Desorption behavior of various volatile organic compounds from activated carbon in supercritical carbon dioxide: Measurement and kinetic modeling

J. of Supercritical Fluids 121 (2017) 41–51

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Desorption behavior of various volatile organic compounds from activated carbon in supercritical carbon dioxide: Measurement and kinetic modeling Ikuo Ushiki a,b , Koichi Kikuchi b , Naoto Takahashi b , Yoshiyuki Sato b , Yasuyuki Ito c , Hiroshi Inomata b,∗ a

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, Tohoku University, Aramaki Aza Aoba, 6-6-11-403, Aoba-Ku, Sendai, Miyagi 980-8579, Japan c Technical Research Laboratory, DAI-DAN Co., Ltd., Kitanagai, 390, Miyoshimachi, Irumagun, Saitama 354-0044, Japan b

a r t i c l e

i n f o

Article history: Received 26 August 2016 Received in revised form 9 November 2016 Accepted 10 November 2016 Available online 11 November 2016 Keywords: Desorption Activated carbon Volatile organic compounds (VOCs) Supercritical carbon dioxide Kinetic model Regeneration Extraction

a b s t r a c t The desorption behavior of various volatile organic compounds (VOCs: toluene, acetone, n-hexane, noctane, methanol, ethanol, 2-propanol, and propylene glycol monomethyl ether) from activated carbon was measured in supercritical carbon dioxide (scCO2 ) using the fixed-bed method at 313–353 K and 10.0–15.0 MPa. The measured behavior strongly depended on the type of VOC, and the CO2 density and volatility of the VOCs were the primary factors influencing this behavior. The desorption behavior was correlated with a kinetic model that assumed material balances in the bulk and pore phases with local adsorption equilibria in the adsorbed phase. The fitting parameters determined using these correlations were reasonably explained by the CO2 density and properties of VOCs, and they provided quantitative information about the desorption phenomena in scCO2 . © 2016 Elsevier B.V. All rights reserved.

1. Introduction Activated carbon is one of the most effective adsorbents for removing hazardous substances such as volatile organic compounds (VOCs) [1,2]. Regeneration methods for activated carbon are required to reuse the adsorbent from environmental and economic viewpoints in industrial-scale adsorption processes [3]. Thermal treatments are widely used as conventional regeneration methods in many industries. However, they can cause carbonization and destroy the structure of activated carbon owing to the high operating temperatures over 1000 K in usual cases [4,5]. Supercritical carbon dioxide (scCO2 ) is a promising solvent for regenerating activated carbon owing to its high diffusivity into the micropores of the adsorbent and the low damage caused to the structure of the adsorbent resulting from the extremely low surface tension and operation capability under relatively mild temperatures (critical temperature, Tc = 304.12 K [6]). Experimental data of the desorption behavior of organics from the adsorbent under

∗ Corresponding author. E-mail address: [email protected] (H. Inomata). http://dx.doi.org/10.1016/j.supflu.2016.11.007 0896-8446/© 2016 Elsevier B.V. All rights reserved.

scCO2 is required for designing the regeneration process. Thus far, the desorption behavior of organics including VOCs from activated carbon in scCO2 has been widely studied [7–20]. Many researchers have noted that the desorption behavior of VOCs strongly depends on the CO2 density, which varies with temperature and pressure. However, most of them only studied one or two VOC species, and therefore, little information is available about the effects of the properties of VOCs on desorption phenomena from activated carbon in scCO2 . For investigating the effects of the properties of VOCs on the desorption behavior, our previous work [21] demonstrated the desorption behavior of various types of VOCs (toluene, n-hexane, n-decane, methanol, and acetone) from activated carbon in scCO2 . It was found that the desorption behavior strongly depended on the physical and chemical properties of VOCs, especially the vapor pressure of the VOCs and affinity of the VOCs for the adsorbent. However, desorption data about other types of VOC species are urgently required to obtain a detailed understanding of the effects of the properties of VOCs on the desorption behavior. Additionally, regeneration processes using scCO2 can have many operating conditions with various types of VOCs that need to be removed from the adsorbent. Therefore, the desorption behavior

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I. Ushiki et al. / J. of Supercritical Fluids 121 (2017) 41–51

Nomenclature Ca Cb Cp DR Daz De Dm dp K kf L M mac N Q qads qdes qsat Rp r t u Vp z

Concentration of VOCs in the adsorbed phase (mol/kg-adsorbent) Concentration of VOCs in the bulk phase (mol/m3 ) Concentration of VOCs in the pore phase (mol/m3 ) Desorption ratio of VOCs (%) Axial dispersion coefficient (m2 /s) Effective diffusion coefficient of VOCs in the pore phase (m2 /s) Molecular diffusion coefficient of carbon dioxide (m2 /s) Mean particle diameter of the activated carbon (m) Adsorption equilibrium constant (m3 /mol) Mass transfer coefficient (m/s) Axial length of the column (m) Molar mass of VOCs (g/mol) Mass of activated carbon loaded in the column (kg) Number of data points (−) Mass flow rate of CO2 in the column (kg-CO2 /s) Initial amount of adsorbed VOC (mol/kg-adsorbent) Amount of desorbed VOC (mol/kg-adsorbent) Saturated amount of adsorbed VOC (mol/kgadsorbent) Mean particle radius of the activated carbon (m) Radial coordinates of the particle (m) Time (s) Superficial velocity in the column (m/s) Pore volume of the adsorbent (m3 /kg-adsorbent) Axial coordinate of the column (m)

Greek letters Porosity of the activated carbon (−) εp εb Void fraction in the column (−)  Viscosity of carbon dioxide in the column (Pa · s)  Density of carbon dioxide in the column (kgCO2 /m3 ) Solid density of the activated carbon (kgs adsorbent/m3 )  vdW van der Waals diameter of VOCs (nm) Subscripts 0 Initial value Experimental value exp calc Calculated value

must be theoretically analyzed using an appropriate model for the efficient design of the processes along with experimental data. One of the most popular models for correlating the desorption behavior was represented by partial differential equations of material balances in the bulk phase and effective diffusion in the pores of the adsorbent. It showed high applicability to the desorption behavior of organics from activated carbon in scCO2 [8,9,11,16,19,20]. The application of such types of kinetic models to the desorption behavior of various VOCs can provide an important basis for designing regeneration processes using scCO2 in consideration of the properties of VOCs. In this study, eight types of VOCs with different chemical and physical properties (aromatics, paraffin, ketone, alcohol, and ether)—toluene, n-hexane, n-octane, acetone, methanol, ethanol, 2propanol, and propylene glycol monomethyl ether (PGME)—were chosen as target adsorbates. Then, the desorption behavior of these VOCs from activated carbon was studied over a wide range of scCO2 conditions (T = 313–353 K, P = 10.0–15.0 MPa) via measure-

Table 1 Properties of activated carbon. Property

Value

Specific surface area (m2 /g)a Mean pore diameter (nm)a Pore volume (cm3 /g)a Mean particle diameter (␮m) Solid density (g/cm3 )b Porosityc

1300 0.69 0.441 100 2.21 0.494

a b c

Determined by a nitrogen adsorption measurement with t method [22]. Determined by the helium buoyancy with a magnetic suspension balance [23]. Calculated from the solid density, pore volume and mass of the adsorbent.

Table 2 Characteristics of desorption column. Property

Value

Inner diameter (mm) Length (mm) Volume (cm3 ) Mass of activated carbon (g) Void fraction (−)a

4.35 100 1.485 0.705 0.576

a Determined with the column volume, solid density, pore volume and mass of the adsorbent.

ments and kinetic modeling to investigate the effects of the VOC properties on the desorption phenomena. The first part of this paper discusses the experimental data of the desorption behavior of four VOCs (n-octane, ethanol, 2-propanol, and PGME) from activated carbon that were newly measured in this study. Then, the correlations of the measured data by a kinetic model and the determined fitting parameters are discussed with the desorption data of other VOCs (n-hexane, methanol, acetone, and toluene) that were reported previously [21]. 2. Experimental 2.1. Materials Carbon dioxide (purity: 99.99 vol%) was obtained from Showa Denko Gas Products Co., Ltd., Japan. n-octane (purity: 98.0 mass%), ethanol (purity: 99.5 mass%), and 2-propanol (purity: 99.7 mass%) were purchased from Wako Pure Chemical Industries, Japan. PGME (purity: 99.5 mass%) was obtained from Sigma-Aldrich Co. LLC., USA. These chemicals were used without further purification. Activated carbon was obtained from Cambridge Filter Japan, Ltd.; its properties are listed in Table 1. The specific surface area, mean pore diameter, and pore volume of activated carbon were determined by the t method [22]. The solid density of the adsorbent was determined by helium buoyancy with a magnetic suspension balance [23]. The adsorbent was loaded into an adsorption (and also desorption) column (1/4-inch SUS316 steel tube) and pretreated by heating in argon gas atmosphere at 573 K for 8 h to remove physisorbed water and possible impurities. The characteristics of the column are summarized in Table 2. 2.2. Method The desorption behavior of VOCs from activated carbon in scCO2 was measured by using the fixed-bed method at 313–353 K and 10.0–15.0 MPa. The details of the experimental apparatus and procedure are described in our previous paper [21]. The experimental desorption ratio of VOCs (DRexp ) is given as follows: DRexp [%] =

qdes,exp (t) qads

× 100

(1)

I. Ushiki et al. / J. of Supercritical Fluids 121 (2017) 41–51

43

Fig. 1. Schematics of the kinetic model for desorption behavior of VOCs from activated carbon in supercritical carbon dioxide.

where qdes (t) is the amount of desorbed VOC at desorption time t. qads is the initial amount of adsorbed VOC that was determined using breakthrough curve measurements with the fixed-bed method [21] under the same operating temperature and pressure conditions as those for the desorption measurement, and the values of qads were summarized in Table S1 as Supplementary data. The desorption behavior of each VOC can be compared by normalization using Eq. (1). The validation of the desorption measurements was described in detail in the previous report [21]. 3. Kinetic model for desorption behavior of VOCs in scCO2 The measured desorption behavior of VOCs in scCO2 was correlated by a kinetic model based on the extraction model proposed by Salimi et al. [24]. The present model is similar to that reported by Madras et al. [20] except for the adsorption isotherm used in the adsorbed phase (this study: the Langmuir model [25] (see Eq. (11)), Madras et al. [20]: the Freundlich model [26]). Fig. 1 shows the schematics of the model. This model uses the following assumptions: 1 The fixed bed consists of activated carbon as the stationary phase and scCO2 as the mobile phase with plug flow. 2 The system was isothermal and isobaric, and the physical properties of CO2 were constant during the desorption process. 3 All particles were assumed to be spherical with constant radius (Rp ) and porosity (εp ), and the initial amount of adsorbed VOC (qads ) was uniformly distributed in the adsorbed phase in the particles. 4 The axial dispersion in the bulk phase and effective diffusion of VOCs in the pore phase were considered in the model formulation by partial differential equations. 5 The material balance of VOCs between the pore phase and the adsorbed phase in the particles was described by the Langmuir equation [25] with the assumption of local adsorption equilibria. 6 The initial concentration of VOCs in the pore phase (Cp,0 ) was assumed to be a back-calculated value by the Langmuir equation with the initial concentration of VOCs in the adsorbed phase (Ca,0 ) (see Eq. (8)). According to these assumptions, the material balance in the bulk phase and the corresponding initial and boundary conditions are given as follows:

  ∂C b ∂C ∂ Cb 3kf εb − (1 − εb ) Cb − Cp |r = Rp (2) = −u b + εb Daz Rp ∂t ∂z ∂z 2 2

Cb = 0 at t = 0

(3)

Cb =

εb Daz ∂Cb at z = 0 u ∂z

(4)

∂Cb = 0 at z = L ∂z

(5)

where Cb and Cp are the concertations of VOCs in the bulk and pore phases, respectively. Daz is the axial dispersion coefficient, and kf is the mass transfer coefficient from the pore phase to the bulk phase. z and r are the axial and radial coordinates in the column and particles, respectively. u and ␧b are the superficial velocity and void fraction in the column, respectively. L is the column length. The material balances in the pore phase and adsorbed phase of the particles are described by the following equations with the corresponding initial and boundary conditions: εp

∂C p De ∂ = 2 r ∂r ∂t



r2

∂Cp ∂r



− (1 − εp )s

∂Ca ∂t

Ca = Ca,0 = qads at t = 0 Cp = Cp,0 =

(7)

Ca,0 at t = 0 (qsat − Ca,0 )K

∂Cp = 0 at r = 0 ∂r De

(8)

(9)

  ∂C p = kf Cb − Cp |r = Rp at r = Rp ∂r

Ca =

(6)

qsat KCp 1 + KCp

(10) (11)

where Ca is the VOC concentration in the adsorbed phase, and De is the effective diffusion coefficient of VOCs in the pore phase. εp and s are the porosity and solid density of the particles, respectively. Eq. (11) corresponds to the Langmuir equation [25], where qsat and K are the saturated adsorption amount and the adsorption equilibrium constant, respectively. In Eqs. (2), (4), and (10), kf and Daz were predicted with the relationships of the Sherwood (Sh), Reynolds (Re), Schmidt (Sc) and Peclet (Pe) numbers as follows [27,28]:



Sh = 0.82 · Re0.66 · Sc 0.33 Sh =



(12)

kf dp Dm

Pe = 1.634Re0.265 · Sc −0.919 , Pe =

(13), ; udp εb Daz

(14)

where dp is the particle diameter. Dm , , and  are the molecular diffusion coefficient, viscosity, and density of the fluid in the bulk

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I. Ushiki et al. / J. of Supercritical Fluids 121 (2017) 41–51

Table 3 Parameters used in kinetic model. T (K)

P (MPa)

 (kg/m3 )a

u×103 (m/s)b

×105 (Pa s)c

Dm ×108 (m2 /s)d

kf ×103 (m/s)e

Daz ×107 (m2 /s)e

353

15.0 12.5 10.0 15.0 12.5 10.0 15.0 12.5 10.0

427.2 317.6 221.6 604.1 471.5 290.0 780.2 731.2 628.6

3.28 4.41 6.32 2.32 2.97 4.83 1.80 1.92 2.23

3.50 2.88 2.41 4.75 3.70 2.64 6.85 6.13 4.93

5.86 7.92 11.26 3.75 5.05 8.27 2.34 2.62 3.28

1.93 2.78 4.20 1.15 1.66 3.03 0.68 0.78 1.03

2.84 3.02 3.53 3.16 2.88 3.12 4.61 4.11 3.46

333

313

a b c d e

Calculated with the Span-Wagner equation of state [31]. Superficial velocity of CO2 in the desorption column. Determined with the prediction model proposed by Chung et al. [30]. Predicted by the model proposed by Liu and Macedo [29]. Determined with Eqs. (12)–(14).

(a)

80 60 40

80 60 40 20

20 0

(b)

100 Desorption ratio [%]

Desorption ratio [%]

100

0

2

4 6 Desorption time [min]

8

10

0

0

2

4 6 Desorption time [min]

8

10

Fig. 2. Measurement and correlation results of desorption behavior of VOCs from activated carbon in supercritical carbon dioxide at (a) 353 K − 15.0 MPa and (b) 313 K − , ethanol; , acetone [21]; , 2-propanol; , n-hexane [21]; , PGME; , n-octane; , toluene [21]; solid lines, correlation with the 10.0 MPa. ( , methanol [21]; kinetic model).

phase, respectively. Because the mole fraction of VOCs in the bulk phase (yVOC ) was very small in this study (ca. yVOC = ∼1.0 × 10−2 ), Dm , , and  were assumed to be those of pure CO2 at the corresponding temperature and pressure conditions. Dm was predicted using the density expansion method proposed by Liu and Macedo [29].  was calculated using the model proposed by Chung et al. [30].  was calculated using the Span-Wagner equation of state [31]. These values are summarized in Table 3. The partial differential equations (Eqs. (2) and (6)) were converted to dimensionless formulas and solved numerically by the implicit method with the initial and boundary conditions. After validating the numerical calculations, the calculation steps r/Rp , z/L, and t were set to 0.2, 0.002, and 1 s, respectively. The amount of desorbed VOCs (qdes,calc ) per mass of activated carbon (mac ) was calculated by integrating the VOC concentration in the bulk phase at the column exit (Cb |z =L ) with respect to time: qdes,calc (t) =

(Q/CO2 )

t 0

Cb (t)| z=L dt − mac Vp Cp,0 mac

(15)

where Q and ␳CO2 are the mass flow rate and density of CO2 in the desorption column, respectively, and Vp is the pore volume of activated carbon. In Eq. (15), the term mac Vp Cp,0 corresponds to the initial amount of VOCs in the pore phase. The calculated desorption ratio (DRcalc ) was defined as follows: DRcalc [%] =

qdes,calc (t) × 100 qads

(16)

About the three unknown parameters (De , qsat and K), the Langmuir constants (qsat and K) in Eq. (11) can be determined with corresponding adsorption equilibrium data of the VOCs on the same activated carbon in scCO2 if they are available. However, the

adsorption equilibrium data of the VOCs were not available except for acetone [32], n-hexane [32], and toluene [32,33]. In addition, although De can be estimated with the molecular diffusion coefficient of adsorbates and physical properties of adsorbents such as the tortuosity and porosity [34], data of molecular diffusion coefficient of the VOCs in scCO2 were extremely limited, and determination of the tortuosity of the activated carbon was not easy. Therefore, De , qsat , and K in the kinetic model were used as fitting parameters to correlate the measured desorption behavior with minimization of the average relative deviation (ARD) as follows: 1  DRcalc,i − DRexp,i | | × 100 N DRexp,i N

ARD [%] =

(17)

i=1

The ARD values were minimized at DRexp values of 0%–99.5% using a simplex optimization method in Matlab 2016a. 4. Results and discussion 4.1. Experimental results 4.1.1. VOC dependence of desorption behavior in scCO2 Fig. 2 shows the measurement results of the desorption behavior of VOCs (n-octane, PGME, ethanol, and 2-propanol) from activated carbon in scCO2 at 353 K–15.0 MPa and 313 K–10.0 MPa compared with those of other VOCs (methanol, acetone, n-hexane, and toluene) that were reported previously [21]. These results indicate that the desorption behavior strongly depended on the VOC species. The VOC dependence of the desorption behavior may be explained by two primary factors: the interaction of VOCs with the adsorbent and the volatility of VOCs. Figs. 3 and 4 show the relationship between the physical properties of VOCs (Table 4) and the

I. Ushiki et al. / J. of Supercritical Fluids 121 (2017) 41–51

45

Table 4 Physical properties of volatile organic compounds (VOCs). VOCs

M (g/mol)a

Vm (cm3 /mol)b

Pvap,313 (kPa)c

Pvap,353 (kPa)d

vdW

(nm)e

Methanol Ethanol 2-Propanol PGME Acetone n-Hexane n-Octane Toluene

32.042 46.069 60.096 90.121 58.080 86.177 114.229 92.141

40.73 58.68 76.92 98.39 73.94 131.59 163.53 106.87

35.4 17.9 14.2 3.6 56.6 37.3 4.1 7.9

180.8 108.5 92.5 24.2 215.2 142.5 23.3 38.9

0.410 0.466 0.511 0.562 0.498 0.601 0.655 0.574

ıVOC

(MPa1/2 )f

ı (MPa1/2 )h

29.6 26.5 23.5 23.0g 20.0 14.9 15.5 18.2

18.8 15.7 12.7 12.2 9.2 4.1 4.7 7.4

a

Molar mass of VOCs [6,43]. Molar volume of VOCs for the saturated liquids at 298.15 K [43]. c Saturated vapor pressure of VOCs at 313.15 K calculated with the Antoine equation [6] [36]. d Saturated vapor pressure of VOCs at 353.15 K calculated with the Antoine equation [6] [36]. e van der Waals diameter of VOC molecules determined with Bondi’s method [35]. f The Hildebrand solubility parameter of VOCs for saturated liquids at 298.15 K [37]. g Predicted with the group contribution method by Fedors [38]. h Absolute deviation of the Hildebrand solubility parameters for CO2 (ıCO2 ) and VOC (ıVOC ), ı = |ı VOC - ıCO2 |. ıCO2 (=10.8 MPa1/2 ) is the value for saturated liquid at 298.15 K predicted with the method by Williams et al. [39]. b

80

100

Methanol Ethanol

60

Acetone 2-Propanol n-Hexane

40 PGME

20 Toluene

0 0.4

n-Octane

Desorption ratio at t = 2 min [%]

Desorption ratio at t = 2 min [%]

100

80 60

0.7

Fig. 3. Relationship between the van der Waals diameter of VOCs [35] (Table 4) and desorption ratio of VOCs from activated carbon at desorption time t = 2 min in , ethanol; , acetone [21]; supercritical carbon dioxide. ( , methanol [21]; , 2-propanol; , n-hexane [21]; , PGME; , n-octane; , toluene [21]; closed symbols, at 353 K and 15.0 MPa; open symbols, at 313 K and 10.0 MPa).

desorption ratio of VOCs from the activated carbon at desorption time t = 2 min in scCO2 . As shown in Fig. 3, VOCs that have larger van der Waals diameter ( vdW ) [35] and lower polarity, such as noctane, indicate a slower desorption rate compared with those that have smaller  vdW and higher polarity, such as methanol and acetone. This is because VOCs with larger  vdW and lower polarity can interact strongly with the activated carbon inside the pore structure (mean pore diameter: 0.69 nm, Table 1), and accordingly, the desorption rate of n-octane can be smaller than those of methanol and acetone. Additionally, Table 4 summarizes the saturated vapor pressure (Pvap ) of the VOCs at the operating temperature calculated with the Antoine equation [6,36], and Fig. 4 shows the relationship between the desorption ratio at t = 2 min and Pvap of the VOCs. VOCs with smaller Pvap , such as n-octane and toluene, cannot vaporize easily from the adsorbed phase to the bulk phase in scCO2 , and therefore, their desorption rates could be smaller than those of other VOCs such as methanol and acetone with larger Pvap . These discussions suggest that the desorption behavior of VOCs from activated carbon in scCO2 depended strongly on the interaction of VOCs for the adsorbent and the volatility of VOCs. 4.1.2. Pressure dependence of desorption behavior in scCO2 Fig. 5 shows the pressure dependence of the desorption behavior of ethanol, 2-propanol, n-octane, and PGME from activated carbon in scCO2 at 353 K. These results indicate that the desorption

Acetone

2-Propanol

40

PGME n-Hexane n-Octane

20

Toluene

0

0.5 0.6 van der Waals diameter of VOCs [nm]

Methanol Ethanol

0

50 100 150 200 250 Saturated vapor pressure of VOCs [kPa]

Fig. 4. Relationship between the saturated vapor pressure of VOCs (Table 4) and desorption ratio of VOCs from activated carbon at desorption time t = 2 min in super, ethanol; , acetone [21]; , critical carbon dioxide. ( , methanol [21]; , n-hexane [21]; , PGME; , n-octane; , toluene [21]; closed 2-propanol; symbols, at 353 K and 15.0 MPa; open symbols, at 313 K and 10.0 MPa). The saturated vapor pressure of VOCs is that of the pure component at the experimental temperature calculated by the Antoine equation.

rate of the VOCs increased with pressure, which was also observed in the cases of other VOCs [21] and at other temperatures. The pressure dependence can be caused by increasing driving force of desorption with an increase in the partitioning of VOCs from the adsorbed phase to the bulk phase at higher CO2 density (CO2 ) (e.g., CO2 = 222 kg/m3 at 353 K and 10.0 MPa, CO2 = 427 kg/m3 at 353 K and 15.0 MPa [31]). Some researchers [8,11–13,15] have also reported similar pressure dependence of the desorption behavior of VOCs from activated carbon in scCO2 with respect to the CO2 density effect. Consequently, the CO2 density can be a primary factor influencing the desorption behavior of VOCs from activated carbon under scCO2 . 4.1.3. Temperature dependence of desorption behavior in scCO2 Fig. 6 shows the temperature dependence of the desorption behavior of ethanol, 2-propanol, n-octane, and PGME from activated carbon in scCO2 at 10.0 MPa. The temperature dependence differed with the VOC species. In the cases of 2-propanol, n-octane, and PGME, the desorption rates decreased with an increase in the temperature; this temperature dependence was also observed in the cases of toluene, acetone, and n-hexane [21]. In general, the desorption of adsorbates from adsorbents is promoted by an increase in temperature because of the increase in the volatility of the adsorbates. However, under scCO2 , the CO2 density decreases

46

I. Ushiki et al. / J. of Supercritical Fluids 121 (2017) 41–51

100

(a)

80

Desorption ratio [%]

Desorption ratio [%]

100

60 40 20 0

0

2

4 6 Desorption time [min]

8

60 40

0

10

0

100

(c)

80

Desorption ratio [%]

Desorption ratio [%]

80

20

100

60 40

5 10 Desorption time [min]

15

10 15 Desorption time [min]

20

(d)

80 60 40 20

20 0

(b)

0

20

40 60 Desorption time [min]

80

100

0

0

5

Fig. 5. Pressure dependence of VOCs ((a) ethanol, (b) 2-propanol, (c) n-octane, and (d) PGME) desorption behavior from activated carbon in supercritical carbon dioxide at 353 K. (

, 10.0 MPa;

, 12.5 MPa;

, 15.0 MPa; solid lines, correlation with the kinetic model).

with increasing temperature; this can prevent the desorption of VOCs because of the decreasing driving force of desorption in a manner similar to pressure dependence, as mentioned above. On the other hand, in the cases of ethanol, the desorption rate at 353 K was larger than that at 333 K, as shown in Fig. 6, and a similar trend was also reported in the cases of methanol [21]. The temperature dependence for these alcohols can be explained by the solubility parameter of the VOCs (ıVOC ) [37,38] and CO2 (ıCO2 ) [39] as shown in Table 4. In the cases of methanol and ethanol, the values of the absolute deviation of the solubility parameters for VOC and CO2 , ı (=|ıVOC − ıCO2 |), are larger than those of other VOCs such as n-hexane and n-octane (Table 4). This means the lower affinity of these alcohols for CO2 , and therefore, the temperature effect of volatility on the desorption behavior might be dominant in comparison with the CO2 density effect. Consequently, it was implied that the temperature dependence of the desorption behavior differed with the VOC species; this difference was explained by the properties of the VOCs.

4.2. Correlation results of desorption behavior The solid lines in Figs. 2, 5 and 6 show the correlation results of the desorption behavior of the VOCs by the kinetic model. Table 5 lists the values of the ARD of the correlation and the determined fitting parameters (De , qsat , and K). The kinetic model could correlate the desorption behavior to within 4% at all conditions (Table 5). To verify the desorption mechanism of the model, Fig. 7 shows the normalized concentration profiles in the adsorbed (Ca ), pore (Cp ), and bulk (Cb ) phases at different particle and column posi-

tions in the calculation of the desorption behavior of n-octane at 313 K and 10.0 MPa. As shown in Fig. 7, the desorption of the VOC started at the particle surface and column entrance, and ended at the center of the particle and column exit. In addition, Fig. 7(a) and (b) indicate that the values of Ca and Cp at r/Rp = 1 decreased quickly after the beginning of the desorption, and then increased and decreased gradually. These concentration profiles corresponded to the expected desorption phenomena of VOCs from the adsorbent in scCO2 , as shown in Fig. 1. Similar concentration profiles of the desorption model were also obtained in the other VOCs and operating conditions, which could validate the calculation results obtained by the kinetic model. 4.3. Fitting parameters The three fitting parameters De , qsat , and K were determined using the correlations by the kinetic model for various VOCs under scCO2 , and the values are listed in Table 5. In this section, the effects of the operating conditions and VOC species on the fitting parameters were discussed to quantitatively understand the desorption behavior of VOCs from activated carbon in scCO2 . 4.3.1. Parameter De (effective diffusion coefficient in pore phase) De increased with temperature at all VOCs and pressure conditions, as shown in Table 5. This is attributed to the increase in the mobility of VOCs with increasing temperature in a manner similar to the general temperature dependence of diffusion phenomena. Fig. 8(a) shows the CO2 density dependence of De as determined using the correlation (Table 5). For all VOCs, De decreased with

I. Ushiki et al. / J. of Supercritical Fluids 121 (2017) 41–51

100

(a)

80

Desorption ratio [%]

Desorption ratio [%]

100

60 40 20 0

0

5 Desorption time [min]

80 60 40

0

10

0

100

(c)

80

Desorption ratio [%]

Desorption ratio [%]

(b)

20

100

60 40 20 0

47

5 Desorption time [min]

10

10 15 Desorption time [min]

20

(d)

80 60 40 20

0

10

20 30 40 50 Desorption time [min]

60

0

70

0

5

Fig. 6. Temperature dependence of VOCs ((a) ethanol, (b) 2-propanol, (c) n-octane, and (d) PGME) desorption behavior from activated carbon in supercritical carbon dioxide at 10.0 MPa (

, 313 K;

, 333 K;

, 353 K; solid lines, correlation with the kinetic model).

(b) 1.0

0.8

0.8

0.6

Cp/Cp,0 [-]

Ca/Ca,0 [-]

(a) 1.0

at z/L=0.50 r/Rp=0

0.4

r/Rp=0.40

0.2

r/Rp=0.80

at z/L=0.50 r/Rp=0 r/Rp=0.40 r/Rp=0.60 r/Rp=0.80

0.6

r/Rp=1

0.4

r/Rp=0.60

0.2

r/Rp=1 0.0

0.0 0

0.8

5 Desorption time [min]

0

5 Desorption time [min]

10

(c) z/L=0 z/L=0.10 z/L=0.25 z/L=0.50 z/L=1

0.6 Cb/Cp,0 [-]

10

0.4

0.2

0.0 0

5 Desorption time [min]

10

Fig. 7. Concentration profiles of (a) Ca /Ca,0 at z/L = 0.50, (b) Cp /Cp,0 at z/L = 0.50, and (c) Cb /Cp,0 at different particle (r/Rp ) and column (z/L) positions in the calculations of the desorption behavior of the VOC (n-octane) from activated carbon in supercritical carbon dioxide at 313 K and 10.0 MPa.

48

I. Ushiki et al. / J. of Supercritical Fluids 121 (2017) 41–51

Table 5 Correlation results of desorption behavior of VOCs from activated carbon in supercritical carbon dioxide by the kinetic model. VOCs

T (K) d

Methanol

353

333

313

Ethanol

353

333

313

2-Propanol

353

333

313

PGME

353

333

313

Acetoned

353

333

313

n-Hexaned

353

333

313

n-Octane

353 333 313

Toluened

353

333 313

a b c d

P (MPa) 15.0 12.5 10.0 15.0 12.5 10.0 15.0 12.5 10.0 15.0 12.5 10.0 15.0 12.5 10.0 15.0 12.5 10.0 15.0 12.5 10.0 15.0 12.5 10.0 15.0 12.5 10.0 15.0 12.5 10.0 15.0 12.5 10.0 15.0 12.5 10.0 15.0 12.5 10.0 15.0 12.5 10.0 15.0 12.5 10.0 15.0 12.5 10.0 15.0 12.5 10.0 15.0 12.5 10.0 15.0 10.0 15.0 15.0 12.5 10.0 15.0 12.5 10.0 10.0 15.0 12.5 10.0

Fitting parameter of the correlations in Eqs. (6) and (10). Fitting parameters of the correlations in Eq. (11). Average relative deviation defined by Eq. (17). Experimental data obtained from the previous research [21].

De ×109 (m2 /s)a 6.78 8.36 10.26 4.97 6.08 8.53 4.64 3.77 3.64 4.06 5.55 6.84 3.27 4.01 5.67 3.20 2.93 3.05 1.88 2.33 2.88 1.37 1.68 2.38 1.00 1.09 1.27 0.34 0.43 0.56 0.33 0.34 0.50 0.20 0.24 0.27 1.06 1.34 1.69 0.85 0.90 1.27 0.65 0.70 0.82 0.67 0.90 1.15 0.37 0.58 0.68 0.32 0.29 0.33 0.33 0.50 0.23 0.18 0.19 0.19 0.44 0.56 0.56 0.45 0.35 0.33 0.33

qsat (mol/kg)b 7.15 10.73 16.01 5.90 10.86 16.66 5.02 7.13 9.30 5.87 8.01 12.30 5.77 8.01 11.15 4.39 5.33 6.64 2.96 4.01 4.90 2.61 3.95 5.09 2.32 2.93 3.56 2.59 2.90 3.91 2.45 2.68 3.29 2.12 2.17 2.53 1.81 2.19 2.81 1.31 1.68 2.46 1.12 1.15 1.36 2.47 3.06 3.86 2.52 2.42 3.48 1.65 2.27 2.16 1.47 1.69 1.17 1.03 1.04 1.19 2.55 2.78 3.20 3.81 2.47 2.25 2.52

K (m3 /mol)b −3

1.61 × 10 1.89 × 10−3 2.21 × 10−3 1.25 × 10−3 1.22 × 10−3 2.19 × 10−3 1.27 × 10−3 1.00 × 10−3 1.16 × 10−3 2.52 × 10−3 3.81 × 10−3 4.56 × 10−3 1.63 × 10−3 2.18 × 10−3 4.58 × 10−3 2.09 × 10−3 2.00 × 10−3 2.46 × 10−3 7.09 × 10−3 9.94 × 10−3 1.83 × 10−2 5.73 × 10−3 5.82 × 10−3 1.23 × 10−2 3.94 × 10−3 3.93 × 10−3 4.22 × 10−3 2.51 × 10−2 5.30 × 10−2 1.01 × 10−1 1.54 × 10−2 2.70 × 10−2 7.40 × 10−2 1.09 × 10−2 1.33 × 10−2 1.82 × 10−2 1.17 × 10−2 1.62 × 10−2 2.69 × 10−2 9.55 × 10−3 1.17 × 10−2 2.17 × 10−2 7.10 × 10−3 8.24 × 10−3 1.01 × 10−2 1.57 × 10−2 2.49 × 10−2 4.16 × 10−2 9.90 × 10−3 1.50 × 10−2 2.71 × 10−2 1.07 × 10−2 6.20 × 10−3 8.99 × 10−3 1.81 × 10−1 8.05 × 10−1 1.24 × 10−1 1.03 × 10−1 1.06 × 10−1 1.15 × 10−1 1.29 × 10−1 1.85 × 10−1 3.92 × 10−1 1.41 × 10−1 6.64 × 10−2 8.60 × 10−2 9.42 × 10−2

ARD (%)c 0.8 0.6 0.5 0.5 0.8 0.6 1.0 1.1 0.9 1.0 1.5 0.8 0.8 0.6 1.0 1.7 1.8 1.9 1.3 1.0 0.9 2.4 1.5 1.0 1.4 1.5 1.1 0.6 0.7 0.8 0.9 1.0 0.4 1.0 0.9 0.6 1.3 1.5 1.6 1.3 1.4 1.5 1.3 1.4 1.3 2.5 1.3 1.4 1.3 1.6 1.1 2.0 0.6 0.2 2.1 0.7 3.1 3.9 2.8 0.9 1.4 2.1 1.5 1.2 1.7 1.7 1.5

I. Ushiki et al. / J. of Supercritical Fluids 121 (2017) 41–51 353 K 333 K 313 K

(a) Methanol

10-10

10-8

Ethanol 2-Propanol Acetone n-Hexane PGME Toluene n-Octane

10-9

0

200

(b)

15.0 MPa 12.5 MPa 10.0 MPa

De [m2/s]

De [m2/s]

10-8

400

49

600

800

10-9

10-10 20

40

Density of CO2 [kg/m3]

60

80

100

120

Molar mass of VOCs [g/mol]

Fig. 8. (a) CO2 density dependence of De determined with the correlations by the kinetic model at 313–353 K and 10.0–15.0 MPa in supercritical carbon dioxide. (b) Relationship between the determined De (䊉, 353 K − 10.0 MPa; , 313 K − 10.0 MPa) and the molar mass of VOCs (Table 4) with literature values reported by Heidari et al. [8] for desorption of cyclohexane from activated carbon in supercritical carbon dioxide at 315 K − 10.5 MPa ( ) and 328 K − 10.5 MPa ( ). (pink symbols, methanol; purple symbols, ethanol; light blue symbols, 2-propanol; red symbols, acetone; brown symbols, PGME; green symbols, n-hexane; blue symbols, toluene; orange symbols, n-octane). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

(a)

(b)

353 K 333 K 313 K 15.0 MPa 12.5 MPa 10.0 MPa

qsat [mol/kg-adsorbent]

qsat [mol/kg-adsorbent]

100

Methanol Ethanol

10 2-Propanol n-Hexane PGME Toluene Acetone n-Octane

1

10

1 0

200

400

600

800

0

50

100

150

200

Molar volume of VOCs [cm3/mol]

3

Density of CO2 [kg/m ]

Fig. 9. (a) CO2 density dependence of qsat determined with the correlations by the kinetic model at temperatures of at 313–353 K and 10.0–15.0 MPa in supercritical carbon dioxide. (b) Relationship between the determined qsat (䊉, 353 K − 10.0 MPa; , 313 K − 10.0 MPa) and the molar volume of VOCs (Table 4). (pink symbols, methanol; purple symbols, ethanol; light blue symbols, 2-propanol; red symbols, acetone; brown symbols, PGME; green symbols, n-hexane; blue symbols, toluene; orange symbols, n-octane). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

353 K 333 K 313 K

(a)

100

(b)

Toluene

10-1

10-2

K [m3/mol]

K [m3/mol]

n-Octane

100

15.0 MPa 12.5 MPa 10.0 MPa

PGME n-Hexane Acetone 2-Propanol

10-1

10-2

Ethanol Methanol

10-3 0

200

400

600

800

Density of CO2 [kg/m3]

10-3 0.4

0.5

0.6

0.7

van der Waals diameter of VOCs [nm]

Fig. 10. (a) CO2 density dependence of K determined with the correlations by the kinetic model at 313–353 K and 10.0–15.0 MPa in supercritical carbon dioxide. (b) Relationship between the determined K (䊉, 353 K − 10.0 MPa; , 313 K − 10.0 MPa) and the van der Waals diameter of VOCs [35] (Table 4). (pink symbols, methanol; purple symbols, ethanol; light blue symbols, 2-propanol; red symbols, acetone; brown symbols, PGME; green symbols, n-hexane; blue symbols, toluene; orange symbols, n-octane). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

an increase in the CO2 density. This is because the diffusion of the VOC molecules is prevented by CO2 molecules under higher CO2 density. Similar CO2 density dependence was also reported in the cases of the molecular diffusion coefficient of VOCs (acetone [40], toluene [41], n-octane [42], and n-hexane [42]) in scCO2 . In addition, because De was smaller than those of the molecular dif-

fusion coefficients of VOCs (∼10−7 –10−8 m2 /s [40–42]) in scCO2 , the determined De values appear reasonable. Furthermore, De varied greatly with the VOC species, as shown in Fig. 8(a). Fig. 8(b) shows the relationship between De determined by the correlations (353 K − 10.0 MPa and 313 K − 10.0 MPa) and the molar mass of VOCs [6,43] with literature data reported by Heidari

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I. Ushiki et al. / J. of Supercritical Fluids 121 (2017) 41–51

et al. [8] for desorption of cyclohexane from activated carbon in scCO2 that were determined with the similar kinetic model in this study. Fig. 8(b) demonstrates a clear trend of De for the molar mass of the VOCs. This may be because VOCs with larger molar mass, such as n-octane, have lower mobility than those with smaller molar mass, such as methanol. These expected results support the validity of the determined De values with the correlations. 4.3.2. Parameter qsat (saturated adsorption amount of VOCs) Fig. 9(a) shows the CO2 density dependence of qsat that was determined from the correlation of the desorption behavior. qsat strongly depended on the CO2 density for all VOCs. This may be because the saturated adsorption capacity of VOCs decreases with increasing CO2 density owing to the increasing amount of adsorbed CO2 that can competitively adsorb with the VOCs. Fig. 9(b) shows the relationship between the molar volume of VOCs [43] and qsat at 353 K − 10.0 MPa and 313 K − 10.0 MPa, which indicates the clear dependence of qsat on the molar volume of VOCs for all VOCs. This may be because VOCs with smaller molar volume, such as methanol, have larger adsorption capacity in the pore structure of the adsorbent on a molar basis compared with those with larger molar volume, such as n-octane. 4.3.3. Parameter K (adsorption equilibrium constant) Fig. 10(a) shows the CO2 density dependence of K that was determined from the correlations. K decreased with an increase in the CO2 density in a manner similar to De and qsat , as described above. This may be because the affinity of VOCs for activated carbon decreases with increasing CO2 density owing to increased partition of VOCs from the adsorbed phase to the bulk phase. Fig. 10(b) shows the relationship between the van der Waals diameter of VOCs [35] and K determined at 353 K − 10.0 MPa and 313 K − 10.0 MPa. K increases with the van der Waals diameter of VOCs for all VOCs. The trend of K may be because VOCs with larger molecular size, such as n-octane, may interact strongly with the adsorbent in the pore structure compared to those with smaller molecular size, such as methanol. Consequently, De , qsat , and K determined using the correlations showed reasonable trends to the related properties of VOCs and CO2 in consideration of the physical meanings, and they provided quantitative information that can be useful for designing regeneration processes for activated carbon using scCO2 . Additionally, it may be possible to develop generalized relations of these fitting parameters using the related physical properties of CO2 and VOCs. This suggests the possibility for predicting desorption behavior in the cases of other operating conditions and other VOCs although more experimental data may be required. 5. Conclusions The desorption behavior of VOCs from activated carbon under scCO2 was studied. The measured behavior clearly depends on the physical properties of the VOC species. The pressure and temperature dependence of this behavior showed that the CO2 density and volatility of VOCs are the primary factors influencing the desorption phenomena. The kinetic model could correlate the desorption behavior within 4% of the average relative deviation by using three fitting parameters, and the determined fitting parameters provide quantitative information about the desorption processes in scCO2 in consideration of the properties of the VOCs and CO2 . Acknowledgments This research was financially supported by the JSPS (Japan Society for the Promotion of Science) KAKENHI (No: 25289271 and

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