Multicomponent (Binary and Ternary) Adsorption Equilibria of Volatile

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Multicomponent (Binary and Ternary) Adsorption Equilibria of Volatile Organic Compounds (Acetone, Toluene, and n‑Hexane) on Activated Carbon in Supercritical Carbon Dioxide Ikuo Ushiki,*,†,‡ Yoshiyuki Sato,‡ Masaki Ota,‡ and Hiroshi Inomata‡ †

Graduate School of Environmental Studies, Tohoku University, Aramaki Aza Aoba, 6-6-11-414, Aoba-Ku, Sendai, Miyagi 980-8579, Japan ‡ Research Center of Supercritical Fluid Technology, Graduate school of Engineering, Tohoku University, Aramaki Aza Aoba, 6-6-11-403, Aoba-Ku, Sendai, Miyagi 980-8579, Japan S Supporting Information *

ABSTRACT: The multicomponent (binary and ternary) adsorption equilibria of three volatile organic compounds (VOCs) (acetone, toluene, and n-hexane) on activated carbon were studied under supercritical carbon dioxide (scCO2) conditions. The multicomponent adsorption equilibrium data were obtained at 313−353 K and 4.2−10.0 MPa and depended on the affinities of the adsorbates for the adsorbent. The amounts of adsorbed VOCs decreased with increases in the pressure and decreases in the temperature, owing to the effects of the CO2 density. The measured adsorption equilibria were correlated within 5.5% of the average relative deviation to the Dubinin−Astakhov equation using two parameters. These parameters, which were determined based on these correlations, provided information on the multicomponent adsorption equilibria of the VOCs under scCO2 conditions while considering the interactions between the VOCs and the adsorbent, the bulk phase CO2 density, and the competitive adsorption of the VOCs and CO2 in the adsorbed phase.

1. INTRODUCTION Supercritical carbon dioxide (scCO2) is used widely as a solvent in the fields of extraction1−3 and material production,4−7 as well as in reactions8 and for cleaning.9−11 ScCO2 can dissolve various hydrocarbons, whose solubility in scCO2 can be controlled by tuning the temperature and pressure. From the practical viewpoint, separating the solvent once it has been used is essential for obtaining the target components and for removing the impurities that might be present in the waste stream of scCO2. Adsorption is a promising separation technology, as it can be used to remove dilute solutes with the appropriate adsorbents in the used scCO2 stream. Adsorption equilibrium data are essential for designing separation processes that take place under scCO2 conditions. Some researchers have reported the adsorption equilibria of various organics with respect to typical adsorbents such as activated carbon12−25 in scCO2. We had also reported the adsorption equilibria of volatile organic compounds (VOCs) on activated carbon under scCO2 conditions.26,27 However, most of these reports were about adsorption equilibria of single components in scCO 2 . Accordingly, these studies are insufficient for developing adsorption processes, because various solutes can be used in scCO2 processes. Therefore, multicomponent adsorption equilibrium data are critical for designing practical adsorption processes under scCO2 conditions. One common approach for obtaining multicomponent adsorption equilibrium data is prediction from adsorption equilibrium data of each pure component by using an appropriate predictive model such as the ideal adsorbed solution theory (IAST).28 However, the IAST can cause large predictive deviations of adsorption equilibria of single VOC in © XXXX American Chemical Society

scCO2 mainly because of possible nonideality in the highpressure conditions;29 therefore, measurements of multicomponent adsorption equilibrium are indispensable at the first step of designing the adsorption processes. In addition, there can be many combinations of the temperature and pressure with respect to multicomponent adsorption processes. Therefore, theoretical analyses based on the appropriate model are essential for the efficient design of adsorption processes under scCO2 conditions. A few conventional models such as the Langmuir equation12,14−17,19,24,30−32 and the Freundlich equation12,14,17,19,30 have been employed to correlate the adsorption equilibria of organics on activated carbon in scCO2. However, the Langmuir equation assumes monolayer adsorption, while the Freundlich equation is an empirical formula. Accordingly, these models are not very applicable in the case of possible nonideal adsorption phenomena on activated carbon in scCO2, because both competitive and multilayer adsorption can occur in the pores of the adsorbents at higher pressures. The Dubinin−Astakhov (DA) equation33 (see also eqs 5−7), on the other hand, can be regarded as a possible model for describing adsorption phenomena in scCO2, because it makes thermodynamic assumptions based on the potential theory proposed by Polanyi.34 This equation approximates adsorption phenomena such as pore filling by liquefaction. Furthermore, the equilibrium relationship between the bulk phase and the Received: November 19, 2015 Revised: January 14, 2016 Accepted: February 1, 2016

A

DOI: 10.1021/acs.iecr.5b04383 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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Industrial & Engineering Chemistry Research adsorbed phase is thermodynamically defined on the basis of the fugacities in the two phases (see also eq 5 and Figure 1).

Table 1. Physical Properties of Activated Carbon property

value

specific surface area (m2/g)a pore volume (cm3/kg)a mean pore diameter (nm)a solid density (g/cm3)b

1300 441 0.69 2.21

a

Determined by nitrogen adsorption with t method.26 bDetermined by helium loading with a magnetic suspension balance.29

Table 2. Characteristics of Adsorption Column Figure 1. Physical meaning of the Dubinin−Astakhov equation for multicomponent adsorption equilibria of VOCs on activated carbon under supercritical carbon dioxide conditions.

Therefore, the physical meanings of the fitting parameters of the DA equation (EVOC(i) and W0,VOC(i) in eq 6) are thermodynamically clear. Accordingly, it is considered that these parameters can provide quantitative information regarding adsorption equilibria in scCO2 for the efficient design of separation processes. We had previously demonstrated that the DA equation can correlate the adsorption equilibria of the individual VOCs on activated carbon within 6.5% of the average relative deviation (ARD).26 In addition, the fitting parameters determined on the basis of the obtained correlations clearly depended on the properties of the adsorbates and the CO2 density in the cases of the single-component VOC systems.26 This suggests that the DA equation should be highly applicable in the case of multicomponent systems for analyzing the adsorption equilibria of VOCs under scCO2 conditions. In this study, we selected activated carbon as a representative adsorbent with a high specific surface area and high affinity for many organics and selected three VOCs (toluene, acetone, and n-hexane) as typical adsorbates with different chemical properties. Then, the multicomponent (binary and ternary) adsorption equilibria of the VOCs on the adsorbent in scCO2 were investigated at temperatures of 313−353 K and pressures of 4.2−10.0 MPa. Finally, the correlations between the measured data were determined using the DA equation, and the fitting parameters obtained using the model were analyzed to obtain quantitative information regarding the multicomponent adsorption equilibria of the VOCs under scCO2 conditions.

property

value

amount of activated carbon (g) length (mm) inner diameter (mm) volume (cm3) void fraction (−)a

0.705 100 4.35 1.49 0.57

a

Calculated from the column volume, solid density, and pore volume of the adsorbent.

Figure 2. Apparatus for measuring multicomponent adsorption equilibria of VOCs in supercritical carbon dioxide: (1) carbon dioxide cylinder; (2) mixture of VOCs; (3) syringe pump; (4) cooling unit; (5) oven; (6) six-way valve; (7) preheater; (8) mixing column; (9) adsorption column; (10) temperature sensor; (11) split; (12) FID detector; (13) UV−vis detector; (14) pressure sensor; (15) backpressure regulator; (16) dry gas meter.

were cooled to 278 K using a refrigerated circulator (F25-MA, Julabo Inc., Germany). The temperature of the adsorption column was controlled with an oven (GC353B, GL Science Inc., Japan). The flow rate of CO2 was measured with a dry gas meter (DC-2, Shinagawa Co., Japan) and kept constant at 700 cm3 (SATP)/min. The pressure in the system was kept at the desired level by using a back-pressure regulator (SCF-Bpg/M, JASCO Co., Japan); it was measured with a pressure sensor (PTX621, F.S. 25 MPa, ± 0.08% F.S., GE Sensing, US). The overall concentration of the VOCs in the scCO2 was determined using a flame ionization detector (FID). The concentrations of the individual VOCs except n-hexane were determined with an ultraviolet−visible (UV−vis) spectroscopy system (MD-2018, JASCO Co., Japan) with a high-pressure cell (maximum pressure, 25.0 MPa; optical path length, 5 mm). 2.3. Procedure for Measuring Adsorption Equilibria of VOCs. In the first step of the measurement process, CO2 and the mixture of the VOCs were loaded separately in the two syringe pumps. The concentrations of the VOCs loaded in the pump are listed in Table 3. Next, the CO2 and the mixture of the VOCs were mixed using a column that was packed with glass beads. This CO2−VOCs mixture was introduced into the system at a constant flow rate. The instantaneous values of the VOC concentrations in the CO2 were determined using the UV−vis spectrometer and the FID on the basis of the

2. EXPERIMENTAL SECTION 2.1. Materials. Acetone (purity, 99.7 mass%), toluene (purity, 99.8 mass%), and n-hexane (purity, 96 mass%) were purchased from Wako Pure Chemical Industries, Japan. CO2 (purity 99.99 vol %) was obtained from Showa Denko Gas Products Co., Ltd., Japan. Activated carbon was supplied by Cambridge Filter Japan, Ltd. The adsorbent was loaded into an adsorption column (1/4 in. SUS316 steel tube) and pretreated by being heated in an argon gas atmosphere at 573 K for 8 h to remove all possible impurities and water. The physical properties of the adsorbent and the characteristics of the adsorption column are listed in Tables 1 and 2, respectively. 2.2. Apparatus for Measuring Adsorption Equilibria of VOCs. Figure 2 shows the apparatus used for measuring the multicomponent adsorption equilibria of the VOCs under scCO2 conditions. ScCO2 and a mixture of the VOCs were supplied from two syringe pumps (model 500D and 100DX, Teledyne Isco Inc., US) at constant flow rates. The two pumps B


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case, the amounts of adsorbed VOCs (acetone and toluene) i, qVOC(i), were obtained from the area of the breakthrough curve of the individual VOC determined from the corresponding UV signal as follows:

Table 3. VOCs Mixture for the Measuring Multicomponent Adsorption Equilibria in Supercritical Carbon Dioxide

a

number of components

VOCs mixturea

binary binary binary ternary

acetone (50.0 mol %) − toluene (50.0 mol %) toluene (50.0 mol %) − n-hexane (50.0 mol %) acetone (50.0 mol %) − n-hexane (50.0 mol %) acetone (33.3 mol %) − n-hexane (33.3 mol %) − toluene (33.3 mol %)

∫0

qVOC(i) = [

te, i

(C0, i − Ci)Q (ρ0,CO /ρ 2

CO2

)dt − εcVC0, i]/mad (1)

where C0,i and Ci are the concentrations of VOC i at the entrance and exit of the adsorption column, respectively, and te,i is the end time of the breakthrough curve of VOC i. te,i was determined as the time at which Ci became 99% of C0,i in the breakthrough curve. Furthermore, mad is the mass of the adsorbent packed in the column, Q is the volumetric flow rate as determined using the dry gas meter, V is the column volume, and εc is the column void fraction. In addition, ρCO2 is the CO2 density in the adsorption column, and ρ0,CO2 is the CO2 density at the dry gas meter. The CO2 densities were determined using the Span−Wagner equation of state.35 As shown in Figure 4a, the FID signal changed in a stepwise manner at the breakthrough times of acetone and toluene, which were detected from the UV signals. Therefore, the amounts of adsorbed acetone and toluene could also be determined by using the stepwise breakthrough curve based on the FID signal, as shown in Figure 5a. Figure 5b presents the adsorption equilibria of acetone and toluene as calculated using the breakthrough curves determined from the UV and FID signals, respectively. These results indicated that the amounts of adsorbed acetone and toluene as determined using the UV signals were in good agreement with those determined using the FID signals and were within 2% of the ARD. Thus, the validation of the measured multicomponent adsorption equilibria of the VOCs in scCO2 was confirmed by comparing the values obtained using the UV and FID signals. 2.4.2. Adsorption of Binary Mixture of VOCs (Acetone−nHexane and n-Hexane−Toluene; One VOC Exhibits UV Absorptivity and the Other Does Not). Next, we considered the adsorption of binary mixtures of the VOCs (acetone−nhexane and n-hexane−toluene; n-hexane does not exhibit UV absorptivity). In these cases, the amounts of adsorbed acetone and toluene were determined from the breakthrough curves based on the UV signals using eq 1, as shown in panels b and c of Figure 4, respectively. On the other hand, the amount of adsorbed n-hexane was determined by subtracting the adsorption amount of the other VOC (acetone or toluene) from the total amount of adsorbed VOCs as calculated from the overall breakthrough curve determined based on the FID signal. 2.4.3. Adsorption of Ternary Mixture of VOCs (Acetone−nHexane−Toluene). When the adsorption equilibria of a ternary mixture of the VOCs were measured, the amounts of adsorbed acetone and toluene were determined using eq 1, and the breakthrough curves of these VOCs, which were obtained based on the UV signals, as shown in Figure 6. On the other hand, the amount of adsorbed n-hexane was determined by subtracting the adsorption amounts of the other VOCs (acetone and toluene) from the total amount of adsorbed VOCs as calculated from the overall breakthrough curve obtained based on the FID signal as mentioned in the previous section.

Prepared by using a graduated cylinder (1000 ± 5 cm3).

respective calibration curves. When the UV−vis spectrometer and FID readouts showed constant outputs corresponding to the desired VOC concentrations, the six-way valve was switched to the adsorption column and the experimental run was started. When the activated carbon became saturated, the FID signal returned to its initial value, indicating that the saturation breakthrough of the adsorbent had been reached. 2.4. Method for Analyzing Multicomponent Adsorption Equilibria of VOCs. The method for analyzing the multicomponent (binary and ternary) adsorption equilibria of the VOCs was different for each system, because the chemical species used exhibited different UV absorption features. Therefore, this section presents the methods to analyze the adsorption equilibria for each system separately. 2.4.1. Adsorption of Binary Mixture of VOCs (Acetone and Toluene, Which Exhibit UV Absorptivity). Figure 3 shows the

Figure 3. UV−vis spectra of acetone-toluene (solid black line), acetone (red dotted line), and toluene (blue dashed line) in supercritical carbon dioxide at 353 K and 10.0 MPa. The mole fractions of the VOCs in supercritical carbon dioxide (yVOC) are yacetone = ytoluene = 1.0 × 10−3.

measured UV spectra of a binary VOC mixture (acetone− toluene) and the individual VOCs (acetone and toluene) in scCO2 at 353 K and 10.0 MPa. When these UV spectra were measured, the baselines of the UV spectrum of pure CO2 were subtracted at each temperature and pressure condition. In the binary system, toluene and acetone showed characteristic peaks (220 and 280 nm, respectively). Thus, the VOCs were not affected by each other. Accordingly, we used these characteristic peaks at the mentioned wavelengths to determine the concentrations of toluene and acetone. Figure 4a presents the breakthrough curves for the adsorption of the binary VOC mixture (acetone−toluene) on activated carbon in scCO2; the curves were obtained by using the fixed wavelengths for each VOC (acetone, 280 nm; toluene, 220 nm). The FID signal of the VOC mixture in scCO2 is also shown in Figure 4a. In this C


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Figure 4. Breakthrough curves of binary VOCs adsorption on activated carbon in supercritical carbon dioxide at 353 K and 10.0 MPa. (a) Acetone− toluene (mole fractions of VOCs in the bulk phase: yacetone = ytoluene = 1.0 × 10−3). (b) Acetone−n-hexane (yacetone = yn‑hexane = 1.1 × 10−3). (c) nHexane−toluene (yn‑hexane = ytoluene = 9.2 × 10−4). The breakthrough curves of acetone and toluene were measured by the UV−vis detector at the wavelength of 280 nm (red dotted line) and 220 nm (blue dashed line), respectively. The overall breakthrough curve of VOCs (black solid line) was measured by the FID.

Figure 5. Validation of the measurement results of multicomponent adsorption equilibria of VOCs under supercritical carbon dioxide conditions. (a) Breakthrough curves of binary VOCs (acetone−toluene) adsorption on activated carbon in supercritical carbon dioxide detected by the UV and FID signals at 353 K and 10.0 MPa. (b) Comparison of measurement results of the binary VOCs (acetone (○, UV; ×, FID); toluene (△, UV; *, FID)) adsorption equilibria by using the breakthrough curves detected by the UV and FID signals at 353 K and 10.0 MPa.

3. RESULTS AND DISCUSSION

probably the competitive adsorption of the other VOCs in the adsorbed phase. 3.2. Pressure Dependence of Multicomponent Adsorption Equilibria of VOCs. Figures 8−10 show the adsorption equilibria of the binary mixtures of the VOCs (acetone−toluene, n-hexane−toluene, and acetone−n-hexane) on activated carbon under scCO2 conditions at 313−353 K and 4.2−10.0 MPa. Figure 11 shows the adsorption equilibria of the ternary mixture of the VOCs (acetone−n-hexane−toluene) on activated carbon in scCO2. The results of the measurements of the adsorption equilibria are listed in Tables S1−S4 in Supporting Information. These results indicated that the amounts of adsorbed VOCs decreased with the increase in the pressure for all the systems. A similar pressure dependence has also been reported in the case of the adsorption equilibria

3.1. Comparison of Adsorption Equilibria of Individual VOCs. Figure 7 shows the results of the measurements of the adsorption equilibria of the binary mixture of the VOCs (acetone−toluene) on activated carbon as well as those of the individual VOCs (acetone26 and toluene27) in scCO2 as a function of the mole fraction of VOC i in the bulk phase (yVOC(i)) at 353 K and 10.0 MPa. As can be seen in the figure, the amounts of adsorbed toluene and acetone in the binary system were relatively smaller than those in the corresponding systems with the individual components. This tendency was also observed in the case of the other binary systems (acetone− n-hexane and n-hexane−toluene). The reason for the decrease in the amounts of adsorbed VOCs in the binary systems was D


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Figure 6. Breakthrough curves of ternary VOCs (acetone−n-hexane− toluene) adsorption on activated carbon in supercritical carbon dioxide at 353 K and 10.0 MPa. (Mole fractions of VOCs in the bulk phase: yacetone= yn‑hexane= ytoluene= 3.5 × 10−4). The breakthrough curves of acetone and toluene were measured by the UV−vis detector at the wavelength of 280 nm (red dotted line) and 220 nm (blue dashed line), respectively. The overall breakthrough curve of VOCs (black solid line) was measured by the FID.

Figure 8. Measurement and correlated results of binary VOCs (acetone−toluene) adsorption equilibria on activated carbon in supercritical carbon dioxide at conditions of 353 K and 4.2 MPa (acetone (red circles) − toluene (blue circles)), 353 K and 10.0 MPa (acetone (red diamonds) − toluene (blue diamonds)), and 313 K and 10.0 MPa (acetone (red stars) − toluene (blue stars)). Lines (solid for 353 K and 4.2 MPa, dashed for 353 K and 10.0 MPa, and dotted for 313 K and 10.0 MPa) are correlated results by the Dubinin−Astakhov equation.

Figure 7. Comparison of the measurement results of VOCs adsorption equilibria of binary system (acetone (solid red diamonds)−toluene (solid blue circles)) and single-component system (acetone (open red diamonds)26 and toluene (open blue circles)27) on activated carbon in supercritical carbon dioxide at 353 K and 10.0 MPa. Lines (solid for the binary system, dashed for the single-component system26) are correlated results by using the Dubinin−Astakhov equation.

Figure 9. Measurement and correlated results of binary VOCs (nhexane−toluene) adsorption equilibria on activated carbon in supercritical carbon dioxide at conditions of 353 K and 4.2 MPa (nhexane (green circles) − toluene (blue circles)), 353 K and 10.0 MPa (n-hexane (green diamonds) − toluene (blue diamonds)) and 313 K and 10.0 MPa (n-hexane (green stars) − toluene (blue stars)). Lines (solid for 353 K and 4.2 MPa, dashed for 353 K and 10.0 MPa, and dotted for 313 K and 10.0 MPa) are correlated results by the Dubinin−Astakhov equation.

of individual VOCs on activated carbon in scCO2.18,26,30 The pressure dependence of the adsorption equilibria of the VOCs in scCO2 can be explained by two factors related to an increase in the CO2 density (ρCO2) at higher pressures (e.g., ρCO2 = 72 kg/m3 at 353 K and 4.2 MPa, ρCO2 = 222 kg/m3 at 353 K and 10.0 MPa35). One possible factor is that the increase in the CO2 density can induce increasing partition of the VOCs from the adsorbed phase into the bulk phase. The other is that the amount of CO2 in the adsorbed phase increases with the increase in the CO2 density. As a result, the adsorption capacity of the VOCs decreased with the increase in the amount of adsorbed CO2. Therefore, these results implied that the characteristic pressure dependence of the adsorption equilibria of the VOCs on activated carbon in scCO2 in the case of multicomponent adsorption systems was the same as that for the single-component systems. 3.3. Temperature Dependence of Multicomponent Adsorption Equilibria of VOCs. Figures 8−11 also show the temperature dependence of the multicomponent adsorption equilibria of the VOCs. These results indicated that the

amounts of adsorbed VOCs decreased with a decrease in the temperature, in contrast to what is typically observed in the case of the adsorption of liquids or gases.36 A similar temperature dependence of the adsorption equilibria on activated carbon has been reported by others as well18,26 in the cases of single-component VOC systems. This temperature dependence can also be attributed to the increase in the CO2 density with the decrease in the temperature of the system (e.g., ρCO2 = 222 kg/m3 at 353 K and 10.0 MPa, ρCO2 = 629 kg/m3 at 313 K and 10.0 MPa35), in a manner similar to that resulting from the increase in the pressure, as mentioned above. Consequently, the CO2 density is probably the primary factor determining the multicomponent adsorption equilibria of VOCs, in contrast to the temperature, which is conventionally the main factor affecting adsorption. 3.4. Effects of Properties of VOCs on Multicomponent Adsorption Equilibria. As shown in Figures 8−11, the E


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Table 4. Properties of Volatile Organic Compounds (VOCs) VOCs

MVOC(i) (g/mol)a

E (kJ/mol)b

kij (−)c

acetone toluene n-hexane

58.080 92.141 86.177

15.91 27.27 26.21

0.01541 0.10639 0.09040

a Molar mass of VOC i.38 bCharacteristic adsorption energy29 between VOC and adsorbent determined with the pure component adsorption equilibrium data of each VOC by using the Dubinin−Astakhov equation.33 cBinary interaction parameters between CO2 and VOC in the van der Waals one-fluid mixing rule for the Peng−Robinson equation of state37 determined from phase equilibrium data of corresponding CO2−VOC binaries.

Figure 10. Measurement and correlated results of binary VOCs (acetone−n-hexane) adsorption equilibria on activated carbon in supercritical carbon dioxide at conditions of 353 K and 4.2 MPa (acetone (red circles) − n-hexane (green circles)), 353 K and 10.0 MPa (acetone (red diamonds) − n-hexane (green diamonds)), and 313 K and 10.0 MPa (acetone (red stars) − n-hexane (green stars)). Lines (solid for 353 K and 4.2 MPa, dashed for 353 K and 10.0 MPa, and dotted for 313 K and 10.0 MPa) are correlated results by the Dubinin−Astakhov equation.

4. MODEL 4.1. Correlation Method Based on the Dubinin− Astakhov Equation. The original version of the DA equation33 is as follows: ⎡ ⎛ ε ⎞n ⎤ W = W0 exp⎢ −⎜ ⎟ ⎥ ⎣ ⎝E⎠ ⎦ (2) ⎡ p (T ) ⎤ ⎥ ε = RT ln⎢ s ⎣ p ⎦

(3)

ρW (4) M where W0 is the saturated adsorption volume and W is the adsorption amount (volume basis). Furthermore, E is the characteristic adsorption energy, n is a dimensionless parameter, and ε is the adsorption potential defined by eq 3, where p is the partial pressure of the adsorbate in the bulk phase and ps is the saturated vapor pressure of the adsorbate at the operating temperature (T). In eq 4, q is the adsorption amount (molar basis), ρ is the density of the adsorbate in the adsorbed phase, and M is the molar mass of the adsorbate. To apply these equations in the case of the multicomponent adsorption equilibria in scCO2, the pressures of the adsorbates in eq 3 should be replaced by the corresponding fugacity to account for the nonideality under the high-pressure conditions. Therefore, the adsorption potential of VOC i in CO2 (εVOC(i)) is given by the following equation: q=

Figure 11. Measurement and correlated results of ternary VOCs (acetone−n-hexane−toluene) adsorption equilibria on activated carbon in supercritical carbon dioxide at conditions of 353 K and 4.2 MPa (acetone (red circles) − n-hexane (green circles) − toluene (blue circles)), 353 K and 10.0 MPa (acetone (red diamonds) − nhexane (green diamonds) − toluene (blue diamonds)), and 313 K and 10.0 MPa (acetone (red stars) − n-hexane (green stars) − toluene (blue stars)). Lines (solid for 353 K and 4.2 MPa, dashed for 353 K and 10.0 MPa, and dotted for 313 K and 10.0 MPa) are correlated results by the Dubinin−Astakhov equation.

⎡ ⎤ fs,VOC(i) (T ) ⎢ ⎥ εVOC(i) = RT ln ⎢⎣ f (T , P , yVOC(i) , yVOC(j) , yVOC(k)) ⎥⎦ VOC(i) (5)

adsorption amounts of the individual VOCs varied greatly. These differences in the amounts of adsorbed VOCs can be explained on the basis of the differences in the affinities of the VOCs for the adsorbent. We had previously reported29 the characteristic adsorption energy (E) values of VOCs with respect to activated carbon by measuring the pure component adsorption equilibria of these VOCs on the adsorbent using the DA equation; the result is shown in Table 4. The VOCs with larger values (toluene in Figures 8 and 9 and n-hexane in Figure 10) of E were adsorbed in larger amounts than the other VOCs in the systems. This trend was also observed in the case of the ternary adsorption equilibria of the VOCs, as shown in Figure 11. Therefore, these results suggested that the amounts of adsorbed VOCs in the case of multicomponent systems under scCO2 conditions depend strongly on the affinities of the VOCs for the adsorbent.

where fs,VOC(i) is the saturated fugacity of the VOC i in the adsorbed phase. The saturated fugacity assumed to be that of pure VOC i and was determined via calculations of the saturated vapor pressure for a given temperature T by using the Peng−Robinson equation of state.37 Furthermore, f VOC(i) is the fugacity of VOC i in the bulk phase of the CO2−VOCs multicomponent system at temperature T and pressure P, with the mole fractions of the VOCs i, j, and k being yVOC(i), yVOC(j), and yVOC(k), respectively. The f VOC(i) was calculated using the Peng−Robinson equation of state.37 For the CO2−VOCs multicomponent system, f VOC(i) was calculated using the interaction parameter kij and the van der Waals one-fluid mixing rule.38 The kij values for CO2 and the VOCs were determined using the vapor−liquid equilibrium data of the corresponding CO2−VOC binaries (toluene,39 n-hexane,40 and F


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Industrial & Engineering Chemistry Research acetone41); these values are listed in Table 4. The kij values for the VOCs in the multicomponent systems were assumed to be equal to zero, because the interaction between two VOCs in the bulk phase can be ignored, given the very low concentrations of the VOCs in the bulk phase (less than 0.5 mol % in this study). To perform these calculations, the critical properties and acentric factors of the components were obtained from the handbook by Poling et al.38 By using εVOC(i) from eq 5, the DA equation for the multicomponent adsorption equilibria of VOCs under scCO2 conditions can be derived as follows: ⎡ ⎛ε ⎞n ⎤ VOC(i) ⎥ ⎢ ⎟ WVOC(i) = W0,VOC(i) exp −⎜⎜ ⎢⎣ ⎝ E VOC(i) ⎟⎠ ⎥⎦ qVOC(i) =

equation can yield satisfactory correlations for the multicomponent adsorption equilibria within an ARD of 5.5%. 4.3. Parameter EVOC(i) Determined Using the DA Correlations. Figure 12 shows the value of the parameter

(6)

ρVOC(i)WVOC(i) MVOC(i)

(7)

where WVOC(i) and qVOC(i) are the amount of adsorbed VOC on volume and molar basis, respectively. W0,VOC(i) is the saturated adsorption capacity of the adsorbent for VOC i, and EVOC(i) is the characteristic energy of adsorption between VOC i and the adsorbent. Figure 1 shows the physical meanings of the parameters W0,VOC(i) and EVOC(i) in the presence of CO2. These parameters can be affected by the other VOCs and CO2 in the bulk and adsorbed phases, as shown in Figure 1. The adsorption potential of VOC (εVOC(i)) in eq 5 corresponds to the driving force of adsorption phenomena of VOC i from the bulk phase to the adsorbed phase; thereby, εVOC(i) was described as a vertical arrow in Figure 1. In eq 7, ρVOC(i) is the density of VOC i in the adsorbed phase, and MVOC(i) is the molar mass of VOC i. To determine ρVOC(i), we assumed36 that ρVOC(i) can be approximated as the saturated liquid density42 at the operating temperature. Regarding the parameter n in the DA equation, Suzuki43 proposed a classification method that suggested n can be fixed to 2 for microporous adsorbents (e.g., activated carbon). We26 as well as Shojibara et al.18 had demonstrated previously that the DA equation provides satisfactory correlations in the case of the single-component adsorption equilibria of VOCs on activated carbon in scCO2 when n is fixed to 2 according to Suzuki’s classification system. Consequently, for the multicomponent systems of the VOCs, n was set to 2 in the DA equation. Therefore, the measured multicomponent adsorption equilibria of the VOCs on activated carbon in scCO2 could be correlated by using the two fitting parameters of the DA equation, namely, W0,VOC(i) and EVOC(i), for each VOC in the multicomponent system, with the minimization of the ARD being defined as follows: ARD[%] =

1 N

∑

× 100

Figure 12. CO2 density dependence of EVOC(i) determined with the Dubinin−Astakhov correlations of binary VOCs (acetone (red circles) − toluene (blue circles); n-hexane (green stars) − toluene (blue stars); acetone (red diamonds) − n-hexane (green diamonds)) adsorption equilibria on activated carbon in supercritical carbon dioxide at various conditions (open symbols, 353 K and 4.2 MPa; open symbols with cross, 353 K and 10.0 MPa; closed symbols, 313 K and 10.0 MPa).

EVOC(i) determined based on the DA correlations of the binary adsorption equilibria of the VOCs on activated carbon in scCO2 as a function of the CO2 density. The value of EVOC(i) decreased with an increase in the CO2 density for all the binary systems. This dependence of the parameter EVOC(i) on the CO2 density was also observed in the cases of the single-component adsorption equilibria of VOCs on activated carbon in scCO2.26 The most likely reason for the CO2 density dependence of EVOC(i) is that the degree of interaction between the VOC and the activated carbon decreased with an increase in the amount of CO2 in the adsorbed phase, as shown in Figure 13.

Figure 13. CO2 density effects on the parameters of the Dubinin− Astakhov equation for the binary adsorption equilibria of VOCs on activated carbon in supercritical carbon dioxide at (a) lower CO2 density conditions and (b) higher CO2 density conditions.

qVOC(i),correlated − qVOC(i),experiment qVOC(i),experiment

Therefore, the CO2 dependence of the parameter EVOC(i) was also confirmed in the cases of the multicomponent adsorption equilibria of the VOCs, in addition to the single-component systems of the VOCs. On the other hand, it was obvious that the values of the parameter EVOC(i) for toluene and n-hexane were larger than that for acetone in all the binary systems, as shown in Figure 12. Taking the hydrophobic surface of the carbon material36 into consideration, one possible cause for these differences in the EVOC(i) values is the fact the interactions between the

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4.2. Correlations Obtained Using the Dubinin− Astakhov Equation. The lines in Figures 7−11 represent the correlations of the multicomponent adsorption equilibria of the VOCs on activated carbon under scCO2 conditions as determined using the DA equation. Table S5 lists the values of the determined fitting parameters and the values of the ARD for the correlations. These results demonstrated that the DA G


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toluene and n-hexane being higher than that of acetone, as shown in Figures 8 and 10. Accordingly, these differences in the adsorption amounts of the VOCs would affect the W0,VOC(i) values of the components, because the W0,VOC(i) values correspond to the saturated adsorption amounts of the corresponding VOCs in the scCO2 systems. 4.5. Effects of Number of Components on Parameters EVOC(i) and W0,VOC Determined Using DA Equation. Figures 15 and 16 show the effects of the number of components in the multicomponent systems on the parameters EVOC(i) and W0,VOC(i), determined using the DA equation. Figure 15 shows that the dependence of the parameter EVOC(i) on the number of components was very small. One possible reason for the small dependence of EVOC(i) is that this parameter corresponds to the interaction between the respective VOC and the activated carbon. Figure 17 shows possible effects of number of components on the parameters EVOC(i) and W0,VOC(i) of the DA equation for the adsorption equilibria of VOCs on activated carbon in scCO2. Accordingly, as shown in Figure 17, it can be considered that EVOC(i) was not affected by the other VOCs, which were competitively adsorbed in the adsorbed phase. Consequently, the interactions between the VOCs and the adsorbent can be considered the dominant factor determining the value of the parameter EVOC(i), whereas the effects of the competitive adsorption of the other VOCs present in the multicomponent system are negligibly small in these systems. On the other hand, Figure 16 shows that the values of W0,VOC(i) clearly decreased with an increase in the number of the components in the multicomponent systems. This was probably because the adsorption capacity of each VOC decreased with the increase in the number of the VOCs, which were competitively adsorbed on the adsorbent, as shown in Figure 17. It can be concluded from the above discussion that the parameters EVOC(i) and W0,VOC(i) determined on the basis of the DA correlations could provide quantitative information regarding the multicomponent adsorption equilibria of the VOCs under scCO2 conditions while taking into account the effects of the interactions between the adsorbates and the adsorbent, those of the CO2 density in the bulk phase, and the possible competitive adsorption in the adsorbed phase.

hydrophobic adsorbates (toluene and n-hexane) and the activated carbon were stronger than that between the hydrophilic adsorbate (acetone) and the adsorbent. The effect of the interaction between the VOCs and the adsorbents on the EVOC(i) values can also be rationalized by the adsorption energy of each pure VOC, as shown in Table 4. 4.4. Parameter W0,VOC(i) Determined Using the DA Correlation. Figure 14 shows the values of the parameter

Figure 14. CO2 density dependence of W0,VOC(i) determined with the Dubinin−Astakhov correlations of binary VOCs (acetone (red circles) − toluene (blue circles); n-hexane (green stars) − toluene (blue stars); acetone (red diamonds) − n-hexane (green diamonds)) adsorption equilibria on activated carbon in supercritical carbon dioxide at various conditions (open symbols, 353 K and 4.2 MPa; open symbols with cross, 353 K and 10.0 MPa; closed symbols, 313 K and 10.0 MPa).

W0,VOC(i) determined using the DA correlations of the binary adsorption equilibria of the VOCs on activated carbon in scCO2 as a function of the CO2 density. The value of the parameter W0,VOC(i) decreased with an increase in the CO2 density; this was true for all the binary systems and was probably because the adsorption capacity of the VOCs decreased with an increase in the competitive adsorption of CO2, as shown in Figure 13. Figure 14 also indicates that the W0,VOC(i) values of toluene and n-hexane were larger than that of acetone for all the cases. These differences can be attributed to the amounts of adsorbed

Figure 15. Effects of number of VOCs on the parameter EVOC(i) determined with the Dubinin−Astakhov correlations of single-component (acetone (red squares)26; n-hexane (green crosses)26; toluene (blue, left triangles)26), binary (acetone (red circles) − toluene (blue circles); n-hexane (green stars) − toluene (blue stars); acetone (red diamonds) − n-hexane (green diamonds)) and ternary (acetone (red triangles) − n-hexane (green triangles) − toluene (blue, up triangles)) adsorption equilibria on activated carbon in supercritical carbon dioxide at (a) 353 K and 4.2 MPa, (b) 353 K and 10.0 MPa, and (c) 313 K and 10.0 MPa. H


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Figure 16. Effects of number of VOCs on the parameter W0,VOC(i) determined with the Dubinin−Astakhov correlations of single component (acetone (red squares)26; n-hexane (green crosses)26; toluene (blue, left triangles)26), binary (acetone (red circles) − toluene (blue circles); nhexane (green stars) − toluene (blue stars); acetone (red diamonds) − n-hexane (green diamonds)) and ternary (acetone (red triangles) − n-hexane (green triangles) − toluene (blue, up triangles)) adsorption equilibria on activated carbon in supercritical carbon dioxide at (a) 353 K and 4.2 MPa, (b) 353 K and 10.0 MPa, and (c) 313 K and 10.0 MPa.

Figure 17. Effects of number of components on the parameters of the Dubinin−Astakhov equation for the multicomponent adsorption equilibria of VOCs on activated carbon under supercritical carbon dioxide conditions.

5. CONCLUSIONS The multicomponent adsorption equilibria of three VOCs (acetone, toluene, and n-hexane) on activated carbon were measured under scCO2 conditions, and the correlations between them were determined. The measured adsorption equilibrium data were strongly dependent on the adsorbate properties, temperature, and pressure; this could be explained on the basis of the affinities of the VOCs for the adsorbent and the effects of the CO2 density. The DA equation yielded satisfactory correlations based on the measured data when values of the parameters within 5.5% of the ARD were used. The DA parameters determined on the basis of the correlations provided quantitative information on the multicomponent adsorption equilibria of the VOCs while taking into consideration the affinity of the VOCs for the adsorbent, the CO2 density in the bulk phase, and the competitive adsorption of the VOCs and CO2 in the adsorbed phase.

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for the Promotion of Science (JSPS). I.U. is a JSPS Research Fellow (PD) and received financial support from the JSPS Research Fellowships for Young Scientists program (15J02431). Notes

The authors declare no competing financial interest.

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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.5b04383. Measured adsorption equilibrium data (Tables S1−S4) and correlation result of the measured adsorption equilibrium data by using the Dubinin−Astakhov equation (Table S5) (PDF)

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AUTHOR INFORMATION

Corresponding Author

*Tel: +81-22-795-5864. Fax +81-22-795-5864. E-mail: iushiki@ scf.che.tohoku.ac.jp. Funding

This research was financially supported by a Grant-in-Aid for Scientific Research (B) (25289271) and a Grant-in-Aid for Research Activity Start-up (26889011) from the Japan Society I

NOMENCLATURE Ci = concentration of VOC i at the column exit (mol/m3) C0,i = concentration of VOC i at the column entrance (mol/ m3) E = characteristic adsorption energy (J/mol) EVOC(i) = characteristic adsorption energy between VOC i and adsorbent (J/mol) f VOC(i) = fugacity of VOC i in the bulk phase (MPa) fs,VOC(i) = saturated fugacity of VOC i (MPa) M = molar mass of adsorbate (g/mol) MVOC(i) = molar mass of VOC i (g/mol) mad = mass of adsorbent packed in the adsorption column (kg) N = number of data points (−) n = exponent in the Dubinin−Astakhov equation (−) P = total pressure (MPa) p = partial pressure of adsorbate in the bulk phase (MPa) ps = saturated vapor pressure of adsorbate (MPa) Q = volumetric flow rate in the dry gas meter (m3/s) q = adsorption amount (mol/kg-adsorbent) qVOC(i) = amount of adsorbed VOC i (mol-VOC/kgadsorbent) qVOC(i),correlated = correlated value of the amount of adsorbed VOC i (mol-VOC/kg-adsorbent) qVOC(i),experiment = experimental value of the amount of adsorbed VOC i (mol-VOC/kg-adsorbent) R = gas constant (J/(mol·K)) T = temperature (K) DOI: 10.1021/acs.iecr.5b04383 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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t = time (s) te,i = end time of breakthrough curve of VOC i (s) V = column volume (m3) W = occupied adsorption volume (cm3/kg-adsorbent) WVOC(i) = amount of adsorbed VOC i on a volume basis (cm3/kg-adsorbent) W0 = saturated adsorption volume (cm3/kg-adsorbent) W0,VOC(i) = saturated adsorption capacity of adsorbent with respect to VOC i (cm3/kg-adsorbent) yVOC(i) = mole fraction of VOC i in the bulk phase (−) ε = adsorption potential of the Dubinin−Astakhov equation (J/mol) εc = void fraction of the adsorption column (−) εVOC(i) = adsorption potential of VOC i in scCO2 for the Dubinin−Astakhov equation (J/mol) ρ = density of adsorbate in the adsorbed phase (g/cm3) ρCO2 = density of carbon dioxide in the adsorption column (kg/m3) ρ0,CO2 = density of carbon dioxide in the dry gas meter (kg/ m3) ρVOC(i) = density of VOC i in the adsorbed phase (g/cm3) Subscripts

i, j, k = identifiers for the VOCs

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Multicomponent (Binary and Ternary) Adsorption Equilibria of Volatile

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