Experimental Determination and Prediction of Gas Solubility Data for

Jul 15, 2003 - Jörn Kiepe, Sven Horstmann, Kai Fischer, and Jürgen Gmehling. Industrial & Engineering Chemistry Research 2004 43 (20), 6607-6615...
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Ind. Eng. Chem. Res. 2003, 42, 3851-3856

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Experimental Determination and Prediction of Gas Solubility Data for CO2 + H2O Mixtures Containing NaNO3 or KNO3 Jo1 rn Kiepe,† Sven Horstmann,‡ Kai Fischer,‡ and Ju 1 rgen Gmehling*,† Department of Industrial Chemistry, University of Oldenburg, D-26111 Oldenburg, Germany, and Laboratory for Thermophysical Properties (LTP GmbH), Institute at the University of Oldenburg, D-26111 Oldenburg, Germany

In a continuation of earlier investigations, gas solubility data of carbon dioxide (CO2) in aqueous sodium and potassium nitrate solutions (NaNO3, KNO3) were measured using the static synthetic method in a temperature range from 313 to 373 K, for pressures up to 10 MPa and molalities up to 10 mol‚kg-1. Additionally, Henry coefficients were derived from these experimental P-x data, and the experimental data were used to fit interaction parameters for an equation of state approach, which consists of a combination of the predictive Soave-Redlich-Kwong (PSRK) group contribution equation of state and the LIFAC method for the prediction of vapor-liquid equilibria in systems with strong electrolytes. 1. Introduction Reliable information on phase equilibrium behavior is required for the design and optimization of thermal separation and chemical conversion processes as an important topic in chemical engineering. The predictive Soave-Redlich-Kwong (PSRK) group contribution equation of state (EoS)1,2 is widely used in commercial process simulations for the prediction of vapor-liquid equilibria and gas solubilities of nonelectrolyte systems. In many cases, for example, petroleum refining, gas processing, coal gasification, environmental protection, gas antisolvent salt crystallization, petroleum and natural gas exploitation, gas hydrate formation, and various absorption processes, the influence of electrolytes on the phase equilibrium behavior has to be considered for the design of the different industrial processes. To describe also the phase equilibrium behavior of electrolyte systems containing supercritical components, the PSRK EoS was extended by being combined with the LIFAC group contribution method.3 In this approach, the influence of the strong electrolytes on the activity coefficients of the nonelectrolytes is considered using the LIFAC model in the PSRK mixing rule.4 The published group interaction parameters of the PSRK and LIFAC model can be used directly, and only the gas-ion interaction parameters have to be fitted to experimental data. In an earlier article, several experimental gas solubility data for the systems CO2 + H2O + NaCl (KCl) obtained with the static synthetic technique were presented.5 The reliability of the experimental approach has been verified on the basis of experimental data from different authors. These investigations are continued herein as an ongoing investigation of CO2 solubility in aqueous NaNO3 and KNO3 mixtures at temperatures between 40 and 100 °C and pressures up to 10 MPa. * To whom correspondence should be addressed. Tel.: +49(0)441-798-3831. Fax: +49-(0)441-798-3330. E-mail: [email protected]. † Department of Industrial Chemistry, University of Oldenburg. ‡ Laboratory for Thermophysical Properties (LTP GmbH), Institute at the University of Oldenburg.

The experimental P-x data and derived Henry coefficients obtained in this work are presented in comparison to results calculated using regressed interaction parameters for the PSRK model and also to the data of the former work,5 to show the influence of the different ionic species on the phase equilibrium behavior. Experimental Section 2.1. Materials. Water was distilled twice and then degassed as described before.6 Carbon dioxide (Lu¨bke, purity 99.995%) was used without any further purification. Sodium nitrate and potassium nitrate (Roth, purity > 99%) were dried in a vacuum oven at 80 °C. 2.2. Apparatus and Procedure. For the gas solubility measurements (isothermal P-x data), the same static apparatus as described by Kiepe et al.5 was used. The equipment and measurement procedure were described in detail before.6,7 In this synthetic method, the system pressure is measured at constant temperature for different overall compositions. The apparatus can be operated at temperatures between 200 and 500 K and pressures up to 15 MPa. To determine the global compositions, the quantities of pure substances charged into the stirred equilibrium cell have to be known precisely. The salts are weighed into the cell, after which the cell is evacuated and placed in a thermoregulated oil bath. The purified and degassed water and liquefied carbon dioxide are charged into the cell as compressed liquids using piston injectors (Ruska, model 2200-801), which allows for precise recording of volume differences. After equilibration is reached, the pressure inside the cell is measured with a pressure sensor (Druck, model PDCR 911, range ) 0-13.5 MPa, accuracy ) 0.1 kPa + 0.0001P), and the temperature is monitored with a Pt(100) resistance thermometer (Hart Scientific, model 1560, estimated accuracy ) 0.03 K). The pressure sensor was calibrated with a pressure balance (Desgranges & Huot, model 21 000). Because only temperatures, pressures, total loadings, and total volumes are measured, the compositions of the coexisting phases have to be determined by evaluation of the raw data. This evaluation procedure is quite complex and was described in detail by Fischer and

10.1021/ie030197e CCC: $25.00 © 2003 American Chemical Society Published on Web 07/15/2003

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Table 1. Experimental Gas Solubility Data for the System CO2 (1) + H2O (2) + NaNO3 (3) at 40 °C and Different Salt Concentrations m ) 1.00 mol ‚(kg of water)-1 T ) 313.19 K

m ) 2.49 mol ‚(kg of water)-1 T ) 313.20 K

Table 2. Experimental Gas Solubility Data for the System CO2 (1) + H2O (2) + NaNO3 (3) at 80 °C and Different Salt Concentrations m ) 1.00 mol‚(kg of water)-1 T ) 353.13 K

m ) 2.50 mol‚(kg of water)-1 T ) 353.15 K

x1,salt-free

P (kPa)

x1,salt-free

P (kPa)

x1,salt-free

P (kPa)

x1,salt-free

P (kPa)

0.000 00 0.000 20 0.001 05 0.002 95 0.004 11 0.005 93 0.009 39 0.015 41 0.021 09

6.94 59.92 288.44 809.22 1134.2 1657.0 2701.2 4773.3 7463.2

0.000 00 0.001 01 0.001 98 0.002 93 0.004 74 0.007 85 0.016 24 0.019 41

6.71 303.76 593.72 881.71 1447.2 2474.0 5908.7 7931.2

0.000 00 0.000 17 0.001 00 0.001 76 0.003 14 0.009 15 0.010 65 0.013 28 0.015 41 0.017 21

46.78 127.81 515.02 880.97 1554.8 4788.2 5702.1 7466.2 9116.4 10 762

0.000 00 0.000 26 0.000 66 0.001 09 0.001 61 0.005 34 0.007 37 0.011 03 0.012 77 0.014 40 0.015 56

45.25 195.97 428.23 672.95 973.68 3156.9 4387.8 6719.2 7911.4 9116.8 10 054

m ) 5.00 mol‚(kg of water)-1 T ) 313.21 K

m ) 9.79 mol‚(kg of water)-1 T ) 313.18 K

x1,salt-free

P (kPa)

x1,salt-free

P (kPa)

0.000 00 0.000 89 0.001 75 0.003 16 0.004 41 0.007 34 0.010 13 0.014 32

6.60 342.15 672.17 1227.6 1742.5 3030.2 4424.8 7233.0

0.000 00 0.000 77 0.001 55 0.002 28 0.002 98 0.004 87 0.007 65 0.008 98 0.010 86

6.40 396.84 796.86 1186.6 1566.7 2664.6 4537.4 5612.0 7612.9

Wilken.7 From the known solvent feed (water + salt), the liquid-phase volume is determined using precise information about the density of the electrolyte solution inside the equilibrium chamber. Therefore, liquid densities of water + salt mixtures were measured as functions of temperature and salt content using a vibrating tube densimeter (Anton Paar, model DMA 4500).8 From the total volume of the cell, the remaining gas-phase volume can be calculated precisely. At given equilibrium conditions (temperature, gas-phase volume, and CO2 pressure), the amounts of CO2 in the gas phase and thus, also in the liquid phase are obtained. The reliability of this experimental method was verified before, and the results were compared to those obtained via a different experimental method.5 In the static method, several factors have an influence on the resulting liquid-phase compositions and derived Henry coefficients. These factors are the small amounts of solvents in the gas phase, the compressibility of the solvent under the gas pressure, the partial molar volume of the dissolved gas, and the solvent activity coefficient. They can be taken into account in two different ways, as described by Fischer and Wilken.7 In the first method, all effects are considered in an iterative isothermal and isochoric algorithm by solving the mass and volume balances. The second method makes use of EoS models, which offer the advantage of providing the auxiliary desired quantities given above directly. To test the reliability of the data treatment, both methods were applied to the raw data measured in this and the former work,5 whereupon identical results were obtained. The experimental error in the compositions can be found as σ(xi) ) 0.0001. 3. Results and Discussion The experimental P-x data from this work, which were obtained with the EoS raw data treatment approach mentioned above, are listed in Tables 1-6. From these data, Henry coefficients, H12, were derived using

m ) 5.00 mol‚(kg of water)-1 T ) 353.18 K

m ) 10.00 mol‚(kg of water)-1 T ) 353.20 K

x1,salt-free

P (kPa)

x1,salt-free

P (kPa)

0.000 00 0.000 99 0.001 53 0.001 72 0.002 18 0.004 31 0.006 43 0.008 37 0.010 25 0.011 85 0.013 47

42.63 718.76 1083.4 1214.8 1524.6 3001.5 4512.6 5965.8 7472.3 8868.6 10 446

0.000 00 0.000 07 0.000 23 0.000 48 0.000 94 0.001 43 0.002 57 0.004 01 0.005 34 0.006 67 0.007 76

37.97 118.63 284.00 537.10 1016.3 1536.3 2810.1 4554.6 6372.3 8483.0 10 620

Table 3. Experimental Gas Solubility Data for the System CO2 (1) + H2O (2) + NaNO3 (3) at 100 °C and Different Salt Concentrations m ) 1.01 mol‚(kg of water)-1 T ) 373.14 K

m ) 2.50 mol‚(kg of water)-1 T ) 373.20 K

x1,salt-free

P (kPa)

x1,salt-free

P (kPa)

0.000 00 0.000 62 0.001 89 0.002 53 0.009 40 0.010 71 0.011 62 0.013 57 0.015 76

96.01 445.85 1158.8 1524.0 5721.6 6598.9 7237.4 8675.3 10 448

0.000 00 0.000 20 0.001 12 0.001 74 0.003 02 0.005 31 0.007 31 0.008 97 0.011 20 0.012 44

94.56 225.53 807.56 1208.1 2055.5 3643.0 5138.7 6470.4 8439.8 9833.9

m ) 5.01 mol‚(kg of water)-1 T ) 373.22 K

m ) 10.08 mol‚(kg of water)-1 T ) 373.24 K

x1,salt-free

P (kPa)

x1,salt-free

P (kPa)

0.000 00 0.000 09 0.000 30 0.000 68 0.001 01 0.001 88 0.003 39 0.004 78 0.006 44 0.007 73 0.008 87 0.010 08

84.56 170.17 335.93 645.63 910.60 1626.5 2921.2 4189.4 5816.3 7191.6 8513.0 10 055

0.000 00 0.000 08 0.000 23 0.000 31 0.000 62 0.001 05 0.002 37 0.003 45 0.004 30 0.005 36 0.006 07

75.47 196.30 388.55 491.90 891.54 1460.8 3287.1 4906.3 6325.3 8277.0 9784.8

the EoS data treatment approach by computing

f1 ) φ∞1 PS2 x1f0x1

H12 ) lim

where f1 is the fugacity of the gas in the gas phase; x1 is the mole fraction of the gas in the liquid phase; φ∞1 is

Ind. Eng. Chem. Res., Vol. 42, No. 16, 2003 3853 Table 4. Experimental Gas Solubility Data for the System CO2 (1) + H2O (2) + KNO3 (3) at 40 °C and Different Salt Concentrations m ) 0.99 mol‚(kg of water)-1 T ) 313.19 K

m ) 2.50 mol‚(kg of water)-1 T ) 313.16 K

m ) 4.96 mol‚(kg of water)-1 T ) 313.20 K

x1,salt-free

P (kPa)

x1,salt-free

P (kPa)

x1,salt-free

0.000 00 0.001 03 0.002 94 0.004 25 0.006 07 0.011 88 0.015 19 0.019 11 0.022 62 0.023 71 0.024 45

7.44 278.20 785.35 1140.7 1639.5 3338.0 4406.4 5849.4 7506.9 8236.3 9072.5

0.000 00 0.000 95 0.001 91 0.003 73 0.005 49 0.010 40 0.012 66 0.016 81 0.019 27 0.021 77 0.022 54

7.21 274.21 545.78 1069.2 1587.7 3114.7 3874.8 5433.2 6534.6 8011.3 8789.3

P (kPa)

0.000 00 6.85 0.000 28 97.30 0.000 66 216.68 0.001 40 455.32 0.002 40 780.69 0.004 10 1346.4 0.007 59 2570.9 0.011 04 3900.1 0.014 40 5391.0 0.017 10 6874.6 0.018 70 8079.3 0.019 40 8986.8 Table 5. Experimental Gas Solubility Data for the System CO2 (1) + H2O (2) + KNO3 (3) at 80 °C and Different Salt Concentrations m ) 1.00 mol‚(kg of water)-1 T ) 353.32 K

m ) 2.49 mol‚(kg of water)-1 T ) 353.31 K

m ) 4.99 mol‚(kg of water)-1 T ) 353.17 K

x1,salt-free

P (kPa)

x1,salt-free

P (kPa)

x1,salt-free

P (kPa)

0.000 00 0.000 50 0.001 21 0.001 97 0.003 27 0.006 30 0.008 18 0.010 76 0.013 10 0.015 27 0.016 87

49.28 274.35 598.02 950.85 1570.7 3073.6 4071.3 5548.4 7023.7 8571.0 9878.9

0.000 00 0.000 63 0.001 46 0.002 35 0.003 12 0.005 90 0.007 51 0.009 95 0.011 93 0.013 63 0.015 29

45.77 362.64 781.05 1244.4 1650.2 3175.0 4122.0 5662.3 7046.9 8366.4 9838.3

0.000 00 0.000 55 0.001 13 0.001 93 0.003 24 0.004 86 0.006 63 0.007 98 0.010 00 0.011 42 0.012 37

43.53 382.67 739.57 1249.3 2107.1 3236.1 4565.0 5675.0 7527.4 9047.1 10 209

Table 6. Experimental Gas Solubility Data for the System CO2 (1) + H2O (2) + KNO3 (3) at 100 °C and Different Salt Concentrations m ) 1.00 mol‚(kg of water)-1

m ) 2.50 mol‚(kg of water)-1

m ) 4.99 mol‚(kg of water)-1

x1,salt-free

x1,salt-free

x1,salt-free

P (kPa)

0.000 00 97.24 0.000 00 96.07 0.000 00 0.000 55 407.55 0.000 18 210.76 0.000 30 0.001 08 707.11 0.000 59 464.99 0.000 70 0.001 61 1001.5 0.001 59 1099.4 0.001 22 0.002 13 1296.6 0.002 21 1497.3 0.002 01 0.002 84 1697.7 0.004 05 2720.5 0.003 44 0.004 88 2867.9 0.005 81 3951.9 0.005 34 0.011 36 6780.3 0.007 28 5037.6 0.006 78 0.012 95 7819.8 0.010 46 7618.1 0.008 46 0.015 24 9395.7 0.011 76 8802.2 0.009 68 Table 7. Experimental and Predicted Henry Coefficients of CO2 in the Different Solutions

91.03 341.73 661.04 1090.2 1748.7 3002.6 4806.2 6303.5 8248.2 9845.3

P (kPa)

m [mol‚(kg of water)-1]

T (K)

Hexp (MPa)

1.00 1.00 1.01 2.49 2.50 2.50

313.19 353.13 373.14 313.20 353.15 373.20

267 463 547 291 522 618

P (kPa)

Hcalc (MPa) (PSRK)

m [mol‚(kg of water)-1]

CO2 (1) + H2O (2) + NaNO3 (3) 248 5.00 417 5.00 501 5.01 272 9.79 470 10.00 570 10.08

CO2 (1) + H2O (2) + KNO3 (3) 0.99 313.19 261 241 2.50 1.00 353.32 449 431 4.96 1.00 373.18 552 527 4.99 2.50 313.16 279 248 4.99 2.49 353.31 494 479 Table 8. Gas-Ion Interaction Parameters for the PSRK Model short-range (SR)

a

T (K)

Hexp (MPa)

Hcalc (MPa) (PSRK)

313.21 353.18 373.22 313.18 353.20 373.24

372 670 781 497 1006 1231

334 599 735 468 930 1182

373.18 313.20 353.17 373.15

611 317 602 786

603 306 643 768

middle-range (MR)

i

j

aij (K)

aji (K)

bij

bji

Rij

βij

CO2a CO2a CO2b

Na+ K+ NO3-

-205.37 630.19 -1063.48

67.178 -1060.0 413.342

0.109 84 4.4101 2.353 14

-0.111 73 2.5230 2.353 65

-0.124 94 0.396 71 -0.043 64

-0.138 10 0.223 77 0.061 53

Taken from Kiepe et al.5

b

Parameters fitted in this work.

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Figure 1. Experimental and predicted P-x data for the system CO2 (1) + H2O (2) + NaNO3 (3) at (a) 40, (b), 80, and (c) 100 °C. Experimental data from this work: (9) m ) (a,b) 1.00, (c) 1.01 mol‚(kg of water)-1; (2) m ) (a) 2.49, (b,c) 2.50 mol‚(kg of water)-1; (b) m ) (a,b) 5.00, (c) 5.01 mol‚(kg of water)-1; ([) m ) (a) 9.79, (b) 10.0, (c) 10.08 mol‚(kg of water)-1. Kiepe et al.,5 m ) 0 mol‚(kg of water)-1 (a) ], (b) 0, (c) 4. (s) PSRK; (- - -) PSRK salt-free.

Figure 2. Experimental and predicted P-x data for the system CO2 (1) + H2O (2) + KNO3 (3) at (a) 40, (b), 80, and (c) 100 °C. Experimental data from this work: (9) m ) (a) 0.99, (b,c) 1.00 mol‚(kg of water)-1; (2) m ) (a,c) 2.50, (b) 2.49 mol‚(kg of water)-1; (b) m ) (a) 4.96, (b,c) 4.99 mol‚(kg of water)-1. Kiepe et al.,5 m ) 0 mol‚(kg of water)-1 (a) ], (b) 0, (c) 4. (s) PSRK; (- - -) PSRK salt-free.

the fugacity coefficient of the gas at infinite dilution; and PS2 is the vapor pressure of the aqueous mixture (water + salt), which was experimentally determined. The values are given in Table 7. For the system CO2 + H2O + NaNO3, experimental gas solubility data at several fixed salt concentrations

up to 10 mol‚(kg of water)-1 were determined experimentally at 40, 80, and 100 °C. In Figure 1a-c, they are compared to the results for the salt-free system and the results obtained using the PSRK model at 40, 80, and 100 °C. A salting-out effect leading to larger Henry coefficients, i.e., smaller CO2 solubilities, with increasing

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Figure 4. Experimental and predicted P-x data for the systems CO2 + H2O + (]) KNO3, (4) NaNO3, (0) KCl, and (O) NaCl at 40 °C and m ) 2.50 mol‚(kg of water)-1. Data for KNO3 and NaNO3 are experimental data from this work; those for KCl and NaCl are from Kiepe et al.5 (s) PSRK; (- - -) PSRK salt-free.

also described accurately using the same set of parameters for the CO2-NO3- interaction. Figure 4 shows the influence of NaNO3 and KNO3 on the gas solubility of CO2 in water at m ) 2.5 mol‚kg-1 and 40 °C in comparison to the solubilities for NaCl and KCl reported by Kiepe et al.5 The experimental data are in excellent agreement with the calculated data. Furthermore, it can be seen that the Na+ cation has a stronger effect on the CO2 solubility than the K+ cation. Accordingly, the influence of the Cl- anion is larger than that of the NO3- anion. 4. Conclusions Figure 3. Experimental and predicted Henry coefficients for the systems (a) CO2 (1) in H2O (2) + NaNO3 (3) and (b) CO2 (1) in H2O (2) + KNO3 (3). Experimental data from this work: (b) 40, (9) 80, ([) 100 °C. PSRK (s).

salt concentration is observed. It can be also seen that the effect of the electrolyte on the gas solubility decreases with increasing the temperature. Using the CO2-K+ and CO2-Na+ interaction parameters given by Kiepe et al.,5 the CO2-NO3- interaction parameters, which were simultaneously fitted to NaNO3 and KNO3 data, enable the reliable description of the solubility of CO2 in the electrolyte solution as a function of the salt concentration and temperature. The obtained interaction parameters (short-range and middle-range) are given in Table 8. For the short-range parameters, the following temperature dependence is used

parij ) aij + bijT where T and parij have units of Kelvin. In Figure 2a-c, P-x data for the system CO2 + H2O + KNO3 at 40, 80, and 100 °C are presented, together with the calculated results using the same PSRK interaction parameters. For this system, the observed salt effect is generally smaller than for the NaNO3 system. This can also be concluded from the Henry coefficients given in Table 7 and plotted against temperature in Figure 3a,b. For the KNO3 system, the salting-out effect and its temperature dependence are

Reliable gas solubility data (isothermal P-x data) for CO2 in aqueous NaNO3 and KNO3 solutions were measured up to 10 MPa over wide concentration and temperature ranges with a static apparatus, following an experimental approach whose reliability has already been demonstrated.5 CO2-NO3- interaction parameters for the PSRK method were regressed to the experimental data of this work. All systems containing NaNO3 and KNO3 can be described with this set of interactions parameters, which is evidence of the flexibility and consistency of the model. The salting-out effect, as well as the temperature dependence of the solubility behavior, is represented correctly. To summarize, it was possible to extend the PSRK model successfully to electrolyte systems by linking this method with the LIFAC model. Further experimental results (CH4 solubility in aqueous salt mixtures) will be published soon to fill existing gaps in the PSRK parameter matrix. Acknowledgment The authors thank the “Bundesministerium fu¨r Wirtschaft” via “Arbeitsgemeinschaft industrieller Forschungsvereinigungen” (AIF project 12219N) for financial support. Literature Cited (1) Holderbaum, T.; Gmehling, J. PSRK: A group contribution equation of state based on UNIFAC. Fluid Phase Equilib. 1991, 70, 251-265.

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(2) Horstmann, S.; Fischer, F.; Gmehling, J. Application of PSRK for process design. Chem. Eng. Commun. 2003, manuscript accepted. (3) Yan, W.; Topphoff, M.; Rose, C.; Gmehling, J. Prediction of vapor-liquid equilibria in mixed-solvent electrolyte systems using the group contribution concept. Fluid Phase Equilib. 1999, 162, 97-113. (4) Li, J.; Topphoff, M.; Fischer, K.; Gmehling, J. Prediction of gas solubilities in aqueous electrolyte systems using the predictive Soave-Redlich-Kwong model. Ind. Eng. Chem. Res. 2001, 40, 3703-3710. (5) Kiepe, J.; Horstmann, S.; Gmehling, J. Experimental Determination and Prediction of Gas Solubility Data for CO2 + H2O Mixtures Containing NaCl or KCl at Temperatures between 313 and 393 K and Pressures up to 10 MPa. Ind. Eng. Chem. Res. 2002, 41, 4393-4398.

(6) Fischer, K.; Gmehling, J. P-x and γ∞ data for the different binary butanol-water systems at 50 °C. J. Chem. Eng. Data 1994, 39, 309-315. (7) Fischer, K.; Wilken, M. Experimental determination of oxygen and nitrogen solubility in organic solvents up to 10 MPa at temperatures between 298 K and 398 K. J. Chem. Thermodyn. 2001, 33, 1285-1308. (8) Kiepe, J.; de Arau´jo Rodrigues, A. K.; Horstmann, S.; Gmehling, J. Experimental Determination and Correlation of Liquid Density Data of Electrolyte Mixtures Containing Water or Methanol. Ind. Eng. Chem. Res. 2003, 42, 2022-2029.

Received for review February 28, 2003 Revised manuscript received June 4, 2003 Accepted June 11, 2003 IE030197E