2760
Ind. Eng. Chem. Res. 1997, 36, 2760-2765
Correlation and Prediction of the Solubility of CO2 and H2S in Aqueous Solutions of Methyldiethanolamine Yi-gui Li† and Alan E. Mather* Department of Chemical and Materials Engineering, University of Alberta, Edmonton, Alberta T6G 2G6, Canada
The simplified Clegg-Pitzer equations are used to correlate the solubility data for CO2 and H2S over a wide range of solvent concentrations (12-50 wt % methyldiethanolamine (MDEA) aqueous solutions), temperature (25-120 °C), partial pressure of acid gases (0.001-5290 kPa), and acid gas loading (0.001-1.0 mol/mol) from different authors. The interaction parameters thus obtained can be used to predict the solubility data for the mixed acid gases in CO2-H2S-MDEAH2O systems without any additional adjustable parameters. Introduction
Thermodynamic Framework
Aqueous alkanolamine solutions are frequently used for the removal of acidic gases, such as CO2 and H2S, from industrial and natural gases. Methyldiethanolamine (MDEA) has received increased use over other alkanolamines due to its lower heat of absorption, slower reaction with CO2 and lower corrosivity, which leads to lower energy requirements for regeneration, and selective removal of H2S from process streams containing CO2. Up to date there have been many sets of experimental solubility data of CO2 and H2S in aqueous MDEA solutions at various temperatures, pressures and solvent concentrations from different investigators, which have been summarized in previous papers (Jou et al., 1993b; Weiland et al., 1993). Several different thermodynamic models have also been proposed and developed for this system: Kent and Eisenberg (1976); Desmukh and Mather (1981); Austgen et al. (1991); Li and Mather (1994). Clegg and Pitzer (1992) presented a model for activity coefficient in electrolyte solutions with more than one solvent. The authors simplified the Clegg-Pitzer equations and applied it to the MDEA-CO2-H2O system (Li and Mather, 1994) and the MDEA-H2S-H2O system (Qian et al., 1995). But in these papers, we only correlated the solubility data with one solvent composition (30 wt % MDEA for the MDEA-CO2-H2O system and 35 wt % MDEA for the MDEA-H2S-H2O system). The interaction parameters thus obtained can only be used to predict the solubility data of CO2 and H2S in mixed amines or in gas mixtures with the same or nearly the same solvent composition. Recently, we extended the simplified Clegg-Pitzer equations to correlate and predict the solubility data for the TEA-CO2-H2S-H2O system over a wide range of solvent composition (0.5-5 M TEA) (Li and Mather, 1996). In this paper, we would like to use the experimental solubility data of CO2 and H2S for the MDEA system over a wide range of temperatures, pressures, and MDEA concentrations and from different authors to test the capability of correlation and prediction of the Clegg-Pitzer equation. * To whom correspondence should be addressed. Telephone: (403) 492-3957. Fax: (403) 492-2881. E-mail:
[email protected]. † Permanent address: Department of Chemical Engineering, Tsinghua University, Beijing, 100084, China. S0888-5885(97)00061-4 CCC: $14.00
Chemical Equilibria. In the aqueous phase for the MDEA-CO2-H2S-H2O system, the following chemical equilibria are involved:
CO2 + 2H2O a H3O+ + HCO3-
(1)
H2S + H2O a H3O+ + HS-
(2)
H2O + MDEAH+ a H3O+ + MDEA
(3)
The thermodynamic equilibrium constants used in this work are based on the mole fraction scale. Here we use the new correlation equation for deprotonation equilibrium constant of MDEA (eq 3) given by Posey and Rochelle (1996) based on the measured data from 25 to 150 °C (Oscarson et al., 1989) instead of the old one (2560 °C, Schwabe et al., 1959). Recently, Kamps and Maurer (1996) have measured the dissociation constant for MDEA over the temperature range 5-95 °C. Their results are in agreement with those of Oscarson et al. (1989). The temperature dependence of the equilibrium constants together with those of the Henry constants are listed in Table 1. The Henry constants have the unit of pascals. Thermodynamic Expression. For the MDEACO2-H2S-H2O quaternary system, we neglect the ionic species of CO32- and S2- in the aqueous phase and the nonideality of the gas phase. So there are four neutral species, MDEA, H2O, CO2, and H2S, and three ionic species, MDEAH+, HCO3-, and HS- in the equilibrium liquid phase. The concentration of the neutral solutes, CO2 and H2S, in the equilibrated liquid phase can be obtained based on the chemical equilibrium by iteration. The activity coefficient expressions for neutral solvents and ionic solutes are the same as those in our previous paper (Li and Mather, 1996) and are not introduced here again. In these expressions we neglect the interactions between CO2 and other species and between H2S and other species. The parameter F in the Clegg-Pitzer equations is related to the hard-core collision diameter, which is given in mixed solvent systems by Li and Mather (1994) as follows:
∑Cn/1000DmT)1/2
F ) 2150(18.02dm
(4)
where dm and Dm are the density and dielectric constants for mixed solvents and Cn is the molar concentra© 1997 American Chemical Society
Ind. Eng. Chem. Res., Vol. 36, No. 7, 1997 2761 Table 1. Temperature Dependence of the Equilibrium Constants for Reactions 1-3 and Henry’s Constants for CO2 and H2S ln H or ln K ) C1 + (C2/T) + C3 ln T + C4T reaction
compd
C1
C2
C3
C4
temp range (°C)
source
1 2 3 HCO2 HH2S
CO2 H2S MDEA CO2 H2S
231.465 214.582 -56.27 110.03 358.138
-12092.1 -12995.4 -4044.8 -6789.04 -13236.8
-36.7816 -33.5471 7.848 -11.452 -55.0551
0.0 0.0 0.0 -0.0105 0.059565
0-225 0-150 25-150 25-120 0-150
a a b b a
a
Edwards et al. (1978). b Posey and Rochelle (1996).
Table 2. Temperature Dependence of the Density for Pure Solvents
solvent H2O MDEA a
MW
temp range (°C)
expression
Table 5. Fitted Values of Interaction Parameters between Solvents
Amn ) a + b/T source
18.02 d ) 0.999382 + 0.00007208t - 30-75 (7.28491 × 10-6)t2 + (2.65177 × 10-8)t3 119.16 d ) 1.0553-0.0007663t 20-90
b
Littel et al. (1992). Wang et al. (1992).
Table 3. Temperature Dependence of the Aqueous MDEA Solutions
Densitya
of
(25-80 °C)
MDEA concn M
wt %
a
b
c
1.0 1.69 1.73 1.98 2.0 2.596 3.0 3.042 4.28 4.3 4.392
11.8 19.7 20.0 23.1 23.3 30.0 34.5 35.0 48.8 49.0 50.0
1.014 578 1.023 227 1.023 535 1.026 991 1.027 155 1.034 725 1.039 792 1.040 315 1.054 609 1.054 821 1.055 721
-0.217858 × 10-3 -0.279548 × 10-3 -0.281708 × 10-3 -0.307139 × 10-3 -0.308243 × 10-3 -0.363228 × 10-3 -0.399596 × 10-3 -0.403357 × 10-3 -0.491445 × 10-3 -0.492006 × 10-3 -0.495424 × 10-3
-0.276755 × 10-5 -0.253206 × 10-5 -0.252419 × 10-5 -0.242468 × 10-5 -0.242101 × 10-5 -0.221739 × 10-5 -0.209163 × 10-5 -0.207909 × 10-5 -0.192616 × 10-5 -0.193280 × 10-5 -0.194385 × 10-5
a
Table 4. Temperature Dependence of the Dielectric Constants for Pure Solvents
H2O MDEA a
expression D ) 78.54[1 - 4.579 × - 25) + 1.19 × 10-5(t - 25)2 2.8 × 10-8(t - 25)3] D ) 24.74 + 8989.3(1/T - 1/273.15) 10-3(t
m-n
Amn A12 A21
a
temp range (°C)
source
0-100
a
25-50
b
b
Maryott and Smith (1951). Austgen et al. (1991).
tion of solvent n. For aqueous MDEA solutions the calculated values of F change in a narrow range (F ) 13.82-14.75 in 12-50 wt % MDEA aqueous solutions at 25-200 °C). The temperature dependence of the density of the pure liquid solvents is listed in Table 2. The temperature dependence of the density of the aqueous MDEA solution for different MDEA concentrations was regressed from the experimental data (Teng et al., 1994) and is listed in Table 3. The temperature dependence of the dielectric constant of the pure solvents is listed in Table 4. Data Regression: Determining Interaction Parameters Binary System. For the MDEA-H2O system, the three-suffix Margules interaction parameters (A12 and
b, K
40 °C
100 °C
8.780443 -3196.153 -1.426017 0.215113 -7.191494 1857.672 -1.259282 -2.213142
1 ) MDEA, 2 ) H2O.
A21) were regressed based on the literature (Chang et al., 1993), where the NRTL parameters for this binary system are available from both the total pressure and osmolality data. The parameters with their temperature coefficients thus obtained are listed in Table 5. Ternary System. We use the experimental solubility data of CO2 from the MDEA-CO2-H2O ternary system to regress the interaction parameters BMX, W1,MX, and W2,MX with their temperature coefficients and those of H2S from the MDEA-H2S-H2O ternary system to regress the interaction parameters BMY, W1,MY, and W2,MY with their temperature coefficients, respectively. Here 1, 2, M, X, and Y denote MDEA, H2O, MDEAH+, HCO3-, and HS-, respectively. The objective function used in this study is as follows:
∑(pcal - pexp)2/(pexppcal)} × 100%
F ) (1/n){
Density data from Teng et al. (1994).
solvent
a
MDEA-H2O H2O-MDEA a
b
d(g/cm3) ) a + bt + ct2
Amn
a
(5)
Published experimental data of CO2 and H2S solubility in MDEA aqueous solutions by different authors show significant discrepancy, especially at low loading of acid gas (Huang and Ng, 1996; Posey and Rochelle, 1996). At first, we used all the existing experimental data from different authors to regress the interaction parameters. The average deviation of the correlation is very large both for the MDEA-CO2-H2O and for the MDEA-H2S-H2O systems. We plotted a lot of equilibrium curves at the same temperatures and the same MDEA initial concentrations but from different authors. We also used the method of Weiland et al. (1993) to discard some “bad” data points. (Here we only consider the Debye-Hu¨ckel term and the A12 and A21 terms for the nonideality of MDEA-H2O system.) Then, we decided to select and not use all the published solubility data to regress the interaction parameters in the CleggPitzer equations. The experimental data for MDEACO2-H2O and MDEA-H2S-H2O ternary systems we used to regress the interaction parameters in this paper and their correlation deviations are all listed in Tables 6 and 7, respectively. From the tables it can be seen that these experimental data cover a very wide range of temperatures and solvent compositions. The acid gas loadings are in the range of 0.001-1.0 mol/mol and the partial pressures of acid gases are 0.001-5290 kPa. The parameters thus obtained with their temperature coefficients are listed in Tables 8 and 9, respectively. The
2762 Ind. Eng. Chem. Res., Vol. 36, No. 7, 1997 Table 6. Experimental Solubility Data Used To Regress the Interaction Parameters for the MDEA-CO2-H2O Ternary System
reference Maddox et al. (1987) Jou et al. (1982) MacGregor and Mather (1991) Austgen et al. (1991) Jou et al. (1994) Jou et al. (1993) Jou et al. (1982) Ho and Eguren (1988)
MDEA concn, wt %
temp (°C)
11.8 20.0 23.3 23.3 23.3
25 37.8, 65.6, 115.6 25, 50 25, 40, 70, 100, 120 40
23.3
40
30.0 35.0 48.8 49.0
25, 40, 80, 120 40, 100 25, 40, 70, 100, 120 40, 100
data δ% points (corr) figure
total a
4 31 15 34 4
15.7 8.96 32.9 40.3 15.9
2 2
8
15.2
2
24 37 48 7
20.1 19.4 20.1 23.7
3 3
213
25.7
1
δ% ) (1/n)∑|pcal - pexp|/pex. × 100%.
Table 7. Experimental Solubility Data Used To Regress the Interaction Parameters for the MDEA-H2S-H2O Ternary System MDEA concn (wt %)
reference Maddox et al. (1987) Jou et al. (1982) MacGregor and Mather (1991) Jou et al. (1993a) Jou et al. (1982)
data δ% points (corr) figure
temp (°C)
11.8
25
7
30.2
20.0 23.3 23.3
37.8, 65.6, 115.6 40, 100 40
20 17 21
17.9 51.0 43.5
4 5 5
35.0 48.8 48.8
40, 100 40 25, 40, 70, 100, 120
35 14 40
21.0 41.6 26.5
6 6
154
30.6
total
Figure 1. Solubility of CO2 in 20 wt % MDEA aqueous solutions at 37.8, 65.6, and 115.6 °C.
Table 8. Fitted Values of Interaction Parameters for MDEA-CO2-H2O Systema
B (or W) ) a + b/T B (or W) BMX W1,MX W2,MX a
a
b, K
40 °C
100 °C
112.101 5 22.339 28 -5.966 249
-42291.33 -7087.959 1538.104
-22.949 84 -0.295 11 -1.054 532
-1.234 5 3.344 347 -1.844 303
Subscripts: 1 ) MDEA, 2 ) H2O, M ) MDEAH+, X ) HCO3-.
Table 9. Fitted Values of Interaction Parameters for the MDEA-H2S-H2O Systema
B (or W) ) a + b/T B (or W) BMY W1,MY W2,MY a
a
b, K
40 °C
100 °C
533.74 56 7.673 291 3.704 295
-166222.0 -2726.153 -1042.695
2.939 272 -1.032 291 0.374 597
88.289 34 0.367 508 0.909 991
Subscripts: 1 ) MDEA, 2 ) H2O, M ) MDEAH+, Y ) HS-.
total average correlation deviations for CO2 are less than those for H2S. Figures 1-6 show some correlation results. Among them, the experimental data for CO2 in 20 wt % MDEA aqueous solution from Maddox et al. (1987) have the smallest correlation deviations (see Figure 1). In 23.3 wt % MDEA solutions, the experimental data of CO2 from various authors coincide with each other, particularly at 40 °C (see Figure 2). For the series of data from Jou et al. (1982, 1993a, and 1994), the 30, 35, and 48.8 wt % MDEA for CO2 and the 35 wt
Figure 2. Solubility of CO2 in 23.1 and 23.3 wt % MDEA aqueous solutions at 40 and 100 °C.
% MDEA for H2S have the smallest correlation deviations (see Tables 6 and 7 and Figure 3). But in the 48.8 and 50 wt % MDEA systems, both for CO2 and H2S, there is significant discrepancy among different sources (see Figures 3 and 6). Jou et al. (1982) and Ho and Eguren (1988) coincide with each other on one side, while Austgen et al. (1991) and Huang and Ng (1996) agree with each other on the other side (see Figure 3). The solubility data of H2S in 23 wt % MDEA solution also have some disagreement among Huang and Ng (1996) and others (see Figure 5). These interaction parameters were used to predict some solubility data, which were not used for regression. The results are listed in Tables 10 and 11 and are shown in Figures 2, 3, 5, and 6 (Huang and Ng, 1986; Chakma and Meisen, 1987). The solubility data of CO2 in 19.7 wt % MDEA solution from Chakma and Meisen (1987) have the best prediction results (see Table 10 and Figure 7), and those of H2S in 11.8 wt % MDEA solution from
Ind. Eng. Chem. Res., Vol. 36, No. 7, 1997 2763
Figure 3. Solubility of CO2 in 48.8, 49, and 50 wt % MDEA aqueous solutions at 40 and 100 °C.
Figure 5. Solubility of H2S in 23.1 and 23.3 wt % MDEA aqueous solutions at 40 and 100 °C.
Figure 4. Solubility of H2S in 20 wt % MDEA aqueous solutions at 37.8, 65.6, and 115.6 °C.
Jou et al. (1982) and those of CO2 in 48.8 wt % MDEA from Chakma and Meisen (1987) in the high-temperature range have the poorest results (see Table 11). As a whole, the correlation and prediction deviations for CO2 are much better than those for H2S. The larger deviation and significant discrepancy seem to indicate some systematic errors in the experimental data rather than in the model used. After this work was completed, new experimental data for the ternary systems MDEACO2-H2O and MDEA-H2S-H2O were published by Kuranov et al. (1996). These data were not used in the regression. Prediction of CO2 and H2S Solubility of Acid Gas Mixtures for MDEA-CO2-H2S-H2O Systems We use the above regressed interaction parameters, which are obtained from the single acid gas systems, to predict the solubility of mixtures of CO2 and H2S for
Figure 6. Solubility of H2S in 48.8 and 50 wt % MDEA aqueous solutions at 40 and 100 °C. Table 10. Prediction Results for the MDEA-CO2-H2O Ternary System
reference Chakma and Meisen (1987) Huang and Ng (1996) Austgen et al. (1991) Chakma and Meisen (1987) total
MDEA concn (wt %) 19.7
temp (°C)
data δ% points (pred) figure 35
19.3
7
23.1
100, 140, 160, 180, 200 40, 70, 100, 120
21
24.3
2
50.0 48.8
40, 70, 100, 120 40
34 6
31.3 45.4
3 3
48.8
100, 140, 160, 180, 200
36
54.7
3
132
34.0
the quaternary mixed solvent systems. The sources of these predicted acid gas mixture systems are listed in Table 12. These data also cover a wide range of acid loadings (0.00017-0.965 mol of CO2/mol of MDEA and
2764 Ind. Eng. Chem. Res., Vol. 36, No. 7, 1997
Figure 7. Solubility of CO2 in 19.7 wt % MDEA aqueous solutions at 100, 140, 160, 180, and 200 °C. Table 11. Prediction Results for the MDEA-H2S-H2O Ternary System
reference Jou et al. (1982) Huang and Ng (1996) Huang and Ng (1996)
MDEA concn (wt %)
temp (°C)
11.8 23.1
25, 40, 70, 100, 120 40, 100, 120
39 9
80.7 32.5
5
50.0
40, 70, 100, 120
26
44.2
6
74
62.0
Figure 8. Comparison of predicted and experimentally measured values of CO2 equilibrium partial pressure for acid gas mixtures over 35, 49, and 50 wt % MDEA aqueous solutions at 40 and 100 °C.
data δ% points (pred) figure
total
Table 12. Prediction Results for the MDEA-CO2-H2S-H2O Quaternary Systems reference
MDEA concn, (wt %)
temp (°C)
Jou et al. (1993b) Ho and Eguren (1988) Huang and Ng (1996) Jou et al. (1996)
35.0 49.0 50.0 50.0
40, 100 40, 100 40, 100 40, 100
total
δ% (pred) data points CO2 H2S figures 106 18 15 28
20.8 53.1 28.2 29.5
19.1 52.5 40.3 39.4
167
26.4 28.0
8, 9 8, 9 8, 9 8, 9
0.00231-0.95 mol of H2S/mol of MDEA) and partial pressures (0.0051-6790 kPa for CO2 and 0.0323-1590 kPa for H2S). The average predicted deviations are also listed in Table 12. The predicted results are shown in Figures 8 and 9. It can be seen from the figures and table that the prediction results are good for 35 wt % MDEA from Jou et al. (1993b). The results for CO2 in 50 wt % MDEA solution from Huang and Ng (1996) and Jou et al. (1996) are also acceptable. The prediction results for both CO2 and H2S in 49 wt % MDEA solution from Ho and Eguren (1988) are poor. This work has proved again that the simplified Clegg-Pitzer equations are capable of correlation and prediction of the solubility of an acid gas in a mixed solvent system with chemical equilibria over a wide range of solvent compositions (12-50 wt % MDEA), temperature (25-120°C), partial pressure of acid gases (0.001-5290 kPa), and acid gas loading (0.001-1.0 mol/ mol) from different authors without any parameters for the ternary system obtained from other types of data
Figure 9. Comparison of predicted and experimentally measured values of H2S equilibrium partial pressure for acid gas mixtures over 35, 49, and 50 wt % MDEA aqueous solutions at 40 and 100 °C.
or any additional adjustable parameters for the quaternary system. Acknowledgment This work was supported financially by the Natural Sciences and Engineering Research Council of Canada. Nomenclature A ) interaction parameter between and among neutral molecules a, b ) coefficients in Tables 5, 8, and 9 B ) interaction parameter between ions C1-C4 ) coefficients in Table 1 C ) molar concentration
Ind. Eng. Chem. Res., Vol. 36, No. 7, 1997 2765 d ) density, g/mL D ) dielectric constant F ) objective function H ) Henry’s constant, Pa K ) thermodynamic chemical equilibrium constant p ) partial pressure, Pa or kPa as noted t ) temperature, °C T ) absolute temperature, K W ) interaction parameter between and among neutral and ionic species Greek Letters δ ) average relative deviation, % F ) Pitzer parameter relating to the hard-core collision diameter between ions Subscripts 1 ) MDEA 2 ) H2O M ) MDEAH+ X ) HCO3Y ) HScal ) calculated value corr ) correlation exp ) experimental value pred ) prediction
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Received for review January 21, 1997 Revised manuscript received April 17, 1997 Accepted April 18, 1997X IE970061E
Abstract published in Advance ACS Abstracts, June 1, 1997. X
