Solubility of H2S in H2O+ N-Methyldiethanolamine+(H2SO4 or Na2SO4)

Solubility of H2S in H2O + N-Methyldiethanolamine + (H2SO4 or ... The solubility of hydrogen sulfide in aqueous solutions of N-methyldiethanolamine (M...
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Ind. Eng. Chem. Res. 2002, 41, 2571-2578

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Solubility of H2S in H2O + N-Methyldiethanolamine + (H2SO4 or Na2SO4) Yuri Anoufrikov,† A Ä lvaro Pe´ rez-Salado Kamps,‡ Bernd Rumpf,‡ Natalia A. Smirnova,† and Gerd Maurer*,‡ Lehrstuhl fu¨ r Technische Thermodynamik, Universita¨ t Kaiserslautern, D-67653 Kaiserslautern, Federal Republic of Germany, and Department of Chemistry, St. Petersburg State University, St. Petersburg, Russia

The solubility of hydrogen sulfide in aqueous solutions of N-methyldiethanolamine (MDEA) and MDEA sulfate (2 and 1 m, respectively) and in aqueous solutions of MDEA and sodium sulfate (2 and 1 m, respectively) was measured at temperatures from 313 to 393 K and total pressures up to about 3.9 MPa. The experimental results are used to extend and test a model for the thermodynamic equilibrium encountered in the solubility of hydrogen sulfide in such aqueous solutions. Introduction Aqueous N-methyldiethanolamine (2,2′-methyliminodiethanol; MDEA) is an effective solvent for sour gases. It is widely used for the sweetening of gas mixtures containing sulfuric compounds (such as hydrogen sulfide, methylmercaptan, carbonyl sulfide, or carbon disulfide) and carbon dioxide. Because the absorption of carbon dioxide is hindered by slow kinetics, the sulfuric compounds are selectively absorbed in aqueous MDEA. The gas mixtures often contain some sulfur trioxide. In aqueous solutions sulfur trioxide is converted to sulfuric acid. Sulfuric acid reduces the absorption capacity of the aqueous MDEA solution because it reacts with MDEA to MDEA sulfate. In addition, MDEA sulfate influences the thermodynamic equilibrium because it reduces, like many other strong electrolytes, the gas solubility (“salting out”). In some processes sodium hydroxide is added to convert MDEA sulfate to sodium sulfate and MDEA. The absorption medium is then an aqueous solution of MDEA and sodium sulfate. A reliable computer-assisted design of such ab-/desorption equipment requires, on the one hand, the knowledge of transport and reaction kinetics and, on the other hand, a reliable model for the thermodynamic equilibrium, i.e., the phase equilibrium and the chemical reaction equilibria, because deviation from equilibrium provides the driving force for the kinetics. The development of such models has to be based on experimental data. The present contribution aims to provide reliable experimental data on the solubility of hydrogen sulfide in aqueous solutions of MDEA + MDEA sulfate (2 and 1 m, respectively) and of MDEA + sodium sulfate (also 2 and 1 m, respectively) at temperatures from 313 to 393 K and total pressures up to about 3.9 MPa. Furthermore, that experimental data is used together with literature data for the phase equilibrium in binary and ternary subsystems (e.g., H2S + H2O, H2SO4 + H2O, * To whom correspondence should be addressed. Phone: +49 631 205 2410. Fax: +49 631 205 3835. E-mail: gmaurer@ rhrk.uni-kl.de. † St. Petersburg State University. ‡ Universita ¨ t Kaiserslautern.

Na2SO4 + H2O, H2S + MDEA + H2O, H2S + Na2SO4 + H2O) to extend and test a thermodynamic model for the solubility of hydrogen sulfide in aqueous solutions of MDEA.1,2 An extension of that model to include the solubility of carbon dioxide in aqueous solutions of MDEA and the strong electrolytes MDEA sulfate and sodium sulfate has recently been presented.3 Thus, a method to calculate the vapor-liquid equilibrium of the industrial important system CO2 + H2S + MDEA + H2SO4 + Na2SO4 + H2O is now available. Experimental Section The experimental equipment and procedure are basically the same as those in previous investigations (cf., for example, ref 4); therefore, only a few essentials are given here. In an experiment, a thermostated high-pressure cell (material, Hastelloy C4; volume, about 30 cm3) with two sapphire windows is partially filled with a known amount of the aqueous solvent. A known amount of gas is added to the cell from a storage tank. Step by step, more aqueous solvent is added to the cell by a calibrated high-pressure displacement pump, until the gas is completely dissolved in the liquid phase. The amount of solvent charged to the cell is only slightly above the minimum amount needed to dissolve the gas completely. After equilibration, which is achieved after a rather long period of time (about 2 h), very small amounts of the liquid mixture are withdrawn stepwise from the cell until the first very small stable bubbles appear. That pressure is the equilibrium pressure to dissolve the charged amount of the gas in the charged amount of solvent at the fixed temperature. The mass of the charged gas (up to about 2.7 g) is determined by weighing with an uncertainty of (0.008 g. The volume of the aqueous solvent needed to dissolve the gas is determined by measuring the position of the high-pressure displacer piston before and after each experiment. The mass of the solvent is calculated, with a relative uncertainty of a maximum of 0.7%, from its known density (from separate measurements with a vibrating tube densimeter). Two pressure transducers

10.1021/ie010747d CCC: $22.00 © 2002 American Chemical Society Published on Web 04/17/2002

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Table 1. Experimental Conditions of the Present Investigation strong electrolyte M2X

m j MX/ (mol/kg)

m j MDEA/ (mol/kg)

H2SO4

1

4

Na2SO4

0.95

1.9

(max) / m jH 2S (mol/kg)

T/K

p(max)/ MPa

4.33 3.52 3.02 3.41 3.09 2.63

313 353 393 313 353 393

2.71 3.16 3.66 2.81 3.87 3.77

Table 2. Solubility of Hydrogen Sulfide in Aqueous Solutions of MDEA and H2SO4 (m j MDEA ) 3.992 mol/kg; m j H2SO4 ) 0.9862 mol/kg) T/K

m j H2S/ (mol/kg)

10p/MPa

T/K

m j H2S/ (mol/kg)

10p/MPa

313.15 313.15 313.14 313.15 313.16 313.15 313.15 353.16 353.17 353.16 353.18 353.17 353.17 353.16

1.629 2.091 2.613 3.167 3.361 3.839 4.331 1.403 1.901 2.321 2.819 2.825 3.115 3.517

0.958 2.846 8.063 13.92 15.84 21.24 27.08 2.522 5.517 10.72 18.75 18.93 24.21 31.58

393.13 393.16 393.14 393.17 393.13 393.15 393.15

0.6262 1.276 1.790 2.202 2.364 2.695 3.017

3.561 7.218 12.76 19.11 22.50 28.93 36.56

(WIKA GmbH, Klingenberg, Germany) for pressures ranging to 0.6 MPa and to 4 MPa were used to determine the solubility pressure. Before and after each series of measurements, the transducers were calibrated against a high-precision pressure gauge (Desgranges & Huot, Aubervilliers, France). The maximum uncertainty in the pressure measurement is 0.1% of each transducer’s maximum reading. The temperature is determined with two calibrated platinum resistance thermometers placed in the heating jacket of the cell with an uncertainty below (0.1 K. The aqueous solutions were prepared in a storage tank by dissolving known amounts of MDEA and H2SO4 or Na2SO4 in pure water. The molalities of MDEA and Na2SO4 in the aqueous solution were determined gravimetrically with relative uncertainties smaller than (0.1%. The relative uncertainty in the molality of H2SO4 was less than (0.1% because it was taken from a Fixanal tube. Substances. Hydrogen sulfide (g98 mol %) was purchased from Messer-Griesheim, Ludwigshafen, Germany. It was used without further purification. MDEA (g98 mass %; Merck-Griesheim, Ludwigshafen, Germany) was degassed under vacuum. Sulfuric acid (Fixanal, 0.5 mol; Riedel de Hae¨n AG, Seelze, Germany) was used without further purification. Sodium sulfate (g99.0 mass %; Riedel de Hae¨n AG, Seelze, Germany) was degassed and dried under vacuum. Deionized water was degassed by vacuum distillation. Experimental Results Table 1 gives an overview of the experiments of the present work for the solubility of hydrogen sulfide in aqueous solutions of MDEA and one of the single strong electrolytes sulfuric acid and sodium sulfate. Throughout the paper, molality (i.e., the number of moles per

Figure 1. Total pressure above aqueous solutions of H2S + MDEA + H2SO4 (m j MDEA ≈ 4 mol/kg; m j H2SO4 ≈ 1 mol/kg): (O, 4, 0) exptl results, this work; (s) correlation, this work.

Figure 2. Total pressure above aqueous solutions of H2S + MDEA + Na2SO4 (m j MDEA ≈ 2 mol/kg; m j Na2SO4 ≈ 1 mol/kg): (O, 4, 0) exptl results, this work; (s) prediction, this work; (- -) correlation (with τNa+,HS-,SO42- and τH2S,Na+,MDEAH+ according to Table 4), this work.

kilogram of water) is used for describing the concentration of a solute. In a first series of measurements, the

Ind. Eng. Chem. Res., Vol. 41, No. 10, 2002 2573

spent by the chemical reactions and more sour gas can no longer be absorbed chemically, i.e., in nonvolatile ionic form, but has to be dissolved physically. The new experimental results will be compared to correlations/predictions in the following chapters. Modeling Figure 3 shows a scheme of the model applied to correlate the solubility of hydrogen sulfide in aqueous solutions of MDEA and the strong electrolytes sulfuric acid and sodium sulfate. The vapor-liquid equilibrium is described by the extended Raoult’s law for water s s pH φH exp 2O 2O

(

)

s vH2O(p - pH ) 2O

RT

aH2O ) yH2Opφ′′H2O (1)

and by the extended Henry’s law for hydrogen sulfide Figure 3. Vapor-liquid equilibrium and chemical reactions in the H2S + MDEA + H2SO4 + Na2SO4 + H2O system. Table 3. Solubility of Hydrogen Sulfide in Aqueous Solutions of MDEA and Na2SO4 (m j MDEA ) 1.900 mol/kg; m j Na2SO4 ) 0.9566 mol/kg) T/K

m j H2S/ (mol/kg)

10p/MPa

313.15 313.15 313.15 313.15 313.14 313.14 313.15 313.15 313.15 353.15 353.13 353.13 353.11 353.15 353.18 353.16

1.314 1.623 1.718 2.079 2.429 2.938 3.089 3.138 3.412 1.316 1.706 1.982 2.124 2.588 2.790 3.090

0.327 0.757 0.958 4.746 10.11 18.51 21.20 22.45 28.06 1.736 4.006 7.891 10.69 22.85 30.52 38.66

T/K

m j H2S/ (mol/kg)

10p/MPa

393.15 393.15 393.13 393.14 393.13 393.14 393.13 393.15 393.16

0.5567 0.9239 1.458 1.857 1.933 2.012 2.030 2.354 2.626

2.658 3.654 7.507 14.10 16.16 18.13 18.53 28.57 37.69

solubility of H2S was measured in about 4 m MDEA + 1 m H2SO4 aqueous solutions at temperatures of 313, 353, and 393 K (cf. Table 2). Because the strong (sulfuric) acid is completely neutralized, the solvent can be treated as a 2 m MDEA + 1 m (MDEAH)2SO4 aqueous solution. The experimental results for the total pressure above that solution are plotted in Figure 1 versus the stoichiometric molality of hydrogen sulfide. In a second series of measurements, the solubility of H2S was measured in a 2 m MDEA + 1 m Na2SO4 aqueous solution at temperatures of 313, 353, and 393 K. The experimental results for the total pressure above those solutions are given in Table 3. They are plotted in Figure 2 versus the stoichiometric molality of hydrogen sulfide. The behavior of the quaternary system H2S + MDEA + Na2SO4 + H2O is very similar to that observed for the salt-free system.2 Adding hydrogen sulfide to an MDEA- and Na2SO4-containing aqueous solution at first only slightly increases the total pressure above the solution because the sour gas is mostly dissolved in nonvolatile, ionic form. When the stoichiometric molality of the sour gas surmounts that of MDEA, the total pressure increases steeply because MDEA has been

(m) s (T,pH ) HH 2S,H2O 2O

(

exp

)

∞ s vH (p - pH ) 2S,H2O 2O

RT

/ mH2SγH ) 2S

yH2Spφ′′H2S (2)

In principle, MDEA might also be present in the vapor phase. However, because the vapor pressure of pure MDEA is very small in the temperature range considered here (cf. ref 5), the presence of MDEA in the vapor phase is neglected. Furthermore, it is worthwhile to mention that the solubility of hydrogen sulfide in the aqueous phase is limited by the appearance of a second liquid but hydrogen sulfide rich phase (see, e.g., refs 6-8). However, that solubility limit was not reached in the present work. The molality of hydrogen sulfide in the liquid phase differs from the corresponding stoichiometric molality as hydrogen sulfide reacts with MDEA. The model takes into account the following chemical reaction equilibria in the liquid phase: the formation and dissociation of bisulfide (reactions R1 and R2), the autoprotolysis of water (reaction R3), the dissociation of protonated MDEA (reaction R4), and the formation of bisulfate (reaction R5). Although reaction R5 is not significant in the concentration ranges considered in this work, it was included in the model in order to enable extrapolations/predictions in other concentration regions. It is assumed that the strong electrolytes sulfuric acid and sodium sulfate are fully dissociated in the aqueous phase. The condition for chemical equilibrium yields the following equation for a chemical reaction R:

KR(T) )

∏i aνi

i,R

(3)

where νi,R is the stoichiometric factor of component i in reaction R (νi,R > 0 for a product and νi,R < 0 for an educt). For any dissolved species (but not for the solvent water), the activity ai is

ai ) miγ/i

(4)

The activity of water follows from the activities of the solutes by applying the Gibbs-Duhem equation. To determine the molalities of all (neutral and ionic) species in the liquid phase for given temperature and

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stoichiometric mole numbers of MDEA (n j MDEA ) m j MDEA), j H2S), water (n j H2O ) 1/MH2O), hydrogen sulfide (n j H2S ) m j H2SO4), and sodium sulfate sulfuric acid (n j H2SO4 ) m j Na2SO4) in the liquid phase, the equations (n j Na2SO4 ) m for chemical reaction equilibrium have to be solved simultaneously with the mass balance equations:

n j H2O ) nH2O + nOH-

(5)

n j H2S ) nH2S + nHS- + nS2-

(6)

n j MDEA ) nMDEA + nMDEAH+

(7)

n j H2SO4 + n j Na2SO4 ) nSO2+ nHSO-4 4

(8)

2n j Na2SO4 ) nNa+

(9)

and the condition for electroneutrality of the aqueous phase:

nMDEAH+ + nH+ + nNa+ ) nHS- + 2nS2- + nOH- + 2nSO42- + nHSO4- (10) The model requires the following thermodynamic s properties: (i) Vapor pressure of water, pH , which 2O 9 was taken from Saul and Wagner. (ii) Molar volume of liquid water, vH2O, which was approximated by s .9 the molar volume of saturated liquid water, vH 2O (m) (iii) Henry’s constant (on the molality scale) HH2S,H2O for the solubility of H2S in pure water, which was taken from Edwards et al.10 (iv) Partial molar volume of H2S ∞ , which was calat infinite dilution in water, vH 2S,H2O culated as recommended by Brelvi and O’Connell.11 (v) s , and Fugacity coefficients (for saturated water, φH 2O for water and hydrogen sulfide in the vapor phase, φ′′i). They were calculated from the virial equation of state truncated after the second virial coefficient. The virial coefficients BH2S,H2S and BH2S,H2O were calculated as recommended by Hayden and O’Connell.12 BH2O,H2O was calculated from a correlation given by Rumpf and Maurer,4 which is based on the data collection by Dymond and Smith.13 (vi) Chemical reaction equilibrium constants (on the molality scale), KR(T) (R } R1, ..., R5): KR1 and KR2 were taken from Kawazuishi and Prausnitz,14 KR3 from Edwards et al.,10 and KR4 from Pe´rez-Salado Kamps and Maurer,15 and KR5 was obtained from Pitzer et al.16 (vii) Activity of water, aH2O, and activity coefficients, γ/i , of all solute species, which were calculated from a modified Pitzer model17 for the excess Gibbs energy GE of aqueous solutions containing strong electrolytes. The resulting expressions are given, e.g., by Pe´rez-Salado Kamps et al.2 As far as possible, (0) (1) interaction parameters (βi,j , βi,j , and τi,j,k) for the interesting system H2S + MDEA + H2SO4 + Na2SO4 + H2O are taken from the literature on binary and ternary subsystems. Interaction Parameters in Pitzer’s GE Model From Binary Subsystems. (i) H2S + H2O and MDEA + H2O. When one of the single components H2S 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 solutes, only interaction parameters (0) and τi,i,i (for i being H2S or MDEA) can be deterβi,i mined. However, in the concentration range of interest in the present work, all of those parameters, with the (0) , can be neglected. The correlation exception of βH 2S,H2S of Kuranov et al.1 was taken to describe the influence (0) of temperature on βH for temperatures from 283 to 2S,H2S 453 K. (ii) H2SO4 + H2O and NaOH + H2O. Interaction parameters for the system H2SO4 + H2O were taken from Pitzer et al.16 They are valid for temperatures around 298 K, but they were adopted also for temperatures up to 413 K. Interaction parameters for the system NaOH + H2O (for temperatures from 273 to 623 K) were taken from Pabalan and Pitzer.18 Although they are not significant in the concentration ranges considered in this work (very small amounts of H+ ions as well as of OH- ions), they were included in the model in order to enable extrapolations/predictions to other concentration regions. (iii) Na2SO4 + H2O. Interaction parameters for the system Na2SO4 + H2O (for temperatures from 303 to 473 K) were taken from Rogers and Pitzer.19 From Ternary and Quaternary Subsystems. (i) H2S + MDEA + H2O. Pe´rez-Salado Kamps et al.2 described experimental results for the solubility of hydrogen sulfide in aqueous solutions of MDEA (m j MDEA e 8 m) in the temperature range from 313 to 413 K and for pressures up to 4.9 MPa applying Pitzer’s expression for the excess Gibbs energy of the aqueous solution. The set of parameters was adopted here. (Of course, the (0) , determined from the binary subparameter βH 2S,H2S system H2O + H2S, was taken into account in that description.) (ii) H2S + (MDEAH)2SO4 + H2O. To describe the solubility of hydrogen sulfide in aqueous solutions of (MDEAH)2SO4, parameters for the binary subsystems H2S + H2O and (MDEAH)2SO4 + H2O should be taken into account. However, because no experimental data are available for the binary subsystem (MDEAH)2SO4 + H2O, parameters between MDEAH+ and SO42- had to be neglected. (0) The three parameters BH , 2S,(MDEAH)2SO4 ΓH2S,(MDEAH)2SO4,(MDEAH)2SO4, and ΓH2S,H2S,(MDEAH)2SO4 should be considered in order to describe the solubility of H2S in aqueous solutions of (MDEAH)2SO4. However, because no experimental data are available for the solubility of H2S in aqueous solutions of (MDEAH)2SO4, the discussion is postponed to the next section, which treats the solubility of H2S in aqueous solutions of MDEA and (MDEAH)2SO4. (iii) H2S + MDEA + (MDEAH)2SO4 + H2O. Figure 4 shows calculations for the species distribution in an aqueous solution of 2 m MDEA + 1 m (MDEAH)2SO4 at 353 K, when hydrogen sulfide is added. For hydrogen sulfide molalities above about 2 m, merely species H2S, MDEAH+, HS-, and SO42- are present in considerable concentrations. Such solutions can, therefore, be approximated by a “nonreacting” mixture of water, hydrogen sulfide, and the two strong electrolytes MDEAHHS and (MDEAH)2SO4. The solubility data for this system

Ind. Eng. Chem. Res., Vol. 41, No. 10, 2002 2575 Table 4. Additional Interaction Parameters for Pitzer’s Equation (This Work) f(T) ) q1 + q2/T parameter

q1

q2

0.071 024

-20.352

(0) BH 2S,NaHS

-0.068 381

48.941

ΓH2S,NaHS,NaHS τNa+,HS-,SO24 τH2S,Na+,MDEAH+

0.033 150 0.311 652 -0.001 983

-10.995 -85.167 -1.440

(0) BH 2S,(MDEAH)2SO4

subsystem

T/K

H2S + MDEA + (MDEAH)2SO4 + H2O

313-393

fitted

H2S + NaOH + H2O

313-393

predicted

H2S + MDEA + Na2SO4 + H2O

313-393

fitted fitted fitted

(v) H2S + (NH4)2SO4 + H2O. This system is not a subsystem of the system H2S + MDEA + H2SO4 + Na2SO4 + H2O. However, the interaction parameters (0) for this system (BH and ΓH2S,(NH4)2SO4,(NH4)2SO4, 2S,(NH4)2SO4 given by Xia et al.6 for temperatures from 313 to 393 K) were taken into account. With the conventions mentioned in a previous work (see, e.g., ref 3): (0) + ) 0 βG,NH 4

(11)

τG,M,M ) τG,X,X ) 0

(12)

τG,G,NH4+ ) 0

(13)

one finds (cf. work by Pe´rez-Salado Kamps et al.2) Figure 4. Predicted species distribution in the H2S + MDEA + H2SO4 + H2O system at 353 K (m j MDEA ) 4 mol/kg; m j H2SO4 ) 1 mol/kg).

might, therefore, be described with interaction parameters for the binary subsystems H2S + H2O, MDEAHHS + H2O, and (MDEAH)2SO4 + H2O and for the ternary subsystems H2S + MDEAHHS + H2O and H2S + (MDEAH)2SO4 + H2O. As mentioned above, interaction parameters for the binary subsystem H2S + H2O are available, whereas those for the binary subsystem (MDEAH)2SO4 + H2O had to be neglected. Interaction parameters for the binary subsystem MDEAHHS + H2O and for the ternary subsystem H2S + MDEAHHS + H2O are available from a model for the solubility of hydrogen sulfide in pure water and in aqueous solutions of MDEA.2 Therefore, the new experimental data for the system H2S + MDEA + (MDEAH)2SO4 + H2O (cf. Table 2) were used to determine those parameters which, in principle, should be accessible from experimental investigations on the solubility of H2S in aqueous solutions (0) i.e., BH , of (MDEAH)2SO4, 2S,(MDEAH)2SO4 ΓH2S,(MDEAH)2SO4,(MDEAH)2SO4, and ΓH2S,H2S,(MDEAH)2SO4. With (0) BH alone (i.e., setting 2S,(MDEAH)2SO4 ΓH2S,(MDEAH)2SO4,(MDEAH)2SO4 ) ΓH2S,H2S,(MDEAH)2SO4 ) 0), the experimental results for the total pressure can be correlated with an average relative deviation of 3.3%. The maximum relative deviation in the total pressure is 9.3%, occurring at T ) 313.15 K and p ) 0.0958 MPa, where the calculated pressure is too small by about 0.009 MPa. No essential improvement could be achieved by additionally considering one of the ternary param(0) eters. BH is given in Table 4. The results of 2S,(MDEAH)2SO4 the correlation are compared with the experimental data in Figure 1. (iv) H2S + Na2SO4 + H2O. Interaction parameters (0) for that system (BH and ΓH2S,Na2SO4,Na2SO4) were 2S,Na2SO4 taken from Xia et al.6 (for temperatures from 313 to 393 K).

(0) (0) 2- ) B βH H2S,(NH4)2SO4 2S,SO4

(14)

1 (0) (0) (0) - BH ] βH [B + ) 2S,Na 2S,(NH4)2SO4 2 H2S,Na2SO4

(15)

1 τH2S,Na+,SO2) ΓH2S,Na2SO4,Na2SO4 4 4

(16)

1 (0) (0) (0) [B - BH ] (17) βH + ) 2S,MDEAH 2S,(NH4)2SO4 2 H2S,(MDEAH)2SO4 (0) (0) (0) βH - ) BH S,MDEAHHS - βH S,MDEAH+ 2S,HS 2 2

(18)

(vi) H2S + NaOH + H2O. When hydrogen sulfide is dissolved in an aqueous solution of MDEA and NaOH, interactions between (molecular) H2S and (dissociated) NaHS become important particularly at high amine j MDEA), when NaOH is nearly loading (i.e., m j H 2S g m completely converted to NaHS. The binary parameters (0) (0) βH + and βH S,HS- are given through eqs 15 and 18. 2S,Na 2 (0) They can be used to determine BH as 2S,NaHS (0) (0) (0) ) βH BH + + βH S,HS2S,NaHS 2S,Na 2

(19)

However, also ternary parameters (ΓH2S,NaHS,NaHS and ΓH2S,H2S,NaHS) might have an essential influence. Therefore, one would like to have a chance to test model predictions against experimental data. Such a test is possible because Xia et al.7 reported experimental results for the solubility of H2S in about 1 and 2 m aqueous solutions of NaOH at temperatures from 313 to 393 K and pressures up to about 9.3 MPa, which cover j NaOH. also the region of high amine loading, i.e., m j H2S g m The experimental results for the 2 m NaOH solutions are shown in Figure 5. A second hydrogen sulfide rich liquid phase is observed at high hydrogen sulfide concentrations. For stoichiometric hydrogen sulfide molalities up to about 2 m, H2S is practically completely dissolved in ionic form (as HS-). For higher stoichio-

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Figure 6. Predicted species distribution in the H2S + MDEA + Na2SO4 + H2O system at 353 K (m j MDEA ) 2 mol/kg; m j Na2SO4 ) 1 mol/kg).

Figure 5. Total pressure in the system H2S + NaOH + H2O (m j NaOH ≈ 2 mol/kg): (O, 4, 0, ×) exptl results, Xia et al.;7 (s) correlation, this work.

metric hydrogen sulfide molalities, the “true” molality of HS- is constant and equal to 2 m; i.e., additionally added H2S is no longer being dissolved chemically but physically up to the solubility limit of H2S. To predict the data given by Xia et al.7 with Pitzer’s equation (following the procedure given by those authors), parameters for interactions between (1) hydrogen sulfide (system H2S + H2O), (2) sodium hydroxide (system NaOH + H2O), and (3) hydrogen sulfide and (0) (0) sodium bisulfide (parameters βH + and βH S,HS-, i.e., 2S,Na 2 (0) parameter BH2S,NaHS) were taken into account, while ΓH2S,NaHS,NaHS and ΓH2S,H2S,NaHS were set to zero. The experimental results for the total pressure above H2S + NaOH + H2O (in the whole hydrogen sulfide concentration range) are predicted with an average relative deviation of 7.6%. By fitting of ΓH2S,NaHS,NaHS to that experimental data, this average relative deviation is only slightly reduced to 7.1%. If one neglects data points j NaOH, where the total pressure is with m j H2S e 1.1m nearly not changed by the addition of hydrogen sulfide and where the relative uncertainty in the pressure readings can reach up to 5%, the average relative deviation in the total pressures amounts to 4.5% when ternary parameters are disregarded and 3.9% when (0) and ΓH2S,NaHS,NaHS is taken into account. BH 2S,NaHS ΓH2S,NaHS,NaHS are given in Table 4. ΓH2S,NaHS,NaHS is related to τH2S,Na+,HS- by (cf. ref 2)

1 τH2S,Na+,HS- ) ΓH2S,NaHS,NaHS 2

(20)

A comparison between correlated and experimentally determined total pressures above H2S-NaOH-H2O (for the 2 m NaOH solutions) is shown in Figure 5.

It should be mentioned that the set of interaction parameters given in Table 4 for predicting the solubility of H2S in H2O + NaOH differs from the set of parameters used by Xia et al.7 for similar predictions only in (0) (0) 7 the numbers for βH -. Xia et al. estimated βH S,HS2S,HS 2 (0) from BH2S,NH4HS, which was reported by Rumpf et al.20 as a result of a correlation for the simultaneous solubility of NH3 and H2S in H2O. Such predictions give a somewhat less accurate description of the pressures above aqueous solutions of H2S and NaOH (the average relative deviation is 8.8% versus 7.6% here). If the (0) binary parameter βH - is fitted to the data by Xia et 2S,HS 7 al. while the ternary parameters are set to zero, there is only a minor improvement over the results given above. (The average relative deviation in the total pressures is only reduced to 7.5%.) (vii) H2S + MDEA + Na2SO4 + H2O. The solubility of hydrogen sulfide in an aqueous solution of both MDEA and sodium sulfate can be predicted from the model described before. The predictions for the total pressure are compared to experimental results in Figure 2. There is only a qualitative agreement because relative deviations between the experiment and prediction amount up to about 20%. However, such large deviations should not be a surprise because in those predictions parameters for some important interactions had to be neglected. This becomes evident from Figure 6, where predicted “true” liquid-phase molalities of all species (besides H+, OH-, S2-, and HSO4-) are shown when H2S is added to an aqueous solution of 2 m MDEA and 1 m Na2SO4 at 353 K. These species concentrations illustrate that previously neglected, ternary interaction parameters may have an influence on the total pressure, e.g., τMDEA,Na+,SO42-, τMDEA,Na+,HS-, and τMDEA,MDEAH+,HSat low stoichiometric molalities of H2S and, e.g., τH2S,Na+,MDEAH+, τH2S,HS-,SO42-, and τNa+,HS-,SO42- at high stoichiometric molalities of H2S. An improvement between calculated and measured total pressures can be achieved by fitting some of those interaction parameters. However, it is very difficult to assess which ternary parameters should be selected for such a fit. For example, τMDEA,Na+,SO42- should be accessible from the osmotic pressure above aqueous solutions of MDEA and sodium sulfate, and τMDEA,MDEAH+,HS- is, at least in

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principle, accessible from investigations on the solubility of H2S in aqueous solutions of MDEA at low loading. However, such experimental data are missing in the literature. In any way, the selected parameters should have no or only a very small influence on the calculation for the vapor-liquid equilibrium of any of the already discussed subsystems. In a more or less empirical manner, in the present work two ternary parameters (τNa+,HS-,SO42- and τH2S,Na+,MDEAH+) were used to improve the description of the experimental data for the system H2S + MDEA + Na2SO4 + H2O. Fitting these parameters reduces the average deviation between calculated and measured total pressures (for preset temperature and stoichiometric liquid-phase composition) to 3.8%. This improvement is also shown in Figure 2 (dashed lines). The resulting numbers for parameters τNa+,HS-,SO42- and τH2S,Na+,MDEAH+ are also given in Table 4. A similar good agreement might also be possible by adjusting other ternary interaction parameters. However, the experimental data are not sufficient to decide which set of parameters is most reasonable. Therefore, the set of adjusted parameters is regarded as a preliminary correlation that should be revised when more experimental data, e.g., for the solubility of Na2SO4 in such solutions become available. With the current set of (adjusted) parameters a precipitation of Na2SO4 is predicted when the molality of H2S increases beyond about 3 (at 353 K) and about 1.5 (at 393 K). However, no precipitation was observed in the experiments. Conclusions Sour gas sweetening is often achieved by absorption in aqueous solutions of amines. The basic design of such absorption processes requires a thermodynamic model for the solubility of sour gases, e.g., carbon dioxide and hydrogen sulfide, in aqueous solutions of an amine, e.g., MDEA. However, during the ab- and desorption cycles, strong electrolytes, e.g., sulfuric acid and sodium sulfate, may enrich the absorption media. Therefore, the present work deals with the solubility of hydrogen sulfide in aqueous solutions of MDEA + H2SO4 and MDEA + Na2SO4. It is an extension of previous work on the solubility of the single gases carbon dioxide and hydrogen sulfide in aqueous solutions of MDEA1,2 and on the solubility of carbon dioxide in aqueous solutions of either MDEA + H2SO4 or MDEA + Na2SO4 by Pe´rez-Salado Kamps et al.3 The thermodynamic framework developed in that previous work has been extended, and new experimental data on the solubility of hydrogen sulfide in such solutions are presented and used to assess model predictions as well as to improve the model performance. Acknowledgment Financial support of this investigation by the Volkswagen-Stiftung, Hannover (Grant I/72069), is gratefully acknowledged. Nomenclature ai ) activity of component i Bi,j ) second virial coefficient for interactions between components i and j

BG,MX(r) ) effective second osmotic virial coefficient in Pitzer’s equation for interactions between a gas G and a salt MX (r ) 0, 1) f ) function GE ) excess Gibbs energy (m) HH ) Henry’s constant for the solubility of H2S in 2S,H2O pure water (on the molality scale) KR ) equilibrium constant for chemical reaction R (on the molality scale) MH2O ) molar mass of water in kg/mol mi ) true molality of component i m j i ) stoichiometric molality of component i M ) cation M ni ) true number of moles of component i n j i ) stoichiometric number of moles of component i p ) pressure pi ) partial pressure of component i qi ) coefficients R ) universal gas constant T ) absolute temperature v ) (partial) molar volume X ) anion X y ) vapor-phase mole fraction Greek Letters β(0),β(1) ) binary interaction parameters in Pitzer’s equation γ/i ) activity coefficient of component i normalized to infinite dilution (on the molality scale) νi,R ) stoichiometric coefficient of component i in reaction R τ ) third virial coefficient in Pitzer’s equation Γ ) third osmotic virial coefficient in Pitzer’s equation φ ) fugacity coefficient Subscripts exptl ) experimental i, j, k ) components i, j, and k MX ) strong electrolyte R ) reaction R Superscripts max ) maximum s ) saturation * ) normalized to infinite dilution ∞ ) infinite dilution in pure water ′ ) liquid phase ′′ ) vapor phase

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(6) Xia, J.; Pe´rez-Salado Kamps, A Ä .; Rumpf, B.; Maurer, G. Solubility of Hydrogen Sulfide in Aqueous Solutions of the Single Salts Sodium Sulfate, Ammonium Sulfate, Sodium Chloride, and Ammonium Chloride at Temperatures from 313 to 393 K and Total Pressures up to 10 MPa. Ind. Eng. Chem. Res. 2000, 39, 10641073. (7) Xia, J.; Pe´rez-Salado Kamps, A Ä .; Rumpf, B.; Maurer, G. Solubility of Hydrogen Sulfide in Aqueous Solutions of the Single Strong Electrolytes Sodium Nitrate, Ammonium Nitrate, and Sodium Hydroxide at Temperatures from 313 to 393 K and Total Pressures up to 10 MPa. Fluid Phase Equilib. 2000, 167, 263284. (8) Xia, J.; Pe´rez-Salado Kamps, A Ä .; Rumpf, B.; Maurer, G. Solubility of H2S in (H2O + CH3COONa) and (H2O + CH3COONH4) from 313 to 393 K and at Pressures up to 10 MPa. J. Chem. Eng. Data 2000, 45, 194-201. (9) Saul, A.; Wagner, W. International equations for the saturation properties of ordinary water substance. J. Phys. Chem. Ref. Data 1987, 16, 893-901. (10) Edwards, T. J.; Maurer, G.; Newman, J.; Prausnitz, J. M. Vapor-liquid equilibria in multicomponent aqueous solutions of volatile weak electrolytes. AIChE J. 1978, 24, 966-976. (11) Brelvi, S. W.; O’Connell, J. P. Corresponding states correlations for liquid compressibility and partial molal volumes of gases at infinite dilution in liquids. AIChE J. 1972, 18, 12391243. (12) Hayden, J. G.; O’Connell, J. P. A generalized method for predicting second virial coefficients. Ind. Eng. Chem. Process Des. Dev. 1975, 14, 209-216.

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Received for review September 10, 2001 Revised manuscript received February 18, 2002 Accepted February 21, 2002 IE010747D