Ind. Eng. Chem. Res. 1998, 37, 3133-3141
3133
Solubility of Carbon Dioxide in Aqueous Solutions of 2-Amino-2-methyl-1-propanol and N-Methyldiethanolamine and Their Mixtures in the Temperature Range from 313 to 353 K and Pressures up to 2.7 MPa Dirk Silkenba1 umer, Bernd Rumpf,† and Ru 1 diger N. Lichtenthaler* Angewandte Thermodynamik, Physikalisch-Chemisches Institut, Im Neuenheimer Feld 253, Universita¨ t Heidelberg, 69120 Heidelberg, Germany
The solubility of carbon dioxide in aqueous solutions containing 2-amino-2-methyl-1-propanol (AMP) was measured in the temperature range from 313 to 353 K at total pressures up to 2.7 MPa using an analytical method. A model taking into account chemical reactions in the liquid phase as well as physical interactions is used to correlate the new data. To test the predictive capability of the model, the solubility of carbon dioxide in an aqueous solution containing AMP and N-methyldiethanolamine (MDEA) was measured at 313 K. Experimental results are reported and compared to literature data and calculations. Introduction Aqueous solutions containing water-soluble amines like monoethanolamine (MEA), N-methyldiethanolamine (MDEA), or sterically hindered amines like 2-amino-2-methyl-1-propanol (AMP) are widely used to separate acid gases like carbon dioxide and hydrogen sulfide from gaseous effluents contaminated with these components (Sartori and Savage (1983), Xu et al. (1992)). Typical examples are the cleaning of raw gases in coal gasification processes or applications in the natural gas industry. Often, aqueous solutions containing “blended” amines like mixtures of MEA and MDEA or MDEA and AMP are used (Jane and Li (1997)). The proper design of absorption columns requires information on vapor-liquid equilibria, caloric effects, and also information on the kinetics of mass transfer and chemical reactions. Due to chemical reactions in the liquid phase and a strong deviation from ideality, the thermodynamic description of aqueous systems containing alkanolamines like MEA, MDEA, or AMP and sour gases like carbon dioxide or hydrogen sulfide is a difficult task. Reliable experimental data at least for the solubility of a single gas in aqueous solutions containing alkanolamines are required to develop and test physicochemical models to describe vapor-liquid equilibria in these systems. But reliable data on vaporliquid equilibria in these systems are often scarce or scatter (Xu et al. (1992), Kuranov et al. (1996)). Thus, the solubility of carbon dioxide in aqueous solutions containing AMP was measured in the temperature range from 313 to 353 K at pressures up to 2.7 MPa. The physicochemical model originally developed by Edwards et al. (1978) and recently applied to aqueous solutions containing sour gases and MDEA by Kuranov et al. (1996) was used to correlate the data. To test the predictive capability of the model, the solubility of carbon dioxide in an aqueous solution containing AMP * Author to whom correspondence should be addressed. E-mail:
[email protected]. † Lehrstuhl fu ¨ r Technische Thermodynamik, Universita¨t Kaiserslautern, 67653 Kaiserlautern, Germany. E-mail:
[email protected].
and MDEA was measured at 313 K. Experimental results are reported and compared to model calculations and literature data. Experimental Section Measurements of the vapor-liquid equilibrium (VLE) were carried out using the apparatus shown schematically in Figure 1. The equilibrium cell (EC) is made of stainless steel and has a volume of approximately 950 cm3. The cell is thermostated in a water bath at the desired temperature with an accuracy of (0.1 K. The mixture is stirred by a propeller stirrer (PS), which is coupled magnetically to the motor drive. When the pressure (LPR, HPR) and temperature readings (TR) remain constant (after approximately 2 h), complete chemical and vapor-liquid equilibrium has been established. The temperature is measured by a resistance thermometer (RT, PT 100, Lauda, Lauda-Ko¨nigshofen) with an accuracy of (0.04 K. The pressure is measured using two different pressure transducers, a low-pressure sensor (LPS, MKS Baratron, Mu¨nchen) with an accuracy of (0.2% of the reading for pressures up to 0.5 MPa and a high pressure sensor (HPS, Burster, Gernsbach) for pressures up to 10 MPa (accuracy (0.1% of full scale). The membrane capacitors are located outside the water bath. The capacitors themselves and the tubes connecting the equilibrium cell with LPS and HPS are thermostated at a temperature (Th2) higher than the temperature in the equilibrium cell in order to avoid condensation. The composition of the liquid and the gaseous phase is analyzed using a gas chromatograph (GC, Siemens) with a computerized integration unit (IU). The liquid phase is circulated through the liquid sample injection valve (LSV) by means of a gear pump (GP). The valve which allows injection of samples of 1 µL is mounted on the top of the gas chromatograph. In order to analyze the gaseous phase, a Valco sixway valve (6-WV, gaseous sample injection valve) is used, which is located inside the water bath Th1. The sample loop has a volume of 1 mL. Two additional magnetically operated bellows valves (V5, V6) are
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3134 Ind. Eng. Chem. Res., Vol. 37, No. 8, 1998 Table 1. Experimental Results for the Solubility of Carbon Dioxide in Water at 293 K
Figure 1. Schematic view of the experimental equipment. (EC, equilibrium cell; SV, storage vessel; Th1/Th2, thermostat; GC, gas chromatograph; IN, injector; IU, integrator unit; GP, gear pump; LSV, liquid sampling valve; 6-WV, 6-way valve; RT, resistance thermometer; TR, temperature reading; LPS, low-pressure sensor; HPS, high-pressure sensor; LPR/HPR, pressure readings; PS, propeller stirrer; M, magnetic coupling; V1-V11, bellows valves; F1/F2, adapter.)
needed for the injection procedure. The process of analyzing is performed automatically. All the valves are operated online by the gas chromatographic control unit. Each registered data point is the mean value of at least five samples taken from either of the two phases. The samples are taken alternately. The experimental procedure applied to the system carbon dioxide-water-AMP was as follows. The aqueous degassed AMP solution to be investigated was prepared in the store vessel (SV). The molality of the AMP solution was determined by weighing with an accuracy of (0.001 mol/kg. The solution was then poured into the equilibrium cell until it was half-filled by establishing a pressure gradient from the store vessel (SV) to the equilibrium cell. For this purpose the vessel was thermostated at a temperature higher than the temperature in the equilibrium cell. The gaseous carbon dioxide was added through the valve V4. By filling the cell in the described manner, carbon dioxide is quickly absorbed in the liquid to an extent close to the thermodynamic equilibrium. The samples of the liquid phase were vaporized during the injection process into the GC. In the vaporized state, the chemical reactions were shifted completely to the educts; thus, only carbon dioxide, water, and AMP were detected by the gas chromatograph. The gas chromatograph was equipped with a capillary separation column packed with Poropak Q (10 m × 0.53 mm) and a thermal conductivity detector. The peak areas obtained by GC were calibrated using so-called response factors. The response factor is the ratio of the molar amount to the area of a gas chromatographic peak. The response factor of CO2 related to that of water was determined by filling the equilibrium cell with the pure substances and taking samples with the
p/MPa
m j CO2,literature/(mol/kg)
m j CO2,experimental/(mol/kg)
0.5215 1.012 1.507 2.020 2.533
0.189 0.358 0.519 0.675 0.835
0.188 0.382 0.524 0.686 0.827
Figure 2. Solubility of carbon dioxide in water: Comparison between our own measurements at 293 K (b) and literature data (Crovetto (1991), Landolt-Bo¨rnstein (1968)).
LSV (for water) and the 6-WV (for CO2). The ratio of the volumes of the liquid and gaseous sample was known, and then the response factor was determined with an accuracy of (2.7%. The reproducibility of analyzing the liquid phase was better than (3% (for details cf. Silkenba¨umer (1997)). Substances. Carbon dioxide (g99.995 mass %) was purchased from Messer-Griesheim, Ludwigshafen, and used without any further purification. Water (g99.9 mass %) and AMP (g99 mass %) were purchased from Merck, Darmstadt, and degassed by vacuum distillation. MDEA (Aldrich, g99 mass %) was also degassed before usage. Results Test of Procedure: Results for the System CO2H2O. To check the experimental arrangement and procedure, the solubility of carbon dioxide in water was measured at 293.15 K. The experimental results are given in Table 1. The molality of CO2 was about 0.83 mol/kg at maximum, resulting in total pressures up to 2.5 MPa. In Figure 2 the results are compared to literature data (Crovetto (1991), Landolt-Bo¨rnstein (1968)). The new data agree well with the literature data. The average relative deviation in the molality of carbon dioxide between the new experimental data and the literature data is 2%. Results for the System CO2-MDEA-H2O. The experimental results for the solubility of carbon dioxide in an aqueous solution containing about 2.6 mol/kg of MDEA at 313 K are given in Table 2. In Figure 3, the experimental results for the total pressure are plotted versus the overall amount of carbon dioxide dissolved in the liquid phase. Furthermore, Figure 3 contains
Ind. Eng. Chem. Res., Vol. 37, No. 8, 1998 3135 Table 2. Experimental Results for the Solubility of Carbon Dioxide in Aqueous Solutions of MDEA (m j MDEA ) 2.632 mol/kg) at 313 K m j CO2/(mol/kg)
p/MPa
0.634 1.068 1.371 1.756 2.117 2.348 2.601 2.921 3.114 3.267 3.435
0.0120 0.0182 0.0252 0.0445 0.0868 0.2230 0.5440 1.160 2.117 3.029 4.080
Table 3. Experimental Results for the Solubility of Carbon Dioxide in Aqueous Solutions of AMP m j AMP ) 2.430 mol/kg T ) 313.15 K
m j AMP ) 2.451 mol/kg T ) 333.15 K
m j AMP ) 2.443 mol/kg T ) 353.15 K
m j CO2/(mol/kg) p/MPa m j CO2/(mol/kg) p/MPa m j CO2/(mol/kg) p/MPa 0.557 1.447 1.906 1.999 2.082 2.229 2.416 2.581 2.735 2.903
0.0073 0.0093 0.0183 0.0295 0.0430 0.0726 0.233 0.615 1.197 2.052
m j AMP ) 6.135 mol/kg T ) 313.15 K
0.672 1.002 1.268 1.874 2.022 2.183 2.270 2.362 2.420 2.432 2.681 2.849
0.0204 0.0226 0.0253 0.0486 0.0711 0.1083 0.1550 0.2244 0.3201 0.521 1.052 2.023
m j AMP ) 6.477 mol/kg T ) 333.15 K
0.375 0.748 0.892 1.231 1.640 2.038 2.086 2.172 2.265 2.504 2.590 2.596 2.613
0.0473 0.0526 0.0576 0.0751 0.1238 0.2691 0.2766 0.3836 0.564 1.061 1.633 1.754 1.938
m j AMP ) 6.242 mol/kg T ) 353.15 K
m j CO2/(mol/kg) p/MPa m j CO2/(mol/kg) p/MPa m j CO2/(mol/kg) p/MPa 1.786 2.255 2.905 3.442 3.928 4.460 4.830 5.386 5.652 5.897 6.098 6.210
Figure 3. Solubility of carbon dioxide in an aqueous solution of MDEA at 313 K: b: experimental results, this work (m j MDEA ) 2.63 mol/kg). s: results calculated from a correlation by Kuranov et al. (1996).
results calculated from a correlation by Kuranov et al. (1996) based on their data for the system CO2-MDEAH2O. Adding carbon dioxide to an MDEA-containing solution at first results in nearly no change in 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 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 also physically. There is a fair-to-good agreement with the correlation by Kuranov et al., although at constant pressure the experimental results for the overall molality of carbon dioxide in the liquid phase are slightly, but systematically higher. The average relative deviation in the total pressure of the new data from the correlation by Kuranov et al. (1996) is 19%, and the average absolute deviation is 0.23 MPa. However, these comparably large deviations mostly result from a few data points at carbon dioxide molalities where the slope of the total pressure curve is rather steep. For example, at m j CO2 ) 3.44 mol/kg, the experimentally determined total pressure is 4.08 MPa whereas the calculated total pressure is 4.85 MPa. Vice versa at p ) 4.08 MPa, the calculated overall molality of carbon dioxide in the liquid phase is 3.33 mol/kg. Thus, small errors in the overall
0.0073 0.0076 0.0083 0.0102 0.0138 0.0258 0.0447 0.1275 0.2867 0.6380 1.2100 1.9960
1.833 2.547 3.252 3.728 4.314 5.244 5.812 5.932 6.057 6.382
0.0221 0.0278 0.0380 0.0532 0.1045 0.2500 0.680 1.095 1.730 2.743
0.975 1.528 2.253 3.029 3.613 4.135 4.756 5.178 5.447
0.0498 0.0585 0.0785 0.1055 0.1650 0.2738 0.4539 0.745 1.117
molality of carbon dioxide lead to comparably large errors in the total pressure. Results for the System CO2-AMP-H2O. The results for the solubility of carbon dioxide in aqueous solutions of AMP in the temperature range from 313 to 353 K are given in Table 3. Two overall molalities of AMP (m j AMP ≈ 2.4 and ≈ 6.2 mol/kg) were investigated. The maximum overall molality of carbon dioxide is about 6.3 mol/kg, corresponding to a total pressure of about 3 MPa. In the upper parts of Figures 4 and 5 the results for the total pressure above aqueous solutions containing about 2.4 and 6.2 mol of AMP/kg of water at 313, 333, and 353 K are plotted versus the overall molality of carbon dioxide dissolved in the liquid phase. Figures 4 and 5 also show the results of the correlation of the new data (see below). As it was expected, the total pressure shows a similar behavior as in the system CO2-MDEAH2O. In the lower parts of Figures 4 and 5 the total pressure above the aqueous solution is plotted versus the so-called loading of the AMP solution (i.e., the ratio m j CO2/m j AMP). Due to the temperature dependencies of the chemical reactions in the liquid phase and of the physical solubility of carbon dioxide, at constant pressure the overall amount of carbon dioxide in the liquid phase decreases with increasing temperature. Results for the System CO2-MDEA-AMP-H2O. In order to investigate the simultaneous influence of MDEA and AMP on the solubility of carbon dioxide, the solubility of carbon dioxide in an aqueous solution containing 1.266 mol/kg of MDEA and 1.278 mol/kg of AMP was measured (cf. Table 4). In Figure 6, the results for the total pressure are compared to the results for the two ternary systems CO2-MDEA-H2O and
3136 Ind. Eng. Chem. Res., Vol. 37, No. 8, 1998
CO2-AMP-H2O. Figure 6 furthermore contains calculated results for the two ternary systems as well as predicted results for the quaternary system (see below). The overall alkanolamine molality in all solutions is comparable. As AMP is a stronger base than MDEA, at a constant total pressure an aqueous solution containing AMP has a higher carbon dioxide loading than an MDEA-solution. The model based only on data for the ternary systems CO2-MDEA-H2O and CO2-AMPH2O (see below) predicts well the solubility of carbon dioxide in the aqueous solution containing MDEA and AMP simultaneously. Modeling Figure 7 shows a scheme of the model applied to calculate the solubility of carbon dioxide in aqueous solutions containing MDEA and AMP. Due to chemical reactions in the liquid phase, carbon dioxide is dissolved in the liquid phase not only in neutral but also in nonvolatile, ionic form. The following chemical reactions are considered (R denotes the HO-CH2-C(CH3)2 group in AMP):
CO2 + H2O H HCO3- + H+
(I)
HCO3- H CO32- + H+
(II)
RNH2 + H2O H RNH3+ + OH-
(III)
RNH2 + HCO3- H RNHCOO- + H2O
(IV)
MDEA + H2O H MDEAH+ + OH-
(V)
H2O H H+ + OH-
(VI)
The condition for chemical equilibrium yields the following equation for a chemical reaction R:
KR(T) )
∏i ai
νi,R
R ) I...VI
(1)
The balance equation for the number of moles ni of species i in the liquid phase is
ji + ni ) n
νi,RξR ∑ R
(2)
where n j i is the overall number of moles of species i, νi,R is the stoichiometric coefficient for species i in reaction R (νi,R > 0 for products and νi,R < 0 for educts), and ξR is the extent of reaction R. Together with an expression for the excess Gibbs energy of the liquid phase, eqs 1 and 2 may be solved in an iterative procedure to yield the true number of moles ni as well as the true molalities mi of all species in the liquid phase for given overall molalities of carbon dioxide, MDEA, and AMP and a given temperature. The condition of vapor-liquid equilibrium is then applied to calculate the total pressure and the composition of the gas phase. For water, extended Raoult’s law is used:
pywφ′′w )
psw
φsw
(
)
νw(p - psw) exp aw RT
(3)
Figure 4. Solubility of carbon dioxide in aqueous solutions of AMP, O, 0, 4, experimental results, this work: O: m j AMP ) 2.43 mol/kg, T ) 313.15 K. 0: m j AMP ) 2.45 mol/kg, T ) 333.15 K. 4: m j AMP ) 2.44 mol/kg, T ) 353.15 K. s: correlation, this work.
while for carbon dioxide, extended Henry’s law is used:
pyCO2φ′′CO2 ) (m) (T,psw) HCO 2,w
(
exp
)
∞ νCO (p - psw) 2,w
RT
mCO2γ*CO2 (4)
As the vapor pressures of pure AMP and MDEA are rather small in the temperature range considered here (cf. Xu et. al (1991), (1992)), the presence of AMP and MDEA in the vapor phase is neglected. The calculation requires the knowledge of the six temperature-dependent equilibrium constants KR, the activities ai of all species present in the liquid phase, (m) Henry’s constant HCO for the solubility of carbon 2,w dioxide in pure water, the vapor pressure psw and molar volume νw of pure water, the partial molar volume ∞ of carbon dioxide dissolved at infinite dilution in νCO 2,w water, and information on the vapor-phase nonideality. Equilibrium constants KI and KII are taken from Bieling et al. (1989), KIII from Littel et al. (1990), KIV from Xu et al. (1992), KV from Kuranov et al. (1996), and KVI from Edwards et al. (1978) (cf. Table 5). Henry's constant for carbon dioxide is taken from Rumpf and Maurer (1993) (cf. Table 6). The vapor pressure and molar volume of water is taken from Saul and Wagner (1987). A truncated virial equation of state is used to
Ind. Eng. Chem. Res., Vol. 37, No. 8, 1998 3137
Figure 6. Solubility of carbon dioxide in aqueous alkanolamine solutions at 313 K, b, O, 3, experimental results, this work: b: m j MDEA ) 2.632 mol/kg, O: m j AMP ) 2.430 mol/kg. 3: m j MDEA ) 1.266 mol/kg, m j AMP ) 1.278 mol/kg. s: calculated results, this work and Kuranov et al. (1996).
Figure 5. Solubility of carbon dioxide in aqueous solutions of AMP, O, 0, 4, experimental results, this work: O: m j AMP ) 6.14 mol/kg, T ) 313.15 K. 0: m j AMP ) 6.48 mol/kg, T ) 333.15 K. 4: m j AMP ) 6.24 mol/kg, T ) 353.15 K. s: correlation, this work. Table 4. Experimental Results for the Solubility of Carbon Dioxide in an Aqueous Solution Containing MDEA and AMP (m j MDEA ) 1.278 mol/kg, m j AMP ) 1.266 mol/kg) at 313 K
Figure 7. VLE and chemical reactions in the system CO2MDEA-AMP-H2O.
m j CO2/(mol/kg)
p/MPa
solution:
1.159 1.404 1.854 2.250 2.413 2.682 2.853 3.087 3.251 3.411
0.0125 0.0197 0.0443 0.1100 0.1890 0.4550 1.082 2.072 3.012 4.020
GE
calculate the fugacity coefficients φi. Pure-component second virial coefficients Bi,j for carbon dioxide and water are calculated from a correlation on the basis of data recommended by Dymond and Smith (1980) (cf. Table 7). The mixed second virial coefficient BCO2,w is calculated as recommended by Hayden and O’Connell (1975) (cf. Table 8). The partial molar volume of carbon dioxide at infinite dilution in water is calculated as recommended by Brelvi and O’Connell (1972) (cf. Table 8). Activity coefficients of both molecular and ionic species were calculated from the Pitzer (1973) equation for the excess Gibbs energy of an aqueous electrolyte
RTnwMw
) f1(I) +
∑
(0) (1) mimj(βi,j + βi,j f2(I)) +
(i,j)*w
∑
mimjmkτi,j,k (5)
(i,j,k)*w
where f1 is a modified Debye-Hu¨ckel term. Both f1 and f2 are functions of ionic strength I:
I)
1
mizi2 ∑ 2 i
(6)
(0) (1) In eq 5, βi,j , βi,j , and τi,j,k are binary and ternary interaction parameters. The resulting expressions for the activity coefficients 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 which was taken from Bradley and Pitzer (1979). Interaction parameters for the ternary system CO2MDEA-H2O were taken from Kuranov et al. (cf. Table
3138 Ind. Eng. Chem. Res., Vol. 37, No. 8, 1998 Table 5. Equilibrium Constants for Chemical Reactions I-VI (Schwabe, 1959; Edwards et al., 1978; Bieling et al., 1989; Littel et al., 1990; Xu et al., 1992)
ln KR ) AR/(T/K) + BR ln(T/K) + CR(T/K) + DR R I II IIIa IV Va VI a
AR
BR
CR × 102
DR
-7742.6 -8982.0 -7261.78 2546.2 -13445.9 -13445.9
-14.506 -18.112 -22.4773 0 -22.4773 -22.4773
-2.8104 -2.2249 0 0 -4.1447 0
102.28 116.73 142.58612 -11.555 173.1912 140.932
reaction -
H+
CO2 + H2O H HCO3 + HCO3- H CO32- + H+ RNH2 + H2O H RNH3+ + OHRNH2 + HCO3- H RNHCOO- + H2O MDEA + H2O H MDEAH+ + OHH2O H H+ + OH-
Note: Numbers for reactions III and V are given on molarity scale.
Table 6. Henry’s Constant for the Solubility of Carbon Dioxide in Pure Water (273 e T/K e 473) (Rumpf and Maurer, 1993)
When the concentration of hydrogen and hydroxide ions is neglected, the condition for electroneutrality of the liquid phase is
(m) ln HCO (T,psw)/(MPa kg mol-1) ) ACO2,w + BCO2,w/(T/K) + 2,w
mRNH3+ ) mRNHCOO- + mHCO3- + 2mCO32-
CCO2,w(T/K) + DCO2,w ln(T/K) ACO2,w
BCO2,w
CCO2,w
DCO2,w
192.876
-9624.4
0.014 41
-28.749
(8)
Introducing that equation into eq 7 leads to (0) (0) + mRNH2βCO + ln γ*CO2 ) 2(mCO2βCO 2,CO2 2,RNH2
Table 7. Pure-Component Second Virial Coefficients (273 e T/K e 473)
(0) (0) mRNHCOO-(βCO + + βCO ,RNHCOO-) + 2,RNH3 2 (0) (0) mHCO3-(βCO + + βCO ,HCO -) + 2,RNH3 2 3
Bi,j/(cm3/mol) ) ai,j + bi,j(ci,j/(T/K))di,j i
ai,j
bi,j
ci,j
di,j
CO2 H2O
65.703 -53.53
-184.854 -39.29
304.16 647.3
1.4 4.3
Table 8. Mixed Second Virial Coefficients and Partial Molar Volume for Carbon Dioxide at Infinite Dilution in Water T/K
BCO2,w/(cm3/mol)
∞ νCO /(cm3/mol) 2,w
313.15 333.15 353.15
-163.1 -144.6 -129
33.4 34.7 36.3
9) while those for the system CO2-AMP-H2O were determined from the experimental data of the present work as follows (cf. Kuranov et al. (1996)): In the system CO2-AMP-H2O eight species (CO2, RNH2, RNH3+, RNHCOO-, HCO3-, CO32-, H+, and OH-) are present in the liquid phase. As the concentrations of hydrogen and hydroxide ions remain rather small compared to those of the other species, all interaction parameters involving H+ or OH- were set to zero. As no reliable experimental information for the binary system AMP(0) H2O is available, interaction parameters βRNH 2,RNH2 and τRNH2,RNH2,RNH2 had to be set to zero. Furthermore, the ionic strength dependence of the second virial coefficient in eq 5 is neglected for a neutral species (i.e., (1) (1) βRNH ) βCO ) 0). 2,j 2,j The remaining parameters describing interactions between molecular-dissolved carbon dioxide and other species were determined following Kuranov et al. (1996): Considering only binary parameters in the following derivation, the activity coefficient of carbon dioxide in an aqueous solution of AMP is (0) (0) ln γ* CO2 ) 2(mCO2βCO2,CO2 + mRNH2βCO2,RNH2 + (0) (0) mRNH3+βCO + + mRNHCOO-βCO ,RNHCOO- + 2,RNH3 2 (0) (0) mHCO3-βCO - + mCO 2-βCO ,CO 2-) (7) 2,HCO3 3 2 3
(0) (0) mCO32-(2βCO + + βCO ,CO 2-)) (9) 2,RNH3 2 3
Following Rumpf and Maurer (1993) and Kuranov et (0) al. (1996), the binary parameters β(0) G,C and βG,A describing interactions between a dissolved gas G and a strong electrolyte CνCAνA cannot be determined separately. Therefore, introducing (0) (0) B(0) G,CA ) νCβG,C + νAβG,A
(10)
where C denotes RNH3+ and A denotes RNHCOO- or HCO3- or CO32- into eq 9 results in (0) (0) ln γ*CO2 ) 2(mCO2βCO + mRNH2βCO + 2,CO2 2,RNH2 (0) mRNHCOO-BCO - + + 2,RNH3 RNHCOO (0) (0) mHCO3-BCO + - + mCO 2-BCO ,(RNH3+) CO 2-) 2,RNH3 HCO3 3 2 2 3
(11) where (0) (0) (0) BCO + - ) βCO ,RNH + + βCO ,RNHCOO2,RNH3 RNHCOO 2 3 2
(12)
(0) (0) (0) BCO + - ) βCO ,RNH + + βCO ,HCO 2,RNH3 HCO3 2 3 2 3
(13)
(0) (0) (0) BCO + 2- ) 2βCO ,RNH + + βCO ,CO 22,(RNH3 )2CO3 2 3 2 3
(14)
As can be seen from eqs 11-14, in principle only four (0) (0) additional binary parameters (βCO , βCO -, 2,RNH2 2,RNHCOO (0) (0) βCO2,HCO32-, and βCO2,CO32- are required to describe the activity coefficient of carbon dioxide in the system CO2AMP-H2O. A similar argument holds for the ternary parameters describing interactions between moleculardissolved carbon dioxide and other species. The resulting combinations of ternary interaction parameters which directly appear in the expression for the activity
Ind. Eng. Chem. Res., Vol. 37, No. 8, 1998 3139 Table 9. Interaction Parameters for the System CO2-MDEA-AMP-H2O
f(T) ) q0 + q1/(T/K) parameter (0) βCO 2,HCO3 (0) βCO + 2,RNH3 (0) βCO ,RNHCOO 2 (0) βRNH + 3 ,HCO3 (0) βRNH + 23 ,CO3 (1) βRNH3+,HCO3-
τCO2,RNH3+,HCO3τRNH3+,HCO3-,HCO3(0) βCO + 2,MDEAH (0) βMDEAH +,HCO 3 (1) βMDEAH +,HCO 3 τMDEAH+,HCO3-,HCO3-
q0
q1
Tmin/K
Tmax/K
subsystem
0.084 3 -0.403 84 0.403 84 0.021 18 3.587 54 3.793 63 0.005 72 0.007 45 -0.414 7 -0.541 8 1.328 4 0.033 8
-16.15 88.4057 -88.4057 -30.8522 -1042.0259 -1147.3168 0 0 119.96 251.43 -787.13 -16.164
313 313 313 313 313 313 313 313 313 313 313 313
473 353 353 353 353 353 353 353 413 413 413 413
NH3-CO2-H2O CO2-AMP-H2O CO2-AMP-H2O CO2-AMP-H2O CO2-AMP-H2O CO2-AMP-H2O CO2-AMP-H2O CO2-AMP-H2O CO2-MDEA-H2O CO2-MDEA-H2O CO2-MDEA-H2O CO2-MDEA-H2O
coeffcient of carbon dioxide are (Rumpf and Maurer (1993)):
ΓG,G,CA ) νCτG,G,C + νAτG,G,A ΓG,CA,CA ) νC2τG,G,C + 2νCνAτG,C,A + νA2τG,A,A
(15) (16)
As in eqs 12-14, only certain “observable” combinations of interaction parameters may be determined. As molecular-dissolved carbon dioxide and AMP are simultaneously present only in very small amounts, the (0) was set to zero. The binary binary parameter βCO 2,RNH2 (0) (0) parameters βCO2,HCO3- and βCO 2- were taken from 2,CO3 Kurz et al. (1995). Preliminary calculations showed that the calculated true molality of the carbamate ion remains small compared to the other species. Therefore, parameter BCO2,RNH3+RNHCOO- was set to zero. As the amount of molecular-dissolved carbon dioxide remains small in the pressure range investigated here, all ternary interaction parameters τCO2,CO2,j were set to zero. A sensitivity study then showed that it is sufficient to (0) include the binary parameter βCO + as well as the 2,RNH3 ternary parameter τCO2,RNH3+,HCO3-. Besides the parameters describing interactions between neutral carbon dioxide and other species, there are several other parameters in eq 5 describing inter(0) actions between charged species (e.g., βRNH + -, 3 ,HCO3 (0) (0) βRNH3+,CO32-, βRNH3+,RNHCOO-, and ternary parameters like τRNH3+,RNH3+,HCO3-, τRNH3+,RNH3+,CO32-, and τRNH3+,RNH3+,RNHCOO-. Although those parameters do not have a direct influence on the activity coefficient of carbon dioxide (cf. eq 11), they strongly influence the calculated species distribution in the liquid phase (i.e., the “true” molalities of carbon dioxide and AMP). To further reduce the number of adjustable parameters, it is common practice to neglect all interaction parameters involving only species with the same sign of charge. A sensitivity study then showed that it is sufficient to take into account the following parameters describing inter(0) actions between charged species: βRNH + -, 3 ,HCO3 (1) (0) βRNH3+,HCO3-, βRNH3+,CO32-, and the ternary parameter τRNH3+,HCO3-,HCO3-. The influence of temperature on the binary parameters had to be taken into account. It was approximated by
f (T) ) q0 + q1/(T/K)
(17)
whereas the ternary parameters were treated as independent of temperature. Together with the ternary parameters mentioned above, parameters q0 and q1 were fitted simultaneously to the new results for the solubility of carbon dioxide in aqueous solutions containing AMP. The resulting set of parameters is given in Table 9. The model correlates the new experimental data in the temperature range from 313 to 353 K with an average relative deviation of 8.5%; the average absolute deviation is 0.04 MPa (cf. Figures 4 and 5). To test the predictive capability of the model, the parameter set as determined from the new experimental data for the system CO2-AMP-H2O was combined with the interaction parameters for CO2-MDEA-H2O as taken from Kuranov et al. (1996) (cf. Table 9). As can be seen from Figure 6, a good agreement between the experimental data for the total pressure above CO2MDEA-AMP-H2O and the prediction is observed. However, in the range up to about 0.1 MPa calculated total pressures are slightly, but systematically smaller than the experimental numbers. The average relative deviation in the predicted total pressure is 23%; the average absolute deviation is 0.22 MPa. Vice versa at constant pressure, the average relative deviation between the experimental data for the overall molality of carbon dioxide in the liquid phase and the prediction is only 4.5%; the average absolute deviation in m j CO2 is 0.09 mol/kg. Comparison with Literature Data Several authors measured the solubility of carbon dioxide in aqueous solutions of AMP (Sartori and Savage (1983), Roberts and Mather (1988), Teng and Mather (1989), (1990), Tontiwachwuthikul et al. (1991), Li and Chang (1994)). Some authors used molarity as a concentration scale for AMP. To convert this data to the molality scale, the reference temperature at which the solutions were prepared must be known as the density required for this conversion depends on temperature. But as that temperature was not given in all of the publications cited above, the molarity given in those publications was converted to molality by using the density of AMP-H2O at 298.15 K. The density of the system AMP-H2O was taken from Xu et al. (1991). To determine the overall molality of carbon dioxide in the liquid phase, the authors cited above used wet chemical techniques (i.e., the liquid phase was analyzed).
3140 Ind. Eng. Chem. Res., Vol. 37, No. 8, 1998
containing 2 mol/L of AMP at 343 K agree well with the results of the present correlation also at high partial pressure of carbon dioxide (cf. part I of Figure 8). The deviation between their data and the prediction is in the range of the combined experimental errors. Conclusions The solubility of carbon dioxide in aqueous solutions containing 2-amino-2-methyl-1-propanol (AMP) was measured in the temperature range from 313 to 353 K at total pressures up to 2.7 MPa. A model taking into account chemical reactions in the liquid phase as well as physical interactions was used to correlate the new data. Using a reasonable number of adjustable interaction parameters, the model is able to correlate the new data mostly within the experimental uncertainty. A comparison with the limited literature data in nearly all cases yields fair to good agreement. To test the predictive capability of the model, the solubility of carbon dioxide in an aqueous solution containing MDEA and AMP was measured at 313 K. The model predictions agree well with the experimental data for this complex, chemically reactive system. Acknowledgment Financial support of this investigation by the Deutsche Forschungsgemeinschaft, Bonn, Germany, is gratefully acknowledged. Nomenclature
Figure 8. Partial pressure of carbon dioxide above aqueous solutions of AMP. Part I: m j AMP ) 2.45 mol/kg. O, 0, 4: T ) 313, 333, and 353 K, experimental results, Tontiwachwuthikul et al. (1991). ]: T ) 313 K, experimental results, Roberts and Mather (1988). 3: T ) 343 K, experimental results, Teng and Mather (1990). s:calculated results, this work. Part II: m j AMP ) 4.12 mol/ kg. O, 0, 4: T ) 313, 333, and 353 K, experimental results, Tontiwachwuthikul et al. (1991). ]: T ) 313 K, experimental results, Roberts and Mather (1988). s: calculated results, this work.
Some literature data are compared to the results of the present correlation in Figure 8. Roberts and Mather (1988) measured the partial pressure of carbon dioxide above aqueous solutions of AMP at 313 K for AMP molarities of 2 and 3 mol/L and partial pressures of carbon dioxide up to about 5.9 MPa. There is a good agreement between the correlation and their data at lower pressures (cf. parts I and II of Figure 8). However, at high partial pressures for carbon dioxide the literature data are systematically higher than the correlation based on the data of this work. Tontiwachwuthikul et al. (1991) determined the solubility of carbon dioxide in 2 and 3 mol/L solutions of AMP in the temperature range from 293 to 353 K and partial pressures of carbon dioxide up to 0.1 MPa. Their results agree well with the present correlation at 333 and 353 K at both concentrations (cf. parts I and II of Figure 8); however, at 313 K and 3 mol/L of AMP the calculated partial pressures of carbon dioxide are smaller than the experimental data. The data from Teng and Mather (1990) for the partial pressure of carbon dioxide above aqueous solutions
ACO2,w...DCO2,w ) coefficients for the temperature dependence of Henry’s constant of carbon dioxide in water AR...DR ) coefficients for the temperature dependence of equilibrium constants ai,j...di,j ) coefficients for the temperature dependence of second virial coefficients ai ) activity of component i (0) BG,CA ) “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) HCO ) Henry’s constant for the solubility of carbon 2,w dioxide 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 q0, q1 ) 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
Ind. Eng. Chem. Res., Vol. 37, No. 8, 1998 3141 Greek Letters j CO2/(m j AMP + m j MDEA)) RCO2 ) loading (i.e., m β(0), β(1) ) interaction parameters in Pitzer’s equation ΓG,CA,CA, ΓG,G,CA ) “observable” combination of ternary interaction parameters 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 ξR ) extent of reaction R Subscripts A ) anion A C ) cation C CA ) salt CνCAνA G ) gas G i, j, k ) component i, j, k max ) maximum min ) minimum R ) reaction R w ) water Superscripts m ) on molality scale s ) saturation * ) normalized to infinite dilution ∞ ) infinite dilution ′ ) liquid phase ′′ ) gas phase
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Received for review December 3, 1997 Revised manuscript received March 31, 1998 Accepted April 3, 1998 IE970925W
