The influence of Na2SO4 on the CO2 solubility in water at high pressure

Fluid Phase Equilibria 238 (2005) 220–228

The influence of Na2SO4 on the CO2 solubility in water at high pressure M.D. Bermejo a , A. Mart´ın a , L.J. Florusse b , C.J. Peters b,∗ , M.J. Cocero a a

Department of Chemical Engineering and Environmental Technology, University of Valladolid, Prado de la Magdalena s/n, 47011 Valladolid, Spain b Physical Chemistry and Molecular Thermodynamics, Department of Chemical Technology, Faculty of Applied Sciences, Delft University of Technology, Julianalaan 136, 2628 BL Delft, The Netherlands Received 23 March 2004; received in revised form 5 October 2005; accepted 6 October 2005

Abstract Supercritical water oxidation (SCWO) is a very efficient process for the destruction of organic wastes. In this type of processes, conversions higher than 99% can be achieved with residence times shorter than a minute. The effluent of this process is a mixture of water, CO2 and inorganic salts. For modeling this process, it is necessary to have reliable experimental data of the system water–carbon dioxide–inorganic salts. These data are scarce in literature, especially at high pressures. The solubility of CO2 in water and aqueous solutions of Na2 SO4 was determined in the temperature range between 288 and 368 K, pressures up to 14 MPa were applied, Na2 SO4 concentrations of 0.25, 0.5 and 1 mol Na2 SO4 /kg water were used, and the CO2 molar fractions were 0.0075, 0.01 and 0.0125. As expected, the data obtained showed that equilibrium pressure increases with temperature and CO2 concentration. A salting out effect is observed. The experimental data were compared to available literature data and the CO2 –water data were consistent with literature data, but for the equilibrium pressure of the bubble points in a solution of 1 mol Na2 SO4 /kg water, a systematic overpressure of approximately about 1 MPa with respect to some of literature data is found. The system CO2 –H2 O–Na2 SO4 was modeled using the Anderko–Pitzer EOS, specially developed for water–salt systems at high temperatures and pressures. Experimental data were used for obtaining parameters in the range of pressure and temperature of the data. In this range they differ with an average deviation of %
P = 4.64% in total pressure from the experimental results. However, extrapolated results from the Anderko–Pitzer EOS are poor. In order to extend the region of applicability of the EOS, it will be necessary to adjust the parameters in the appropriate range of temperature and concentration. © 2005 Elsevier B.V. All rights reserved. Keywords: CO2 solubility; Electrolyte solution; LV equilibrium; Sodium sulphate; Anderko–Pitzer EOS; SCWO

1. Introduction Supercritical water oxidation (SCWO) is the process that comprises the oxidation of organic solutes in an aqueous medium at temperatures and pressures above the critical point of water (647.3 K and 22.12 MPa). Its main application is destruction of organic waste. Conversions higher than 99% can be achieved with residence times shorter than a minute. High conversions can be explained by the sharp change in the thermo-physical properties of water near its critical point. The dielectric constant

∗

Corresponding author. E-mail addresses: [email protected] (C.J. Peters), [email protected] (M.J. Cocero). 0378-3812/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.fluid.2005.10.006

of water decreases sharply in the near critical region, so SCW behaves then as a non-polar solvent, i.e., non-polar compounds are completely soluble in SCW, while salts become insoluble in water at supercritical conditions. Supercritical water also shows complete miscibility with “permanent gases” as oxygen and nitrogen [1]. The combination of solvation properties and other physical properties makes SCW a very suitable medium for the oxidation of organic wastes. Products of hydrocarbon oxidation in SCWO are carbon dioxide and water. Hetero-atomic groups are converted into inorganic compounds, usually acids, salts, or oxides in high oxidation states [2]. The study of the system CO2 –water–inorganic salts is important in the SCWO process, as the effluent of the SCWO reactor mainly consists of these components. But this is not the only field where this system plays an important role. Solubility data

M.D. Bermejo et al. / Fluid Phase Equilibria 238 (2005) 220–228

of weak electrolyte gases, like carbon dioxide, must be known for the design of separation equipment in many applications in the oil related industry [3]. A high-pressure study of this system is important for the design of supercritical extraction processes [4]. Solubility data of carbon dioxide in water and aqueous salt solutions is required in the modeling of many enhanced oil and bitumen recovery processes [5]. Application is also found in geochemistry and natural gas systems as well as in the design of power cycles, the latter application for apparent reasons being closely related to the SCWO process. Several data series of the system CO2 –water and CO2 – water–inorganic salts have been found in literature. To mention only a few: (1) Nighswander et al. measured the CO2 solubility in pure water and in a 1 wt% aqueous NaCl solution at pressures up to 10 MPa and temperatures from 353 up to 473 K. The system was modeled using the Peng–Robinson EOS to represent the vapor phase and an empirical Henry’s law constant correlation for the liquid phase [5]. (2) Bamberger et al. reported data of the system CO2 –water from 313 up to 353 K and pressures up to 14 MPa. Their results are correlated using the modification of Melhem for the Peng–Robinson EOS and the mixing rule of Panagiopoulos and Reid, including temperature-dependent binary interaction parameters [4]. (3) Wiebe and Gaddy measured the solubility of CO2 in liquid water at pressures up to 70 MPa and temperatures up to 373 K [6,7]. Also the vapor phase composition of CO2 –water mixtures at various temperatures and at pressures up to 70 MPa [8] has been determined experimentally. (4) Zawisza and Malesinka measured the solubility of CO2 in liquid water and also of water in gaseous CO2 in the range 0.2–5 MPa at temperatures up to 473 K [9]. (5) Some reviews that collects, evaluate and develop different models for predicting the solubility of CO2 in water has been published recently [10–12]. (6) Prutton and Savage published the solubility of CO2 in water and CaCl2 solutions at 348, 373 and 393 K and pressures up to 70 MPa [13]. (7) Rumpf et al. measured the solubility of CO2 in aqueous Na2 SO4 solutions (1 and 2 mol Na2 SO4 /kg water) and (NH4 )2 SO4 (2 and 4 mol Na2 SO4 /kg water) in a temperature range from 313 to 433 K and pressures up to 10 MPa [3]. Some data of this systems can be found in [14] and data of this systems an other CO2 –water–electrolyte systems at low pressures can be found in [15] and [16]. (8) Other papers that contains experimental data of the CO2 –water–electrolyte systems are [17–21]. The objective of this work is to study the system CO2 –water in presence of an inorganic salt in order to get enough data to validate a thermodynamic model to describe the system. Therefore, it was decided to measure the CO2 solubility in water and aqueous solutions of Na2 SO4 (0.25, 0.5 and 1 mol Na2 SO4 /kg H2 O) for various CO2 molar fractions (0.0075, 0.01 and 0.0125), in

221

the temperature range between 288 and 368 K and for pressures up to 14 MPa. For the correlation of the experimental data, the Anderko and Pitzer EOS [22] has been chosen. This EOS was developed in order to represent volumetric properties as well as vapor–liquid and solid–liquid equilibria of aqueous salt solutions in water at high pressures and temperatures. The equation consists of a reference part and a perturbation contribution. The reference part represents the properties of a mixture of hard sphere ion pair and dipolar solvent molecules. This EOS considers a fully ion-paired molecular basis for the salt. This basis is satisfactory for concentrated solutions and for diluted solutions at vapor-like densities, and precludes accuracy in the dilute region when the dielectric constant is large enough to allow substantial dissociation. In the Anderko and Pitzer [22] model, the EOS parameters were fitted to an extensive amount of experimental data of the system water–NaCl in the temperature range from 573 to 773 K and to a more limited amount of data above 773 K and pressures up to 500 MPa. In both temperature regions, the EOS reproduces the LV equilibrium, volumetric properties and solubility of solid NaCl within the experimental uncertainty. Anderko–Pitzer also used their EOS for fitting water–KCl data and water–NaCl–KCl data in the same PT range [23]. Jiang and Pitzer used the EOS for the Water–CaCl2 system [24]. Later Duan et al. used the EOS for the systems H2 O–CO2 –NaCl [25], H2 O–CH4 –NaCl and H2 O–CO2 –CH4 –NaCl [26]. In 2001, Kosinski and Anderko extended the EOS to multicomponent water–salt–non-electrolyte systems and developed a corresponding-states methodology for systems for which very little experimental information is available. In addition, they readjusted water and salt parameters for temperatures below 573 K [27]. 2. Experimental For all measurements, a Cailletet apparatus was used. It operates according to the synthetic method, i.e., a sample of known overall composition was used. A schematic representation of the Cailletet apparatus is given in Fig. 1.

Fig. 1. Schematic representation of a Cailletet apparatus.

M.D. Bermejo et al. / Fluid Phase Equilibria 238 (2005) 220–228

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The Cailletet tube consists of a thick-walled Pyrex glass and has a length of about 500 mm and an inner and outer diameter of 3 and 10 mm, respectively. One end is closed and the other end is open. Close to the open end of the tube, a conical thickening is present that allows the tube to be mounted into a stainless steel autoclave. The sample can be confined inside the closed end of the Cailletet tube using mercury as a sealing and pressure transmitting fluid. Within the autoclave, the open end of the tube is always immersed in mercury separating the sample from the hydraulic oil. A hand screw pump outside the autoclave pressurizes the system. A small steel ball inside the top of the tube allows stirring of the sample magnetically. A pressure balance (Budenberg) in combination with a hand screw pump was used to measure pressures and to maintain a constant pressure. The pressure balance has been designed for a range of 0.35–14 MPa, with a maximum accuracy of 0.005 MPa. The Cailletet tube is jacketed and water is employed as a thermostatic fluid. The range of working temperatures is from 283 to 368 K. The thermometer employed is a Pt 100 with an accuracy of 0.01 K. A more detailed description about the experimental facility and the experimental procedures as well can be found elsewhere [28,29]. The measurements obtained from the Cailletet facility comprise the determination of liquid–vapor two-phase boundary. Therefore, first the temperature is adjusted at a fixed value and the pressure is brought to a value where two phases, liquid and vapor, exist. Then the pressure is gradually increased until the vapor phase just disappears. It is essential that after each change in pressure, equilibrium between the coexisting phases be established. At the pressure where the vapor phase just disappears a homogeneous liquid phase is obtained and consequently the composition of this liquid is the same as the original overall composition. A point on the two-phase boundary is obtained when a small change in pressure results in formation of a vapor phase or elimination of the existing vapor phase. In preparing the sample, the top of the Cailletet tube is filled with a weighted amount of the aqueous Na2 SO4 solution, weighed with an accuracy of 0.0001 g. Then the aqueous solution is degasified: the sample is frozen, employing for freezing a mixture of ethyl alcohol and liquid nitrogen, and melted and

the released gases are removed several times under high vacuum conditions. The next step is adding a known quantity of CO2 into the top of the Cailletet tube, using mercury. For that purpose, a known volume of 67.43 cm3 is filled with a quantity of CO2 whose temperature and pressure are measured (pressure error = 0.01 cm Hg, temperature error = 0.1 K). Finally, the Cailletet tube is removed from the gas-dosing apparatus and then mounted into the stainless steel autoclave, the autoclave is closed and by means of a hydraulic system pressure is applied. For the experiments double distilled water was used. CO2 (99.995 vol%) and Na2 SO4 ·10H2 O (purity > 99 wt%) were purchased from Hoek-Loos and Merck, respectively. All chemicals were used without further purification. 3. Experimental results The solubility of CO2 in water and Na2 SO4 solutions (0.25, 0.5 and 1 mol/kg water) for different CO2 molar fractions (0.0075, 0.01 and 0.0125) were measured. Experimental results are shown in Tables 1–5. The measured isopleths for different Na2 SO4 solutions are shown in Fig. 2. It can be seen that the equilibrium pressure of the bubble point increases with temperature, and CO2 concentration. Also a salting-out effect exists, where for higher Na2 SO4 concentrations the solubility of CO2 decreases for the same temperature and pressure. It can be seen too, that for very similar CO2 and salt concentration the equilibrium pressure can be quite different. 4. Modeling 4.1. The Ankerko–Pitzer EOS The Anderko–Pitzer EOS for aqueous salt solutions [22,27] has been used to fit the experimental data presented in this work. The EOS has been generated from Helmholtz energy. It consists of a reference part and a perturbation contribution, as is shown in Eq. (1): ares = aref + aper

(1)

Table 1 Results for the system containing 0.986703 ± 0.000018 mol Na2 SO4 /kg H2 O xCO2 = 0.00773 ± 0.00003

xCO2 = 0.01026 ± 0.00003

xCO2 = 0.01155 ± 0.00004

xCO2 = 0.01304 ± 0.00004

P (MPa)

T (K)

P (MPa)

T (K)

P (MPa)

T (K)

P (MPa)

T (K)

3.54 4.35 5.27 5.90 6.40

299.31 307.78 317.53 322.93 327.19

4.70 6.54 8.09 9.16 10.09 10.51 11.82 12.44 13.11

298.30 310.86 319.63 325.29 330.34 332.74 340.10 344.05 349.42

4.47 5.02 5.39 6.27 7.32 8.04 8.57 9.77 10.50 10.80 12.15 12.79

291.75 295.23 297.63 302.59 307.71 310.66 312.88 316.64 318.77 319.73 323.60 325.37

4.84 5.28 5.76 7.16 7.96 9.66 10.17

286.97 289.51 291.57 295.03 296.31 297.63 298.15

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Table 2 Results for the system containing approx. 1 mol Na2 SO4 /kg H2 O mNa2 SO4 = 0.996313 ± 0.000018

mNa2 SO4 = 0.995676 ± 0.000018

xCO2 = 0.01161 ± 0.00004

xCO2 = 0.01154 ± 0.00004

xCO2 = 0.00986 ± 0.00003

P (MPa)

T (K)

P (MPa)

T (K)

P (MPa)

T (K)

4.80 5.62 6.72 7.14 7.64 8.06 8.55 9.46 10.48

294.20 299.02 304.65 306.52 308.12 310.03 311.69 313.77 316.51

5.72 8.89

300.42 313.45

4.65 5.19 5.88 6.86 7.39 8.56 9.31 10.26 11.24 11.63

298.97 303.13 308.02 314.54 317.86 325.03 329.54 335.38 342.19 345.02

Table 3 Results for the system containing 0.50154 ± 0.00004 mol Na2 SO4 /kg H2 O xCO2 = 0.00744 ± 0.00004

xCO2 = 0.01002 ± 0.00004

xCO2 = 0.01249 ± 0.00005

P (MPa)

T (K)

P (MPa)

T (K)

P (MPa)

T (K)

2.50 2.74 3.15 3.35 3.71 4.04 4.44 5.07 5.69 6.21 6.66

298.84 304.01 309.52 312.44 317.79 322.30 328.34 338.06 347.87 357.52 367.20

3.56 3.72 3.97 4.62 5.14 5.50 6.27 7.19 8.17 8.86 9.32 3.08 4.50

298.02 300.06 302.97 310.27 315.71 319.73 327.87 337.41 348.39 356.66 362.62 299.05 309.67

3.03 3.25 3.44 4.04 5.24 6.58 8.10 8.90 9.84 11.00 11.13

289.23 291.45 293.38 298.89 308.51 318.04 328.08 333.26 339.66 348.05 349.26

Table 4 Results for the system containing 0.249711 ± 0.000016 mol Na2 SO4 /kg H2 O xCO2 = 0.00780 ± 0.00003

xCO2 = 0.01026 ± 0.00004

xCO2 = 0.01289 ± 0.00005

P (MPa)

T (K)

P (MPa)

T (K)

P (MPa)

T (K)

1.98 2.46 3.10 3.63 4.28 4.75 5.25 5.71

298.40 307.73 318.98 328.26 339.37 348.45 358.07 368.81

2.57 3.22 4.06 4.89 5.69 6.41 7.13 7.72

298.20 307.19 317.60 327.45 337.20 345.93 355.81 364.57

3.54 4.69 5.64 6.96 8.26 9.66 10.64 11.32

298.20 309.18 318.04 327.87 337.88 349.65 359.57 367.44

The reference part: represents the properties of a mixture of hard sphere ion pairs and dipolar solvent molecules, as can be seen in Eq. (2): aref (T, v, x) = aion pair

ion pair

+ asolvent

+ aion pair

solvent

solvent

(2)

The ion pairs can be treated as a strong dipole, and the solvent molecules can be approximated by dipoles of smaller magnitude. Therefore, Eq. (3) can be written as:

aref (T, v, x) = arep (v, x) + adip (T, v, x)

(3)

A mixture of hard spheres of diameters σ i is used as the repulsive contribution. The Helmholtz energy for a hard sphere mixture is given by Eq. (4): arep (3 · DE/F )η − (E3 /F 2 ) (E3 /F 2 ) = + RT 1−η (1 − η)2
3  E + − 1 · ln(1 − η) F2

(4)

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224 Table 5 Results for the system CO2 –H2 O xCO2 = 0.00764 ± 0.00003

xCO2 = 0.01000 ± 0.00003

xCO2 = 0.01258 ± 0.00004

P (MPa)

T (K)

P (MPa)

T (K)

P (MPa)

T (K)

1.55 2.02 2.56 2.74 3.04 3.58 4.07 4.28 4.67 5.07

296.73 307.68 319.03 323.08 327.92 338.12 347.35 352.67 358.73 367.86

1.99 2.53 3.17 3.72 4.49 5.03 5.61 6.09

299.82 309.39 318.93 327.35 338.40 347.48 357.84 366.54

2.63 3.24 4.07 5.01 5.94 6.70 7.54 8.34

299.98 307.81 317.53 327.84 338.17 347.03 357.42 369.65

where D, E and F can be calculated from molar fractions and hard sphere diameters. The reduced density η is defined by Eq. (5): η=

bi 4v

(5)

where A2 and A3 for pure dipolar fluid are calculated from Eqs. (7) and (8): A2 =

−4 4 µ · η · I2 (η) 3 R

(7)

A3 =

10 6 2 µ · η · I3 (η) 9 R

(8)

where v is the molar volume and b is the van der Waal’s covolume parameter. The dipolar contribution to the Helmholtz energy is expressed as shown in Eq. (6):

with µR as the reduced dipole moment, which is defined by Eq. (9).
2 1/2 µ (9) µR = σ 3 kT

adip A2 = A2 + A 3 + · · · ≈ RT 1 − A2 /A3

In Eq. (9), µ is the dipole moment and k is the Boltzmann constant.

(6)

Fig. 2. Comparison of the calculated data vs. the experimental data. (a) CO2 solubility in water, (b) CO2 solubility in an aqueous solution of Na2 SO4 (0.25 mol/kg H2 O), (c) CO2 solubility in an aqueous solution of Na2 SO4 (0.5 mol/kg H2 O) and (d) CO2 solubility in an aqueous solution of Na2SO4 (1 mol/kg H2 O).

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225

The perturbation contribution takes into account effects that are not represented by the reference terms and comprises a virial-type expansion truncated after the fifth virial coefficient, as shown in Eq. (10).

Table 6 Coefficients for calculating pure CO2 parameters for T < 400 K

aper

0 1 2 3 4 5

RT

=−

4a η(1 + cη + dη2 + eη3 ) RTb

(10)

The first term of this equation is equivalent to the van der Waals’ attractive term. The correction coefficients c, d and e are necessary to represent the properties of pure water with an accuracy that is necessary for further applications of the equation to mixtures. The coefficients a, c, d and e are different for any pure component, and may be fitted using experimental volumetric and equilibrium data. The expression developed for mixtures by Anderko and Pitzer [22] is presented in Eqs. (11) and (12).
 aper 1 a acb adb2 aeb3 =− + (11) + + RT RT v 4v2 16v3 64v4 In the mixing rules binary, ternary, etc., parameters (α, γ, δ and ε) are present, which have to be estimated by fitting to experimental data of the binary or ternary system. Further information about the calculation with this EOS is available in [22].

i

The parameters a, b, c, d and e for pure water were fitted by Kosinski and Anderko [27] to data generated from the comprehensive EOS of Hill [30]. PVT data from 373 to 1200 K and pressures up to 550 MPa were used for this purpose. With these parameters the EOS reproduce vapor pressures of water and densities of pure water from 373 to 1200 K.

a × 10−7 (bar cm6 mol−1 )

c

d

e

9.3158 −52.201 118.06 −129.85 69.802 −14.713

−83.506 470.74 −1051.9 1149.2 −614.78 129.18

21.933 −51.352 49.416 −16.109 0 0

−176.44 500.78 −491.38 163.02 0 0

4.4. Pure CO2 parameters Pure CO2 parameters were fitted using density and vapor pressure data generated by the Span–Wagner reference EOS [31] up to temperatures of 400 K. The dipole moment of CO2 was taken µ = 0. The resulting parameters are shown in Eqs. (15) and (16). The coefficient p in Eq. (16) represents coefficients a, c, d and e. The values of the coefficients pi (= ai , ci , di , ei ) of Eq. (16) are presented in Table 6. bCO2 (cm3 mol−1 ) = 49.52 p=

4.2. Pure water parameters

p

(15)

p5 p4 p3 p2 p1 + 4+ 3+ 2+ + p0 Tr5 Tr Tr Tr Tr

(16)

4.5. Binary parameters H2 O–CO2 The binary parameters of the system H2 O–CO2 were fitted using the equilibrium data of the system CO2 –water presented in this work. The calculation of the parameter is shown in Eqs. (17) and (18):

4.3. Pure Na2 SO4 parameters

αij = α3 · T 2 + α1 · T + α0

(17)

The parameters a, b, c, d and e for Na2 SO4 were calculated from the NaCl parameters fitted by Kosinsky and Anderko [27] for temperatures higher than 573.15 K. Using these parameters, the Na2 SO4 parameters and dipole moment can be calculated by the corresponding states principle, as proposed by Kosinski and Anderko [27], for systems where the experimental data are scarce, as shown in Eqs. (12)–(14).

γijk = δijkl = εeijklm = 1

(18)

aNa2 SO4 = kNa2 SO4

NaCl

· aNaCl

(12)

bNa2 SO4 = lNa2 SO4

NaCl

· bNaCl

(13)

µNa2 SO4 = mNa2 SO4

NaCl

· µNaCl

where i, j, k, l, m = H2 O and CO2 . The coefficients of these equations are shown in Table 7. 4.6. Binary parameters H2 O–Na2 SO4 For the binary interaction parameters of the system H2 O–Na2 SO4 parameters fitted Kosinsky and Anderko [27] for the system H2 O–NaCl were used.

(14)

In these equations, k, l, m are temperature-independent proportionality constants that must be fitted for each salt, and a and b are the first parameters of the pure salt and µ is the dipole moment of NaCl (µNaCl = 6.4 D). For the other parameters those adjusted for NaCl can be taken in the same temperature range. In this work, the values of the k, l and m are taken as 1, i.e., k=l=m=1

Table 7 Coefficients for calculating binary interaction parameters in the system H2 O–CO2 i

αi

0 1 2

−5.5910 3.1189 × 10−2 −3.7559 × 10−5

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226

Table 8 Coefficients for calculating binary parameters for the system CO2 –Na2 SO4 i

αi

0 1 2 3

−46.686 4.1452 × 10−1 −1.1943 × 10−3 1.1549 × 10−6

The ternary parameters are γ ijk = δijkl = εijklm = 1, where i, j, k, l, m = H2 O, CO2 and Na2 SO4 . 5. Discussion 5.1. Modeling

4.7. Binary parameters for the system CO2 –Na2 SO4 and ternary parameters for the system H2 O–CO2 –Na2 SO4 The binary parameters of the system CO2 –Na2 SO4 and the ternary parameters of the system H2 O–CO2 –Na2 SO4 were evaluated from the experimental data of the ternary system H2 O–CO2 –Na2 SO4 presented in this work, i.e., they are valid at temperatures from 300 to 370 K. The binary parameter for the system CO2 –Na2 SO4 are presented in Eqs. (19) and (20): αij = α3 · T 2 + α2 · T 2 + α1 · T + α0

(19)

γijk = δijkl = εijklm = 1

(20)

where i, j, k, l, m = CO2 and Na2 SO4 . The coefficients of Eq. (19) are summarized in Table 8.

Fig. 2 shows the bubble point predictions of CO2 as calculated by the Anderko–Pitzer EOS. Moreover, Fig. 2 also compares to the experimental data to the model predictions. It can be seen that the EOS reproduces accurately the liquid–vapor equilibrium of the system in the experimental region. The equilibrium pressures are calculated with an average deviation of %
P = 4.6% and a maximum deviation of %
P = 18.4% at a temperature at 286 K with a salt concentration of 1 mol Na2 SO4 /kg H2 O. 5.2. Comparison to literature data In order to compare the experimental data with the literature data, an interpolation is made. For that purpose, the data are calculated at 313.15, 323.15, 333.15, 348.15 and 353.15 K, and plotted as a curve of pressure versus xCO2 (see Fig. 3). These data have been calculated with the Anderko–Pitzer EOS

Fig. 3. Comparison of our data with those from literature, and validation of the EOS results. (a) CO2 solubility in water at 313.15 K, (b) CO2 solubility in water at 323.15 K, (c) CO2 solubility in water at 333.15 K, (d) CO2 solubility in water at 348.15 K and (e) CO2 solubility in water at 353.15 K.

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227

in order to show the behavior of the EOS with another series of data. It can be seen that the presented data, in general, do agree well with literature data. In the system CO2 –water, the literature data correlates our data with an relative average deviation in total pressure of %
P = 3.4%, but in the system of concentration 1 mol/kg H2 O of Na2 SO4 exists a systematic overpressure of about 1 MPa with respect literature data, and the relative average deviation is %
P = 13.6%. The correspondence between calculated data and experimental data is very good. For the CO2 –H2 O system, the average deviation in total pressure is %
P = 3.73% and it is possible to extrapolate to higher CO2 concentrations. For the CO2 –H2 O–Na2 SO4 system, the average total pressure deviation is %
P = 4.64% in the range of validity of the parameters, salt concentration the extrapolation becomes poor, predicting lower pressure than those of experimental data found in literature [3,14]. This is probably because this EOS is very sensitive to the value of the parameters. In order to apply this EOS in a wider P–T–x range, a new fitting will be necessary.

d e k P R T Tr v x

6. Conclusions

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The solubility of CO2 in water and aqueous solutions of Na2 SO4 was determined in the temperature range between 288 and 368 K, pressures up to 14 MPa were applied, Na2 SO4 concentrations of 0.25, 0.5 and 1 mol Na2 SO4 /kg water were used, and the CO2 molar fractions were 0.0075, 0.01 and 0.0125. As expected, the data obtained showed that equilibrium pressure increases with temperature and CO2 concentration. A salting out effect is observed. The experimental data were compared to available literature data and the CO2 –water data were consistent with literature data, but for the equilibrium pressure of the bubble points in a solution of 1 mol Na2 SO4 /kg water, a systematic overpressure of approximately about 1 MPa with respect to some of literature data [3] is found. The system CO2 –H2 O–Na2 SO4 was modeled using the Anderko–Pitzer EOS. Experimental data were used for obtaining parameters in the range of pressure and temperature of the data. In this range, model predictions differ with an average deviation of %
P = 4.64% in total pressure from the experimental results and it is possible to extrapolate to higher CO2 concentrations. However, calculated vapor pressures, increasing salt concentrations, are lower than literature data. In order to extend the region of applicability of the EOS, it will be necessary to adjust the parameters in the appropriate range of temperature and concentration. List of symbols a pure substance parameter of Anderko–Pitzer EOS (bar cm6 mol−1 ) b pure substance parameter of Anderko–Pitzer EOS (cm3 mol−1 ) c pure substance parameter of Anderko–Pitzer EOS

pure substance parameter of Anderko–Pitzer EOS pure substance parameter of Anderko–Pitzer EOS Boltzman constant (J K−1 ) pressure (MPa) Ideal gases constant (J mol−1 K−1 ) temperature (K) reduced temperature molar volume (cm3 mol−1 ) molar fraction in the liquid

Greek letters α interaction parameter of Anderko–Pitzer EOS δ interaction parameter of Anderko–Pitzer EOS ε interaction parameter of Anderko–Pitzer EOS γ interaction parameter of Anderko–Pitzer EOS µ dipole moment (D) µR dipole moment η reduced density σ Hard sphere diameter (cm) References

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