Solubility of Single Gases Carbon Dioxide and Hydrogen Sulfide in

Jun 6, 1996 - Figure 1 Solubility of hydrogen sulfide in water at 313 K: (·) experimental results of this work; .... 413.15, 0, 1.9493, 3.464, 393.13...
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Ind. Eng. Chem. Res. 1996, 35, 1959-1966

1959

Solubility of Single Gases Carbon Dioxide and Hydrogen Sulfide in Aqueous Solutions of N-Methyldiethanolamine in the Temperature Range 313-413 K at Pressures up to 5 MPa George Kuranov,‡ 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

Experimental results for the solubility of the single gases carbon dioxide and hydrogen sulfide in aqueous solutions of 2,2′-methyliminodiethanol (N-methyldiethanolamine (MDEA)) at temperatures between 313 and 413 K and total pressures up to 5 MPa are reported. A model taking into account chemical reactions as well as physical interactions is used to correlate the new data. The correlation is also used to compare the new experimental data with literature data. Introduction Aqueous alkanolamine solutions are widely used to separate acid gases like carbon dioxide or hydrogen sulfide from gaseous effluents contaminated with these components. Especially N-methyldiethanolamine (MDEA) is widely used for the selective removal of hydrogen sulfide from streams containing both carbon dioxide and hydrogen sulfide. Separation of both gases is achieved in a kinetically controlled process taking advantage of the difference in absorption/reaction kinetics between hydrogen sulfide and carbon dioxide. In a properly designed absorption column, carbon dioxide is driven off on top whereas a hydrogen sulfide rich solution is obtained as a bottom product. As the reaction between hydrogen sulfide and MDEA is reversible, the solution rich in hydrogen sulfide may be regenerated in a subsequent desorption step, thereby producing hydrogen sulfide as a top product. Furthermore, in comparison to other chemical absorbents like for example mono- or diethanolamine, MDEA has a low vapor pressure, resulting in smaller solvent losses. Although the competitive chemical absorption of carbon dioxide and hydrogen sulfide is kinetically controlled, the design of such separation equipment also requires the knowledge of vapor-liquid equilibrium as deviation from equilibrium provides the force to drive the kinetically controlled process. Modeling phase equilibrium for the simultaneous solubility of CO2 and H2S in aqueous solutions of MDEA at first requires reliable information on the solubility of the single gases. A literature review revealed that most of the published data scatter. Therefore, a systematic investigation on the solubility of carbon dioxide and hydrogen sulfide in aqueous solutions of MDEA was performed in the temperature range from 313 to 413 K at total pressures up to 5 MPa and amine concentrations up to 4 mol/kg of water. Experimental results are reported and compared to literature data, and correlations are established. Experimental Section The experimental equipment was basically the same as used in previous work on the solubility of single gases in aqueous electrolyte solutions (see for example Rumpf * Author to whom correspondence should be addressed. † Universita ¨ t Kaiserslautern. ‡ St. Petersburg State University.

S0888-5885(95)00538-0 CCC: $12.00

and Maurer (1993)), therefore only a short outline of the apparatus and procedure is given here. A thermostatted, high-pressure cell (volume of about 30 cm3) equipped with sapphire windows is partially filled with a known amount of the aqueous solvent. Then, a known amount of gas is added from a storage tank. More aqueous solvent is added step by step by a calibrated high-pressure displacer until the gas is completely dissolved. After equilibration, the pressure is decreased stepwise by withdrawing very small amounts of the liquid mixture until the first stable bubble appears. The mass of the gas filled into the cell is determined by weighing with an uncertainty of about (0.008 g. The mass of the solvent needed to dissolve the gas is calculated from the displacement of the displacer piston and the density of the aqueous solutions. The pressure is determined by pressure transducers (WIKA GmbH, Klingenberg, Germany) with ranges of 0-0.6, 0-1.6, and 0-10 MPa. The transducers were calibrated against a high precision pressure gauge before and after each series of measurements. The maximum uncertainty in the pressure measurement is about 0.1% of each transducers maximum reading. Temperature was determined with two calibrated platinum resistance thermometers placed in the thermostatted bath around the cell. The uncertainty in the temperature measurement is estimated to be (0.1 K. The aqueous solutions were prepared by dissolving known amounts of MDEA in water in a storage tank. The relative uncertainty of the concentration of MDEA in the aqueous solution is less than (0.1%. Substances. Carbon dioxide (g99.995 mol %) and hydrogen sulfide (g98 mol %) (Messer-Griesheim, Ludwigshafen, Germany) were used without further purification. N-Methyldiethanolamine (g98 mass %) (Merck AG, Darmstadt, Germany) was degassed by vacuum distillation. Water was deionized and further purified by vacuum distillation. Results Test of Procedure: Results for the System H2SH2O. To check the experimental arrangement and procedure, the solubility of hydrogen sulfide in water was measured at 313 K. The results are given in Table 1. The molality of H2S was about 1.7 mol/kg at maximum, resulting in total pressures up to about 2.5 MPa. As usual, throughout the paper molality is used for the number of moles per kilogram of water. © 1996 American Chemical Society

1960

Ind. Eng. Chem. Res., Vol. 35, No. 6, 1996 Table 2. Solubility of Carbon Dioxide in Aqueous Solutions of MDEA m j CO2 m j MDEA 10(p) T (K) (mol/kg) (mol/kg) (MPa)

Figure 1. Solubility of hydrogen sulfide in water at 313 K: (b) experimental results of this work; (O) experimental results of Lee and Mather (1977); (-) correlation this work. Table 1. Experimental Results for the Solubility of H2S in Pure Water T (K)

m j H2S (mol/kg)

10(p) (MPa)

313.15 313.15 313.15 313.15 313.15 313.18 313.15 313.16 313.16

0.3340 0.3853 0.5157 0.8537 0.9203 0.9204 1.2337 1.5318 1.7194

4.704 5.348 7.081 12.015 12.937 12.962 17.379 21.749 24.895

In Figure 1, the new results for the solubility of hydrogen sulfide in water are compared to experimental results of Lee and Mather (1977). Furthermore, calculated results from a correlation solely based on the data of Lee and Mather (1977) are shown (see below). The new data agree well with the literature data. At hydrogen sulfide molalities up to about 1 mol/kg, the maximum deviation in the total pressure is about 2% corresponding to a maximum deviation (at constant pressure) of 1.9% in the amount of dissolved hydrogen sulfide. At higher molalities of H2S, the new results for the total pressure are slightly, but systematically, below the data of Lee and Mather. The maximum relative deviation in the total pressure is below 3%. However, in that range the literature data show a somewhat larger scattering. Results for the Systems CO2-MDEA-H2O and H2S-MDEA-H2O. The results for the solubility of carbon dioxide in aqueous solutions of MDEA in the temperature range from 313 to 413 K are given in Table 2, and those for hydrogen sulfide are in Table 3. Two molalities of MDEA (m j MDEA ≈ 2 and 4 mol/kg) were investigated. The maximum overall molalities of carbon dioxide and hydrogen sulfide are about 4.6 and 6.5 mol/ kg, respectively. The maximum total pressure is about 5 MPa. In Figures 2 and 3, the experimental results for the total pressure above aqueous solutions containing about 2 and 4 mol of MDEA per kg of water at 313 K are plotted versus the overall amount of carbon dioxide and hydrogen sulfide dissolved in the liquid phase. Adding a sour gas to a MDEA-containing solution at first only slightly increases the total pressure above the aqueous solution as in that range the sour gas is mostly dissolved in nonvolatile, ionic form. When the overall molality of the sour gas surmounts the overall molality of MDEA, the total pressure increases steeply as most of the

313.24 313.12 313.13 313.15 313.15 313.25 313.19 313.20 313.11 313.13 313.16 333.13 333.16 333.16 333.15 333.15 333.15 333.15 373.16 373.14 373.14 373.15 373.15 373.15 373.15 373.15 373.16 393.17 393.15 393.14 393.13 393.14 393.14 393.13 413.15 413.16 413.16 413.14 413.13 413.16 413.15

1.5659 1.8523 1.9433 2.0788 2.0790 2.2468 2.3074 2.4536 2.4557 2.4950 2.6240 1.3679 1.6712 1.8370 1.9224 2.0604 2.1427 2.4433 0.5793 0.9730 1.3020 1.5720 1.6087 1.6805 1.8402 2.0340 2.0711 0 0.4075 0.7240 0.9572 1.3192 1.6944 1.9016 0 0.3575 0.5592 0.8601 0.9295 1.1991 1.3365

1.9938 1.9938 1.9938 1.9938 1.9938 1.9938 1.9938 1.9938 1.9938 1.9938 1.9938 1.9493 1.9493 1.9493 1.9493 1.9493 1.9493 1.9493 1.9493 1.9493 1.9493 1.9493 1.9493 1.9493 1.9493 1.9493 1.9493 1.9493 1.9493 1.9493 1.9493 1.9493 1.9493 1.9493 1.9493 1.9493 1.9493 1.9493 1.9493 1.9493 1.9493

0.740 2.149 3.470 7.192 7.098 14.079 17.652 25.273 25.185 27.852 35.982 1.395 3.217 5.895 8.301 13.916 18.671 40.248 2.269 4.686 8.596 14.744 15.977 18.372 25.554 37.831 40.808 1.909 3.717 6.964 10.735 19.870 36.732 50.367 3.464 6.969 10.798 18.931 21.328 32.247 39.329

m j CO2 m j MDEA 10(p) T (K) (mol/kg) (mol/kg) (MPa) 313.15 313.16 313.15 313.14 313.15 313.13 313.15 313.14 313.14 313.15 333.15 333.15 333.16 333.16 333.13 333.14 333.15 333.14 333.14 373.15 373.14 373.15 373.17 373.15 373.15 373.16 373.14 393.15 393.12 393.14 393.16 393.14 393.14 393.14 393.13 413.15 413.16 413.14 413.15 413.16 413.15

2.6729 3.4102 3.5280 3.8605 3.8948 4.1771 4.2020 4.2881 4.4696 4.5950 2.6569 3.0688 3.5576 3.6540 3.7989 3.8643 3.8696 3.9906 4.2985 1.3732 1.8457 2.1065 2.5317 2.7752 2.9767 3.2863 3.5422 0 0.7730 0.9995 1.4826 1.8253 2.1660 2.4392 2.7827 0 0.4175 0.8583 1.0110 1.5394 1.7402

3.9707 3.9707 3.9707 3.9707 3.9707 3.9707 3.9707 3.9707 3.9707 3.9707 3.9707 3.9707 3.9707 3.9707 3.9707 3.9707 3.9707 3.9707 3.9707 3.9707 3.9707 3.9707 3.9707 3.9707 3.9707 3.9707 3.9707 3.9707 3.9707 3.9707 3.9707 3.9707 3.9707 3.9707 3.9707 3.9707 3.9707 3.9707 3.9707 3.9707 3.9707

0.735 2.023 2.545 5.931 6.738 16.054 15.858 19.732 28.862 36.608 2.054 3.352 6.944 8.523 11.588 14.966 13.566 17.909 33.630 4.397 6.856 8.932 13.344 17.099 20.722 29.238 38.705 1.862 5.242 7.025 12.053 16.825 22.893 29.055 38.962 3.386 6.601 12.956 15.467 27.447 33.961

MDEA has been spent by the chemical reactions and added sour gas can no longer be absorbed chemically, i.e. in nonvolatile ionic form, but has to be dissolved physically. Qualitatively the same behavior is observed for the other isotherms investigated. Modeling Figure 4 shows a scheme of the model applied to correlate the solubility of the single gases carbon dioxide and hydrogen sulfide in aqueous solutions of MDEA. Due to chemical reactions in the liquid phase, carbon dioxide and hydrogen sulfide are dissolved in the liquid phase not only in neutral but also in nonvolatile, ionic form. The following chemical reactions are considered. + CO2 + H2O h HCO3 + H

(1)

2+ HCO3 h CO3 + H

(2)

H2S h HS- + H+

(3)

HS- h S2- + H+

(4)

H2O h H+ + OH-

(5)

MDEA + H+ h MDEAH+

(6)

The condition for chemical equilibrium yields the

Ind. Eng. Chem. Res., Vol. 35, No. 6, 1996 1961

Figure 2. Solubility of carbon dioxide in aqueous solutions of MDEA at 313 K: (0) experimental results of this work, m j MDEA ) 2 mol/kg; (O) experimental results of this work, m j MDEA ) 4 mol/ kg.

Figure 4. VLE and chemical reactions in the CO2-H2S-MDEAH2O system. Table 3. Solubility of Hydrogen Sulfide in Aqueous Solutions of MDEA m j H 2S m j MDEA 10(p) T (K) (mol/kg) (mol/kg) (MPa)

Figure 3. Solubility of hydrogen sulfide in aqueous solutions of MDEA at 313 K: (0) experimental results of this work, m j MDEA ) 2 mol/kg; (O) experimental results of this work, m j MDEA ) 4 mol/ kg.

following equation for a chemical reaction R:

KR(T) )

∏i avi

i,R

(7)

The balance equations for the overall amounts of carbon dioxide, hydrogen sulfide, MDEA, and water result in

n j CO2 ) nCO2 + nHCO-3 + nCO23

(8)

n j H2S ) nH2S + nHS- + nS2-

(9)

n j MDEA ) nMDEA + nMDEAH+

(10)

+ nOHn j w ) nw + nHCO-3 + nCO23

(11)

313.16 313.15 313.16 313.18 313.19 313.16 313.16 313.16 313.14 333.16 333.15 333.15 333.15 333.14 333.13 373.15 373.15 373.15 373.15 373.15 373.16 373.16 393.15 393.15 393.15 393.15 393.15 393.15 393.15 413.15 413.15 413.15 413.15 413.15 413.14

1.9249 1.9695 2.3297 2.4531 2.8607 3.0414 3.0755 3.4333 3.7295 1.6798 2.0911 2.4654 2.6843 2.9688 3.2427 1.1903 1.6120 1.6982 1.9583 2.6428 3.0106 3.5181 0.9619 1.6625 1.9445 2.2895 2.7519 2.8793 3.2542 1.1632 1.6108 2.2339 2.2482 2.7836 2.9507

1.9288 1.9288 1.9288 1.9288 1.9288 1.9288 1.9288 1.9288 1.9288 1.9288 1.9288 1.9288 1.9288 1.9288 1.9288 1.9288 1.9288 1.9288 1.9288 1.9288 1.9288 1.9288 1.9288 1.9288 1.9288 1.9288 1.9288 1.9288 1.9288 1.9288 1.9288 1.9288 1.9288 1.9288 1.9288

1.942 2.165 5.282 6.540 10.827 12.871 13.172 17.227 20.642 1.834 4.938 9.716 12.716 16.977 21.636 2.877 5.321 6.160 9.196 21.392 29.337 40.738 4.105 9.706 13.721 20.098 30.011 33.057 42.411 9.042 14.415 25.661 25.751 38.665 42.531

m j H 2S m j MDEA 10(p) T (K) (mol/kg) (mol/kg) (MPa) 313.16 313.13 313.14 313.14 313.16 313.14 313.15 333.15 333.15 333.14 333.14 333.14 333.14 333.14 333.14 373.14 373.15 373.14 373.15 373.14 373.15 373.15 373.15 393.15 393.15 393.15 393.16 393.15 393.15 393.15 413.16 413.14 413.15 413.16 413.15 413.15

3.6103 4.1478 4.8645 5.1462 5.8464 6.2492 6.5050 3.8196 4.5106 4.5035 4.5954 4.7342 5.6458 5.6967 6.2525 2.3534 3.3457 3.9180 4.3562 5.1096 5.1382 5.4695 5.7825 1.9153 3.2924 4.0551 4.6307 4.9041 5.0379 5.6614 2.0283 2.8245 2.8887 3.6208 4.1127 4.6468

3.9868 3.9868 3.9868 3.9868 3.9868 3.9868 3.9868 3.9868 3.9868 3.9868 3.9868 3.9868 3.9868 3.9868 3.9868 3.9868 3.9868 3.9868 3.9868 3.9868 3.9868 3.9868 3.9868 3.9868 3.9868 3.9868 3.9868 3.9868 3.9868 3.9868 3.9868 3.9868 3.9868 3.9868 3.9868 3.9868

1.652 3.911 9.126 11.415 17.441 20.687 23.044 4.315 9.705 9.849 10.551 11.887 22.115 22.695 29.292 3.991 8.437 13.385 18.524 29.387 30.036 35.355 40.854 5.422 13.710 22.395 30.655 35.225 37.483 48.959 10.412 16.527 17.246 25.551 32.603 41.493

composition of the gas phase:

The condition for liquid phase electroneutrality is

∑i nizi ) 0

(12)

Solving this set of equations for a given temperature and given overall mole numbers n j i of mixed components (i.e. CO2, H2S, MDEA, H2O) results in the “true” composition of the liquid phase, i.e. the molalities of true species i. The condition of liquid-vapor equilibrium can then be applied to calculate the total pressure and the

(

pywφ′′w ) pswφsw exp

(

(m) pyiφ′′i ) Hi,w (T,psw) exp

)

vw(p - psw) aw RT

)

(13)

∞ vi,w (p - psw) miγ*i RT i ) H2S,CO2 (14)

In principle, MDEA might also be present in the vapor phase. However, as the vapor pressure of pure MDEA remains rather small in the temperature range considered here (cf. Xu et al. (1991)), the presence of MDEA in the vapor phase was neglected.

1962

Ind. Eng. Chem. Res., Vol. 35, No. 6, 1996

Table 4. Equilibrium Constants for Chemical Reactions 1-6a

ln KR ) AR/(T/K) + BR ln(T/K) + CR(T/K) + DR reaction

AR

BR

CR(102)

DR

CO2 + H2O h HCO3- + H+ HCO3- h CO32- + H+ H2S h HS- + H+ HS- h S2- + H+ H2 O h H+ + OHMDEA + H+ h MDEAH+b

-7742.6 -8982.0 -18034.72 -406.0035 -13445.9 -13445.9

-14.506 -18.112 -78.07186 33.88898 -22.4773 -22.4773

-2.8104 -2.2249 9.19824 -5.411082 0 -4.1447

102.28 116.73 461.7162 -214.5592 140.932 173.1912

a Edwards et al. (1978), Bieling et al. (1989), and Schwabe (1959). b Note: Values given are for the equilibrium constant of MDEA on molarity scale.

Table 5. Henry’s Constant for the Solubility of H2S and CO2 in Pure Watera

Table 6. Pure Component Second Virial Coefficientsa

Bi,i/(cm3/mol) ) ai,i + bi,i(ci,i/(T/K))di,i

(m) ln Hi,w (T,psw)/(MPa kg mol-1) ) Ai,w + Bi,w/(T/K) + Ci,w(T/K) + Di,w ln(T/K)

i

Ai,w

Bi,w

Ci,w

Di,w

H2S CO2

340.305 192.876

-13236.8 -9624.4

0.0595651 0.01441

-55.0551 -28.749

a 273.15 e T/K e 473.15. Edwards et al. (1978), Rumpf and Maurer (1993).

The calculation requires the knowledge of the temperature dependent equilibrium constants K1-K6, the activities ai of all species present in the liquid phase, Henry’s constants H(m) i,w for carbon dioxide and hydrogen sulfide in pure water, the vapor pressure psw and molar volume vw of pure water, and the partial molar volumes v∞i,w of the dissolved gases at infinite dilution in water as well as information on the vapor phase nonideality. Equilibrium constants K1 and K2 were taken from Bieling et al. (1989) and K3-K5 from Edwards et al. (1978) while K6 was obtained from Schwabe (1959) (cf. Table 4). Henry’s constants for carbon dioxide and hydrogen sulfide were taken from Rumpf and Maurer (1993) and Edwards et al. (1978), respectively (cf. Table 5). The vapor pressure and molar volume of water were taken from Saul and Wagner (1987). A truncated virial equation of state was used to calculate the fugacity coefficients. Pure component second virial coefficients Bi,i for carbon dioxide and water were calculated from a correlation based on data recommended by Dymond and Smith (1980) (cf. Table 6). Pure component virial coefficient BH2S,H2S as well as mixed second virial coefficients Bi,j were taken from Hayden and O’Connell (1975) (cf. Table 7). The partial molar volumes of the dissolved gases were calculated as recommended by Brelvi and O’Connell (1972) (cf. Table 7). Activity coefficients of both molecular and ionic species were calculated from the Pitzer (1973) equation for the excess Gibbs energy of an electrolyte solution:

G

E

RTnwMw

) f1(I) +

∑

(i,j)*w

i

ai,i

bi,i

ci,i

di,i

CO2 H2O

65.703 -53.53

-184.854 -39.29

304.16 647.3

1.4 4.3

a

273.15 e T/K e 473.15.

Table 7. Pure Component Second Virial Coefficient for H2S and Mixed Second Virial Coefficients and Partial Molar Volumes for CO2 and H2S at Infinite Dilution in Water T (K) 313.15 333.15 373.15 393.15 413.15

BH2S,H2S BCO2,w BH2S,w v∞CO2,w v∞H2S,w (cm3/mol) (cm3/mol) (cm3/mol) (cm3/mol) (cm3/mol) -182.1 -161.8 -130.4 -117.9 -107.0

-163.1 -144.6 -115.7 -104.3 -94.3

-380.7 -317.9 -232.5 -202.7 -178.5

+

∑

(1) βi,j f2(I))

35.9 37.2 41.1 43.7 47.0

which was taken from Bradley and Pitzer (1979). Interaction parameters required to describe the solubility of carbon dioxide or hydrogen sulfide in aqueous solutions of MDEA were determined as follows: (1) Binary Systems CO2-H2O, H2S-H2O, and MDEA-H2O: When one of the single components CO2, or 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 the mentioned components, only interaction parameters (0) (1) βi,i , βi,i , and τi,i,i (for i being either H2S, CO2, or MDEA) can be determined. However, a detailed investigation revealed that in the concentration range being of interest in the present work, all parameters except (0) βH can be neglected. That parameter was deter2S,H2S mined from experimental results for the solubility of hydrogen sulfide in water as reported by Lee and Mather (1977). The influence of temperature on that parameter was taken into account by the approximation (0) ) q1 + βH 2S,H2S

(0) mimj(βi,j

33.4 34.7 38.3 40.8 43.8

q2 T/K

(16)

+

mimjmkτi,j,k (15)

(i,j,k)*w

where f1 is a modified Debye-Hu¨ckel term. Both f1 and (0) f2 are functions of ionic strength I ) 1/2∑imizi‚βi,j , and (1) βi,j and τi,j,k are binary and ternary interaction parameters. The resulting expressions for the activity coefficient of a dissolved species i and for the activity of water are given elsewhere (Bieling et al. (1995)). Calculations require the dielectric constant of pure water

Numbers for q1 and q2 are given in Table 8. (2) Ternary Systems CO2-MDEA-H2O and H2SMDEA-H2O: In the ternary systems CO2-MDEAH2O and H2S-MDEA-H2O, the concentrations of hydrogen and hydroxide ions remain small compared to the concentrations of the other species. Therefore, all interaction parameters involving H+ or OH- were set to zero. Furthermore, all binary and ternary parameters β(1) G,j, τG,i,j, and τG,G,j where G ) (CO2 or H2S) and i and j represent any other dissolved species were set to zero. Then, the activity coefficient of a single gas

Ind. Eng. Chem. Res., Vol. 35, No. 6, 1996 1963 Table 8. Interaction Parameters for the Systems CO2-MDEA-H2O and H2S-MDEA-H2O

f(T) ) q1 + q2/(T/K) parameter

q1

β(0)H2S,H2S β(0)CO2,HCO3β(0)H2S,HSβ(0)CO2,MDEAH+ β(0)HCO3-,MDEAH+ β(1)HCO3-,MDEAH+ τHCO3-,HCO3-,MDEAH+ β(0)H2S,MDEAH+ β(0)HS-,MDEAH+ β(1)HS-,MDEAH+ τHS-,HS-,MDEAH+

-0.26156 0.0843 0.0407 -0.4147 -0.5418 1.3284 0.0338 -0.04738 0.079578 -0.064837 -0.0006998

q2

Tmin (K)

Tmax (K)

subsystem

69.751 -16.15 3.68879 119.96 251.43 -787.13 -16.164 -18.0146 -25.1513 -94.707

283 313 353 313

453 473 393 413

H2S-H2O NH3-CO2-H2O NH3-H2S-H2O CO2-MDEA-H2O

313

413

H2S-MDEA-H2O

G (either CO2 or H2S) dissolved in an aqueous solution of MDEA is (0) (0) (0) (0) ln γ* G ) 2(mGβG,G + mMβG,M + mXβG,X + mYβG,Y + (0) mMDEAβG,MDEA ) (17)

where subscript M always represents MDEAH+ while when carbon dioxide is dissolved X stands for HCO3and Y for CO32- whereas X stands for HS- and Y for S2- when hydrogen sulfide is dissolved, respectively. Neglecting the concentrations of hydrogen and hydroxide ions, the charge balance is

mM ) mX + 2mY

(18)

Combining eqs 17 and 18 leads to (0) (0) (0) ln γ* G ) 2(mGβG,G + mX(βG,M + βG,X) + (0) (0) mY(2β(0) G,M + βG,Y) + mMDEAβG,MDEA) (19) (0) As binary parameters β(0) G,C and βG,A describing interactions between a dissolved gas G and an strong electrolyte CvcAvA in aqueous solution cannot be determined separately, it is common practice (cf. Rumpf and Maurer (1993)) to introduce a single binary parameter

(0) (0) ) vCβG,C + vAβ(0) BG,CA G,A

(20)

(0) (0) B(0) G,MX ) βG,M + βG,X

(21)

(0) (0) ) 2β(0) BG,M G,M + βG,Y 2Y

(22)

resulting in

and

Equation 19 then becomes (0) (0) (0) ln γ* G ) 2(mGβG,G + mXBG,MX + mYBG,M2Y + (0) mMDEAβG,MDEA ) (23)

Equation 23 reveals that for calculating the activity coefficient of carbon dioxide in an aqueous solution of MDEA the only additional binary parameters needed (0) (0) (0) are as follows: βCO -, βCO ,CO2-, βCO ,MDEA, and 2,HCO3 2 2 3 (0) βCO2,MDEAH+. As molecular carbon dioxide and molecular MDEA are simultaneously present in only very small (0) concentrations, neglecting βCO is a reasonable 2,MDEA (0) (0) approximation. βCO2,HCO3- and βCO 2- were taken 2,CO3 from a recently published correlation for VLE and VLSE in the system NH3-CO2-H2O (Kurz et al. (1995)).

(0) Thus, only βCO + was determined using the ex2,MDEAH perimental results of the present work. Similarly for calculating the activity coefficient of hydrogen sulfide in an aqueous solution of MDEA (0) (0) (0) βH was neglected, and βH - and βH S,S2- were 2S,MDEA 2S,HS 2 obtained from correlating vapor-liquid equilibrium data of the system NH3-H2S-H2O as reported by Miles and (0) Wilson (1975), and βH + was determined using 2S,MDEAH the new experimental data for the solubility of hydrogen sulfide in aqueous solutions of MDEA. However, there are more interaction parameters in eq 15 which do not directly appear in the expression for the activity coefficient of the dissolved gas (i.e. eqs 17, 19, and 23) but have an significant influence on the liquid phase species distribution, i.e. on the “true” molalities mi. Among those are for example binary (0) (1) interaction parameters βHCO + and βHCO-,MDEAH+ 3 ,MDEAH 3 and ternary parameter τHCO3-,HCO3-,MDEAH+ or binary in(0) (1) teraction parameters βHS -,MDEAH+ and βHS-,MDEAH+ and ternary parameter τHS-,HS-,MDEAH+ when either carbon dioxide or hydrogen sulfide is dissolved in an aqueous solution of MDEA. To reduce the number of parameters, as usual all binary and ternary interaction parameters involving two or three particles with the same sign of charge were neglected, respectively. Furthermore, a sensitivity study revealed that all other parameters besides those mentioned before can be neglected without reducing the accuracy of the description of the new experimental data. However, the influence of temperature on those parameters had to be taken into account. It was achieved by applying eq 16. The corresponding numbers for q1,i and q2,i where i stands for each parameter necessary to correlate the data are given in Table 8. The new experimental data for the total pressure above aqueous solutions of MDEA and carbon dioxide are correlated with an average relative deviation of 5.6% and those for the system H2S-MDEA-H2O with an average deviation of 2%. As an example, Figures 5 and 6 show a comparison between experimental and calculated total pressures above aqueous 4 m solutions of MDEA. As can be seen from those figures, the model correlates the new data well. For both systems, increasing deviations are found with increasing temperature. However, it should be noted that the influence of temperature on the equilibrium constant for the protonation of MDEA (i.e. reaction 6) is rather uncertain as experimental data are only available at temperatures between 298 and 333 K.

Comparison with Literature Data CO2-MDEA-H2O. Several authors measured the solubility of carbon dioxide in aqueous solutions of

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Figure 5. Solubility of carbon dioxide in aqueous solutions of MDEA: (O) experimental results of this work, m j MDEA ) 4 mol/kg; (-) correlation this work.

Figure 7. Partial pressure of carbon dioxide above aqueous solutions of MDEA: (0,O,4,+,×) experimental results of Jou et al. (1982), m j MDEA ) 2.6 mol/kg; (-) correlation this work.

Figure 6. Solubility of hydrogen sulfide in aqueous solutions of MDEA: (O) experimental results of this work, m j MDEA ) 4 mol/kg; (-) correlation this work.

Figure 8. Partial pressure of carbon dioxide above aqueous solutions of MDEA: (0,O,4) experimental results of Jou et al. (1994), m j MDEA ) 3.6 mol/kg; (-) correlation this work.

MDEA (Austgen et al. (1991), Bhairi (1984), Chakma and Meisen (1987), Dawodu and Meisen (1994), Ho and Eguren (1988), Jou et al. (1982, 1994), Shen and Li (1992)). Some authors used molarity as a concentration scale for MDEA. However, in some of the articles cited above, the reference temperature at which the solutions were prepared was not given. Consequently, the comparison with literature data is limited to those sources where the concentration of MDEA could be converted to molality scale unambiguously. Jou et al. (1982) measured the partial pressure of carbon dioxide above aqueous solutions of MDEA in the temperature range from 298 to 393 K, MDEA molarities of 1, 2, and 4.28 mol/dm3 (at 295 K), and partial pressures of carbon dioxide up to about 6 MPa. Their data for the solution containing 2 mol of MDEA per dm3 are compared to the results of the present correlation in Figure 7. The correlation based on the new data yields partial pressures of carbon dioxide much larger than those reported by Jou et al. (1982), especially at higher pressures. In a recent publication, Jou et al. (1994) published new results for the partial pressure of carbon dioxide above solutions containing 30 wt % (m j MDEA ) 3.6 mol/ kg) of MDEA. These results agree better with the present correlation than the results published earlier by Jou et al. (1982). In Figure 8, for temperatures from 313 to 393 K the results of Jou et al. (1994) are compared to the results of the present correlation. Up

to partial pressures of about 2 MPa, a satisfactory agreement is observed. For example at 353 K, the relative error in the partial pressure of carbon dioxide in most cases is smaller than 10%. However, at higher molalities of carbon dioxide the literature data systematically fall below the results of the correlation. The data of Bhairi (1984) for the partial pressure of carbon dioxide above aqueous solutions containing about 2.1 mol of MDEA per kg of water are compared to results of the present correlation in Figure 9. Up to about 4 MPa, there is good agreement between the correlation and Bhairis’ data. In most cases, relative errors do not exceed 10%. H2S-MDEA-H2O. Jou et al. (1993) investigated the solubility of hydrogen sulfide in aqueous solutions of MDEA at 313 and 373 K. Their data for solutions containing about 4.5 mol of MDEA per kg of water are compared to the results of the present correlation in Figure 10. At 313 K and molalities of H2S up to about 3 mol/kg, a good agreement is observed. At higher molalities, the correlation yields partial pressures of H2S which are systematically larger than the experimental data. The opposite behavior is observed at 373 K. A better agreement is again found for Bhairis’ (1984) data for the partial pressure of H2S above aqueous solutions containing about 2.1 mol of MDEA per kg of water (cf. Figure 11).

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most cases describes the new data within the experimental uncertainty. A comparison with literature data in nearly all cases showed large and systematic deviations which are by far larger than the combined experimental uncertainties, but the new data agree favorably with data by Bhairi (1984), i.e. deviations are in most cases within the sum of the experimental uncertainties of both works. Acknowledgment Financial support of this investigation by the Volkswagen-Stiftung, Hannover (Grant No. I/68708) is gratefully acknowledged. The authors also like to thank Y. Anoufrikov for performing some measurements on the solubility of H2S in aqueous solutions of MDEA. Figure 9. Partial pressure of carbon dioxide above aqueous solutions of MDEA: (0,O,4) experimental results of Bhairi (1984), m j MDEA ) 2.1 mol/kg; (-) correlation this work.

Figure 10. Partial pressure of hydrogen sulfide above aqueous solutions of MDEA: (0,O) experimental results of Jou et al. (1993), m j MDEA ) 4.5 mol/kg; (-) correlation this work.

Nomenclature Ai,w...Di,w ) coefficients for the temperature dependence of Henry’s constants AR...DR ) coefficients for the temperature dependence of equilibrium constants ai,i...di,i ) coefficients for the temperature dependence of second virial coefficients ai ) activity of component i (0) BG,MX ) “observable” combination of binary interaction parameters Bi,j ) second virial coefficient for interactions between species i and j f ) function for the temperature dependence of interaction parameters f1, f2 ) functions in Pitzer’s equation GE ) excess Gibbs energy (m) Hi,w ) Henry’s constant for the solubility of gas i in pure water (on molality scale) I ) ionic strength (on molality scale) KR ) equilibrium constant for chemical reaction R (on molality scale) Mw ) molar mass of water in kg/mol m j i ) overall molality of component i mi ) true molality of component i n j i ) overall number of moles of component i ni ) true number of moles of component i p ) total pressure pi ) partial pressure of component i qi ) coefficients for the temperature dependence of interaction parameters R ) universal gas constant T ) absolute temperature v ) partial molar volume y ) mole fraction in vapor zi ) number of charges of component i Greek Letters

Figure 11. Partial pressure of hydrogen sulfide above aqueous solutions of MDEA: (0,O,4) experimental results of Bhairi (1984), m j MDEA ) 2.1 mol/kg; (-) correlation this work.

Conclusions The solubilities of the single gases carbon dioxide and hydrogen sulfide in aqueous solutions of MDEA were measured in the temperature range from 313 to 413 K and total pressures up to 5 MPa. A model taking into account chemical reactions as well as physical interactions was used to correlate the new data. The model in

β(0), β(1) ) binary interaction parameters in Pitzer’s equation γ* ) activity coefficient normalized to infinite dilution (on molality scale) νi,R ) stoichiometric coefficient of component i in reaction R τ ) ternary interaction parameter in Pitzer’s equation φ ) fugacity coefficient Subscripts G ) gas G i, j, k ) component i, j, k max ) maximum min ) minimum R ) reaction R w ) water

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Superscripts m ) on molality scale s ) saturation * ) normalized to infinite dilution ∞ ) infinite dilution ′ ) liquid phase ′′ ) gas phase

Literature Cited Austgen, D. M.; Rochelle, G. T.; Chen, C. C. Model of vapor-liquid equilibria for aqueous acid gas-alkanolamine systems. 2. Representation of H2S and CO2 solubility in aqueous MDEA and CO2 solubility in aqueous mixtures of MDEA with MEA or DEA. Ind. Eng. Chem. Res. 1991, 30, 543-555. Bieling, V.; Rumpf, B.; Strepp, F.; Maurer, G. An evolutionary optimization method for modeling the solubility of ammonia and carbon dioxide in aqueous solutions. Fluid Phase Equilib. 1989, 53, 251-259. Bieling, V.; Kurz, F.; Rumpf, B.; Maurer, G. Simultaneous solubility of ammonia and carbon dioxide in aqueous solutions of sodium sulfate in the temperature range from 313 to 393 K and pressures up to 3 MPa. Ind. Eng. Chem. Res. 1995, 34, 14491459. Bhairi, A. M. Experimental equilibrium between acid gases and ethanolamine solutions. Ph.D. Dissertation, Stillwater, OK, 1984. Bradley, D. J.; Pitzer, K. S. Thermodynamics of electrolytes. 12. Dielectric properties of water and Debye-Hu¨ckel parameters to 350 °C and 1 kbar. J. Phys. Chem. 1979, 83, 1599-1603. 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, 1239-1243. Chakma, A.; Meisen, A. Solubility of CO2 in aqueous methyldiethanolamine and N,N-Bis(hydroxyethyl)piperazine solutions. Ind. Eng. Chem. Res. 1987, 26, 2461-2466. Dawodu, O. F.; Meisen, A. Solubility of carbon dioxide in aqueous mixtures of alkanolamines. J. Chem. Eng. Data 1994, 39, 548552. Dymond, J. H.; Smith, E. B. The virial coefficients of pure gases and mixtures; Oxford University Press: Oxford, UK, 1980. Edwards, T. J.; Maurer, G.; Newman, J.; Prausnitz, J. M. Vaporliquid equilibria in multicomponent aqueous solutions of volatile weak electrolytes. AIChE J. 1978, 24, 966-976. Hayden, J. G.; O’Connell, J. P. A generalized method for predicting second virial coefficients. Ind. Eng. Chem. Proc. Des. Dev. 1975, 14, 209-216.

Ho, B. S.; Eguren, R. R. Solubility of acidic gases in aqueous DEA and MDEA solutions. Paper presented at the 1988 Spring National Meeting, New Orleans, March 6-10. Jou, F.; Mather, A. E.; Otto, F. D. Solubility of H2S and CO2 in aqueous Methyldiethanolamine solutions. Ind. Eng. Chem. Proc. Des. Dev. 1982, 21, 539-544. Jou, F.; Carroll, J. J.; Mather, A. E.; Otto, F. D. The solubility of carbon dioxide and hydrogen sulfide in a 35 wt% solution of Methyldiethanolamine. Can. J. Chem. Eng. 1993, 71, 264-268. Jou, F.; Otto, F. D.; Mather, A. E. Vapor-liquid equilibrium of carbon dioxide in aqueous mixtures of Monoethanolamine and Methyldiethanolamine. Ind. Eng. Chem. Res. 1994, 33, 20022005. Kurz, F.; Rumpf, B.; Maurer, G. Vapor-liquid-solid phase equilibria in the system NH3-CO2-H2 O from around 310 to 470 K: New experimental data and modeling. Fluid Phase Equilib. 1995, 104, 261-275. Lee, J. I.; Mather, A. E. Solubility of hydrogen sulfide in water. Ber. Bunsen-Ges. Phys. Chem. 1977, 81, 1020-1023. Miles, D. H.; Wilson, G. Vapor-liquid equilibrium data for design of sour water strippers. Annual Report to API, 1975, 1-25. Pitzer, K. S. Thermodynamics of electrolytes. 1. Theoretical basis and general equations. J. Phys. Chem. 1973, 77, 268-277. Rumpf, B.; Maurer, G. An experimental and theoretical investigation on the solubility of carbon dioxide in aqueous electrolyte solutions. Ber. Bunsen-Ges. Phys. Chem. 1993, 97, 85-97. Saul, A.; Wagner, W. International equations for the saturation properties of ordinary water substance. J. Phys. Chem. Ref. Data 1987, 16, 893-901. Schwabe, K. Physikalisch-chemische Untersuchungen an Alkanolaminen. Z. Phys. Chem. Neue Folge 1959, 20, 68-82. Shen, K. P.; Li, M. H. Solubility of carbon dioxide in aqueous mixtures of Monoethanolamine with Methyldiethanolamine. J. Chem. Eng. Data 1992, 37, 96-100. Xu, S.; Qing, S.; Zhen, Z.; Zhang, C.; Caroll, J. J. Vapor pressure measurements of aqueous N-methyldiethanolamine solutions. Fluid Phase Equilib. 1991, 67, 197-201.

Received for review August 28, 1995 Revised manuscript received February 13, 1996 Accepted February 14, 1996X IE950538R

X Abstract published in Advance ACS Abstracts, April 15, 1996.