Bioresource Technology 100 (2009) 5633–5640

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Bioresource Technology

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Modeling, simulation, and experimental validation for continuous Cr(VI)removal from aqueous solutions using sawdust as an adsorbent

Suresh Gupta, B.V. Babu *

Chemical Engineering Department, Birla Institute of Technology and Science (BITS), Vidya Vihar Campus, Pilani 333031, Rajasthan, India

a r t i c l e i n f o a b s t r a c t

Article history:Received 28 March 2009Received in revised form 8 June 2009Accepted 9 June 2009Available online 1 July 2009

Keywords:AdsorptionSawdustCr(VI) removalMathematical modelingContinuous studies

0960-8524/$ - see front matter � 2009 Elsevier Ltd. Adoi:10.1016/j.biortech.2009.06.025

* Corresponding author. Tel.: +91 01596 245073x2E-mail addresses: sureshg@bits-pilani.ac.in (S. Gup

(B.V. Babu).

Continuous adsorption experiments were performed in a fixed-bed adsorption column to evaluate theperformance of low-cost adsorbent (sawdust) developed for the removal of Cr(VI) from aqueous solu-tions. The effects of influencing parameters such as flow rate, mass of adsorbent, initial Cr(VI) concentra-tion were studied and the corresponding breakthrough curves were obtained. The fixed-bed adsorptionprocess parameters such as breakthrough time, total percentage removal of Cr(VI), adsorption exhaustionrate and fraction of unused bed-length were obtained. A mathematical model for fixed-bed adsorptioncolumn was proposed by incorporating the effect of velocity variation along the bed-length in the exist-ing model. Pore and solid diffusion models were used to describe the intra-particle mechanism for Cr(VI)adsorption. The proposed mathematical model was validated with the literature data and the experimen-tal data obtained in the present study and the model was found to be good for explaining the behavior ofbreakthrough curves.

� 2009 Elsevier Ltd. All rights reserved.

1. Introduction

Hexavalent chromium [Cr(VI)] is considered as a major pollu-tant in water pollution and has a dominant presence in most ofthe effluent streams. Cr(VI) is present in many compounds thathave a variety of industrial applications and used in various indus-tries such as glass, ceramics, fungicides, rubber, fertilizers, tanning,mining, metallurgical, etc. (Namasivayam and Yamuna, 1995; San-kararamakrishnan et al., 2006; Kumar et al., 2007; Babu and Gupta,2008a). Cr(VI) is highly mobile and is considered acutely toxic, car-cinogenic and mutagenic to living organisms, and hence more haz-ardous than the other heavy metals (ATSDR, 1993; Babu andGupta, 2008b). Concentration of Cr(VI) present in industrial efflu-ent streams are in the range of 50–200 mg L�1 (Contreras-Ramoset al., 2004; Kumar et al., 2007). The permissible limit of Cr(VI)in potable water is 0.05 mg L�1 (Selvaraj et al., 2003).

In order to comply with the permissible limit, it is essential thatindustries treat their effluents to reduce the Cr(VI) concentration inwater and wastewater to the acceptable levels before its disposalor recycling into the natural environment. Adsorption is provedto be an efficient and cost effective method for the removal ofCr(VI) (Kumar et al., 2007; Babu and Gupta, 2008a). The advantagesof the adsorption process prompt to extend the use of other lowcost and abundantly available materials. If a suitable low-cost

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59; fax: +91 01596 244183.ta), bvbabu@bits-pilani.ac.in

adsorbent is identified, the cost also could be further broughtdown.

Adsorption is an important step in the industrial downstreamprocessing. At an industrial scale, the time of stopping the opera-tion (breakpoint time) must be determined after an economicand, eventually, environmental evaluation of the process. As notonly the amount of solute adsorbed, but also the operating timehas an important impact on the effective use of the column andon the final throughput of the process. The dynamic behavior ofa fixed-bed adsorption column can be better explained and thecharacteristic breakthrough curve of the adsorption phenomenacan be obtained through mathematical models.

It is observed from the literature that the few past studies haveincluded the work on continuous adsorption studies for the Cr(VI)removal (Malkoc et al., 2006; Mungasavalli et al., 2007; Yan et al.,2001; Gode and Moral, 2008). Continuous adsorption studies arerequired to collect the experimental data for the design of adsorp-tion column and for subsequent scale-up from pilot plant to indus-trial scale operation. Researchers mainly focused on analyticalapproach of solving the dynamics of fixed-bed adsorption column(Liao and Shiau, 2000; Bautista et al., 2003; Sotelo et al., 2004; Liet al., 2008). The mathematical models that were reported in theliterature, exclude some of the important physical aspects suchas axial dispersion, intra-particle resistances and velocity variationalong the bed-length. Ahmad et al. (in press) evaluated the com-bined Cr(VI) removal capacities of nonliving (untreated rubberwood sawdust, URWS) and living biomass (URWS-immobilizedAcinetobacter haemolyticus) in a continuous laboratory scale

Nomenclature

aP equivalent particle diameter, mAc area under the breakthrough curve, m2

b Langmuir isotherm constant, L g�1

c adsorbate concentration inside the pellet, mg L�1

Cad concentration of Cr(VI) adsorbed, mg L�1

Cb adsorbate concentration in mobile phase, mg L�1

Cb0 initial Cr(VI) concentration, mg L�1

Ce concentration of Cr(VI) at equilibrium, mg L�1

Cexp experimental Cr(VI) concentration in mobile phase,mg L�1

Cmodel model values of Cr(VI) concentration in mobile phase,mg L�1

DL axial dispersion coefficient, m2 s�1

Dp pore diffusivity, m2 s�1

Ds solid diffusion coefficient, m2 s�1

EBRT empty bed residence time, skf external mass transfer coefficient, m s�1

L bed-height, mmt total amount of Cr(VI) sent to the column, mgN number of data points, –qp average solid phase adsorbate concentration, mg g�1

qe equilibrium solid phase concentration, mg g�1

qt amount of adsorbate adsorbed at time, t, by the adsor-bent, mg g�1

qm maximum monolayer adsorption capacity, mg g�1

Q flow rate, mL min�1

r radial distance, mRa adsorption exhaustion rate, g mL�1

S percentage removal of Cr(VI) in fixed-bed adsorptioncolumn, –

s.d. standard deviation, –, s:d: ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiP ðCexp�CmodelÞ2

N

qt time, stb breakthrough time, stf final time of adsorption, stt time equivalent to stoichiometric capacity of the col-

umn, sV superficial velocity, m s�1

V0 initial superficial velocity, m s�1

W weight of adsorbent, gy fraction of unused bed-lengthz axial coordinate, m

Greek symbolsH fractional coverage, –e bed porosity, –ep particle porosity, –qb bed density, kg m�3

ql liquid density, kg m�3

qs density of adsorbent, kg m�3

21

3

4

5

6

7

8

1 Stored Cr(VI) solution 2 Outlet collection tank 3 Pump 4 Fixed-bed column 5 Feed of Cr(VI) solution 6 Outlet control valve 7 Inlet control valve 8 Base 9 Liquid Rotameter

9

Fig. 1. Fixed-bed continuous adsorption experimental setup for Cr(VI) removalfrom wastewater.

5634 S. Gupta, B.V. Babu / Bioresource Technology 100 (2009) 5633–5640

downward-flow two column system. Preconcentration and separa-tion of Cr(III) and Cr(VI) using sawdust as a sorbent was carried outby Memon et al. (2005). The adsorption of Cr(VI) from aqueoussolutions on sawdust (SD), base extracted sawdust (BESD) and tar-taric acid modified sawdust (TASD) of Turkish red pine tree (Pinusnigra), a timber industry waste, was studied by Gode et al. (2008).Yu et al. (2003) conducted batch studies for adsorption of Cr(VI)from aqueous solutions using maple sawdust as an adsorbent.

In the present study, sawdust, a low-cost adsorbent was usedfor Cr(VI) removal. Continuous adsorption experiments were con-ducted to understand and quantify the effect of influencing param-eters such as flow rate, mass of adsorbent, initial Cr(VI)concentration on breakthrough curve. A mathematical model forfixed-bed adsorption column was proposed which takes into ac-count of both the external and internal mass transfer resistancesas well as of non-ideal plug flow behavior and velocity variationalong the column. The mathematical model proposed was vali-dated with the data reported in the literature and the obtainedexperimental results of the present study with the application ofsolid and pore diffusion resistances.

2. Methods

2.1. Adsorbent preparation

Sawdust (yellow brownish) was collected from the carpentrysection of the institute’s workshop (BITS – Pilani, India). It waswashed repeatedly with distilled water to remove dust and solubleimpurities. It was then kept for drying at a room temperature of25–30 �C in shade for 8 h. The specific surface area, bulk densityand average particle diameter of sawdust were 0.86 m2 g�1,0.125 g cm�3 and 1.84 mm, respectively.

2.2. Continuous experiments

A stock solution of 1000 mg L�1 of Cr(VI) was prepared by dis-solving 2.8287 g of 99.9% potassium dichromate (K2Cr2O7) in water

and solution volume was made up to 1000 mL. This solution wasdiluted as required to obtain standard solutions containing 50–100 mg L�1 of Cr(VI).

Continuous fixed-bed experiments were performed to removeCr(VI) from aqueous solutions using sawdust as an adsorbent.The schematic diagram of the experimental setup is shown inFig. 1. The fixed-bed column was made of a glass of 1.5 cm internaldiameter. The adsorbent bed was packed with the sawdust in a

S. Gupta, B.V. Babu / Bioresource Technology 100 (2009) 5633–5640 5635

stepwise procedure. Initially, 2 g of adsorbent was transferred intothe column and was shaken manually in order to have dense pack-ing. This procedure was continued till the complete amount ofadsorbent was transferred into the column. After following thisprocedure, 500 mL of distilled water was passed through thepacked bed to make the packing more compact packing. Stocksolutions of Cr(VI) were allowed to flow in down flow modethrough the fixed-bed of sawdust controlled by a valve. The con-stant level of feed of Cr(VI) solution in overhead tank was main-tained by pumping the solution from the tank containing stocksolution of Cr(VI) as shown in Fig. 1. The parameters varied inthe continuous experiments were flow rate, mass of adsorbent(bed-height), and inlet Cr(VI) concentration. The flow rate wasmaintained constant using a liquid rotameter (0–15 L min�1). Thefixed mass of the adsorbent and the stock solution of initial Cr(VI)concentration was used to maintain the higher accuracy in columnexperiments. The continuous experiments were carried out at anoptimum pH value of 1 obtained by batch experiments (Guptaand Babu, 2009). The selection of this low pH was also based onthe actual pH value of industrial effluents such as chromium plat-ing effluent (at pH 1) (Selvaraj et al., 2003), tannery effluent (at pH2) (Contreras-Ramos et al., 2004) and electroplating effluent (at pH2.2) (Kumar et al., 2007) and the experimental studies reported inthe literature (Malkoc et al., 2006; Sarin et al., 2006).

In the present work, di-phenyl carbazide method was used forthe analysis of Cr(VI) ions in the aqueous solutions which onlymeasures the amount of Cr(VI). This method has been reportedlyused in several studies for analysis of Cr(VI) at low pH (Malkocand Nuhoglu, 2007). The concentration of Cr(VI) ions in the effluentwas determined spectrophotometrically by developing a purple-violet color with 1,5-di-phenyl carbazide in acidic solution as acomplexing agent (APHA, 1985). The absorbance of the purple-vio-let colored solution was measured at 540 nm. The deviation of ana-lytical method of Cr(VI) concentration was calculated by preparingthe calibration curve from standard solutions. The standard devia-tion obtained for the calibration curve was 0.00453 which is indic-ative of a good fit of the data and within the error limits of ±1.64%.This ensured high confidence limits of the experimentalmeasurements.

3. Mathematical modeling and simulation

The dynamics of a fixed-bed was described by a set of convec-tive diffusion equations, coupled with source terms due to adsorp-tion and diffusion inside the adsorbent particles. The moleculesfrom the bulk interstitial phase were transported via axial convec-tion and Fickian diffusion (film diffusion) onto the particle surface.Inside the particle, the molecules can diffuse via solid diffusion, orpore diffusion, or both. This study was focused on understandingthe surface and pore diffusion mechanisms. The linear velocity var-iation along the bed was important, which affect the design of anadsorption column significantly (Babu and Gupta, 2005). In thepresent study, the linear velocity variation along the bed wasincorporated in the mathematical model for fixed-bed adsorptioncolumn. The proposed model is generalized by addressing the lim-itations of earlier models. This model can be widely used for under-standing the dynamics of fixed-bed adsorption column for theadsorption of organic and inorganic (metal ions) compounds.

To formulate a generalized model to predict the fixed-bedadsorption dynamics which include external film diffusion fol-lowed by internal diffusion, following assumptions were made:

1. The system is operated under isothermal conditions.2. The equilibrium of adsorption is described by Langmuir iso-

therm (a non-linear isotherm).

3. Mass transfer across the boundary layer surrounding the solidparticles is characterized by the external-film mass transfercoefficient, kf.

4. The linear velocity of the liquid phase varies along the column.5. The macro porous adsorbent particles are spherical and homo-

geneous in size and density.

Based on the preceding assumptions, the net rate of accumula-tion or depletion is given by Eq. (1):

�DL@2Cb

@zþ V

@Cb

@zþ Cb

@V@zþ @Cb

@tþ 1� e

e

� �qs

@qp

@z¼ 0 ð1Þ

The initial conditions considered are given by Eqs. (2) and (3):

Cb ¼ Cb0; z ¼ 0; t ¼ 0 ð2Þ

Cb ¼ 0; 0 < z 6 L; t ¼ 0 ð3Þ

The contour conditions at both ends of the column are given by Eqs.(4) and (5):

DL@Cb

@z¼ �V0ðCb0 � CbÞ; z ¼ 0; t > 0 ð4Þ

@Cb

@z¼ 0; z ¼ L; t P 0 ð5Þ

The superficial velocity, V, in fixed-bed adsorption is not con-stant because of adsorption of Cr(VI). For liquid adsorption, assum-ing the liquid density to be constant, the total mass balance isgiven by Eq. (6), which was used to estimate (dV/dz), i.e. the vari-ation of velocity of bulk fluid along the axial direction of the bed.

ql@V@z¼ �ð1� eÞqs

@qp

@tð6Þ

Velocity boundary conditions are given by Eqs. (7) and (8):

V ¼ V0; z ¼ 0; t > 0 ð7Þ

@V@t¼ 0; z ¼ L; t > 0 ð8Þ

For adsorption in spherical pellets, the inter-phase mass trans-fer rate may be expressed by Eq. (9):

qs

@qp

@t¼ 3kf

apðCb � CeÞ ð9Þ

The intra-pellet adsorbate transport mechanism is defined bypore diffusion and solid diffusion resistances and the associatedisotherm for the system considered was Langmuir isotherm, whichare discussed in Sections 3.1–3.3.

3.1. Pore diffusion

Intra-particle mass transport is due to Fickian diffusion, and it ischaracterized by the pore diffusion coefficient, DP. The mass bal-ance equation for the pore fluid phase in a spherical particle canbe written as Eq. (10):

ep@c@tþ ð1� epÞqs

@qp

@t¼ Dp

@2c@r2 þ

2r@c@r

!ð10Þ

Assuming instantaneous equilibrium as given by Eq. (11):@qp

@t¼ @c@t

@qp

@cð11Þ

Eq. (10) is rearranged to get Eq. (12):

@c@t¼ 1

1þ qs1�ePeP

� �@qp@c

h i Dp

ep

� �@2c@r2 þ

2r@c@r

!ð12Þ

5636 S. Gupta, B.V. Babu / Bioresource Technology 100 (2009) 5633–5640

The initial condition considered was given by Eq. (13):

c ¼ 0; qp ¼ 0; 0 < r < ap; t ¼ 0 ð13Þ

The symmetry condition at the center of the particles and the con-tinuity condition on the external surface of the adsorbent bed areexpressed by Eqs. (14) and (15), respectively:

@c@r¼ 0; r ¼ 0; t > 0 ð14Þ

kf ðCb � CeÞ ¼ DpeP@c@r; r ¼ ap; t > 0 ð15Þ

3.2. Solid diffusion

The mass balance equation for the intra-particle solute trans-port due to the solid diffusion mechanism is given by Eq. (16):

@qp

@t¼ Ds

r2

@

@rr2 @qp

@r

� �ð16Þ

The symmetry condition at the center of the particles and the con-tinuity condition on the external surface of the adsorbent bed areexpressed by Eqs. (17) and (18), respectively:

@qp

@r¼ 0; r ¼ 0; t > 0 ð17Þ

kf ðCb � CeÞ ¼ DsqP

@qp

@r; r ¼ ap; t > 0 ð18Þ

3.3. Adsorption isotherm

The adsorption isotherm for the present system of Cr(VI) re-moval using sawdust was found to be favorable and non-linear,is well described by Langmuir isotherm (Langmuir, 1918), and isgiven by Eq. (19):

h ¼ qe

qm¼ bCe

1þ bCeð19Þ

4. Solution algorithm

Since the non-linear adsorption equilibrium was considered,the preceding set of partial differential equations (Eqs. (1)–(19))was solved numerically by reduction to a set of algebraic equationsusing the Explicit Finite Difference technique. Finite differencetechnique has been successfully applied to solve such type of par-tial differential equations in other studies by the authors group(Babu and Gupta, 2005). An algorithm to solve these coupled equa-tions was developed and implemented into a computer programusing MATLAB (v.6.1) software.

5. Results and discussion

The performance of sawdust as an adsorbent was investigatedin a batch system and reported in previous study (Gupta and Babu,2009). The adsorbent capacity of sawdust for Cr(VI) removal wasalso compared with other low-cost adsorbent and found to be apromising alternative for removal of Cr(VI) from aqueous solutions.

5.1. Continuous adsorption experiments

Fixed-bed adsorption studies were conducted to evaluate thedynamic behavior of Cr(VI) removal onto the sawdust. The mostimportant criterion in the design of fixed-bed adsorption systemsis the prediction of fixed-bed column breakthrough curves or the

shape of the adsorption wave front, which determine the operationlife span of the bed. The designs of fixed-bed adsorption column in-clude the estimation of the shape of the breakthrough curve andthe appearance of the breakpoint time. The breakpoint time isusually defined as the time of adsorption when the effluent con-centration from the column was about 1–5% of the influent con-centration. The total quantity of adsorbed Cr(VI) (qt, mg) in thecolumn for a given inlet Cr(VI) concentration and flow rate was cal-culated from Eq. (20):

qt ¼QAc

1000¼ Q

1000

Z t¼ttotal

t¼0Caddt ð20Þ

The area under the breakthrough curve (Ac) was obtained byplotting the adsorbed concentration (Cad, mg L�1) versus time (t,min). Total amount of Cr(VI) sent to column (mt) was calculatedfrom Eq. (21):

mt ¼Cb0Qtt

1000ð21Þ

where tt is the time equivalent to total capacity of the columnwhich is defined by Eq. (22):

tt ¼qt

mttf ð22Þ

Total percentage removal of Cr(VI) was calculated from Eq. (23):

Total percentage removal of CrðVIÞðSÞ ¼ qt

mt� 100 ð23Þ

The empty bed residence time (EBRT) is the time required forthe liquid to fill the empty column. The EBRT is given by Eq. (24):

EBRT ¼ Bed volumeVolumetric flow rate of the liquid

ð24Þ

The adsorbent exhaustion rate (Ra) is the mass of adsorbent used(W) per volume of liquid treated at breakthrough point which is gi-ven by Eq. (25):

Adsorbent exhaustion rate ðRaÞ

¼ mass of adsorbent in columnvolume treated at breakthrough

ð25Þ

The fraction of unused bed-length was calculated from Eq. (26):

y ¼ 1� tb

ttð26Þ

Various parameters such as tt, tf, tb, qt, mt, S, EBRT, Ra and y wereevaluated for the Cr(VI) removal using sawdust in the fixed-bedadsorption column for different operating conditions and reportedin Table 1. The effect of column parameters such as flow rate, massof adsorbent and the inlet Cr(VI) concentration on the performanceof the breakthrough curves were investigated.

5.1.1. Effect of flow rateFlow rate of wastewater stream is an important parameter for

the design of an adsorption column. Studies were conducted at dif-ferent values of flow rates varied from 10 to 20 mL min�1 while themass of adsorbent and the inlet Cr(VI) concentration were keptconstant at 25 g and 50 mg L�1, respectively at a pH value of 1.The effect of flow rate on the breakthrough curve is shown inFig. 2. As can be seen from the breakthrough curves, higher break-point time of the process was achieved at a lower flow rate. As theflow rate increases, breakthrough time was obtained earlier. Thiscan be explained by the fact that at a low value of EBRT, the diffu-sion process that controls the adsorption becomes slow, and hence,the adsorbent need more time to bind with the metals efficiently.The breakthrough times obtained are 630, 440 and 240 min for theflow rate values of 10, 15 and 20 mL min�1, respectively. The total

Table 1Different parameters for the Cr(VI) removal using sawdust in a fixed-bed adsorption column for different operating conditions.

S. no. Cb0 (mg L�1) W (g) Q (mL min�1) tt (min) tf (min) tb (min) qt (mg) mt (mg) S (%) EBRT (s) Ra (g L�1) y (–)

1 50 25 10 1080 1450 630 540 725 74.5 20 3.9 0.422 50 25 15 860 1240 440 645 930 69.4 13.3 3.8 0.483 50 25 20 660 990 240 660 990 66.6 10 5.2 0.634 50 30 10 1260 1690 850 630 845 74.6 24 3.5 0.315 50 15 10 660 1110 310 330 555 59.4 12 4.8 0.536 75 25 10 940 1470 420 705 1102 63.9 20 5.9 0.557 100 25 10 740 1330 280 740 1330 55.6 20 8.9 0.62

S. Gupta, B.V. Babu / Bioresource Technology 100 (2009) 5633–5640 5637

time, corresponding to the stoichiometric capacity of the column,was found to be decreasing from 1080 to 660 min with an increasein the flow rate from 10 to 20 mL min�1 as given in Table 1. The to-tal percentage removal of Cr(VI) for the fixed-bed adsorption col-umn was found to decrease from 74.5% to 66.6% with an increasein the flow rate from 10 to 20 mL min�1 (Table 1). The fraction ofunused bed-length at breakthrough point shows an increasingtrend (0.42–0.63) with an increase in the flow rate (10–20 mL min�1). Fig. 1 shows that as the flow rate increases, thebreakthrough curve becomes steeper.

The decrease in the breakthrough time with an increase in theflow rate may be due to a fixed saturation capacity of the bed basedon the same driving force giving rise to a shorter time for satura-tion at higher flow rates. The probable reason for the increase inthe steepness of breakthrough curve and the decrease in the re-moval efficiency (74.5–66.6%) with increase in the flow rate (10–20 mL min�1) is that, when the residence time of Cr(VI) in the col-umn is not long enough for the adsorption equilibrium to bereached at that flow rate, the Cr(VI) solution leaves the column be-fore equilibrium occurs. And hence the contact time for Cr(VI)using sawdust was very short at higher flow rates, which causeda reduction in the removal efficiency (Table 1). Another reasonfor the faster saturation of the adsorbent bed at higher flow ratescould be that with an increase in the flow rate, mixing increasesand the thickness of the liquid film surrounding the adsorbent par-ticle decreases, thus reducing the film transfer resistance andhence an increase in the mass transfer rate.

5.1.2. Effect of mass of adsorbentThe breakpoint time also depends on the mass of adsorbent

(bed-length) used in the fixed-bed adsorption column. The effectof the mass of adsorbent was studied for 15, 25 and 30 g for saw-

0 200 400 600 800 1000 1200 14000.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Cb/C

bo

Time (min)

Q = 10 mL min-1

Q = 15 mL min-1

Q = 20 mL min-1

Fig. 2. Effect of flow rate on breakthrough curve for Cr(VI) removal using sawdust(Cb0 = 50 mg L�1 and W = 25 g).

dust while maintaining the constant flow rate and the initial Cr(VI)concentration as 10 mL min�1 and 50 mg L�1, respectively at a pHvalue of 1. Fig. 3 shows the performance of breakthrough curvesat different values of mass of adsorbent. It is evident from Fig. 3that as the mass of adsorbent increases, the obtained value ofbreakthrough time increases. The breakthrough times were ob-tained as 310, 630 and 850 min for 15, 25 and 30 g of sawdust,respectively. The total time, corresponding to the stoichiometriccapacity of the column, shows an increasing trend (660–1260 min) with an increase in the mass of adsorbent (15–30 g) (Ta-ble 1). The removal efficiency of Cr(VI) for the fixed-bed adsorptioncolumn increased from 59.4% to 74.6% with an increase in the massof adsorbent from 15 to 30 g (Table 1). The fraction of unused bed-length at the breakthrough point was found to decrease in therange of 0.53–0.31 for the sawdust amount of 15–30 g (Table 1).The rate of adsorbent exhaustion was decreased from 4.8 to3.5 g L�1 with an increase in the mass of sawdust from 15 to 30 g.

Fig. 3 shows that with an increase in the amount of adsorbent,the capacity of the adsorption column to adsorb Cr(VI) increaseswhich results in a delay to obtain the breakpoint time. This maybe due to the increase in the adsorbent surface area with increasein the adsorbent amount which provides more binding sites for theadsorption. For smaller bed-length, the rate of adsorbent exhaus-tion was higher which shows a faster exhaustion of the fixed-bed.

5.1.3. Effect of initial Cr(VI) concentrationA change in the initial Cr(VI) concentration has a significant

influence on the characteristics of the breakthrough curve. Theadsorption performance of sawdust was tested by varying the inletCr(VI) concentration from 50 to 100 mg L�1. The breakthroughcurves for sawdust obtained at different initial Cr(VI) concentra-tions are shown in Fig. 4. As the initial Cr(VI) concentration was

0 200 400 600 800 1000 1200 1400 1600 18000.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Cb/C

bo

Time (min)

Mass = 15 g Mass = 25 g Mass = 30 g

Fig. 3. Effect of mass of adsorbent on breakthrough curve for Cr(VI) removal usingsawdust (Cb0 = 50 mg L�1 and Q = 10 mL min�1).

0 200 400 600 800 1000 1200 1400 16000.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Cb/C

bo

Time (min)

Cb0

= 50 mg L-1

Cb0

= 75 mg L-1

Cb0

= 100 mg L-1

Fig. 4. Effect of initial Cr(VI) concentration on breakthrough curve for Cr(VI)removal using sawdust (W = 25 g and Q = 10 mL min�1).

Table 2Model parameters values used for simulation.

Parameter Values(Bautista et al., 2003)

Values(present study)

e, Bed porosity (–) 0.58 0.4ep, Particle porosity (–) 0.53 0.3qp, Particle density (kg m�3) 1970 1200qb, Bed densitya (kg m�3) 900 125ql, Liquid densitya (kg m�3) 1000 1000DL, Axial dispersion coefficienta

(m2 s�1)5.9 � 10�10 4.31 � 10�9

qm, Maximum adsorption capacity(mg g�1)

45.4 41.9

b, Langmuir isotherm constant(mL mg�1)

0.84 0.43

Dp, Pore diffusivity (m2 s�1) 2.5 � 10�11 6.62 � 10�9

Ds, Solid diffusion coefficient(m2 s�1)

– 8.60 � 10�13

kf, External mass transfercoefficient (m s�1)

1.5 � 10�6 2.5 � 10�5

D, Bed diameter (m) 0.016 0.015

a Assumed values based on the usual ranges reported in the literature (Malkocet al., 2006; Ruthven, 1984).

5638 S. Gupta, B.V. Babu / Bioresource Technology 100 (2009) 5633–5640

increased from 50 to 100 mg L�1, the break point time decreasedfrom 630 to 280 min. The total time for adsorption, correspondingto the stoichiometric capacity of the column, was found to be de-creased from 1080 to 740 min with an increase in the initial Cr(VI)concentration from 50 to 100 mg L�1 (Table 1). The total percent-age removal of Cr(VI) for the fixed-bed adsorption column was de-creased from 74.5% to 55.6% with an increase in the initial Cr(VI)concentration (Table 1). The fraction of unused bed-length atbreakthrough point was obtained in the range of 0.42–0.62 for50–100 mg L�1 of the initial Cr(VI) concentration (Table 1). Therate of adsorbent exhaustion was increased from 3.9 to 8.9 g L�1

with an increase in the initial Cr(VI) concentration from 50 to100 mg L�1.

The increase in the initial Cr(VI) concentration led to reach bedsaturation earlier and the breakthrough time was quickly obtaineddue to the relatively slower transport because of a decrease in dif-fusion coefficient and the decreased mass transfer coefficient atlow Cr(VI) concentration (Ruthven, 1984). Binding sites, quicklyfilled at higher initial concentration, result in a decrease in thebreakthrough time. It is observed that the adsorbent gets saturatedfaster at higher concentrations of adsorbate due to the higher rateof adsorbent exhaustion at higher Cr(VI) concentration. For a lowinitial Cr(VI) concentration, breakthrough occurs very late andthe surface of the adsorbents is saturated with Cr(VI) at a relativelylonger time. This fact is probably associated with the availability ofadsorption sites around or inside the adsorbent particles that areable to capture the Cr(VI) at a lesser retention time.

5.2. Mechanism of Cr(VI) adsorption

In adsorption, atoms, ions or molecules of an adsorbate diffuseto the surface of the solid adsorbent, where they either chemicallybond with the solid surface or are physically held with weak inter-molecular forces. The electrostatic, chemisorptive and functionalgroup interactions define the affinity of an adsorbent for a specificadsorbate. The metallic ions uptake on sawdust mainly depends on(1) the metal ions concentration, and (2) the adsorption and reduc-tion phenomena that simultaneously take place on the sawdustsurface. These phenomena are strongly related to the solutionpH. The solution pH plays a major role in the adsorption of Cr(VI)and it can be related to the type and ionic state of the functionalgroup present on the adsorbent surface (Babu and Gupta,2008a,b; Gupta and Babu, 2009).

The ionic state of the functional group on the sawdust surfacedepends on the pHzpc (zero point of charge) value of adsorbent.The value of pHzpc of sawdust was obtained as 6.0, and below thispH value, the surface charge of the sawdust is positive (Suksabyeet al., 2007). In the present study, the pH of the initial Cr(VI) solu-tion was maintained as 1 which was less than the value of pHzpc.This indicates that the active sites of sawdust are positivelycharged. Within the solution pH range of 1.0–3.0, chromium ionscan exist in the form of HCrO4�. At lower solution pH value of 1,the increase in Cr(VI) adsorption is due to the electrostatic attrac-tion between positively charged groups of sawdust surface and theHCrO4�.

5.3. Mathematical modeling and simulation

In the present work, the linear velocity variation along the col-umn height is considered in the mathematical model for fixed-bedadsorption column. The proposed mathematical model is simu-lated and validated using the parametric values reported by Bautis-ta et al. (2003) (Table 2). The present model is also compared withthe experimental data reported by Bautista et al. (2003) with thepredicted results obtained using the present model and the modelproposed by Bautista et al. (2003) as shown in Fig. 5. The obtainedvalue of standard deviation (s.d.) indicates that the present model(s.d. = 0.113) shows an improvement over the previous model(s.d. = 0.139) given by Bautista et al. (2003). The incorporation ofvelocity variation along the bed results in a better steepness ofthe breakthrough curve as stated by Ruthven (1984) and Maet al. (1996). This establishes the fact that the effect of velocity var-iation on breakthrough curve is significant.

The comparison of experimental results and the model predic-tions (pore diffusion and solid diffusion models) for Cr(VI) adsorp-tion using sawdust is shown in Fig. 6. Model parameter values forsimulation in the present study are listed in Table 2. The shape ofthe breakthrough curves obtained using the pore diffusion and so-lid diffusion models were found to be almost similar for Cr(VI) re-moval. This indicates the suitability of both the models for Cr(VI)removal using sawdust. Suitability of both the models is also con-firmed by the values of standard deviation obtained in the range of0.063–0.105 for pore diffusion and 0.036–0.13 for solid diffusionfor different operating conditions (Table 3). In case of pore diffu-sion, Cr(VI) ions are adsorbed outside the surface of the adsorbentas well as inside the pores of the adsorbent. Moreover, for solid dif-

0 400 800 1200 1600 2000 24000.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0C

b/Cbo

Time (sec)

With velocity variation (Present model) Without velocity variation (Bautista et al., 2003) Experimental

Fig. 5. Comparison between theoretical and experimental results obtained usingproposed mathematical model (Cb0 = 1000 mg L�1, Q = 1 mL min�1 and W = 30 g).

0 400 800 1200 1600 2000 24000.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Cb/C

bo

Time (min)

Pore diffusion Solid diffusion Experimental

Fig. 6. Comparison of experimental and theoretical breakthrough curve for Cr(VI)removal using sawdust (Q = 10 mL min�1, C0 = 50 mg L�1 and W = 30 g).

Table 3Standard deviation values for Cr(VI) adsorption on sawdust by fixed-bed adsorptioncolumn on different operating conditions.

S.no.

Cb0

(mg L�1)W(g)

Q(mL min�1)

Standard deviation (s.d.)

Pore diffusionmodel

Solid diffusionmodel

1 50 25 10 0.093 0.0772 50 25 15 0.066 0.0973 50 25 20 0.105 0.1304 50 30 10 0.063 0.0365 50 15 10 0.072 0.1186 75 25 10 0.071 0.1067 100 25 10 0.099 0.118

S. Gupta, B.V. Babu / Bioresource Technology 100 (2009) 5633–5640 5639

fusion, most of the Cr(VI) diffusion takes place at the outer surfaceof the adsorbent. In the present study, the adsorbent used is saw-dust having a lesser bulk and particle density which signifies thatthe most of the surface of sawdust is available for adsorption. Sothe shape of the breakthrough curves obtained for pore diffusion

and solid diffusion models are similar. It can be observed fromFig. 6 that the experimental data for Cr(VI) adsorption using saw-dust fit well with the models during the initial time period ofadsorption, but not so in the latter part of adsorption as reflectedin the respective breakthrough curves. This may be due to the highfraction of unutilized bed-length (0.31–0.62) which is responsiblefor more flattening of the breakthrough curve at the latter stageof adsorption (McCabe et al., 2007). Langmuir isotherm model isfound to be better than the Freundlich isotherm model to describethe equilibrium data for Cr(VI) adsorption on sawdust (Gupta andBabu, 2009). Langmuir isotherm is considered as favorable iso-therm, whereas the Freundlich isotherm is accepted as a stronglyfavorable isotherm. The unused bed-length for favorable isothermis higher than the strongly favorable isotherm (McCabe et al.,2007).

After having seen the good agreement between model predictedvalues and the experimental results, the proposed model is sub-jected to parametric study. The adsorption column performanceis also affected by the other model parameters such as particle ra-dius and external-film mass transfer coefficient. The obtainedbreakthrough time was highly sensitive to the particle radius andexternal-film mass transfer coefficient. The corresponding sensitiv-ity values obtained were 2.638 � 104 min m�1 and �3.125 � 103

min2 m�1, respectively.

6. Conclusions

This study, on fixed-bed column adsorption using a low-costadsorbent (sawdust), showed that Cr(VI) removal is a strong func-tion of the flow rate, the mass of adsorbent and the initial Cr(VI)concentration. The obtained breakthrough curves are strong func-tions of the percentage removal, the adsorption exhaustion rateand the fraction of unused bed-length. The proposed mathematicalmodel was successfully validated with the literature data and theobtained experimental data of this study. The pore diffusion andsolid diffusion models were found to be suitable for explainingthe breakthrough behavior attained for Cr(VI) removal usingsawdust.

Acknowledgements

Authors thank University Grants Commission (UGC), New Delhi,India for their financial support.

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