Sigmoid Correlations for Gas Solubility and ... - ACS Publications

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Sigmoid Correlations for Gas Solubility and Enthalpy Change of Chemical Absorption of CO2 Kuan Huang,†,‡ You-Ting Wu,*,‡ and Sheng Dai*,†,§ †

Department of Chemistry, University of Tennessee, Knoxville, Tennessee 37996, United States School of Chemistry and Chemical Engineering, Nanjing University, Nanjing, Jiangsu 210093, P. R. China § Chemical Sciences Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, United States ‡

S Supporting Information *

ABSTRACT: Knowledge of the relationship between gas solubility and enthalpy change of chemical absorption of CO2 is very important for exploring energy-efficient absorbents for CO2 capture. To this end, equations that can directly correlate gas solubility with absorption enthalpy were derived through combining the van’t Hoff equation with the reaction equilibrium thermodynamic model (RETM). Two typical reaction mechanisms for chemical absorption of CO2 (1:1 and 1:2) were considered for RETM. The variations of gas solubility with enthalpy change were found to be distinctively sigmoid functions, regardless of the investigated temperature and pressure or assumed reaction forms between CO2 and the absorbent molecule. Theoretically calculated variation curves of gas solubility vs enthalpy change agreed well with experimental results reported in literature. On the basis of the trade-off relationship between gas solubility and enthalpy change, criterions for evaluating energyefficient chemical absorbents for CO2 capture were proposed.

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INTRODUCTION As the concentration of atmospheric CO2 continuously increases, the resulting global warming is attracting widespread attention across academic and industrial communities because of its potentially destructive impact on the environment and ecosystems. CO2 is mainly emitted in flue gases, which results from the combustion of fossil fuels.1 A widely used strategy to eliminate CO2 from industrial gas streams is reversible absorption in liquids.2 For the purpose of capturing CO2 from flue gases, chemical absorption is preferred over physical absorption, as the concentration of CO2 in flue gas is low (10− 15 v/v %).3 However, the chemical absorption method typically consumes high amounts of energy during the desorption process.4 Gas solubility and absorption enthalpy are two vital thermodynamic properties for evaluating the performance of chemical absorbents for CO2 capture. The former indicates how much gas an absorbent can accommodate, and the latter reflects the strength of interaction between the gas and absorbent. For chemical absorbents designated for CO2 capture, those with high absorption capacity and low enthalpy change are particularly attractive.5,6 High CO2 loading is required to reduce the volume of circulation of the absorbents, and low enthalpy change is meaningful for reducing the energy consumed during desorption. However, there is a contradictory relationship between gas solubility and absorption enthalpy since a low enthalpy change in an absorbent is generally accompanied by a low absorption capacity.7,8 Therefore, finding a proper balance between gas solubility and absorption enthalpy is very important in selecting energy-efficient chemical absorbents for CO2 capture. Despite the significance of gas solubility and absorption enthalpy, they have usually been treated separately in previous research. Notably, Deshmukh et al.9 proposed a thermody© XXXX American Chemical Society

namic model based on the extended Debye−Huckel theory of electrolyte solutions for the solubility of CO2 in alkanolamine solutions, and this model was further used by Aroua et al.10 Both Meisen et al.11 and Lichtenthaler et al.12 derived model equations from chemical reaction equilibrium equations and Henry’s law equation for the calculation of CO2 solubility in aqueous MDEA and PZ solutions. McCann et al.13 simulated the capacity of CO2 absorption by aqueous amine systems and calculated the corresponding enthalpy change from van’t Hoff equation, and further predicted the overall enthalpy of CO2 absorption in aqueous amine systems from experimentally determined reaction enthalpy.14 More recently, Rochelle et al.15 correlated the solubility data for CO2 in aqueous PZ/MDEA solutions with the NRTL model while Voutsas et al.16 modeled the CO2 solubility in aqueous solutions of MEA, MDEA, and their blends using the electrolyte−LCVM model. The CO2 capture in amine solvents was also modeled using the extended UNIQUAC model.17 Arcis et al.18 calculated the enthalpy of CO2 absorption in aqueous solutions of primary alkanolamines from a thermodynamic model based on chemical equilibriums and vapor−liquid equilibriums. Henni et al.19 correlated the heat of CO2 absorption in aqueous solutions of MDEA and DMAP using a rigorous thermodynamic model. There are not yet equations that can directly correlate the two thermodynamic properties. Such a correlation would be very instructive for exploring the balance between them. In this effort, we tried to derive theoretical equations to demonstrate the distinctive trade-off relationship between gas solubility and enthalpy change for chemical absorption of CO2 by combining Received: June 13, 2015 Revised: September 28, 2015 Accepted: October 1, 2015

A

DOI: 10.1021/acs.iecr.5b02145 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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Industrial & Engineering Chemistry Research

Material balance equations of CO2 in 1:1 chemical absorption and 1:2 chemical absorption are

the van’t Hoff equation with the reaction equilibrium thermodynamic model (RETM).20,21

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DERIVATION OF CORRELATION EQUATIONS Normally, absorption enthalpy ΔH° is calculated from the integral form of the van’t Hoff equation by assuming ΔH° is a constant within a specific temperature range:13 ΔH ° ΔS° + RT R

ln K ° = −

(9)

In eqs 5−11, m° is the standard molality (1 mol·kg ); P° is the standard pressure (1 bar); and mLCO2, mLA, mLCO2‑A, and mLCO2‑2A are the molality concentrations of physically dissolved CO2, the free absorbent, the CO2-A complex, and the CO2-2A complex in the liquid phase, respectively. PGCO2 is the pressure of CO2 in gas phase, Hm is the Henry’s constant of CO2 in molality scale, m0CO2 is the total solubility of CO2 including chemically reacted and physically dissolved in the molality scale, and m0A is the initial molality concentration of absorbent that can be calculated from mA0 =

r= (3)

(4)

(5)

G K °PCO 2 G 1 + K °PCO 2

+

G PCO 2

HmmA0

(13)

Hm = Hr MA

(14)

mAL m°

2

( )

(6)

L mCO 2

m°

G K °PCO 2 G 1 + K °PCO 2

+

G PCO 2

Hr

(15)

Actually, Islam et al. had empirically proposed an equation similar to eq 15 for correlating the gas solubility of reactive absorption of SO2, NH3, Cl, and HCl in water. Herein, we provide the theoretical basis for eq 15. In eq 15, the terms K°PGCO2/(1 + K°PGCO2) and PGCO2/Hr represent chemically and physically absorbed CO2, respectively. Similarly, combining eqs 6, 7, 9, and 11, followed by simple deduction, results in

The Henry’s law equation for eq 4 is PCO2 = Hm

=

24

m° P°

mA0

HmmA0 =

r=

·m°

·

0 mCO 2

Therefore, eq 13 was rewritten as

m° G L PCO 2 mA

G PCO 2

(12)

In eq 13, r is the solubility of CO2 in the molar ratio. The term Hmm0A can be transformed to Henry’s constant in the molar ratio scale Hr from the following deduction:

L mCO 2 ‐ 2A

K° =

1 MA

In eq 12, MA is the molecular weight of absorbent in kg/mol. Combining eqs 5, 7, 8, and 10 results in

(2)

L mCO 2 ‐A

P°

(11) −1

The reaction equilibrium equations for eqs 2 and 3 are

K° =

(10)

L mA0 = mAL + 2mCO 2 ‐ 2A

In eqs 2 and 3, A denotes the absorbent molecule. G and L denote the gas phase and liquid phase, respectively. The physical dissolution of CO2 is expressed as CO2 (G) → CO2 (L)

0 L L mCO = mCO + mCO 2 2 2 ‐ 2A

L mA0 = mAL + mCO 2 ‐A

(1)

1:2 reaction mechanism: CO2 (G) + 2A(L) → CO2 ‐2A(L)

(8)

Material balance equations of the absorbent in 1:1 chemical absorption and 1:2 chemical absorption are

In eq 1, K° is the equilibrium constant for the reaction between gas and absorbent. When eq 1 is used, the absorption enthalpy ΔH° is calculated from the slope of the linear fit between ln K° and 1/T. Note that it is usually difficult to measure K° directly in experiments. A common approach is to correlate the isothermal solubility data with a proper thermodynamic model with K° as a parameter to be fitted. In our previous work on chemical absorption of acidic gas in ionic liquids, we developed a reaction equilibrium thermodynamic model (RETM)20,21 to correlate isothermal gas solubility. The principle of the RETM is also applied in this work. For chemical absorption of CO2 in liquids, gas solubility can be divided into two parts, one contributed by the chemical reaction and the other by physical dissolution. Typically, there are two forms of chemical reaction between CO2 and an absorbent molecule:3,22,23 1:1 reaction mechanism: CO2 (G) + A(L) → CO2 ‐A(L)

0 L L mCO = mCO + mCO 2 2 2 ‐A

(7)

r=

Equations 5−7 are based on the assumption that the liquid phase is an idea solution to avoid the calculation of activity coefficients. Meisen et al.11 used a similar method for the calculation of CO2 solubility in aqueous MDEA and PZ solutions, without taking the liquid phase activity coefficients into consideration, and calculated solubility was in good agreement with experimental data. Therefore, the negligence of activity coefficients is thought to be reasonable for the derivation of the RETM equations.

G + MA − 4K °PCO 2

G + MA )MA (8K °PCO 2

G 8K °PCO 2

+

G PCO 2

Hr (16)

For the absorption of CO2 in chemical absorbents, when PGCO2 is not high (usually lower than atmospheric pressure), the contribution of physical dissolution to total solubility is very small in comparison with the contribution of chemical reaction.25−27 For instance, Rochelle et al.28 differentiated the physical solubility of CO2 from the chemical solubility of CO2 B


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Industrial & Engineering Chemistry Research in aqueous MDEA solutions, and the Henry’s constant of CO2 in 20 wt % MDEA was estimated to be 51.4 (atm·L)/mol at 298.15 K. That is to say, the physical solubility of CO2 was only 0.012 mol/mol at 298.15 K and 1 atm, accounting for less than 2 % of the total solubility (∼1 mol/mol). Therefore, the term PGCO2/Hr in eqs 15 and 16 can be neglected; thus they were simplified to r=

1

G K °PCO 2 G + K °PCO 2

r=

G +1 4(e−(ΔH °+ 8.314T ln MA)/8.314T − 140/8.314)PCO 2 G 8(e−(ΔH °+ 8.314T ln MA)/8.314T − 140/8.314)PCO 2

−

G +1 8(e−(ΔH °+ 8.314T ln MA)/8.314T − 140/8.314)PCO 2 G 8(e−(ΔH °+ 8.314T ln MA)/8.314T − 140/8.314)PCO 2

(24)

We defined a new parameter h as pseudo-absorption enthalpy: h = ΔH ° + 8.314T ln MA

(17)

(25)

Thus, eq 24 was transformed to r=

G + MA − 4K °PCO 2

G + MA )MA (8K °PCO 2

G 8K °PCO 2

r=

(18)

As seen from eqs 1, 17, and 18, gas solubility r and absorption enthalpy ΔH° are connected with each other through the “bridge” of equilibrium constant K°. Rearranging eq 1 results in K° = e

−ΔH ° / RT +ΔS ° / R

■

(19)

r=

(20)

G + MA 4e−ΔH ° /8.314T +ΔS ° /8.314PCO 2 G 8e−ΔH ° /8.314T +ΔS ° /8.314PCO 2

−

G +1 8(e−h /8.314T − 140/8.314)PCO 2 G 8(e−h /8.314T − 140/8.314)PCO 2

(26)

DISCUSSION 1:1. Chemical Absorption. According to eq 22, the variation of r with ΔH° is dependent on T and PGCO2. This is understandable since the strength of interaction between CO2 and absorbents varies with temperature and pressure. To investigate the relationship between gas solubility r and enthalpy change ΔH° for a 1:1 chemical absorption of CO2, a standard state of T = 298.15 K and PGCO2 = 1 bar was first applied to eq 22 as an example. We depicted the variation curve of r vs ΔH° in Figure 1. It is interesting that r is found to be a

G PCO 2 G eΔH ° /8.314T −ΔS ° /8.314 + PCO 2

G 8(e−h /8.314T − 140/8.314)PCO 2

−

By inserting eq 19 and R = 8.314 J/(K·mol) into eqs 17 and 18, the following equations that correlate gas solubility directly with absorption enthalpy were obtained: r=

G +1 4(e−h /8.314T − 140/8.314)PCO 2

G + MA )MA (8e−ΔH ° /8.314T +ΔS ° /8.314PCO 2 G 8e−ΔH ° /8.314T +ΔS ° /8.314PCO 2

(21)

In eqs 20 and 21, PGCO2 and T are experimentally measurable parameters. Entropy change ΔS°can be assigned a unified value for reactions 2 or 3 involving different absorbents, because ΔS° of absorption process is determined by the entropy loss of the CO2 molecule during the transformation from a gas to a liquid phase, and most liquid CO2 absorbents have very similar values of ΔS° at a standard condition.6,29 According to the Campbell’s Rule,30−32 the entropy change ΔS° at 298.15 K can be estimated as −140 J/(K·mol) for each net mole of gas consumed in the balanced chemical reaction. Therefore, eqs 20 and 21 were rewritten as r=

r=

G PCO 2 G eΔH ° /8.314T + 140/8.314 + PCO 2

Figure 1. Variation of gas solubility with enthalpy change for CO2 absorption in 1:1 chemical absorbents at T = 298.15 K and PGCO2 = 1 bar (black solid line, theoretically calculated from eq 22; blue triangles, physical absorbents, including normal organic solvents and ionic liquids; black squares, chemically tunable ionic liquids with aprotic heterocyclic anions and amino acid anions; red circle, 25 wt % aqueous MDEA).

(22)

G + MA 4e−ΔH ° /8.314T − 140/8.314PCO 2 G 8e−ΔH ° /8.314T − 140/8.314PCO 2

−

G + MA )MA (8e−ΔH ° /8.314T − 140/8.314PCO 2 G 8e−ΔH ° /8.314T − 140/8.314PCO 2

distinctively sigmoid function of ΔH°. This sigmoid curve can be divided into three parts with ΔHr°= 0.05 = −34.5 kJ/mol and ΔHr°= 0.95 = −49.1 kJ/mol as the demarcation points. In Region I (|ΔH°| < 34.5 kJ/mol), the value of r remains at a low level and almost unchanged with respect to ΔH°. Note that eq 22 is not applicable in Region I, since the interaction of CO2 with the

(23)

In eq 23, MA and ΔH° are both inherent properties of absorbents, and one cannot set a unified value of MA for different absorbents when discussing the relationship between r and ΔH°. To avoid the discussion of MA, eq 23 was rewritten as C


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these ionic liquids. Therefore, we used the ΔH° calculated by DFT method as the experimental values for these ionic liquids. This may result in significant deviations between the predicted and experimental solubilities of CO2. Taking into account the low content of CO2 in flue gas (10− 15 v/v %),3 it is significant to extend the variation curve of r vs ΔH° to low pressures. This extension is reasonable, since ΔH° and ΔS° are both independent of PGCO2. Therefore, T = 298.15 K and PGCO2 = 0.15 bar were applied to eq 22, and the variation curve of r vs ΔH° was depicted in Figure 2. Obviously, the

absorbent molecule is so weak that the absorption of CO2 in this region is actually a physical type. Therefore, Region I absorbents are physical absorbents, while eq 22 is only applicable for chemical absorbents. The purpose of presenting the variation curve of r vs ΔH° in Region I is to give a full description for the relationship between r and ΔH°. However, due to the very low solubility of CO2 in physical absorbents (normally less than 0.05 mol/mol at T = 298.15 K and PGCO2 = 1 bar, see Table S1) in comparison with the whole scale (1 mol/ mol), including physical absorbents in Region I has very little influence on the overall sigmoid profile of r vs ΔH°. In Region II (34.5 < |ΔH°| < 49.1 kJ/mol), the chemical reaction dominates the CO2 absorption and the increase of |ΔH°| has a significant and positive contribution to improving the value of r. In Region III (|ΔH°| > 49.1 kJ/mol), the value of r approaches the stoichiometric ratio of the chemical reaction between CO2 and the absorbent molecule (1:1 molar ratio), and the further increase in |ΔH°| has little effect on the value of r due to the limitation of chemical equilibrium. Therefore, according to the trade-off relationship between r and ΔH° as demonstrated in Figure 1, we designated ΔHef = −49.1 kJ/mol as the criterion of energy-efficient 1:1 chemical absorbents for CO2 capture at T = 298.15 K and PGCO2 = 1 bar. It is important to compare the theoretically calculated curve with the experimental results. We summarized the reported values of r at T = 298.15 K and PGCO2 = 1 bar and the corresponding ΔH° values of various absorbents (including physical absorbents and 1:1 chemical absorbents)7,25,33−39 in Tables S1 and S2 in the Supporting Information. These experimental values were also plotted in Figure 1. Previous research on liquid absorbents for CO2 capture relied highly on normal organic solvents (e.g., PC, NMP, SUF, and PEG150)33,34 and aqueous organic amines (e.g., MDEA).36 As classified in Figure 1, they are representatives of Region I and Region III absorbents, respectively. The absence of experimental results in Region II leads to the neglect of such a distinctively sigmoid relationship between r and ΔH°. Fortunately, the emergence of ionic liquids provides an opportunity to explore this issue. Ionic liquids have tunable structures and properties.40 Brennecke et al.25,38,39 and our group7,37 both investigated a variety of chemically tunable ionic liquids with aprotic heterocyclic anions and amino acid anions that exhibit 1:1 chemical reactivity with CO2. The enthalpy change of CO2 absorption in these ionic liquids covers a wide range of values. As can be seen in Figure 1, the calculated curve is in excellent agreement with the experimental results, verifying the reliability of using eq 22 to predict the relationship between r and ΔH° of 1:1 chemical absorption of CO2. Obviously, traditional 25 wt % aqueous MDEA (r = 0.989 mol/mol and ΔH° = −65.0 kJ/mol) is a relatively energy-intensive absorbent, whereas an ionic liquid [P66614][6-BrBnIm] (r = 0.90 mol/mol and ΔH°= −48 kJ/mol) is highly suitable for energy-efficient capture of CO2 at T = 298.15 K and PGCO2 = 1 bar. It should be noted that for some chemically tunable ionic liquids with aprotic heterocyclic anions, their absorption enthalpy for CO2 (ΔH°) was actually calculated by the DFT method based on gas-phase reactions according to literature (see Table S2). The DFT method can provide reasonable values of ΔH° for the absorption of CO2 in ionic liquids in most of the cases but sometimes can introduce considerable errors. There are no values of ΔH° calculated from van’t Hoff equation or determined directly by calorimetry method for

Figure 2. Variation of gas solubility with enthalpy change for CO2 absorption in 1:1 chemical absorbents at T = 298.15 K and PGCO2 = 0.15 bar (black solid line, theoretically calculated from eq 22; blue triangles, physical absorbents including normal organic solvents and ionic liquids; black squares, chemically tunable ionic liquids with aprotic heterocyclic anions and amino acid anions; red circle, 25 wt % aqueous MDEA). Inset illustration: comparison of the variation curves of gas solubility vs enthalpy change at different pressures and temperatures (red line, T = 298.15 K and PGCO2 = 1 bar; black line, T = 298.15 K and PGCO2 = 0.15 bar; blue line, T = 348.15 K and PGCO2 = 0.15 bar).

relationship between r and ΔH° is still a sigmoid function at PGCO2 = 0.15 bar. However, the sigmoid curve moves toward a more exothermic direction when the value of PGCO2 decreases from 1 to 0.15 bar (see the inset illustration in Figure 2). As a result, chemical absorbents of more exothermic chemical reaction with CO2 are required to capture low-pressure CO2 (ΔHef = −53.8 kJ/mol). We also summarized the reported values of r at T = 298.15 K and PGCO2 = 0.15 bar and the corresponding ΔH° values of various absorbents25,33−36,38,39 in Tables S1 and S2. These experimental values were plotted in Figure 2. It can be seen that at a low pressure of PGCO2 = 0.15 bar, the calculated curve still agrees well with the experimental results. The slight overestimation of r for two amino acid ionic liquids [P66614][Met] and [P66614][Pro] in Region III is supposed to be a result of the activity effect. The RETM used in this work is based on the assumption of an ideal solution, and the activity coefficients of species in the liquid phase were all set to be unity. However, the activity effect would apparently “deactivate” part of the ionic liquids. Brennecke et al.27 analyzed systematically the deactivation phenomenon for CO2 absorption in amino acid ionic liquids, and the molar ratio of active ionic liquids to total ionic liquids was calculated to be 0.8−0.9 at 295.15 K. This is consistent D


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(including MEA, imidazolium carboxylate ionic liquids, and silylamines)41−44 in Table S3. These experimental values were also plotted in Figure 3. The experimental values of r for CO2 absorption in 50 wt % aqueous MEA and silylamines exceed the stoichiometric ratio of the chemical reaction between CO2 and the absorbent molecule (1:2 molar ratio). This is because CO2 absorption in 50 wt % aqueous MEA and silylamines is actually a combination of 1:1 and 1:2 chemical absorption.41,44 However, CO2 absorption in imidazolium carboxylate ionic liquids is completely a result of 1:2 chemical absorption.43 Unfortunately, the theoretical curve represented by eq 26 deviates significantly from the experimental results of r vs h for CO2 absorption in imidazolium carboxylate ionic liquids. This deviation may arise from the improper assignment of ΔS° = −140 J/(K·mol) to eq 21. We had even calculated the reaction equilibrium constant K°and enthalpy change ΔH°of CO2 absorption in [emim][Ac], and the resulting values were 0.92 and −33.2 kJ/mol at T = 298.15 K.20 According to eq 1, ΔS° is thus calculated to be −112 J/(K·mol), which is different from the estimated value using the Campbell’s Rule.31−33 Therefore, eq 26 was modified by reassigning ΔS° = −112 J/(K·mol) to eq 21:

with the overestimation ratio of 0.1−0.2 for [P66614][Met] and [P66614][Pro] displayed in Region III. We further extended the variation curve of r vs ΔH° to a high temperature of T = 348.15 K, which is a typical temperature of flue gas. Although the derivation of eq 22 was based on the Campbell’s Rule,30−32 that ΔS° was estimated as −140 J/(K· mol) at 298.15 K, ΔS° can still be regarded as a constant within this small temperature deviation. As shown by the inset illustration in Figure 2, the sigmoid curve moves toward a more exothermic direction when the value of T increases from 298.15 K to 348.15 K, indicating that more exothermic chemical absorption is required to capture CO2 at high temperatures (ΔHef = −62.8 kJ/mol). Because of the absence of sufficient experimental data covering a wide range of ΔH° under such a condition, the reliability of using eq 22 to predict the relationship between r and ΔH° of 1:1 chemical absorption of CO2 at high temperatures remains to be validated. However, the distinctively sigmoid correlation for r and ΔH° is wellfounded regardless of the values of T, PGCO2, and ΔS°. As discussed above, the value of ΔHefis not independent of T and PGCO2, and different kinds of 1:1 chemical absorbents are required at different operation conditions. To set up a uniform criterion for the calculation of ΔHef, ΔHef can be expressed as a function of T and PGCO2 by setting the value of r to be 0.95 for eq 22: G ΔHef = 8.314T ln PCO − 164.5T 2

r=

(27)

G +1 4(e−h /8.314T − 112/8.314)PCO 2 G 8(e−h /8.314T − 112/8.314)PCO 2

−

1:2. Chemical Absorption. Similarly, we then investigated the relationship between gas solubility r and pseudo-enthalpy change h for 1:2 chemical absorption of CO2. At first, we used eq 26 to calculate the variation curve of r vs h at a standard state of T = 298.15 K and PGCO2 = 1 bar. As shown in Figure 3, r is also a distinctively sigmoid function of h, although eq 26 is different from that of eq 22. We summarized the reported values of r at T = 298.15 K and PGCO2 = 1 bar and the corresponding h values of various 1:2 chemical absorbents

G +1 8(e−h /8.314T − 112/8.314)PCO 2 G 8(e−h /8.314T − 112/8.314)PCO 2

(28)

The variation curve of r vs h was recalculated from eq 28, as shown in Figure 3. With the modification of the value of ΔS°, the recalculated curve agrees well with the experimental results. In the case of 1:2 chemical absorption, hr=0.025 mol/mol = −24.0 kJ/mol and hr=0.475 mol/mol = −45.9 kJ/mol were defined as the two demarcation points for Regions I, II, and III. Therefore, hef = −45.9 kJ/mol was designated as the criterion of energyefficient 1:2 chemical absorbents for CO2 capture at T = 298.15 K and PGCO2 = 1 bar. As shown in Figure 3, 50 wt % aqueous MEA and silylamines are highly energy-intensive absorbents for CO2 capture. However, new absorbents with optimized values of h still remain to be explored. Since h is a pseudo-property and is not the real absorption enthalpy ΔH°, it is essential to have a look at the relationship between h and ΔH°. According to eq 25, h equals ΔH° plus a correction term 8.314T ln MA. Most of the 1:2 chemical absorbents have a molecular weight (MA) of 0.1−0.5 kg/mol (see Table S3). Therefore, at a temperature of T = 298.15 K, the correction term 8.314T ln MA has a value of −5.7 to −1.7 kJ/mol. At the designated energy-efficient point hef = −45.9 kJ/ mol, it corresponds to ΔHef° = −40.2 to −44.2 kJ/mol. Obviously, ΔHef° deviates only slightly from hef. We then extended the variation curve of r vs h for 1:2 chemical absorption of CO2 to a low pressure by applying T = 298.15 K and PGCO2 = 0.15 bar to eq 28. As shown in Figure 4, the calculated curve agrees well with the experimental results. Similar to the case of 1:1 chemical absorption, the sigmoid curve moves toward a more exothermic direction when the value of PGCO2 decreases from 1 to 0.15 bar (see the inset illustration in Figure 4). As a result, absorbents of more exothermic chemical reaction with CO2 are required to capture low-pressure CO2 (hef = −50.5 kJ/mol or ΔHef° = −44.8 to −

Figure 3. Variation of gas solubility with pseudo-enthalpy change for CO2 absorption in 1:2 chemical absorbents at T = 298.15 K and PGCO2 = 1 bar (black dash line, theoretically calculated from eq 26; black solid line, theoretically calculated from eq 28; blue triangles, physical absorbents including normal organic solvents and ionic liquids; black squares, imidazolium carboxylate ionic liquids; red stars, nonaqueous silylamines; red circle, 50 wt % aqueous MEA). E


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5. The experimental data cited from literature were summarized in Tables S1−S3 in the Supporting Information. Totally, 59

Figure 4. Variation of gas solubility with pseudo-enthalpy change for CO2 absorption in 1:2 chemical absorbents at T = 298.15 K and PGCO2 = 0.15 bar (black solid line, theoretically calculated from eq 28; blue triangles, physical absorbents including normal organic solvents and ionic liquids; black squares, imidazolium carboxylate ionic liquids; red circle, 50 wt % aqueous MEA). Inset illustration: comparison of the variation curves of gas solubility vs pseudo-enthalpy change at different pressures and temperatures (red line, T = 298.15 K and PGCO2 = 1 bar; black line, T = 298.15 K and PGCO2 = 0.15 bar; blue line, T = 348.15 K and PGCO2 = 0.15 bar).

Figure 5. Comparison of the calculated gas solubility in this work vs experimental or calculated gas solubility in literature (see the Supporting Information for the references of literature data).

data points were used and the average absolute deviation (AAD) and average relative deviation (ARD) are 0.11 mol/mol and 27.9%, respectively. These prediction results are fairly acceptable considering the simplicity of the model equations derived in this work. It should be further noticed that the major purpose of eqs 22 and 28 is to demonstrate the variation trend of r vs ΔH° (or h). The variation curves of r vs ΔH° (or h) calculated by eqs 22 and 28 fit well with the experimental data (see Figures 1 to 4), thus demonstrating the sigmoid relationship between the two thermodynamic properties.

58.8 kJ/mol). The variation curve of r vs h was subsequently extended to higher temperature by applying T = 348.15 K and PGCO2 = 0.15 bar to eq 28. As shown by the inset illustration in Figure 4, the sigmoid curve moves toward a more exothermic direction when the value of T increases from 298.15 to 348.15 K, indicating that absorbents of more exothermic chemical reaction with CO2 are required to capture CO2 at high temperatures (hef = −58.9 kJ/molor ΔH°ef = −52.2 to − 56.9 kJ/mol). Similar to the case of ΔHef, the value of hef is also not independent of T and PGCO2, and different kinds of 1:2 chemical absorbents are required at different operation conditions. To set up a uniform criterion for the calculation of hef, hef can be expressed as a function of T and PGCO2 by setting the value of r to be 0.475 for eq 28: G hef = 8.314T ln PCO − 155.6T 2

■

CONCLUSIONS Equations that can directly describe the relationship between gas solubility and enthalpy change of chemical absorption of CO2 were theoretically derived. Based on these equations, the sigmoid correlations for gas solubility and enthalpy change were illustrated. Through analyzing the variation trend of gas solubility vs enthalpy change, 1:1 chemical absorbents with an absorption enthalpy of −49.1 kJ/mol and 1:2 chemical absorbents with a pseudo-absorption enthalpy of −45.9 kJ/mol were designated as the most suitable solvents for energyefficient capture of CO2 at 298.15 K and 1 bar. Decreasing pressure or increasing temperature requires absorbents of more exothermic chemical reaction with CO2. The results obtained in this work provide fundamental guidance for exploring energyefficient chemical absorbents for CO2 capture.

(29)

On the basis of the discussion above, if a chemical absorbent has an absorption enthalpy of ΔHef (or hef), it can be regarded as the energy-efficient chemical absorbent. From the sigmoid curves of r vs ΔH° (or h), it can be found that absorbents with absorption enthalpy smaller than ΔH ef (or h ef ) have significantly decreased gas solubility; however, absorbents with absorption enthalpy larger than ΔHef (or hef) do not have obviously superior gas solubility. Therefore, ΔHef (or hef) is the largest acceptable value of enthalpy change. This is the scientific meaning of “energy-efficient” chemical absorbents. Prediction of Gas Solubility. According to eqs 22 and (28), the solubility of CO2 in chemical absorbents can be predicted from enthalpy change. To present a comparison between the prediction results from this work and other works, we plotted the calculated gas solubility in this work vs experimental or calculated gas solubility from the literature, as shown in Figure

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.iecr.5b02145. Experimental gas solubility and enthalpy change of various liquid absorbents cited from literature (PDF)

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. F


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Industrial & Engineering Chemistry Research Notes

(17) Neveux, T.; Le Moullec, Y.; Corriou, J.; Favre, E. Modeling CO2 capture in amine solvents: Prediction of performance and insights on limiting phenomena. Ind. Eng. Chem. Res. 2013, 52, 4266−4279. (18) Arcis, H.; Coulier, Y.; Ballerat-Busserolles, K.; Rodier, L.; Coxam, J. Enthalpy of solution of CO2 in aqueous solutions of primary alkanolamines: A comparative study of hindered and nonhindered amine-based solvents. Ind. Eng. Chem. Res. 2014, 53, 10876−10885. (19) Rayer, A. V.; Henni, A. Heats of Absorption of CO2 in aqueous solutions of tertiary amines: N-Methyldiethanolamine, 3-dimethylamino-1-propanol, and 1-dimethylamino-2-propanol. Ind. Eng. Chem. Res. 2014, 53, 4953−4965. (20) Huang, K.; Cai, D.; Chen, Y.; Wu, Y.; Hu, X.; Zhang, Z. Thermodynamic validation of 1-alkyl-3-methylimidazolium carboxylates as task-specific ionic liquids for H2S absorption. AIChE J. 2013, 59, 2227−2235. (21) Huang, K.; Chen, Y.; Zhang, X.; Xia, S.; Wu, Y.; Hu, X. SO2 absorption in acid salt ionic liquids/sulfolane binary mixtures: Experimental study and thermodynamic analysis. Chem. Eng. J. 2014, 237, 478−486. (22) Zhang, X. P.; Zhang, X. C.; Dong, H. F.; Zhao, Z. J.; Zhang, S. J.; Huang, Y. Carbon capture with ionic liquids: Overview and progress. Energy Environ. Sci. 2012, 5, 6668−6681. (23) Wang, C. M.; Luo, X. Y.; Zhu, X.; Cui, G. K.; Jiang, D. E.; Deng, D. S.; Li, H. R.; Dai, S. The strategies for improving carbon dioxide chemisorption by functionalized ionic liquids. RSC Adv. 2013, 3, 15518−15527. (24) Islam, M. A.; Kalam, M. A.; Khan, M. R. Reactive gas solubility in water: An empirical relation. Ind. Eng. Chem. Res. 2000, 39, 2627− 2630. (25) Seo, S.; Quiroz-Guzman, M.; DeSilva, M. A.; Lee, T. B.; Huang, Y.; Goodrich, B. F.; Schneider, W. F.; Brennecke, J. F. Chemically tunable ionic liquids with aprotic heterocyclic anion (AHA) for CO2 capture. J. Phys. Chem. B 2014, 118, 5740−5751. (26) Goodrich, B. F.; de la Fuente, J. C.; Gurkan, B. E.; Lopez, Z. K.; Price, E. A.; Huang, Y.; Brennecke, J. F. Effect of water and temperature on absorption of CO2 by amine-functionalized aniontethered ionic liquids. J. Phys. Chem. B 2011, 115, 9140−9150. (27) Goodrich, B. F.; de la Fuente, J. C.; Gurkan, B. E.; Zadigian, D. J.; Price, E. A.; Huang, Y.; Brennecke, J. F. Experimental measurements of amine-functionalized anion-tethered ionic liquids with carbon dioxide. Ind. Eng. Chem. Res. 2011, 50, 111−118. (28) Bishnoi, S.; Rochelle, G. Physical and chemical solubility of carbon dioxide in aqueous methyldiethanolamine. Fluid Phase Equilib. 2000, 168, 241−258. (29) Wang, T.; Lackner, K. S.; Wright, A. B. Moisture-swing sorption for carbon dioxide capture from ambient air: a thermodynamic analysis. Phys. Chem. Chem. Phys. 2013, 15, 504−514. (30) Campbell, J. A. Le Chatelier’s principle, temperature effects and entropy. J. Chem. Educ. 1985, 62, 231−232. (31) Craig, N. C. Campbell’s rule for estimating entropy changes in gas-producing and gas-consuming reactions and related gerneralizations about entropies and enthalpies. J. Chem. Educ. 2003, 80, 1432− 1436. (32) Jensen, W. B. Campbell’s rule for estimating entropy changes. J. Chem. Educ. 2004, 81, 1570−1571. (33) Murrietaguevara, F.; Romeromartinez, A.; Trejo, A. Solubilities of carbon dioxide and hydrogen sulfide in propylene carbonate, Nmethylpyrolidone and sulfolane. Fluid Phase Equilib. 1988, 44, 105− 115. (34) Li, J.; Ye, Y. M.; Chen, L. F.; Qi, Z. W. Solubilities of CO2 in poly(ethylene glycols) from (303.15 to 333.15) K. J. Chem. Eng. Data 2012, 57, 610−616. (35) Anthony, J. L.; Anderson, J. L.; Maginn, E. J.; Brennecke, J. F. Anion effects on gas solubility in ionic liquids. J. Phys. Chem. B 2005, 109, 6366−6374. (36) Jou, F. Y.; Mather, A. E.; Otto, F. D. Solubility of H2S and CO2 in aqueous methyldiethanolamine solutions. Ind. Eng. Chem. Process Des. Dev. 1982, 21, 539−544.

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS S.D. was sponsored by the Division of Chemical Sciences, Geosciences, and Biosciences, Office of Basic Energy Sciences, U.S. Department of Energy, under Contract No. De-AC0500OR22725 with Oak Ridge National Laboratory managed and operated by UT-Battelle, LLC. Y.W. was supported by the National Natural Science Foundation of China under Agreement 21376115. K.H. acknowledges China Scholarship Council for partial financial support.

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REFERENCES

(1) Figueroa, J. D.; Fout, T.; Plasynski, S.; McIlvried, H.; Srivastava, R. D. Advances in CO2 capture technologyThe US Department of Energy’s carbon sequestration program. Int. J. Greenhouse Gas Control 2008, 2, 9−20. (2) MacDowell, N.; Florin, N.; Buchard, A.; Hallett, J.; Galindo, A.; Jackson, G.; Adjiman, C. S.; Williams, C. K.; Shah, N.; Fennell, P. An overview of CO2 capture technologies. Energy Environ. Sci. 2010, 3, 1645−1669. (3) Ramdin, M.; de Loos, T. W.; Vlugt, T. J. H. State-of-the-art of CO2 capture with ionic liquids. Ind. Eng. Chem. Res. 2012, 51, 8149− 8177. (4) Rochelle, G. T. Amine scrubbing for CO2 capture. Science 2009, 325, 1652−1654. (5) Goto, K.; Okabe, H.; Shimizu, S.; Onoda, M.; Fujioka, Y. Evaluation method of novel absorbents for CO2 capture. Energy Procedia 2009, 1, 1083−1089. (6) van Nierop, E. A.; Hormoz, S.; House, K. Z.; Aziz, M. J. Effect of absorption enthalpy on temperature-swing CO2 separation process performance. Energy Procedia 2011, 4, 1783−1790. (7) Wang, C.; Luo, X.; Luo, H.; Jiang, D.; Li, H.; Dai, S. Tuning the basicity of ionic liquids for equimolar CO2 capture. Angew. Chem., Int. Ed. 2011, 50, 4918−4922. (8) Wang, C.; Luo, H.; Li, H.; Zhu, X.; Yu, B.; Dai, S. Tuning the physicochemical properties of diverse phenolic ionic liquids for equimolar CO2 capture by the substituent on the anion. Chem. - Eur. J. 2012, 18, 2153−2160. (9) Deshmukh, R. D.; Mather, A. E. A mathematical model for equilibrium solubiity of hydrogen sulfide and carbon dioxide in aqueous alkanolamine solutions. Chem. Eng. Sci. 1981, 36, 355−362. (10) Benamor, A.; Aroua, M. K. Modeling of CO2 solubility and carbamate concentration in DEA, MDEA and their mixtures using the Deshmukh-Mather model. Fluid Phase Equilib. 2005, 231, 150−162. (11) Chakma, A.; Meisen, A. Solubility of CO2 in aqueous methyldiethanolamine and N,N-bis(hydroxyethyl)piperazine solutions. Ind. Eng. Chem. Res. 1987, 26, 2461−2466. (12) Silkenbaumer, D.; Rumpf, B.; Lichtenthaler, R. N. Solubility of carbon dioxide in aqueous solutions of 2-amino-2-methyl-1-propanol and N-methyldiethanolamine and their mixtures in the temperature range from 313 to 353 K and pressures up to 2.7 MPa. Ind. Eng. Chem. Res. 1998, 37, 3133−3141. (13) McCann, N.; Maeder, M.; Attalla, M. Simulation of enthalpy and capacity of CO2 absorption by aqueous amine systems. Ind. Eng. Chem. Res. 2008, 47, 2002−2009. (14) McCann, N.; Maeder, M.; Hasse, H. Prediction of the overall enthalpy of CO2 absorption in aqueous amine systems from experimentally determined reaction enthalpies. Energy Procedia 2011, 4, 1542−1549. (15) Bishnoi, S.; Rochelle, G. T. Thermodynamics of piperazine/ methyldiethanolamine/water/carbon dioxide. Ind. Eng. Chem. Res. 2002, 41, 604−612. (16) Vrachnos, A.; Kontogeorgis, G.; Voutsas, E. Thermodynamic modeling of acidic gas solubility in aqueous solutions of MEA, MDEA and MEA-MDEA blends. Ind. Eng. Chem. Res. 2006, 45, 5148−5154. G


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Industrial & Engineering Chemistry Research (37) Wang, C.; Luo, H.; Jiang, D.; Li, H.; Dai, S. Carbon dioxide capture by superbase-derived protic ionic liquids. Angew. Chem., Int. Ed. 2010, 49, 5978−5981. (38) Gurkan, B.; Goodrich, B. F.; Mindrup, E. M.; Ficke, L. E.; Massel, M.; Seo, S.; Senftle, T. P.; Wu, H.; Glaser, M. F.; Shah, J. K.; Maginn, E. J.; Brennecke, J. F.; Schneider, W. F. Molecular design of high capacity, low viscosity, chemically tunable ionic liquids for CO2 capture. J. Phys. Chem. Lett. 2010, 1, 3494−3499. (39) Gurkan, B. E.; de la Fuente, J. C.; Mindrup, E. M.; Ficke, L. E.; Goodrich, B. F.; Price, E. A.; Schneider, W. F.; Brennecke, J. F. Equimolar CO2 absorption by anion-functionalized ionic liquids. J. Am. Chem. Soc. 2010, 132, 2116−2117. (40) Brennecke, J. F.; Maginn, E. J. Ionic liquids: Innovative fluids for chemical processing. AIChE J. 2001, 47, 2384−2389. (41) Lee, J. I.; Otto, F. D.; Mather, A. E. Equilibrium between carbon dioxide and aqueous monoethanolamine solutions. J. Appl. Chem. Biotechnol. 1976, 26, 541−549. (42) Kim, I.; Svendsen, H. F. Heat of absorption of carbon dioxide (CO 2 ) in monoethanolamine (MEA) and 2-(aminoethyl)ethanolamine (AEEA) solutions. Ind. Eng. Chem. Res. 2007, 46, 5803−5809. (43) Yokozeki, A.; Shiflett, M. B.; Junk, C. P.; Grieco, L. M.; Foo, T. Physical and chemical absorptions of carbon dioxide in roomtemperature ionic liquids. J. Phys. Chem. B 2008, 112, 16654−16663. (44) Switzer, J. R.; Ethier, A. L.; Hart, E. C.; Flack, K. M.; Rumple, A. C.; Donaldson, J. C.; Bembry, A. T.; Scott, O. M.; Biddinger, E. J.; Talreja, M.; Song, M.; Pollet, P.; Eckert, C. A.; Liotta, C. L. Design, synthesis and evaluation of nonaqueous silylamines for efficient CO2 capture. ChemSusChem 2014, 7, 299−307.

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