New Approach for Absorbent Species Selection with Excess Gibbs

Article pubs.acs.org/IECR

New Approach for Absorbent Species Selection with Excess Gibbs Function Danxing Zheng,* Li Dong, and Xianghong Wu College of Chemical Engineering, Beijing University of Chemical Technology, Beijing 100029, China S Supporting Information *

ABSTRACT: Absorption capacities were analyzed based on 33 sets of vapor−liquid equilibrium literature data that focused on eight solute-based binary systems, namely, carbon dioxide, dimethyl ether, ethylene, difluoromethane, water, methane, 1,1,1,2tetrafluoroethane, and sulfur dioxide. The absorbents were classified into solvent type and ionic liquid type. The regularities of the excess Gibbs function (GE) of the binary systems were investigated by evaluating the macroscopic properties and the influence of intermolecular interactions between the solute and the absorbent based on the concept of local composition model. The extreme value (GEmax) and the absorption potential (ψi) were proposed as absorbent selection criteria. An evaluation method predicting the activity coefficient and evaluating the systems with GEmax and ψi through the UNIFAC model was established. Consequently, the validity study of the new approach for the eight solute-based binary systems was in agreement with previously assessed experimental behavior trends.

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been a hot research topic in physical chemistry. Wilhelm6 focused on the rigorous thermodynamic formalism relevant to vapor−liquid equilibrium (VLE) involving supercritical compounds and its rational implementation in determining the Henry coefficients and related quantities. The working pair of an absorption heat pump is composed of a refrigerant and an absorbent. Water (H2O) is generally chosen as a refrigerant for air conditioning, which is highly latent heat, natural, easily available, and inexpensive. And environmentally friendly hydrofluorocarbon (HFC) as refrigerant, such as difluoromethane (R32), 1,1,1,2-tetrafluoroethane (R134a), combined with appropriate absorbents, can be adopted as working pair for absorption cycles, which can be used in numerous applications, such as heat pump, air conditioner, and refrigeration driving by low-grade heat. Investigations on novel working pairs have shown great progress in the recent decade. Some scholars determined the effect of the thermodynamic characteristics of the solvent, such as the activity coefficient, the heat of dilution, and other key aspects. The activity coefficient of the solvent determines the decrease in vapor pressure over the solution; hence, it is the main reason for the deviation of pressure from Raoult’s law. The activity coefficients are smaller than unity, indicating the nonideal behavior and the increasing attractive forces in the liquid. Iedema7 presented the effects of key mixture properties to determine the absorption heat pump performance and described the ratio of the enthalpies of dilution and evaporation, their absolute values, the deviation from Raoult’s Law, and the operating pressure. Morrissey et al.8 proposed that a solution exhibiting a positive heat has a relatively low heat of

INTRODUCTION Absorption or gas sweetening is an important gas processing technology widely used in many engineering processes, such as low-carbon chemical productions and polluted gas removal, as well as in new energy-utilization technologies, such as carbon dioxide (CO2) absorption capture,1 ethylene (C2H4) absorption in natural gas-based oxidative coupling of methane (CH4) processing,2 and separation of products from coal-based onestep dimethyl ether (DME) synthesis.3 Energy resources have prompted increased efforts to develop a process to produce liquid fuel alternatives, such as those from coal. During the initial stages of coal dissolution in a coal-derived recycle solvent, various light gases are produced, such as CH4, CO2, sulfur dioxide (SO2), and so on. The phase behaviors of gas in liquid are required in the effective design and operation of absorption separation processes. Studies of the gas solubility in liquid are also of interest in the processing of petroleum products, CO2 removal, desulfuration, enhanced oil recovery, and supercritical fluid processes.4 Low-grade heat recovery has been used to advance absorption heat pumps and develop energy-cascade utilization and zero emission systems for an energy efficient and environmentally friendly society.5 The development of advanced absorbents is crucial in the progress of absorption separation technology. High-performance absorbents improve production capacity and significantly reduce power consumption and product costs. Since the 1980s, these absorbents have been selected for gas absorption processes with high efficiency and low energy consumption.6−15 Gas solubility in liquid is commonly used to evaluate the affinity between the solute and the absorbent. Generally, if the partial pressure of the solute is relatively lower at the absorption temperature and if the partial pressure is relatively higher at the desorption temperature, the absorbent exhibits better absorption capacity on the solute. In addition, the solute, which has similar solubility parameters as the absorbent, usually possesses higher solubility in the absorbent. Gas solubility in liquid has © 2013 American Chemical Society

Received: Revised: Accepted: Published: 9480

March 14, 2013 June 13, 2013 June 19, 2013 June 19, 2013 dx.doi.org/10.1021/ie400826s | Ind. Eng. Chem. Res. 2013, 52, 9480−9489

Industrial & Engineering Chemistry Research

Article

pairs that contain ionic liquids (ILs). The γi∞ combined with the UNIFAC method was adopted as evaluation criteria for the selection of novel working pairs. The investigation was based on the solubility data of 18 HFC+IL binary systems obtained from the combination of 9 HFCs and 8 ILs. This study aims to reveal the theoretical fundamentals of using GE as thermodynamic criterion and to establish a new method for novel absorbent selection. The investigation is based on the literature data of 33 systems, which are the combinations of CO2, DME, C2H4, R32, H2O, CH4, R134a, and SO2 with different absorbents. The characteristics and regularities of the GE of the systems were studied, including the association between system macroscopic properties and microscopic thermodynamic descriptions. The influence of their interactions on VLE behavior was studied. To validate the new approach, the eight solute-based absorption systems were assessed.

hydration. Ions in solution are less hydrated with a greater tendency to escape from the solution, thereby increasing the vapor pressure. Investigating the interaction between the refrigerant and the absorbent and considering the influence of mixture properties are necessary to establish methods for the evaluation of absorption cycle working pairs. Full understanding of the nature and magnitude of excess properties is mandatory. Mixture properties can be characterized by the excess Gibbs function (GE) of the system. On the basis of this theory, Narodoslawsky et al.9,10 established criteria for selecting working pairs and proposed that compatible working pairs show high heat of evaporation for the refrigerant and highly negative extreme value of the excess Gibbs function (GEmax). Kernen et al.11 considered that a positive separation behavior and a low vapor pressure in an absorber are due to the large temperature dependence of GE because low activity coefficients at absorber temperatures require highly negative GE values. At generator conditions, GE must be positive to ensure separation. Thus, GE must increase sharply as the temperature increases. In our previous work, we improved the criterion of GEmax for working pair selection and pointed out that GEmax is an essential factor describing the absorption cycle performance for the evaluation of new working pairs. We modified Morrissey and Odonnell’s assertion and proposed that systems showing negative deviation from Raoult’s law are valid within an appropriate range, that one or several systems exist, and that the performance of these systems is better than that of others.12,13 Compared with traditional tentative working pair selection method, the method associated GE with the absorption cycle characteristic, is able to do computer simulation analysis, targeted, less work, and easy to carry out extensive screening. The new method can expand the scope of evaluation in maximum and get suitable working pairs in large numbers of possible combinations in the lack of experimental data. When the new criterion was adopted, the UNIFAC model is used to estimate and predict the GEmax and the infinite dilution activity coefficient (γi∞). GE, together with some quantitative understanding of the rating scale, has been proposed as an evaluation tool. Tufano14 suggested that the working pairs for absorption are negative deviation systems, that the GE of the negative deviation system is less than 0, and that the activity coefficient is less than 1. Nonideal pairs show attraction in the liquid phase, i.e., the activity coefficients are smaller than unity and the negative excess enthalpies of solution must be considered. Morrissey and Narodoslawsky8,9 successively presented that a strong nonideality with a GE extreme between −1000 and −2000 J mol−1 at high refrigerant concentrations is usually recommended for good absorption heat pump performance. Zheng et al.13 evaluated various working pairs using GE criteria, including water+triethylene glycol, water+glycerol, water+diethylene glycol, water+glycol, and water+sulfolane systems. Zehioua et al.15 predicted the Gibbs energy of working pairs, including water+mono-, di-, and triethylene glycol, water +glycerol, and ethanol+di- and triethylene glycol mixtures, and adopted it as a preliminary evaluation of the suitability of the binary systems. In recent years, we have adopted the GE evaluation method to select absorbents for DME absorption, C2H4 absorption, and CO2 capture, and to evaluate the absorption cycle working pairs of H2O, NH3, and HFC as refrigerants.16−27 Dong et al.28 extended the GE criterion to evaluate absorption cycle working

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BASIC VLE BEHAVIOR OF THE ABSORPTION SYSTEMS CO2, DME, C2H4, R32, H2O, CH4, R134a, and SO2 were selected as solute-based binary absorption systems. In accordance with the VLE data of relevant systems, 33 sets of isothermal VLE data for binary systems were collected.21,23,26,27,29−51 The eight solute-based binary absorption systems were classified as solutes (CO2, DME, C2H4, CH4, and SO2) and refrigerants (R32, H2O, and R134a). The solutes were based on the absorption process technology, whereas the refrigerants were applied in the absorption heat pump technology. The absorption capacities of the different absorbents on solutes were further analyzed by comparing their phase equilibrium ratios using the experimental data gathered at similar pressure and temperature conditions. The VLE data for various binary systems are listed in Supporting Information Table S1. The first column lists CO2, DME, C2H4, R32, H2O, CH4, R134a, and SO2 as solutes (1), and the second column lists the absorbents paired with various solutes (2). For example, the solute CO2 has five solute-based binary absorption systems, namely, CO2+H2O, CO2+methanol, CO2+ethanol, CO2+diisopropyl ether, and CO2+butyl ether. ILs such as [BMIM]PF6, [BMIM]BF4, [BMIM]OTf, [EMIM]Tf2N, etc. were selected as absorbents to evaluate R32 and H2O as solutes. Table S1 also gives the temperatures from the cited literature, the compared pressures, and the corresponding phase equilibrium ratios. The sequence numbers of the cited literatures are listed in the last column. For comparison purposes, the isothermal VLE data of each system were noted at an approximate temperature, taking into consideration the significant influence of temperature on VLE behavior. For example, data collection for the binary systems containing CO2 and DME took place from 298.15 to 304.20 K and from 348.55 to 353.15 K, respectively. Based on the experimental data obtained from the literature, the p−xi diagrams of the systems are plotted in Figures 1−8. The corresponding composition was taken at similar temperature and pressure conditions, and the phase equilibrium ratio yi/xi was calculated (Table S1, Supporting Information). For example, data collection for the binary systems containing CO2 took place from 2.483 to 3.750 MPa. For the sake of clarity, the appropriate dashed lines were marked in Figures 1−8. As shown in Figures 1−8, the different binary absorption systems containing the same gas solute but different absorbents 9481

dx.doi.org/10.1021/ie400826s | Ind. Eng. Chem. Res. 2013, 52, 9480−9489


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Figure 1. Isothermal p−xi diagram for CO2 and various absorbents. ■, H2O; □, Methanol; ▲, Ethanol; △, Diisopropyl ether; ●, Butyl ether.

Figure 5. Isothermal p−xi diagram for H2O and various absorbents. ■, [EMIM]OTf; □, [EMIM]EtSO4; ▲, [DMIM]BF4; △, [DMIM]DMP.

Figure 6. Isothermal p−xi diagram for CH4 and various absorbents. ■, Ethylene glycol; □, Aniline; ▲, Benzene; △, Dodecane.

Figure 2. Isothermal p−xi diagram for DME and various absorbents. ■, H2O; □, Methanol; ▲, Ethanol; △, 2-Propanol.

Figure 7. Isothermal p−xi diagram for R134a and various absorbents. ■, DMF; □, DMEMEG; ▲, DMEDEG; △, DMETrEG.

Figure 3. Isothermal p−xi diagram for C2H4 and various absorbents. ■, Benzene; □, Toluene; ▲, Mesitylene.

Figure 8. Isothermal p−xi diagram for SO2 and various absorbents. ■, Chloroform; □, Toluene; ▲, m-Xylene; △, Mesitylene; ●, Acetone.

Figure 4. Isothermal p−xi diagram for R32 and various absorbents. ■, [BMIM]BF4; □, [BMIM]OTf; ▲, [BMIM]PF6; △, [EMIM]Tf2N.

exhibit different behaviors, especially those with large differences in molecular structure. For example, the p−xi relationship curve of the CO2+H2O system is very steep, as shown in Figure 1. The p−xi relationship curves of the CO2+methanol and CO2+ethanol systems and of the CO2+diisopropyl ether and CO2+butyl ether systems are different. According to the difference in basic molecular structure of the groups, these

systems can be divided into two sets: alcohol and ether. As shown in Figures 2−8, the solute-based binary absorption systems with DME, C2H4, R32, H2O, CH4, R134a, and SO2 as solutes have similar expressions. The differences between the R32- and R134a-based systems are less obvious than those between other systems. 9482



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where yi and γi denote the vapor-phase mole fraction and the activity coefficient of the species i, respectively, and p is the system pressure. On the basis of eqs 1 and 2, the deviation between the real partial pressure and the Raoult’s law partial pressure at the system temperature can be expressed by the activity coefficient γi of the species i as

For the same type of system, at the appropriate pressure level, the closer to the right-hand the curve is, the more solutes in the liquid phase it represents (i.e., higher solubility). For instance, in the CO2-based systems (Figure 1), the CO2+butyl ether system can dissolve more CO2 than the CO2+H2O system. In addition, Supporting Information Table S1 shows that the phase equilibrium ratio of the CO2+butyl ether system (1.996) is significantly less than that of the CO2+H2O system (73.746). As shown in Figures 2−8, the solute-based absorption systems with DME, C2H4, R32, H2O, CH4, R134a, and SO2 as solutes demonstrate similar differences in solubility. Although the first three cations [BMIM]+ have one more ethyl group in the side chain than the last cation [EMIM]+, the solubilities still increase in accordance with the anions, following the order [BF4]−, [OTf]−, [PF6]−, and [Tf2N]− (Figure 4). For the CO2-based systems (Supporting Information Table S1), the phase equilibrium ratio of the CO2+butyl ether system is low, indicating that the absorption capacity of butyl ether on CO2 is relatively stronger. For the systems with DME, C2H4, R32, H2O, CH4, R134a, and SO2 as solutes, the phase equilibrium ratio values of the DME+2-propanol, C2H4+mesitylene, R32+[EMIM]Tf2N, H2O+[DMIM]DMP, CH4+dodecane, R134a+DMETrEG, and SO2+acetone systems are relatively smaller. This finding suggests that 2-propanol, mesitylene, [EMIM]Tf2N, [DMIM]DMP, dodecane, DMETrEG, and acetone have better absorption capacities than other absorbents on DME, C2H4, R32, H2O, CH4, R134a, and SO2, respectively. Based on the aforementioned data and diagram analyses, the different absorption characteristics of the absorbents can be observed by comparing their phase equilibrium ratios at given pressures. However, the evaluation method is restricted by the accuracy of experimental data, the test range, the number of experimental points, etc. Evaluating the absorption capacities of absorbents without experimental data is difficult. The different gas solubilities in different solvents depend on intermolecular interaction. Moreover, the thermodynamic properties of the systems can reflect the energy of intermolecular interaction, implying the possibility of using thermodynamic properties to predict the solubility characteristics of the gas in different solvents.

[pi − piRL (T )]/piRL (T ) = γi − 1 (i = 1, 2...N )

Therefore, the system behavior shows positive deviation from Raoult’s law when the value of γi is greater than 1, the system behavior shows negative deviation from Raoult’s law when γi is less than 1, and the system is regarded as an ideal mixture when γi is equal to 1. Under a lower pressure range, liquid mixtures show a positive or negative deviation from Raoult’s law depending on the value of γi. In the view of vapor pressure criterion for selecting absorption cycle working pairs, the systems with strong absorption capacities are usually classified as those that exhibit negative deviation from Raoult’s law. Morrissey7 found that working pairs exhibiting highly negative deviation from Raoult’s law give the best result. The solvent vapor pressure descends as the affinity of the solvent molecules in the liquid phase to the solute molecules increases. As a result, the liquid phase from the ideal mixtures shows a negative deviation, with γi values less than 1. Furthermore, in a VLE system composed of N species at higher pressure, the partial molar Gibbs functions of the species i in gas phase and in liquid phase are equal.52 Gi̅ v(T , p , y̲ ) = Gi̅ l(T , p , x̲ ) (i = 1, 2...N )

G̅ vi (T,

v

∧

v yp (T , p , y̲ ) = xiγipisat (T )ϕisat(T )exp{Vil(T )[p − pisat (T )] i i

/(RT )} (i = 1, 2...N )

ϕvi (T,

pi = yp = i

(i = 1, 2...N )

(6)

ϕsat i (T)

where p, y)̲ and are the values of the fugacity coefficient in gas phase and saturated liquid or saturated vapor at the system temperature, and Vli(T) expresses the molar volume of saturated liquid at the system temperature. The phase equilibrium ratio of the species i is given as

(1)

sat where pRL i (T) is the partial pressure of species i, xi and pi (T) denote the liquid-phase mole fraction and the saturated vapor pressure of species i at the system temperature T, respectively. In a p−x(y) diagram, eq 1 appears as a straight line. The p− x(y) curve of the nonideal mixtures displaying positive deviation from Raoult’s law falls above the line, whereas the p−x(y) curve of the nonideal mixtures showing negative deviation from Raoult’s law falls below the line. Under a lower pressure range, the partial vapor pressure of a nonideal system species i at the system temperature T is expressed as

xiγipisat (T )

l

fi ̂ (T , p , y̲ ) = fi ̂ (T , p , x̲ ) (i = 1, 2...N ) (5) v̂ l̂ where fi (T, p, y)̲ and fi(T, p, x̲) are the vapor-phase and liquidphase fugacity of the species i, respectively. Generally, eq 5 can be expressed by the fugacity coefficient and the activity coefficient as

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(i = 1, 2...N )

(4)

G̅ li(T,

where p, y)̲ and p, x̲) are the vapor-phase and liquid-phase partial molar Gibbs functions of the species i, respectively. Equation 4 can be rewritten as

THERMODYNAMIC CRITERIA FOR ABSORBENT SELECTION The partial pressure of Raoult’s law used for describing the VLE behavior of any species i in an ideal liquid mixtures is piRL (T ) = xipisat (T )

(3)

K i ≡ yi /xi = γipisat (T )ϕisat(T )exp{Vil(T )[p − pisat (T )] ∧

/(RT )}/[pϕiv(T , p , y̲ )] (i = 1, 2...N )

(7)

The absorption factor is commonly used in the analysis of the absorption. The absorption factor of the species i is defined as Ai ≡ L /(K iV ) (i = 1, 2...N )

(8)

where L and V are the liquid and gas flow rates for an absorption unit, respectively. The value of Ai considers the gas flow rate, liquid flow rate, and VLE relations in the absorption

(2) 9483



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unit. Under a constant value of L/V, the smaller the Ki of the species i is, the more conducive the absorption of the species i will be. As shown in eqs 7 and 8, at given temperature and pressure conditions, the values of γi and Ki are both smaller, thereby giving a greater value of Ai. Therefore, at given temperature and pressure conditions, smaller γi is more beneficial for species i enrichment in liquid phase, i.e., it is more conducive to the species i being absorbed. Closely associated with γi, the excess Gibbs function GE describes the deviation of multispecies systems from the ideal mixtures.

GE ≡ G − Gid

is less than 0 (i.e., negative), indicating that the affinity between species is relatively stronger. Thus, for a binary system at given temperature and pressure conditions, negative GE is beneficial for solute absorption. The more negative the value of GE is, the better the absorption effect will be. At given temperature and pressure conditions, GE is a continuous function of system composition that may exist at more than one extreme point. The extreme point of GE is the characteristic of the thermodynamic properties of the system. Therefore, this work proposes that the extreme point of GE be presented as a selection criterion for evaluating suitable absorbents for gas absorption. In other words, at given temperature and pressure conditions, the more negative the value of the extreme point of GE for the solute-absorbent binary system is, the stronger the absorption capacity of the absorbent will be. On the other hand, Kolbe et al.55 proposed to select the extractant for extraction separation using the selectivity at the infinite dilution S∞ ij , which is defined as

(9)

where G and Gid are the actual Gibbs function value of a solution and the value it would have as an ideal solution at the same temperature, pressure, and composition, respectively. In addition, ln γi can be regarded as the partial molar property of the dimensionless value GE/RT. ⎡ ∂(nGE) ⎤ ln γi = ⎢ (i = 1, 2...N ) ⎥ ⎣ ∂ni ⎦ p , T , n j

Sij∞ ≡

(10)

GE has the summation relationship. N

GE =

⎡ ∂(nG ) ⎤ ⎥ ⎣ ∂ni ⎦

∑ xi⎢ i=1

i=1

(11)

According to the Flory-Huggins equation, the GE of the binary system can be expressed as53 ⎛ ϕ ϕ ⎞ GE = −TS E = RT ⎜x1ln 1 + x 2 ln 2 ⎟ x1 x2 ⎠ ⎝

ψ1 ≡

(12)

where SE is the excess entropy, ϕ1 and ϕ2 are the volume fractions of species 1 and 2, respectively, which are defined as ϕi ≡ xiVil(T )/∑ xiVil(T ) (i = 1, 2) i

1 γ1∞

(17)

where ψ1 denotes the absorption potential, is the infinite dilution activity coefficient of a solute (1) in a binary system. At given temperature and pressure conditions, γ1 is smaller, which is more beneficial for solute enrichment in liquid phase. Therefore, at given temperature and pressure conditions, if γ∞ 1 is smaller or if ψ1 is larger, more solutes are absorbed by the absorbent. ψ1 is proposed as the other absorbent selection criterion for gas absorption. At given temperature and pressure conditions, the larger the ψ1 is, the stronger the absorption capacity of the absorbent will be. The criterion based on the analysis of the extreme point of GE is called “the criterion of minimum extreme value of the GE−x relationship,” whereas that based on the analysis of the absorption potential of solute is called “the criterion of maximum value of the absorption potential.” Both criteria are necessary to evaluate the solute binary system. The former criterion is a macroscopic trend analysis based on relatively more data points, whereas the latter criterion is a local state view requiring only a small amount of data. In the case pressed for available VLE data, the latter criterion may be more convenient. However, the combination of the two methods can obtain more comprehensive evaluation conclusions. In addition, for the criterion of minimum extreme value of the GE−x relationship, the absolute value of the minimum extreme value of GE is commonly marked as GEmax.

(13)

ξii ≡ xiiVil(T )/∑ xjiV jl(T ) (i = 1, 2) (14)

The xi in eq 13, which expresses the macro-composition mole fraction of the species i, is replaced by the local mole fraction xji, which denotes the microstructural composition of a different molecule, and the volume fraction ϕi is replaced by the local volume fraction ξii. Thus, GE can be written as ⎛ ξ ξ ⎞ GE = RT ⎜x1ln 11 + x 2 ln 22 ⎟ x1 x2 ⎠ ⎝

(16)

γ∞ 1

where V1 and V2 are the liquid molar volumes of species 1 and 2, respectively. On the basis of the concept of local composition, Wilson54 defined the local volume fraction ξii. j

(i = 1, 2...N ; j = 1, 2...M )

where is the infinite dilution activity coefficient of the species i in a binary system composed of the species i and extractant. Similarly, γj∞ is the infinite dilution activity coefficient of the species j. However, S∞ ij cannot be used to select the absorbent for gas absorption separation because no extractant acts as the third species in the process. We can extend this definition to gas absorption and define the absorption potential as

= RT ∑ xi ln γi p , T , nj

γj∞

γ∞ i

N

E

γi∞

(15)

Therefore, when the attraction between different molecules is stronger than that between the same molecules, there is x11 < x1, x22 < x2. Namely, due to more different molecules around molecules 1 and 2, the microscopic composition of the same molecular is smaller than the macroscopic composition. If the molar volumes are approximately V1 ≈ V2, then ξ11 ≈ x11 and ξ22 ≈ x22. That is, ξ22 < x2, which makes the value of GE negative. Therefore, when the attraction between different molecules is stronger than that between the same molecules, GE

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TOOL AND METHOD VALIDATION The activity coefficients of interested systems are the basic information for using the aforementioned thermodynamic 9484



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series of data points are calculated using the aforementioned method. Then, γ1∞ can be obtained by extrapolating the γ1−x relationship to the zero concentration of the solute, whereas γ1−x exhibits a linear relationship. For example, the GE and the γ1 of the seven solute-based absorption systems with CO2, DME, C2H4, R32, H2O, CH4, and R134a as solutes was calculated using the UNIFAC model at the corresponding temperature. The values of the GE and the γ1 for SO2 system were obtained from literature.51 The parameters of UNIFAC model used in the Aspen Plus software were used in this work for CO2, DME, C2H4, CH4, and R134a systems. And for R32 and H2O systems the parameters came from our previous related works.28,62 The results of GEmax and ψ1 are listed in Supporting Information Table S2, which corresponds to Supporting Information Table S1. Among the CO2-based absorption systems with H2O, methanol, ethanol, diisopropyl ether, and butyl ether as absorbents, the CO2+butyl ether binary system has the lowest GEmax and γ∞ 1 , and the highest ψ1 (Table S2, Supporting Information). The absorbent selection criteria indicate that among the absorbents used, butyl ether has the strongest absorption capacity toward CO2. Among the DME-based absorption systems with H2O, methanol, ethanol, and 2-propanol as absorbents, the DME +2-propanol binary system has the lowest GEmax and γ∞ 1 , and the highest ψ1. This result indicates that 2-propanol has the strongest absorption capacity toward DME. Among the C2H4based absorption systems, the C2H4+mesitylene binary system has the lowest GEmax and γ∞ 1 , and the highest ψ1. This finding suggests that mesitylene has the strongest absorption capacity toward C2H4. Among the R32-based absorption systems with IL absorbents of [BMIM]PF6, [BMIM]BF4, [BMIM]OTf, and [EMIM]Tf2N, the R32+[EMIM]Tf2N binary system has the lowest GEmax and γ∞ 1 , and the highest ψ1. This result shows that [EMIM]Tf2N has the strongest absorption capacity toward R32. Compared with the other absorbents, [DMIM]DMP, dodecane, DMETrEG, and acetone show stronger absorption capacities toward H2O, CH4, R134a, and SO2, respectively. Compared the calculated data in Supporting Information Table S2 with the experimental data in Supporting Information Table S1, we found that the predicted values of GEmax and ψ1 are similar to the experimental values of Ki obtained from the literature. The assessment results obtained through the GEmax and ψ1 of the system are in essential agreement with the experimental data analysis. In addition, the GE−x relationships are respectively plotted in Figures 9−16, which correspond to Figures 1−8. The behavior differences of each system are significant and regular. As shown

criteria. In the absence of experimental data on phase equilibrium, the UNIFAC method is currently widely used in predicting the liquid phase activity coefficient, GE, and γ∞ i for binary or multi-species systems. The size and binary interaction parameters are available for different types of functional groups.56−59 An original UNIFAC model that combines the functional group concept with a model for activity coefficients based on an extension of the quasi-chemical theory of liquid mixtures (UNIQUAC) was proposed by Fredenalund et al.60 in 1975. The model is shown in eq 18.61

ln γi = ln γiC + ln γi R

(18)

γCi

where is the combinatorial contribution to the activity coefficient and γRi is the residual contribution. The former is essentially due to differences in size and shape of the molecules, whereas the latter is essentially due to energetic interactions. For the combinatorial part, the equation is ln γiC = 1 − Vi + ln Vi − 5qi[1 − Vi /Fi + ln(Vi /Fi )] (19)

Fi = qi /∑ qixiVi = ri /∑ rx i i

(20)

The pure species parameters ri and qi are relative to molecular van der Waal’s volumes and molecular surface areas, respectively. These parameters were respectively calculated as the sum of the group volume and group area parameters Rk and Qk: rk =

∑ vk(i)R kqk = ∑ vk(i)Q k k

(21)

k

where ν(i) is an integer number of the group k in the k component i. The residual part was calculated as follows: ln γi R =

∑ vk(i)[ln Γk − ln Γ(ki)]

(22)

k

where Γk denotes the group residual activity coefficient, and Γ(i) k is the residual activity coefficient of the group k in the reference solution containing only the component i. These parameters can be expressed as ln Γk = Q k[1 − ln(∑ θmφmk ) − m

∑ (θmφkm/∑ θnφnm)] m

n

(23)

θm = Q mX m/∑ Q nX nX m =

∑ vm(i)xi/(∑ ∑ vk(i)xi) i

i

k

(24)

where Xm is the fraction of the group m in the mixture. And the parameter φnm of eq 23 can be expressed as φnm = exp[− (anm /T )]

(25)

The parameter anm characterizes the interaction between the groups n and m. For each group−group interaction, there are parameters anm ≠ amn. For the evaluation of binary systems, selecting the appropriate temperature and using the UNIFAC model to calculate the activity coefficient are necessary. The Gibbs function and composition of the system can be obtained from eq 11. As a result, GEmax can also be obtained by appraising the GE−x relationship. The value of γ1∞ is needed to calculate ψ1. In the range of low concentrations, the activity coefficients of a

Figure 9. GE−xCO2 for CO2 systems at 298.15 K. ■, H2O; □, Methanol; ▲, Ethanol; △, Diisopropyl ether; ●, Butyl ether. 9485



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in Figure 9, the GE−x curve of the CO2+H2O system significantly displays in the positive region. It gradually varies from the CO2+H2O system to the CO2+ethanol system. The GE−x curve of the CO2+butyl ether system is the most negative. As shown in Figure 10, all the systems show positive

Figure 13. GE−xH2O for H2O systems at 323.15 K. ■, [EMIM]OTf; □, [EMIM]EtSO4; ▲, [DMIM]BF4; △, [DMIM]DMP.

Figure 10. GE−xDME for DME systems at 353.15 K. ■, H2O; □, Methanol; ▲, Ethanol; △, 2-Propanol.

deviation. However, the DME+2-propanol system is relatively lower. The differences of the three systems in Figure 11 are evident, and the GE−x curve of the C2H4+mesitylene is the most negative. Figure 14. GE−xCH4 for CH4 systems at 323.20 K. ■, Ethylene glycol; □,

Aniline;

▲,

Benzene;

△,

Dodecane.

Figure 11. GE−xC2H4 for C2H4 systems at 333.15 K. ■, Benzene; □, Toluene; ▲, Mesitylene. Figure 15. GE−xR134a for R134a systems at 303.15 K. ■, DMF; □, DMEMEG; ▲, DMEDEG; △, DMETrEG.

The curves in Figure 12 are particularly different, except for the R32+[BMIM]OTf system. The other three systems are

GE values of the four systems are also negative, with the R134a +DMETrEG system having the lowest value. As shown in Figure 16, the GE−x curve of the SO2+chloroform system is positive, whereas that of the SO2+acetone system is the most negative. The GE values of the SO2+toluene, SO2+m-xylene, and SO2+mesitylene systems are close.

Figure 12. GE−xR32 for R32 systems at 298.20 K. ■, [BMIM]BF4; □, [BMIM]OTf; ▲, [BMIM]PF6; △, [EMIM]Tf2N.

shown as negative. The R32+[BMIM]OTf system before and after the R32 mol fraction of approximately 0.83 is initially negative and then turned into positive. In Figure 13, the GE values of the four systems are all negative, and the GEmax value of the H2O+[DMIM]DMP system is the lowest. As shown in Figure 14, the GE−x curve of the CH4+dodecane system exhibits the most negative deviation. As shown in Figure 15, the

Figure 16. GE−xSO2 for SO2 systems at 227.60K. ■, Chloroform; □, Toluene; ▲, m-Xylene; △, Mesitylene; ●, Acetone. 9486



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given temperature and pressure conditions, the greater the ψ1 value is, the stronger the absorption capacity of the absorbent will be. A theoretical evaluation method for suitable absorbent selection, without depending on the experiments, was established. This thermodynamic method uses the UNIFAC model to predict the activity coefficient and determine the absorption characteristics of the system based on GEmax and ψ1. Therefore, the 33 systems were verified and calculated with the new approach. The results indicated that butyl ether, 2propanol, mesitylene, [EMIM]Tf2N, [DMIM]DMP, dodecane, DMETrEG, and acetone showed relatively perfect absorption characteristics for CO2, DME, C2H4, R32, H2O, CH4, R134a, and SO2, respectively. The results are in essential agreement with the assessed VLE behavior trends of the literature data, thereby proving the effectiveness of the new approach.

Based on the GE−x analysis of the eight solute-based absorption systems (Figures 9−16), a system showing the most extreme has relatively optimal absorption capacity. The validation studies show that the state analysis method is based on “the criterion of maximum value of the absorption potential” and that the trend analysis method is based on “the criterion of minimum extreme value of the GE−x relationship.” The combination of the two methods gives comprehensive evaluation conclusions. Morrissey and Narodoslawsky8,9 proposed that a strong nonideality system should possess GEmax values between −1000 and −2000 J mol−1. However, the GEmax values of the example systems listed in Supporting Information Table S2 range from 933.06 to −4852.14 J mol−1. Evidently, the study results of some systems in this work have gone beyond the value restriction. Almost all of the systems to be evaluated exhibit deficiencies in absorption capacity. However, the values of GEmax to achieve a very low level for some binary systems cannot be ruled out. Thus, the absorption processes of the system are simple, whereas the desorption processes are complex (e.g., the wellknown ammonia+H2O system). Alternatively, the absorption processes of the system are easy, but the desorption processes are not difficult (e.g., the system H2O+[DMIM]DMP with a GEmax value of −4852.14 J mol−1). Our primary studies for advanced absorbent selection involved systems with inadequate absorption capacities. However, trade-off is not the study target. Further studies should be conducted to improve the absorbent selection criteria proposed in the present study. The validation study for the new approach proposed in this work is based on the limited literature data and the specified calculation method of the activity coefficient. Further validation studies for extensive systems are expected. The applicability of the UNIFAC model for the evaluation system affects the conclusion. Future research can attempt other methods to determine the activity coefficient. However, these developing works should not influence the reasonability of the new approach essentially.

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ASSOCIATED CONTENT

* Supporting Information S

The VLE data, the ψ1 and GEmax for the solute CO2, DME, C2H4, R32, H2O, CH4, R134a, and SO2 binary systems are supported in the Supporting Information Table S1 and S2. This material is available free of charge via the Internet at http:// pubs.acs.org.

■

AUTHOR INFORMATION

Corresponding Author

*Tel. and Fax: +86-10-6441-6406. E-mail: [email protected]. cn. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS The support provided by the National Natural Science Foundation of China (No. 50890184, 51276010) and the National Basic Research Program of China (No. 2010CB227304) for the completion of the present work is gratefully acknowledged.

■

■

CONCLUSION In this paper, eight solute-based binary absorption systems were selected, namely, CO2, DME, C2H4, R32, H2O, CH4, R134a, and SO2. The VLE behavior of the absorption features was compared and analyzed based on the 33 sets of literature data. The p−xi relationships exhibit different regular changes because of the structural differences of molecular basic groups and the different substances. The comparison of phase equilibrium ratio at a given pressure further demonstrates the different absorption characteristics of the different systems. The characteristics and the regularity of the Gibbs function of the system in the gas absorption process were investigated. The influences of the activity coefficient on the absorption characteristics were analyzed based on the association of the macroscopic properties, such as the activity coefficient, the phase equilibrium ratio, and the absorption factor of the solutes. Based on the local composition concept GE model, negative GE indicates that the affinity between the molecules is relatively strong. GEmax was proposed as an absorbent selection criterion of gas absorption: the smaller the GEmax of the soluteabsorbent binary absorption system is, the stronger the absorption capacity of the absorbent will be. In addition, ψ1 was defined as the reciprocal of γ1∞ for the solute species. It was also proposed as another absorbent selection criterion: at

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New Approach for Absorbent Species Selection with Excess Gibbs

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