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Chemical Engineering and Processing 46 (2007) 477–485

Application of film-pore diffusion model for the adsorptionof metal ions on coir in a fixed-bed column

S.Y. Quek a,∗, B. Al-Duri b

a Chemistry Department, University of Auckland, Private Bag 92019, Auckland, New Zealandb Chemical Engineering, University of Birmingham, Edgbaston, Birmingham, United Kingdom

Received 10 November 2005; received in revised form 30 April 2006; accepted 5 June 2006Available online 22 September 2006

bstract

The most important criterion in the design of fixed-bed adsorption systems is the prediction of column breakthrough or the shape of the adsorptionave front, which determines the operating life-span of the bed and the regeneration time. In this study, the investigation of column breakthroughas carried out using coir, a by-product from coconut processing industry, as adsorbent to remove Pb(II) and Cu(II) from aqueous solutions. A two

esistance film-pore diffusion (FPD) model was applied to predict the concentration profiles for various system variables in this study, includingetal solution concentration, flow rate and bed height. It was found that the FPD model could be applied to predict the breakthrough kinetics of the

olumn. The systems under investigation (Pb/coir and Cu/coir) could be described by a single effective diffusivity (Deff) over the operating range ofow rates and initial metal concentrations. The Deff values were (1.31 ± 0.36) × 10−5 cm2/s and (8.24 ± 1.03) × 10−6 cm2/s for Pb/coir and Cu/coir

ystems, respectively. On the other hand, the values of external mass transfer coefficient (βc) were found to increase with decreasing flow ratesnd remained constant for the variation in initial adsorbate concentration. Biot number was used as an indicator for the intraparticle diffusion. Theiot number was found to increase with increasing flow rate and initial concentration, indicating an increase in intraparticle diffusion resistance.2006 Elsevier B.V. All rights reserved.

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eywords: Adsorption; Film-pore diffusion model; Fixed-bed column; Coir; M

. Introduction

Many waste by-products from food industry have been eval-ated for their ability to remove metal ions from water in searchf cost-effective adsorbents [1–19]. Coir or coconut husk fibre,s a waste by-products from the coconut processing industries.t is abundantly available in the tropical countries and can bebtained free or at a minimal cost. Coir was previously proveno have ability to remove heavy metals from aqueous solutionn batch system [20]. However, the information obtained fromdsorption isotherms and contact time study in a batch systems useful in determining the effectiveness of the metal-adsorbentystem. It is not sufficient to give all the accurate scale-up

ata required when designing effluent treatment systems whichmploy adsorption columns. For example, fixed-bed columns doot necessarily operate under equilibrium conditions because the

∗ Corresponding author. Tel.: +64 9 373 7599x85852; fax: +64 9 373 7422.E-mail address: sy.quek@auckland.ac.nz (S.Y. Quek).

tictpaH

255-2701/$ – see front matter © 2006 Elsevier B.V. All rights reserved.oi:10.1016/j.cep.2006.06.019

ons; Diffusion; Mass transfer; Biot number

ontact time is not sufficiently long for the attainment of equilib-ium. Besides, other operational problems such as uneven flowattern (chanelling) in the column, recycling and regenerationannot be studied in batch experiments. Therefore, it is neces-ary to perform flow tests using columns.

Mathematical models have been incorporated into adsorp-ion design in order to predict the concentration profiles withindsorption columns at a wide range of system conditions. Aumber of two-resistance models have been presented whichescribed adsorption systems with varying accuracy [21]. Theseodels tend to differ in their description of the adsorption mech-

nism occurring within the adsorbent particle, assuming eitherore diffusion within the liquid-phase, or solid diffusion withinhe solid phase. In this study, a film-pore diffusion (FPD) models applied to investigate the mass transfer process in the fixed-bedolumn. This model has been successfully employed to describe

he adsorption of phenol and dyes onto carbon, silica, lignite andith in both column and batch experiments [22–26] as well as thedsorption of cadmium and copper ions onto bone char [15,16].owever, it has not been applied to coir previously.

478 S.Y. Quek, B. Al-Duri / Chemical Engineerin

2

wSTfisTbfmac

oorbvwu

l

(

(

(

(

fη

r

i

i

aa

[c

η

∫

dt(e

Fig. 1. A conceptual diagram of unreacted core theory.

. Theory

The film-pore diffusion (FPD) model of interest in this workas proposed by Spahn and Schlunder [27] and Brauch andchlunder [28], based on the unreacted core theory [29,30].his model describes the occurance of adsorption by externallm mass transfer followed by intraparticle pore diffusion to theorption sites where solute molecules (adsorbate) are taken up.he adsorbent particle is regarded as a porous solid. The adsor-ate in the solution is adsorbed in a well defined concentrationront which starts at the outer surface of adsorbent particles,oving radially inward with a certain velocity, leaving an unre-

cted zone at the center. A conceptual diagram of the unreactedore theory is shown in Fig. 1.

A few assumptions are made for this theory: (i) the transferf solute molecules within the pores of an adsorbent particleccurred only by molecular diffusion; (ii) adsorption equilib-ium occurs between the pore and solute solution and adsor-ent surface throughout the particle; (iii) the adsorption is irre-ersible; (iv) the concentration of solute molecules in the poreater is negligible as compared with that on the adsorbent pernit volume.

The main mathematical steps of the FPD model are as out-ined below:

1) External mass transfer from the external liquid phase:

N(t) = kfA(Ct − Ce) = kf4πR2(Ct − Ce) (1)

2) Diffusion in the liquid-filled pore occurs according to Fick’sfirst law:

N(t) = 4πDeff

(1/rf) − (1/R)Ce(t) (2)

3) The velocity of the concentration front is obtained from themass balance on a spherical element:

N(t) = −4πr2f q

heρ

(drfdt

)(3)

A∫

g and Processing 46 (2007) 477–485

4) The average concentration in the solid is given by

q = qhe

(1 − r3

f

R

). (4)

By introducing the following dimensionless parameters:

η = q

qhe, ψ = Ct

Co, τ = Co

ρqhe

Dteff

R2 ,

Bi = kfR

Deff, Ch = qh

em

CoV

The adsorption rate for a single particle can be expressed as aunction of adsorbate concentration, Ψ ; in the adsorbent phase,; the capacity factor, Ch and of the Biot number, Bi, and isepresented by

dη

dτ=[

3(1 − Chη)(1 − η)0.33

1 − 1 − (1/Bi)(1 − η)0.33

](5)

The adsorption rate equation (Eq. (5)) can be incorporatednto the fixed bed kinetic Eq. (6):

δη

δτ= ψf (η)Bi (6)

This Eq. (6) is combined with the differential mass balancen the column:

δψ

δα+ δη

δτ= 0 (7)

nd yields a differential equation for the prediction of the localnd time dependent concentration profile in the solid phase:

δ2η

δτδα

f ′(η)

f (η)

δη

δτ

δη

δα

δη

δτf (η) = 0 (8)

A general solution of Eq. (8) was developed by Van Meel31] and Brauch and Schlunder [28] for the following boundaryonditions:

(α, 0) = 0,δη(α, 0)

δα= 0

Hence, Eq. (8) becomes:

1

f (n)

δη

δα+ η = 0 (9)

Integration of Eq. (9) yields the general solution:

η

δη

ηf (η)= −

∫α

δα (10)

This equation was solved by Brauch and Schlunder [28] byividing the integration region into two sections separated by aime, τ1. This time τ1 is reached when the first adsorbent layerα= 0) at the adsorber entrance is saturated. The mathematicalquations leading to the solution were described by McKay [32].

s a summary, the limit for the first integration region are:α

1

δα

α=∫ η

η(0,t)

δη

η(11)

neerin

α

∫

y

α

tt

psttp(Te

3

3

Escl(pswdc

3

S.Y. Quek, B. Al-Duri / Chemical Engi

Hence:

(α, τ) = η(α, τ)

η(0, τ)(12)

The limit for the second integration region are:

α

1

δα

α=∫ η

1

δη

η(13)

ielding:

(α, τ) = η(α, τ) (14)

Eq. (12) predicts the liquid phase sorbate concentrations upo time τ1, and Eq. (14) predicts the sorbate concentration afterhe constant pattern breakthrough curve is fully developed.

These mathematical steps have been developed in a Fortranrogramme which related the solute on adsorbent, η, to dimen-ionless time, τ1, and solute in the effluent, ψ, to dimensionless

ime, τ [32]. Since monitoring the solute in effluent is the par-icular aim of this study, the Fortran programme is adapted torint out the dimensionless solute concentration in effluent Ct/C0ψ) against dimensionless time, τ and also the volume treated.he theoretical breakthrough curves can then be compared withxperimental curves.

F2w7ec

Fig. 2. Schematic diagram of th

g and Processing 46 (2007) 477–485 479

. Materials and method

.1. Materials

Coir was dried in an oven (Gallenkamp, Model OV-160,ngland) at 105 ◦C in a large size tray for 24 h. It was thencreened through a mesh sieve to obtain adsorbents with a parti-le size range of 500–1000 �m. Stock solutions (1000 mg/l) ofead and copper were prepared from lead nitrate (Pb(NO3)2)Sigma–Aldrich Dorset, England) and hydrated copper sul-hate (CuSO4·5H2O) (Fisons, Loughborough, England) by dis-olving the appropriate amounts of metal salts in 1 l distilledater. Solutions of various concentrations were obtained byiluting the stock solution with distilled water to the desiredoncentration.

.2. Column experiments

The apparatus for column studies are shown schematically inig. 2. The adsorption unit is a glass column with inner diameter.5 cm and length 25.0 cm. The column was designed in such a

ay that samples could be taken at various points (i.e. 2.5 cm,.5 cm, 12.5 cm, 17.5 cm and 22.5 cm) in the column for thevaluation of breakthrough curves at different bed heights. Theolumn was packed with 14.5 g coir to give a total column height

e experimental apparatus.

4 neerin

opmblpse

wcaat(aia

i5cr2wt0mab

4

4

coci

Fi

tswbttfooptm

biaw7urw

4

f1oweaiwcba more prominent effect of film transfer resistance, larger mass

80 S.Y. Quek, B. Al-Duri / Chemical Engi

f 24.5 cm approximately. The adsorbent was boiled for 5 minrior to the packing process to get rid of air bubbles. A fineesh and a layer of gravel (about 0.5 cm) were placed at the

ottom of the adsorbent bed to support the bed while anotherayer of gravel was placed on the top of the adsorbent bed torevent carry over of sorbent particles. The column was thenealed with grease and a glass stopper (contains fine mesh at thend).

During the experiments, the column was fed continuouslyith a metal solution (either Pb or Cu) which was kept in a

onstant head influent tank (60 l capacity) using a pump (Stu-rt Turner Ltd., Oxon, UK). The pH of metal solutions wasdjusted to 4.5 and pH 5.0 for lead and copper respectively, prioro the experiments. The flow rates were regulated by a rotameterModel OMM 1037 NGT, CT Platon Ltd., Basingstoke, UK)nd the overflow from the rotameter was collected back to thenfluent tank. Up-flow conditions were chosen to facilitate theccurate control of adsorbate flow rate.

The column was operated at four different flow rates rang-ng from 25 ml/min to 75 ml/min for copper solutions and0–200 ml/min for lead solutions. The effect of adsorbate con-entration was studied using initial adsorbate concentrationsanging from 10 mg/l to 50 mg/l for copper solutions and from5 mg/l to 100 mg/l for lead solutions. Samples (∼3 ml) wereithdrawn using syringes with needles in certain intervals of

ime at different bed heights and then filtered instantly through.45 �m cellulose acetate membrane filter (Whatman). Theetal concentrations of the samples were analysed using atomic

bsorption spectrophotometer (ATI UNICAM Model 939, Cam-ridge, England) with an acetylene–air flame.

. Results and discussion

.1. Effect of bed height

The adsorption column used in this study was designed to

ontain sampling points at 5 cm interval, to facilitate the studyf the effect of bed height on the life-span of the column. Typi-al breakthrough curves for different bed heights are illustratedn Fig. 3 for Pb/coir system as plots of dimensionless concen-

ig. 3. Typical breakthrough curves for Pb/coir system (flow rate = 75 ml/min,nitial metal concentration = 50 mg/l).

tst

Fc

g and Processing 46 (2007) 477–485

ration versus the volume of influent treated. The resulting plothowed the typical ‘S’ shape of a packed-bed adsorption systemith an initial period of minimal solute, followed by gradualreakthrough that would slowly reach the feed metal concentra-ion. This flow pattern was repeated over the entire duration ofhe experiment for different bed heights. The “S’ shape profileor column adsorption is generally associated with adsorbatef smaller molecular weight and simple structure and is notbserved in larger molecular such as dyes [33–36]. This flowrofile has been observed previously by other researchers forhe adsorption of Cu(II), Ni(II) and Cd(II) onto banana pith and

oss [10,37].Results indicate that an increase in bed height increases the

reakthrough volume and hence the breakthrough time, resultingn longer service time. This is because of the increase in themount of adsorbent packed and therefore in the binding sitesith increasing bed height. From Fig. 3, an increase of about0% in breakthrough volume was obtained at 50% breakthroughpon increasing the bed height from 7.5 cm to 12.5 cm at a flowate of 75 ml/min for Pb/coir system. Similarly, the service timeas extended from 53.33 min to 90.67 min.

.2. Effect of flow rate

Fig. 4 shows the plot of breakthrough curves at four dif-erent flow rates for Pb/coir system, at a fixed bed height of2.5 cm and initial metal concentration of 50 mg/l. The shapef the breakthrough curve would indicate the internal resistanceithin the column and the relative effects of mass transfer param-

ters throughout the operating conditions. It is observed thatt higher flow rates, the breakthrough point occurred earlier,ndicating a shorter column life. Also, the breakthrough curvesere sharper for higher flow rates, implying higher intraparti-

le diffusion effect and a smaller mass transfer zone [28]. Thereakthrough curves were flatter for lower flow rates indicating

ransfer zone and longer service time for the column. This is rea-onable because at higher flow rates the boundary layer aroundhe particles is thinner, which reduces external mass transfer

ig. 4. Breakthrough curves for Pb/coir at four different flow rates (initial Pb(II)oncentration = 50 mg/l, bed height = 12.5 cm).

S.Y. Quek, B. Al-Duri / Chemical Engineering and Processing 46 (2007) 477–485 481

Table 1Effect of flow rates on the volume of wastewater treated when Ct/C0 = 0.2 (20% breakthrough) at a bed height of 12.5 cm

Pb/coir Cu/coir

Flow rate (ml/min) Volume treated (l)when Ct/C0 = 0.2

Time (min) Flow rate (ml/min) Volume treated (l)when Ct/C0 = 0.2

Time (min)

50 6.3 125.0 20 2.9 146.675 5.7 75.0 35 2.7 77.0

12

(flsafiS

i((tflatrtte

4

chtrhca

Ft

Ocathsta

4

rfldipd

D

wot

00 5.4 54.200 5.2 24.0

film) resistance. The opposite is true for systems with lowerow rates. The shape of breakthrough curves for Cu/coir systemhow similar trend as those of Pb/coir system. The effect of filmnd intraparticle resistance and both external mass transfer coef-cient (βc) and intraparticle diffusion (Deff) will be evaluated inection 4.4.

Results also indicate that for a fixed bed height, an increasen flow rate decreases the volume treated until breakthroughFig. 10). However, this decrease was not very significantTable 1). For example, a breakthrough volume (for 20% break-hrough) increases from 5.2 l to 6.3 l was observed on changingow rate from 200 ml/min to 50 ml/min, for Pb/coir system, atfixed bed height of 12.5 cm. However, the time for the break-

hrough volume was increased from 24 min to 125 min. The sameesults were also observed for the Cu/coir system. This suggestshat the adsorption of these metals on the column is rapid andhe use of slower flow rates do not significantly improve thefficiency of the column performance.

.3. Effect of initial metal concentration

Fig. 5 shows the breakthrough curves for various initial soluteoncentrations of Pb(II) at a flow rate of 50 ml/min and bedeight of 12.5 cm. The difference in shape observed in the break-hrough curves would be attributed to the variation in column

esistance and adsorption driving forces because these systemsave similar flow rates, i.e., same hydraulic loading. At loweroncentrations, the breakthrough curves were flatter, indicatingrelatively wider mass transfer zone and film controlled process.

ig. 5. Breakthrough curves for Pb/coir system for four initial metal concentra-ions (flow rate = 50 ml/min, bed height = 12.5 cm).

povet

maeiiimt

pl

β

50 2.5 52.575 2.5 35.0

n the contrary, the breakthrough curves were sharper at higheroncentrations, implying a relatively smaller mass transfer zonend a more intraparticle diffusion controlled process. Clearly,he volumes of the metal solution treated decreased (Fig. 5) andence the service times were shorter for the systems of higherorbate concentrations because of the high adsorbate concentra-ions saturating the adsorbent more quickly. The same trend waslso observed for the Cu/coir system.

.4. Film-pore diffusion (FPD) model fitting

The Fortran computer program that solves the FPD modelequired system parameters as input. These include the influentow rate, initial metal concentration, adsorbent particle size andensity, liquid viscosity, column dimensions, equilibrium capac-ty of the adsorbent, adsorbate molecular diffusivity and effectiveore diffusivity. The molecular diffusivities (Dmol) were initiallyetermined using the Wilke–Chang correlation [38] as follows:

mol = 7.4 × 10−8 (xaM)0.5T

μV 0.6M

(15)

here xa is the association parameter, M the molecular weightf solute (g/mol), T the temperature (K), μ the viscosity of solu-ion (cP) and VM is the molal volume of solute at normal boilingoint (ml/g mol). Wilke–Chang correlation has an average errorf 10%, as estimated by Skelland (1974) [32]. In this work, Dmolalues of 1.146 × 10−5 cm2/s and 9.00 × 10−6 cm2/s has beenstimated for lead(II) solution and copper(II) solution, respec-ively.

The equilibrium capacities are obtained from the Lang-uir isotherm because the FPD model is based on irreversible

dsorption. Mathematically, the Langmuir isotherm is the clos-st isotherm to rectangular shape of isotherm which impliedrreversible adsorption. Results have shown that the Langmuirsotherm could be applied satisfactory to the two systems undernvestigation, namely, Pb(II)/coir and Cu(II)/coir, where the

onolayer capacities for Pb(II)/coir system and Cu(II)/coir sys-em were 48.84 mg/g and 19.30 mg/g, respectively [20].

The value of the mass transfer coefficient, βc, in the liquidhase in the column is computed by the program using a corre-

ation proposed by Carberry [39] and Kataoka et al. [40]:

c = 1.15Dmol

dp

(dpρμ0

ν

)1/2(ν

Dmol

)1/3

(16)

482 S.Y. Quek, B. Al-Duri / Chemical Engineering and Processing 46 (2007) 477–485

Ffl

wbsisel

PFiavdteuttapr

Fa

Fig. 8. Application of the FPDM to various flow rates at a bed height of 12.5 cmfor Pb/coir system.

Fh

McKay and Bino [22]. It was found that the solid phase equilib-

ig. 6. Application of the FPDM to various bed heights for Pb/coir system at aow rate of 50 ml/min and initial metal concentration of 25 mg/l.

here Dmol is the molecular diffusivity, dp the diameter of adsor-ent particle, ρ the density of adsorbent, μ0 the initial soluteolution velocity and ν is the kinematic viscosity. The rate ofntraparticle diffusion is described by the effective pore diffu-ivity (Deff), which is obtained by fitting the theoretical plots toxperimental data, by trial and error, using Deff values from theiterature as guideline.

Figs. 6 and 7 show the application of the FPD model tob(II)/coir and Cu(II)/coir systems at various bed heights. ThePD model fitting of Pb/coir system at different flow rates and

nitial metal concentrations is shown in Figs. 8–10. All figuresre illustrated as plots of dimensionless concentration versus ser-ice time except Fig. 10, which is plotted to show the variation ofimensionless concentration with the volume of metal solutionreated. Generally, good agreement was obtained between thexperiment and theory. This implied that the FPD model could besed to predict the breakthrough kinetics of these adsorption sys-ems. However, in some cases, especially for Cu/coir system, theheoretical simulation could not fit the experimental curves well

t high Ct/C0 value. This deviation is possibly due to the incom-lete attainment of equilibrium in the column and also someeversibility of the adsorption system as previously reported by

ig. 7. Application of the FPD model to various bed heights for Cu/coir systemt a flow rate of 50 ml/min and initial concentration of 10 mg/l.

rw1

Ff

ig. 9. Application of the FPDM to various initial Pb(II) concentrations at a bedeight of 12.5 cm.

ium adsorption capacity value fitting the breakthrough curvesas 15.5 mg/g for Cu/coir system even though this value was9.30 mg/g when calculated from the Langmuir isotherm.

ig. 10. Application of the FPDM to various flow rates at a bed height of 12.5 cmor Pb/coir system: plot of Ct/Co vs. volume treated (l).

S.Y. Quek, B. Al-Duri / Chemical Engineering and Processing 46 (2007) 477–485 483

Table 2The value of βc, Deff and Bi for the systems under investigation

System Flow rate(ml/min)

βc (×10−3 cm/s) Deff (×10−5 cm2/s) Bi

(a) Effect of flow ratea

Pb coir 50 6.71 1.00 9.7375 8.22 1.25 9.83

100 9.50 1.45 9.86200 13.4 1.65 12.2

Cu coir 20 3.60 0.70 7.7235 4.77 0.84 8.5250 5.70 0.90 9.5075 6.89 1.00 10.5

System C0 (mg/l) βc (×10−3 cm/s) Deff (×10−5 cm2/s) Bi

(b) Effect of initial metal concentrationb

Pb/coir 25 6.71 2.00 5.0350 6.71 1.00 9.7375 6.71 0.95 10.6

100 6.71 0.90 11.2

Cu/coir 10 5.70 1.00 8.5525 5.70 0.90 9.5035 5.70 0.75 11.450 5.70 0.68 12.6

niuflfeo(Phfvtfzo[(aonTofwsvv

w

bawCflittattefcf

BnBrdciitph(ittfl

a C0 for Pb/coir and Cu/coir systems were 50 mg/l and 25 mg/l, respectively.b Flow rates for both Pb/coir and Cu/coir systems were 50 ml/min.

Table 2 gives the values of the mass transfer parameters,amely the external mass transfer coefficient, βc (cm/s), andntraparticle diffusivity, Deff (cm2/s), which describe the systemsnder investigation. Deff was found to increase with increasingow rate and decreasing initial metal concentration. However,or the two present systems, a single Deff could be adequatelymployed to describe each system, over the operating rangef flow rates and adsorbate concentrations. These value were1.31 ± 0.36) × 10−5 cm2/s and (8.24 ± 1.03) × 10−6 cm2/s forb/coir and Cu/coir system, respectively. The same observationsave been reported by other researchers. Using the FPD modelor column studies, Murray and Allen [23] had reported thealue of 1.6 × 10−7 cm2/s to 3.0 × 10−7 cm2/s for the adsorp-ion of basic red 22 onto lignite; while McKay and Bino [22]ound the value of 5.0 × 10−7 cm2/s for the adsorption of astra-one blue on silica and 2.5 × 10−5 cm2/s for the adsorptionf phenol on carbon. On the other hand, Buck and Al-Duri24] reported the Deff values of (2.5 ± 0.25) × 10−7 cm2/s and4.5 ± 0.50) × 10−7 cm2/s for the adsorption of basic blue 41nd basic red 46 onto carbon. As a comparison, the Deff valuesbtained from the current study are close to the value for phe-ol/carbon system but much larger than the adsorption of dyes.his is probably attributed to the relatively smaller diametersf both phenol and metal ions compared to dyes molecules, theactor that gives them much higher diffusivity values. However,hen compared with the results of Ko et al. [16] who studied

orption of copper and cadmium ions onto bone char, the Deff

alues obtained from this study were higher. This means that Deffalues are specific to each different adsorbate/adsorbent system.

The external mass transfer coefficient, βc, was found to varyith different flow rates but to remain constant for the adsor-

lesp

Fig. 11. Correlation between flow rate and Biot number.

ate concentration ranges under investigation. This is in goodgreement with the results of Ko et al. [16]. The values of βcere 6.71 × 10−3 cm/s and 5.70 × 10−3 cm/s for Pb/coir andu/coir system, respectively. βc increased with increasing theow rates because the turbulence increased in the column caus-

ng reduction in the film resistance as the boundary layer aroundhe particles became thinner. For fixed-bed adsorption, film massransfer would have a more pronounced effect than in batchdsorption. This is because of the presence of the boundary layerhat would be prominent due to the nature of fixed-bed adsorp-ion, and thus would enhance the effect of film mass transfer. Thexternal mass transfer coefficient, βc, remained constant for dif-erent concentration ranges because the hydraulic loading wasonstant (i.e., 50 ml/min for both Pb/coir and Cu/coir systems)or all concentration ranges.

The Fortran program has also been adapted to calculate theiot number (Bi). Bi measures the ratio of internal to exter-al mass transfer resistances within the column. An increasedi value would indicate an increase of intraparticle diffusion

esistance. Therefore, Bi would approach ∝ for an intraparticleiffusion controlled process, and approach 0 for a film diffusionontrolled process [28]. The Bi values for the systems undernvestigation are shown in Table 2. It is observed that Bi, slowlyncrease with the increased of flow rates (Fig. 11). This showedhat as flow rate increased, film resistance decreased and therocess would become more intraparticle diffusion controlled,ence breakthrough curves became sharper as observed earlierFigs. 4 and 8). However, the residence time would decrease withncreasing flow rates and the bed service time became shorter. Athe same time, the volume of metal solution treated until break-hrough, i.e., the liquid removal efficiency, would decrease asow rate increased (Fig. 10). In contrast, a decrease in flow rate

ead to a longer column life and an increase in liquid removalfficiency, provided that the bed length and adsorbent particleize were constant. Nevertheless, this does not mean that the bederformance will improve much because film transfer resistance

484 S.Y. Quek, B. Al-Duri / Chemical Engineerin

wvtforp

miamgctmfl

5

tPdsaficii

A

AB

C

CCCdDDkMqq

qrrrRtTV

x

Gα

β

ε

η

μ

μ

ν

ρ

τ

ψ

R

Fig. 12. Correlation between initial concentration and Biot number.

ill increase and the liquid removal efficiency will not improveery significantly, as discussed in Section 4.2. Therefore, forreating large volume of effluent, it is more efficient to operate aew columns in parallel with moderate flow rate (i.e., 75 ml/minr 50 ml/min), rather than using one column with very high flowate. In addition, applying very high flow rate will increase theumping cost.

Bi was also found to increase with the increase of initialetal concentration (Table 2, Fig. 12). This indicated a more

ntraparticle controlled process and a shorter bed service times initial metal concentration increase. Therefore, if the initialetal concentration of the waste water is high, column with big-

er diameter and longer length may be used. Alternatively, a fewolumns operating in parallel can be applied. Overall, the sys-em under current investigation is more suitable for treating low

etal concentration wastewater in small volume using moderateow rates.

. Conclusions

The theoretical mass transfer model based on external massransfer and pore diffusion was successfully applied to theb/coir and Cu/coir systems. Breakthrough curves were pre-icted using a single effective pore diffusivity (Deff) for eachystem for the studies involving various bed heights, flow ratesnd initial metal concentrations. The external mass transfer coef-cients (βc) increased with increasing flow rate but remainedonstant at different initial concentrations. The Biot numberncreased with increasing flow rate and initial concentration,ndicating an increase in intraparticle diffusion resistance.

ppendix A. Nomenclature

total surface area of an adsorbent (m2/g)i βcR/Deff, Biot number

g and Processing 46 (2007) 477–485

e equilibrium liquid-phase concentration of adsorbate(mg/l)

h capacity factor in FPDM (qhem/C0V )

t liquid-phase concentration of adsorbate at time t (mg/l)0 initial liquid-phase concentration of adsorbate (mg/l)p mean particle size (cm, m)eff effective diffusivity (cm2/s)mol molecular diffusivity (cm2/s)

f external mass transfer coefficient (cm/s)molecular weight of solute (g/mol)

e equilibrium solid-phase concentration (mg/g)he hypothetical concentration of solute on adsorbent at

equilibrium (mg/g)(t) mean concentration of solute on adsorbent (mg/g)

radial co-ordinate (cm)2 correlation coefficientf radius of the unreacted zone at the particle centre (cm)

radius of particle (cm)time (min, s)temperature (◦C, K)

M molal volume of solute at normal boiling point(ml/g mol)association parameter in Wilke–Chang correlation ofDmol

reek symbolsdimensionless column bed height

c external mass transfer coefficient in FPD model (cm/s)particle porosityq/qe, dimensionless solid phase concentrationviscosity of solution (cP)

0 solute solution velocity (m/s)kinematic viscosity (Stoke or cm2/s)particle density (solid phase) (g/cm3)dimensionless timeCt/C0, dimensionless liquid phase concentration

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S.Y. Quek, B. Al-Duri / Chemical Engi

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