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Modeling and experiments of equilibrium solubility of carbon dioxide in aqueous N-(2-hydroxyethyl) pyrrolidine solution
Journal of the Taiwan Institute of Chemical Engineers 85 (2018) 132–140
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Modeling and experiments of equilibrium solubility of carbon dioxide in aqueous N-(2-hydroxyethyl) pyrrolidine solution Wenchao Zheng a,†, Min Xiao a,†, Helei Liu b,∗, Hongxia Gao a, Zhiwu Liang a,b,∗∗ a
Joint International Center for CO2 Capture and Storage (iCCS), Provincial Hunan Key Laboratory for Cost-effective Utilization of Fossil Fuel Aimed at Reducing CO2 Emissions, College of Chemistry and Chemical Engineering, Hunan University, Changsha 410082, PR China Clean Energy Technologies Research Institute (CETRI), Faculty of Engineering and Applied Science, University of Regina, Regina, Saskatchewan S4S 0A2, Canada
b
a r t i c l e
i n f o
Article history: Received 22 September 2017 Revised 22 December 2017 Accepted 17 January 2018 Available online 21 February 2018 Keywords: Carbon dioxide N-(2-HE) PRLD VLE equilibrium Semi-empirical thermodynamic models
a b s t r a c t In this work, the equilibrium CO2 solubilities of the aqueous N-(2-hydroxyethyl) pyrrolidine (N-(2-HE) PRLD) at different concentrations (1.0 mol/L–5.0 mol/L) were measured at different temperatures (298 K– 333 K) and pressures (8 kPa–101 kPa), using a vapor–liquid equilibrium apparatus. Four semi-empirical thermodynamic models (Cf model, Kent–Eisenberg model, Hu–Chakma model and Li–Shen model) were used to correlate and predict the CO2 solubility data of the N-(2-HE) PRLD-CO2 –H2 O system. The results showed that the Hu–Chakma model, which is one of the models that incorporates the effect of amine concentration and CO2 loading, and accounted for nonideality caused by higher temperature, species concentrations and CO2 loadings, was best able to predict results that are in agreement with the experimental vapor–liquid equilibrium measurements in this work. © 2018 Taiwan Institute of Chemical Engineers. Published by Elsevier B.V. All rights reserved.
1. Introduction The rapid development of the global economy, massive mining, and utilization of fossil fuel for the production of energy have caused increasing amounts of greenhouse gases (GHGs) to be released into the atmosphere. CO2 is the most abundant GHG (accounting for 60% of the greenhouse gases [1]) and is considered to be one of the most significant contributors to global warming. Global warming is giving rise to a series of increasingly severe problems like melting of ice caps, rising sea level, drought, and intense storms. For the sake of sustainable development of the global economy and the protection of the environment, the capture of GHGs like carbon dioxide from flue gases is a key technology that needs to be developed and implemented. In China, energy supply is still predominantly based on fossil fuels such as coal. Over 10 billion tons of CO2 are discharged into the atmosphere each year, making China the largest CO2 emitting ∗ Corresponding author at: Clean Energy Technologies Research Institute (CETRI), Faculty of Engineering and Applied Science, University of Regina, Regina, Saskatchewan S4S 0A2, Canada. ∗∗ Corresponding author at: Joint International Center for CO2 Capture and Storage (iCCS), Provincial Hunan Key Laboratory for Cost-effective Utilization of Fossil Fuel Aimed at Reducing CO2 Emissions, College of Chemistry and Chemical Engineering, Hunan University, Changsha 410082, PR China. E-mail addresses: [email protected] (H. Liu), [email protected] (Z. Liang). † Author contributions: Wenchao Zheng and Min Xiao contributed equally to this work.
country in the world. China’s rapidly advancing economy is also resulting in the country having the most rapid increase in per capita emissions [2]. The capture of CO2 from point sources such as thermal power plants which contribute 63% of China’s electrical energy [3], is the most feasible plan for reducing or stabilizing CO2 concentration in the atmosphere. Among all the methods to capture CO2 (such as pre-combustion, post-combustion, and oxy-fuel combustion [4–6]), post-combustion CO2 capture is the most effective method of reducing CO2 emissions, especially from thermal power plants, using chemical reagents such as aqueous alkanolamine solutions. It is a mature technology that has already been applied in industry [7]. In order to obtain the ideal alkanolamine for CO2 capture, the reaction rate, absorption capacity, energy of CO2 desorption, renewability and industrial maturity must be considered. Many primary, secondary, and tertiary alkanolamines have already been tested in the last few years. N-(2-Hydroxyethyl) pyrrolidine (N-(2HE) PRLD) is a new cyclic tertiary amine with considerable potential because of its noticeable behavior in CO2 capture. Studies have shown that N-(2-HE) PRLD exhibits a higher CO2 cyclic capacity than MDEA (the most used commercial tertiary amine currently) and relatively higher absorption rate in comparison with any other tertiary amine (i.e. dimethylmono-ethanolamine) [8]. Moreover, the protonation constant and kinetics of N-(2-HE) PRLD have already been tested. Liu et al. deduced a formula for the protonation constant and confirmed that the reaction
https://doi.org/10.1016/j.jtice.2018.01.021 1876-1070/© 2018 Taiwan Institute of Chemical Engineers. Published by Elsevier B.V. All rights reserved.
W. Zheng et al. / Journal of the Taiwan Institute of Chemical Engineers 85 (2018) 132–140
between CO2 and N-(2-HE) PRLD is a pseudo-first-order reaction [9]. Other work on N-(2-HE) PRLD has also been done, however, the vapor–liquid equilibrium (VLE) has not yet been studied. To develop an efficient amine scrubbing process using the N-(2-HE) PRLD-H2 O–CO2 system, a thermodynamic model is indispensable to predict and describe its VLE as a function of temperature and the partial pressure of CO2 over an aqueous solution of the alkanolamine. Various models for the correlation and the prediction of the phase equilibria have already been proposed using the equilibrium solubility data of CO2 . Moreover, many sophisticated models that take the non-ideality into account have been developed. For the sake of appropriate model selection for the VLE prediction, Maulud et al. [10] presented a concise classification and review of classical thermodynamic models for acid gas absorption classified these models into three classes (semi-empirical models, activity coefficient models and EoS/GE models), as for example, the Deshmukh–Mather model [11], the electrolyte-NRTL model [12,13], Chen–Evans model [14], and UNIQUAC model [7,15]. Also, based on a previous study by Xiao et al. [16], N-(2-HE) PRLD showed an extremely high CO2 absorption capacity with a theoretical boundary of 1 mol CO2 /mol amine compared with conventional amines such as MEA (0.5 mol CO2 /mol·amine). In this work, theoretical and experimental investigations of CO2 solubility in N-(2-HE) PRLD were completed. Equilibrium solubility of CO2 in aqueous N-(2-HE) PRLD solution was measured under different temperatures (298 K–333 K), CO2 partial pressures (8 kPa–101 kPa) and amine concentrations (1 mol/L–5 mol/L). In order to explore the correlation between the VLE equilibrium of 1-(2-HE) PRLD-H2 O–CO2 system and the three factors (temperature, amine concentration and loading of CO2 ), four semi-empirical thermodynamic models (Kent–Eisenberg, Li–Shen, Hu–Chakma and Cf models) were used to correlate the resulting data for equilibrium solubility of CO2 in aqueous N-(2-HE) PRLD solution.
N-(2-Hydroxyethyl) pyrrolidine (N-(2-HE) PRLD) Fig. 1. The structure of solvent used in this work. Table 1 The values of K3 , K4 , K5 and HeCO2 for N-(2-HE) PRLD-H2 O–CO2 system [22]. 298 K Expressions
Ki /H0CO2 = exp A +
HCO2 K3 K4 K5
3035.9623 4.599E−07 4.621E−11 1.06E−14
(1)
The hydrolysis of carbon dioxide: K2
H2 O + RR R N + CO2 RR R NH+ + HCO3 −
(2)
Formation of bicarbonate ion: K3
H2 O + CO2 H+ + HCO3 −
(3)
Dissociation of bicarbonate ion: K4
HCO3 − H+ + CO3 2−
(4)
K5
HCO2 =
4083.9944 5.448E−07 6.163E−11 2.84E−14
H0CO2 7.50061
5558.9249 5.575E-07 7.28E−11 9.113E−14
(6)
RR R N H
K2 =
+ RR R N H HCO− 3 = K3 /K1
K3 =
(7)
RR R N C O2(aq )
[H + ] HCO− 3
C O2(aq )
HCO− 3
[H + ] CO23−
K5 = H +
(8)
OH −
(9)
(10)
where Ki represents the chemical equilibrium constants of reaction i. It is not difficult to find that there are only four independent equilibrium constants (K1 , K3 , K4 , and K5 ) in Eqs. (6)–(10). In addition, the physical solubility of CO2 in N-(2-HE) PRLD solution can be expressed by using Henry’s law [18] as follows:
PCO 2 = H eCO 2 C O2(aq )
(11)
where PCO2 is the partial pressure of CO2 in the gas phase, and HeCO2 represents the Henry’s law constant of CO2 in water. The Henry’s law constant applied to the absorption of CO2 into the liquid phase was obtained from literature [19]. The values of chemical equilibrium constants K3 , K4 , K5 and HeCO2 for N-(2-HE) PRLD-H2 O–CO2 system are obtained from the literature as listed in Table 1. In order to determine the value of K1 as well as the concentrations of all species, the following balances are introduced: Total amine balance:
Ionization of water:
H2 O H+ + OH−
C D B + + + ; T T T T
+ R R R N [H ] K1 = +
K4 =
K1
333 K
E
For every chemical reaction, there is a corresponding equilibrium constant, which can be presented as follows:
RR R NH+ RR R N+H+
313 K
2. Method In 1980, a widely accepted base-catalyzed hydration mechanism [17] was proposed to explain the reaction between carbon dioxide and tertiary amines. In this mechanism, tertiary amine was regarded as an alkali catalyst that catalyzes the reaction between water and carbon dioxide. The phase and chemical equilibrium reactions for N-(2-HE) PRLD-H2 O–CO2 system can be represented as follows: Protonation of N-(2-HE)-PRLD:
133
RR R N
0
= RR R N H + + RR R N
(12)
Total carbon balance:
(5)
where RR’R”N represents N-(2-HE) PRLD. It is a five membered nitrogen containing heterocyclic compound with a hydroxyethyl group attached in N atom. Fig. 1 shows the structure of N-(2-HE) PRLD.
α × RR R N 0 = C O2(aq) + HCO−3 + CO23−
The charge balance:
2− RR R N H + + H + = HCO− + OH − 3 + 2 CO3
(13)
(14)
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W. Zheng et al. / Journal of the Taiwan Institute of Chemical Engineers 85 (2018) 132–140
Fig. 2. Schematic diagram of the experimental setup for CO2 loading measurement.
3. Materials and experiment 3.1. Materials CO2 and N2 each with purity of 99% were bought from Changsha RiZhen Gas Co., Ltd. 1-(2-hydroxyethyl) pyrrolidine (N-(2-HE) PRLD with purity of 97%) was purchased in Accela ChemBio Co., Ltd. Deionized water was used to prepare aqueous solutions of different 1-(2-HE) PRLD concentrations. In addition, deionized water was prepared in the iCCS laboratory using a water treater obtained from Taoshi water equipment engineering Co., Ltd. Flow meters (D08-2F) were obtained from Beijing Sevenstar Electronics Co., Ltd. (Beijing). The thermostatic water bath (DC-5010) was obtained from Fandilang Info Technology Co., Ltd. (Nanjing). 3.2. Experiment Fig. 2 [20] shows the schematic diagram of the experimental set up for a typical carbon dioxide equilibrium loading system. The equipment was used to measure the VLE of CO2 in 1-(2-hydroxyethyl)-pyrrolidine solution of different concentrations at different CO2 partial pressures and temperatures (298 K, 313 K, 333 K). The water-dampening device and reactor were set in a thermostatic water bath at the desired temperature with an uncertainty of ±0.1 K. A glass-scrubbing bottle (reactor) was filled with approximately 20 mL of absorbent with mole concentrations of 1.0 mol/L, 2.0 mol/L and 5.0 mol/L. For the purpose of acquisition of a steady absorption process, the inlet gas with different ratios of N2 and CO2 was introduced into the glass scrubbing bottle through a gas dispersion tube attached at the bottom of the liquid phase at a total flow rate of 250 mL/min. During the experiment, a shell and coil condenser was used to reduce amine loss caused by volatilization from the reactor. A liquid sample was tested every 1-h time interval to confirm if VLE was reached. The acid–base titration method [16] was employed in this experiment to measure the equilibrium CO2 solubility of the solution. The burette was filled with 1.0 mol/L hydrochloric acid. Then, 1 mL liquid sample and 2–3 drops of methyl orange indicator were placed into a conical flask by a pipette and the system was kept airtight with a water seal. After that, hydrochloric acid was added dropwise to the sample while recording the volume consumed. Af-
ter the color of the methyl orange indicator changed, hydrochloric acid was continued to be added to strip out all CO2 that was dissolved in the aqueous N-(2-HE) PRLD solutions. Equilibrium CO2 loading (defined as mol CO2 ·mol amine−1 ) was calculated using the following equation.
α=
V − VHC l2 273.15 × 22.4 × ca min eVHC l1 273.15 + T
(15)
where α represents CO2 loading, V is the volume of CO2 released from the liquid sample, VHCl1 is the volume of HCl consumed when the color of methyl orange indicator changed, VHCl2 is the total volume of HCl consumed during titration, T denotes the room temperature, and camine denotes the amine concentration of the liquid sample. Uncertainties are u(V )= 0.05 cm3 ; u(VHCl )= 0.01 mL; u(T) = 0.01 °C (level of confidence = 0.95). When the difference of CO2 loading of two successive samples is smaller than 0.01, we deem that VLE has been reached. The equilibrium loading of CO2 was measured at the temperatures of 298 K, 313 K and 333 K, CO2 partial pressures of 8 kPa, 15 kPa, 30 kPa, 60 kPa and 101 kPa and amine concentration of 1.0 mol/L, 2.0 mol/L and 5.0 mol/L. 4. Results and discussion 4.1. Equilibrium solubility of CO2 Equilibrium solubility of CO2 is of crucial importance in the testing and development of theoretical models and correlations, and is of great interest to process design software developers and researchers who are working on solvent screening studies. The overall cost of CO2 capture is partially determined by the thermophysical properties of the solvent. Moreover, incorrect estimates of the absorber size can lead to overly large columns, and failure to meet product specifications are quite often the result of inaccurate VLE data [21]. The experimental determinations of the equilibrium solubility of CO2 in aqueous N-(2-HE) PRLD solutions were done under various temperatures, CO2 partial pressures and amine concentrations. The experimental results are shown in Tables 2–4 and Figs. 3–8. It is obvious that the equilibrium loading of CO2 in N-(2-HE) PRLD is very high. Moreover, as observed from Figs. 3–5, with the increases
W. Zheng et al. / Journal of the Taiwan Institute of Chemical Engineers 85 (2018) 132–140
135
Table 2 Equilibrium loading of CO2 in 1.0 mol/L aqueous N-(2-HE) PRLD solutions. 298 K
313 K
333 K
CO2 partial pressure
CO2 equilibrium loading
CO2 partial pressure
CO2 equilibrium loading
CO2 partial pressure
CO2 equilibrium loading
8.00 15.00 30.00 60.00 101.00
0.855 0.898 0.925 0.959 0.973
8.00 15.00 30.00 60.00 101.00
0.806 0.823 0.862 0.890 0.911
8.00 15.00 30.00 60.00 101.00
0.619 0.680 0.779 0.851 0.872
Table 3 Equilibrium loading of CO2 in 2.0 mol/L aqueous N-(2-HE) PRLD solutions. 298 K
313 K
333 K
CO2 partial pressure
CO2 equilibrium loading
CO2 partial pressure
CO2 equilibrium loading
CO2 partial pressure
CO2 equilibrium loading
8.00 15.00 30.00 60.00 101.00
0.804 0.854 0.910 0.939 0.970
8.00 15.00 30.00 60.00 101.00
0.691 0.783 0.845 0.888 0.907
8.00 15.00 30.00 60.00 101.00
0.471 0.619 0.731 0.775 0.838
298 K
1.0
CO2 loading/(mol CO2/mol amine)
Table 4 Equilibrium loading of CO2 in 5.0 mol/L aqueous N-(2-HE) PRLD solutions.
0.9
CO2 partial pressure
CO2 equilibrium loading
8.00 15.00 30.00 60.00 101.00
0.503 0.560 0.753 0.820 0.859
0.8
0.7 0.6
CO2 loading/(mol CO2/mol amine)
1.0
298K 313K 333K
0.5
0.9
0.4
0
20
40
60
80
100
CO2 partial pressure(kPa) 0.8 Fig. 4. Equilibrium loading of CO2 in 2.0 mol/L aqueous N-(2-HE) PRLD solutions.
0.7
298K 313K 333K
0.6 0
20
40
60
80
100
CO2 partial pressure(kPa) Fig. 3. Equilibrium loading of CO2 in 1.0 mol/L aqueous N-(2-HE) PRLD solutions.
of temperature, the equilibrium solubility of CO2 decreased, and with the increase of CO2 partial pressure the equilibrium solubility of CO2 increased. Figs. 6–8 show the comparisons of experimental results for equilibrium solubility of CO2 in aqueous N-(2HE) PRLD solutions at temperatures of 298 K, 313 K and 333 K, respectively. It can be seen from the figures that with the increase in concentration of N-(2-HE) PRLD, equilibrium solubility of CO2 in aqueous N-(2-HE) PRLD solutions decreased. For example, Fig. 6 shows that the equilibrium solubility of CO2 of 5.0 mol/L aqueous N-(2-HE) PRLD solutions at 298 K is much lower (0.503 mol CO2 •mol amine−1 ) than the equilibrium solubility of CO2 in 1.0 mol/L N-(2-HE) PRLD at the same temperature, 298 K. These phenomena can be explained as follows. According to Le Chatelier’s
principle, when the concentration of amine is high, the reaction equilibrium (Eq. 2) will shift toward the right side. However, the ratio of reacted amine will decrease, which leads to the decrease of equilibrium CO2 solubility. In addition, the equilibrium loading of CO2 was observed to decrease with increasing temperature. This is because physical solubility of carbon dioxide is reduced with the increase of temperature and the CO2 absorption in amine solution is an exothermic process. In contrast, the loading of amine increased with CO2 partial pressure. This is mainly due to higher CO2 physical solubility in the solution which drives the reaction equilibrium of chemical Eqs. (2) and (3) toward the right side. Therefore, CO2 absorption with the amine solution is promoted. 4.2. Calculation of equilibrium CO2 loading In order to predict the equilibrium CO2 loading, a correlation for K1 is required. It is easy to find that there are 9 equations (Eqs. 6–14, 8 independent equations) and 8 unknown parameters. By simultaneously solving the equation set, the eight unknowns, namely, K1 , K2 , [RR R N], [H+ ], [RR R NH + ], [HCO3 − ], [CO3 2− ] [OH− ], [CO2(aq) ], can be calculated. Then, the obtained K1 can be fitted with several models (Kent–Eisenberg model, Hu– Chakma model, Li–Shen model and Cf models). The parameters of the models were obtained by using a nonlinear regression (NLREG)
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W. Zheng et al. / Journal of the Taiwan Institute of Chemical Engineers 85 (2018) 132–140
CO2 loading(mol CO2/mol amine)
CO2 loading/(mol CO2/mol amine)
0.9
0.8
0.7
0.6
1.125 1mol/L
0.675 0.45
0.225 0. 8
0.5
15 30 60 CO2 partial pressure(kPa)
298K 0
20
40
60
80
2mol/L
0.9
101
Fig. 8. Equilibrium loading of CO2 in 1.0, 2.0 mol/L aqueous N-(2-HE) PRLD solutions at 333 K.
100
Fig. 5. Equilibrium loading of CO2 in 5.0 mol/L aqueous N-(2-HE) PRLD solutions.
CO2 loading(mol CO2/mol amine)
1.
1mol/L
2mol/L
5mol/L
0.75
0.5
0.25
0.
8
15
30 60 CO2 paral pressure(kPa)
CO2 loading(mol CO2/mol amine)
1mol/L
2mol/L
0.25
0. 30
60
101
CO2 paral pressure(kPa) Fig. 7. Equilibrium loading of CO2 in 1.0, 2.0 mol/L aqueous N-(2-HE) PRLD solutions at 313 K.
program in MATLAB. The prediction of the equilibrium CO2 solubility is the reverse process of correlation. α solu was obtained by solving the above equations with a known value of K1 . In Fig. 9, the dots represent the calculated values while the curves represent the experimental values. It can be concluded that this model agrees with the experimental values well. The accuracy of the model is shown in terms of the average absolute deviation (AAD). AAD is defined as follows:
AAD =
1 αexp − αcal αexp × 100% N
0.8
0.6
0.4
0.6
0.8
1.0
Experimental equilibrium CO2 loading Fig. 9. Comparison of experimental equilibrium CO2 loading and calculated equilibrium CO2 loading of Kent–Eisenberg model.
4.2.1. Kent–Eisenberg Model The Kent–Eisenberg (KE) model [19] which was proposed in 1976 is considered to be a simple model because it is only related to temperature. Equilibrium CO2 partial pressure (PCO2 ) is related to the physically dissolved CO2 concentration in the liquid phase by the Henry law expression. In the original work, the model was used to calculate the equilibrium solubility of H2 S and CO2 in aqueous solutions of MEA and DEA by fitting the experimental solubility results. The model regressed some of the equilibrium constants as a function of temperature involving the main amine reactions. The model is expressed as shown in the following equation:
0.5
15
Kent- Eisenberg
0.4
0.75
8
1.0
101
Fig. 6. Equilibrium loading of CO2 in 1.0, 2.0, 5.0 mol/L aqueous N-(2-HE) PRLD solutions at 298 K.
1.
Calculated equilibrium CO2 loading
CO2 partial pressure(kPa)
(16)
Ki = exp A +
B C D E + 2 + 3 + 4 T T T T
(17)
In the present work, the KE model is applied to the 1-(2-HE) PRLD-CO2 –H2 O system. The values of the parameters (A, B, C, D, and E) are obtained by correlating K1 with temperature. The parameters are given in Table 5. The result in Fig. 9 shows that the equilibrium CO2 solubility can be predicted with AAD of 13.5% by the Kent–Eisenberg model, which is not good enough. As shown in this Fig. 9, it can be seen that the most calculated results are lower than the experimental results. It is because KE model only included one parameter (Temperature). In order to better preform the solubility of CO2 in N-(2-HE) PRLD system, other parameters should be added in the correlation.
W. Zheng et al. / Journal of the Taiwan Institute of Chemical Engineers 85 (2018) 132–140 Table 7 Parameters for the Hu–Chakma model for K1 in Eq. (19).
Table 5 Parameters for the Kent–Eisenberg model for K1 in Eq. (17). Parameters for K1
Value
Parameters for K1
Value
A B C D E
6.604 −6484 545.3 −18.03 −755
D1 D2 D3 D4
−34.78806224 0.041516362 50.51249543 −0.335956118
1.0
Parameters for K1
Value
A1 A2 A3 B1 B2 B3 B4
−8.44906 0.960128 0.999842 −7.27896 −7.05603 1.401108 −0.57362
Calculated equilibrium CO2 loading
Table 6 The parameters (A1 , A2 , A3 , B1 , B2 , B3 , and B4 ) for K1 in Eq. (18).
1.0
Calculated equilibrium CO2 loading
137
Li- Shen
Hu-Chakma 0.9
0.8
0.7
0.6
0.5
0.9 0.5
0.8
0.6
0.7
0.8
0.9
1.0
Experimental equilibrium CO2 loading Fig. 11. Comparison of experimental equilibrium CO2 loading and calculated equilibrium CO2 loading of Hu–Chakma model.
0.7
0.6
using the Li–sheng gives a better predicted results than KE model with an AAD of 6.6%.
0.5 0.5
0.6
0.7
0.8
0.9
1.0
Experimental equilibrium CO2 loading Fig. 10. Comparison of experimental equilibrium CO2 loading and calculated equilibrium CO2 loading of Li–Shen model.
4.2.2. Li–Shen model The Li–Shen model [22] is also an upgraded version of the Kent–Eisenberg model. The chemical equilibrium constants involving the amines are expressed as functions of not only temperature, but also of the total amine concentration and CO2 loading. In Li–Shen’s work, the equilibrium solubility of CO2 in aqueous mixtures of monoethanolamine (MEA) with methyldiethanolamine (MDEA) was correlated. The constants in the model were determined by fitting to the solubility data of carbon dioxide in aqueous MEA/MDEA solutions for temperatures ranging from 40 °C to 100 °C and for partial pressures of carbon dioxide up to 20 0 0 kPa. Satisfactory results were obtained for calculations of the solubility of carbon dioxide in aqueous MEA/MDEA solutions for the systems tested. The model can be expressed by the following equation:
A2 A3 B1 B2 Ki = exp A1 + + 2 + B3 α + + + B4 ln RR R N 0 T α α2 T
(18)
The values of the parameters (A1 , A2 , A3 , B1 , B2 and B3 ) calculated from K1 are presented in Table 6. As mention in the previous discussion, other parameters should be added in the correlation. In the correlation of Li–sheng Model, CO2 loading and the free amine are added in. As shown in Fig. 10, it happens that the correlation
4.2.3. Hu–Chakma model A modified mathematical model [23] named Hu–Chakma model was proposed for the prediction of equilibrium solubility of CO2 –H2 S–H2 O-2-amino-2-methyl-1-propanol (AMP) and CO2 –H2 SH2 O-Diglycolamine (DGA). The model showed that the equilibrium constant, K1 , governing the main amine reaction is expressed as a function of not only temperature but also the acid gas partial pressure and the total amine concentration. Model predictions agree favorably with experimental data. For the present study, the physically dissolved CO2 concentration in aqueous 1-(2-HE)-PRLD solutions was calculated using Eq. (18). The model can be expressed as the following equation:
Ki = exp D1 + D2 T + D3
PCO 2 + D4 ln RR R N 0 H eCO 2
(19)
PCO2 /HeCO2 is equal to [CO2 (aq) ] which is the physical solubility of CO2 in N-(2-HE) PRLD aqueous solutions. HeCO2 can be calculated from the work of Kent–Eisenberg. The values of parameters (D1 , D2 , D3 and D4 ) were calculated from K1 using the Hu–Chakma model and presented in Table 7. By applying the Hu– Chakma model, the results of the predicted equilibrium solubility of CO2 were found to agree with the experimental results very well with an AAD (plotted in Fig. 11) of 4.3%. This fact implies that another important parameter, the CO2 physical solubility ([CO2 (aq) ]) should be added into the correlation. As shown in Fig. 11, the deviation is very high around the CO2 solubility of 0.4–0.6. This is because the prediction of CO2 solubility is based on correlation equation. Therefore, the reason might be the mathematical equation of the correlation cannot describe the equilibrium constant well at the stated condition.
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1.0
Parameters for the Cf
Value
a b c
0.001549 0.00253 1.003103
4.2.4. Cf model In 2016, Xiao et al. proposed a new thermodynamic model named the Cf model [24]. In that work, to correct the non-ideality of aqueous amine solution, a correction factor (Cf ) was developed for predicting the equilibrium CO2 solubility for N-(2-HE) PRLDH2 O–CO2 system. This correction factor was developed as in the following equation:
H+ = C f H+
where
∗
(20)
(21)
− The concentrations of[RR R N], [CO23− ], [HCO− 3 ], [OH ] can be expressed as functions of [H+ ], Ki and [CO2 (aq) ].
RR R N =
[H + ]
OH − =
0
(22)
K3 K4
K3 C O2(aq )
HCO− 3 =
K1 + [H + ]
K1 × RR R N
CO23− = C O2(aq )
(23)
2
(24)
[H + ]
K5 [H + ]
(25)
The pKa value can be obtained as in Liu’s work by the following equation [9]:
pKa =
1668 + 4.54(R2 = 0.999 ) T
(26)
We can then calculate K1 by lgK1 = −pKa. Then, by substituting Eqs. (22)–(25), Eq. (12) can be transformed as follows:
α × RR R N 0 K K K = 3+ + 1 + 3 42 [H ]
C O2(aq )
(27)
[H + ]
The [H+ ] value is obtained by solving Eq. (27). Moreover, the equation of charge balance can be expressed using a polynomial equation in terms of [H+ ] as follows:
A H+
4
+ B H+
3
where A = 1
Cf 0.9
0.8
0.7
0.6
0.5 0.5
0.6
0.7
0.8
0.9
1.0
Expermental equilibrium CO2 loading
C f = exp a · ln [C O2 ] + b · ln RR R N + c
Calculated equilibrium CO2 loading
Table 8 Parameters for the Cf Model in Eq. (21).
+ C H+
2
+ D H+ + E = 0
(28)
B = K1 + RR R N
0 C = − K3 C O2(aq ) + K5
D = − K1 K3 C O2(aq ) + 2K4 K3 C O2(aq ) + K5 K1 E = −2K4 K3 K1 C O2(aq ) The other value of [H+ ], that is [H+ ]∗ , can be obtained by solving Eq. (28). The calculation of [H + ]∗ is based on the assumption of an ideal solution of infinite dilution. By fitting [H+ ]∗ and [H + ] values at different conditions into Eq. (20), Cf values can be obtained, and then, all parameters, namely, a, b and c in Eq. (20) are obtained using a nonlinear regression program, as summarized in Table 8. The Cf model for the N-(2-HE) PRLD-H2 O–CO2 is thus established. Fig. 12 shows that the equilibrium CO2 solubility can be predicted very well with an AAD of 4.9% by the Cf model. Just like Fig. 11, Fig. 12 also gives the high deviation at the CO2 loading
Fig. 12. Comparison of experimental equilibrium CO2 loading and calculated equilibrium CO2 loading of Cf model.
of 0.4–0.6. This is also because the prediction of CO2 solubility is based on correlation equation. Therefore, the reason might be the mathematical equation of the correlation cannot describe the equilibrium constant well at the stated condition. Fig. 13 shows the comparison of experimental equilibrium CO2 loading and calculated equilibrium CO2 loading of all four models. We can observe that the predicted results decreased with the increase of temperature and amine concentration compared to experimental results. This might be because the effect of non-ideality is more obvious at low loading. The low loading area is commonly corresponding to the high temperature and amine concentration. Some models are unable to describe the non-ideality very well. In this work, four semi-empirical models (the Kent–Eisenberg, Li–Shen, Hu–Chakma and Cf models) were adapted to predict the equilibrium loading of CO2 in aqueous N-(2-HE) PRLD solution, respectively. The Kent–Eisenberg model showed a somewhat poor prediction for CO2 equilibrium loading in aqueous N-(2-HE) PRLD solution with an AAD of 13.5%. This is because the Kent–Eisenberg model only considers the chemical equilibrium constant (Ki ) to be dependent on temperature whereas our experimental results show that the chemical equilibrium constant is strongly related to the chemical reaction and equilibrium concentration of the involved species. For the sake of better prediction, it has been suggested by various researchers [22,25] that the equilibrium constant which governs the reaction between amines and acid gas should not only be dependent on temperature, but also on other parameters such as acid gas loading, the concentration of free amine, and the physical acid gas solubility. Thus, it is suggested that the equilibrium constants derived from the reaction between amine and acid gas should also be considered to be functions of all the above parameters (temperature, acid gas loading, free amine concentration and physical acid gas solubility). The Li–Shen model and the Hu– Chakma model are two representatives. In order to obtain a better prediction of the equilibrium acid gas solubility, Li and Shen modified the model by taking three parameters, temperature, amine concentration and acid gas loading into consideration, as shown in Eq. (19). The result of the Li–Shen model showed a much better performance than the Kent–Eisenberg model in terms of the prediction of equilibrium loading of CO2 with a lower AAD of 6.6%. Hu and Chakma took another non-negligible parameter, physical CO2 solubility, into consideration to improve the Hu–Chakma model, as shown in Eq. (18). For the prediction of CO2 equilibrium loading in aqueous N-(2-HE) PRLD solution, the Hu and Chakma
W. Zheng et al. / Journal of the Taiwan Institute of Chemical Engineers 85 (2018) 132–140
139
Fig. 13. Comparison of experimental equilibrium CO2 loading and calculated equilibrium CO2 loading using four models.
model provided the lowest deviation from experimental results of CO2 equilibrium loading, with an AAD of 4.3%. In the Hu–Chakma Model, the CO2 loading, which represented the capacity of the aqueous amine, was replaced by the parameter of physical CO2 solubility in the aqueous N-(2-HE) PRLD solution. According to the value of AAD, it can be summarized that the physical CO2 solubility (CO2 concentration in the gas–liquid interface) is an important parameter in the prediction of CO2 equilibrium solubility. Moreover, the physical CO2 solubility determines the driving force for CO2 transfer into the liquid phase and affects the mass transfer of CO2 to the bulk aqueous N-(2-HE) PRLD solution, which has a significant effect on CO2 solubility. Thus, the introduction of the parameter, physically dissolved CO2 concentration, results in the lowest deviation (AAD = 4.3%) in the prediction of CO2 equilibrium solubility by the Hu–Chakma model. The Cf model also showed a good performance with an AAD of 4.9%, because the influential factors (i.e., temperature, physical CO2 solubility, and amine concentration) were also taken into consideration in the Cf model as in the Hu–Chakma model. To sum up, of all the models, the Hu–Chakma model proved to give the most accurate predicted results of CO2 equilibrium
loading in comparison with the experimental data. The Cf model took second place ahead of the Li–Shen model. The Kent–Eisenberg model demonstrated the worst performance. Theoretically, these models refer to very dilute solutions where viscosity is not a problem, but for practical situations, higher concentrations are used. Therefore, it is helpful that the additional parameters in the Li– Shen, Hu–Chakma and Cf model account for non-idealities caused by higher concentrations and higher CO2 loadings. The authors prefer Cf model because it shows only a little higher AAD (4.9% versus 4.3%) and need less parameters (a, b, c versus D1 , D2 , D3 , D4 ) compared to Hu–Chakma model. When it comes to the difference of prediction between Cf and Hu–Chakma model, although Hu–Chama and Cf model are similar in correlating expression and use of correction/correlation parameters, there is some difference in modeling. Hu–Chakma model tries to correlate data using equilibrium constant K1 as a function of some experimental factors while Cf model proposes a new correction factor toward concentration of species [H+ ]. Thus the handling of experimental data is quite different as well as different correlation of 0.6%.
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5. Conclusions To develop an efficient amine scrubbing process, a validated thermodynamic model of the vapor–liquid equilibrium (VLE) is of crucial importance. In the present work, the equilibrium CO2 loading of N-(2-hydroxyethyl) pyrrolidine (N-(2-HE) PRLD) was studied at CO2 partial pressure of 8–101 kPa, over the temperature range of 298 K–313 K and molar concentration varying from 1 mol/L to 5.0 mol/L. It was found that aqueous N-(2-HE) PRLD exhibits very good CO2 absorption capacity. However, with an increase in temperature and amine concentration, CO2 equilibrium loading decreased. Higher CO2 partial pressure resulted in a higher equilibrium CO2 loading. The Kent–Eisenberg, Li–Shen, Hu–Chakma and Cf models were used to predict the equilibrium CO2 loading. It was found that Hu–Chakma model performed very well with an AAD of 4.3%, Cf took the second place with an AAD of 4.9%, Li– Shen took the third place with an AAD of 6.6% and Kent–Eisenberg came in last with an AAD of 13.6%. The use of extra parameters in the Li–Shen model, Hu–Chakma model and Cf model accounted for nonidealities caused by higher species concentrations and higher CO2 loadings. These led to better prediction accuracies for Li–Shen model, Hu–Chakma model and Cf model for CO2 equilibrium solubility. Acknowledgments The financial support from the National Natural Science Foundation of China (NSFC-Nos. 21536003, 21476064, 21376067, 21606078 and 51521006), National Key Technology R&D Program (MOST-No. 2014BAC18B04), Innovative Research Team Development Plan (MOE-No. IRT1238), Guangxi Natural Science Foundation (No. 2016GXNSFAA380190) and China Outstanding Engineer Training Plan for Students of Chemical Engineering & Technology in Hunan University (MOE-No. 2011-40) are gratefully acknowledged. References [1] Fang M, Luo ZY, Li MY, Gao L, Hu JC, Yan WP, Guo XQ, Shi Y, Zeng RS. Technology of carbon dioxide capture storage and usage. China Electric Power Press; 2012. [2] National Book of Statistics. Statistical bulletin of the national economic and social development of the People’s Republic of China in 2015. People’s Daily; 2016. [3] China. Statistics. Yearbook. Department of Energy Statistics, National Bureau of statistics of China. China energy statistical yearbook, Beijing: China Statistical Press; 2015. Available at http://data.stats.gov.cn/workspace/index. [4] Tontiwachwuthikul P, Idem R, Gelowitz D, Liang ZH, Supap T, Chan CW, et al. Recent progress and new development of post-combustion carbon-capture technology using reactive solvents. Carbon Manage 2011;2:261–3.
[5] Jijun L, Xintong Y, Weiming W, et al. Key factors controlling the gas adsorption capacity of shale: A study based on parallel experiments. Applied Geochemistry 2015;58:88–96. [6] Xiong J, Liu X, Liang L, Zeng Q. Adsorption of methane in organic-rich shale nanopores, An experimental and molecular simulation study. Fuel 2017;200:299–315. [7] Darde V, Maribo-Mogensen B, van Well WJM, Stenby EH, Thomsen K. Process simulation of CO2 capture with aqueous ammonia using The Extended UNIQUAC model. Int J Greenhouse Gas Control 2012;10:74–87. [8] Chowdhury FA, Yamada H, Higashii T, Goto K, Onoda M. CO2 capture by tertiary amine absorbents: a performance comparison study. Ind Eng Chem Res 2013;52:8323–31. [9] Liu H, Li M, Idem R, Tontiwachwuthikul P, Liang Z. Analysis of solubility, absorption heat and kinetics of CO2 absorption into 1-(2-hydroxyethyl)pyrrolidine solvent. Chem Eng Sci 2017;162:120–30. [10] Maulud AS. Review and selection criteria of classical thermodynamic models for acid gas absorption in aqueous alkanolamines: reviews in chemical engineering. Rev Chem Eng 2015;31:599–639. [11] Deshmukh R, Mather A. A mathematical model for equilibrium solubility of hydrogen sulfide and carbon dioxide in aqueous alkanolamine solutions. Chem Eng Sci 1981;36:355–62. [12] Renon H, Prausnitz J. Derivation of the three-parameter Wilson equation for the excess Gibbs energy of liquid mixtures. AIChE J 1969;15 785–785. [13] Plaza JM, Wagener DV, Rochelle GT. Modeling CO2 capture with aqueous monoethanolamine. Energy Proc 2009;1:1171–8. [14] Chen CC, Evans LB. A local composition model for the excess Gibbs energy of aqueous electrolyte systems. AIChE J 1986;32:444–54. [15] Faramarzi L, Kontogeorgis GM, Thomsen K, Stenby EH. Extended UNIQUAC model for thermodynamic modeling of CO2 absorption in aqueous alkanolamine solutions. Fluid Phase Equilib 2009;282:121–32. [16] Xiao M, Liu H, Idem R, Tontiwachwuthikul P, Liang Z. A study of structure–activity relationships of commercial tertiary amines for post-combustion CO2 capture. Appl Energy 2016;184:219–29. [17] Donaldson TL, Nguyen YN. Carbon dioxide reaction kinetics and transport in aqueous amine membranes. Ind Eng Chem Fundam 1980;19:260–6. [18] Sema T, Naami A, Idem R, Tontiwachwuthikul P. Correlations for equilibrium solubility of carbon dioxide in aqueous 4-(diethylamino)-2-butanol solutions. Ind Eng Chem Res 2011;50:14008–15. [19] Kent RL, Elsenberg B. Better data for amine treating. Hydrocarbon Process 1976;55:87–90. [20] Xiao M, Liu H, Idem R, Tontiwachwuthikul P, Liang Z. A study of structure–activity relationships of commercial tertiary amines for post-combustion CO2 capture. Appl Energy 2016;184:219–29. [21] Rayer AV, Sumon KZ, Sema T, Henni A, Idem RO, Tontiwachwuthikul P. Part 5c: Solvent chemistry: solubility of CO2 in reactive solvents for post-combustion CO2 . Carbon Manage 2012;3:467–84. [22] Li M-H, Shen K-P. Calculation of equilibrium solubility of carbon dioxide in aqueous mixtures of monoethanolamine with methyldiethanolamine. Fluid Phase Equilib 1993;85:129–40. [23] Hu W, Chakma A. Modelling of equilibrium solubility of CO2 and H2 S in aqueous amino-methyl-propanol (AMP) solutions. Chem Eng Commun 1990;94:53–61. [24] Xiao M, Cui D, Liu H, Tontiwachwuthikul P, Liang Z. A new model for correlation and prediction of equilibrium CO2 solubility in N-methyl-4-piperidinol solvent. AIChE J 2017;63:3395–403. [25] Lee JI, Otto FD, Mather AE. The measurement and prediction of the solubility of mixtures of carbon dioxide and hydrogen sulphide in a 2.5 N monoethanolamine solution. Can J Chem Eng 1976;54:214–19.
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Journal of the Taiwan Institute of Chemical Engineers journal homepage: www.elsevier.com/locate/jtice
Modeling and experiments of equilibrium solubility of carbon dioxide in aqueous N-(2-hydroxyethyl) pyrrolidine solution Wenchao Zheng a,†, Min Xiao a,†, Helei Liu b,∗, Hongxia Gao a, Zhiwu Liang a,b,∗∗ a
Joint International Center for CO2 Capture and Storage (iCCS), Provincial Hunan Key Laboratory for Cost-effective Utilization of Fossil Fuel Aimed at Reducing CO2 Emissions, College of Chemistry and Chemical Engineering, Hunan University, Changsha 410082, PR China Clean Energy Technologies Research Institute (CETRI), Faculty of Engineering and Applied Science, University of Regina, Regina, Saskatchewan S4S 0A2, Canada
b
a r t i c l e
i n f o
Article history: Received 22 September 2017 Revised 22 December 2017 Accepted 17 January 2018 Available online 21 February 2018 Keywords: Carbon dioxide N-(2-HE) PRLD VLE equilibrium Semi-empirical thermodynamic models
a b s t r a c t In this work, the equilibrium CO2 solubilities of the aqueous N-(2-hydroxyethyl) pyrrolidine (N-(2-HE) PRLD) at different concentrations (1.0 mol/L–5.0 mol/L) were measured at different temperatures (298 K– 333 K) and pressures (8 kPa–101 kPa), using a vapor–liquid equilibrium apparatus. Four semi-empirical thermodynamic models (Cf model, Kent–Eisenberg model, Hu–Chakma model and Li–Shen model) were used to correlate and predict the CO2 solubility data of the N-(2-HE) PRLD-CO2 –H2 O system. The results showed that the Hu–Chakma model, which is one of the models that incorporates the effect of amine concentration and CO2 loading, and accounted for nonideality caused by higher temperature, species concentrations and CO2 loadings, was best able to predict results that are in agreement with the experimental vapor–liquid equilibrium measurements in this work. © 2018 Taiwan Institute of Chemical Engineers. Published by Elsevier B.V. All rights reserved.
1. Introduction The rapid development of the global economy, massive mining, and utilization of fossil fuel for the production of energy have caused increasing amounts of greenhouse gases (GHGs) to be released into the atmosphere. CO2 is the most abundant GHG (accounting for 60% of the greenhouse gases [1]) and is considered to be one of the most significant contributors to global warming. Global warming is giving rise to a series of increasingly severe problems like melting of ice caps, rising sea level, drought, and intense storms. For the sake of sustainable development of the global economy and the protection of the environment, the capture of GHGs like carbon dioxide from flue gases is a key technology that needs to be developed and implemented. In China, energy supply is still predominantly based on fossil fuels such as coal. Over 10 billion tons of CO2 are discharged into the atmosphere each year, making China the largest CO2 emitting ∗ Corresponding author at: Clean Energy Technologies Research Institute (CETRI), Faculty of Engineering and Applied Science, University of Regina, Regina, Saskatchewan S4S 0A2, Canada. ∗∗ Corresponding author at: Joint International Center for CO2 Capture and Storage (iCCS), Provincial Hunan Key Laboratory for Cost-effective Utilization of Fossil Fuel Aimed at Reducing CO2 Emissions, College of Chemistry and Chemical Engineering, Hunan University, Changsha 410082, PR China. E-mail addresses: [email protected] (H. Liu), [email protected] (Z. Liang). † Author contributions: Wenchao Zheng and Min Xiao contributed equally to this work.
country in the world. China’s rapidly advancing economy is also resulting in the country having the most rapid increase in per capita emissions [2]. The capture of CO2 from point sources such as thermal power plants which contribute 63% of China’s electrical energy [3], is the most feasible plan for reducing or stabilizing CO2 concentration in the atmosphere. Among all the methods to capture CO2 (such as pre-combustion, post-combustion, and oxy-fuel combustion [4–6]), post-combustion CO2 capture is the most effective method of reducing CO2 emissions, especially from thermal power plants, using chemical reagents such as aqueous alkanolamine solutions. It is a mature technology that has already been applied in industry [7]. In order to obtain the ideal alkanolamine for CO2 capture, the reaction rate, absorption capacity, energy of CO2 desorption, renewability and industrial maturity must be considered. Many primary, secondary, and tertiary alkanolamines have already been tested in the last few years. N-(2-Hydroxyethyl) pyrrolidine (N-(2HE) PRLD) is a new cyclic tertiary amine with considerable potential because of its noticeable behavior in CO2 capture. Studies have shown that N-(2-HE) PRLD exhibits a higher CO2 cyclic capacity than MDEA (the most used commercial tertiary amine currently) and relatively higher absorption rate in comparison with any other tertiary amine (i.e. dimethylmono-ethanolamine) [8]. Moreover, the protonation constant and kinetics of N-(2-HE) PRLD have already been tested. Liu et al. deduced a formula for the protonation constant and confirmed that the reaction
https://doi.org/10.1016/j.jtice.2018.01.021 1876-1070/© 2018 Taiwan Institute of Chemical Engineers. Published by Elsevier B.V. All rights reserved.
W. Zheng et al. / Journal of the Taiwan Institute of Chemical Engineers 85 (2018) 132–140
between CO2 and N-(2-HE) PRLD is a pseudo-first-order reaction [9]. Other work on N-(2-HE) PRLD has also been done, however, the vapor–liquid equilibrium (VLE) has not yet been studied. To develop an efficient amine scrubbing process using the N-(2-HE) PRLD-H2 O–CO2 system, a thermodynamic model is indispensable to predict and describe its VLE as a function of temperature and the partial pressure of CO2 over an aqueous solution of the alkanolamine. Various models for the correlation and the prediction of the phase equilibria have already been proposed using the equilibrium solubility data of CO2 . Moreover, many sophisticated models that take the non-ideality into account have been developed. For the sake of appropriate model selection for the VLE prediction, Maulud et al. [10] presented a concise classification and review of classical thermodynamic models for acid gas absorption classified these models into three classes (semi-empirical models, activity coefficient models and EoS/GE models), as for example, the Deshmukh–Mather model [11], the electrolyte-NRTL model [12,13], Chen–Evans model [14], and UNIQUAC model [7,15]. Also, based on a previous study by Xiao et al. [16], N-(2-HE) PRLD showed an extremely high CO2 absorption capacity with a theoretical boundary of 1 mol CO2 /mol amine compared with conventional amines such as MEA (0.5 mol CO2 /mol·amine). In this work, theoretical and experimental investigations of CO2 solubility in N-(2-HE) PRLD were completed. Equilibrium solubility of CO2 in aqueous N-(2-HE) PRLD solution was measured under different temperatures (298 K–333 K), CO2 partial pressures (8 kPa–101 kPa) and amine concentrations (1 mol/L–5 mol/L). In order to explore the correlation between the VLE equilibrium of 1-(2-HE) PRLD-H2 O–CO2 system and the three factors (temperature, amine concentration and loading of CO2 ), four semi-empirical thermodynamic models (Kent–Eisenberg, Li–Shen, Hu–Chakma and Cf models) were used to correlate the resulting data for equilibrium solubility of CO2 in aqueous N-(2-HE) PRLD solution.
N-(2-Hydroxyethyl) pyrrolidine (N-(2-HE) PRLD) Fig. 1. The structure of solvent used in this work. Table 1 The values of K3 , K4 , K5 and HeCO2 for N-(2-HE) PRLD-H2 O–CO2 system [22]. 298 K Expressions
Ki /H0CO2 = exp A +
HCO2 K3 K4 K5
3035.9623 4.599E−07 4.621E−11 1.06E−14
(1)
The hydrolysis of carbon dioxide: K2
H2 O + RR R N + CO2 RR R NH+ + HCO3 −
(2)
Formation of bicarbonate ion: K3
H2 O + CO2 H+ + HCO3 −
(3)
Dissociation of bicarbonate ion: K4
HCO3 − H+ + CO3 2−
(4)
K5
HCO2 =
4083.9944 5.448E−07 6.163E−11 2.84E−14
H0CO2 7.50061
5558.9249 5.575E-07 7.28E−11 9.113E−14
(6)
RR R N H
K2 =
+ RR R N H HCO− 3 = K3 /K1
K3 =
(7)
RR R N C O2(aq )
[H + ] HCO− 3
C O2(aq )
HCO− 3
[H + ] CO23−
K5 = H +
(8)
OH −
(9)
(10)
where Ki represents the chemical equilibrium constants of reaction i. It is not difficult to find that there are only four independent equilibrium constants (K1 , K3 , K4 , and K5 ) in Eqs. (6)–(10). In addition, the physical solubility of CO2 in N-(2-HE) PRLD solution can be expressed by using Henry’s law [18] as follows:
PCO 2 = H eCO 2 C O2(aq )
(11)
where PCO2 is the partial pressure of CO2 in the gas phase, and HeCO2 represents the Henry’s law constant of CO2 in water. The Henry’s law constant applied to the absorption of CO2 into the liquid phase was obtained from literature [19]. The values of chemical equilibrium constants K3 , K4 , K5 and HeCO2 for N-(2-HE) PRLD-H2 O–CO2 system are obtained from the literature as listed in Table 1. In order to determine the value of K1 as well as the concentrations of all species, the following balances are introduced: Total amine balance:
Ionization of water:
H2 O H+ + OH−
C D B + + + ; T T T T
+ R R R N [H ] K1 = +
K4 =
K1
333 K
E
For every chemical reaction, there is a corresponding equilibrium constant, which can be presented as follows:
RR R NH+ RR R N+H+
313 K
2. Method In 1980, a widely accepted base-catalyzed hydration mechanism [17] was proposed to explain the reaction between carbon dioxide and tertiary amines. In this mechanism, tertiary amine was regarded as an alkali catalyst that catalyzes the reaction between water and carbon dioxide. The phase and chemical equilibrium reactions for N-(2-HE) PRLD-H2 O–CO2 system can be represented as follows: Protonation of N-(2-HE)-PRLD:
133
RR R N
0
= RR R N H + + RR R N
(12)
Total carbon balance:
(5)
where RR’R”N represents N-(2-HE) PRLD. It is a five membered nitrogen containing heterocyclic compound with a hydroxyethyl group attached in N atom. Fig. 1 shows the structure of N-(2-HE) PRLD.
α × RR R N 0 = C O2(aq) + HCO−3 + CO23−
The charge balance:
2− RR R N H + + H + = HCO− + OH − 3 + 2 CO3
(13)
(14)
134
W. Zheng et al. / Journal of the Taiwan Institute of Chemical Engineers 85 (2018) 132–140
Fig. 2. Schematic diagram of the experimental setup for CO2 loading measurement.
3. Materials and experiment 3.1. Materials CO2 and N2 each with purity of 99% were bought from Changsha RiZhen Gas Co., Ltd. 1-(2-hydroxyethyl) pyrrolidine (N-(2-HE) PRLD with purity of 97%) was purchased in Accela ChemBio Co., Ltd. Deionized water was used to prepare aqueous solutions of different 1-(2-HE) PRLD concentrations. In addition, deionized water was prepared in the iCCS laboratory using a water treater obtained from Taoshi water equipment engineering Co., Ltd. Flow meters (D08-2F) were obtained from Beijing Sevenstar Electronics Co., Ltd. (Beijing). The thermostatic water bath (DC-5010) was obtained from Fandilang Info Technology Co., Ltd. (Nanjing). 3.2. Experiment Fig. 2 [20] shows the schematic diagram of the experimental set up for a typical carbon dioxide equilibrium loading system. The equipment was used to measure the VLE of CO2 in 1-(2-hydroxyethyl)-pyrrolidine solution of different concentrations at different CO2 partial pressures and temperatures (298 K, 313 K, 333 K). The water-dampening device and reactor were set in a thermostatic water bath at the desired temperature with an uncertainty of ±0.1 K. A glass-scrubbing bottle (reactor) was filled with approximately 20 mL of absorbent with mole concentrations of 1.0 mol/L, 2.0 mol/L and 5.0 mol/L. For the purpose of acquisition of a steady absorption process, the inlet gas with different ratios of N2 and CO2 was introduced into the glass scrubbing bottle through a gas dispersion tube attached at the bottom of the liquid phase at a total flow rate of 250 mL/min. During the experiment, a shell and coil condenser was used to reduce amine loss caused by volatilization from the reactor. A liquid sample was tested every 1-h time interval to confirm if VLE was reached. The acid–base titration method [16] was employed in this experiment to measure the equilibrium CO2 solubility of the solution. The burette was filled with 1.0 mol/L hydrochloric acid. Then, 1 mL liquid sample and 2–3 drops of methyl orange indicator were placed into a conical flask by a pipette and the system was kept airtight with a water seal. After that, hydrochloric acid was added dropwise to the sample while recording the volume consumed. Af-
ter the color of the methyl orange indicator changed, hydrochloric acid was continued to be added to strip out all CO2 that was dissolved in the aqueous N-(2-HE) PRLD solutions. Equilibrium CO2 loading (defined as mol CO2 ·mol amine−1 ) was calculated using the following equation.
α=
V − VHC l2 273.15 × 22.4 × ca min eVHC l1 273.15 + T
(15)
where α represents CO2 loading, V is the volume of CO2 released from the liquid sample, VHCl1 is the volume of HCl consumed when the color of methyl orange indicator changed, VHCl2 is the total volume of HCl consumed during titration, T denotes the room temperature, and camine denotes the amine concentration of the liquid sample. Uncertainties are u(V )= 0.05 cm3 ; u(VHCl )= 0.01 mL; u(T) = 0.01 °C (level of confidence = 0.95). When the difference of CO2 loading of two successive samples is smaller than 0.01, we deem that VLE has been reached. The equilibrium loading of CO2 was measured at the temperatures of 298 K, 313 K and 333 K, CO2 partial pressures of 8 kPa, 15 kPa, 30 kPa, 60 kPa and 101 kPa and amine concentration of 1.0 mol/L, 2.0 mol/L and 5.0 mol/L. 4. Results and discussion 4.1. Equilibrium solubility of CO2 Equilibrium solubility of CO2 is of crucial importance in the testing and development of theoretical models and correlations, and is of great interest to process design software developers and researchers who are working on solvent screening studies. The overall cost of CO2 capture is partially determined by the thermophysical properties of the solvent. Moreover, incorrect estimates of the absorber size can lead to overly large columns, and failure to meet product specifications are quite often the result of inaccurate VLE data [21]. The experimental determinations of the equilibrium solubility of CO2 in aqueous N-(2-HE) PRLD solutions were done under various temperatures, CO2 partial pressures and amine concentrations. The experimental results are shown in Tables 2–4 and Figs. 3–8. It is obvious that the equilibrium loading of CO2 in N-(2-HE) PRLD is very high. Moreover, as observed from Figs. 3–5, with the increases
W. Zheng et al. / Journal of the Taiwan Institute of Chemical Engineers 85 (2018) 132–140
135
Table 2 Equilibrium loading of CO2 in 1.0 mol/L aqueous N-(2-HE) PRLD solutions. 298 K
313 K
333 K
CO2 partial pressure
CO2 equilibrium loading
CO2 partial pressure
CO2 equilibrium loading
CO2 partial pressure
CO2 equilibrium loading
8.00 15.00 30.00 60.00 101.00
0.855 0.898 0.925 0.959 0.973
8.00 15.00 30.00 60.00 101.00
0.806 0.823 0.862 0.890 0.911
8.00 15.00 30.00 60.00 101.00
0.619 0.680 0.779 0.851 0.872
Table 3 Equilibrium loading of CO2 in 2.0 mol/L aqueous N-(2-HE) PRLD solutions. 298 K
313 K
333 K
CO2 partial pressure
CO2 equilibrium loading
CO2 partial pressure
CO2 equilibrium loading
CO2 partial pressure
CO2 equilibrium loading
8.00 15.00 30.00 60.00 101.00
0.804 0.854 0.910 0.939 0.970
8.00 15.00 30.00 60.00 101.00
0.691 0.783 0.845 0.888 0.907
8.00 15.00 30.00 60.00 101.00
0.471 0.619 0.731 0.775 0.838
298 K
1.0
CO2 loading/(mol CO2/mol amine)
Table 4 Equilibrium loading of CO2 in 5.0 mol/L aqueous N-(2-HE) PRLD solutions.
0.9
CO2 partial pressure
CO2 equilibrium loading
8.00 15.00 30.00 60.00 101.00
0.503 0.560 0.753 0.820 0.859
0.8
0.7 0.6
CO2 loading/(mol CO2/mol amine)
1.0
298K 313K 333K
0.5
0.9
0.4
0
20
40
60
80
100
CO2 partial pressure(kPa) 0.8 Fig. 4. Equilibrium loading of CO2 in 2.0 mol/L aqueous N-(2-HE) PRLD solutions.
0.7
298K 313K 333K
0.6 0
20
40
60
80
100
CO2 partial pressure(kPa) Fig. 3. Equilibrium loading of CO2 in 1.0 mol/L aqueous N-(2-HE) PRLD solutions.
of temperature, the equilibrium solubility of CO2 decreased, and with the increase of CO2 partial pressure the equilibrium solubility of CO2 increased. Figs. 6–8 show the comparisons of experimental results for equilibrium solubility of CO2 in aqueous N-(2HE) PRLD solutions at temperatures of 298 K, 313 K and 333 K, respectively. It can be seen from the figures that with the increase in concentration of N-(2-HE) PRLD, equilibrium solubility of CO2 in aqueous N-(2-HE) PRLD solutions decreased. For example, Fig. 6 shows that the equilibrium solubility of CO2 of 5.0 mol/L aqueous N-(2-HE) PRLD solutions at 298 K is much lower (0.503 mol CO2 •mol amine−1 ) than the equilibrium solubility of CO2 in 1.0 mol/L N-(2-HE) PRLD at the same temperature, 298 K. These phenomena can be explained as follows. According to Le Chatelier’s
principle, when the concentration of amine is high, the reaction equilibrium (Eq. 2) will shift toward the right side. However, the ratio of reacted amine will decrease, which leads to the decrease of equilibrium CO2 solubility. In addition, the equilibrium loading of CO2 was observed to decrease with increasing temperature. This is because physical solubility of carbon dioxide is reduced with the increase of temperature and the CO2 absorption in amine solution is an exothermic process. In contrast, the loading of amine increased with CO2 partial pressure. This is mainly due to higher CO2 physical solubility in the solution which drives the reaction equilibrium of chemical Eqs. (2) and (3) toward the right side. Therefore, CO2 absorption with the amine solution is promoted. 4.2. Calculation of equilibrium CO2 loading In order to predict the equilibrium CO2 loading, a correlation for K1 is required. It is easy to find that there are 9 equations (Eqs. 6–14, 8 independent equations) and 8 unknown parameters. By simultaneously solving the equation set, the eight unknowns, namely, K1 , K2 , [RR R N], [H+ ], [RR R NH + ], [HCO3 − ], [CO3 2− ] [OH− ], [CO2(aq) ], can be calculated. Then, the obtained K1 can be fitted with several models (Kent–Eisenberg model, Hu– Chakma model, Li–Shen model and Cf models). The parameters of the models were obtained by using a nonlinear regression (NLREG)
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CO2 loading(mol CO2/mol amine)
CO2 loading/(mol CO2/mol amine)
0.9
0.8
0.7
0.6
1.125 1mol/L
0.675 0.45
0.225 0. 8
0.5
15 30 60 CO2 partial pressure(kPa)
298K 0
20
40
60
80
2mol/L
0.9
101
Fig. 8. Equilibrium loading of CO2 in 1.0, 2.0 mol/L aqueous N-(2-HE) PRLD solutions at 333 K.
100
Fig. 5. Equilibrium loading of CO2 in 5.0 mol/L aqueous N-(2-HE) PRLD solutions.
CO2 loading(mol CO2/mol amine)
1.
1mol/L
2mol/L
5mol/L
0.75
0.5
0.25
0.
8
15
30 60 CO2 paral pressure(kPa)
CO2 loading(mol CO2/mol amine)
1mol/L
2mol/L
0.25
0. 30
60
101
CO2 paral pressure(kPa) Fig. 7. Equilibrium loading of CO2 in 1.0, 2.0 mol/L aqueous N-(2-HE) PRLD solutions at 313 K.
program in MATLAB. The prediction of the equilibrium CO2 solubility is the reverse process of correlation. α solu was obtained by solving the above equations with a known value of K1 . In Fig. 9, the dots represent the calculated values while the curves represent the experimental values. It can be concluded that this model agrees with the experimental values well. The accuracy of the model is shown in terms of the average absolute deviation (AAD). AAD is defined as follows:
AAD =
1 αexp − αcal αexp × 100% N
0.8
0.6
0.4
0.6
0.8
1.0
Experimental equilibrium CO2 loading Fig. 9. Comparison of experimental equilibrium CO2 loading and calculated equilibrium CO2 loading of Kent–Eisenberg model.
4.2.1. Kent–Eisenberg Model The Kent–Eisenberg (KE) model [19] which was proposed in 1976 is considered to be a simple model because it is only related to temperature. Equilibrium CO2 partial pressure (PCO2 ) is related to the physically dissolved CO2 concentration in the liquid phase by the Henry law expression. In the original work, the model was used to calculate the equilibrium solubility of H2 S and CO2 in aqueous solutions of MEA and DEA by fitting the experimental solubility results. The model regressed some of the equilibrium constants as a function of temperature involving the main amine reactions. The model is expressed as shown in the following equation:
0.5
15
Kent- Eisenberg
0.4
0.75
8
1.0
101
Fig. 6. Equilibrium loading of CO2 in 1.0, 2.0, 5.0 mol/L aqueous N-(2-HE) PRLD solutions at 298 K.
1.
Calculated equilibrium CO2 loading
CO2 partial pressure(kPa)
(16)
Ki = exp A +
B C D E + 2 + 3 + 4 T T T T
(17)
In the present work, the KE model is applied to the 1-(2-HE) PRLD-CO2 –H2 O system. The values of the parameters (A, B, C, D, and E) are obtained by correlating K1 with temperature. The parameters are given in Table 5. The result in Fig. 9 shows that the equilibrium CO2 solubility can be predicted with AAD of 13.5% by the Kent–Eisenberg model, which is not good enough. As shown in this Fig. 9, it can be seen that the most calculated results are lower than the experimental results. It is because KE model only included one parameter (Temperature). In order to better preform the solubility of CO2 in N-(2-HE) PRLD system, other parameters should be added in the correlation.
W. Zheng et al. / Journal of the Taiwan Institute of Chemical Engineers 85 (2018) 132–140 Table 7 Parameters for the Hu–Chakma model for K1 in Eq. (19).
Table 5 Parameters for the Kent–Eisenberg model for K1 in Eq. (17). Parameters for K1
Value
Parameters for K1
Value
A B C D E
6.604 −6484 545.3 −18.03 −755
D1 D2 D3 D4
−34.78806224 0.041516362 50.51249543 −0.335956118
1.0
Parameters for K1
Value
A1 A2 A3 B1 B2 B3 B4
−8.44906 0.960128 0.999842 −7.27896 −7.05603 1.401108 −0.57362
Calculated equilibrium CO2 loading
Table 6 The parameters (A1 , A2 , A3 , B1 , B2 , B3 , and B4 ) for K1 in Eq. (18).
1.0
Calculated equilibrium CO2 loading
137
Li- Shen
Hu-Chakma 0.9
0.8
0.7
0.6
0.5
0.9 0.5
0.8
0.6
0.7
0.8
0.9
1.0
Experimental equilibrium CO2 loading Fig. 11. Comparison of experimental equilibrium CO2 loading and calculated equilibrium CO2 loading of Hu–Chakma model.
0.7
0.6
using the Li–sheng gives a better predicted results than KE model with an AAD of 6.6%.
0.5 0.5
0.6
0.7
0.8
0.9
1.0
Experimental equilibrium CO2 loading Fig. 10. Comparison of experimental equilibrium CO2 loading and calculated equilibrium CO2 loading of Li–Shen model.
4.2.2. Li–Shen model The Li–Shen model [22] is also an upgraded version of the Kent–Eisenberg model. The chemical equilibrium constants involving the amines are expressed as functions of not only temperature, but also of the total amine concentration and CO2 loading. In Li–Shen’s work, the equilibrium solubility of CO2 in aqueous mixtures of monoethanolamine (MEA) with methyldiethanolamine (MDEA) was correlated. The constants in the model were determined by fitting to the solubility data of carbon dioxide in aqueous MEA/MDEA solutions for temperatures ranging from 40 °C to 100 °C and for partial pressures of carbon dioxide up to 20 0 0 kPa. Satisfactory results were obtained for calculations of the solubility of carbon dioxide in aqueous MEA/MDEA solutions for the systems tested. The model can be expressed by the following equation:
A2 A3 B1 B2 Ki = exp A1 + + 2 + B3 α + + + B4 ln RR R N 0 T α α2 T
(18)
The values of the parameters (A1 , A2 , A3 , B1 , B2 and B3 ) calculated from K1 are presented in Table 6. As mention in the previous discussion, other parameters should be added in the correlation. In the correlation of Li–sheng Model, CO2 loading and the free amine are added in. As shown in Fig. 10, it happens that the correlation
4.2.3. Hu–Chakma model A modified mathematical model [23] named Hu–Chakma model was proposed for the prediction of equilibrium solubility of CO2 –H2 S–H2 O-2-amino-2-methyl-1-propanol (AMP) and CO2 –H2 SH2 O-Diglycolamine (DGA). The model showed that the equilibrium constant, K1 , governing the main amine reaction is expressed as a function of not only temperature but also the acid gas partial pressure and the total amine concentration. Model predictions agree favorably with experimental data. For the present study, the physically dissolved CO2 concentration in aqueous 1-(2-HE)-PRLD solutions was calculated using Eq. (18). The model can be expressed as the following equation:
Ki = exp D1 + D2 T + D3
PCO 2 + D4 ln RR R N 0 H eCO 2
(19)
PCO2 /HeCO2 is equal to [CO2 (aq) ] which is the physical solubility of CO2 in N-(2-HE) PRLD aqueous solutions. HeCO2 can be calculated from the work of Kent–Eisenberg. The values of parameters (D1 , D2 , D3 and D4 ) were calculated from K1 using the Hu–Chakma model and presented in Table 7. By applying the Hu– Chakma model, the results of the predicted equilibrium solubility of CO2 were found to agree with the experimental results very well with an AAD (plotted in Fig. 11) of 4.3%. This fact implies that another important parameter, the CO2 physical solubility ([CO2 (aq) ]) should be added into the correlation. As shown in Fig. 11, the deviation is very high around the CO2 solubility of 0.4–0.6. This is because the prediction of CO2 solubility is based on correlation equation. Therefore, the reason might be the mathematical equation of the correlation cannot describe the equilibrium constant well at the stated condition.
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1.0
Parameters for the Cf
Value
a b c
0.001549 0.00253 1.003103
4.2.4. Cf model In 2016, Xiao et al. proposed a new thermodynamic model named the Cf model [24]. In that work, to correct the non-ideality of aqueous amine solution, a correction factor (Cf ) was developed for predicting the equilibrium CO2 solubility for N-(2-HE) PRLDH2 O–CO2 system. This correction factor was developed as in the following equation:
H+ = C f H+
where
∗
(20)
(21)
− The concentrations of[RR R N], [CO23− ], [HCO− 3 ], [OH ] can be expressed as functions of [H+ ], Ki and [CO2 (aq) ].
RR R N =
[H + ]
OH − =
0
(22)
K3 K4
K3 C O2(aq )
HCO− 3 =
K1 + [H + ]
K1 × RR R N
CO23− = C O2(aq )
(23)
2
(24)
[H + ]
K5 [H + ]
(25)
The pKa value can be obtained as in Liu’s work by the following equation [9]:
pKa =
1668 + 4.54(R2 = 0.999 ) T
(26)
We can then calculate K1 by lgK1 = −pKa. Then, by substituting Eqs. (22)–(25), Eq. (12) can be transformed as follows:
α × RR R N 0 K K K = 3+ + 1 + 3 42 [H ]
C O2(aq )
(27)
[H + ]
The [H+ ] value is obtained by solving Eq. (27). Moreover, the equation of charge balance can be expressed using a polynomial equation in terms of [H+ ] as follows:
A H+
4
+ B H+
3
where A = 1
Cf 0.9
0.8
0.7
0.6
0.5 0.5
0.6
0.7
0.8
0.9
1.0
Expermental equilibrium CO2 loading
C f = exp a · ln [C O2 ] + b · ln RR R N + c
Calculated equilibrium CO2 loading
Table 8 Parameters for the Cf Model in Eq. (21).
+ C H+
2
+ D H+ + E = 0
(28)
B = K1 + RR R N
0 C = − K3 C O2(aq ) + K5
D = − K1 K3 C O2(aq ) + 2K4 K3 C O2(aq ) + K5 K1 E = −2K4 K3 K1 C O2(aq ) The other value of [H+ ], that is [H+ ]∗ , can be obtained by solving Eq. (28). The calculation of [H + ]∗ is based on the assumption of an ideal solution of infinite dilution. By fitting [H+ ]∗ and [H + ] values at different conditions into Eq. (20), Cf values can be obtained, and then, all parameters, namely, a, b and c in Eq. (20) are obtained using a nonlinear regression program, as summarized in Table 8. The Cf model for the N-(2-HE) PRLD-H2 O–CO2 is thus established. Fig. 12 shows that the equilibrium CO2 solubility can be predicted very well with an AAD of 4.9% by the Cf model. Just like Fig. 11, Fig. 12 also gives the high deviation at the CO2 loading
Fig. 12. Comparison of experimental equilibrium CO2 loading and calculated equilibrium CO2 loading of Cf model.
of 0.4–0.6. This is also because the prediction of CO2 solubility is based on correlation equation. Therefore, the reason might be the mathematical equation of the correlation cannot describe the equilibrium constant well at the stated condition. Fig. 13 shows the comparison of experimental equilibrium CO2 loading and calculated equilibrium CO2 loading of all four models. We can observe that the predicted results decreased with the increase of temperature and amine concentration compared to experimental results. This might be because the effect of non-ideality is more obvious at low loading. The low loading area is commonly corresponding to the high temperature and amine concentration. Some models are unable to describe the non-ideality very well. In this work, four semi-empirical models (the Kent–Eisenberg, Li–Shen, Hu–Chakma and Cf models) were adapted to predict the equilibrium loading of CO2 in aqueous N-(2-HE) PRLD solution, respectively. The Kent–Eisenberg model showed a somewhat poor prediction for CO2 equilibrium loading in aqueous N-(2-HE) PRLD solution with an AAD of 13.5%. This is because the Kent–Eisenberg model only considers the chemical equilibrium constant (Ki ) to be dependent on temperature whereas our experimental results show that the chemical equilibrium constant is strongly related to the chemical reaction and equilibrium concentration of the involved species. For the sake of better prediction, it has been suggested by various researchers [22,25] that the equilibrium constant which governs the reaction between amines and acid gas should not only be dependent on temperature, but also on other parameters such as acid gas loading, the concentration of free amine, and the physical acid gas solubility. Thus, it is suggested that the equilibrium constants derived from the reaction between amine and acid gas should also be considered to be functions of all the above parameters (temperature, acid gas loading, free amine concentration and physical acid gas solubility). The Li–Shen model and the Hu– Chakma model are two representatives. In order to obtain a better prediction of the equilibrium acid gas solubility, Li and Shen modified the model by taking three parameters, temperature, amine concentration and acid gas loading into consideration, as shown in Eq. (19). The result of the Li–Shen model showed a much better performance than the Kent–Eisenberg model in terms of the prediction of equilibrium loading of CO2 with a lower AAD of 6.6%. Hu and Chakma took another non-negligible parameter, physical CO2 solubility, into consideration to improve the Hu–Chakma model, as shown in Eq. (18). For the prediction of CO2 equilibrium loading in aqueous N-(2-HE) PRLD solution, the Hu and Chakma
W. Zheng et al. / Journal of the Taiwan Institute of Chemical Engineers 85 (2018) 132–140
139
Fig. 13. Comparison of experimental equilibrium CO2 loading and calculated equilibrium CO2 loading using four models.
model provided the lowest deviation from experimental results of CO2 equilibrium loading, with an AAD of 4.3%. In the Hu–Chakma Model, the CO2 loading, which represented the capacity of the aqueous amine, was replaced by the parameter of physical CO2 solubility in the aqueous N-(2-HE) PRLD solution. According to the value of AAD, it can be summarized that the physical CO2 solubility (CO2 concentration in the gas–liquid interface) is an important parameter in the prediction of CO2 equilibrium solubility. Moreover, the physical CO2 solubility determines the driving force for CO2 transfer into the liquid phase and affects the mass transfer of CO2 to the bulk aqueous N-(2-HE) PRLD solution, which has a significant effect on CO2 solubility. Thus, the introduction of the parameter, physically dissolved CO2 concentration, results in the lowest deviation (AAD = 4.3%) in the prediction of CO2 equilibrium solubility by the Hu–Chakma model. The Cf model also showed a good performance with an AAD of 4.9%, because the influential factors (i.e., temperature, physical CO2 solubility, and amine concentration) were also taken into consideration in the Cf model as in the Hu–Chakma model. To sum up, of all the models, the Hu–Chakma model proved to give the most accurate predicted results of CO2 equilibrium
loading in comparison with the experimental data. The Cf model took second place ahead of the Li–Shen model. The Kent–Eisenberg model demonstrated the worst performance. Theoretically, these models refer to very dilute solutions where viscosity is not a problem, but for practical situations, higher concentrations are used. Therefore, it is helpful that the additional parameters in the Li– Shen, Hu–Chakma and Cf model account for non-idealities caused by higher concentrations and higher CO2 loadings. The authors prefer Cf model because it shows only a little higher AAD (4.9% versus 4.3%) and need less parameters (a, b, c versus D1 , D2 , D3 , D4 ) compared to Hu–Chakma model. When it comes to the difference of prediction between Cf and Hu–Chakma model, although Hu–Chama and Cf model are similar in correlating expression and use of correction/correlation parameters, there is some difference in modeling. Hu–Chakma model tries to correlate data using equilibrium constant K1 as a function of some experimental factors while Cf model proposes a new correction factor toward concentration of species [H+ ]. Thus the handling of experimental data is quite different as well as different correlation of 0.6%.
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5. Conclusions To develop an efficient amine scrubbing process, a validated thermodynamic model of the vapor–liquid equilibrium (VLE) is of crucial importance. In the present work, the equilibrium CO2 loading of N-(2-hydroxyethyl) pyrrolidine (N-(2-HE) PRLD) was studied at CO2 partial pressure of 8–101 kPa, over the temperature range of 298 K–313 K and molar concentration varying from 1 mol/L to 5.0 mol/L. It was found that aqueous N-(2-HE) PRLD exhibits very good CO2 absorption capacity. However, with an increase in temperature and amine concentration, CO2 equilibrium loading decreased. Higher CO2 partial pressure resulted in a higher equilibrium CO2 loading. The Kent–Eisenberg, Li–Shen, Hu–Chakma and Cf models were used to predict the equilibrium CO2 loading. It was found that Hu–Chakma model performed very well with an AAD of 4.3%, Cf took the second place with an AAD of 4.9%, Li– Shen took the third place with an AAD of 6.6% and Kent–Eisenberg came in last with an AAD of 13.6%. The use of extra parameters in the Li–Shen model, Hu–Chakma model and Cf model accounted for nonidealities caused by higher species concentrations and higher CO2 loadings. These led to better prediction accuracies for Li–Shen model, Hu–Chakma model and Cf model for CO2 equilibrium solubility. Acknowledgments The financial support from the National Natural Science Foundation of China (NSFC-Nos. 21536003, 21476064, 21376067, 21606078 and 51521006), National Key Technology R&D Program (MOST-No. 2014BAC18B04), Innovative Research Team Development Plan (MOE-No. IRT1238), Guangxi Natural Science Foundation (No. 2016GXNSFAA380190) and China Outstanding Engineer Training Plan for Students of Chemical Engineering & Technology in Hunan University (MOE-No. 2011-40) are gratefully acknowledged. References [1] Fang M, Luo ZY, Li MY, Gao L, Hu JC, Yan WP, Guo XQ, Shi Y, Zeng RS. Technology of carbon dioxide capture storage and usage. China Electric Power Press; 2012. [2] National Book of Statistics. Statistical bulletin of the national economic and social development of the People’s Republic of China in 2015. People’s Daily; 2016. [3] China. Statistics. Yearbook. Department of Energy Statistics, National Bureau of statistics of China. China energy statistical yearbook, Beijing: China Statistical Press; 2015. Available at http://data.stats.gov.cn/workspace/index. [4] Tontiwachwuthikul P, Idem R, Gelowitz D, Liang ZH, Supap T, Chan CW, et al. Recent progress and new development of post-combustion carbon-capture technology using reactive solvents. Carbon Manage 2011;2:261–3.
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