4804
Ind. Eng. Chem. Res. 1996, 35, 4804-4809
CORRELATIONS Correlation and Prediction of the Solubility of CO2 and H2S in Aqueous Solutions of Triethanolamine 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 in 0.5, 2, 3.5, and 5 M triethanolamine aqueous solutions at 0, 25, 50, 70, 75, 100, and 125 °C at acid gas loadings below 1.0 and partial pressures of the acid gases ranging from 0.01 to 6700 kPa. The interaction parameters thus obtained can be used to predict the solubility data for the mixed acid gases in CO2-H2S-TEA-H2O systems over a wide range of solvent composition, temperature, and pressure without any additional adjustable parameters. Introduction Triethanolamine (TEA) was one of the first amines used for the removal of H2S and CO2 from gas streams. Although it was superceded by methyldiethanolamine (MDEA) and monoethanolamine (MEA), up to now there have been available a lot of experimental solubility data of CO2 and H2S in aqueous triethanolamine solutions in a wide range of temperatures, pressures, solvent compositions, and acid gas loadings. Mason and Dodge (1936) determined the solubility of CO2 in TEA solutions (0.5, 1, 2, 3.5, and 5 M TEA) at 0, 25, 50, and 75 °C over a wide range of acid gas loadings (0.01-1.1). Lyudkovskaya and Leibush (1949) measured the equilibrium absorption of CO2 by TEA aqueous solutions (0.5, 2, 3.5, and 5 M) at 25, 50, and 75 °C in the high acid gas loading region. They also proposed a correlation equation with three parameters for each temperature based on regular solution theory and the GibbsDuhem equation. Jou et al. (1985) measured the equilibrium solubility of H2S and CO2 separately in 2, 3.5, and 5 M TEA solutions at temperatures of 25, 50, 75, 100, and 125 °C and at acid gas partial pressures ranging from 0.01 to 6700 kPa. They used the method of Kent and Eisenberg (1976) with 16 parameters to correlate their experimental data. Recently, Jou et al. (1996) measured the solubility data of acid gas mixtures (H2S and CO2) in 2, 3.5, and 5 M TEA aqueous solutions at 50, 75, and 100 °C. In this paper, we use these experimental data for the triethanolamine system to test the capability of correlation and prediction of the Clegg-Pitzer equation (Clegg and Pitzer, 1992). The original Pitzer (1973) general equation did not consider the solvent molecules in the system as interacting particles. Thus, it is not suitable for the thermodynamic description of mixed-solvent systems. The mole-fraction-based ion-interaction model of Pitzer and Simonson (1986) and Clegg and Pitzer (1992) has been developed, in which all the species in a system are considered as interacting particles. Their equations can * To whom correspondence should be addressed. E-mail:
[email protected]. Telephone: (403) 492-3957. Fax: (403) 492-2881. † Permanent address: Department of Chemical Engineering, Tsinghua University, Beijing 100084, China.
S0888-5885(96)00244-8 CCC: $12.00
be used for electrolyte aqueous solutions with high ionic concentrations (such as the HNO3-H2O system up to 100% HNO3 (Clegg and Brimblecombe, 1990) and the H2SO4-H2O system to 40 m H2SO4 (Clegg and Brimblecombe, 1995)). However, their applications were all restricted to electrolyte aqueous solutions. Recently, the authors simplified the Clegg-Pitzer equations and applied them to mixed-solvent gas purification systems (such as MDEA-MEA-CO2-H2O (Li and Mather, 1994) and sulfolane-MDEA-CO2-H2S-H2O (Qian et al., 1995)). We found that this equation has predictive capability. It can predict the solubility of CO2 in a mixed-amine solvent MDEA-MEA-H2O system with the interaction parameters obtained from the singleamine aqueous systems. It can also predict the solubility of CO2 and H2S of an acid gas mixture in a mixedsolvent system with the parameters from the single-acid gas systems, but our predictions for acid gas mixtures were limited to one or two solvent compositions. Our correlations for a single-acid gas with the Clegg-Pitzer equations were also restricted to systems with limited solvent compositions, because of limited experimental data available from the literature. Thermodynamic Framework Chemical Equilibria. In the aqueous phase for the TEA-CO2-H2S-H2O system, the following chemical equilibria are involved: K1
CO2 + 2H2O w\x H3O+ + HCO3K2
H2S + H2O w\x H3O+ + HSK3
H2O + TEAH+ w\x H3O+ + TEA
(1a) (2a) (3a)
The thermodynamic equilibrium constants used in this work are based on the mole fraction scale. Henry’s constants have the unit of pascals. Their temperature dependence is listed in Table 1. Thermodynamic Expression. For the TEA-CO2H2S-H2O quaternary system, the activity coefficient expressions for neutral solvent (TEA) and ionic solute © 1996 American Chemical Society
Ind. Eng. Chem. Res., Vol. 35, No. 12, 1996 4805 Table 1. Temperature Dependence of the Equilibrium Constants for Reactions 1a-3a and Henry's Constants for CO2 and H2S
ln H or ln K ) C1 + C2/T + C3 ln T + C4T reaction
comp
C1
C2
C3
C4
temp range (°C)
source
1a 2a 3a HCO2 HH2S
CO2 H2S TEA CO2 H2S
231.465 214.582 -10.6518 170.7126 358.138
-12092.1 -12995.4 -3088.69 -8477.711 -13236.8
-36.7816 -33.5471 0.0 -21.95743 -55.0551
0.0 0.0 0.010517 0.005781 0.059565
0-225 0-150 0-50 0-100 0-150
a a b c a
a
Edwards et al. (1978). b Bates and Allen (1960). c Chen et al. (1979).
Table 2. Temperature Dependence of the Density of Aqueous TEA Solutionsa
d (g/cm3) ) a + bt + ct2
a
TEA (M)
conc. (wt %)
a
b
c
temp range (°C)
0.5 2.0 3.5 5.0 7.5
7.37 28.48 48.36 67.47 100.0
1.013 801 1.049 807 1.085 67 1.117 067 1.134 496
-0.147 087 × 10-3 -0.264 297 × 10-3 -0.411 853 × 10-3 -0.549 33 × 10-3 -0.512 693 × 10-3
-0.317 999 × 10-5 -0.271 442 × 10-5 -0.198 888 × 10-5 -0.117 507 × 10-5 -0.635 384 × 10-5
25-80 25-80 25-80 25-80 25-80
Experimental data from Maham et al. (1994).
Table 3. Temperature Dependence of the Dielectric Constant for Pure Solvents solvent H2O MEA DEA TEA a
expression
temp range (°C)
D ) 78.54[1 - 4.579 × - 25) + 1.19 × 2.8 × 10-8(t - 25)3] D ) 35.76 + 14836(1/T - 1/273.15) D ) 28.01 + 9277(1/T - 1/273.15) D ) 20.26 + 3718(1/T - 1/273.15) 10-3(t
10-5(t
-
25)2
-
source
0-100
a
-20 to 20 0-50
b b
Maryott and Smith (1951). b Ikada et al. (1968).
Table 4. Fitted Values of Interaction Parameters for the TEA-CO2-H2O and TEA-H2S-H2O Systemsa
A (or B or W) ) a + b/T A (or B or W) A12 A21 BMX W1,MX W2,MX BMY W1,MY W2,MY a
a
b, K
25 °C
50 °C
75 °C
100 °C
125 °C
2.178765 25.11269 -348.234 14.3357 -13.94361 -232.034 24.64052 -10.82494
714.6700 -9837.897 112798.7 -4387.563 4728.127 92961.13 -8546.694 4470.593
4.58 -7.88 30.09 -0.38 1.91 79.76 -4.03 4.17
4.39 -5.33 0.83 0.76 0.69 55.64 -1.81 3.01
4.23 -3.14 -24.24 1.73 -0.36 34.98 0.09 2.02
4.09 -1.25 -45.95 2.58 -1.27 17.09 1.74 1.16
3.97 0.40 -64.93 3.32 -2.07 1.45 3.17 0.40
Subscripts: 1 ) TEA, 2 ) H2O, M ) TEAH+, X ) HCO3-, Y ) HS-.
(TEAH+) are as follows:
ln γ1 ) (2AxIx3/2)/(1 + FIx1/2) xMxXBMX exp(-RIx1/2) - xMxYBMY exp(-RIx1/2) + A12(1 - 2x1)x22 + 2A21x1x2(1 - x1) + (1 - x1)xI(FxW1,MX + FYW1,MY) x2xI(FxW2,MX + FYW2,MY) (1) ln γM* ) -zM2Ax((2/F) ln(1 + FIx1/2) + Ix1/2(1 - 2Ix/zM2)/(1 + FIx1/2)) + xMBMXg(RIx1/2) + xYBMYg(RIx1/2) - xM(xXBMX + xYBMY)(zM2g(RIx1/2)/2Ix + 2
(1 - zM /2Ix) exp(-RIx1/2)) - 2x1x2(A12x2 + A21x1) + x1(1 - xI)(FXW1,MX + FYW1,MY) + x2(1 - xI)(FXW2,MX + FYW2,MY) (2) Here the subscripts 1, 2, 3, 4, M, X, and Y represent
TEA, H2O, CO2, H2S, TEAH+, HCO3-, and HS-, respectively.
g(x) ) 2(1 - (1 + x) exp(-x))/x2 FX ) 2xX/xI,
FY ) 2xY/xI
xI ) xM + xX + xY ) 1 - x1 - x2
(3) (4) (5)
x’s are the mole fractions in the equilibrated liquid phase. The nomenclature for the other symbols in the above expressions is the same as that in our previous papers (Li and Mather, 1994; Qian et al., 1995) and is presented in the Nomenclature section. The temperature dependence of the density of the pure liquid TEA and aqueous TEA solutions was regressed from the experimental data (Maham et al., 1994) and is listed in Table 2. The dielectric constant of TEA at 25 °C is available in the literature (Bhattacharyya and Nakhate, 1947); however, the values given are discordant. We assume that the differences of the
4806 Ind. Eng. Chem. Res., Vol. 35, No. 12, 1996
Figure 1. Solubility of CO2 in a 3.5 M TEA aqueous solution.
Figure 2. Solubility of CO2 in a 5.0 M TEA aqueous solution.
dielectric constant between MEA and DEA and those between DEA and TEA are the same. The dielectric constants of MEA and DEA are known from the literature (Ikada et al., 1968). By using this method, we obtain the temperature dependence of the dielectric constant of TEA (see Table 3).
the free neutral CO2 species in the equilibrated liquid phase, which can be obtained by solving a cubic equation based on the following chemical equilibrium:
Data Regression: Determining Interaction Parameters Binary System. For the TEA-H2O system, we use the total vapor pressure curves of aqueous triethanolamine solutions (Dow Chemical Co., 1981) to obtain the activity coefficients of H2O and use the Gibbs-Duhem equation to integrate the activity coefficient of TEA. The Margules interaction parameters (A12 and A21) thus regressed cannot be used for the ternary systems (TEACO2-H2O and TEA-H2S-H2O systems). The correlation deviations for ternary systems are very large if we keep the interaction parameters constant in different solvent compositions. So, we have to abandon this method and regress A12 and A21 from the ternary systems. Perhaps the P-t curves shown in the figure are not accurate (no data listed). The experimental VLE data for the TEA-H2O system at 30-100 °C from Leibush and Shorina (1947) are not sufficient to obtain the interaction parameters. However, their statement that the nonidealities for the TEA-H2O system are negative only in the range 30-50 °C and turn positive at high temperatures is correct. Although there are some activity coefficient data for the TEA-H2O binary system at -15 to 0 °C obtained by use of the freezing point depression method (Chang et al., 1993), it cannot be extended to the high-temperature region. Ternary System. For the TEA-CO2-H2O system, the interaction parameters (BMX, W1,MX, and W2,MX) were regressed with A12 and A21 simultaneously from the solubility data of CO2 loading below 1.0 for 2, 3.5, and 5 M aqueous TEA at 25, 50, 75, 100, and 125 °C (Jou et al., 1985), those for purified TEA in 0.5, 2, 3.5, and 5 M aqueous TEA at 0, 25, 50, and 75 °C (Mason and Dodge, 1936), and those for 0.5, 2, 3.5, and 5 M aqueous TEA at 25, 50, and 75 °C (Lyudkovskaya and Leibush, 1949). The pK3 value for TEA is the smallest one among many alkanolamines: TEA (7.762), MDEA (8.52), DEA (8.883), MEA (9.50) (Kim et al., 1987) and 2-PE (10.14) (Xu et al., 1993). So we should consider the concentration of
K4
H2O + CO2 + TEA \ w x TEAH+ + HCO3- (4a) K4 ) K1/K3 ) xMγM*xXγX*/x1γ1x2γ2x3γ3*
(6)
K4X ) xMxX/x1x2x3 ) K4γ1γ2γ3*/γM*γX*
(7)
(K4X - 1)CM3 + (C20 + C10(1 + R1))(1 - K4X)CM2 + (C20 + (C10 + C20)R1)K4XC10CM - C102C20R1K4X ) 0 (8) C3 ) C10R1 - CM
(9)
The apparent chemical equilibrium constant Kx changes with the concentration of each species. The above equation was solved by an iterative method. For the TEA-H2S-H2O system, the interaction parameters (BMY, W1,MY, and W2,MY) with A12 and A21 were regressed simultaneously from the solubility data of H2S loading below 1.0 for 2, 3.5, and 5 M aqueous TEA at 25, 50, 75, 100, and 125 °C (Jou et al., 1985). Because the thermodynamic equilibrium constant for the following chemical equilibrium is also small, we should consider the concentration of the free neutral H2S species in the equilibrated liquid phase, which can be solved from a quadratic equation. K5
H2S + TEA \ w x TEAH+ + HS-
(5a)
K5 ) K2/K3 ) xMγM*xYγY*/x1γ1x4γ4*
(10)
K5X ) xMxY/x1x4 ) K5γ1γ4*/γM*γY*
(11)
(K5X - 1)CM2 - K5XC10(1 + R2)CM + K5XC102R2 ) 0 (12) C4 ) C10R2 - CM
(13)
It should be pointed out that these two sets of parameters for two ternary systems with 330 data points must be regressed simultaneously with the
Ind. Eng. Chem. Res., Vol. 35, No. 12, 1996 4807 Table 5. Average Deviation for Correlation and Prediction of VLE Data in Various Systems and Sources of Experimental Data δe (%) system TEA-CO2-H2O
TEA-CO2-H2O TEA-H2S-H2O TEA-CO2-H2S-H2O
no. of data points
temp range (°C)
solvent comp
corr
20 77 69 83 5 28 29 25 27 27
0-75 25-125 25-125 25-125 0 25 25-125 25-125 25-125 50
0.5 M TEA 2M 3.5 M 5M 2M 0.5-5 M 2M 3.5 M 5M 2, 3.5, 5 M
18.8 21.7 17.1 18.0
49
75
2, 3.5, 5 M
40
100
2, 3.5, 5 M
a Mason and Dodge (1936). b Lyudkovskaya and Leibush (1949). c Jou et al. (1985). × 100%.
Figure 3. Solubility of H2S in a 3.5 M TEA aqueous solution.
pred
1 2 33.6 14.4
24.5 13.1 13.6 20.7 (CO2) 22.5 (H2S) 15.6 (CO2) 23.7 (H2S) 17.8 (CO2) 16.1 (H2S) d
Figure
5 3 4 6 6
source a, b a, b, c b, c a, b, c a a c c c d d d
Jou et al. (1996). e δ ) {(1/n)∑|pi,cal - pi,exp|/pi,exp}
Figure 4. Solubility of H2S in a 5.0 M TEA aqueous solution.
temperature coefficients. Otherwise, we cannot obtain the same A12 and A21 values for two ternary systems with the smallest correlation deviation. The objective function used for the regression is
∑|pcal - pexp|/pexp} × 100%
F ) (1/n){
(14)
The parameters thus obtained with their temperature coefficients are listed in Table 4, and part of the correlation results are shown in Figures 1-4. The correlation deviations are listed in Table 5. The total average correlation deviation for these two ternary systems is 18.6% (with 330 data points). We use the above regressed interaction parameters to predict the solubility of CO2 in 2 M TEA at 0 °C and in 0.5-5 M TEA at 25 °C. The prediction results are shown in Table 5 and Figure 5. Prediction of CO2 and H2S Solubility of Acid Gas Mixtures for TEA-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 the quaternary mixed-solvent systems in 2, 3.5, and 5 M TEA and at 50, 75, and 100 °C (Jou et al., 1996). The concentrations of the free neutral CO2 and H2S species
Figure 5. Solubility of CO2 in 0.5-5 M TEA aqueous solutions at 25 °C.
in the equilibrated liquid phase must be calculated by solving two simultaneous equations (eqs 7 and 11) based on chemical equilibria with an iterative method. The deviations in the prediction are listed in Table 5, and
4808 Ind. Eng. Chem. Res., Vol. 35, No. 12, 1996 W ) interaction parameter between and among neutral and ionic species x ) liquid phase mole fraction based on the true species, molecular and ionic z ) valence of an ion Greek Letters R ) Pitzer universal constant in eqs 1 and 2 R1 ) CO2 loading in the liquid phase, mol of CO2/mol of TEA R2 ) H2S loading in the liquid phase, mol of H2S/mol of TEA γ ) activity coefficient δ ) average relative deviation, % F ) Pitzer parameter relating to the hard-core collision diameter between ions Superscripts ° ) initial concentration * ) unsymmetric convention Figure 6. Comparison of predicted and experimentally measured values of CO2 and H2S equilibrium partial pressure over 2-5 M TEA aqueous solutions at 50 °C.
part of the results are shown in Figure 6. From the figure, it can be seen that the agreement between predicted and experimental partial pressures is acceptable. The larger deviation for the partial pressure of H2S in 5 M aqueous TEA seems to indicate some systematic error in the experimental data rather than the model used. This work has proved again that the Clegg-Pitzer equations are capable of correlation and prediction of the solubility of an acid gas mixture in a mixed-solvent system with chemical equilibria over a wide range of solvent compositions (0.5-5 M TEA; the molarity of 100% pure TEA liquid is only 7.5 M at 25 °C), temperature (0-125 °C), pressure (0.01-6700 kPa), and acid gas loading (0.0001-1.0 mol/mol) without any additional adjustable parameters even though the nonideal behavior of the binary solvent system (TEA-H2O) is not wellknown. 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 Ax ) Debye-Hu¨ckel parameter on a mole fraction basis a, b ) coefficients in Table 4 B ) interaction parameter between ions C1-C4 ) coefficients in Table 1 C ) molar concentration d ) density, g/mL D ) dielectric constant F ) ionic fraction F ) objective function H ) Henry’s constant, Pa Ix ) ionic strength on mole fraction basis K ) thermodynamic chemical equilibrium constant Kx ) apparent chemical equilibrium constant, expressed in mole fraction concentrations p ) partial pressure, Pa or kPa as noted t ) temperature, °C T ) absolute temperature, K
Subscripts 1 ) TEA 2 ) H2O 3 ) CO2 4 ) H2S M ) TEAH+ X ) HCO3Y ) HScal ) calculated value corr ) correlation exp ) experimental value pred ) prediction
Literature Cited Bates, R. G.; Allen, G. F. Acid Dissociation Constant and Related Thermodynamic Quantities for Triethanolammonium Ion in Water from 0 to 50 °C . J. Res. Natl. Bur. Stand. 1960, 64A, 343. Bhattacharyya, S. K.; Nakhate, S. N. Conductance of salts in NonAqueous Solvents. Part I. Conductance of salts in triethanolamine. J. Indian Chem. Soc. 1947, 24, 1. Chang, H.-T.; Posey, M.; Rochelle, G. T. Thermodynamics of Alkanolamine-Water Solutions from Freezing Point Measurements. Ind. Eng. Chem. Res. 1993, 32, 2324. Chen, C.-C.; Britt, H. I.; Boston, J. F.; Evans, L. B. Extension and Application of the Pitzer Equation for Vapor-Liquid Equilibrium of Aqueous Electrolyte Systems with Molecular Solutes. AIChE J. 1979, 25, 820. Clegg, S. L.; Brimblecombe, P. Equilibrium Partial Pressures and Mean Activity and Osmotic coefficients of 0-100% Nitric Acid as a Function of Temperature. J. Phys. Chem. 1990, 94, 5369. Clegg, S. L.; Pitzer, K. S. Thermodynamics of Multicomponent, Miscible, Ionic Solutions: Generalized Equations for Symmetrical Electrolytes. J. Phys. Chem. 1992, 96, 3513. Clegg, S. L.; Brimblecombe, P. Application of a Multicomponent Thermodynamic Model to Activities and Thermal Properties of 0-40 mol/kg Aqueous Sulfuric Acid from
