Solubility of Single Gases Carbon Dioxide and Hydrogen Sulfide in

of Chemistry, St. Petersburg State University, St. Petersburg, Russia ... Publication Date (Web): December 19, 2000 .... Modeling CO2 Solubility i...
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696

Ind. Eng. Chem. Res. 2001, 40, 696-706

Solubility of Single Gases Carbon Dioxide and Hydrogen Sulfide in Aqueous Solutions of N-Methyldiethanolamine at Temperatures from 313 to 393 K and Pressures up to 7.6 MPa: New Experimental Data and Model Extension A Ä lvaro Pe´ rez-Salado Kamps,† Anton Balaban,‡ Michael Jo1 decke,† George Kuranov,‡ 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

New experimental results for the solubility of the single gases carbon dioxide and hydrogen sulfide in 8 m (i.e., 48.8 wt %) aqueous solutions of 2,2′-methyliminodiethanol (N-methyldiethanolamine; MDEA) at temperatures between 313 and 393 K and total pressures up to 7.6 MPa are reported. A thermodynamic model for describing such phase equilibria is revised and extended using the new data. Introduction The sweetening of sour gases, particularly hydrogen sulfide, is done in transport- and reaction-controlled absorption processes by applying aqueous solutions of N-methyldiethanolamine (MDEA). Such a kinetically controlled absorption is necessary in order to reduce the simultaneously occurring absorption of carbon dioxide. Although the competitive chemical absorption of carbon dioxide and hydrogen sulfide is kinetically controlled, the reliable design of such separation equipment requires a knowledge of the vapor-liquid equilibrium, as deviation from equilibrium provides the driving force in that kinetical 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 (see, e.g., Kuranov et al.)1 reveals that most of the published data scatter widely. In the present work, an earlier investigation on the solubility of the single gases carbon dioxide and hydrogen sulfide in aqueous MDEA solutions (Kuranov et al.),1 at temperatures from 313 to 413 K at total pressures up to 5 MPa, and at overall amine molalities of about 2 and 4 mol/kg of water, has been extended to higher MDEA concentrations. New experimental data are presented for overall MDEA molalities of about 8 mol/kg of water. The thermodynamic model of Kuranov et al.1 for the vapor-liquid equilibrium is revised and extended to these higher amine concentrations. Experimental Section The experimental equipment and procedure are basically the same as in previous investigations (see, for example, Rumpf and Maurer);2 therefore, only a few essentials are given here. * Author to whom correspondence should be addressed. Phone: +49 631 205 2410. Fax: +49 631 205 3835. E-mail: [email protected]. † Universita ¨ t Kaiserslautern. ‡ St. Petersburg State University.

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 displacer 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, very small amounts of the liquid mixture are withdrawn stepwise from the cell until the first very small stable bubble appears. That pressure is the equilibrium pressure to dissolve the charged amount of gas in the charged amount of solvent at the fixed temperature. The mass of the charged gas (up to about 5.9 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 0.7% at a maximum, from its known density (from separate measurements). Three pressure transducers (WIKA GmbH, Klingenberg, Germany) for pressures ranging to 0.6, to 4, and to 10 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 estimated maximum uncertainty of (0.1 K. The aqueous solutions were prepared in a storage tank by dissolving known amounts of MDEA in water. The molality of MDEA in the aqueous solution was determined gravimetrically with a relative uncertainty not surmounting (0.1%.

10.1021/ie000441r CCC: $20.00 © 2001 American Chemical Society Published on Web 12/19/2000

Ind. Eng. Chem. Res., Vol. 40, No. 2, 2001 697 Table 1. Solubility of Carbon Dioxide in Aqueous Solutions of MDEA at 313 K (m j MDEA ) 3.954 mol/kg)

Table 3. Solubility of Hydrogen Sulfide in Aqueous Solutions of MDEA (m j MDEA ) 8.001 mol/kg) T (K)

m j H2S (mol/kg)

10p (MPa)

T (K)

m j H2S (mol/kg)

10p (MPa)

313.11 313.14 313.17 313.12 313.13 313.12 313.15 313.18 353.17 353.14 353.19 353.16 353.18

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

1.479 3.906 4.715 6.05 8.43 16.10 18.79 21.59 3.442 4.940 6.39 9.88 10.33

353.15 353.16 353.16 353.14 353.19 393.16 393.16 393.15 393.15 393.15 393.15 393.15 393.15

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

11.98 12.20 15.95 22.51 27.83 3.515 5.393 8.71 13.92 18.01 22.04 21.48 26.78

10p (MPa) T (K)

m j CO2 (mol/kg)

exp

model by Kuranov et al.1

313.09 313.10 313.15 313.11 313.13

3.338 3.477 3.898 4.562 4.914

1.765 2.293 7.09 36.90 64.69

1.863 2.397 6.89 38.03 68.45

Table 2. Solubility of Carbon Dioxide in Aqueous Solutions of MDEA (m j MDEA ) 7.994 mol/kg) T (K)

m j CO2 (mol/kg)

10p (MPa)

313.11 313.18 313.13 313.14 313.14 313.15 313.15 313.13 353.17 353.17 353.17 353.16

6.363 6.815 7.387 7.748 7.887 8.471 8.947 9.227 2.518 3.188 4.426 5.494

2.280 3.759 6.50 11.47 14.56 30.82 60.15 75.65 2.931 4.216 7.86 13.43

T (K)

m j CO2 (mol/kg)

10p (MPa)

353.17 353.18 353.15 353.16 393.11 393.17 393.12 393.16 393.12 393.11 393.12

6.183 6.616 7.153 7.554 1.007 1.617 2.588 3.308 3.823 4.440 4.761

19.99 26.14 39.20 54.03 6.85 11.10 21.00 31.37 40.46 53.10 61.17

Substances. Carbon dioxide (g99.995 mol %) and hydrogen sulfide (g98 mol %) were purchased from Messer-Griesheim, Ludwigshafen, Germany. Carbon dioxide was used without further purification, whereas hydrogen sulfide was sublimated and degassed under vacuum at temperatures well below 210 K. N-Methyldiethanolamine (g98 mass %, Merck-Griesheim, Ludwigshafen, Germany) was degassed under vacuum. Deionized water was degassed by vacuum distillation.

Figure 1. Vapor-liquid equilibrium and chemical reactions in the MDEA + CO2 + H2S + H2O system.

Experimental Results To check the experimental arrangement and procedure, the solubility of carbon dioxide in an aqueous 4 m MDEA solution was measured at 313 K. The molality of CO2 was about 4.9 mol/kg at a maximum, resulting in total pressures of up to about 6.5 MPa. As usual, throughout the paper molality is used for the number of moles per kilogram of water. The new experimental results are compared to results calculated with the model of Kuranov et al.1 in Table 1. The correlation of Kuranov et al.1 is based solely on experimental data published by these authors. The correlation gives the total pressure above an aqueous solution (at given temperature and concentrations of MDEA and CO2) from these experiments with an average relative deviation of 4%. The new data for the total pressure also agree with the correlation with an average relative deviation of 4%. The data point at the highest carbon dioxide molality, about 4.9 mol/kg, which is outside the range of the correlation, reveals a relative deviation in the total pressure of 5.8%. The solubility of the single gases carbon dioxide and hydrogen sulfide in aqueous solutions of MDEA (m j MDEA ≈ 8 mol/kg) was measured at 313, 353, and 393 K. Experimental results are given in Tables 2 and 3. The maximum overall molalities of carbon dioxide and hydrogen sulfide are about 9.2 and 11.5 mol/kg, respectively. The maximum total pressure is about 7.6 MPa. The correlation of Kuranov et al.1 was used to predict the pressure above the aqueous solutions of MDEA and

either CO2 or H2S at such high concentration of MDEA. Systematic deviations between predictions and experiments were observed. Therefore, the model had to be revised and extended. The results will be discussed and compared to the correlation in the following sections. Modeling Figure 1 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. Because of 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: the formation and dissociation of bicarbonate (reactions R1 and R2) and bisulfide (reactions R3 and R4), the autoprotolysis of water (reaction R5), and the dissociation of protonated methyldiethanolamine (reaction R6). The condition for chemical equilibrium yields the following equation for a chemical reaction R:

KR(T) )

∏i aνi

i,R

(1)

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

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Table 4. Equilibrium Constants for Chemical Reactions R1-R6

ln KR ) A +

E B + C ln (T/K) + D(T/K) + (T/K) (T/K)2

reaction

A

B

C

102 × D

E

T (K)

R1 R2 R3 R4 R5 R6

-1203.01 175.360 461.7162 -214.5592 140.932 -79.474

68359.6 -7230.60 -18034.72 -406.0035 -13445.9 -819.7

188.444 -30.6509 -78.07186 33.88898 -22.4773 10.9756

-20.6424 1.31478 9.19824 -5.411082 -

-4.71291 × 106 -3.72805 × 105 -

273-673 273-523 273-548 273-498 273-498 278-422

n˜ CO2 ) nCO2 + nHCO3- + nCO32-

(2)

n˜ H2S ) nH2S + nHS- + nS2-

(3)

n˜ MDEA ) nMDEA + nMDEAH+

(4)

n˜ w ) nw + nHCO3- + nCO32- + nOH-

(5)

The condition for liquid-phase electroneutrality is

nMDEAH+ + nH+ ) nHCO3- + 2nCO32- + nHS- + 2nS2- + nOH- (6) 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, and H2O) results in the “true” composition of the liquid phase, i.e., the molalities of all neutral and ionic species. The condition of vaporliquid equilibrium can then be applied to calculate the total pressure and the composition of the vapor as follows:

pSwφSw Hi,w(T,pSw)

[

[

]

vw(p - pSw) exp aw ) ywpφ′′w RT

]

Table 5. Henry’s Constants for the Solubility of CO2 and H2S in Pure Water

ln

[

]

Hi,w(T,pSw) B + C ln (T/K) + D(T/K) )A+ MPa kg/mol (T/K)

i

A

B

C

D × 102

T (K)

CO2 H2S

192.876 340.305

-9624.41 -13236.8

-28.7488 -55.0551

1.44074 5.95651

273-473 273-423

Table 6. Pure-Component Second Virial Coefficient for H2S, Mixed Second Virial Coefficients, and Partial Molar Volumes for CO2 and H2S at Infinite Dilution in Water T (K) 313.15 353.15 393.15

∞ ∞ vCO vH BH2S,H2S BCO2,w BH2S,w 2,w 2S,w 3 3 3 3 (cm /mol) (cm /mol) (cm /mol) (cm /mol) (cm3/mol)

-182.1 -144.8 -117.9

-163.1 -129.0 -104.3

Bi,i (cm /mol)

∞ vi,w (p - pSw) miγ/i ) yipφ′′i exp RT i ) CO2, H2S (8)

In principle, MDEA might also be present in the vapor phase. However, as the vapor pressure of pure MDEA is very small in the temperature range considered here (cf. Xu et al.),3 the presence of MDEA in the vapor phase is neglected. The calculation requires a knowledge of the temperature-dependent equilibrium constants K1-K6, the Henry’s constants Hi,w(T,pSw) for carbon dioxide and hydrogen sulfide in pure water, the vapor pressure pSw and molar volume vw of pure water, and the partial molar ∞ of the dissolved gases at infinite dilution volumes vi,w in liquid water and information on the vapor phase nonideality as well as the activities ai of all species present in the liquid phase. Equilibrium constants K1 and K2 were taken from Patterson et al.,4,5 K3 and K4 from Kawazuishi and Prausnitz,6 K5 from Edwards et al.,7 and K6 from Pe´rez-Salado Kamps and Maurer8 (cf. Table 4). Henry’s constants for carbon dioxide and hydrogen sulfide were taken from Rumpf and Maurer2 and Edwards et al.,7 respectively (cf. Table 5). The vapor pressure of water was taken from Saul and Wagner.9 The molar volume of liquid water was approximated by the molar volume of saturated liquid water, which was also taken from Saul and Wagner.9 The partial molar volumes of the dissolved gases were calculated as

33.4 36.3 40.8

35.9 38.9 43.7

Table 7. Pure-Component Second Virial Coefficients for CO2 and H2O 3

(7)

-380.7 -269.9 -202.7

)a+b

c (T/K )

d

i

a

b

c

d

T (K)

CO2 H2O

65.703 -53.53

-184.854 -39.29

304.16 647.3

1.36 4.28

273-473 273-473

recommended by Brelvi and O’Connell10 (cf. Table 6). A truncated virial equation of state was used to calculate 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 Smith11 (cf. Table 7). BH2S,H2S as well as the mixed second virial coefficients Bi,j were calculated as recommended by Hayden and O’Connell12 (cf. Table 6). Gibbs Excess Energy Activity coefficients of both molecular and ionic species were calculated from Pitzer’s13 equation for the excess Gibbs energy of an aqueous solution

GE nwRTMw

) f1(I) +

(0) (1) mimj[βi,j + βi,j f2(I)] + ∑ ∑ i*w j*w

∑ ∑ ∑ mimjmkτi,j,k

(9)

i*w j*w k*m

where f1 is a modified Debye-Hu¨ckel term. Both f1 and (0) (1) f2 are functions of ionic strength I ) 1/2∑imiz2i . βi,j , βi,j , and τi,j,k are binary and ternary interaction parameters, which can depend on temperature. The resulting expressions for the activity of all species are given elsewhere (e.g., Xia et al.).14 Calculations require the

Ind. Eng. Chem. Res., Vol. 40, No. 2, 2001 699 Table 8. Interaction Parameters for the Systems CO2-MDEA-H2O and H2S-MDEA-H2O

f(T) ) q1 + parameter (0) βCO 2,HCO3 (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) βMDEA,CO 23

τMDEAH+,HCO3-,HCO3τMDEAH+,CO32-,CO32τCO2,MDEAH+,HCO3(0) βH 2S,H2S (0) βH2S,HS(0) βMDEA,HS (0) βMDEAH +,HS(1) βMDEAH +,HSτMDEAH+,HS-,HSτH2S,MDEAH+,HS-

q1

q2

T (K)

subsystem

0.23042 -0.13952 -0.46353 × 10-2 0.21287 × 10-1 0.31729 0.22476 × 10-1 -0.68478 0.58421 -0.55509 × 10-2 0.28235 × 10-2 -0.61812 × 10-3 -0.26156 0.93110 × 10-2 0.21219 0.46239 × 10-1 4.2817 -0.78170 × 10-4 0.32440 × 10-3

-22.012 -4.4825 49.422 -90.860 290.29 1.5327 69.751 19.099 -49.933 -2.3092 -1392.96 0.14980 -0.083383

313-413

CO2-MDEA-H2O

283-453 313-413

H2S-H2O H2S-MDEA-H2O

dielectric constant of pure water, which was taken from Bradley and Pitzer.15 Interaction Parameters Binary Systems CO2 + H2O, H2S + H2O, and MDEA + H2O. When one of the single components CO2, 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 β(0) i,i and τi,i,i (for i being either H2S, CO2, or MDEA) can be determined. However, in the concentration range of interest in the present work, with the exception of (0) βH , all of those parameters can be neglected (cf. 2S,H2S (0) Kuranov et al.).1 βH was taken from Kuranov et 2S,H2S 1 al. (cf. Table 8). Ternary Systems (CO2 or H2S) + MDEA + H2O. As usual, it is assumed that interaction parameters are symmetric. (r) (r) βi,j ) βj,i r ) 0, 1

(10)

τi,j,k ) τi,k,j ) τj,i,k ) τj,k,i ) τk,i,j ) τk,j,i

(11)

It is common practice to neglect all parameters between ionic species carrying either only positive or only negative charges. “Symmetrical and unsymmetrical mixing terms” (cf. Pitzer)16 are also neglected. Because of the very small amounts of H+ and OH- ions, all interaction parameters involving one of these species were set to zero. For binary systems (water + strong electrolyte Mν+Xν-), (1) φ φ it is common practice to report β(0) M,X, βM,X, and CMX. CMX is the third osmotic virial coefficient, which combines the ternary parameters τM,M,X and τM,X,X.

()

ν+ 1 φ CMX ) 3 ν-

1/2

q2 (T/K)

τM,M,X +

() ν+ ν-

1/2

τM,X,X

(12)

As there is usually no means to separate the influence of τM,M,X from that of τM,X,X, one of those parameters is set to zero (for example, τM,M,X ) 0). For ternary systems (water + strong electrolyte Mν+Xν- + gas G), the influence of M and X on the solute G cannot be separated, and therefore, it is common practice to use the following comprehensive parameters: (r) (r) B(r) G,MX ) ν+βG,M + ν-βG,X r ) 0, 1

(13)

ΓG,MX,MX ) ν2+τG,M,M + 2ν+ν-τG,M,X + ν2-τG,X,X (14) ΓG,G,MX ) ν+τG,G,M + ν-τG,G,X

(15)

B(1) G,MX is rarely needed to describe the solubility of a gas in an aqueous solution of a strong electrolyte. B(0) G,MX, ΓG,MX,MX, and ΓG,G,MX are usually reported. In (0) (0) B(0) G,MX, one can arbitrarily set either βG,M or βG,X to zero; in ΓG,MX,MX, one can arbitrarily set two of the three parameters τG,G,M, τG,M,X, and τG,X,X to zero; and in ΓG,G,MX, one can arbitrarily set either τG,G,M or τG,G,X to zero. CO2 + MDEA + H2O. Adding a sour gas to an aqueous MDEA solution reduces the amount of neutral MDEA, thereby producing protonated MDEA, bicarbonate, and carbonate ions. If the overall amount of MDEA is not too high, the concentration of carbonate ions will be comparatively low, and it will be reasonable to neglect interaction parameters involving this species (cf. Kuranov et al.).1 For overall MDEA molalities above about 4 m, the carbonate concentration is comparatively high, so interaction parameters involving carbonate ions had to be taken into account. A sensitivity analysis revealed that the following parameters must be considered: (a) for inter(0) actions between MDEAH+ and HCO3 , βMDEAH+,HCO3-, (1) βMDEAH+,HCO3-, and τMDEAH+,HCO3-HCO3-; (b) for inter(0) actions between MDEAH+ and CO23 , βMDEAH+,CO32-, (1) 22+ βMDEAH +,CO 2-, and τMDEAH ,CO3 ,CO3 ; (c) for interac3 tions between CO2 on one side and MDEAH+ and

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HCO3 on the other side, only one binary and one (0) ternary parameter are considered (BCO and 2,MDEAHHCO3 τCO2,MDEAH+,HCO3-); and (d) for interactions between CO2 on one side and MDEAH+ and CO23 on the other side, only one single binary parameter is considered (0) (BCO ). Equation 13 gives 2,MDEAH2CO3 (0) (0) (0) BCO ) βCO + + βCO ,HCO 2,MDEAH 2 3 2,MDEAHHCO3

(16)

(0) (0) (0) BCO ) 2βCO + + βCO ,CO 22,MDEAH 2 3 2,MDEAH2CO3

(17)

As molecular carbon dioxide and carbonate ions are simultaneously present in only small concentrations, (0) (0) (0) βCO 2- was set to zero, and βCO ,MDEAH+ and βCO ,HCO 2,CO3 2 2 3 were considered as independent. Finally, (e) in the low gas loading region, the model is sensitive to the two (0) (0) parameters βMDEA,HCO - and βMDEA,CO 2-. As the partial 3 3 pressure of MDEA can be neglected, these parameters only indirectly influence the partial and total pressures by affecting the species distribution. The parameters were fitted to the data by Kuranov j MDEA e 4 mol/kg and to the new experimenet al.1 for m tal data. The resulting values are given in Table 8. H2S + MDEA + H2O. Preliminary calculations revealed that the concentration of sulfide ions is very small, even at high MDEA overall molalities. Therefore, all interaction parameters involving this species were set to zero. The selection of parameters followed the ideas outlined before (with CO2 as the sour gas), resulting in the following selection of adjustable parameters: (a) for interactions between MDEAH+ and HS-, (0) (1) βMDEAH βMDEAH and τMDEAH+,HS-,HS-; and +,HS-, +,HS-, (b) for interactions between H2S on one side and (0) MDEAH+ and HS- on the other side, BH and 2S,MDEAHHS + τH2S,MDEAH ,HS . Equation 13 gives (0) (0) (0) BH ) βH + + βH S,HS2S,MDEAHHS 2S,MDEAH 2

Figure 2. Total pressure in the system MDEA + CO2 + H2O (m j MDEA ≈ 2 mol/kg): (0) experimental results, Kuranov et al.;1 (s) correlation, this work.

(18)

(0) (0) Either βH + or βH S,HS- can arbitrarily be set to 2S,MDEAH 2 (0) zero without losing any generality (here, βH + ) 2S,MDEAH 0). In addition, (c) in the low gas loading region, the (0) model is sensitive to binary parameter βMDEA,HS -. As the partial pressure of MDEA can be neglected, (0) βMDEA,HS - only indirectly influences the partial and total pressures by affecting the species distribution. The parameters were fitted to the data by Kuranov j MDEA e 4 mol/kg and to the new experimenet al.1 for m tal data. The resulting values are given in Table 8.

Discussion The experimental data for the total pressure above aqueous solutions of MDEA and carbon dioxide or hydrogen sulfide (i.e., the data by Kuranov et al.1 and the new experimental data) are correlated with an average relative deviation of 2.9% or 2.2%, respectively. j MDEA ) 2, 4, and 8 mol/kg, (CO2: 3.0, 2.4, and 3.6% at m j MDEA ) 2, 4, respectively. H2S: 1.6, 1.5, and 3.9% at m and 8 mol/kg, respectively.) Figures 2-7 show a comparison between experimental and calculated total pressures (for preset temperature and overall molality of MDEA and the sour gas) above aqueous 2, 4, and 8 m solutions of MDEA. As a typical example, the results shown in Figures 2-7 at T ) 313 K are briefly discussed. Adding a sour

Figure 3. Total pressure in the system MDEA + CO2 + H2O (m j MDEA ≈ 4 mol/kg): (9) experimental results, this work; (0) experimental results, Kuranov et al.;1 (s) correlation, this work.

gas to an MDEA-containing solution at this temperature 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 MDEA has been spent by the chemical reactions and additional sour gas can no longer be absorbed chemi-

Ind. Eng. Chem. Res., Vol. 40, No. 2, 2001 701

Figure 4. Total pressure in the system MDEA + CO2 + H2O (m j MDEA ≈ 8 mol/kg): (9) experimental results, this work; (s) correlation, this work.

Figure 6. Total pressure in the system MDEA + H2S + H2O (m j MDEA ≈ 4 mol/kg): (0) experimental results, Kuranov et al.;1 (s) correlation, this work.

Figure 5. Total pressure in the system MDEA + H2S + H2O (m j MDEA ≈ 2 mol/kg): (0) experimental results, Kuranov et al.;1 (s) correlation, this work.

Figure 7. Total pressure in the system MDEA + H2S + H2O (m j MDEA ≈ 8 mol/kg): (9) experimental results, this work; (s) correlation, this work.

cally, i.e., in nonvolatile ionic form, but rather must be dissolved physically. Qualitatively, the same behavior is observed for the other isotherms. Comparison with Literature Data. For both systems CO2 + MDEA + H2O and H2S + MDEA + H2O, a comparison of model correlations/predictions with experimental data from the literature was already given by Kuranov et al.1 for overall MDEA molalities up to 4

m. As the new model gives practically equal results up to that MDEA concentration, the new comparison is restricted to MDEA molalities above about 4 m. Furthermore, all data published recently (after Kuranov et al.)1 are considered. Some authors used molarity as a concentration scale for MDEA. However, in many of the articles cited below, the reference temperature at which the solutions were

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Figure 8. Partial pressure of carbon dioxide above aqueous solutions of MDEA: (0, O, 4, +, ×) experimental results of Jou et al.17 (m j MDEA ) 8.0 mol/kg); (s) correlation, this work.

prepared was not given. In that case, Tref ) 293.15 K was assumed to convert molarities into molalities. The density of aqueous MDEA solutions was known from our own measurements. CO2 + MDEA + H2O. Apart from Kuranov et al.,1 several other authors measured the solubility of carbon dioxide in aqueous solutions of MDEA (Jou et al.17-19, Bhairi,20 Chakma and Meisen,21 Ho and Eguren,22 Austgen et al.,23 MacGregor and Mather,24 Shen and Li,25 Dawodu and Meisen,26 Rogers et al.,27 and Xu et al.).28 The data of Jou et al.17 for solutions containing 8.0 mol of MDEA per kilogram of water (T ) 298-393 K, m j CO2,max ) 11 mol/kg, pCO2,max ) 6.57 MPa) are compared to the results of the present correlation in Figure 8. The correlation based on the new data yields partial pressures of carbon dioxide much larger than those reported by Jou et al.,17 especially at higher pressures. The data of Chakma and Meisen21 for solutions containing 8.0 mol of MDEA per kilogram of water (T ) 373-473 K, m j CO2,max ) 7.6 mol/kg, pCO2,max ) 4.93 MPa) are compared to calculations in Figure 9. The calculated partial pressures of carbon dioxide are always higher than those reported by Chakma and Meisen21 (average relative deviation ) 42 %). Relative deviations are calculated throughout this paper using 100% × (xcalc - xexp)/xexp. The experimental carbon dioxide partial pressures reported by Ho and Eguren22 for solutions containing 8.06 mol of MDEA per kilogram of water (T ) 313 and 373 K, m j CO2,max ) 4.6 mol/kg, pCO2,max ) 1.84 MPa) are predicted with an average relative deviation of 21%. With the exception of two data points (out of eight), the calculated carbon dioxide partial pressures are always higher than experimental results. Austgen et al.23 reported partial pressures of carbon dioxide over 8.0 m MDEA solutions at 313 K for overall carbon dioxide molalities from 0.025 to 5.4 mol/kg

Figure 9. Partial pressure of carbon dioxide above aqueous solutions of MDEA: (0, O, 4, +, ×) experimental results of Chakma and Meisen21 (m j MDEA ) 8.0 mol/kg); (s) correlation, this work

(pCO2,max ) 0.094 MPa), which deviate from the calculated values by about 50%. Relative deviations range from -85% (for the lowest gas loading point) to +26% (for the highest gas loading point). The data of Jou et al.18 for solutions containing 4.5 mol of MDEA per kilogram of water (T ) 313 and 373 K, m j CO2,max ) 3.6 mol/kg, pCO2,max ) 0.26 MPa) are compared to predictions in Figure 10 (average relative deviation ) 37%). At 313 K, relative deviations range from -92% (for the lowest gas loading point) to +81% (for one of the highest gas loading points). At 373 K, deviations are not systematic. The experimental results for the partial pressure of carbon dioxide reported by Dawodu and Meisen26 for solutions containing 8.0 mol of MDEA per kilogram of water (T ) 373 and 393 K, m j CO2,max ) 6.6 mol/kg, pCO2,max ) 3.83 MPa) are predicted with an average relative deviation of 20% (28% at 373 K and 11% at 393 K, cf. Figure 11). At 373 K, relative deviations range from -8% (for the lowest gas loading point) to +64% (for the highest gas loading point). At 393 K, the calculated carbon dioxide partial pressures are always larger than experimental results. Rogers et al.27 reported partial pressures of carbon dioxide over 2.5 m MDEA solutions at 313 and 323 K and over 8.4 m MDEA solutions at 313 K for low gas loadings (overall carbon dioxide molalities from 0.0015 to 0.31 mol/kg, partial pressures of carbon dioxide from 0.07 to 1002 Pa). Disregarding data points with pCO2 < 1 Pa, the experimental data over 2.5 m MDEA solutions are predicted with an average relative deviation of 22% (cf. Figure 12). In 2.5 m MDEA solutions at 313 K (323 K), relative deviations range from -73% (-53%) at low gas loadings to +21% (-3%) at high gas loadings. The predicted carbon dioxide partial pressures systematically fall below the experimental data over 8.4 m MDEA solutions by about 80%.

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Figure 10. Partial pressure of carbon dioxide above aqueous solutions of MDEA: (0, O) experimental results of Jou et al.18 (m j MDEA ) 4.52 mol/kg); (s) correlation, this work.

Figure 12. Partial pressure of carbon dioxide above aqueous solutions of MDEA: (0, O, 4) experimental results of Rogers et al.;27 (s) correlation, this work.

Figure 11. Partial pressure of carbon dioxide above aqueous solutions of MDEA: (0) experimental results of Dawodu and Meisen26 (m j MDEA ) 8.0 mol/kg); (s) correlation, this work.

Figure 13. Partial pressure of carbon dioxide above aqueous solutions of MDEA: (0, O, 4, +, ×) experimental results of Xu et al.28 (m j MDEA ) 8.0 mol/kg); (s) correlation, this work.

Xu et al.28 reported partial pressures of carbon dioxide over 4.5, 5.5, and 8.0 m MDEA solutions (T ) 313-373 K, m j CO2,max ) 7.0 mol/kg, pCO2,max ) 1.0 MPa), which are predicted with average relative deviations of 16, 27, and 22%, respectively. For 4.5 and 5.5 m MDEA solutions, nearly all of the predicted carbon dioxide partial pressures fall below the experimental data. In Figure 13, the results of Xu et al.28 over 8.0 m MDEA solutions

are compared to the results of the present correlation. For that MDEA concentration, and for temperatures up to 343 K, the predicted carbon dioxide partial pressures systematically fall below the experimental data. At higher temperatures, deviations between experiment and prediction are not systematic. H2S + MDEA + H2O. In addition to Kuranov et al.,1 the solubility of hydrogen sulfide in aqueous solutions

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Figure 14. Partial pressure of hydrogen sulfide above aqueous solutions of MDEA: (0, O, 4, +, ×) experimental results of Jou et al.17 (m j MDEA ) 8.0 mol/kg); (s) correlation, this work; (- - -) extrapolation, this work.

of MDEA was measured by Jou et al.,17,18 Bhairi,20 MacGregor and Mather,24 and Li and Shen.29 The data of Jou et al.17 for solutions containing 8.0 mol of MDEA per kilogram of water (T ) 298-393 K, m j H2S,max ) 13.8 mol/kg, pH2S,max ) 5.84 MPa) are compared to predicted results in Figure 14. At 298, 313, 343, 373, and 393 K, relative deviations range from 307, 409, 369, 227, and 218% (at the lowest gas loading point) to 9, 4, -16, -18, and -20% (at the highest gas loading point), respectively. At those high MDEA molalities, a decrease in the slope of the predicted isotherms at high hydrogen sulfide molalities is observed, which is merely an artifact of the model, as interaction parameters were only fitted to pressures up to about 3 MPa. If reliable VLE data were available in those concentration and pressure ranges, this model behavior could be corrected. Jou et al.18 investigated the solubility of hydrogen sulfide in aqueous solutions of MDEA at 313 and 373 K. Their data for solutions containing about 4.5 and 8.4 mol of MDEA per kg of water are compared to the results of the present correlation in Figures 15 and 16, repectively. For m j MDEA ) 4.5 mol/kg and T ) 313 K, the correlation yields partial pressures of H2S that are larger than the experimental data. Relative deviations range from 165% (at the lowest gas loading point) to 4.4% (at m j H2S ) 3 mol/kg). However, at H2S molalities above 3 mol/kg, the disagreement between experiment and prediction again becomes larger. For m j MDEA ) 4.5 mol/kg and T ) 373 K, deviations between experiment and prediction are not systematic (average relative deviation ) 18%). For the 8.4 m MDEA solution, the correlation yields partial pressures of H2S that are larger than the experimental data. With the exception of two data points with pH2S,exp < 110 Pa, the predicted hydrogen sulfide partial pressures are systematically larger than the experimental data by about 45%.

Figure 15. Partial pressure of hydrogen sulfide above aqueous solutions of MDEA: (0, O) experimental results of Jou et al.18 (m j MDEA ) 4.52 mol/kg); (s) correlation, this work.

Figure 16. Partial pressure of hydrogen sulfide above aqueous solutions of MDEA: (0, O) experimental results of Jou et al.18 (m j MDEA ) 8.39 mol/kg); (s) correlation, this work.

Conclusions Literature data for the vapor-liquid equilibrium in the systems CO2 + MDEA + H2O and H2S + MDEA + H2O show large disagreements. For that reason, new VLE data covering wide ranges of temperature as well as MDEA and gas concentrations are required. Therefore, an earlier investigation (Kuranov et al.)1 on the

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solubility of the single gases CO2 and H2S in aqueous MDEA solutions, for temperatures from 313 to 413 K, total pressures up to 5 MPa, and overall amine molalities of about 2 and 4 m, is extended in the present work. New experimental results in the temperature range from 313 to 393 K, at total pressures up to 7.6 MPa and for an overall amine molality of about 8 m are reported. A thermodynamic model for describing the phase equilibria, which takes into account chemical reactions as well as physical interactions, correlates the experimental data within the experimental uncertainty. Acknowledgment Financial support of this investigation by the Volkswagen-Stiftung, Hannover (Grant I/72069) is gratefully acknowledged. Nomenclature A, ..., D ) coefficients for the temperature dependence of the Henry’s constant for the solubility of gas i in pure water A, ..., E ) coefficients for the temperature dependence of the chemical equilibrium constants ai,i ... di,i ) coefficients for the temperature dependence of the second virial coefficients ai ) activity of component i Bi,j ) second virial coefficient for interactions between components i and j B(r) G,MX ) effective second osmotic virial coefficient in Pitzer’s equation for interactions between a gas G and a salt MX (r ) 0, 1) Cφ ) third osmotic virial coefficient in Pitzer’s equation f ) function for the temperature dependence of interaction parameters f1, f2 ) functions in Pitzer’s equation G ) gas (here, CO2 and H2S) GE ) excess Gibbs energy Hi,w ) Henry’s constant for the solubility of gas i in pure water (on a molality scale) I ) ionic strength (on a molality scale) KR ) equilibrium constant for chemical reaction R (on a molality scale) mi ) true molality of component i m j i ) overall molality of component i M ) cation M Mw ) molar mass of water in kg/mol ni ) true number of moles of component i n j i ) overall number of moles of component i p ) pressure pi ) partial pressure of component i qi ) coefficients for the temperature dependence of interaction parameters R ) universal gas constant T ) absolute temperature x ) p or pi v ) (partial) molar volume X ) anion X y ) vapor phase mole fraction zi ) number of charges of component i 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 a molality scale) φ ) fugacity coefficient Γ ) third osmotic virial coefficient in Pitzer’s equation νi,R ) stoichiometric coefficient of component i in reaction R

ν+, ν- ) number of cations and anions in electrolyte MX τ ) third virial coefficient in Pitzer’s equation Subscripts calc ) calculated exp ) experimental G ) gas i, j, k ) component i, j, k max ) maximum MX ) strong electrolyte R ) reaction R ref ) reference w ) water Superscripts S ) saturation * ) normalized to infinite dilution ∞ ) infinite dilution in pure water ′ ) liquid phase ′′ ) vapor phase

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Received for review May 2, 2000 Revised manuscript received October 17, 2000 Accepted October 19, 2000 IE000441R