Modeling VOCs adsorption onto activated carbon

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Modeling VOCs adsorption onto activated carbon

C.L. Chuang

a

, P.C. Chiang

a,*

, E.E. Chang

b

a

Graduate Institute of Environmental Engineering, National Taiwan University, 71 Chou-Shan road, Taipei, Taiwan

b

Department of Biochemistry, Taipei Medical University, Taipei, Taiwan

Received 15 October 2002; received in revised form 26 February 2003; accepted 25 March 2003

Abstract

The activated carbon adsorption process is aﬀected by the characteristics of adsorbent, adsorbate and environmental conditions. In this study, both adsorption and desorption processes are assumed to occur simultaneously and a nu-merical model was developed with a non-linear driving force in conjunction with the Langmuir model for predicting the overall adsorption process. The numerical model provides both adsorption and desorption rate constants and acti-vation energies. The resultant equilibrium constants are of the same order of magnitude as reported by other studies. Results show that the model could well predict the adsorption isotherms and breakthrough curves under various conditions.

Keywords: Activated carbon; VOCs; Adsorption; Desorption; Kinetics

1. Introduction

Activated carbon is a common adsorbent for the removal of hazardous pollutants. It has been reported that factors, such as characteristics of activated carbon, the nature and concentration of adsorbates, and reac-tion condireac-tions including temperature and humidity, can aﬀect the adsorption process. Pressure swing adsorption and thermal swing adsorption are the most common methods used to study the adsorption process (Hwang and Lee, 1994). King and Do (1996) used the Fourier transfer-infrared technique to evaluate the eﬀect of temperature on the adsorption capability of ethane, propane, and n-butane onto activated carbon. They re-ported that the equilibrium time at high temperatures was shorter than that at low temperatures. Wood (1992) observed a good correlation between the molar polar-ization of adsorbent and adsorption capacity. Other researchers (Jonas and Rehrmann, 1972; Vahdat et al.,

1995) considered the activated carbon bed adsorption process as a ﬁrst-order reaction and found the Wheeler equation to be successful for application to several or-ganic gases.

For the column adsorption studies, the most com-monly used adsorption models include the linear driving force (LDF) approximation (Gkueckauf, 1955; Critten-den and Weber, 1978; Malek and Farooq, 1996, 1997), the empirical method (Yoon and Nelson, 1984), and the Wheeler equilibrium approach (Jonas and Rehrmann, 1972; Vahdat, 1997) (Table 1). According to the LDF method, the reaction rate is governed by the diﬀerence between the temporal and the equilibrium concentra-tions of the gas adsorbate (Gkueckauf, 1955). The LDF model was utilized with a linear or non-linear equilib-rium adsorption isotherm for practical consideration (Malek and Farooq, 1996, 1997). Hwang and Lee (1994) used the LDF model to successfully describe the ad-sorption and dead-sorption behavior of carbon monoxide and carbon dioxide onto activated carbon. Yoon and Nelson (1984) developed an empirical model to predict the breakthrough curve of activated carbon beds. Based on the thermodynamic characteristic of each solute at Chemosphere 53 (2003) 17–27

www.elsevier.com/locate/chemosphere

*

Corresponding author. Fax: +886-2-23661642. E-mail address:pcchiang@ntu.edu.tw(P.C. Chiang).

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equilibrium, Myers and Prausnitz (1965) developed an ideal adsorbed solution theory to predict the adsorption of organic vapors onto activated carbon. The adsorption equilibrium of the gas mixture can be predicted from the individual single-gas isotherm using the Toch equation (Myers and Valenzuela, 1986) and/or the Dubinin/ Radushkevich equation (Dubinin, 1989). The desorption behavior of carbon ﬁlms was also observed based on the Arrhenius equation and thermal desorption spectro-scopy (Pigram et al., 1994).

The above methods are generally successful in pre-dicting the adsorption of volatile organic compounds (VOCs) onto activated carbon under speciﬁc conditions. However, the thermodynamic method considers ad-sorption as an equilibrium process. The empirical method lacks a theoretical rigor. In this study, based on the basic dynamical reaction (BDR) theory, a thermo-dynamic model, called BDR model, involving non-linear driving force was used to predict the kinetics of the adsorption of three VOCs onto activated carbon. Im-portant kinetic parameters, such as adsorption rate constant and activation energy were determined to ob-tain the adsorption isotherm and evaluate the adsorp-tion behavior under diﬀerent operaadsorp-tional condiadsorp-tions. This non-linear reaction kinetic approach can also be used to predict the adsorption rate of VOCs in column operations.

2. Experimental method 2.1. Materials

Benzene (C6H6), carbon tetrachloride (CCl4) and

trichloromethane (CHCl3) were the adsorbent VOCs

studied. The activated carbon was of pellet form with a

diameter of 3 mm and a density of 880 kg/m3

(Sorbon-orit 3, N(Sorbon-orit, the Netherlands). The activated carbon was ground ﬁrst then sieved to a size fraction from 0.35 to 0.50 mm (or 35 to 45 mesh) and heated to 573 K in a

N2atmosphere (purity 99.99%) over 24 h to remove any

adsorbed gas. The treated activated carbon was stored in

a N2-ﬁlling chamber (300 K) before experiments.

VOC was generated by passing a stream of water and

hydrocarbon-free N2gas over a series of diﬀusion tubes

containing the pure liquid of interest. The VOC con-centrations were controlled by the number of diffusion tubes and temperature as well as the carrier gas flow rate (1.2 l/min at 303 K by a mass flow meter, Instrument Inc., Sierra). The temperature of the VOC vapor was controlled by a thermostat (283–363 K) before entering the reaction column (Fig. 1). The concentrations of

C6H6, CCl4 and CHCl3 studied were in the

concentra-tion range of 8–150, 6–300 and 10–220 mmol/m3_,

re-spectively.

2.2. Adsorption and desorption in activated carbon bed For VOC adsorption experiments, about 600–2000 mg of treated activated carbon was packed in a small

glass column (height¼ 9–30 mm and cross-section

area¼ 1.76 cm2_{). The column temperature was}

main-tained at the range from 283 to 363 K for 3 h before testing. During adsorption experiments the outlet gas was continuously monitored for VOC with a portable photoionization air monitor (Perkinelmer, Photovac Model 2020). The measurements were calibrated by gas chromatography (HP 5890A; column: Supel Co., VOCOLe, #9354-04A) with a ﬂame ionization detector. After the termination of the adsorption experiment, the

inlet gas was changed to the N2 carried gas and the

outlet gas was continuously monitored with the same portable photoionization air monitor for obtaining

de-sorption data. The detection limits of C6H6, CCl4 and

CHCl3were 4.0 106, 1.2 106and 1.2 106mmol/m3,

respectively.

3. Mathematical model

The concentration change of the contaminant in the column can be described by the following equation: Table 1

Adsorption models

Column adsorption model Typical model equation Reference

Linear driving force approximation oq

ot ¼ kðq

_qÞ _{Gkueckauf (1955), Crittenden and Weber (1978),}

Malek and Farooq (1996, 1997)

Empirical method t¼ t1=2þ 1 k0ln C C0 C

Yoon and Nelson (1984) k0_¼kCQ We t1=2¼ t when C ¼ C0=2 Wheeler equation t¼ We CQ W qBQ k ln C0 C

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oC ot DL o2_C o2_Lþ U oC oLþ 1 e e q oq ot ¼ 0 ð1Þ

where DL, C, L, U , e, q, and q are the dispersion

coef-ﬁcient (m2_{/s), the concentration of VOC in the gas phase}

(mol/m3_{), the length of activated carbon bed (m), the gas}

velocity (m/s), the bed void fraction, the density of

ac-tivated carbon (g/m3_{), and the adsorption capacity (g/g),}

respectively. By assuming the process as a non-equilib-rium surface reaction and since the column is relatively short, the diﬀusion term can be negligible. Base on thermodynamic consideration, the forward reaction rate

(Ra, 1/s) is a function of the adsorbent concentration and

free surface site ratio (1 h), i.e.,

Ra¼ kað1 hÞC ð2Þ

where kais the adsorption rate constant, m3/(s mol) and

his the surface coverage, equal to q=q0, where q0is the

maximum adsorptive capacity at the monolayer level (g/g).

Likewise, the backward reaction rate (Rd) is closely

re-lated to h:

Rd¼ kdh ð3Þ

where kd is the desorption rate constant (1/s). The net

reaction rate (R, 1/s) is equal to the subtraction of Rd

from Ra:

R¼oh

ot ¼ kað1 hÞC kdh ð4Þ

In Eq. (1), ð1 eÞ=e means the ratio of solid phase

volume to gas phase volume. In a packed activated carbon bed, the solid phase volume equal to W =q and

the gas phase volume equal to (LA W =q), where W is

the weight of activated carbon (g), A the cross-sectional

area of the adsorption bed (m2_{). Eq. (1) can be rewritten}

as: oC ot ¼ U oC oL oh otS ð5Þ

where S (g/m3_{) is a conversion factor between solid and}

gas phase, which can be expressed by the following re-lation:

S¼ q0W

LA W =q ð6Þ

It is known that the ﬂow rate, Q (m3_{/s), has the following}

expression: Q¼ UA 1 W q LA 1 A ð7Þ

It is assumed that the activated carbon bed can be

treated as an entity consisting n-series (n¼ 50) of

con-stant volume units, i.e., the physicochemical conditions within each unit are identical, and that the adsorption/ desorption process follows the Langmuir model. Let Dt

(s) and DV (m3_{) be the reaction time and the gas volume}

in each unit. At the ith unit and experimental time, t, the concentration change in the solid phase and the gas phase can be determined by a ﬁnite diﬀerence method:

In the solid phase from Eq. (4), one has htþDt_i ¼ ht

iþ ½kað1 htiÞC t

i kdhtiDt ð8Þ

In the gas phase from Eq. (5), it yields C_itþDt¼ Ct iþ QDt DV ðC t i C t i1Þ þ ½kað1 htiÞC t iþ kdhtiSDt ð9Þ Accordingly, DV can be expressed by the following equation:

DV ¼LA

W q

n ð10Þ

Fig. 2 shows the conceptual presentation of the model-ing approach. Mass Flow Controller Temperature Controller N2 Gas Dehydration Dehydrocarbon VOC Generator Carbon bed Air monitor OutletGas

Gas flow direction

Diffusion tubes

Fig. 1. Experimental apparatus.

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By deﬁnition, the equilibrium adsorption mass, We,

can be calculated by the following equation:

We¼

Z 1

0

ðC0 CbÞQ dt ð11Þ

where C0 and Cbare the inlet and outlet organic vapor

concentrations, respectively, and We is the equilibrium

adsorption mass. From We, it is possible to calculate the

parameters of Langmuir isotherm, i.e., q0and KL. In this

study a SYSTAT software package was used.

To perform the numerical modeling computation, a

series of known variables (q, A, C0, W , L, Q and T ) and

estimated parameters (kaand kd) were input into Eqs. (8)

and (9) followed by iteration to obtain the breakthrough

curves, and the reaction rates (Ra, Rd, and R) were well

known, too. The best ﬁt of ka and kd was veriﬁed by

evaluating the root mean square error, d:

d¼ 1 C0 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 N XN n¼1 ðCb C0Þ 2 v u u t ð12Þ

where Cb and C0 are the observed and calculated

con-centrations at breakthrough, respectively, and N is the number measured in each test.

4. Results and discussion

4.1. Determination reaction rate constant and activation energy (ka, kd, Ea, and Ed)

Table 2 shows the results of column operation under various experimental conditions. Note that the retention

time, s, is deﬁned asðLA W =qÞ=Q. Clearly, the BDR

model can reasonably predict the outlet VOC

concen-tration (d¼ 0:01–0.07). As would be expected, both

adsorption and desorption rates increased with temper-ature. For example, the desorption rate constant of

CHCl3increased from 4.7 104to 1.6 1011/s as the

temperature increased from 283 to 363 K with the

cor-responding adsorption rate constant 1.5 101_{and 1.05}

m3_{/(s mol). It is also noted that the increase in the}

de-sorption rate constant was greater than that of the ad-sorption rate constant. Consequently, the equilibrium

constant (K¼ ka=kd) decreased by two orders of

mag-nitude (319–6.5 m3_{/mol), indicating the adsorption being}

an exothermic process (DH < 0). Results also show that

CCl4 exhibited the highest equilibrium adsorption

con-stant and C6H6 possessed the lowest.

Table 3 presents the equilibrium constants calculated from the Langmuir isotherm, LDF and BDR models which indicate that there is no signiﬁcant diﬀerence in

i-th unit In solid phase t Rt , i t i t t i =θ + ∆ θ+∆ θ Eq. 8 In gas phase

(

C C

)

R V t Q C C t c , i t 1 i t i t i t+t∆ i − + ∆t ∆ ∆ + = − Eq. 9 VOC C0 Q i = 1 i = 2 i = 3

•

Cti-1 θti-1 i i = n Ctb Q

•

i = n-1 Outlet gas Cti=1 θti=1 L Cti=n θti=n Cross Section Area: A Cti θti Cti Cti-1

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Table 2

Adsorption conditions, parameters and statistics

VOC Adsorption conditions and parameters Unit Run 1 Run 2 Run 3 Run 4 Run 5

283 K 303 K 323 K 343 K 363 K

C6H6 Reaction conditions Weight of carbon, W g 2.001 2.005 2.001 2.002 2.001

Length of carbon bed, L cm 3 3.1 3 3 3

Inﬂuent concentration, C0 mmol/m3 116 132 108 103 88

Saturation concentration, Csat mol/m3 2.6 6.3 13.5 25.8 45.1

Flow rate, Q l/min 1.14 1.2 1.3 1.38 1.46

Retention time, s s 1.60 101 _1.59₁₀1 _1.41₁₀1 _1.33₁₀1 _1.25₁₀1

Reaction parameters Adsorption rate constant, ka m3/(s mol) 1.3 102 1.6 102 1.9 102 4.0 102 6.0 102

Desorption rate constant, kd 1/s 1.0 104 4.4 104 1.6 103 5.0 103 1.1 102

Equilibrium constant, K¼ ka=kd m3/mol 130 37 12 8.0 5.4

Measured equilibrium constant, KL m3/mol 112 40 23 11 6.3

Statistics Measured number in each test, N – 27 29 41 32 26

Root mean square error, d – 0.02 0.03 0.03 0.05 0.04

Arrhenius equations – lnðkaÞ ¼ 2000=T þ 2:6, R2¼ 0:90, Ea¼ 4:0 kcal/mol, a ¼ 13:0 m3/(s mol)

– lnðkdÞ ¼ 6100=T þ 13, R2¼ 0:99, Ed¼ 12:2 kcal/mol, a ¼ 2:6 1051/s

– lnðKÞ ¼ 4100=T 9:9, R2_{¼ 0:96, E ¼ 8:2 kcal/mol, a ¼ 1:9 10}4_m3_/mol

CCl4 Reaction conditions Weight of carbon, W g 0.600 0.600 0.600 0.600 0.600

Length of carbon bed, L cm 0.9 0.9 0.9 0.9 0.9

Inﬂuent concentration, C0 mmol/m3 26.8 23.7 22.5 22.2 20.6

Flow rate, Q l/min 1.15 1.21 1.31 1.39 1.47

Retention time, s s 4.70 102 _4.46₁₀2 _4.14₁₀2 _3.89₁₀2 _3.68₁₀2

Reaction parameters Adsorption rate constant, ka m3/(s mol) 7.5 102 1.0 101 1.5 101 2.0 101 6.0 101

Desorption rate constant, kd 1/s 4.0 105 1.1 103 3.0 103 4.8 103 3.1 102

Equilibrium constant, K¼ ka=kd m3/mol 1900 90 50 42 19

Measured equilibrium constant, KL m3/mol 2200 100 78 40 17

Statistics Measured number in each test, N – 41 29 24 22 19

Root mean square error, d – 0.04 0.07 0.02 0.02 0.03

Arrhenius equations – lnðkaÞ ¼ 2400=T þ 5:8, R2¼ 0:87, Ea¼ 4:8 kcal/mol, a ¼ 340 m3/(s mol)

– lnðkdÞ ¼ 7700=T þ 18, R2¼ 0:93, Ed¼ 15:3 kcal/mol, a ¼ 4:6 1071/s

– lnðKÞ ¼ 5200=T 12, R2_{¼ 0:83, E ¼ 10:4 kcal/mol, a ¼ 1:4 10}5_m3_/mol

CHCl3 Reaction conditions Weight of carbon, W g 0.600 0.600 0.600 0.600 0.600

Length of carbon bed, L cm 0.9 0.9 0.9 0.9 0.9

Inﬂuent concentration, C0 mmol/m3 32.6 83.3 71.8 69.1 64.9

C.L. Chuang et al. / Chemosph ere 53 (2003) 17–27 21

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those equilibrium constants. In general, the equilibrium constants calculated from the BDR model were located between those calculated from Langmuir isotherm and

LDF model with the exception of CCl4. The equilibrium

constants of CCl4 were higher than that of C6H6 and

CHCl3 which implied that CCl4 was a stronger

adsor-bate than C6H6 and CHCl3.

Based on the Arrhenius equation, the activation en-ergy and frequency coeﬃcient can be calculated from the corresponding models and shown in Table 2. Fig. 3 shows the correlation of the reaction constants (ln k) and the temperature (1=T ), in which the determination of the relevant activation energy associated with the selected

VOCs were revealed. For instance, the Eaof C6H6, CCl4

and CHCl3were 4.0, 4.8 and 5.1 kcal/mol, respectively;

and the respective Ed values were 12.2, 15.3 and 15.8

kcal/mol. For the Langmuir model, the aaof C6H6, CCl4

and CHCl3 were 13, 340 and 1240 m3/(s mol),

respec-tively; the respective ad values were 2.6 105, 4.6 107

and 6.4 108 _{1/s. Consequently, the heat of adsorption}

of C6H6, CCl4and CHCl3can be determined; the values

are )8.2, )10.4 and )10.7 kcal/mol, respectively, and

these values are similar to those reported by Chiang et al.

(2001). Summary, CHCl3 has a larger adsorption rate

constant, desorption rate constant, adsorption activa-tion energy, and desorpactiva-tion activaactiva-tion energy but a lower heat of adsorption and adsorption capacity than

that of C6H6and CCl4.

Table 4 presents the model (LDF and BDR) com-parison from the aspects of principle and applications. In principle, LDF assumes the adsorption rate should be linearly proportional to a driving force which is deter-mined by the diﬀerence between the surface concentra-Table 3

Comparison of equilibrium constants from diﬀerent models

VOC Model Temperature (K)

283 303 323 343 363 C6H6 Langmuir isotherm (KL) 112 40 23 11 6.3 LDFa_(K LDF) 150 37 12 8.2 5.5 BDR (this study) (ka=kd) 130 37 12 8.0 5.4 CCl4 Langmuir isotherm (KL) 2200 100 78 40 17 LDFa_(K LDF) 2000 95 50 42 19 BDR (this study) (ka=kd) 1900 90 50 42 19 CHCl3 Langmuir isotherm (KL) 530 100 25 12 7.3 LDFa_(K LDF) 450 170 22 11 6.5 BDR (this study) (ka=kd) 320 140 21 11 6.5 a

LDF with Langmuir isotherm.

Table 2 (conti nued ) VOC Adsorp tion cond itions and param eters Unit Run 1 Run 2 Run 3 Run 4 Run 5 283 K 303 K 323 K 343 K 363 K Flo w rate, Q l/min 1.14 1.22 1.30 1.38 1.47 Rete ntion time , s s 4.57 10 2 4.44 10 2 4.16 10 2 3.92 10 2 3.68 10 2 Reactio n param eters Ads orption rate consta nt, ka m 3/(s mo l) 1.5 10 1 2.0 10 1 4.0 10 1 6.5 10 1 1.1 10 0 De sorptio n rat e co nstant, kd 1/s 4.7 10 4 1.4 10 3 1.9 10 2 6.1 10 2 1.6 10 1 Equi librium consta nt, K ¼ ka = kd m 3/mol 320 140 21 11 6.5 M easured equilib rium consta nt, KL m 3/mol 530 100 25 12 7.3 Statistic s M easured numb er in each test, N – 5 54 23 3 3 03 1 Root mean square error, d – 0.02 0.01 0.01 0.01 0.01 Arrh enius equa tions – ln ðka Þ¼ 2600 = T þ 7 :1, R 2¼ 0 :98, Ea ¼ 5 :2 kcal/ mol, a ¼ 1 :4 10 3m 3/(s mo l) –l n ðkd Þ¼ 8000 = T þ 20, R 2¼ 0 :98, Ed ¼ 15 :8 kcal/ mol, a ¼ 6 :4 10 8 1/s –l n ðK Þ¼ 5400 = T 13, R 2¼ 0 :97, E ¼ 10 :6 kcal/mo l, a ¼ 4 :3 10 5 m 3/mol Experimental conditi ons: density ¼ 880 kg/m 3, bed cross-se ction area ¼ 1.76 cm 2and q0 460 mg/ g for C6 H6 , 600 mg/g for CC l4 , and 297 mg/g for CHCl 3 at 303 K.

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tion (q_{) and the average adsorbed-phase concentration}

(q) (Gkueckauf, 1955). The surface concentration can be expressed either by Langmuir or Freundlich isotherms. The BDR model is based on the basic dynamical reac-tion theory and assumes the adsorpreac-tion and desorpreac-tion rate should be a function of adsorbent concentration

and free surface site ratio (1 h) and desorption of

coverage ratio (h), respectively, which are consistent with the Langmuir isotherm. In addition, the LDF is a lumped-parameter (adsorbed-phase transfer coeﬃcient, k)

model for particle adsorption (Malek and Farooq, 1997) which could be applicable to the non-isothermal, multi-component mixture dynamic-column adsorption pro-cess. The BDR model used adsorption reaction constant

(ka) and desorption reaction constant (kd) to describe the

adsorption process.

4.2. Eﬀect of temperature and concentration

In this study, both C6H6 and CCl4 are non-polar

molecules with a zero dipole moment, whereas CHCl3is

a polar molecule with a dipole moment of 1.1 D. Breysse et al. (1987) studied the adsorption ability of three di-chlorobenzene isomers on activated carbon and reported that dipole moment does not have signiﬁcant eﬀects on the adsorption of VOC for D < 2:5. Fig. 4 shows the adsorption capacity as a function of ‘‘relative

concen-tration’’ where Csatis the saturation concentration. For

ideal gas, C0=Csat is identical to P0=Psat at a given

tem-perature, where P0is inlet partial pressure (atm) and Psat

is the saturation pressure (atm). As expected, the ad-sorption capacity increased with the VOC concentra-tion and/or partial pressure. The Langmuir model was chosen in subsequent numerical model analysis of the adsorption/desorption process. Table 2 shows the

Langmuir constant (KL). At 303 K, the adsorptive

ca-pacity (q0) of C6H6, CCl4 and CHCl3 are 460, 600 and

297 mg/g, respectively, and the KL of C6H6, CCl4 and

CHCl3 are 40, 100 and 100 m3/mol, respectively. The

values of q0 and KLare in the same order of magnitude

as those reported by Vahdat (1997). The results also

indicate that CCl4 has high adsorptive capacity and

adsorption constant, which implies that CCl4 is a

stronger adsorbate towards activated carbon than C6H6

and CHCl3.

Fig. 5 presents the relationship between the model

ﬁtted equilibrium constant, ka=kd, and measured

con-stant, KL, as reported by Vahdat (1997), Chiang et al.

(2001) and this study. The plot indicates a linear

corre-lation between KLand ka=kd. The dimensionless plots in

Fig. 6 show the predicted breakthrough curves as a function of temperature (the reaction conditions are shown in Table 2). The results indicated that, at higher temperatures, an early breakthrough occurs due to re-duced adsorption capacity (lower equilibrium con-stants). Furthermore, the breakthrough curves were steeper at higher temperatures due in part to the eﬀects of kaand kd.

In this study, the adsorption and desorption reaction constants determined at diﬀerent temperatures (from 283 to 363 K) were used to predict the desorption con-centration changes at 343 and 363 K. The desorption eﬃciency, i.e., total adsorption weight/total desorption weight, ranged from 85% to 101%. Results (Fig. 7) show that the numerical model could well predict the

de-sorption process for CHCl3. For the other two VOCs,

(a) C6H6 -8 -4 0 ka kd k (b) CCl4 -8 -4 ln (k) (c) CHCl3 -12 -8 -4 0 0.0025 0.003 0.0035 0.004

Fig. 3. Relationship between rate constants (ka, kd, and k) and

temperature.

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the results show that the measured outlet concentrations were lower than the predicted values. It is also observed

that the Cout=C0 values at higher temperatures decrease

more rapidly than that those at lower temperatures. 4.3. Adsorption and desorption rate

In the present study, the numerical model provides the adsorption and the desorption rate constants, and these parameters can be used to predict the desorption process. Further, the numerical model provides the change in both the adsorption and the desorption rates

as a function of temperature and time (e.g., CCl4 from

283 to 363 K in Fig. 8). The pattern in Fig. 8 plots is of course aﬀected by temperature. At higher adsorption temperatures (323, 343 and 363 K; Fig. 8 top), the adsorption rate appears to be slightly higher than the

desorption rate. Both the adsorption reaction rate, Ra,

and the desorption reaction rate, Rd, increase with time

and eventually reach equilibrium. The net reaction rate, R, reaches a maximum value before approaching zero. At low adsorption temperature (283 and 303 K; Fig. 8 bottom), the adsorption rate is much higher than the desorption rate. The desorption and net reaction rates exhibit the same trend with those at higher adsorption temperatures. On the other hand, the adsorption re-action rates show a diﬀerent trend. It reached a maxi-mum value and then declined to the level equivalent to the desorption rate. Since the adsorption rate is equal

kað1 hÞC, the 1 h value at lower temperatures

changes appreciably than that at higher temperatures.

The increase of C (from 0 to C0) and the decrease of

1 h (from 1 to 1 he) cause the adsorption rate

ex-hibiting a maximum value and then gradually de-creases.

The case of CCl4show the adsorption reaction rates,

the desorption reaction rates and net reaction rates are the function of temperatures, and when adsorption

process approaches equilibrium (i.e., Ra¼ Rd), the

ad-sorption rate (or dead-sorption rate) at high reaction tem-perature is higher than that at low temtem-peratures. For the other two VOCs, the plots show the same trend as in the

case of CCl4.

Fig. 9 presents the changes of adsorption and

de-sorption rates of CCl4 during the desorption process at

two temperatures (343 and 363 K). The results show that the desorption rates are slightly higher than the adsorption rates. At the beginning of desorption ex-periments, both the adsorption and desorption rates at the higher temperature were higher than that at the lower temperature; after that, the adsorption and de-sorption rates at the higher temperature decreased rap-idly than that at the lower temperature, and the net reaction rate indicates a max value and a right-trail curve.

In this study, the experimental data showed that the adsorption process is an exothermic process (DH < 0); a higher temperature will decrease the adsorption

ca-pacity (q=q0). As expected, high temperature will

in-crease both the adsorption and desorption reaction rate constants, high rate constants will cause high reaction rate, and high reaction rate will cause the reaction easy reach the equilibrium state and reduce the reaction time.

Table 4

Comparison between LDF and BDR model

Model LDF BDR Principle Similarities oC ot DL o2_C o2_Lþ U oC oLþ 1 e e q oq ot¼ 0 Dissimilarities oq ot¼ kðq _qÞ oh ot¼ kað1 hÞC kdh The uptake is linearly proportional to a driving

force, deﬁned as the diﬀerence between the surface concentration (q_{) and the average}

adsorbed-phase concentration (q)

Based on the Langmuir hypothesis, the ad-sorption rate is a function of adsorbent con-centration (C) and free surface site ratio (1 h), and desorption rate is a function of coverage ratio (h)

Application Similarities 1. Applied at non-isothermal process 2. Applied at multi-component mixture system Dissimilarities 1. Associated with several isotherms, such as

Langmuir and Freundlich isotherm 2. Only net reaction rate was known 3. Applied at both particle and

dynamic-column adsorption 4. Usually applied at adsorption process

1. Direct associated with Langmuir isotherm 2. Both adsorption and desorption reaction

rates were known

3. Applied at dynamic-column adsorption 4. Applied at both adsorption and desorption

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5. Conclusions

In this study, a BDR model was used to assess the eﬀect of temperature on the adsorption and desorption of three VOCs. Compare with Langmuir isotherm and LDF (with Langmuir) model, the BDR model shown

the same trend with both of them, such as CCl4 has a

larger ka=kd(BDR model) and KL(Langmuir isotherm)

Fig. 5. Relationship of equilibrium constants of Langmuir and adsorption/desorption models.

Fig. 4. Prediction of adsorption isotherms (points are experi-mental data and lines are model predicted).

Fig. 6. Prediction of breakthrough curve of adsorption process as a function of temperature (reaction conditions: see Table 2).

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and k (LDF with Langmuir) than C6H6and CHCl3, and

the ka=kdvalues of CCl4and C6H6 have the same order

of magnitude as those reported by Vahdat (1997) and Chiang et al. (2001). Based on these parameters, it is possible to predict the adsorption isotherms and breakthrough curves under various operational condi-tions. Both experimental and model-predicted data in-dicate that both the adsorption and desorption rate constants increase whereas equilibrium adsorption con-stants decreased under high reaction temperatures. The

adsorption process is an exothermic process (DH < 0); high temperature will decrease the adsorption capacity

(q=q0). From the model prediction, the adsorption rates

were slightly higher than the desorption rates at the adsorption process; on the other hand, the adsorption rates were slightly lower than the desorption rates dur-ing the desorption process.

Fig. 7. Prediction of desorption concentration as a function of temperature (reaction conditions: see Table 2).

Fig. 8. Adsorption and desorption rate change on adsorption process for CCl4(reaction conditions: see Table 2).

Fig. 9. Adsorption and desorption rate change on desorption process for CCl4(reaction conditions: see Table 2).

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