Solubility of Carbon Dioxide in Aqueous Solutions of N

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Ind. Eng. Chem. Res. 2006, 45, 6081-6091

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Solubility of Carbon Dioxide in Aqueous Solutions of N-Methyldiethanolamine in the Low Gas Loading Region Viktor Ermatchkov, A Ä lvaro Pe´ rez-Salado Kamps, and Gerd Maurer* Chair of Applied Thermodynamics, UniVersity of Kaiserslautern, P.O. Box 3049, D-67653 Kaiserslautern, Germany

A headspace gas chromatography technique was applied to determine the solubility of carbon dioxide in aqueous solutions of 2,2′-methyliminodiethanol (N-methyldiethanolamine, MDEA) at low gas loadings (at stoichiometric molar ratios of carbon dioxide to MDEA between about 0.003 and 0.8). A temperature range T ≈ 313-393 K was covered. The stoichiometric molality of MDEA in water amounted to about 2, 4, and 8 mol/(kg of water) (mass fraction of MDEA ≈ 0.192, 0.323, and 0.488). The partial pressure of carbon dioxide was between about 0.1 and 70 kPa. A thermodynamic model for describing the vapor-liquid equilibrium (which applies Pitzer’s molality-scale-based equation for describing the Gibbs excess energy of the aqueous phase) is revised and extended using the new data. Introduction The removal of sour gases, e.g., carbon dioxide and hydrogen sulfide, from natural or synthesis gas is mostly achieved by “chemical” absorption in aqueous solutions of single amines (in many cases alkanolamines, such as, e.g., 2,2′-methyliminodiethanol ) N-methyldiethanolamine ) MDEA) or amine mixtures (e.g., MDEA + piperazine). The competitive chemical absorption of carbon dioxide and hydrogen sulfide is kinetically controlled. However, deviation from equilibrium provides the driving force in a kinetically controlled process. Hence, the reliable design and optimization of the separation equipment at first requires the knowledge of the equilibrium properties, in particular the chemical reaction equilibrium and the vaporliquid equilibrium (VLE), as well as information on the energy to vaporize/condense the mixtures. The gas absorption takes place at low temperatures (around or somewhat above room temperature) and elevated pressures (up to ∼4 MPa or more), whereas the gas desorption (i.e., the solvent regeneration in the stripper) occurs at elevated temperatures (∼390 K or more) and low pressures (in particular at low partial pressures of the gas). Therefore, the aforementioned equilibrium properties need to be explored within relatively wide ranges of temperature, pressure, and amine and gas concentrations. In particular, modeling the phase equilibrium for the simultaneous solubility of carbon dioxide and hydrogen sulfide in aqueous solutions of MDEA or amine mixtures with MDEA requires a reliable and extensive experimental database on the solubility of the single gases in aqueous solutions of the single amines. The present work focuses on one of the interesting subsystems, namely, (CO2 + MDEA + H2O). A literature review revealed1,2 that most of the published gas solubility data for this system3-21 scatter widely. This holds at all temperatures, gas loadings (i.e., at all molar ratios of gas to amine), and pressures (see also refs 22-27). Therefore, in an attempt to improve that database, the solubility of carbon dioxide in aqueous solutions of MDEA was investigated in previous work1,2 with a well-proven and very reliable technique.28-31 This technique is based on the synthetic method and allows for the determination of the total pressure required to dissolve a known * Corresponding author. Tel.: +49 631 205 2410. Fax: +49 631 205 3835. E-mail: [email protected].

amount of gas in a known amount of liquid at given temperature and liquid-phase composition. A temperature range from about 313 to 413 K was covered, MDEA molalities amounted to about 2, 4, and 8 mol/(kg of water), and total pressures ranged from about 0.2 to 8 MPa. On the basis of only this experimental data at high gas loadings, a thermodynamic model describing the vapor-liquid equilibrium of the system (CO2 + MDEA + H2O) was developed.1,2 This model is able to predict the gas solubility in the low gas loading region. Prediction results fall well within the wide scattering ranges of the literature data. However, the industrial need persists to assess the prediction results by comparison with more accurate experimental information in that low gas loading region, in particular at the higher temperatures. The synthetic technique used before is not suited for investigations at low pressures (below about 0.2 MPa), because the experimental determination of the total pressure is subject to high experimental uncertainties caused by the unavoidable presence of small amounts of other gases. In the present work, a headspace gas chromatograph technique32,33 is applied for the reliable determination of the solubility of carbon dioxide in aqueous solutions of MDEA at low gas loadings (see also refs 31 and 34). The temperature amounts to T ≈ 313, 353, and 393 K. The stoichiometric molality of MDEA amounts to about 2, 4, and 8 mol/(kg of water). Partial pressures of carbon dioxide range from about 0.1 to 70 kPa. Experimental Technique Figure 1 shows a scheme of the experimental arrangement. Its main components are a thermostated cell holder, a thermostated sample-valve holder (containing a multiposition valve and the sampling system), two large buffer tanks (volume ≈ 50 L each) filled with high-purity nitrogen, and a gas chromatograph [Agilent (type 6890), which is equipped with a capillary column (Alltech, type Heliflex AT-Q 30 m 0.32 mm i.d.) and a thermal conductivity detector]. In the experiments, eight sample cells (stainless steel vials, volume ≈ 11-30 cm3) are partially filled (to about 1/2 to 3/4 of the total volume) with a liquid mixture of (CO2 + MDEA + H2O) and mounted in the cell holder. Only one of those sample cells is shown in Figure 1. The temperature is measured in the thermostated bath of the cell holder with a platinum resistance thermometer. The overall accuracy of the temperature measure-

10.1021/ie0604270 CCC: $33.50 © 2006 American Chemical Society Published on Web 07/13/2006

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Ind. Eng. Chem. Res., Vol. 45, No. 17, 2006 Table 1. Solubility of Carbon Dioxide in Aqueous Solutions of MDEA at 313.15 K (∆T ) (0.1 K, ∆m j MDEA/m j MDEA ) (0.1 %)

Figure 1. Scheme of the headspace gas chromatography arrangement: (CH) liquid-thermostated cell holder (temperature T1), (VH) liquid-thermostated valve holder (temperature T2 > T1), (A) nitrogen tank (higher pressure), (B) nitrogen tank (lower pressure), (GC) gas chromatograph, (He) Helium (carrier gas), (SC) sample cell, (MV) multiposition valve, (S1-S8) sample positions, (P1-P8) purge positions, (SV) sample valve, (SL) sample loop.

ment is about (0.1 K. At equilibrium, a certain partial pressure of the sour gas is attained in the gaseous phase (the headspace) of the sample cells. That partial pressure is to be measured. First, the cell is pressurized (from buffer tank A) with nitrogen to a constant pressure (0.2, 0.26, and 0.45 MPa for the measurements at 313, 353, and 393 K, respectively) for 2 min. Second, the gas phase in the cell is expanded to the buffer tank B, which is also pressurized to a constant pressure (0.17, 0.2, and 0.37 MPa for the measurements at 313, 353, and 393 K, respectively), and the sample loop is filled. The sample valve is then switched, and the sample is transferred to the gas chromatograph. After the sample is taken, the sampling system is purged with nitrogen. The multiposition valve (Valco Instruments Co. Inc., type 2CSD16MWE-HC) allows one to connect each of the eight sample cells (by stainless steel capillaries, inner diameter ) 0.25 mm) to the sample loop. The other eight positions of the multiposition valve are used for purging. The multiposition valve and the sample valve are both operated pneumatically by an electronic controller. The temperature of the valve holder is kept at 15-20 K higher than in the cell holder. Also, the feed line to the gas chromatograph is thermostated to a higher temperature in order to avoid condensation in the sampling system. The primary data collected in the headspace chromatographic measurements is the peak area of carbon dioxide. From this peak area, the partial pressure of carbon dioxide can be determined. The peak area is proportional to the mass of that gas passing the detector, i.e., to the mass of the gas in the sample loop. As the volume and temperature of the sample loop are constant, and according to the ideal gas law, the peak area of the gas is proportional to the partial pressure of the gas in the sample loop and, hence, also in the sample cell. The relation between peak area and partial pressure in the cell is determined by calibration measurements with pure carbon dioxide and a high-precision pressure transducer (Scha¨fer Datametrics, Langen, Germany, type 590A-1000T-2Q1-V1X-4D). In that calibration, the pressure ranged from 7 to 70 kPa. The maximum systematic uncertainty in the pressure measurement ranges from about (0.05 kPa at p ≈ 10 kPa to about (0.15 kPa at p ≈ 70 kPa. The maximum relative deviation between the measured pressures and the calibration line amounted to 2%. Of course,

m j MDEA, mol‚kg-1

m j CO2, mol‚kg-1

pCO2, kPa

∆pCO2,repr, kPa

2.051 2.051 2.192 2.051 2.051 2.620 1.905 1.905 1.905 2.051 1.905 1.905 4.030 4.030 4.030 4.030 4.030 4.016 4.016 4.016 3.949 4.141 4.380 4.229 4.189 3.918 7.623 7.927 7.331 7.623 8.339 7.623 7.663 7.623 8.345 7.998 7.623 7.437 7.437

0.1923 ( 0.0007 0.2956 ( 0.0006 0.4312 ( 0.0007 0.5278 ( 0.0008 0.6979 ( 0.0009 0.874 ( 0.001 0.836 ( 0.001 0.960 ( 0.002 1.122 ( 0.002 1.222 ( 0.003 1.305 ( 0.004 1.494 ( 0.007 0.1807 ( 0.0007 0.4157 ( 0.0007 0.5953 ( 0.0008 0.7953 ( 0.0008 1.013 ( 0.001 1.106 ( 0.001 1.317 ( 0.001 1.486 ( 0.002 1.616 ( 0.002 1.864 ( 0.003 2.220 ( 0.004 2.422 ( 0.005 2.655 ( 0.007 2.834 ( 0.009 0.378 ( 0.001 0.770 ( 0.001 0.906 ( 0.001 1.141 ( 0.001 1.563 ( 0.002 1.893 ( 0.002 2.201 ( 0.003 2.596 ( 0.003 3.187 ( 0.005 3.674 ( 0.007 3.649 ( 0.007 4.152 ( 0.009 4.695 ( 0.012

0.53 ( 0.02 1.11 ( 0.03 2.08 ( 0.06 3.17 ( 0.09 5.57 ( 0.15 6.66 ( 0.18 9.33 ( 0.26 13.1 ( 0.36 19.9 ( 0.58 21.7 ( 0.64 33.7 ( 1.11 58.4 ( 2.64 0.31 ( 0.01 1.23 ( 0.03 2.30 ( 0.06 3.67 ( 0.10 5.68 ( 0.15 6.93 ( 0.18 9.63 ( 0.26 12.0 ( 0.32 14.3 ( 0.39 18.8 ( 0.51 25.0 ( 0.70 33.8 ( 0.97 43.2 ( 1.34 63.8 ( 2.40 0.96 ( 0.03 2.84 ( 0.08 3.58 ( 0.10 4.94 ( 0.14 8.17 ( 0.23 11.3 ( 0.31 14.4 ( 0.39 19.0 ( 0.52 27.0 ( 0.74 35.4 ( 0.98 36.5 ( 1.01 50.3 ( 1.45 69.3 ( 2.20

0.02 0.02 0.06 0.06 0.13 0.19 0.20 0.38 0.25 0.32 0.76 0.73 0.01 0.02 0.06 0.08 0.14 0.17 0.26 0.27 0.41 0.41 0.45 0.91 1.14 0.62 0.02 0.13 0.11 0.09 0.20 0.33 0.29 0.31 0.83 0.60 1.17 0.78 0.57

the operating conditions were kept constant during calibration and measurements. Substances. Carbon dioxide (mole fraction g 0.999 95) was purchased from Messer-Griesheim, Ludwigshafen, Germany. N-methyldiethanolamine (mass fraction g 0.985, Riedel-de Hae¨n, Seelze, Germany) was degassed under vacuum. Deionized water was degassed by vacuum distillation. Sample Preparation. The aqueous MDEA solutions (∼1.4 L) were gravimetrically prepared in a storage tank by dissolving known amounts of the amine in water (under vacuum). A known amount of that aqueous MDEA solution (∼0.25 L) was then transferred to a second (evacuated) storage tank (volume ≈ 0.3 L), then charged with carbon dioxide, rotated for about 4-5 h, and finally stored at room temperature for about 1 day. The sample cells were then partially filled with that liquid mixture and mounted in the cell holder, where they were thermostated to the desired experimental temperature for ∼12 h. As it was confirmed in a series of preliminary experiments, this procedure ensured the attainment of thermodynamic equilibrium in both the second storage tank and the sample cells. A (systematic) correction of the stoichiometric molalities of the gas and the amine was applied to account for the transfer of the sour gas and water to the vapor (in both the second storage tank and the sample cells). (The vapor pressure of MDEA is almost negligible in the temperature range considered here.) Since the vapor-phase volumes (which were estimated) and the partial pressures of carbon dioxide and water (which were either calculated from the previous VLE model2 or known from the experiment) are small, the correction of the stoichiometric molality of carbon

Ind. Eng. Chem. Res., Vol. 45, No. 17, 2006 6083 Table 2. Solubility of Carbon Dioxide in Aqueous Solutions of MDEA at 353.15 K (∆T ) (0.1 K, ∆m j MDEA/m j MDEA ) (0.1 %)

Table 3. Solubility of Carbon Dioxide in Aqueous Solutions of MDEA at 393.15 K (∆T ) (0.1 K, ∆m j MDEA/m j MDEA ) (0.1 %)

m j MDEA, mol‚kg-1

m j CO2, mol‚kg-1

pCO2, kPa

∆pCO2,repr, kPa

m j MDEA, mol‚kg-1

m j CO2, mol‚kg-1

pCO2, kPa

∆pCO2,repr, kPa

1.988 1.988 1.988 1.988 1.906 1.906 1.906 1.906 1.988 1.906 4.175 4.369 4.175 4.175 4.175 3.959 3.959 3.959 3.959 3.959 8.441 8.441 8.441 8.441 8.441 7.699 7.699 7.699 7.699 7.699

0.0423 ( 0.0006 0.1026 ( 0.0006 0.1799 ( 0.0008 0.235 ( 0.001 0.276 ( 0.001 0.359 ( 0.002 0.403 ( 0.002 0.486 ( 0.003 0.565 ( 0.004 0.558 ( 0.004 0.0195 ( 0.0007 0.0501 ( 0.0008 0.0966 ( 0.0007 0.1886 ( 0.0009 0.281 ( 0.001 0.370 ( 0.002 0.471 ( 0.002 0.557 ( 0.003 0.643 ( 0.004 0.763 ( 0.005 0.061 ( 0.001 0.127 ( 0.001 0.303 ( 0.002 0.373 ( 0.002 0.534 ( 0.003 0.653 ( 0.004 0.773 ( 0.005 0.835 ( 0.006 0.894 ( 0.006 1.037 ( 0.008

0.43 ( 0.02 2.20 ( 0.07 5.53 ( 0.17 9.14 ( 0.27 12.3 ( 0.37 19.5 ( 0.62 24.1 ( 0.78 34.3 ( 1.16 43.2 ( 1.52 46.1 ( 1.64 0.12 ( 0.01 0.46 ( 0.02 1.34 ( 0.05 4.12 ( 0.12 8.34 ( 0.24 15.0 ( 0.43 20.8 ( 0.61 25.9 ( 0.77 32.6 ( 1.00 44.1 ( 1.39 0.73 ( 0.04 2.26 ( 0.08 9.44 ( 0.29 12.5 ( 0.38 22.0 ( 0.68 28.2 ( 0.87 35.7 ( 1.13 41.0 ( 1.31 44.3 ( 1.44 55.5 ( 1.84

0.01 0.07 0.16 0.30 0.38 0.66 0.72 0.91 1.36 1.59 0.01 0.02 0.01 0.20 0.11 0.38 0.64 0.35 0.91 1.39 0.02 0.05 0.30 0.72 0.64 0.73 0.54 1.66 1.87 1.30

2.010 2.002 2.002 2.010 2.010 2.010 2.010 2.002 2.015 2.002 3.955 3.955 3.955 4.047 3.955 4.047 4.047 4.047 8.099 7.983 8.099 7.983 8.099 7.983 8.069 8.099 7.996 7.996 7.983 7.996 7.996 8.069

0.0179 ( 0.0006 0.0415 ( 0.0006 0.0554 ( 0.0006 0.0770 ( 0.0008 0.098 ( 0.001 0.119 ( 0.001 0.144 ( 0.002 0.159 ( 0.002 0.192 ( 0.002 0.226 ( 0.003 0.0186 ( 0.0007 0.0795 ( 0.0009 0.117 ( 0.001 0.152 ( 0.002 0.188 ( 0.002 0.208 ( 0.003 0.215 ( 0.003 0.225 ( 0.003 0.0228 ( 0.0009 0.0255 ( 0.0010 0.0457 ( 0.0009 0.0630 ( 0.0011 0.0777 ( 0.0012 0.0851 ( 0.0012 0.110 ( 0.002 0.132 ( 0.002 0.149 ( 0.002 0.163 ( 0.002 0.168 ( 0.002 0.178 ( 0.003 0.201 ( 0.003 0.249 ( 0.004

0.91 ( 0.07 3.70 ( 0.16 5.87 ( 0.25 10.2 ( 0.42 15.7 ( 0.59 21.5 ( 0.81 28.8 ( 1.12 33.3 ( 1.36 46.9 ( 2.03 59.8 ( 2.73 0.83 ( 0.07 8.73 ( 0.34 16.5 ( 0.60 24.8 ( 0.94 35.6 ( 1.39 40.4 ( 1.58 43.0 ( 1.71 45.3 ( 1.81 1.42 ( 0.11 1.80 ( 0.14 4.29 ( 0.22 6.62 ( 0.33 9.07 ( 0.40 10.7 ( 0.48 15.3 ( 0.64 20.0 ( 0.86 23.8 ( 1.01 27.0 ( 1.12 29.1 ( 1.22 31.3 ( 1.33 37.6 ( 1.62 51.5 ( 2.31

0.03 0.03 0.04 0.06 0.04 0.18 0.29 0.33 0.20 0.67 0.02 0.06 0.17 0.21 0.36 0.58 0.28 0.04 0.03 0.03 0.09 0.27 0.03 0.57 0.21 0.23 0.12 0.23 0.59 0.19 0.21 1.47

dioxide is also small (0.1-4.3 %), and the correction of the stoichiometric molality of MDEA is insignificant. The relative gravimetrical uncertainty in the stoichiometric molality of MDEA does not surmount (0.03 %. The total uncertainty in that molality is estimated to be smaller than (0.1 %. The relative uncertainty in the stoichiometric molality of carbon dioxide ranges from about (0.1 % (for the higher MDEA and carbon dioxide molalities) up to about (3.9 % (for the lower MDEA and carbon dioxide molalities). It was estimated from the filling procedure described before (including all corrections) by means of a Gauss error propagation calculation. Experimental Results The solubility of carbon dioxide in aqueous solutions of MDEA was measured at T ≈ 313, 353, and 393 K. The stoichiometric molality of MDEA in water amounted to about 2, 4, and 8 mol/(kg of water) (mass fraction of MDEA ≈ 0.192, 0.323, and 0.488). The stoichiometric molar ratio of carbon dioxide to MDEA ranged from about 0.003 to 0.8. The partial pressure of carbon dioxide was between about 0.1 and 70 kPa. The experimental results are listed in Tables 1-3. These tables include the absolute uncertainty in the stoichiometric molality of carbon dioxide, as estimated from the Gauss error propagation calculation mentioned before. The absolute uncertainty in the partial pressure of carbon dioxide is also reported / in those tables. It is estimated from ∆pCO2 ) ((∆pCO + 2 0.02pCO2). The first contribution accounts for uncertainties in temperature as well as gas and amine molalities. It is determined from a Gauss error propagation calculation (by applying the VLE model described in the next section). The second contribution is the uncertainty of the calibration experiments. To check the reproducibility of the experimental technique, each experimental data point listed in Tables 1-3 was repeated 3-8 times. The absolute standard deviation from the average numerical value for the partial pressure of carbon dioxide is

listed in those tables, too (∆pCO2,repr). For almost all experimental data, ∆pCO2,repr is (well) below the estimated experimental uncertainty of the partial pressure of carbon dioxide (∆pCO2), confirming the reliability of that estimation. In Figures 2, 3, and 4 (left diagrams), the experimental results for the partial pressure of carbon dioxide (open symbols) are plotted versus the stoichiometric molar ratio of carbon dioxide to MDEA (m j CO2/m j MDEA) at preset temperature and stoichiometric MDEA molality of about 2, 4, and 8 mol/(kg of water), respectively. When the sour gas carbon dioxide is added to an aqueous solution of MDEA, the total pressure at first only very slightly increases with an increasing amount of the gas in the liquid. This is due to the basic character of MDEA as well as

Figure 2. Partial pressure of carbon dioxide (left diagram) and total pressure (right diagram) above liquid mixtures of (CO2 + MDEA + H2O), m j MDEA ≈ 2 mol‚kg-1. Experimental results, this work: (4) 313 K, (O) 353 K, (0) 393 K. Experimental results from Kuranov et al.:1 (2) 313 K, (9) 333 K, (*) 373 K, (9) 393 K, (×) 413 K. (s) Correlation (parameter set II), this work. (- - -) Correlation/prediction (parameter set I), this work.

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but also in nonvolatile, ionic form. The following (reversible) chemical reactions are considered in the liquid phase:

autoprotolysis of water: H2O(l) H H+(aq) + OH-(aq)

(I)

formation of bicarbonate (HCO3-) and carbonate (CO32-): CO2(aq) + H2O(l) H HCO3- (aq) + H+(aq)

(II)

HCO3- (aq) H CO32- (aq) + H+(aq)

(III)

protonation of MDEA: MDEA(aq) + H+(aq) H MDEAH+(aq) Figure 3. Partial pressure of carbon dioxide (left diagram) and total pressure (right diagram) above liquid mixtures of (CO2 + MDEA + H2O), m j MDEA ≈ 4 mol‚kg-1. Experimental results, this work: (4) 313 K, (O) 353 K, (0) 393 K. Experimental results from Kuranov et al.:1 (2) 313 K, (9) 333 K, (*) 373 K, (9) 393 K, (×) 413 K. Experimental results from Pe´rez-Salado Kamps et al.2 (after applying a small temperature correction, see Appendix II): (+) 313.7 K. (s) Correlation (parameter set II), this work. (- - -) Correlation/prediction (parameter set I), this work.

The condition for chemical equilibrium for a chemical reaction r ()I, ..., IV) is

Kr(T) )

to the almost negligibly small vapor pressure of the amine. In particular, the partial pressure of carbon dioxide at first (i.e., for low gas loadings m j CO2/m j MDEA) is very small, i.e., carbon dioxide is almost completely dissolved chemically (as bicarbonate and carbonate ions). But it increases rapidly (for higher gas loadings) when, in the liquid phase, MDEA has been spent by chemical reactions, i.e., when MDEA has been protonated, and the sour gas can no longer be absorbed chemically but has to be dissolved physically (see also refs 1 and 2). Thermodynamic Modeling of the Vapor-Liquid Equilibrium A detailed description of the model applied to correlate and predict the solubility of carbon dioxide in aqueous solutions of MDEA can be found in previous publications.1,2 Therefore, only a short outline is repeated here. Because of chemical reactions, the liquid phase contains carbon dioxide and MDEA not only in volatile (i.e., neutral)

∏i aiν

i,r

(1)

The influence of pressure on a chemical reaction equilibrium constant (Kr) is neglected. The term ai is the activity of species i. Only water is treated as solvent species. MDEA, carbon dioxide, and the ions are treated as solute species. The reference state for the chemical potential of water is the pure liquid at system temperature and pressure, whereas for the chemical potential of a solute species, it is the one molal solution of that solute in pure water at system temperature and pressure, with the solute experiencing the same interactions as when infinitely diluted in pure water. νi,r is the stoichiometric factor of reactant i in reaction r (νi,r > 0 for a product and νi,r < 0 for an educt). The balance equation for the amounts of substance (the number of moles) of a species i in the liquid solution is

ni ) nji + Figure 4. Partial pressure of carbon dioxide (left diagram) and total pressure (right diagram) above liquid mixtures of (CO2 + MDEA + H2O), m j MDEA ≈ 8 mol‚kg-1. Experimental results, this work: (4) 313 K, (O) 353 K, (0) 393 K. Experimental results from Pe´rez-Salado Kamps et al.2 (after applying a small temperature correction, see Appendix II): (2) 313.7 K, (b) 354.4 K, (9) 395 K. (s) Correlation (parameter set II), this work. (- - -) Correlation/prediction (parameter set I), this work.

(IV)

∑r νi,rξr

(2)

where ξr is the extent of reaction r. Solving this set of equations for a given temperature and given stoichiometric amounts of substances (number of moles) nji of components H2O, MDEA, and CO2 results in the speciation, i.e., the “true” composition of the liquid phase (the amount of substance ni of all species present). The vapor-liquid equilibrium condition results in the extended Henry’s law for carbon dioxide:

kH,CO2 exp

[

]

∞ VCO (p - psW) 2

RT

aCO2 ) yCO2pφCO2

(3)

and in the extended Raoult’s law for water:

psW φsW exp

[

]

VW(p - psW) aW ) yWpφW RT

(4)

In principle, MDEA might also be present in the vapor phase. However, as the vapor pressure of MDEA is very small in the temperature range considered here,35 its presence in the vapor phase is neglected. From these two equations, the total pressure p and the vapor-phase composition (yi is the vapor-phase mole fraction of component i) are calculated. kH,CO2(T) is Henry’s constant of carbon dioxide in pure water (based on the molality ∞ scale) at the vapor pressure of pure water {psW(T)}. VCO (T) and 2 VW(T) are the partial molar volume of carbon dioxide infinitely

Ind. Eng. Chem. Res., Vol. 45, No. 17, 2006 6085

diluted in water and the molar volume of pure liquid water, respectively. The influence of pressure on these properties is neglected here. The virial equation of state, which was truncated after the second virial coefficient, was used to calculate the vapor-phase fugacity coefficient of component i, φi. Activities are calculated from Pitzer’s molality-scale-based equation for the excess Gibbs energy (GE) of aqueous electrolyte solutions36,37 (see Appendix I). The activity of a solute species i follows from

ai )

mi γ m° i

(5)

where mi is the molality of solute species i, i.e., the number of moles ni of this species i per kilogram of water

ni mi ) / m° M n

(6)

W W

and m° ) 1 mol‚kg-1. M/W is the relative molar mass of water divided by 1000 (M/W ) 0.018 015 28), and nW is the true number of moles of water. The activity coefficient of a solute species γi (on the molality scale) is directly calculated from that GE equation, whereas the activity of water aW is calculated from the activity coefficients of all solute species by applying the Gibbs-Duhem equation. As was already mentioned in previous work,38,39 when Pitzer’s GE equation is applied to chemical reacting systems, it is much easier to use the general equations for the activity coefficient of a solute species (and for the activity of water) as a function (1) (2) of the interaction parameters β(0) ij , βij , βij , and µijk, rather than using rearranged equations as a function of comprehensive (0) parameters (e.g., CφMX, BG,MX , ΓG,MX,MX, ΓG,G,MX; see Appendix I). This does not increase the amount of independent parameters and drastically simplifies the computer codes. Such a procedure was also applied in the present work. Required Thermodynamic Properties. Chemical reaction equilibrium constants (on the molality scale) were adopted from the literature (KI from Edwards et al.,40 KII and KIII from Patterson et al.,41,42 and KIV from Pe´rez-Salado Kamps and Maurer43). Henry’s constant for carbon dioxide in water kH,CO2(T) (on the molality scale) was taken from Rumpf and Maurer.29 The vapor pressure of water was taken from Saul and Wagner.44 The molar volume of liquid water was approximated by the molar volume of saturated liquid water, which was also taken from Saul and Wagner.44 The partial molar ∞ volume of carbon dioxide infinitely diluted in water, VCO , was 2 45 calculated as recommended by Brelvi and O’Connell (see also ref 46). Pure-component second virial coefficients BCO2,CO2 and BH2O,H2O were calculated from a correlation based on data recommended by Dymond and Smith.47 The mixed second virial coefficient BCO2,H2O was calculated as recommended by Hayden and O’Connell.48 Details on the required thermodynamic properties were given previously.2,46 Interaction Parameters in Pitzer’s GE Model Binary Systems (CO2 + H2O) and (MDEA + H2O). When one of the single components CO2 or MDEA is dissolved in pure water, with the exception of very dilute solutions, chemical reactions can be neglected. Thus, from experimental results on the vapor-liquid equilibrium of an aqueous solution of one of the mentioned solute components, only parameters describing

Table 4. Interaction Parameters (Set II) in Pitzer’s GE equation for the System (CO2 + MDEA + H2O)a parameter (0) βCO + 2,MDEAH (0) βMDEA,HCO 3 (0) βMDEA,CO 23 (0) βMDEAH +,HCO 3 (0) βMDEAH +,CO 23 (1) βMDEA,HCO 3 (1) βMDEAH +,HCO 3 (1) βMDEAH +,CO 23

µMDEAH+,HCO3-,HCO3µMDEAH+,CO32- ,CO32µCO2,MDEAH+,HCO3-

q1

q2

T, K

-3.5768 × 10-1 -4.1932 × 10-1 -7.0261 × 10-2 1.2200 × 10-1 1.1972 × 10-1 3.7998 × 10-1 2.0452 1.5220 1.3069 × 10-4 -4.9667 × 10-3 7.9139 × 10-3

115.81 188.06 61.638 -31.004

313-413

-100.93 -606.01 -745.62

-2.7936

The parameter set is based on CO2 gas solubility data in (MDEA + H2O) from Kuranov et al.,1 Pe´rez-Salado Kamps et al.2 (after applying a small temperature correction, see Appendix II), and this work. f(T) ) q1 + q2/(T/K) a

interactions between the single solute components (either CO2 or MDEA) in water can be determined. However, in the pressure region of interest in the absorption/desorption processes, parameters for interactions between CO2 in water can be neglected.29 Furthermore, all parameters for interactions between MDEA in water were neglected, because their influence on the partial pressure of carbon dioxide above liquid mixtures of (CO2 + MDEA + H2O) in the low gas loading region, as well as on the total pressure above those mixtures in the high gas loading region, is insignificant s at least in the amine concentration regions, which are important for the absortion/desorption processes. Ternary System (CO2 + MDEA + H2O). (a) Predictions from the Previous Model. As was already mentioned, the previous model1,2 for the VLE of the system (CO2 + MDEA + H2O) was based alone on experimental gas solubility data at high gas loadings from Kuranov et al.1 (at m j MDEA ≈ 2 and 4 j MDEA mol‚kg-1) and Pe´rez-Salado Kamps et al.2 (basically at m ≈ 8 mol‚kg-1). However, the platinum resistance thermometers used in the work by Pe´rez-Salado Kamps et al.2 were recalibrated straight after those experimental results had been published, showing that a small correction had to be applied to the temperature values. The corrected temperatures are calculated from T ) Told + ∆T, where ∆T ≈ 0.6, 1.2, and 1.8 K at Told ≈ 313.15, 353.15, and 393.15 K, respectively. Therefore, in the previous model, a small correction had to be applied also to the temperature-dependent interaction parameters in Pitzer’s GE equation. For better clarity, both the corrected experimental results for the solubility of carbon dioxide in (MDEA + H2O) by Pe´rez-Salado Kamps et al.2 and the corrected interaction parameters of the previous model for the VLE of the system (CO2 + MDEA + H2O) are listed in Appendix II. That corrected parameter set is here referred to as parameter set I. (For the sake of completeness, the corrected experimental results for the solubility of hydrogen sulfide in (MDEA + H2O) by Pe´rezSalado Kamps et al.2 as well as the corrected interaction parameters of the previous model for the VLE of the system (H2S + MDEA + H2O) are listed in that Appendix II as well.) In Figures 2, 3, and 4 (right diagrams), the (corrected) experimental results for the total pressure by Kuranov et al.1 and by Pe´rez-Salado Kamps et al.2 are plotted versus the stoichiometric molar ratio of carbon dioxide to MDEA (m j CO2/ m j MDEA) at preset temperature and stoichiometric MDEA molality of ∼2, 4, and 8 mol/(kg of water), respectively. In addition, and just to visually corroborate the consistency of the whole

101 118 43 76 10 14 27 5 45 37 12 37 81 22 12 42 34 11 65 13 30 4 15 103 10 34

Prediction this work Jou et al.3 Bhairi4 Chakma & Meisen5 Glasscock et al.6,7 Ho & Eguren8 Austgen et al.9 MacGregor & Mather10 Shen & Li11 Jou et al.12 Dawodu & Meisen13 Jou et al.14 Rho et al.15 Rho et al.15 Baek & Yoon16 Haji-Sulaiman et al.17 Rogers et al.18 Silkenba¨umer et al.19 Xu et al.20 Lemoine et al.21 Park & Sandall22 Addicks et al.23 Ali & Aroua24 Sidi-Boumedine et al.25 Jenab et al.26 Ma’mun et al.27

313-393 298-393 311-389 373-473 298 313-373 313 313 313-373 313-373 373-393 313-393 323-373 323-373 313 303-323 313-323 313 313-373 298 298-373 313 313-353 298-348 298-343 328-358

313-413 314-395 313-393 1.9-8.4 2.6-8.0 2.1 2.1-8.0 2.2 2.5-8.1 2.6-8.0 2.6 3.6 4.5 8.0 3.6 0.4-8.4 25.2 3.6 2.6-7.1 2.5-8.4 2.6 4.5-8.0 2.6 8.4 2.6 2.6 2.9-7.4 2.6-3.4 8.4

1.9-4.0 4.0-8.0 1.9-8.4

m j MDEA, mol/kg

e4.7 e11.0 0.3-2.8 0.1-7.6 e1.7 0.1-4.6 e5.4 e3.1 0.6-4.0 e3.6 0.7-6.6 e5.4 e3.8 0.3-6.9 0.5-4.1 0.1-5.4 e0.3 0.6-3.4 0.1-7.1 e0.7 0.1-4.1 2.8-3.4 0.1-2.0 e8.2 2.2-3.4 1.4-6.8

e4.9 1.0-9.2 e4.7

m j CO2, mol/kg

2.7-4560

1155-4080

12-4080

24-6331

74-5037 177-7565

p, kPa

0.1-95.6 534-4370 101-2320 66-813

0.9-1013 e1.6 0.8-140

0.1-69.3 e6630 19-6164 103-4930 e17.4 e6528 e93.6 1.2-3770 1.1-1979 e262 162-3832 e19854 0.1-173 10-268 1.0-1916 0.1-98.2 e1.0

0.1-69.3

pCO2, kPa

6.1

8.2

15.7

11

3 3.5

|∆p/p|, %

A small temperature correction was applied to the experimental data by Pe´rez-Salado Kamps et al.;2 see Appendix II.

82 28 101

Correlation Kuranov et al.1 Pe´rez-Salado Kamps et al.2 a this work

a

N

source

T, K

experimental ranges

46.9

214

245

255

44.7 85.3

|∆p|, kPa

427 6 76.8 10.1

32.3 22.4 15.7

72.5 12.1 29 9.9 88 10.8 34.5 338 24.5 16.9 26.6 21.0 709 39.5 21.2 22.0

3.9

pCO2 %

,

| |

∆pCO2

parameter set II

6.2 171 511 41.7

96.4 0.08 2.5

931 253 588 0.94 1633 1.9 211 162 6.8 416 893 3.1 508 177 4.2 0.02

0.64

|∆pCO2|, kPa

6.8

8

18.1

11.2

1.7 1.9

|∆p/p|, %

mean relative deviations

48.2

203

239

239

24.2 39.4

|∆p|, kPa

407 6.4 74.5 7.3

24.4 19.6 27.6

16.8 62.6 12.1 35.1 31.2 54.1 28.8 37 361 39 13.4 33.2 24.7 107 54.6 16.1 47.5

pCO2 %

∆pCO2

| |

parameter set I

,

7.8 167 501 28.9

85.8 0.10 5.9

2.6 935 238 681 1.6 1854 3.8 214 162 32.3 352 767 5.0 47.1 170 2.1 0.05

|∆pCO2|, kPa

Table 5. Comparison between Experimental Data from the Literature for the Total and/or Partial Pressure above Aqueous Solutions of MDEA and CO2 and Calculation Results from the Present Model

6086 Ind. Eng. Chem. Res., Vol. 45, No. 17, 2006

Ind. Eng. Chem. Res., Vol. 45, No. 17, 2006 6087

database in both the high and low gas loading regions, the left diagrams of those figures include the partial pressures of carbon dioxide in the high gas loading region (at T ≈ 313, 353, and 393 K), as calculated from the (corrected) experimental total pressures1,2 by subtracting the (small) partial pressure of water, as predicted from the model. As can be seen from Figures 2-4, the previous model (parameter set I, dashed curves) is able to reasonably predict the new experimental results for the partial pressure of carbon dioxide above (CO2 + MDEA + H2O) in the low gas loading region. The average relative (absolute) deviation between experimental and prediction results for pCO2 amounts to 16.8% (2.6 kPa) [12.1% (1.5 kPa), 16.9% (2.5 kPa), and 20.8% (3.6 kPa) at m j MDEA ≈ 2, 4, and 8 mol‚kg-1, respectively]. (b) New Correlation. However, to attain an even better agreement between the new experimental results and the model calculation results for the partial pressure of carbon dioxide above (CO2 + MDEA + H2O) in the low gas loading region, a new set of interaction parameters was determined (parameter set II, see Table 4). It was adjusted to the gas solubility data in both the low gas loading region (data from the present work) and the high gas loading region (data by Kuranov et al.1 and corrected data by Pe´rez-Salado Kamps et al.2). In an optimization procedure, the difference between experimental and calculated results for the partial pressure of carbon dioxide and for the total pressure above (CO2 + MDEA + H2O) (in the low and high gas loading regions, respectively) was minimized. The model accurately (almost within the estimated experimental uncertainty) describes the experimental results for the solubility of CO2 in aqueous solutions of MDEA for both low and high gas loadings (see Figures 2-4, full curves). With parameter set II, the average relative (absolute) deviation between experimental and correlation results for pCO2 (at low gas loadings) amounts to 3.9% (0.6 kPa) [2.9% (0.5 kPa), 5.3% (0.8 kPa), and 3.8% (0.6 kPa) at m j MDEA ≈ 2, 4, and 8 mol‚kg-1, respectively]. The agreement between experimental and correlation results for the total pressure p (at high gas loadings) is only somewhat worse than that with parameter set I. With parameter set II, the average relative (absolute) deviation between experimental and correlation results for p amounts to 3.1% (55 kPa) [2.6% (46 kPa), 3.2% (43 kPa), and 3.9% (96 kPa) at m j MDEA ≈ 2, 4, and 8 mol‚kg-1, respectively], whereas with parameter set I, those deviations amount to 1.7% (28 kPa) [1.3% (19 kPa), 1.9% (29 kPa), and 1.9% (44 kPa) at m j MDEA ≈ 2, 4, and 8 mol‚kg-1, respectively]. Comparison with Literature Data Table 5 reports mean relative and absolute deviations between experimental results for the total pressure and/or the partial pressure of carbon dioxide above liquid mixtures of (CO2 + MDEA + H2O) taken from the literature as well as from the present work and correlation/prediction results from the present model (parameter set II) as well as from the previous model (parameter set I). As was already mentioned before, the database available from the open literature for the solubility of carbon dioxide in aqueous solutions of MDEA is large and the results from the different publications scatter widely. This holds at all temperatures and for both low and high gas loadings. Therefore, it is difficult to assess the quality of these data. As a first example, in Figure 5, some experimental results for the partial pressure of carbon dioxide above an aqueous solution of MDEA (m j MDEA ≈ 2.56 mol‚kg-1) at T ≈ 313 K (from Jou et al.,3 Austgen et al.,9 MacGregor and Mather,10 Haji-Sulaiman et al.,17 Ali and

Figure 5. Partial pressure of carbon dioxide above liquid mixtures of (CO2 + MDEA + H2O), m j MDEA ≈ 2.56 mol‚kg-1, T ) 313 K. Experimental results: Jou et al.3 (2); Austgen et al.9 (0); MacGregor and Mather10 (4); Haji-Sulaiman et al.17 (*); Ali and Aroua24 (]); Jenab et al.26 (O). (s) Prediction (parameter set II), this work. (- - -) Prediction (parameter set I), this work.

Figure 6. Partial pressure of carbon dioxide above liquid mixtures of (CO2 + MDEA + H2O), m j MDEA ≈ 8 mol‚kg-1. Experimental results: Jou et al.3 (2) 313 K, (4) 373 K; Chakma and Meisen5 ([) 373 K; Austgen et al.9 (/) 313 K; Dawodu and Meisen13 (0) 373 K; Xu et al.20 (b) 313 K, (O) 373 K. (s) Prediction (parameter set II), this work. (- - -) Prediction (parameter set I), this work.

Aroua,24 and Jenab et al.26) are plotted versus the stoichiometric molar ratio of carbon dioxide to MDEA. In addition, in Figure 5, they are compared with prediction results from the previous model (parameter set I, dashed curves) and from the present model (parameter set II, full curves). As a second example, in Figure 6, some experimental results for pCO2 above an aqueous solution of MDEA (m j MDEA ≈ 8 mol‚kg-1) at T ≈ 313 K (from 3 Jou et al., Austgen et al.,9 and Xu et al.20) as well as at T ≈ 373 K (from Jou et al.,3 Chakma and Meisen,5 Dawodu and Meisen,13 and Xu et al.20) are plotted versus the stoichiometric molar ratio of carbon dioxide to MDEA and compared with prediction results from the previous and from the present model. Conclusions Modeling the phase equilibrium for the simultaneous solubility of carbon dioxide and hydrogen sulfide in aqueous solutions of MDEA or amine mixtures with MDEA requires a reliable and extensive experimental database on the solubility of the single gases in aqueous solutions of the single amines. However, even for one of the most important subsystems (CO2 + MDEA + H2O), gas solubility data from the open literature scatter

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widely. This holds at all temperatures and gas loadings (i.e., also at all pressures). In an attempt to improve that database, the solubility of carbon dioxide in aqueous solutions of MDEA was investigated in previous work by means of a technique based on the synthetic method1,2 but which is restricted to the high gas loading/elevated pressure region (p > 0.2 MPa). A temperature range from about 313 to 413 K was covered, MDEA molalities amounted to about 2, 4, and 8 mol/(kg of water), and total pressures ranged from about 0.2 to 8 MPa. In the present work, a headspace gas chromatography technique is applied for the reliable determination of the solubility of carbon dioxide in aqueous solutions of MDEA at low gas loadings. The temperature ranges from about 313 to 393 K. The stoichiometric molality of MDEA amounts to about 2, 4, and 8 mol/(kg of water). Partial pressures of carbon dioxide range from about 0.1 to 70 kPa. A previously presented thermodynamic model for describing the phase equilibrium of the system (CO2 + MDEA + H2O), which was solely based on the gas solubility data in the high gas loading region,1,2 is now extended, allowing for the new experimental results in the low gas loading region. Acknowledgment We thank Dirk Speyer for assisting in performing some of the experiments at T ) 393 K. Some small cofinanciation of the experimental part of this work by the Max-Buchner Forschungsstiftung is gratefully acknowledged.

Pitzer’s Molality-Scale-Based Equation for the Gibbs Excess Energy. Pitzer’s molality-scale-based equation for the excess Gibbs energy (GE) of aqueous electrolyte solutions is36,37

M/WnWRT

g(x) )

2 [1 - (1 + x) exp(-x)] x2

(A6)

(1) (2) (1) (2) β(0) ij , βij , βij , Rij , and Rij are binary parameters. In the (2) present work, R(1) ij is set to 2. Furthermore, βij is set to zero; (2) therefore, Rij is not required. When a single (chemically nonreacting) gas G is dissolved in pure water, the model contains only two interaction parameters (β(0) G,G and µG,G,G). For binary systems (water + strong electrolyte Mν+Xν-), it is not possible to separate the influence of µM,M,X from that of µM,X,X. Both ternary parameters are usually summarized in CφMX:

CφMX )

3

xν+ ν-

[ν+ µM,M,X + ν- µM,X,X]

(A7)

It is common practice to set either µM,M,X or µM,X,X to zero and (1) φ to report β(0) M,X, βM,X, and CMX (or µM,X,X or µM,M,X). In ternary systems (water + strong electrolyte Mν+Xν- + gas G) it is similarly not possible to separate the influence of M and X on solute G. Therefore, it is common practice to use the following comprehensive parameters: (j) (j) B(j) G,MX ) ν+ βG,M + ν- βG,X, (j ) 0, 1)

(A8)

ΓG,MX,MX ) ν2+ µG,M,M + 2ν+ ν- µG,M,X + ν2- µG,X,X (A9)

Appendix I

GE

g(x) is defined as

) f(I) +

mi m j

λij(I) + ∑∑ i,j*W m° m° (A1)

R is the universal gas constant, T is the absolute temperature, and f(I) is Pitzer’s modification of the Debye-Hu¨ckel term. As usual, second and third osmotic virial coefficients in Pitzer’s GE equation were treated as symmetric:

λij ) λji

(A2)

µijk ) µikj ) µjik ) µjki ) µkij ) µkji

(A3)

“Symmetrical and unsymmetrical mixing terms”37 as well as all parameters describing interactions between ionic species carrying charges of the same sign were neglected. According to Pitzer’s equations, λij is written as (1) (1) (2) (2) λij ) β(0) ij + βij g(Rij xI) + βij g(Rij xI)

(A4)

where the ionic strength of the solution is given by

I)

1

mi

zi2 ∑ 2 i m°

and where zi is the number of charges on the solute i.

(A10)

(1) is rarely needed to describe the solubility of a gas in an BG,MX (0) aqueous solution of a strong electrolyte. BG,MX , ΓG,MX,MX, and ΓG,G,MX are usually sufficient for a good description of gas

Table 6. Solubility of Carbon Dioxide in Aqueous Solutions of MDEAa

mi mj mk

µijk ∑∑∑ i,j,k*W m° m° m°

ΓG,G,MX ) ν+ µG,G,M + ν- µG,G,X

(A5)

T, K

m j MDEA, mol‚kg-1

m j CO2, mol‚kg-1

p, MPa

313.69 313.70 313.75 313.71 313.73 313.71 313.78 313.73 313.74 313.74 313.75 313.75 313.73 354.38 354.38 354.38 354.37 354.38 354.40 354.36 354.38 394.94 395.00 394.94 394.99 394.95 394.94 394.95

3.954

3.338 3.477 3.898 4.562 4.914 6.363 6.815 7.387 7.748 7.887 8.471 8.947 9.227 2.518 3.188 4.426 5.494 6.183 6.616 7.153 7.554 1.007 1.617 2.588 3.308 3.823 4.440 4.761

0.1765 0.2293 0.7093 3.690 6.469 0.2280 0.3759 0.6495 1.147 1.456 3.082 6.015 7.565 0.2931 0.4216 0.7861 1.343 1.999 2.614 3.920 5.403 0.6851 1.110 2.100 3.137 4.046 5.310 6.117

7.994

7.994

7.994

a Experimental results from Pe ´ rez-Salado Kamps et al.2 (after applying a small temperature correction).

Ind. Eng. Chem. Res., Vol. 45, No. 17, 2006 6089 Table 7. Interaction Parameters (Set I) in Pitzer’s GE equation for the System (CO2 + MDEA + H2O)a parameter (0) βCO 2,HCO3 (0) βCO + 2MDEAH (0) βMDEA,HCO 3 (0) βMDEA,CO 23 (0) βMDEAH +,HCO 3 (0) βMDEAH+,CO32(1) βMDEAH +,HCO 3 (1) βMDEAH+,CO32-

µMDEAH+,HCO3-,HCO3µMDEAH+,CO32-,CO32µCO2,MDEAH+,HCO3-

q1

q2

T, K

T, K

m j MDEA, mol‚kg-1

m j H2S, mol‚kg-1

p, MPa

-1.6572 × 10-2 -4.6893 × 10-2 -5.6784 × 10-2 4.9449 × 10-2 1.7646 × 10-1 6.6557 × 10-2 2.9211 × 10-1 -2.4790 3.6951 × 10-5 3.1413 × 10-4 2.7855 × 10-3

49.690 -26.317 67.376

313-413

313.72 313.74 313.77 313.72 313.73 313.72 313.75 313.78 354.39 354.36 354.40 354.37 354.39 354.36 354.37 354.37 354.35 354.40 394.99 394.99 394.98 394.98 394.98 394.98 394.98 394.98

8.001

6.254 7.594 8.070 8.362 8.954 10.457 11.017 11.428 4.867 5.815 6.217 7.276 7.388 7.706 7.780 8.390 9.481 10.360 1.228 2.560 3.931 5.247 6.122 6.649 6.778 7.266

0.1479 0.3906 0.4715 0.6053 0.8428 1.610 1.879 2.159 0.3442 0.4940 0.6393 0.9883 1.033 1.198 1.220 1.595 2.251 2.783 0.3515 0.5393 0.8710 1.392 1.801 2.204 2.148 2.678

-49.176

897.44

-1.1562

The parameter set is based on CO2 gas solubility data in (MDEA + H2O) from Kuranov et al.1 and Pe´rez-Salado Kamps et al.2 (after applying a small temperature correction). f(T) ) q1 + q2/(T/K). a

(0) BG,MX ,

Table 8. Solubility of Hydrogen Sulfide in Aqueous Solutions of MDEAa

β(0) G,M

β(0) G,X

solubility. In arbitrarily either or may be set to zero; in ΓG,MX,MX, one can arbitrarily set two of the three parameters µG,M,M, µG,M,X, and µG,X,X to zero; and in ΓG,G,MX, one can arbitrarily set either µG,G,M or µG,G,X to zero. Appendix II Corrected Experimental Results by Pe´ rez-Salado Kamps et al.2 (I) System (CO2 + MDEA + H2O). The corrected experimental results for the solubility of CO2 in (MDEA + H2O) and the corrected interaction parameters of the previous model for the VLE of that system are listed in Tables 6 and 7, respectively. The experimental data for the total pressure above (CO2 + MDEA + H2O) by Kuranov et al.1 and Pe´rez-Salado Kamps et al.2 (after applying the temperature correction) are correlated with an average relative deviation of 1.7% (1.3%, 1.9%, and 1.9% at m j MDEA ≈ 2, 4, and 8 mol‚kg-1, respectively) (see also Figures 2-4). (II) System (H2S + MDEA + H2O). The corrected experimental results for the solubility of H2S in (MDEA + H2O) and the corrected interaction parameters of the previous model for the VLE of that system are listed in Tables 8 and 9, respectively. The experimental data for the total pressure above (H2S + MDEA + H2O) by Kuranov et al.1 and Pe´rez-Salado Kamps et al.2 (after applying the temperature correction) are correlated with an average relative deviation of 2.1% (1.7%,

8.001

8.001

a Experimental results from Pe ´ rez-Salado Kamps et al.2 (after applying a small temperature correction).

Table 9. Interaction Parameters in Pitzer’s GE Equation for the System (H2S + MDEA + H2O)a parameter

q1

βH(0)2S,H2Sb βH(0)2S,HS(0) βMDEA,HS (0) βMDEAH +,HS(1) βMDEAH +,HS-

-2.6156 × 10-1 9.6582 × 10-3 2.1482 × 10-1 3.9284 × 10-2 4.4771

q2 69.751 -18.988 -55.014

T, K 283-453 313-413

-1466.8

The parameter set is based on H2S gas solubility data in (MDEA + H2O) from Kuranov et al.1 and Pe´rez-Salado Kamps et al.2 (after applying a small temperature correction). f(T) ) q1 + q2/(T/K) b That parameter is based on H2S gas solubility data in pure water and was adopted from Kuranov et al.1 a

1.4%, and 3.7% at m j MDEA ≈ 2, 4, and 8 mol‚kg-1, respectively) (see also Figure 7).

Figure 7. Total pressure above liquid mixtures of (H2S + MDEA + H2O), m j MDEA ≈ 2 mol‚kg-1 (left diagram), 4 mol‚kg-1 (middle diagram), 8 mol‚kg-1 (right diagram). The left and middle diagrams show experimental results from Kuranov et al.:1 (2) 313 K, (4) 333 K, (9) 373 K, (0) 393 K, (b) 413 K. The right diagram shows experimental results from Pe´rez-Salado Kamps et al.2 (after applying a small temperature correction, see Appendix II): (2) 313.7 K, (3) 354.4 K, (0) 395 K. (s) Correlation, this work.

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Ind. Eng. Chem. Res., Vol. 45, No. 17, 2006

Nomenclature ai ) activity of component i Bi,j ) second virial coefficient for interactions between components i and j B(j) ) effective second osmotic virial coefficient in Pitzer’s GE equation for interactions between gas G and salt MX (j ) 0, 1) Cφ ) effective third osmotic virial coefficient in Pitzer’s GE equation for interactions between M and X f(I) ) Pitzer’s modification of the Debye-Hu¨ckel term f(T) ) function for the temperature dependence of interaction parameters (see Tables 4, 7, and 9) g(x) ) see eq A6 GE ) excess Gibbs energy (on the molality scale) I ) ionic strength (on the molality scale) kH,i ) Henry’s constant for the solubility of gas i in pure water (on the molality scale) Kr ) equilibrium constant for chemical reaction r (on the molality scale) mi ) true molality of component i m j i ) stoichiometric molality of component i m° ) reference molality (m° ) 1 mol‚kg-1) M ) cation M M/W ) relative molar mass of water divided by 1000 (M/W ) 0.018 015 28) ni ) true amount of substance (number of moles) of species i nji ) stoichiometric amount of substance (number of moles) of component i N ) number of experimental points p ) pressure pi ) partial pressure of component i psW ) vapor pressure of pure water qi ) coefficients for the temperature dependence of interaction parameters (see Tables 4, 7, and 9) R ) universal gas constant T ) absolute temperature V∞i ) partial molar volume of gas i infinitely diluted in water VW ) molar volume of water X ) anion X yi ) vapor-phase mole fraction of component i zi ) number of charges of component i Greek Letters E R(k) ij ) binary parameter in Pitzer’s G equation (k ) 1, 2) E equation (k ) 0, 1, 2) β(k) ) parameters in Pitzer’s G ij describing binary interactions (between solutes i and j in water) γi ) activity coefficient of species i (on the molality scale) Γ ) effective third osmotic virial coefficient in Pitzer’s GE equation for interactions between gas G and salt MX ∆z ) generally, experimental uncertainty in property z λij(I) ) second osmotic virial coefficient in Pitzer’s GE equation µijk ) third osmotic virial coefficient in Pitzer’s GE equation ) parameter describing ternary interactions (between solutes i, j, and k in water) νi,r ) stoichiometric factor of reactant i in reaction r (νi,r > 0 for a product and νi,r < 0 for an educt) ν+, ν- ) number of cations and anions, respectively, in electrolyte MX ξr ) extent of reaction r φi ) vapor-phase fugacity coefficient of component i

Subscripts G ) gas

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ReceiVed for reView April 5, 2006 ReVised manuscript receiVed May 31, 2006 Accepted June 6, 2006 IE0604270