Article pubs.acs.org/jced
Modeling of CO2 Solubility in Tertiary Amine Solvents Using pKa Hiroshi Machida,*,†,‡ Shin Yamamoto,‡ and Hidetaka Yamada‡ †
Department of Chemical Engineering, Graduate School of Engineering, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8601, Japan ‡ Chemical Research Group, Research Institute of Innovative Technology for the Earth (RITE), 9-2 Kizugawadai, Kizugawa-shi, Kyoto 619-0292, Japan ABSTRACT: Tertiary amines are widely used to capture CO2 from the gases of high-pressure processes because these compounds have high CO2 solubilities at high pressures of 0.5−1 MPa and low CO2 absorption heats compared to primary and secondary amines. CO2 solubility model for tertiary amine solvents was developed using pKa. This study used selected aqueous solutions of tertiary alkanolamines, tertiary cyclic amines, and tertiary diamines as solvents for modeling. Chemical equilibrium constants were correlated with a linear function of pKa. The generalized parameters provide a method to predict CO2 solubility in a tertiary amine solution from the pKa of the amine.
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CO2 + 2H 2O ↔ HCO3− + H3O+
INTRODUCTION In CO2 capture and storage processes, tertiary amine solutions like N-methyl-diethanolamine (MDEA) have useful characteristics for the capture of CO2 from gases generated in highpressure processes such as those at natural gas stations or in the integrated coal gasification combined cycle (IGCC) process. The favorable traits of tertiary amine solutions are relatively low reaction heats for CO2 absorption and high CO2 solubility in high pressure regions such as 0.5−1 MPa.1 The development of high performance solvent with high CO2 solubility and/or a low reaction heat of CO2 absorption will reduce the energy required for CO2 capture. MDEA has been widely applied as a tertiary amine solvent at commercial scale and CO2 solubility data for MDEA solutions have been measured by many researchers.2−5 Tomizaki et al.6−8 reported the solubility of CO2 in cyclic amine solutions such as morpholine or imidazole that have low reaction heats compared with MDEA. They also measured the CO2 absorbed in amine solution with 13C NMR and found that the ratio of physical absorption increased with an increase in pressure. Machida et al.9 investigated the solubility of CO2 in tertiary diamine solution (N,N,N′,N′- tetramethylethylenediamine). A longer alkyl chain between the two amines led to higher CO2 solubility which was dependent on amine basicity. Many models of the solubility of CO2 in amine solution have been reported. The following equilibria were considered for the solubility of CO2 in tertiary amine solutions. 1. Ionization of water 2H 2O ↔ H3O+ + OH−
(2)
3. Dissociation of bicarbonate HCO3− + H 2O ↔ H3O+ + CO32 −
(3)
4. Dissociation of protonated tertiary amine R3NH+ + H 2O ↔ NR3 + H3O+
(4)
For simplicity, R3 was used to represent three functional groups. Unlike primary and secondary amines, tertiary amine does not form carbamate. In the simple model, bicarbonate dissociation was neglected and a single equilibrium model was applied. NR3 + CO2 + H 2O ↔ NR3H+ + HCO3−
(5)
Suleman et al.10 reviewed the thermodynamic model for acid gas in aqueous alkanol amines. They classified three groups as semiempirical model, activity coefficient model, and equation of state model. For semiempirical model, Posey et al.11 and Gabrielsen et al.12 developed the model using a single equilibrium constant with four temperature-dependent parameters. Al-Rashed et al.13 and Austgen et al.14 developed the model using four equilibrium constants with four temperature-dependent parameters that are based on activity coefficients using either the NRTL-electrolyte model15,16 or UNIQUAC-electrolyte model.17 For equation of state model, Tellez-Arredondo et al.18 developed
(1)
Received: February 1, 2016 Accepted: May 17, 2016
2. Ionization of carbon dioxide © XXXX American Chemical Society
A
DOI: 10.1021/acs.jced.6b00101 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
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the extension model of the cubic two-state EoS to evaluate the fugacities of ionic species. The aim of this work is to develop a simple model predicting CO2 solubility in tertiary alkanolamine solution using amine
basicity (pKa). A simplified chemical equilibrium model was first used to correlate the data on the solubility of CO2 in alkanolamines, cyclic amines, and diamines. Then, a linear relation formula to pKa was developed with a given equilibrium constant.
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Table 1. Data Source of Tertiary Amine Solutions amine MDEA
N-methyl- diethanolamine
HEMO
4-(2-hydroxyethyl) morpholine imidazole 1-methylimidazole 2-methylimidazole 1,2-dimethylimidazole N,N,N′,N′-tetramethyl-ethylenediamine N,N,N′,N′-tetramethyl-1,3diaminopropane N,N,N′,N′-tetramethyl-1,6diaminohexane
Im 1MeIm 2MeIm 1,2-DMIm C2-diamine C3-diamine C6-diamine
molarity, mol/L
weight fraction, wt %
3 3
19.3 32.3 48.8 34.9 37.7
2 4 8 4.50 4.61
8 8
20.0 24.4 24.4 28.9 30.0
3.67 3.93 3.93 4.23 3.69
8 8 8 8 9
30.0
3.29
9
30.0
2.49
9
3 3 3 3
molality, mol/kg ref 3, 4
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CORRELATION MODEL We developed simple equations for chemical equilibria that describe the solubility of CO2 in tertiary amine solutions based on a previous work.9 This model assumes the activity coefficients of each component to be 1, and hydroxide (OH−) and carbonate (CO32−) are not considered because they are expected to have negligibly small concentrations. Similar assumptions have also been used in other CO2 solubility models.11,19 In our previous model, physical absorption of CO2 was assumed to be neglected and one equilibrium parameter depending on Henry constant was considered. This model had a systematic deviation at high pressure region. In this work, to improve the model accuracy at high pressure region, the total CO2 solubility amount was set as a summation of CO2 physical absorption (αphy) and CO2 chemical absorption (αchem)
Table 2. pKa and correlated parameters for tertiary amine solutions MDEA HEMO Im 1MeIm 2MeIm 1,2-DMIm C2-diamine C3-diamine C6-diamine
pKa
K
−ΔHK [kJ/mol]
8.509 6.938 6.998 7.038 7.878 8.008 9.509 6.109 10.19 8.109 10.19 10.19
120 5.73 5.24 3.69 26.0 16.2 500 0.54 878 36.0 893 1316
54.3 33.6 34.1 27.5 54.7 41.4 58.7 40.5 58.1 59.4 68.2 76.7
REFERENCE DATA
Reference data for CO2 solubility in tertiary amine solutions is summarized in Table 1. The data is classified according to alkanolamines, diamines, and cyclic amines. The amine pKa values are shown in Table 2.
α = αphys + αchem
(6)
Two chemical absorptions were considered for the tertiary diamine solution α = αphys + αchem1 + αchem2
(7)
Physical absorption of CO2 was considered proportional to CO2 partial pressure P = HmCO2
(8)
Figure 1. Correlation and prediction results for CO2 solubilities of MDEA solutions. Solid line is the correlation and dashed line is the prediction with generalized parameters (a) mA= 2 mol/kg, ◆ = 313 K, ▲ = 333 K, ● = 373, ■ = 393 K, ◇ = 413 K; (b) mA = 8 mol/kg, ◆ = 313 K, ● = 353 K, ■ = 393 K. B
DOI: 10.1021/acs.jced.6b00101 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
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Figure 2. Correlation and prediction results for CO2 solubilities of cyclic amine solutions. Solid line is correlation, dashed line is the prediction with the generalized parameters: ◆ = 313 K, ▲ = 343 K, ● = 373 K, ■ = 393 K for (a) HEMO mA = 4.61 mol/kg and (b) 1,2-DMIm mA= 4.23 mol/kg.
Figure 3. Correlation and prediction results for CO2 solubilities of diamine solutions. Solid line is correlation and dashed line is prediction with the generalized parameters: ◆ = 313 K, ● = 343 K, ■ = 393 K for (a) C2-diamine mA= 3.69 mol/kg, (b) C6-diamine mA= 2.49 mol/kg.
αphys =
mCO2
=
mA
P mA H
αchem =
(9)
1 + αphysK
=
PK mA H + PK
(13)
where K is the chemical equilibrium constant. αphys and αchem are the CO2 solubilities (molCO2/molamine) for physical absorption and chemical absorption, respectively. The temperature dependence of the equilibrium constant and Henry absorption constant are represented with the van’t Hoff equation
where mA is initial amine molality, mCO2 is CO2 molality in pure water, P/MPa is partial pressure of CO2, H/(MPa kg mol−1) is the Henry absorption constant. The following formula was used for the chemical absorption portion NR3 + CO2 + H 2O → NR3H+ + HCO3−
αphysK
(10)
ln K (T ) = ln K (313) −
ΔHK ⎛ 1 1 ⎞ ⎜ ⎟ − ⎝ R T 313 ⎠
(14)
ln H(T ) = ln H(313) −
ΔHH ⎛ 1 1 ⎞ ⎜ ⎟ − R ⎝T 313 ⎠
(15)
+
K=
K=
HCO−3 ]
[NR3H [NR3][CO2 ]
αchem (1 − αchem)αphys
(11)
where T is temperature and ΔHK/(kJ/mol) is the reaction enthalpy for chemical absorption and ΔHH/(kJ/mol) is the reaction enthalpy for physical absorption.
(12) C
DOI: 10.1021/acs.jced.6b00101 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
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The parameters for physical absorption (H, ΔHH/[kJ/mol]) were determined by fitting the CO2 solubility data in pure water20 H = 5.29 MPa kg mol−1
(16)
ΔHH = 10.68 kJ/mol
(17)
where n is the number of data, αexp is the experimental data from references, and αcalc is calculated data.
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RESULTS Table 2 shows the modeling parameters and the solid lines in Figure 1 show MDEA correlation results for mA = 2 mol/kg (a) and 8 mol/kg (b). These correlation results have good agreement with data in the wide ranges of temperature, pressure, and also amine concentration. The solid lines in Figures 2 and 3 represent the correlation results for cyclic amines and diamines, respectively. The developed model has good correlation for the solutions of both amine types. Table 3 shows the accuracy of measurement and the absolute average deviation (AAD [%]) of correlation results. From these results, the model can be applied for CO2 solubility in tertiary amine solution in the applicable range of 2−8 mol/kg, 313−413 K and 0−7 MPa. This model may not be applied at high pressure range where Henry’s low does not work or high amine concentration region where low water concentration virtually affects the reaction equilibrium. Tomizaki et al.6 reported the CO2 dissolution form in MDEA solution with 13C NMR at pressures ranging from 0.5 to 4 MPa and the amounts of CO2 physically absorbed into the solvents increased with increasing CO2 pressure. Figure 4 shows the comparison of the mole base fraction of physically absorbed CO2 in total CO2 absorption between 13C NMR results and calculation results of our model. Our model can predict the fraction of physically absorbed CO2.
Optimized parameters (K, ΔHK) were obtained to minimize the following objective function (OF) OF = 1/n ∑ |αexp − αcalc|
(18)
Table 3. Accuracy of Measurements, AAD of Correlation Results, and AADa of Calculation with Generalized Parameters
MDEA cyclic amine diamine a
accuracy of measurements
AAD of correlation
AAD of calculation with generalized parameter
0.7% 1% 2%
2.9% 20.0% 8.0%
11.6% 47.0% 17.2%
AAD [%] = (1/n)Σ |α
exp
− αcalc| αexp
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GENERALIZED PARAMETERS A previous study reported good correlation of pKa with chemical equilibrium constant and enthalpy.9 The current work used pKa to estimate the chemical equilibrium constant and the absorption enthalpy of tertiary amine solutions. Figure 5a shows the relationship between pKa and the logarithm of the chemical equilibrium constant, log (K), whereas Figure 5b shows the relationship between pKa and − ΔHK. The linear relationships were observed for both. The following functions were considered in order to predict the solubility of CO2 in tertiary amine solutions Figure 4. Comparison of physical absorption fraction between NMR results and model results (mole base).
log(K ) = 0.7862 × pK a − 4.862
(19)
−ΔHK = 9.193 × pK a − 25.49
(20)
Figure 5. Relationship between (a) pKa and log (K) and (b) pKa and −ΔHK. D
DOI: 10.1021/acs.jced.6b00101 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
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(4) Kuranov, G.; Rumpf, B.; Smirnova, N. A.; Maurer, G. Solubility of single gases carbon dioxide and hydrogen sulfide in aqueous solutions of N-methyldiethanolamine in the temperature range 313−413 K at pressures up to 5 MPa. Ind. Eng. Chem. Res. 1996, 35, 1959−1966. (5) Speyer, D.; Ermatchkov, V.; Maurer, G. Solubility of Carbon Dioxide in Aqueous Solutions of N-Methyldiethanolamine and Piperazine in the Low Gas Loading Region. J. Chem. Eng. Data 2010, 55, 283−290. (6) Tomizaki, K.; Kanakubo, M.; Nanjo, H.; Shimizu, S.; Onoda, M.; Fujioka, Y. (13)C NMR Studies on the Dissolution Mechanisms of Carbon Dioxide in Amine-Containing Aqueous Solvents at High Pressures toward an Integrated Coal Gasification Combined CycleCarbon Capture and Storage Process. Ind. Eng. Chem. Res. 2010, 49, 1222−1228. (7) Tomizaki, K.; Shimizu, S.; Onoda, M.; Fujioka, Y. An acid dissociation constant (pK(a))-based screening of chemical absorbents that preferably capture and release pressurized carbon dioxide for greenhouse gas control. Chem. Lett. 2008, 37, 516−517. (8) Tomizaki, K.; Shimizu, S.; Onoda, M.; Fujioka, Y. Heats of Reaction and Vapor-Liquid Equilibria of Novel Chemical Absorbents for Absorption/Recovery of Pressurized Carbon Dioxide in Integrated Coal Gasification Combined Cycle-Carbon Capture and Storage Process. Ind. Eng. Chem. Res. 2010, 49, 1214−1221. (9) Machida, H.; Yamada, H.; Fujioka, Y.; Yamamoto, S. CO2 Solubility Measurements and Modeling for Tertiary Diamines. J. Chem. Eng. Data 2015, 60, 814−820. (10) Suleman, H.; Maulud, A. S.; Man, Z. Review and selection criteria of classical thermodynamic models for acid gas absorption in aqueous alkanolamines. Rev. Chem. Eng. 2015, 31, 599−639. (11) Posey, M. L.; Tapperson, K. G.; Rochelle, G. T. A simple model for prediction of acid gas solubilities in alkanolamines. Gas Sep. Purif. 1996, 10, 181−186. (12) Gabrielsen, J.; Michelsen, M. L.; Stenby, E. H.; Kontogeorgis, G. M. A model for estimating CO2 solubility in aqueous alkanolamines. Ind. Eng. Chem. Res. 2005, 44, 3348−3354. (13) Al-Rashed, O. A.; Ali, S. H. Modeling the solubility of CO2 and H2S in DEA-MDEA alkanolamine solutions using the electrolyteUNIQUAC model. Sep. Purif. Technol. 2012, 94, 71−83. (14) Austgen, D. M.; Rochelle, G. T.; Peng, X.; Chen, C. C. Model of vapor liquid equilibria for aqueous acid gas alkanolamine systems using the electrolyte NRTL equation. Ind. Eng. Chem. Res. 1989, 28, 1060− 1073. (15) Chen, C. C.; Britt, H. I.; Boston, J. F.; Evans, L. B. Local composition model for excess Gibbs energy of electrolyte systems 0.1. single solvent, single completely dissociated electrolyte systems. AIChE J. 1982, 28, 588−596. (16) Chen, C. C.; Evans, L. B. A local composition model for the excess Gibbs energy of aqueous-electrolyte systems. AIChE J. 1986, 32, 444−454. (17) Sander, B.; Fredenslund, A.; Rasmussen, P. Calculation of vaporliquid-equilibria in mixed-solvent Salt systems using an extended UNIQUAC equation. Chem. Eng. Sci. 1986, 41, 1171−1183. (18) Tellez-Arredondo, P.; Medeiros, M. Modeling CO2 and H2S solubilities in aqueous alkanolamine solutions via an extension of the Cubic-Two-State equation of state. Fluid Phase Equilib. 2013, 344, 45− 58. (19) Fouad, W. A.; Berrouk, A. S. Prediction of H2S and CO2 Solubilities in Aqueous Triethanolamine Solutions Using a Simple Model of Kent-Eisenberg Type. Ind. Eng. Chem. Res. 2012, 51, 6591− 6597. (20) Zawisza, A.; Malesinska, B. Solubility of carbon-dioxide in liquid water and of water in gaseous carbon-dioxide in the range 0.2−5 MPa and at temperatures up to 473 K. J. Chem. Eng. Data 1981, 26, 388− 391. (21) Yamada, H.; Shimizu, S.; Okabe, H.; Matsuzaki, Y.; Chowdhury, F. A.; Fujioka, Y. Prediction of the Basicity of Aqueous Amine Solutions and the Species Distribution in the Amine-H2O-CO2 System Using the COSMO-RS Method. Ind. Eng. Chem. Res. 2010, 49, 2449−2455.
Table 3 shows the accuracy of measurement and the absolute average deviation (AAD [%]) of calculation results using generalized parameters and prediction results with the generalized parameters, shown in Figures 1−3 as dashed lines, indicate a larger deviation from the correlated data. However, the trends of CO2 solubilities are satisfactorily represented. This indicates that the solubility of CO2 in tertiary amines can be predicted using pKa. It should be noted that this model may not be applied at high pressure range or high amine concentration region due to the same reasons as mentioned above.
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CONCLUSIONS CO2 solubilities for tertiary amine solutions were used to determine chemical equilibrium constants. A simple model based on the chemical equilibrium and physical absorption constant shows good agreement with the experimental data of alkanol amines, cyclic amines, and diamines. The chemical equilibrium constants are correlated with linear function in terms of pKa of the amines. The generalized parameters provide a method to predict the solubility of CO2 in tertiary amine solution from pKa. pKa of amines can be predicted with quantum chemical calculations.9,21 Therefore, CO2 solubility could be predicted only from the molecular structure of amine in the future.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Tel.: +81-(0)52-789-3622. Fax: +81-(0)52-789-3272. Notes
The authors declare no competing financial interest.
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NOMENCLATURES P: partial pressure of CO2 (MPa) H: Henry constant (MPa kg mol−1) m: molality (mol kg−1) K: equilibrium constant (−) ΔHK: reaction enthalpy for chemical absorption (kJ mol−1) ΔHH: reaction enthalpy for physical absorption (kJ mol−1) T: temperature (K)
Subscript
A: amine chem: chemical absorption phys: physical absorption Superscript
exp: experimental calc: calculation Greek
α: CO2 solubility (molCO2/molamine)
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REFERENCES
(1) Kanniche, M.; Bouallou, C. CO2 capture study in advanced integrated gasification combined cycle. Appl. Therm. Eng. 2007, 27, 2693−2702. (2) Ermatchkov, V.; Kamps, A. P. S.; Maurer, G. Solubility of carbon dioxide in aqueous solutions of N-methyldiethanolamine in the low gas loading region. Ind. Eng. Chem. Res. 2006, 45, 6081−6091. (3) Kamps, A. P. S.; Balaban, A.; Jodecke, M.; Kuranov, G.; Smirnova, N. A.; Maurer, G. 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. Ind. Eng. Chem. Res. 2001, 40, 696−706. E
DOI: 10.1021/acs.jced.6b00101 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
