Modeling the Breakthrough Behavior of an Activated Carbon Fiber Monolith in N-Butane Adsorption From...

Chemical Engineering Science 61 (2006) 4762–4772www.elsevier.com/locate/ces

Modeling the breakthrough behavior of an activated carbon fiber monolith inn-butane adsorption from diluted streams

Gregorio Marbán∗, Teresa Valdés-Solís, Antonio B. FuertesInstituto Nacional del Carbón, CSIC, Francisco Pintado Fe, 26, 33011 Oviedo, Spain

Received 8 August 2005; received in revised form 31 January 2006; accepted 6 March 2006Available online 13 March 2006

Abstract

A complete breakthrough model is proposed and solved in this work to describe the removal of volatile organic compounds from a dilutedsingle-component gas stream passing through a microporous activated carbon fiber monolith (ACFM) under isothermal conditions. All significantparameters are considered in the model, including type of adsorption isotherm, resistance to external gas diffusion, non-instantaneous adsorptionkinetics at the external surface and type of gas diffusion within the pore system. n-Butane was employed as the test compound for obtainingthe experimental breakthrough curves. The model including non-instantaneous adsorption at the external surface and surface pore diffusiondescribes properly the experimental adsorption results.� 2006 Elsevier Ltd. All rights reserved.

Keywords: Activated carbon; Carbon fibers; Volatile organic compounds; Adsorption; Mass transfer; Diffusion; Simulation; Modeling

1. Introduction

Low-density activated carbon fiber monoliths (ACFMs) havebeen developed recently (Burchell et al., 2000; Burchell andJudkins, 1997; Lee et al., 1997; Marbán et al., 2000; Vila-plana-Ortego et al., 2002) for several gas–solid applicationsdue to their properties such as light-weight, high mechanicalstrength and fast adsorption kinetics. The monolithic structuremakes them easier to handle than packed beds and produces alow resistance to bulk gas flow. Thus, among the possible appli-cations, ACFMs are of interest for the adsorption and recoveryof organic vapors (Fuertes et al., 2003; Marbán and Fuertes,2004), CO2 adsorption (Burchell et al., 1997; Burchell and Jud-kins, 1997), as catalysts or catalyst support for the removal ofSOx and NOx from flue gas (Marbán et al., 2003), water treat-ment (Suzuki, 1991) and for CH4 storage (Muto et al., 2005).

The removal of volatile organic compounds (VOCs), com-monly performed by adsorption, is of great interest for the airquality control. At a low-concentration level, adsorption on ac-tive carbon is the most employed method for the removal of

∗ Corresponding author. Tel.: +34 985 11 90 90; fax:+34 985 29 76 62.E-mail address: [email protected] (G. Marbán).

0009-2509/$ - see front matter � 2006 Elsevier Ltd. All rights reserved.doi:10.1016/j.ces.2006.03.008

VOCs (Centeno et al., 2003; Fuertes et al., 2003). However, theuse of granular packed beds has serious drawbacks, such as thehigh pressure drop associated with the flow of gas through thepacked media, attrition of the granular material, channeling, gasbypassing, etc. These disadvantages can be avoided with theutilization of ACFM that, in addition, exhibits a narrow poros-ity in the micropore range (< 2 nm). Micropores are primarilyresponsible for adsorption at low VOCs concentrations in am-bient air environments due to the overlapping of the attractiveforces of opposite pore walls (Derbyshire et al., 2001; Fosteret al., 1992). In many cases n-butane has been employed asa reference molecule to compare the VOC adsorption capac-ity of various materials (DeLiso et al., 1997; Gadkaree, 2001;Valdés-Solís et al., 2004).

The adsorption of VOCs in carbonaceous materials hasreceived increasing attention in recent years, and several at-tempts to model the process have been published for granularactive carbon (Linders et al., 2001, 2003), ACF (Cheng et al.,2004; Das et al., 2004) and carbon-coated ceramic monoliths(Valdés-Solís et al., 2004). In general, the models found in liter-ature include several simplifications; such as considering onlygas diffusion in the pores or assuming instantaneous adsorptionkinetics (Cheng et al., 2004; Linders et al., 2001, Valdés-Solís

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G. Marbán et al. / Chemical Engineering Science 61 (2006) 4762–4772 4763

et al., 2004), in order to get substantial savings in computationtime. Then, every approximate solution has its own restrictedscope of validity which should be accurately defined.

The objective of this work is to propose and solve a math-ematical breakthrough model for low-concentration gas ad-sorption in ACF monoliths which takes into consideration allsignificant parameters (non-linear adsorption equilibrium,axial dispersion, finite mass transfer resistance, type of porediffusion, etc). Thus, a systematic approach is performed,starting from a simplified and unrealistic model (gas phasediffusion in the micropores with instantaneous adsorption),going through a more complex and realistic model that permitsto analyze the effect of the equilibrium adsorption isotherm(Dubinin–Radushkevich, Freundlich, Toth, etc) on the surfacediffusion-controlled process, to finally include the possibilityof non-instantaneous adsorption kinetics at the external surfaceof the fibers, thanks to which the simulation results permit toeventually match the experimental breakthrough curves.

2. Experimental

2.1. Adsorbent material

The preparation of activated monolith (ACFM) is reportedelsewhere (Marbán et al., 2000). Briefly, rejects of Nomex�fibers (DuPont) were carbonized in N2 at 850 ◦C (heating rate:5 ◦C min−1; soaking time: 1 h). Afterwards, they were milledby conventional blade-mills and the fraction of size 0.1–0.4 mmwas dry-mixed with powdered phenolic resin (Novolak) in amass ratio of 3/1. The mixture was moulded, cured (in air at180 ◦C) and carbonized (in N2 at 700 ◦C). The carbonized com-posite with a bulk density of around 0.25 g cm−3 was activatedat 700 ◦C with a stream of water (∼ 25 vol% in N2) until acti-vation degree (burnoff) of 42 wt% was reached.

2.2. Adsorbent characterization

The textural properties (specific surface area and pore vol-ume) of the adsorbent material were evaluated by means of N2adsorption isotherms (−196 ◦C) obtained with a Micromerit-ics ASAP 2010 analyzer, and by CO2 adsorption at 20 ◦C witha thermogravimetric analyzer (TG CI Electronics). The resultsobtained are presented in Table 1. Data on n-butane adsorptionexperiments performed with the TG system, including parame-ters for the Dubinin–Radushkevich isotherm (i.e., E0) are alsoindicated in Table 1.

2.3. TGA experiments

A differential adsorption experiment was attempted in thethermogravimetric analyzer at 30 ◦C. In order to approach dif-ferential conditions a very low sample weight (1.475 mg) and ahigh value of n-butane gas concentration (100 vol%) were usedat the maximum flow rate allowed by the experimental setup(82 mL/min, 1 atm). The crucible used for these experimentswas specially fabricated with a wired mesh to assure fast ac-

Table 1Textural properties of the adsorbent material (ACFM) and bulk parametersused during the dynamic adsorption experiments

Textural propertiesSBET(m2/g)a 1306

VN2pore(cm3/g)b 0.46(5)

VCO2pore (cm3/g)c 0.44

L0(nm)d 0.93Adsorbed n-butane (mmol/g) at C0 = 106 ppm(30 ◦C) 4.55Adsorbed n-butane (mmol/g) at C0 = 1500 ppm(30 ◦C) 2.02Adsorbent characteristic energy; E0 (kJ/mol) 20.3(Dubinin–Radushkevich)

Fiber dimensions

Diameter DF (�m) 11.6

Bulk parametersWcarbon (mg) 48Diameter D (mm) 5.5Height H (mm) 10.6Aspect ratio (H/D) 1.9Bulk carbon density �b(g/cm3) 0.19Bulk porosity (�b) 0.8

aBET specific surface area obtained by N2 adsorption at −196 ◦CbPore volume obtained by N2 adsorption at −196 ◦C (percentage of meso-

pore volume in brackets).cMicropore volume obtained by CO2 adsorption at 20 ◦CdMean micropore width obtained from n-butane adsorption experiments as

reported in (Centeno et al., 2003).

cess of the gas through the carbonaceous samples. With theseconditions, and considering a fast (adsorbent fully loaded in10 s) and linear adsorption rate, and negligible gas bypassing,the value of the adsorption rate was estimated be below 1.2%the value of the n-butane molar flow rate, which clearly estab-lished differential regime. However, it was determined that ahigh degree of gas bypassing through the annulus between thecrucible and the TGA chamber impeded to attain strict differ-ential conditions, and therefore the TGA results are discussedin the corresponding section from a qualitative perspective.

2.4. Dynamic adsorption experiments

The adsorption chamber used for obtaining the breakthroughcurves was a cylindrical pipe (7 mm i.d.) made of quartz. Thecylindrical ACFM was tightly fitted to the internal wall of thechamber by means of Teflon strips and vacuum grease (ther-mally stable up to 210 ◦C). In this way gas bypassing was com-pletely avoided. The bulk parameters of the ACFM used areshown in Table 1.

For the analysis of dynamic n-butane adsorption, the gasmixture (500–2000 ppm in He; flow rate = 150 mL/ min) wasled into the adsorption chamber by means of a set of mass flowcontrollers. The composition of the gases exiting the adsorp-tion chamber was analyzed continuously by a mass spectrom-eter (Baltzers, Omnistar model 300O) using mass fragments18 for water and 58 for n-butane. The adsorbent temperaturewas measured by a thermocouple inserted into the adsorptionchamber. Prior to the adsorption experiments the adsorbent washeated in He at 160 ◦C for 30 min.

4764 G. Marbán et al. / Chemical Engineering Science 61 (2006) 4762–4772

3. Model

For modeling the dynamic behavior of ACF monoliths underisothermal conditions, axially dispersed plug flow is assumed(DF /D � 1), while mass transfer to the external surface isimplemented by a Sherwood relationship coupled with a non-instantaneous rate of adsorption. The gas phase mass balance ofthe single-adsorptive (n-butane) in the monolithic column canbe calculated, in dimensionless form as (see notation below):

�x

��= 1

Pep

�2x

��2 − 1

�

�x

��− 1 − �b

�b

[qe(C0)

C0

]��

��, (1)

where

� = 3∫ 1

0��2d�. (2)

The particle Peclet number for Re < 1 (experimental value:Re ∼ 0.02) can be estimated as (Linders, 1999; Ruthven, 1984):

Pep = a

ReSc, a = 0.3.0.4. (3)

Depending on the regime and type of adsorbent, the valueof (��/��) will be calculated by different expressions. Twodifferent regimes, described below, are considered:

R1. Gas phase diffusion inside the micropores with instan-taneous equilibrium adsorption: It is generally accepted thatsurface diffusion plays an important role when dealing withadsorption on narrow micropores (Ruthven, 1984), being how-ever less important for meso/macroporous systems (i.e., activecarbon), for which gas phase diffusion inside the pore system isthought to be the dominating diffusion process. Nevertheless,gas phase diffusion will be considered here as a possible optionfor checking and comparative purposes. The appropriate formof the Fickian diffusion equation for a gas diffusion-controlledsystem may be obtained from a differential mass balance on aspherical shell element:[qe(C0)

C0

]��

��+ �p

�y

��=(

4t0Deff

D2eqv

)(�2y

��2 + 2

�

�y

��

). (4)

Assuming equilibrium adsorption within the micropores:

��

��= d�e

dy

�y

��, (5)

where �e is the dimensionless amount of adsorbate in equi-librium at Cp, and is given by the adsorption isotherm at Cp.Rearranging:

�y

��=

(4t0Deff

D2eqv

)

�p +[qe(C0)

C0

]��e

�y

(�2y

��2 + 2

�

�y

��

). (6)

��e/�y can be calculated as the slope of the adsorptionisotherm. For a D–R (Dubinin–Radushkevich) isotherm a cor-rection must be made at the range of the small reduced pressuresbelow the inflection point of the curve (y/ys < 1.4 × 10−16),in which the Henry regime must be considered to ensure ther-modynamic correctness. Thus, two equations can be derivedconsidering the two zones as included below:

Henry regime:

(y

ys

< exp

[− 1

2�2

])D.R regime:

(y

ys

� exp

[− 1

2�2

])

�e = �s exp

(1

4�2

)(y

ys

), (7) �e = �s exp

{−[� ln

(ys

y

)]2}

, (8)

��e

�y=(

�s

ys

)exp

(1

4�2

), (9)

��e

�y= �2 2�s

yln

(ys

y

)exp

{−[� ln

(ys

y

)]2}

. (10)

The effective diffusivity in the pore system can be calcu-lated by means of the Wakao and Smith equation, in which thetortuosity factor was approximated to 1/�p (Wakao and Smith,1962):

Deff = �2p

D−1M + D−1

K

, (11)

where the Knudsen diffusivity (DK ) is a function of the averagepore size (Doraiswamy and Sharma, 1984):

DK = 4.85 × 10−8 × L(nm) ×(

Tads

MW

)0.5

. (12)

For the continuity between the axial concentration profile(Eq. (1)) and the intraparticle concentration profile (Eq. (6)) thefollowing equations are considered:

��

��=(

6�bSh

Bo�2

)(C0

qe(C0)

)(x − y�=1), (13)

(�y

��

)�=1

= DM

Deff

Sh

2(x − y�=1). (14)

Thus, Eq. (14) is the border equation for solving (6) and gettingthe value of y�=1. With this value, the axial concentration profilecan be evaluated by Eqs. (13) and (1).


The Sherwood number (Sh) is estimated here by the stan-dard Ranz and Marshall correlation (Bird et al., 2002; Ruthven,1984):

Sh = 2 + 0.6Re1/2Sc1/3. (15)

Although this correlation is valid for Re > 2, we have decidedto employ it because, according to Ruthven (Ruthven, 1984),most correlations for Re < 2 usually underestimate the Sher-wood number, and therefore it seems advisable to use a correla-tion that yields the value of Sh=2 for the limiting case of Re=0(infinite stagnant fluid around an isolated spherical particle).

R2. Adsorption on highly dispersed microporous particles(i.e., fibrous monoliths): In this kind of systems it is assumedthat diffusion inside the fibers occurs via surface migrationalong their small micropores. Different situations can be found:

• R2.1: External mass transfer towards the external surface ofthe fibers, with instantaneous adsorption at the surface;

• R2.2: Resistance to adsorption at the external surface of thefibers (non-instantaneous adsorption).

It is desirable to use an expression for ��/�� that considerall the above resistances, following a similar formalism to thatused when modeling chemical processes.

R2.1. Instantaneous surface adsorption: In this case, onlyexternal mass transfer and intraparticle diffusion control theprocess. The intraparticle diffusion resistance can be expressedby the following mass balance:

��

��= �

�2

�

��

(�2

��

��

)

= �

[�2�

��2 +(

2

�+ 1

�

��

��

��

)��

��

]. (16)

Similar to Eq. (2) we can integrate (16) to obtain

��

��= 3�

(

��

��

)�=1

. (17)

The dimensionless surface diffusivity now depends on theinstantaneous adsorption and can be evaluated by the thermo-dynamic relation expressed by the Darken equation:

= d Ln(x)

d Ln(�). (18)

Thus, application of the Darken equation to the D–R isothermgives

Henry regime:

(�

�s

< exp

[− 1

4�2

])D.R regime:

(�

�s

� exp

[− 1

4�2

])

= 1, = 1

2�[Ln(�s/�)]1/2 ,

�

��= 0, (19)

�

��= 1

4��[Ln(�s/�)]−3/2. (20)

In a similar way, the Darken equation can be applied to anykind of isotherm (e.g. Langmuir, Toth, etc.). Since adsorptionis instantaneous:

��

��=(

6�bSh

Bo�2

)(C0

qe(C0)

)(x − y�=1)

= kext(x − y�=1). (21)

Combining (1) and (21):

�x

��= 1

Pep

�2x

��2 − 1

�

�x

��− 1 − �b

�b

×(

qe(C0)

C0

)kext(x − y�=1). (22)

Coupling (17) and (21) we can obtain the border equationthat expresses the continuity between the axial and the radialprofile:(

��

��

)�=1

=(

kext

3�

)(x − y�=1)

=(

DM

Dso

Sh

2

)(C0

qe(C0)

)(x − y�=1). (23)

R2.2. Non-instantaneous surface adsorption: In this case theaxial profile is expressed as in the former case by Eq. (22),the radial profile is calculated by the mass balance of Eq. (16)and the external mass transfer resistance is given by Eq. (21),whereas the resistance to external surface adsorption can beaccounted by the following equation, which assumes Lang-muir kinetics and resembles that used in the old Thomas model(Thomas, 1944, 1948):

��

��= kat0C0

[y�=1(�s − ��=1) − ��=1

Ka

]. (24)

By considering the equilibrium isotherm, constant Ka canbe removed from Eq. (24), which turns into

��

��= kat0C0�sy�=1

[1 − ��=1

�e,�=1

], (25)

where �e,�=1 is the dimensionless adsorbed amount in equi-librium with y�=1. By equaling (21) and (25) and removingy�=1

��

��= kextkat0C0�s(1 − ��=1/�e,�=1)x

kext + kat0C0�s(1 − ��=1/�e,�=1). (26)


The value of �e,�=1 for a given value of y�=1 can be evaluatedfor the D–R isotherm as follows:

Henry regime:y�=1

ys

< exp

[− 1

2�2

]D.R regime:

y�=1

ys

� exp

[− 1

2�2

]

�e,�=1

�s

= y�=1

ys

exp

[1

4�2

], (27)

�e,�=1

�s

= exp

{−[� ln

(ys

y�=1

)]2}

. (28)

Again, for a more simple resolution, one can assume

�e,�=1 = y�=1

. (29)

when = 1, this equation takes into consideration the lowadsorptive concentration (dilute gas stream) and thus assumesa Henry regime at the external surface, qe = KC, in which theHenry constant is

K = qe(Cs)

C0exp{−[� ln(Cs/C0)]2}. (30)

In this way, the D–R isotherm is considered also at the exter-nal surface when the breakthrough profile is fully developed.The D–R isotherm can also be considered for any value of y�=1by calculating the appropriate value of in any iteration step.

Coupling (17) and (26) the border equation that expressesthe continuity between the axial and the radial profile can beobtained as:(

��

��

)�=1

= kextkat0C0�s(1 − ��=1/�e,�=1)x

3�[kext + kat0C0�s(1 − ��=1/�e,�=1)] . (31)

This general expression can be simplified by using Eq. (29).In this way, Eqs. (21), (25) and (29) permit to obtain the fol-lowing expression for calculating y�=1:

y�=1 = kextx + kat0C0�s(��=1)

kext + kat0C0�s

, (32)

with this, Eq. (31) becomes(

��

��

)�=1

= kextkat0C0�s(x − ��=1)

3�[kext + kat0C0�s] . (33)

It can be noticed that this equation becomes Eq. (23) whenka = ∞. The rest of border equations are the following:

x = 0 for � < 0 and for all �, (34)

x = x0 for ��0 and � = 0[or x = x0 × (t/ti) for t < ti

for linear increase of feed concentration], (35)

� = 0 for � < 0 and for all �, (36)

�x

��= 0 for � = 0, (37)

�x

��= 0 for � = 1, (38)

��

��= 0 for � = 0. (39)

Resolution of the system of equations for regimes R1 and R2was performed by means of an ad hoc-designed Visual Basicmacro included in an Excel datasheet. For discretizing the ra-dial profile a three-point-based generalized three-level schemewas used, whereas the program allowed the procedure for dis-cretizing the axial profile to be selected among several implicitschemes (backwards difference, Crank Nicholson, three levelschemes) by using either three-point or five-point derivatives.For solving the set of non-linear coupled equations the Thomasalgorithm was used together with a Newton–Raphson iterativeprocedure.

4. Results and discussion

4.1. Differential adsorption

Fig. 1 shows the experimental variation with time of the rel-ative mass increase (�) for ACFM obtained in the TGA at neardifferential conditions (see experimental section). As compari-son, the results obtained by other authors (Linders et al., 2001)with a commercial active carbon are also included (Kureha ac-tive carbon (10.8 mg), 3.7 vol% n-butane/He, F =200 mL/ min,1 atm, 30 ◦C, experiment performed in a TEOM).

According to the results displayed in the figure, both the ac-tive carbon pellets and the ACFM seem to attain equilibrium ata similar rate. However, as commented before, in the case ofthe ACFM, the data were obtained with a TGA that had specificstructural features that made it impossible the establishment ofstrict differential conditions. Therefore, under strict differentialconditions it should be expected that the ACFM adsorbent pre-sented a faster rate of n-butane adsorption than that shown inFig. 1 (experimental results) and consequently also faster thanthat reported for Kureha AC. As will be seen now, the resultsof the model confirm this expectation.

By applying the model at differential conditions with the ki-netic parameters that better fit the dynamic breakthrough pro-files for the ACFM (see Section 4.2 Breakthrough profiles)curves A (obtained with values of gas flow and concentration asthose used for differential experiment with ACFM) and B (ob-tained with values of gas flow and concentration as those usedfor differential experiment with Kureha active carbon (Linderset al., 2001)) in Fig. 1 were obtained (surface diffusion, Darkenequation applied to D–R isotherm, Dso = 1.5 × 10−12 m2 s−1,


0.0

0.2

0.4

0.6

0.8

1.0

0 5 10 15 20time (s)

ACFM

Kureha active carbon (Linders et al., 2001)

A,D

C

B

θ[x

for

curv

e A

]

Fig. 1. Differential adsorption experiments performed with the ACFM in100 vol% n-butane flow. Data for Kureha active carbon were taken from(Linders et al., 2001). Also included the results of the model applied toACFM at differential conditions (curves A to D).

Table 2Parameter values of simulation curves plotted in Fig. 1 (square n-butaneconcentration steps)

Curve C0 Flow rate Diffusion Diffusivity ka(m3 mol−1 s−1)

(ppm) (mL/min) type (m2 s−1)

A 106 82 Surface (D–R) 1.5 × 10−12 20B 37000 200 Surface (D–R) 1.5 × 10−12 20C 106 82 Gas 3.0 × 10−8 ∞D 106 82 Surface (D–R) 1.5 × 10−12 ∞

ka = 20 m3 mol−1 s−1). This procedure is contrary to that gen-erally followed, which consists of firstly evaluating the intra-particle diffusion parameters via fitting the experimental curvesobtained at differential conditions and then predicting the dy-namic profiles with the so-obtained parameters. However, it isfollowed in this work because of the impossibility to use dif-ferential conditions with the available TGA (Table 2).

Curves A and B clearly show that ACFM adsorbent be-comes fully loaded at differential conditions in less than 3 s,which is an indication of the high adsorption rate attainedwith this microporous material. Only when considering in themodel gas phase diffusion inside the pores a faster adsorp-tion rate is obtained (curve C). Obviously the latter is notan operative regime in the microporous adsorbent, as will bedemonstrated with the simulated breakthrough profiles obtainedunder gas phase diffusion conditions (Section 4.2 Breakthroughprofiles).

It is also interesting to note that at differential conditionsthere seems to be no influence of the external adsorption re-sistance (ka) on the results, as deduced from the overlappingof curves A (ka = 20 m3 mol−1 s−1) and D (ka = ∞; Fig. 1),although a clear influence was observed under dynamic con-ditions on the breakthrough profiles (see Section 4.2 Break-through profiles). As will be proved at the end of this section,this is just a consequence of the high value of n-butane con-

Table 3Expressions of evaluated by the Darken equation for different isotherms

Isotherms (Ds/Dso)

Constant diffusivity 1 (19)

Dubinin–Radushkevich1

2�[Ln((�s/�)]1/2 (20)

(D–R) isotherm (Eq. (9))

Langmuir isotherm1

(1 − �/�s )(40)

Chen and Yang for diffusion1

(1 − (1 − �)�/�s )(41)

(Chen and Yang, 1992)

(� = 0.5 for calculations)

Freundlich isotherm1

n(1 − �/�s )(42)

(n = 0.6 for calculations)

Toth isotherm1

1 − (�/�s )t

(43)

(t = 2 for calculations)

centration in the gas phase used for evaluating the � curve atdifferential conditions (C0 = 106 ppm).

Application of the model at differential conditions can of-fer us two practical conclusions for the modeling of the break-through profiles. First of all, the surface diffusion-controlledregime can be analyzed by considering different adsorptionisotherms which will relate in different ways the surface dif-fusivity with the amount of n-butane adsorbed at any momentinside the pore system. This relationship is performed throughthe Darken equation (18). In this work, six expressions of corresponding to different situations and isotherms listed inTable 3 have been analyzed.

In principle, all these expressions of should yield differenttrends in the resulting plot of � versus time for a given initialvalue of surface diffusivity (Dso). This is clearly observed inFig. 2a. Except for the case of constant diffusivity, all expres-sions of predict an increasing value of Dso with the localamount of n-butane adsorbed (�). This is correspondingly re-flected in the trends observed in Fig. 2a, for which the slow-est rate to attain equilibrium belongs precisely to the case ofconstant diffusivity. The fastest rate is obtained when the D–Risotherm applies, as is the case for highly microporous adsor-bents such as ACF monoliths. On the other hand, from a practi-cal point of view it is not clear whether the differences observedin Fig. 2a are an important modeling issue or not, since allisotherms seem to produce converging results for specific values


0.0

0.4

0.6

0.8

1.0

0 1 2 3 4 5time (s)

D.R.

Langmuir

Freundlich

Toth

Yang

Constant

D.R.

Langmuir

Freundlich

Toth

Yang

Constant

θ

Square step

Dso=1.5×10-12

(ka=∞)

(ka=∞)

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Square step

Dso=1.50×10-12

Dso=2.00×10-12

Dso=2.75×10-12

Dso=3.50×10-12

Dso=9.50×10-12

Dso=1.60×10-12

Co=1×106 ppm

Co=500 ppm

0.2

0.0

0.4

0.6

0.8

1.0

θ

0.2

(a)

time (s)(b)

Fig. 2. Application of the model at differential conditions for: (a) differentadsorption isotherms at a given value of Dso(C0 = 106 ppm); (b) differentadsorption isotherms at different values of Dso and C0.

of Dso. This is appreciated in Fig. 2b, in which values of Dso

were found in such a way that all expressions of yielded analmost identical curve (solid lines for C0 =106 ppm). However,when using a much lower gas concentration (C0=500 ppm), thesame values of Dso produced very different curves, as indicatedby dashed lines in Fig. 2b. Under dynamic conditions, beforethe breakthrough is attained, the gas phase inside the monolithmay present values from C = 0 to C0. Therefore, it is obviousthat the breakthrough profiles will be affected by the associateddifferences in adsorption at varying values of gas concentration(Fig. 2b) which permits to conclude that selection of the cor-rect expression for the isotherm to be employed in the model isa key modeling issue. In this work the D–R isotherm was usedfor fitting the experimental breakthrough profiles. The values ofthe parameters of the D–R equation (Table 1) were determinedgravimetrically in specific experiments of n-butane adsorption.

A second observation, already pointed when commentingcurves A and D of Fig. 1, refers to the effect of external adsorp-tion resistance in the shape of the plot of � versus time. Fig. 3shows the simulated curves obtained by applying the model un-der differential conditions for different values of C0, Dso and

0.0

0.2

0.4

0.6

0.8

1.0

0 1 2 3 4 5time (s)

θ

Square stepD-R

Co= 500Dso= 1.50x10-12

ka = ∞

ka ≥ 10Co= 500Dso= 1.50x10-12

ka = 20

ka = 0.1

Co= 1x106

Dso= 1.50x10-13

ka ≥ 10

ka = 0.1Co= 1x106Co= 1x106

Dso= 1.50x10-12Dso= 1.50x10-12

Co= 1x106

Dso= 1.50x10-13

Fig. 3. Application of the model at differential conditions for different valuesof C0, Dso and ka .

ka . As observed, at high values of gas concentration (106 ppm),the resistance to external surface adsorption exerts no effecton the model results for values of ka over 10 m3 mol−1 s−1,whereas for low values of gas concentration (500 ppm) cleardifferences are observed between the curves corresponding toka = 20 m3 mol−1 s−1 and ka = ∞ (dashed curves in Fig. 3).This fact has a clear mathematic explanation since parameterC0 is multiplying ka in the equation that expresses the adsorp-tion resistance (Eq. (33)). Due to the microporous character ofACFM adsorbents, they are thought to have excellent perfor-mance in the removal of contaminants at low concentration.Therefore, according to the results shown in Fig. 3, any possibleexternal adsorption resistance will be detrimental at these spe-cific conditions, whereas it can be unnoticed in environmentswith a high concentration of the adsorptive.

Since adsorption at the external surface and surface diffusioninside the pores of the fibers are serial processes, the externaladsorption resistance has a less marked effect on the modelresults for lower values of surface diffusivity, as can be clearlyobserved in Fig. 3. Finally, from the modeling point of view,it is not possible to find a combination of [Dso, ka] values thatproduces the same curve as that obtained under instantaneousadsorption and, therefore, the existence of non-instantaneousadsorption is a clear modeling issue that can eventually be usedto improve the curve fitting of the breakthrough profile.

4.2. Breakthrough profiles

Fig. 4 shows the results of applying the model to ACFM(C0 = 500 ppm) under two different gas diffusion models. Asexpected (see previous section), the curve corresponding togas phase diffusion inside the micropore system (regimen R1)cannot reproduce the experimental results. Changing the effec-tive diffusivity to lower values, apart from lacking of physicalsignificance since Eq. (11) is not accomplished any more, nei-ther permitted to simulate the actual shape of the experimentalbreakthrough profile. The other simulated curve displayedin Fig. 4 was obtained by considering surface diffusion


0.0

0.2

0.4

0.6

0.8

1.0

700 900 1100 1300 1500

time (s)

Experimental

Gas phase diffusion

Co=500 ppm

Dso=1.5x10-12m2s-1Surface diffusion (D-R)

ka=∞

Deff=1.38x10-8m2s-1

ka=∞

xξ=

1

Fig. 4. Experimental and simulated breakthrough profiles obtained for differentdiffusion models (gas phase diffusion and surface diffusion).

0.0

0.2

0.4

0.6

0.8

1.0

700 900 1100 1300 1500time (s)

250 300 350 400 450 500

time (s)

Experimental

Model

Co=500 ppm

ka=∞

Experimental

Model

Co=2000 ppm

ka=∞

Dso=7.0×10-13m2s-1

Dso=1.0×10-12m2s-1

Dso=1.5×10-12m2s-1

Dso

Dso

Dso

Dso=7.0×10-13m2s-1

Dso=1.0×10-12m2s-1

Dso=1.5×10-12m2s-1

xξ=

1

0.0

0.2

0.4

0.6

0.8

1.0

xξ=

1

s

(a)

(b)

Fig. 5. Experimental and simulated breakthrough profiles obtained at differentvalues of Dso: (a) for C0 = 500 ppm; and (b) for C0 = 2000 ppm.

(D–R)-controlled regime, with Henry regime at the externalsurface (Eq. (29)), and instantaneous adsorption at the exter-nal surface (ka = ∞, regime R2.1). When instantaneous D–Radsorption was considered at the external surface (Eq. (9)) theconstant step resolution used in the VB program avoided to

0.0

0.2

0.4

0.6

0.8

1.0

700 900 1100 1300 1500time (s)

250 300 350 400 450 500time (s)

Experimental

Model

Co= 500 ppm

ka

ka

ka Experimental

Model

Co= 2000 ppm

ka= 20 m3mol-1s-1

ka= 20 m3mol-1s-1

ka= ∞

ka= 20 m3mol-1s-1

ka= ∞

Dso=1.5×10-12m2s-1

Dso=1.5×10-12m2s-1

xξ=

1

0.0

0.2

0.4

0.6

0.8

1.0

1.2

xξ=

1

s

(a)

(b)

Fig. 6. Experimental and simulated breakthrough profiles obtained at differentvalues of ka : (a) for C0 = 500 ppm; and (b) for C0 = 2000 ppm.

deal with the high-concentration gradient produced at the ex-ternal surface in such a way that the whole breakthrough curvecould be resolved in a reasonable time. Added to this, D–Radsorption should only be considered inside the pore systemof the particles and not at their external surface.

A value of initial surface diffusivity of 1.5 × 10−12 m2/sproduced a simulated breakthrough profile that matched thefirst zone of the experimental curve (up to x�=1 ∼ 0.5) witha significant degree of agreement (Fig. 4). This value of sur-face diffusivity is higher than those reported for n-butaneadsorption in molecular sieves (zeolites and molecular sievecarbons) which are around 1 × 10−14 m2/s (Ruthven, 1984).Nevertheless, the average pore size of the ACFM is alsosomewhat higher (∼ 1 nm) than that existing in typical molec-ular sieves (∼ 0.5 nm) so that a higher surface diffusion rate isexpected for the former.

However, there is a patent discrepancy between the simulatedbreakthrough profile and the experimental curve for values ofx�=1 over ∼ 0.5 (Fig. 4). Apart from Dso and ka , the rest of themodel parameters are determined by the adsorption conditions,the adsorbent characteristics and few standard correlations


0.0

0.2

0.4

0.6

0.8

1.0

Experimental

Model

Co

= 1

000

ppm

Co

= 5

00 p

pm

Co

= 1

500

ppm

Co

= 2

000

ppm

xξ=

1

0.0E+00

4.0E-03

8.0E-03

1.2E-02

0 500 1000 1500time (s)

dXξ=

1/dt

(s-1

)

Experimental

Model

Dso =1.5×10-12m2s-1

ka= 20 m3mol-1s-1

(a)

(b)

Fig. 7. Experimental and best fitting simulated breakthrough profiles obtainedat different values of C0: (a) Breakthrough profiles; and (b) breakthroughrates.

(i.e., Sherwood and Peclet numbers). Therefore, it was decidedto make a survey on Dso and ka in an attempt to produce abetter fitting of the upper zone of the breakthrough profile withthe following conditions: (1) not to provoke a worsening of thefitting in the lower zone of the breakthrough profile and (2) topermit simultaneously a reasonable fitting of the breakthroughprofiles obtained at higher n-butane concentrations in the inletgas (1000, 1500 and 2000 ppm).

Fig. 5a shows that a decrease in the value of initial surfacediffusivity allows the curve fitting to be improved in the upperzone of the breakthrough profile corresponding to the experi-ment performed at C0 = 500 ppm, without provoking a signifi-cant worsening of the fitting for x�=1 < 0.5. However, the sameprocedure applied to the profile obtained at C0 = 2000 ppmproduced a significant deterioration of the curve fitting in bothzones of the profile (x�=1 < 0.5 and x�=1 > 0.5), as clearly ob-served in Fig. 5b.

Introducing in the model some resistance to n-butane adsorp-tion on the external surface of the fibers, or, in other words,decreasing the value of ka coefficient, also permitted to im-prove the curve fitting in the upper zone of the breakthroughprofile obtained at C0 = 500 ppm (Fig. 6a), but in this case theprofiles obtained at higher values of C0 were also reasonablywell simulated (Fig. 6b). It was found in this way that valuesfor Dso and ka of 1.5 × 10−12 m2 s−1 and 20 m3 mol−1 s−1,respectively, produced a satisfactory fitting of the profiles ob-tained at the different values of n-butane gas concentration, asshown in Fig. 7. It is worth noting that the time derivative ofx�=1 is also well reproduced by the model for the different val-ues of C0 (Fig. 7b), which expresses the authentic goodness ofthe curve fitting.

5. Conclusions

In this work a model to predict the breakthrough profileof the adsorption n-butane by microporous fibrous adsorbents(ACFM) is proposed. The model includes non-instantaneousadsorption at the external surface and surface diffusion insidethe pores of the fibers. It has been proved that the externalsurface resistance to adsorption for the lower concentrationscannot be neglected. The selection of the appropriate expres-sion for the isotherm to be employed in the model is a keyissue to obtain a suitable fit between the experimental data andthe model, especially for the low-concentration experiments.The model solved for non-instantaneous surface adsorption andD–R-based surface diffusivity in the pore system adequatelysimulates the breakthrough profiles for adsorption of n-butanein diluted streams, since a good agreement between the experi-mental and the simulated data is obtained for the whole profilesat different values of n-butane concentration in the inlet gases.

Notation

B0 Re Sc = Deqvvs

DM, Bodenstein number according to

Levenspiel (Levenspiel, 1996)C adsorptive concentration in the gaseous bulk at

an axial position z in the monolith (0 < z < H ),mol m−3

gasC0 adsorptive concentration in the gaseous bulk at

z < 0, mol m−3gas

Cp adsorptive concentration in the intraparti-cle gaseous phase at an absolute position(r, z)(0 < r < Deqv/2; 0 < z < H), mol m−3

gasCs saturation adsorptive concentration at

Tads, mol m−3gas

D monolith diameter, mDax axial diffusivity, m2 s−1

Deff effective diffusivity in the pore system, m2 s−1

Deqv equivalent diameter of the fibers = 1.5 × DF , mDF fiber diameter, mDK Knudsen diffusivity, m2 s−1

DM molecular diffusivity, m2 s−1

Dso surface diffusivity in the pore system at � = 0,m2 s−1

E0 characteristic energy of the adsorbent, J mol−1

H monolith height, mK Henry constant, m3

gas m−3part

ka external surface adsorption coefficient,m3

gas mol−1 s−1

kext external mass transfer coefficient, m3gas m−2

part s−1

MW adsorptive molecular weight, g mol−1

PepDeqvvs

Dax�b, Bodenstein or particle Peclet number

according to CRC Handbook (CRC, 1984). Axialdispersion number according to Levenspiel(Levenspiel, 1996)

q instantaneous amount of adsorbate, per adsorbentvolume, at an absolute position (r, z), mol m−3

part


qe(Cp) amount of adsorbate in equilibrium at Cp, per ad-sorbent volume, mol m−3

partqe(C0) amount of adsorbate in equilibrium at C0, per ad-

sorbent volume, mol m−3gas

qe(Cs) amount of adsorbate in equilibrium at Cs , per ad-sorbent volume, mol m−3

partr radial position in the particle, mR universal gas constant, 8.31441 J K−1mol−1

Re�gvsDeqv

� , Reynolds numberSc �

�gDM, Schmidt number

ShDeqvkext

DM, Sherwood number

t0H 2�bDeqvvs

, time constant, s

t time, sTads adsorption temperature, Kvs gas superficial velocity, m s−1

x CC0

, dimensionless adsorptive concentration in thegas phase at z

x�=1 dimensionless adsorptive concentration in the gasphase at z = H(� = 1)

y�=1 dimensionless adsorptive concentration in the in-traparticle gaseous phase at the external surface ofthe fibers (� = 1)

yCp

C0, dimensionless adsorptive concentration in the

intraparticle gaseous phase at an absolute position(�, �)

ysCs

C0, ratio of Cs to C0

z axial position in the monolith, m

Greek letters

�DeqvH

, dimensionless size of the monolith affinity coefficient of the adsorbate,� RT ads

E0, dimensionless group of the D–R isotherm

Ds(�)Dso

, dimensionless surface diffusivity�b bed porosity,�p particle porosity,� q

qe(C0), ratio of the amount of adsorbate at an ab-

solute position (r, z) to the equilibrium amount ofadsorbate in equilibrium at C0

�eqe(Cp)

qe(C0), ratio of the amount of adsorbate in equilib-

rium at Cp to the equilibrium amount of adsorbatein equilibrium at C0

�sqe(Cs)qe(C0)

, ratio of the amount of adsorbate in equilib-rium at Cs to the equilibrium amount of adsorbatein equilibrium at C0

� dynamic conditions: average value of � at z; dif-ferential conditions: average ratio of the amount ofadsorbate in the fibers to the equilibrium amount ofadsorbate in equilibrium at C0 [equivalent to frac-tional mass increase (from 0 to 1) during adsorp-tion]

� gas viscosity, g m−1 s−1

� zH

, dimensionless axial position in the monolith(0 < � < 1)

� r(Deqv/2 ), dimensionless radial position in the fibers(0 < � < 1)

�g gas phase density, g m−3gas

� 4t0Dso

D2eqv

, surface diffusion group

� tt0

, dimensionless time

Acknowledgments

TVS acknowledges the CSIC-ESF for the award of an I3Ppostdoc contract.

References

Bird, R.B., Stewart, W.E., Lightfoot, E.N., 2002. Transport Phenomena. Wiley,New York.

Burchell, T.D., Judkins, R.R., 1997. A novel carbon fiber based materialand separation technology. Energy Conversion and Management 38,S99–S104.

Burchell, T.D., Judkins, R.R., Rogers, M.R., Williams, A.M., 1997. A novelprocess and material for the separation of carbon dioxide and hydrogensulfide gas mixtures. Carbon 35, 1279–1294.

Burchell, T.D., Weaver, C.E., Chilcoat, B.R., Derbyshire, F., Jagtoyen, M.,2000. Activated carbon fiber composite material and method of making.US Patent 6030698, Lockheed Martin Energy Research Corporation, OakRidge, TN, US.

Centeno, T.A., Marbán, G., Fuertes, A.B., 2003. Importance of microporesize distribution on adsorption at low adsorbate concentrations. Carbon41, 843–846.

Chen, Y.D., Yang, R.T., 1992. Predicting binary Fickian diffusivities from pure-component fickian diffusivities for surface-diffusion. Chemical EngineeringScience 47, 3895–3905.

Cheng, T.B., Jiang, Y., Zhang, Y.P., Liu, S.Q., 2004. Prediction of breakthroughcurves for adsorption on activated carbon fibers in a fixed bed. Carbon42, 3081–3085.

CRC, 1984. CRC Handbook of Chemistry and Physics. 64th edn. CRC Press,Boca Raton, FL.

Das, D., Gaur, V., Verma, N., 2004. Removal of volatile organic compoundby activated carbon fiber. Carbon 42, 2949–2962.

DeLiso, E.M., Gadkaree, K.P., Mach, J.F., Streicher, K.P., 1997. Carbon-coated inorganic substrates, US Patent 5597617. Corning Inc, Corning,NY, US.

Derbyshire, F., Jagtoyen, M., Andrews, R., Rao, A., Martín-Gullón, I., Grulke,E.A., 2001. Carbon Materials in environmental applications. In: Radovic,L.R., (Ed.), Chemistry and physics of carbon, vol. 27, Marcel Dekker,New York, pp. 1–66.

Doraiswamy, L.K., Sharma, M.M., 1984. Heterogeneous Reactions: Analysis,Examples and Reactor Design. Wiley, New York.

Foster, K.L., Fuerman, R.G., Economy, J., Larson, S.M., Rood, M.J., 1992.Adsorption characteristics of trace volatile organic compounds in gasstreams onto activated carbon fibres. Chemistry of Materials 4, 1068–1073.

Fuertes, A.B., Marbán, G., Nevskaia, D.M., 2003. Adsorption of volatileorganic compounds by means of activated carbon fibre-based monoliths.Carbon 41, 87–96.

Gadkaree, K.P., 2001. Method of making activated carbon bodies havingimproved adsorption properties. US Patent 6187713. Corning Inc., Corning,NY, US.

Lee, J.C., Lee, B.H., Kim, B.G., Park, M.J., Lee, D.Y., Kuk, I.H., Chung,H., Kang, H.S., Lee, H.S., Ahn, D.H., 1997. The effect of carbonizationtemperature of PAN fiber on the properties of activated carbon fibercomposites. Carbon 35, 1479–1484.

Levenspiel, O., 1996. The Chemical Reactor Omnibook. OSU Book Stores,Inc., Corvallis, Oregon.

Linders, M.J.G., 1999. Prediction of breakthrough curves of activated carbonbased sorption systems: from elementary steps to process design. Ph.D.Dissertation. Delft University of Technology, Delft, The Netherlands.


Linders, M.J.G., van de Broeke, L.J.P., Nijhuis, T.A., Kapteijn, F., Moulijn,J.A., 2001. Modelling sorption and diffusion in activated carbon: a novellow pressure pulse-response technique. Carbon 39, 2113–2130.

Linders, M.J.G., Mallens, E.P.J., van Bokhoven, J.J.G.M., Kapteijn, F.,Moulijn, J.A., 2003. Breakthrough of shallow activated carbon beds underconstant and pulsating flow. AIHA Journal 64, 173–180.

Marbán, G., Antuña, R., Fuertes, A.B., 2003. Low-temperature SCR of NOx

with NH3 over activated carbon fiber composite-supported metal oxides.Applied Catalysis B: Environmental 41, 323–338.

Marbán, G., Fuertes, A.B., 2004. Co-adsorption of n-butane/water vapourmixtures on activated carbon fibre-based monoliths. Carbon 42, 71–81.

Marbán, G., Fuertes, A.B., Nevskaia, D.M., 2000. Dry formation of low-density Nomex(TM) rejects-based activated carbon fiber composites.Carbon 38, 2167–2170.

Muto, A., Bhaskar, T., Tsuneishi, S., Sakata, Y., 2005. Activated carbonmonoliths from phenol resin and carbonized cotton fiber for methanestorage. Energy & Fuels 19, 251–257.

Ruthven, D.M., 1984. Principles of Adsorption and Adsorption Processes.Wiley, New York.

Suzuki, M., 1991. Application of fiber adsorbents in water-treatment. WaterScience and Technology 23, 1649–1658.

Thomas, H.C., 1944. Heterogeneous ion exchange in a flowing system. Journalof the American Chemical Society 66, 1664–1666.

Thomas, H.C., 1948. Chromatography—a problem in kinetics. Annals of theNew York Academy of Sciences 49, 161–182.

Valdés-Solís, T., Linders, M.J.G., Kapteijn, F., Marbán, G., Fuertes, A.B.,2004. Adsorption and breakthrough performance of carbon-coated ceramicmonoliths at low-concentration n-butane. Chemical Engineering Science59, 2780–2791.

Vilaplana-Ortego, E., Alcañiz-Monge, J., Cazorla-Amorós, D., Linares-Solano,A., 2002. Activated carbon fibre monoliths. Fuel Processing Technology77–78, 445–451.

Wakao, N., Smith, J.M., 1962. Diffusion in catalyst pellets. ChemicalEngineering Science 17, 825–834.

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