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J. Serb. Chem. Soc. 71 (8–9) 957–967 (2006) JSCS-3489

UDC 546.47+541.183+661.183.48:541.121+66.011 Original scientific paper

Modeling of the adsorption kinetics of zinc onto granular activated carbon and natural zeolite LJILJANA T. MARKOVSKA, VERA D. MESHKO* and MIRKO S. MARINKOVSKI Faculty of Technology and Metallurgy, University "Sts Cyril & Methodius" Ruger Boskovic 16, 1000 Skopje, Republic of Macedonia (e-mail: [email protected]) (Received 15 August, revised 30 November 2005) Abstract: The isotherms and kinetics of zinc adsorption from aqueous solution onto granular activated carbon (GAC) and natural zeolite were studied using an agitated batch adsorber. The maximum adsorption capacities of GAC and natural zeolite towards zinc(II) from Langmuir adsorption isotherms were determined using experimental adsorption equilibrium data. The homogeneous solid diffusion model (HSD-model) combined with external mass transfer resistance was applied to fit the experimental kinetic data. The kinetics simulation study was performed using a computer program based on the proposed mathematical model and developed using gPROMS. As the two-mass transfer resistance approach was applied, two model parameters were fitted during the simulation study. External mass transfer and solid phase diffusion coefficients were obtained to predict the kinetic curves for varying initial Zn(II) concentration at constant agitation speed and constant adsorbent mass. For any particular Zn(II) – adsorbent system, kf was constant, except for the lowest initial concentration, while Ds was found to increase with increasing initial Zn(II) concentration. Keywords: zinc, adsorption, granular activated carbon, natural zeolite, equilibrium, kinetic modeling, homogeneous solid diffusion model. INTRODUCTION

Removal of heavy metals from aqueous solutions is necessary because of the frequent appearance of heavy metals in wastewaters from many industries, including electroplating, metallurgical, chemical manufacturing, mining and battery manufacturing industries. This problem has received a considerable amount of attention in recent years due primarly to concern that heavy metals in wastewater can directly enter the human food chains, thus presenting a high health risk to consumers.1 Many physicochemical methods have been developed for heavy metal removal from aqueous solution, including, chemical coagulation, adsorption, extraction, ion exchange and membrane separation process.2,3 Among these methods, adsorption is a highly popular one and has been widely practiced in industrial wastewater treatment processes. *

Corresponding author.

doi: 10.2298/JSC0609957M

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The major advantages of an adsorption system for water pollution control are less investment in terms of both initial cost and land, simple design and easy operation, and no effect of toxic substances compared to conventional biological treatment processes.4–8 Recent research of low-cost alternatives to activated carbon for waste and wastewater treatment is of interest. The main reason of the interest in natural zeolite is the increasing demand for low-cost adsorbent materials in fields such as pollution control and metal recovery, as well as their wide availability on the Earth. Some of the attractive applications of natural zeolites are given by Cincotti et al.9 where it may be seen that pollution prevention and control represents one of the most important areas of exploitation. Most of the studies on heavy metals adsorption with different adsorbents did not address the fundamental questions needed to implement this technology on a practical basis. However, for an optimal design of an industrial adsorption process, it is important to have accurate modeling and simulation of equlibrium, kinetic and dynamic behavior. A general solution for adsorption kinetics which includes mass transfer effects, interference effects and non-linear complex isotherms is still not available.10 The hitherto developed mathematical models have used different degrees of complexity to describe adsorption processes.11–13 Due to the complexity and non-linearity of the models, it is very difficult to get analytical solutions. Numerical solutions of rigid ordinary and partial differential equations are usually required. The most realistic models are the rate equation models and they generally consider external mass transfer, intraparticle diffusion and equilibrium equations. The relative importance of resistances depends on the materials involved and on the specific operaton conditions.14,15 Several versions of the rate equation model have been used to evalutate the available data to obtain values for diffusion coefficients. Carta and Cincotti16 developed a new approximate rate law for non-linear adsorption and diffusion in a spherical adsorbent particle based on an equivalent film resistance model. The approximation provides descriptions of the effect of the adsorption isotherm for parallel pore and solid diffusion, as well as of the effect of a variable adsorbed-phase diffusivity. All the developed models are not universal and can be used only for particular systems. The objective of this work was to develop a homogeneous diffusion model combined with external mass transfer resistance, which could be used for the evaluation the kinetics of adsorption of zinc onto granular activated carbon and natural zeolites. MATHEMATICAL MODEL

The homogeneous solid diffusion model (HSD-model) basically assumes that the adsorbent particles are homogeneous. The adsorbate molecule is transferred

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MODELING OF THE ADSORPTION KINETICS OF ZINC

through the adsorbent particles by "creeping" from one adsorption site to another on the solid surface. This is mathematically described by Fick's second law of diffusion.17,18 Equilibrium is set between the solid phase and the liquid phase concentrations at the surface of the adsorbent particle. The mass balance equation in spherical coordinates is given by: ¶q 1 ¶ é ¶q Dsr 2 ù = 2 ê ¶t r ¶r ë ¶r úû

0£r£R

t³0

(1)

In general, the diffusivity Ds of adsorbed molecules is concentration dependent.18 To simplify matters, this coefficient is averaged over the concentration range of the experiment and thereby assumed to be constant. Eq. (1) can be solved with appropriate initial and boundary conditions: 0£r£R

q = 0,

¶q =0 ¶r

t³0

(2)

r=0

qe K L ce = qm 1 + K L ce

(3) (4)

r=R

The average concentration throughout the adsorbent particle is defined as: qav =

3 3

R

ò qr

2

(5)

dr

R 0

Introducint external mass transfer resistance into this model, the second boundary condition (Eq. (4)) becomes: Rrp ¶q av ¶q (6) r=R = D s rp = k f (c l - c s ) 3 ¶t ¶r and q = q s,

c = c s,

qs K L cs = qm 1 + K L cs

r=R

(7)

The initial condition (Eq. (2)) and the first boundary condition (Eq. (3)) in the homogeneous diffusion model combined with external mass transfer resistance are the same as in the solid diffusion model. For batch adsorption in general, the adsorbed phase concentration at the solution–pellet interface is a function of time. Equilibrium is set between solid-phase and liquid-phase concentrations at the surface of the adsorbent particle. In this investigation the adsorption equilibrium is described by the Langmuir isotherm. The average adsorbed-phase concentration is defined by Eq. (5). The overall mass balance for a closed batch experiment is given by:

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MARKOVSKA, MESHKO and MARINKOVSKI

V(c2 – c0) = Mqav

(8)

The mathematical model cannot be solved analytically because of its nonlinearity and the complicated boundary condition at the surface of the adsorbent particle. In this investigation, a computer program based on the mathematical model was developed using gPROMS Simulation Language,19 which provides an environment for modeling the behavior of extremely complex systems usually represented by a set of integral, partial differential, ordinary differential and algebraic equations (IPDAEs). The set of IPDAEs defined within gPROMS MODELs are normaly solved using the method-of-lines family of numerical methods. This involves discretisation of the distributed equations with respect to all spatial domains, which reduces the problem to the solution of a set of DAEs. A Third order Orthogonal Collocation on Finite Elements Method (OCFEM) over 30 finite elements was used in the simulation studies. DASOLV mathematical solver for the solution of mixed sets of differential and algebraic equations was used as well. This solver is based on variable time step/variable order Backward Differentiation Formulae (BDF). EXPERIMENTAL Materials and methods Granular activated carbon (GAC) and natural zeolite were used as adsorbents in the investigated systems. The granulated activated carbon (GAC) was supplied by "Miloje Zaki}" – Kru{evac, Serbia. The GAC was repeatedly washed with dionized water to remove any leachable impurities and adherent powder and then dried to constant mass at 110 oC for 24 h. The natural zeolite was supplied by "Nemetali"–Vranjska Banja, Serbia. The mineralogical composition of the natural zeolite was 90 % clinoptiolite and the rest was mordenite and haylandrite. Chemical analysis of the zeolite showed that oxides of silicon, aluminium, calcium and iron were the main constituents while other oxides were present in trace amounts (Table I). Prior to an experiment, the natural zeolite was dried at 300 oC for 48 h in order to remove any traces of moisture or other contaminants. TABLE I. Chemical analysis of natural zeolite SiO2 Al2O3 Fe2O3 TiO2 CaO MgO Na2O K2O Ignition loss

Constitutents

Natural zeolite/% by mass 64.88 12.99 2.00

0.37

3.26

1.07

0.95

0.89

13.59

The properties of the employed adsorbents are listed in Table II. TABLE II. Properties of the adsorbents Property

GAC

Natural zeolite

Particle diameter/mm

1.15–1.35

1–3

Particle density/g

cm-3

Bulk density/g cm-3 Surface

area/cm2 g-1

1.87

2.12

1.0–1.2

1.43

900–1200

20–40

Stock solutions with seven different initial Zn(II) concentration (maximum 250 mg dm-3) were prepared using reagent grade ZnSO4 · 7H2O.

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For the determination of the adsorption isotherms, 0.2 dm3 of a Zn(II) solution were transfered to a flask containing 3 g of pretreated adsorbents. The mixture in the flask was agitated at 500 rpm and maintained at a constant temperature (25 oC) for a maximum of 12 days to ensure adsorption equilibrium. Aqueous samples were taken for Zn(II) concentration measurements using an AERL 3520 atomic absorption spectrophotometer. Kinetic investigations were carried out by contact time experiments using a batch agiated reactor. The uptake experiments were conducted under constant pH values with varying initial metal concentration in the range 50–250 mg dm-3 for the systems Zn(II)–GAC and Zn(II)–natural zeolite. RESULTS AND DISCUSSION

Adsorption isotherms One of the parameters which determines the possibility of using a particular material as an adsorbent for metal ion removal is its adsorption capacity. For this purpose, the adsorption isotherms for the systems Zn(II) – GAC and Zn(II) – natural zeolite at 25 oC were experimentally determined (Figs. 1 and 2). The experimental equilibrium data can be correlated with different models, such as the Langmuir, Freundlich, Redlich–Peterson, and Langmuir–Freundlich equations.17,18

Fig. 1. Comparison of the experimental and estimated data by the Langmuir equilibrium isotherm for the system Zn(II) – GAC. l experimental data; – fitted with the Langmuir equation.

Fig. 2. Comparison of experimental and estimated data by the Langmuir equilibrium isotherm for the system Zn(II) – natural zeolite; l experimental data; – fitted with the Langmuir equation.

As the Langmuir model (Eq. (9)) is the most convenient for the determination of the equilibrium capacity of the employed adsorbent, this equation was intro-

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duced into the kinetic model in this study: qe K L ce = qm 1 + K L ce

(9)

The parameters in the Langmuir adsorption isotherm for both adsorbents were estimated from the experimental equilibrium data using the MATLAB Curve Fitting Tooblox20 and are presented in Table III. Taking into consideration the values of the correlation coefficient as a criteria for the goodness of fit for both systems, the Langmuir model shows satisfactory agreement between the theoretical and experimental data over the whole concentration range. TABLE III. Parameters in the Langmuir equation for the investigated systems Zn(II) – GAC qm KL mg g-1 dm3 mg-1 8.325 0.689

Rc2

0.975

Zn(II) – Natural zeolite qm KL mg g-1 dm3 mg-1 3.644 0.117

Rc2

0.997

Comparing the values of qm for the adsorption of Zn(II) onto GAC and natural zeolite, it can be concluded that Zn(II) showed a 2.3 times greater afinity for GAC than for natural zeolite. The initial part of the isotherm curve for the adsorption of Zn(II) onto GAC practically coincides with the ordinate axis. This indicates that, for low concentrations, Zn(II) was almost completely removed from the solution using GAC. Adsorption kinetics The rate at which adsorption takes phace is an important factor when designing adsorption systems, consequently, it is important to establish the time dependence of contaminant capture under various process conditions. Zinc uptake profiles using GAC and natural zeolite as adsorbents were experimentally determined. 'Uptake' refers to increasing metal concentration in the solid phase with respect to time. A series of experiments were undertaken to study the influence of the initial Zn(II) concentration for both investigated systems i.e., Zn(II)–GAC and Zn(II)–natural zeolite. The results of the contact–time studies are average solid phase concentration (qav) versus time plots. The experimental uptake curves for the systems Zn(II)–GAC and Zn(II)–natural zeolite with varying initial Zn(II) concentration in the range 50–250 mg dm–3 are presented in Figs. 3 and 4, respectively. For favorable isotherms, such as exhibited by the solutes investigated, the slope of the isotherm decreases with increasing equilibrium concentration. In a series of experiments conducted with variable initial concentration, higher initial concentrations will correspond to higher equilibrium concentration being attained. The shapes of the kinetic curves for both systems suggested that a two-step mechanism had occurred. For the system Zn(II)–GAC (Fig. 3), the first portion indicates that a rapid adsorption occurred during the first 400 min, after which equilibrium was showly achieved.

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Fig. 3. Zn(II) adsorption kinetics onto GAC. o c0 = 50 mg dm-3;) c0 = 100 mg dm-3; ' c0 = 120 mg dm-3; ^ c0 = 150 mg dm-3; ; c0 = 180 mg dm-3; \ c0 = 200 mg dm-3; — Fitted curves; O c0 = 250 mg dm-3; Fitted curves.

Fig. 4. Zn(II) adsorption kinetics onto natural zeolite; o c0 = 50 mg dm-3; ) c0 = 100 mg dm-3; ' c0 = 120 mg dm-3; ^ c0 = 150 mg dm-3; ; c0 = 180 mg dm-3; \ c0 = 200 mg dm-3 — Fitted curves; O c0 = 250 mg dm-3;

The kinetic curves for the system Zn(II)–natural zeolite (Fig. 4) suggest a different mechanism of adsorption. Probably, the adsorption of Zn(II) onto the natural zeolite occurred mainly by an ion-exchange mechanism. The natural zeolite contained 90 % clinoptiolite and hence belongs to the seventh group of zeolites.21 Clinoptiolite is considered to be a SiO2–rich structure which is analogous to haylandrite. The three-dimensional crystal structure of zeolite contains two dimensional channels which embody some ion exchangeable cations, such as Na, K, Ca and Mg.22 These cations can be exchanged with organic and inorganic cations. This means that metal cations are placed not only on the extended surface of the adsorbent, but are also exchanged with its cations. In the investigated concentration range, the adsorption rate for the system Zn(II)–natural zeolite was much lower than for the system Zn(II)–GAC. The kinetic curves show that for higher initial concentrations a langer time is needed for equilibrium to be reached, which led to a different form of the equilibrium isotherm. For performing the kinetics simulation study, a computer program based on the proposed mathematical model and developed using gPROMS was used. This program gives theoretical kinetic curves with the corresponding surface equilibrium conditions. As a two-mass transfer resistance approach was used, two model parameters have to be fitted during the simulation study. The range of varying the first parameter i.e., the external mass transfer coefficient, kf, was estimated using a

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Fig. 5. Concentration dependence of the solid diffusivity, Ds, ' Zn(II) – natural zeolite; ; Zn(II) – GAC.

single-resistance model, assuming the initial part of the concentration ns. time plot is decribed by a linear isotherm with negligible intraparticle diffusion. The range of varying the second parameter, i.e., the solid phase diffusivity. Ds was defined by a single-resistance model, assuming Langmuir isotherm and negligible external mass transfer resistance. By changing the values of kf and Ds, it is possible to obtain the best fit to the experimental kinetic curves. Using these values together with the volume of the solution, the mass of adsorbent, particle density, particle size of the adsorbent, initial solute concentration, equilibrium constants, and data relating to the step length for integration, the simulation program gives the theoretical curves qav(t). This program can be used to describe experimental data with a high degree of accuracy. Simultaneously, the graphical output enables an easy comparison of the theoretical and experimentally determined data. The experimental uptake profiles for the systems under study are compared to the solution of the proposed mathematical model (Figs. 3 and 4). The estimated model parameters kf and Ds for Zn(II)–GAC and Zn(II)–natural zeolite in the investigated initial Zn(II) concentration range are listed in Table IV. TABLE IV. Estimated model parameters kf and Ds c0 mg dm-3

Zn(II)–GAC

Zn(II) –natural zeolite

kf · 106 m s-1

Ds · 1011 m2 s-1

kf · 106 m s-1

Ds · 1011 m2 s-1

50

10.0

0.80

1.20

0.06

100

2

1.00

0.95

0.075

120

2

1.30

0.95

0.08

150

2

1.50

0.95

0.11

180

2

2.00

0.95

0.26

200

2

2.02

0.95

0.28

250

2

4.00

0.95

0.39

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The external mass transfer coefficient, kf, was used to describe the boundary layer effects. As kf decrease, the boundary layer resistance increases, causing a slower mass transfer rate to the surface of the particle. At constant agitation rates, for both systems, kf has a bigger value at 50 mg dm–3 initial concentration than when the initial concentration was above 50 mg dm–3 (Table IV). The experimental kinetic curves were fitted with these values of kf and some remarks can be presented. For the system Zn(II)–GAC, good fits between the experimental data and the theoretical curves exist for all the investigated range of initial concentration, except for the higher concentrations (200 and 250 mg dm–3). For these two initial concentrations, the model does not follow the experimental data. For the system Zn(II)–natural zeolite, a discrepancy between the experimental and theoretical curves exist for the lowest initial concentration. The obtained values for Ds increase with initial Zn(II) concentration at constant adsorbent mass. An exponential correlation between Ds and the initial Zn(II) concentration for the investigated systems was found (Fig. 5). With increasing initial Zn(II) concentration at constant adsorbent mass, the slope of the adsorption isotherm at the final equilibrium concentration decreases and the surface coverage increases. An attempt was made to correlate the solid diffusivity with the initial Zn(II) concentration and satisfactorily agreement between the experimental and theoretical data was achieved by using the following correlation: Ds = D0 exp (kc0)

(10)

The constants of Eq (10) for the different investigated systems are given in Table V. The value of the correlation coefficient was used to show the goodness of the fit between the experimental and predicted data of Ds. This analysis leads to conclusion that, in further investigations, the concentration dependence of Ds has to be included in the mathematical model. This means that if the diffusion model with a concentration dependent diffusion coefficient would be used, the model wll be able to predict the adsorption data regardles of variations of the concentration during the adsorption processes. TABLE V. Empirical constants in Equation (10) Parameters

Zn(II)–GAC

Zn(II)–Natural zeolite

D0 · 1011/m2 s-1

0.4922

0,0281

k

0.0078

0.0108

R2

0.9636

0.9151

CONCLUSION

Certain general points may be deduced from the experimental and theoretical analysis of the prediction of the kinetics for adsorption of Zn(II) onto granular activated carbon and natural zeolite:

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1. The equilibrium studies showed that the adsorption capacity of the granular activated carbon for Zn(II) was higher than that of the natural zeolite; 2. In the homogeneous solid diffusion model, the range of varying the external mass transfer coefficient kf was estimated assuming a linear isotherm and negligible interpartical diffusion. The range of varying the solid phase diffusion coefficient Ds was defined by the single resistance model, assuming a non-linear isotherm and negligible external mass transfer resistance; 3. External mass transfer and solid phase diffusion coefficients were obtained to predict the kinetic curves for variying initial Zn(II) concentrations at constant agitation speed and constant adsorbent mass. For any particular system Zn(II) – adsorbent, kf was constant, except for the lowest initial concentration, while Ds was found to increase with unceasing initial Zn(II) concentration; 4. This means that if the diffusion model with a concentration dependent diffusion coefficient would be used, the model will be able to predict the adsorption data regardless of variations of the concentration during the adsorption processes. NOMENCLATURE c0 cl ca cs D0 Ds k kf KL q qav qe qm qs M r R Rc t V rp

Equilibrium liquid phase concentration, mg dm-3 Liquid phase concentration, mg dm-3 Initial liquid phase concentration, mg dm-3 Liquid phase concentration at the liquid pellet interface, mg dm-3 Constant in equation (10) Solid phase diffusivity, m2 s-1 Constant in Equation (10) External mass transfer coefficient, m s-1 Parameter in the Langumir equation, dm3 mg-1 Solid phase concentration, mg g-1 Average solid phase concentration, mg g-1 Equilibrium solid phase concentration, mg g-1 Parameter in the Langmuir equation, mg g-1 Solid phase concentration at the liquid pellet interface, mg g-1 Mass of adsorbent, g Radial distance measured from the center of a pellet, m Pellet radius, m Correlation coefficient Time, s Volume of solution, m3 Particle density, kg m-3

MODELING OF THE ADSORPTION KINETICS OF ZINC

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IZVOD

MODELOVAWE KINETIKE ADSORPCIJE CINKA NA GRANULIRANOM AKTIVNOM UGQU I PRIRODNOM ZEOLITU QIQANA T. MARKOVSKA, VERA D. MESHKO i MIRKO S. MARINKOVSKI Faculty of Technology and Metallurgy, University "Sts Cyril&Methodius" Ruger Boskovic 16, 1000-Skopje, Republic of Macedonia

Ispitivane su izoterme i kinetika adsorpcije cinka iz vodenog rastvora na granuliranom aktivnom ugqu (GAC) i prirodnom zeolitu u {ar`nom adsorberu sa me{awem. Odre|en je maksimalni adsorpcioni kapacitet GAC i prirodnog zeolita za Zn(II) kori{}ewem Langmirove adsorpcione izoterme. Za fitovawe eksperimentalnih kineti~kih podataka primewen je HSD (homogeneous solid diffusion) model u kombinaciji sa otporom na prenos mase na povr{inu ~estice. Kineti~ka simulacija izvedena je kori{}ewem ra~unarskog programa zasnovanog na predlo`enom matemati~kom modelu i razvijenog primenom gPROMS. Po{to je primewen pristup dvostrukog otpora prenosu mase, tokom simulacije fitovana su dva parametra modela. Dobijeni su koeficijent prenosa mase na povr{inu ~estice i koeficijent difuzije u ~vrstoj fazi, pomo}u kojih su predvi|ene kineti~ke krive za varirawe po~etne koncentracije Zn(II) pri konstantnoj brzini me{awa i konstantnoj masi adsorbenta. Za svaki pojedina~ni sistem Zn(II)–adsorbens kf je bio konstantan, osim za najni`u po~etnu koncentraciju, dok se Ds pove}avao sa pove}avawem po~etne koncentracije. (Primqeno 15. avgusta, revidirano 30. novembra 2005)

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