Revista Mexicana de ngeniería - scielo.org.mx · Revista Mexicana de Ingeniería Q uímica aproximaciones deben ser acopladas a un modelo pseudo-heterog CONTENIDO Volumen 8, número

Revista Mexicana de Ingeniería Química

CONTENIDO

Volumen 8, número 3, 2009 / Volume 8, number 3, 2009

213 Derivation and application of the Stefan-Maxwell equations

(Desarrollo y aplicación de las ecuaciones de Stefan-Maxwell)

Stephen Whitaker

Biotecnología / Biotechnology

245 Modelado de la biodegradación en biorreactores de lodos de hidrocarburos totales del petróleo

intemperizados en suelos y sedimentos

(Biodegradation modeling of sludge bioreactors of total petroleum hydrocarbons weathering in soil

and sediments)

S.A. Medina-Moreno, S. Huerta-Ochoa, C.A. Lucho-Constantino, L. Aguilera-Vázquez, A. Jiménez-

González y M. Gutiérrez-Rojas

259 Crecimiento, sobrevivencia y adaptación de Bifidobacterium infantis a condiciones ácidas

(Growth, survival and adaptation of Bifidobacterium infantis to acidic conditions)

L. Mayorga-Reyes, P. Bustamante-Camilo, A. Gutiérrez-Nava, E. Barranco-Florido y A. Azaola-

Espinosa

265 Statistical approach to optimization of ethanol fermentation by Saccharomyces cerevisiae in the

presence of Valfor® zeolite NaA

(Optimización estadística de la fermentación etanólica de Saccharomyces cerevisiae en presencia de

zeolita Valfor® zeolite NaA)

G. Inei-Shizukawa, H. A. Velasco-Bedrán, G. F. Gutiérrez-López and H. Hernández-Sánchez

Ingeniería de procesos / Process engineering

271 Localización de una planta industrial: Revisión crítica y adecuación de los criterios empleados en

esta decisión

(Plant site selection: Critical review and adequation criteria used in this decision)

J.R. Medina, R.L. Romero y G.A. Pérez

Vol. 13, No. 2 (2014) 539-553

MODELLING OF A FIXED BED ADSORBER BASED ON AN ISOTHERM MODELOR AN APPARENT KINETIC MODEL

MODELADO DE UN ADSORBEDOR DE LECHO FIJO BASADO EN UN MODELODE ISOTERMA O UN MODELO CINETICO APARENTE

G. Che-Galicia, C. Martınez-Vera, R.S. Ruiz-Martınez∗ and C.O. Castillo-Araiza∗

Grupo de Procesos de Transporte y Reaccion en Sistemas Multifasicos, Depto. de IPH, Universidad AutonomaMetropolitana - Iztapalapa, Av. San Rafael Atlixco No. 186, C.P. 09340, Mexico D.F., Mexico.

Received March 5, 2014; Accepted May 20, 2014

AbstractIsotherm model and apparent kinetic model are simple approaches, which are indistinctly used to predict the kinetic behaviourof the adsorption phenomena. The main objective in this work was to elucidate when these approaches should be coupled to apseudo-heterogeneous fixed-bed adsorber model to describe reliable breakthrough curves when experimental data at industrialscale are not available. To achieve this, an adsorption column packed with a low-cost natural zeolite was modelled for theremoval of Rhodamine B (RhB). To have certainty in the model predictions, equilibrium and kinetic experiments were carriedout. Freundlich isotherm model and a pseudo second order apparent kinetic model accounting for diffusion phenomena led to themost adequate fit to experimental data. Experimental and simulations results indicated that the use of an isotherm model (LDF-M) or an apparent kinetic model (AkA-M) in the packed bed adsorbed model predicted similar tendencies regarding the effect onthe breakthrough point of the different parameters considered. Nevertheless, the shapes of the breakthrough curves predicted byboth models were significantly different, suggesting that an apparent kinetic model is necessary to have reliable prediction of theindustrial behaviour of this studied zeolite since intraparticle mass transport resistances are significant.

Keywords: packed bed adsorber, breakthrough curves, adsorption kinetics, isotherm model, apparent kinetic model.

ResumenLos modelos de isotermas y de cinetica aparentes de adsorcion son aproximaciones indistintamente utilizadas para describirel comportamiento de un determinado adsorbato-adsorbente. El objetivo principal de este trabajo fue elucidar cuando estasaproximaciones deben ser acopladas a un modelo pseudo-heterogeneo de un adsorbedor de lecho fijo para describir curvasde ruptura confiables cuando no existen datos experimentales a escala industrial. Para lograr esto, se modelo una columna deadsorcion empacada con una zeolita natural de bajo costo que no ha sido estudiada previamente para la remocion de RodaminaB (RhB). Para tener certidumbre en las predicciones del modelo, se llevaron a cabo experimentos de equilibrio y cineticos. Elmodelo de la isoterma de Freundlich y un modelo cinetico aparente de pseudo segundo orden que considera los fenomenos dedifusion presentaron el mejor ajuste a los datos experimentales. Los resultados experimentales y las simulaciones indicaron queel modelado de un adsorbedor de lecho empacado con un modelo de isoterma (LDF-M) o un modelo cinetico aparente (AkA-M), predice tendencias similares en relacion con el efecto en el punto de ruptura de los diferentes parametros considerados. Sinembargo, las formas de las curvas de ruptura predichas por ambos modelos fueron significativamente diferentes, lo que sugiere lanecesidad de un modelo cinetico aparente para describir el comportamiento industrial de esta zeolita debido a que las resistenciasal transporte de masa por difusion en el adsorbente son significativas.

Palabras clave: adsorbedor de lecho empacado, curvas de ruptura, cinetica de adsorcion, modelo de isoterma, modelo cineticoaparente.

∗Corresponding author. E-mail: [email protected] (R.S.R.M.); [email protected] (C.O.C.A.)

Publicado por la Academia Mexicana de Investigacion y Docencia en Ingenierıa Quımica A.C. 539

Che-Galicia et al./ Revista Mexicana de Ingenierıa Quımica Vol. 13, No. 2 (2014) 539-553

1 Introduction

The removal of dyes from textile industry effluents isa critical problem worldwide, since these moleculesare among the most common organic contaminants ingroundwater wells and surface waters, causing adverseeffects to organisms even at low concentrationsdue to their toxic properties (Hutzler et al.,1986; Ozcan et al., 2005; Crini, 2006). There ishence the necessity to minimise the environmentalrelease of dyes. A review of the advantages anddisadvantages of conventional methods for theremoval of harmful pollutants is discussed elsewhere(Robinson et al., 2001). Adsorption is one of themost used and effective processes for the removalof synthetic dyes that are difficult to mineraliseby conventional methods. Activated carbons havedemonstrated their effectiveness in adsorbing thistype of pollutant (Namasivayam and Kavitha, 2002).However, the high-cost of activated carbon andthe costs associated with the adsorbent regenerationprocess have made these materials non-economicallyfeasible for industrial use (Osma et al., 2007). Inthis context, various low-cost adsorbents derivedfrom agricultural waste, biosorbents, industrial waste-materials or natural materials have been investigatedto eliminate synthetic dyes from industrial textileeffluents (Rafatullah et al., 2010). In particular, naturalzeolites have gained commercial and environmentalinterest because of their worldwide abundance, low-cost, and profitable regeneration (Wang and Peng,2010).

The design of industrial adsorbers requires someparameters that must be obtained from extensivelaboratory and pilot plant experiments that are timeconsuming and expensive (Sankararao and Gupta,2007). In this sense, modelling and simulationnormally complement this aim, serving as majorengineering tools to design and optimise the dynamicbehaviour of fixed-bed adsorbers (Liao and Shiau,2000; Inglezakis and Grigoropoulou, 2004). Inthe models used to predict breakthrough curves,mass transport phenomena are well understood andadequately described in the literature (Hall et al.,1966; Wilson et al., 1966, Ruthven, 1984). However,presently there is no unique modelling approachaccepted to describe adsorption kinetics (Marshalland Pigford, 1947; Crittenden and Weber, 1978; Koet al., 2001; Ruthven, 1984; Tien, 1994; Romero-Gonzalez et al., 2005). In some of the approaches,it is assumed that the mobile and stationary phasesinstantly reach equilibrium, and hence make use of an

isotherm equilibrium model to account for adsorptionkinetics (Hutzler et al., 1986; Chern and Chien, 2001).Another approaches account for the surface dynamicsbetween the mobile and stationary phases making useof a proper kinetic model or apparent kinetic modelto describe the adsorption kinetics (Aboudzadeh et al.,2006; Lua and Jia, 2009). Nevertheless, there are noestablished criteria to decide when to couple either anisotherm equilibrium model or a kinetic model to theadsorber model when experimental data is lacking todescribe the kinetic behaviour of the adsorbent in afixed-bed adsorber at an industrial scale.

The main aim of this work was to elucidate whenan equilibrium isotherm model or an apparent kineticmodel should be coupled to a fixed-bed adsorbermodel in order to describe reliable breakthroughcurves. Rhodamine B (RhB) was used as a dyemodel molecule and a Mexican abundant low-cost natural zeolite was used as the adsorbent.Since this material has not been evaluated in anyprevious studies, it has been characterised by meansof N2 physisorption and X-ray powder diffractiontechniques. In the same sense, an experimental studyof the adsorption of RhB on the natural zeoliteat laboratory scale was carried out. In particular,equilibrium and kinetic observations were obtainedat several temperatures, inlet RhB concentrations andparticle diameters. Langmuir and Freundlich isothermmodels were used to fit experimental equilibriumdata. The kinetic experimental data were described bymeans of pseudo first order and pseudo second orderkinetic models. Finally, two pseudo-heterogeneousmodels that accounted for convection, dispersionand interfacial mass transport phenomena coupledto adsorption kinetic phenomena were examinedto predict breakthrough curves from the fixed-bedadsorber. One of these models, named the LinearDriving Force Model (LDF-M), made use of the mostappropriate isotherm equilibrium model. The othermodel, named the Apparent Kinetic Adsorber Model(AkA-M), made use of the most appropriate apparentkinetic model that accounted for both diffusionalmass transport phenomena and the adsorption kineticsitself. These modelling approaches were intentionallyevaluated since they are suitable to describe withcertainty and without computation restraints thepossible behaviour of a new adsorbent in a fixed-bedadsorber at industrial scale.

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Table 1. Characteristics of the Rhodamine B.

Parameter Value Parameter Value

Suggested name Rhodamine B Solubility in water 0.78C.I. number 45170 Solubility in ethanol 1.47C.I. name Basic Violet 10 Molecular size (nm)a 1.44×1.09×0.64

Class Rhodamine Empirical formule C28H31N2O3ClIonization Basic Molecular weight 479.029λmax (nm) 554 CAS number 81-88-9

aReference: Huang et al. (2008)

1

Fig. 1. Chemical structure of Rhodamine B. (a) cationic form (b) three-dimensional 2 structure. 3

4

Fig. 1. Chemical structure of Rhodamine B. (a)cationic form (b) three-dimensional structure.

2 Procedures

2.1 Materials

A basic dye, RhB, purchased from the Sigma-AldrichChemical Company was used as a model molecule toevaluate the adsorption capacity of the natural zeolite.The properties of RhB are shown in Table 1 and itschemical structure is displayed in Fig. 1. A UV-Visiblespectrophotometer (HACH DR 2800) at a wavelengthof 554 nm was used to monitor RhB concentrationthrough the use of the Beer-Lambert law.

The natural zeolite used in this study was obtained

from Etla municipality, Oaxaca, Mexico. This materialwas treated prior to the adsorption experiments. Asample of this material was crushed, sieved (16-20mesh) and washed with deionised water in orderto remove the dust attached to the surface. Thewashed sample was heated at 110 ºC for 24 h toevaporate moisture from particles and to evaporate anyvolatile component that might have been adsorbed.The specific surface area of the natural zeolite wasobtained from the physisorption of nitrogen using aVolumetric Quantachrome Autopore 1L-C instrumentat -197 ºC (at Mexico City 2250 m altitude). Thespecific surface area was calculated according tothe standard Brunauer-Emmet-Teller (BET) method,and the average pore size was determined fromthe desorption branch of the isotherm using theBarrett-Joyner-Halenda (BJH) method (Barrett et al.,1951). X-ray powder diffraction (XRD) was used toinvestigate the crystalline species and bulk phasespresent in the natural zeolite. XRD difractogramspresented in this study were obtained from a SiemensD-500 diffractometer employing a nickel-filtered CuKα radiation (λ = 1.5406 Å, 40 kV, 30 mA) at 0.020°intervals in the range 20° ≤ 2θ ≤ 75° with 1 s countaccumulation per step directly from the natural zeolite.

2.2 Adsorption equilibrium

The adsorption equilibrium data were obtained by animmersion method at different RhB concentrations(10-200 mg/L) and temperatures (20, 35 and 50 ºC).An isothermal well-stirred batch adsorber was fed with0.25 g of the natural zeolite and 50 mL of RhB solutionat the desired initial concentration. The adsorber wascovered to avoid the evaporation of the RhB solution,and heated by a thermostat to the desired temperature.RhB concentration was monitored daily. The obtaineddata were used to calculate the RhB equilibriumconcentrations. The amount of RhB adsorbed atequilibrium (qne) was calculated by a mass balance

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equation given as follows:

qne =V(Cno −Cne)

m(1)

where V is the volume of RhB solution fed to theadsorber, Cno is the initial concentration of RhB, Cne isthe RhB concentration in liquid phase at equilibrium,and m is the mass of the natural zeolite fed to theadsorber.

2.2.1. Isotherm model

The adsorption isotherm suggests how the RhBmolecules distribute between the liquid phase andthe solid phase when the adsorption process reachesequilibrium. The analysis of the observed equilibriumdata by means of an appropriate isotherm modelis used to characterise the adsorption capacity of aspecific adsorbent and, from an engineering point ofview, to design and optimise the adsorption processat an industrial scale when the isotherm model iscoupled to the fixed-bed adsorber model. In thiswork Langmuir and Freundlich isotherm modelswere evaluated to fit our adsorption equilibriumobservations with the aim to determine the bestisotherm model to be coupled to the fixed-bed adsorbermodel to predict breakthrough curves, as presentedfurther.

The Langmuir model assumes that adsorptionoccurs on a homogenous surface, where sites areequally available and energetically equivalent. Eachsite can adsorb at most one molecule of RhB andthere are no interactions between RhB moleculeson adjacent sites. (Al-Duri and Yong, 2000). TheLangmuir model is given by:

qne =qmKLCne

1 + KLCne(2)

where qne is the amount of RhB adsorbed on aunit weight of adsorbent at equilibrium, Cne is theconcentration of RhB in liquid phase at equilibrium,qm is the maximum amount of RhB adsorbed perunit weight of adsorbent at equilibrium, and KL isthe Langmuir adsorption constant related to RhBadsorption affinity on the adsorbent.

The Freundlich model accounts for Langmuirmodel weaknesses. This isotherm model assumes aheterogeneous surface, where each site can adsorbmore than one molecule of RhB and there areinteractions between RhB molecules on adjacentsites (Walker and Weatherley, 2001). The Freundlich

adsorption model is given by:

qne = KFC1/nne (3)

where qne is the amount of RhB adsorbed on aunit weight of adsorbent at equilibrium, Cne is theconcentration of RhB in liquid phase at equilibrium,KF and n are adsorption affinity constants.

2.2.2. Adsorption thermodynamics

Thermodynamic adsorption parameters werecalculated from the dimensionless thermodynamicequilibrium constant, Kc, by means of the well-knownmodified Van’t Hoff equation given by Equation(4) (Namasivayam and Ranganathan, 1995), thatrelates the change in temperature to the change in theequilibrium constant Kc, given the standard enthalpychange, ∆Ho, and standard entropy change, ∆S o, forthe adsorption process.

ln KC =∆S o

R−∆Ho

RT(4)

KC =Cne

Cnse(5)

where Cnse and Cne are the equilibrium concentrationsof the RhB on adsorbent and in the solutionrespectively, R is the ideal gas constant and T isthe system temperature. Standard Gibbs free energy,∆Go (kJ/mol) at various temperatures was calculatedthrough the following thermodynamic relation:

∆Go = −RT ln KC (6)

2.3 Adsorption kinetics

Kinetic experiments were carried out using a rotatingbasket batch adsorber operated isothermally (Carberry,1976). The adsorber was heated by the use of awater bath to the desired temperature. A stainless steelpropeller containing two rectangular baskets of 20 mmheight, 16 mm width and 12 mm depth was used to stirthis batch adsorber. Each basket was loaded with 2.5g of adsorbent. For each experiment 500 mL of RhBsolution at an initial desired concentration was addedto the stirred batch adsorber. The effect of stirringspeed (100-200 rpm), initial RhB concentration (10-200 mg/L), temperature (20, 35 and 50 ºC) and particlesize (1.0 and 2.5 mm) on adsorption rate was studied.

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2.3.1. Kinetic model

Kinetics provides information regarding themechanism and rate of adsorption of the adsorbateon a specific adsorbent. The development of a kineticmodel is essential for designing and optimising anadsorption process. A pseudo-first-order kinetic modelgiven by Equation (7) and a pseudo-second-ordermodel given by Equation (8) are among the kineticmodels most applied to adsorption processes (Ho andMcKay, 1999a, b; Ho, 2006; Crini et al., 2007; Wu etal., 2009; Dawood and Sen, 2012; de la Pena-Torres etal., 2012). In this work, these two kinetic models wereevaluated to determine which one better describesour experimental kinetic observations, and hence tocouple this kinetic model to the fixed-bed adsorbermodel to predict breakthrough curves, as presented inthe following section. The kinetic models are givenby:

dqn

dt= k1(qne − qn) (7)

dqn

dt= k2(qne − qn)2 (8)

where qne is the amount of RhB adsorbed on a unitweight of adsorbent at equilibrium, qn is the amountof RhB adsorbed on a unit weight of adsorbent, k1and k2 are the adsorption rate constants and t is theadsorption time. Parameters involved in the isothermand kinetic models were estimated by a multiresponseand multiparameter Levenberg-Marquardt method,considering a 95% confidence interval (Stewart et al.,1992).

2.4 Fixed-bed adsorber model

With the aim of identifying some criteria for decidingwhen an equilibrium isotherm model or an apparentkinetic model should be coupled to the fixed-bedadsorber model to predict breakthrough curves for adetermined adsorbent-adsorbate system, two pseudoheterogeneous models were evaluated to carry out aparametric sensitivity study of the fixed-bed adsorber.The first model, LDF-M, made use of an isothermalequilibrium model. The second model, AkA-M,made use of an apparent kinetic model. Both modelapproaches are totally accepted in literature to proposethe preliminary dimension of an industrial fixed-bedadsorber elucidating the possible behaviour of a newand specific adsorbent, as in this study (Inglezakis andGrigoropoulou, 2004; Abu-Lail et al., 2012).

These models were based on the followingassumptions: (i) the kinetic model was apparent

since observations were obtained by using pelletsof adsorbent where diffusional mass transportphenomena were involved; (ii) the fixed-bed adsorberwas considered to be operated isothermally; (iii)the adsorbent pellets were assumed to be spheresof uniform size; (iv) there were no velocity profilesinside the fixed-bed adsorber since low values ofinlet superficial velocity were accounted for and thetube to particle diameter ratio was greater than 12(Castillo-Araiza and Lopez-Isunza, 2008); (v) theradial concentration gradients were considered to beinsignificant; and (vi) the mass transport parameters(Dax and kL) were considered to be effective andwere obtained from literature correlations (Wilson andGeankoplis, 1966; Chung and Wen, 1968).

The governing transport equations for the LDF-Mare given by the following equations:

Fluid phase:

ε∂Cn

∂t+ ρB

∂qn

∂t+ vzε

∂Cn

∂z= Daxε

∂2Cn

∂z2 (9)

Solid phase:

ρB∂qn

∂t= (1− ε)kLav(Cn −C∗ns) (10)

The initial conditions are:

t = 0; Cn = 0;qn = 0, f or 0 < z < L (11)

The boundary conditions are:

z = 0; εvzCn − εDax∂Cn

∂z= vzCno; f or t > 0

(12)

z = L;∂Cn

∂z= 0; f or t > 0 (13)

where Dax is the axial dispersion coefficient, kL is theso-called effective LDF mass transfer coefficient, avis the interfacial particle area per unit volume of theadsorbent pellet, Cn is the fluid phase concentrationof the RhB, C∗ns is the RhB liquid concentrationat the liquid-solid interface, which is assumed tobe at equilibrium with the prevailing solid phaseconcentration and hence its value was calculated by anisotherm model (Eqs. (3) or (4)), qn is the amount ofRhB adsorbed on a unit weight of adsorbent, vz is thesuperficial axial velocity of the fluid, calculated as theratio of the volumetric flow rate divided by the cross-sectional area of the bed, ε is the void fraction of thebed, ρB is the density of the bed, t is the operation time,and z is the axial position along the bed.

The governing transport equations for AkA-M aregiven by the following equations:

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Fluid phase:

ε∂Cn

∂t+ vzε

∂Cn

∂z= Daxε

∂2Cn

∂z2 − (1− ε)kLav(Cn −Cns)

(14)Solid phase:

(1− ε)∂Cns

∂t= (1− ε)kLav(Cn −Cns)− ρB

∂qn

∂t(15)

∂qn

∂t= k2(qne − qn)n (16)

The initial conditions are:

t = 0; Cn = 0,Cns = 0 and qn = 0 f or 0 < z < L(17)

The boundary conditions are:

z = 0; vzCn −Dax∂Cn

∂z= vzCno f or t > 0 (18)

z = L;∂Cn

∂z= 0 f or t > 0 (19)

The models solved in this section are given bysets of parabolic partial differential equations, whichwere solved numerically by the method of orthogonalcollocation using 30 interior points of placementin axial coordinates, employing shifted Legendrepolynomials for obtaining the collocation points(Finlayson, 1980). The reduced set of ordinarydifferential equations was integrated by the Runge-Kutta-Fehlberg method (Lapidus and Seinfeld, 1971).

2.4.1. Mass transfer correlations

The axial dispersion coefficient was calculated fromthe equation suggested by Chung and Wen (1968).

Pe =0.2 + 0.011Re0.48

p

ε(20)

Pe =dpvz

Dax(21)

Rep =dpvz

ν(22)

where Pe is the Peclet number, Rep is the particleReynolds number, dp is the particle diameter, ν is thekinematic viscosity of the solution, and ε is the voidfraction of the bed, which for this study was obtainedfrom the empirical equation proposed by de Klerk(2003). The interfacial mass transfer coefficient wascalculated according to the correlation of Wilson andGeankoplis (1966).

S h =1.09ε

Re0.33p S c0.33 (23)

S c =ν

DRhB(24)

S h =kL · dp

DRhB(25)

where Sh is the Sherwood number, Sc is the Schmidtnumber and DRhB is the diffusion coefficient of RhBin water and was calculated by the equation developedby Wilke and Chang (1955).

3 Results and discussion

3.1 Natural zeolite characterisation

An X-ray diffraction pattern for the utilised naturalzeolite is shown in Fig. 2. It consisted of a clay-quartzmaterial with crystalline structure, predominantlycontaining clinoptilolite and to a lesser extentmordenite. The isotherm obtained by nitrogenphysisorption is presented in Fig. 3. The adsorption-desorption isotherm observed was of type IV.Capillary condensation and the capillary evaporationoccurred at almost the same relative pressures but didnot change the shape of the hysteresis loop, indicatingthat a kinetic equilibrium of capillary condensation-evaporation existed in the mesopores. The hysteresisloop at higher-relative pressures was a consequenceof N2 filling the textural pores that were associatedwith the natural zeolite morphology (Gomonaj et al.,2000). Surface area, average pore volume and porediameter of the natural zeolite are given in Table2. The surface area was similar to that obtained forother natural zeolites of the same type (10-20 m2/g)used to remove contaminants from effluents (Motsi etal., 2009; Camacho et al., 2011). Pore volume andpore diameter of the natural zeolite were larger thanRhB dimensions (see Table 1), suggesting that RhBmight access the pores of the adsorbent without spacerestrictions.

Table 2. Physical characteristics of the naturalzeolite

Properties Values

Surface area (m2/g) 14Average pore diameter (nm) 15

Pore volume (cc/g) 0.054

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180

150

120

90

60

30

0

Inte

nsity

[a.u

]

5045403530252015105

2 e [º]

MrMr

MrMr

MrMr

Cp

Cp Cp

Cp

Cp

Cp

Cp CpCpSiO2

SiO2

SiO2

Cp = ClinoptiloliteMr = MordeniteSiO2 = Quartz

1

Fig. 2. X-ray diffraction patterns of the natural zeolite. 2 3

Fig. 2. X-ray diffraction patterns of the natural zeolite.

70

60

50

40

30

20

10

0

Vol

ume

[cc/

g] S

TP

1.00.80.60.40.20.0

Relative pressure [P/P0]

Adsorption Desorption

1

Fig. 3. Nitrogen adsorption/desorption isotherm of the natural zeolite. 2 3

Fig. 3. Nitrogen adsorption/desorption isotherm of thenatural zeolite.

3.2 Adsorption isotherm of RhB

A comparison between the observed and fittedadsorption capacity of the natural zeolite (qne) as afunction of time at different temperatures is presentedin Fig 4. Adsorption equilibrium observations werefitted by means of Langmuir and Freundlich isothermmodels. A non-linear relationship between the amountof RhB adsorbed and RhB concentration in thesolution at equilibrium was observed. The adsorptioncapacity of the natural zeolite decreased as thetemperature increased, as a result of the exothermicityof the adsorption process. Vimonses et al. (2009)reported similar results for Congo Red adsorption onclays, concluding that the lower adsorption capacitiesof the adsorbent at higher temperatures was due to a

8

6

4

2

0

q ne [

mg/

g]

1751501251007550250

Cne [mg/L]

20 ºC Exp Freundlich Langmuir35 ºC Exp Freundlich Langmuir50 ºC Exp Freundlich Langmuir

1

Fig. 4. Adsorption isotherms of Rhodamine B onto natural zeolite at various temperatures. 2 3

Fig. 4. Adsorption isotherms of Rhodamine B ontonatural zeolite at various temperatures.

weaker bonding between the hydrogen from the dyeand adsorbent, and to a weaker Van der Waals typeinteraction between the dye and adsorbent caused byan apparent increment in the vibrational energy ofadsorbed dye leading to its desorption.

The estimated equilibrium parameters involvedin the Langmuir and Freundlich isotherm models arepresented in Table 3. The regression and parameterswere statistically significant. The parameters werenot statistically correlated since components inthe variance-covariance matrix were lower than(±) 0.95. Nevertheless, the R2 for the Freundlichisotherm model was greater than the R2 for theLangmuir isotherm model. The Freundlich modelled to better predictions than the Langmuir modelat initial RhB concentrations higher than 60 mg/L.Therefore, the Freundlich isotherm model waspreferred over the Langmuir model to account forkinetics in the LDF-M to predict breakthroughcurves from the adsorption fixed-bed column.Estimated thermodynamic parameters at differenttemperatures were calculated using Eqs. (4)-(6).The average estimated value of ∆Go 16.8 kJ/molat the studied temperatures indicated a spontaneousphysical adsorption of RhB onto the natural zeolite(Krishna and Bhattacharyya, 2002; Chu et al., 2004).This spontaneous process was consequence of theexothermicity of the adsorption process (∆Ho =-15.7kJ/mol) and to a favourable adsorption disorder ofRhB on the natural zeolite (∆S o = 3.7 J/mol K).

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Table 3. Langmuir and Freundlich parameters for Rhodamine B adsorption ontonatural zeolite.

Temperature (ºC) Langmuir Freundlich

qm KL R2 KF n R2

20 5.6818 0.2351 0.9203 1.5046 3.2254 0.989935 4.7594 0.2072 0.9594 1.0020 2.6544 0.965650 4.6981 0.1308 0.9564 0.7803 2.3889 0.9604

Table 4. Kinetic parameters calculated for adsorption of Rhodamine B onto Natural Zeolite.

Parameters Kinetic models

T Cno dp Stirring speed qne(exp) Pseudo first order model Pseudo second order model(ºC) (mg/L) (mm) (rpm) (mg/g) qne(cal) k1 R2 qne(cal) k2 R2

20 10 1.0 200 1.2148 0.9813 0.0341 0.8802 1.2253 0.1048 0.975220 20 1.0 200 2.3430 1.5026 0.0523 0.9705 2.4032 0.1146 0.997320 50 1.0 200 3.4515 1.8635 0.0462 0.9723 3.4990 0.1009 0.997820 100 1.0 200 4.8047 2.4188 0.0459 0.9612 4.8581 0.0823 0.998335 20 1.0 200 2.1025 1.1755 0.0455 0.9457 2.1437 0.1479 0.998450 20 1.0 200 1.9714 1.0916 0.0520 0.9044 2.0208 0.1613 0.998820 20 2.5 200 1.5042 1.2879 0.0522 0.9830 1.6005 0.0815 0.9955

3.0

2.5

2.0

1.5

1.0

0.5

0.0

q n [m

g/g]

120100806040200Time [h]

0 rpm 50 rpm 100 rpm 200 rpm

1

Fig. 5. Effect of the stirring speed for the adsorption of Rhodamine B on natural zeolite. 2 3

Fig. 5. Effect of the stirring speed for the adsorption ofRhodamine B on natural zeolite.

3.3 Kinetics of RhB adsorption

The influence of the stirring speed on the adsorptioncapacity of the natural zeolite as a function of time ispresented in Fig. 5. These observations suggested that200 rpm is a suitable stirring speed to carry out kineticexperiments in the absence of interparticle masstransport resistances, because there is no significantdifference in the adsorption capacity of the naturalzeolite at stirring speeds over 100 rpm. A comparison

between kinetic experiments and their fitting by thepseudo second order model is presented in Fig. 6.The effect of the initial RhB concentration on theadsorption capacity of the natural zeolite over time atan adsorption temperature of 20 ºC, with an adsorbentmass of 2.5 g and adsorbent particles of 1 mm,is displayed in Fig. 6a. The adsorption of RhB onthe natural zeolite took place during the first 50h, suggesting that the interaction between kineticsand intraparticle mass transport phenomena played animportant role on the RhB adsorption dynamics. Theadsorption capacity of the natural zeolite increasedas the initial concentration of RhB was increased,as is also observed in equilibrium experiments. Sofar at higher initial RhB concentrations an increasein the RhB concentration gradient (driving force)between the RhB in the solution and the RhB intothe adsorbent favoured the adsorption capacity of thenatural zeolite (Jain and Shrisvastava, 2008). Theeffect of temperature on the adsorption capacity ofthe natural zeolite as a function of time at an initialRhB concentration of 20 mg/L, with an adsorbentmass of 2.5 g and adsorbent particles of 1 mm, ispresented in Fig. 6b. Because of the exothermic natureof the adsorption process, a slight decrease in theadsorption capacity of the natural zeolite was observedwhen the adsorption temperature was increased.

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7.0

6.0

5.0

4.0

3.0

2.0

1.0

0.0

q n [m

g/g]

120100806040200

Time [h]

a) Cno= 10 mg/L Exp Pseudo-second-order modelCno= 20 mg/L Exp Pseudo-second-order modelCno= 50 mg/L Exp Pseudo-second-order modelCno= 100 mg/L Exp Pseudo-second-order model

3.5

3.0

2.5

2.0

1.5

1.0

0.5

0.0

q n [m

g/g]

120100806040200

Time [h]

b) T= 20 ºC Exp Pseudo-second-order modelT= 35 ºC Exp Pseudo-second-order modelT= 50 ºC Exp Pseudo-second-order model

3.5

3.0

2.5

2.0

1.5

1.0

0.5

0.0

q n [m

g/g]

120100806040200

Time [h]

c) dp= 1.0 mm Exp Pseudo-second-order modeldp= 2.5 mm Exp Pseudo-second-order model

1

Fig. 6. Kinetic adsorption of Rhodamine B onto natural zeolite for various: (a) initial dye 2 concentration (b) temperatures and (c) particles sizes. 3

4

Fig. 6. Kinetic adsorption of Rhodamine B ontonatural zeolite for various: (a) initial dye concentration(b) temperatures and (c) particles sizes.

Finally, the influence of the adsorbent particle sizeon the adsorption capacity as a function of timeat an initial RhB concentration of 20 mg/L, withand adsorbent mass of 2.5 g and an adsorptiontemperature of 20 ºC, is presented in Fig. 6c. Even

though diffusional mass transport resistances in thenatural zeolite were apparently significant for bothpellet sizes, a decrease in the pellet size led to anincrease in the adsorbent interfacial area, being themain aspect favouring the adsorption capacity of thenatural zeolite.

Apparent kinetic parameters estimated from thepseudo first order and pseudo second order modelsare presented in Table 4. Despite the fact thatthe kinetic parameters accounted for intraparticlediffusion mass transport resistances, these parametersand the regression were statistically significant.The parameters were not statistically correlated.Nevertheless, the R2 indicated that the pseudo secondorder kinetic model better fitted kinetic data than thepseudo first order kinetic model. Therefore the pseudosecond order kinetic model was used to account foradsorption kinetics and intraparticle mass transportdiffusion into the AkA-M to predict breakthroughcurves from the adsorption fixed-bed column.

3.4 Fixed-bed adsorber modelling

In this section LDF-M and AkA-M were evaluatedto predict breakthrough curves from an industrial-scale adsorption column packed with a natural zeoliteduring the removal of RhB under the conditionspresented in Table 5. In particular, breakthroughcurves were predicted at inlet RhB concentrationsvarying from 10 to 100 mg/L (see Fig. 7), at inletsuperficial velocities varying from 1.8 to 9.0 m/h (seeFig. 8), at column temperatures varying from 20 ºC to50 ºC (see Fig. 9), at column lengths varying from 1 to2.5 m (see Fig. 10), and at particle diameters varyingfrom 1.0 to 5.0 mm (see Fig. 11).

Predictions of breakthrough curves at differentinitial RhB concentrations were obtained consideringa 1.5 m column length packed with adsorbent particlesof 1 mm, operated at a superficial velocity of 3.6 m/hand a constant temperature of 20 ºC. Saturation timewas affected by inlet RhB concentration, as observedin Fig. 7. Even though both models predicted anearlier saturation time as the inlet RhB concentrationwas increased, LDF-M led to steeper slopes of thebreakthrough curves than AKA-M. The breakthroughslopes projected by the LDF-M indicated a negligibleeffect of dispersion, inter or intraparticle masstransport resistances on the adsorption process and,hence, saturation time was essentially a functionof the amount of available adsorption active sites.Since LDF-M simulations indicated that dispersion,and interparticle mass transport resistances were

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Table 5 Operational conditions used in bed column simulations

Simulation Cno (mg/L) dp (cm) vz (m/h) ε T (ºC) Lt (cm) dc (cm)

1 20 0.10 1.8 0.383 20 150 102 20 0.10 2.7 0.383 20 150 103 20 0.10 3.6 0.383 20 150 104 20 0.10 9.0 0.383 20 150 105 10 0.10 3.6 0.383 20 150 106 50 0.10 3.6 0.383 20 150 107 100 0.10 3.6 0.383 20 150 108 20 0.10 3.6 0.383 20 100 109 20 0.10 3.6 0.383 20 200 10

10 20 0.10 3.6 0.383 20 250 1011 20 0.10 3.6 0.383 35 150 1012 20 0.10 3.6 0.383 50 150 1013 20 0.25 3.6 0.383 20 150 1014 20 0.50 3.6 0.383 20 150 10

1.0

0.8

0.6

0.4

0.2

0.0

C n/C

no [D

imen

sionl

ess]

24020016012080400

Time [h]

Cno=10 mg/L Cno=20 mg/L Cno=50 mg/L Cno=100 mg/L

1

Fig. 7. Effect of the inlet concentration on the theoretical breakthrough curves. The model 2 using the LDF-M (—); and the model that uses the AkA-M model (- - -). (T=20 ºC, dp=1 3

mm, vz=3.6 m/h, Lt= 150 cm). 4 5

Fig. 7. Effect of the inlet concentration on thetheoretical breakthrough curves. The model using theLDF-M (—–); and the model that uses the AkA-Mmodel (- - -). (T=20 ºC, dp=1 mm, vz=3.6 m/h, Lt=

150 cm).

insignificant, AkA-M predicted breakthrough curveswhose slope essentially indicated the presenceof intraparticle mass transport resistances. Theseintraparticle mass transport resistances were moresignificant at a lower inlet RhB concentration becauseof the role of the concentration gradient (drivingforce) on the diffusion-adsorption process discussedin Section 3.3. These simulations suggested that theAkA-M was more suitable than LDF-M to predictbreakthrough curves, since intraparticle mass transportresistances were accounted for by the apparent kineticmodel rather than by the isotherm model used toaccount for adsorbate-adsorbent interactions.

Predictions for the breakthrough curves atdifferent initial superficial velocities were obtainedby considering a 1.5 m column length packed withadsorbent particles of 1 mm and operated at aninlet RhB concentration of 20 mg/L and a constanttemperature of 20 ºC. Breakthrough curves weresensitive to inlet superficial velocity, as shown inFig 8. Both LDF-M and AkA-M models predictedbreakthrough curves that were affected by theresidence time of RhB in the fixed-bed column, i.e.the saturation time was larger at lower inlet superficialvelocities since a higher residence time favoured RhBtransport from the bulk to the active sites on thenatural zeolite (Han et al., 2009). Nevertheless, LDF-M predicted steeper breakthrough slopes than AkA-M,corroborating that LDF-M was not able to account forintraparticle mass transport phenomena involved in anatural zeolite presenting diffusion limitations such asthe one studied in this work.

Predictions of the breakthrough curves varyingcolumn temperature from 20 to 50 ºC were obtainedat an inlet RhB concentration of 20 mg/L, aninlet superficial velocity of 3.6 m/h, and a columnof 1.5 m length packed with adsorbent particlesof 1 mm. The breakthrough curve was slightlyaffected by temperature, as shown in Fig. 9. Asin the previous results, both models, LDF-M andAkA-M, predicted different breakthrough curvesbut similar adsorption tendencies as reported byBhuvaneshwari and Sivasubramanian (2014), i.e. alower saturation time was obtained by decreasing thecolumn temperature as a result of the exothermicitycharacteristics of the adsorption process discussed inSection 3.2.

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1.0

0.8

0.6

0.4

0.2

0.0

C n/C

no [D

imen

sionl

ess]

24020016012080400

Time [h]

vz=1.8 m/h vz=2.7 m/h vz=3.6 m/h vz=9.0 m/h

1

Fig. 8. Effect of the inlet superficial velocity on the theoretical breakthrough curves. The 2 model using the LDF-M (—); and the model that uses the AkA-M model (- - -). (T=20 ºC, 3

dp=1 mm, Cno=20 mg/L, Lt= 150 cm). 4 5

Fig. 8. Effect of the inlet superficial velocity on thetheoretical breakthrough curves. The model using theLDF-M (—–); and the model that uses the AkA-Mmodel (- - -). (T=20 ºC, dp=1 mm, Cno=20 mg/L, Lt=

150 cm).

1.0

0.8

0.6

0.4

0.2

0.0

C n/C

no [D

imen

sionl

ess]

24020016012080400

Time [h]

T=20 ºC T=35 ºC T=50 ºC

1

Fig. 9. Effect of the temperature on theoretical breakthrough curves. The model using the 2 LDF-M (—); and the model that uses the AkA-M model (- - -). (Cno=20 mg/L, dp=1 mm, 3

vz=3.6 m/h, Lt= 150 cm). 4 5

Fig. 9. Effect of the temperature on theoreticalbreakthrough curves. The model using the LDF-M(−); and the model that uses the AkA-M model (- -).(Cno=20 mg/L, dp=1 mm, vz=3.6 m/h, Lt= 150 cm).

Predictions of the breakthrough curves whenvarying the column length from 1 to 2.5 m wereobtained by considering adsorbent particles of 1 mm,an inlet superficial velocity of 3.6 m/h, an inlet RhBconcentration of 20 mg/L and a constant temperatureof 20 ºC. Since the residence time of RhB and theamount of adsorbent was a function of the columnlength, LDF-M and AKA-M predictions indicated thatthe saturation capacity of the fixed-bed column wasfavoured at larger column lengths, as shown in Fig. 10

1.0

0.8

0.6

0.4

0.2

0.0

C n/C

no [D

imen

sionl

ess]

24020016012080400

Time [h]

Lt=1.0 m Lt=1.5 m Lt=2.0 m Lt=2.5 m

1

Fig. 10. Effect of the bed length on theoretical breakthrough curves. The model using the 2 LDF-M (—); and the model that uses the AkA-M model (- - -). (T=20 ºC, dp=1 mm, vz=3.6 3

m/h, Cno= 20 mg/L). 4 5

Fig. 10. Effect of the bed length on theoreticalbreakthrough curves. The model using the LDF-M(−); and the model that uses the AkA-M model (- -).(T=20 ºC, dp=1 mm, vz=3.6 m/h, Cno= 20 mg/L).

1.0

0.8

0.6

0.4

0.2

0.0

C n/C

no [D

imen

sionl

ess]

24020016012080400

Time [h]

dp=1.0 mm dp=2.5 mm dp=5.0 mm

1

Fig. 11. Effect of the particle size on theoretical breakthrough curves. The model using the 2 LDF-M (—); and the model that uses the AkA-M model (- - -). (T=20 ºC, Cno= 20 mg/L, 3

vz=3.6 m/h, Lt= 150 cm). 4

Fig. 11. Effect of the particle size on theoreticalbreakthrough curves. The model using the LDF-M(−); and the model that uses the AkA-M model (- - -).(T=20 ºC, Cno= 20 mg/L, vz=3.6 m/h, Lt= 150 cm).

and observed from other adsorption studies (Xu et al.,2013).

Predictions of breakthrough curves when varyingthe particle diameter of adsorbent packed in thecolumn from 1.0 to 5.0 mm were obtained atan inlet RhB concentration of 20 mg/L an inletsuperficial velocity of 3.6 m/h, a constant temperatureof 20 ºC and with a column length of 1.5 m.LDF-M accounted for the role of particle size oninterparticle mass transport phenomena, predicting anincrease in the saturation time and a slight change

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in the steepness of the breakthrough slope as theparticle size decreased (see Fig. 11). Smaller particlesizes favoured the interfacial mass transfer of RhBfrom the bulk to the adsorbent increasing columnsaturation capacity. Based on these simulations,AkA-M predicted breakthrough curves whose slopesindicated the presence of both inter and intraparticlemass transport phenomena, but mainly intraparticle asaforementioned and observed from other adsorptionstudies when adsorbents are evaluated at industrialscale (Marin et al., 2014).

ConclusionsCertain general points might be deduced from theexperimental and simulation analysis on the predictionof Rhodamine B adsorption on a Mexican naturalzeolite:

1. The zeolite used as adsorbent was adequatefor RhB separation from aqueous solution.Increasing contact time, zeolite amount and dyeconcentrations resulted in increased adsorption,while the reverse effect was observed byincreasing the temperature and zeolite particlesize.

2. Based on statistical analysis it was found thatthe best fit of the equilibrium adsorption datawas obtained with the Freundlich model, andthat the kinetic behaviour was described bya pseudo-second order model. Thermodynamicresults indicated that the adsorption of RhB isspontaneous and exothermic.

3. The two models, LDF-M and AkA-M,considered for describing fixed-bed adsorptionof RhB on the natural zeolite showedsimilar tendencies regarding the effect onthe breakthrough point of the differentparameters considered. However the shapesof the breakthrough curves predicted by bothmodels were significantly different. For all theconditions considered in the simulations, theslopes for LDF-M breakthrough curves weremuch steeper than those predicted by AkA-M.Furthermore, the breakthrough point times werealways found to be larger for the LDF-M undersimilar conditions, to the extent of being up tothree times larger than those predicted by AkA-M. Such differences between the breakthroughpoint times were reduced by modifying the

operating conditions that favoured particlesurface saturation, such as increasing the inletRhB concentration and the superficial liquidvelocity as well as by reducing the bed height.

From these results AkA-M is a simple but necessaryfirst approach to model the industrial behaviour ofporous adsorbents when the resistances to masstransport by diffusion of adsorbate are significant.Nevertheless, experimental and modelling studiesaccounting for explicitly the diffusion phenomena ofthe natural zeolite have to be carried out further.

AcknowledgmentsThe first author (G. Che-Galicia) is grateful forthe graduate scholarship provided by the ConsejoNacional de Ciencia y Tecnologıa (CONACyT). Theauthors also acknowledge to Dr. Miguel A. HernandezEspinosa for providing the natural zeolite.

NomenclatureRoman lettersav mass transfer area per unit volume of

the particle, m−1

Cn concentration of Rhodamine B in fluidphase, mg/L

Cne concentration of Rhodamine B atequilibrium in fluid phase, mg/L

Cno initial concentration of Rhodamine Bin fluid phase, mg/L

Cns concentration of Rhodamine B in theadsorbent surface, mg/L

Cnse concentration of Rhodamine B atequilibrium in the adsorbent, mg/L

dc column diameter, cmdp particle diameter, mDax axial dispersion coefficient, m2/hDRHB molecular diffusion coefficient of

Rhodamine B in water, m2/sk1 kinetic constant for the pseudo first

order reaction, h−1

k2 kinetic constant for the pseudo secondorder reaction, g/(mg h)

kL external mass transfer coefficient influid phase, m/h

Kc adsorption equilibrium constantKF Freundlich isotherm constant,

(mg1−1/n L1/n)/gKL Langmuir isotherm constant, L/mgLt length of the column, cmm mass of natural zeolite, g

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n Freundlich isotherm constantqm Langmuir isotherm constant, mg/gqn mass of Rhodamine B adsorbed per

unit mass of natural zeolite, mg/gqne mass of Rhodamine B adsorbed at

equilibrium, mg/gR ideal gas constant, 8.314 J/(mol K)t time, hT temperature, Kvz interstitial fluid velocity in the z

direction, m/hV volume of the Rhodamine B solution,

Lz distance in the axial direction of the

column, mGreek lettersε void fraction of the bedρB bed density, kg/m3

ν kinematic viscosity, m2/h∆Go Gibbs free energy, kJ/mol∆Ho enthalpy, kJ/mol∆S o entropy, J/(mol K)

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