated solubility versus experimental solubility data at 323.15 K: ◊, CO2−pure water system; ○, CO2−H2O−1 mol/kg NaCl; △, CO2− H2O−3 mol/kg NaCl; and □, CO2−H2O−6 mol/kg NaCl.

Figure 10. Calculated solubility versus experimental solubility data at 373.15 K: ◊, CO2−pure water system; ○, CO2−H2O−1 mol/kg NaCl; △, CO2− H2O−3 mol/kg NaCl; and □, CO2−H2O−6 mol/kg NaCl.

Figure 11. Calculated solubility versus experimental solubility data at 423.15 K: ◊, CO2−pure water system; ○, CO2−H2O−1 mol/kg NaCl; △, CO2− H2O−3 mol/kg NaCl; and □, CO2−H2O−6 mol/kg NaCl. I



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⎛ (((A(T /K) + B)mNaCl + C(T /K) + D)(P /bar) + (E(T /K) + F )mNaCl + G(T /K) + H ) ⎞ SF(T , P , mNaCl ) = exp⎜ ⎟ R(T /K) ⎝ ⎠ (13)

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with A = 0.006413, B = −2.244, C = −0.10636, D = 46.495, E = −0.1665, F = 497.03, G = 9.0325, and H = −3094.1 The maximum relative standard deviation (RSD) between experimental solubility and results given by the fitted polynomial is 14.58% at 323.15 K, 14.97 MPa, and 3 mol/kg NaCl molality. The minimum RSD obtained is 0.08% at 323.15 K and 10.03 MPa in pure water. The average of all RSDs is 4.73%. In most cases (29 cases), the gap between the calculated and experimental data is less than 6%, and in 8 cases, the deviation is between 6 and 9%; only in 3 cases does the gap exceed 9%. The numerical values for CO2 solubility calculated from this mathematical tool the and RSD are given in Table 4. The consistency of solubility calculated with experimental data at 323.15, 373.15, and 423.15 K is respectively shown in Figures 9, 10, and11.

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CONCLUSIONS A new apparatus and an analytical method were used to investigate the CO2 solubility in salty aqueous solutions. The potentiometric titration was validated through a solubility measurement on a well-investigated CO2−pure water system at 323.15 K and up to 20 MPa. The CO2−H2O−NaCl system at 1 mol/kg in the temperature range of 323.15 to 423.15 K and at 3 mol/kg at 323.15 and 373.15 K was studied, and the data obtained were in agreement with the available literature data. At 3 mol/kg, 423.15 K, and 6 mol/kg, T = (323.15, 373.15, and 423.15 K) data are very scarce, so four original isotherms have been constructed under these conditions. All experimental results presented an uncertainty of 3.5% with the ANOVA calculation method. Forty new experimental solubility data points were obtained. A simple mathematical tool was developed for the CO2 solubility calculation. These new data and the empirical model are now available for the precise calculation of the CO2 storage capacity in saline aquifers or for any other geochemical applications. Furthermore, the experimental device will be used to study the CO2 solubility in other salty solutions, such as CaCl2 and CaSO4 under the same conditions of temperature and pressure. This will allow us to calculate precisely the CO2 solubility in complex salt solutions and open a new range of applications.

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. Funding

This work was supported by ANR grant SIGARRR (ANR-13SEED-0006) and TOTAL SA. (Project Carbon Capture, Use and Storage). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors want to thank Mr. Pierre Chiquet from Total. J



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