Modeling of the adsorption breakthrough behaviors of Pb2+ in a fixed bed of ETS-10 adsorbent

doi:10.1016/j.jcis.2008.04.067

Journal of Colloid and Interface Science

Volume 325, Issue 1, 1 September 2008, Pages 57-63

https://doi.org/10.1016/j.jcis.2008.04.067 Get rights and content

Abstract

On the basis of experimental breakthrough curves of lead ion adsorption on ETS-10 particles in a fixed-bed column, we simulated the breakthrough curves using the two-phase homogeneous diffusion model (TPHDM). Three important model parameters, namely the external mass-transfer coefficient ( $k_{f}$ ), effective intercrystal diffusivity ( $D_{e}$ ), and axial dispersion coefficient ( $D_{L}$ ), were optimally found to be $8.33 \times 10^{−5} m / s$ , $2.57 \times 10^{−10} m^{2} / s$ , and $1.93 \times 10^{−10} m^{2} / s$ , respectively. A good agreement was observed between the numerical simulation and the experimental results. Sensitivity analysis revealed that the value of $D_{e}$ dictates the model performance while the magnitude of $k_{f}$ primarily affects the initial breakthrough point of the breakthrough curves.

Graphical abstract

A two-phase homogeneous diffusion model (TPHDM) has been successfully used to describe and predict breakthrough curves for the fixed-bed sorption of lead ions onto microporous titanosilicate ETS-10 particles. Comparison of model simulation based on the optimized and estimated parameters $D_{L}$ , $k_{f}$ , and $D_{e}$ ( $C_{0} = 5.0 mM$ , $u_{s} = 2.33 \times 10^{−4} m / s$ , $d_{p} = 3.5 \times 10^{−4} m$ ).

Introduction

Adsorption or ion exchange is an effective technology for heavy metal removal from aqueous systems. In general, a fixed-bed column is preferable over a batch adsorber because of its ability to process large quantities of feed under continuous operation of the former. The design of an industrial fixed-bed column requires many parameters, which can be obtained by doing a series of laboratory experiments. However, such practices are time consuming and costly so that accurate modeling and simulation are frequently used as an alternative for predicting the dynamic behavior of fixed-bed systems to optimize column design and operation parameters [1], [2], [3].

Generally, the uptake of heavy metals on an adsorbent or ion exchanger is governed by the following distinct diffusional resistances [4]: (i) diffusion across the liquid film around the particle, and (ii) diffusion through the pores or surfaces of the particle to reach active sites. For fixed-bed columns, sometimes other hydrodynamic effects, i.e., axial dispersion, should be taken into consideration as well. Each of such factors must be appropriately accounted for to accurately simulate the overall column performance. Compared with the various mass-transfer rates, the adsorption rate is often observed to be faster [5]. Therefore, the overall uptake kinetics may be eventually determined by such steps as the mass transfer across the liquid film, diffusion across the macropores among crystals, and surface diffusion. To date, numerous mathematical models [6], [7], [8], [9], [10] based on one or two rate-limiting steps have been developed to predict the breakthrough curves of heavy metal adsorption in a fixed-bed column. Ko, McKay, and co-workers [9], [10] proposed the film-pore and the film-surface diffusion model to successfully simulate the sorption of metal ions on bone chars in a fixed-bed column. Ravindran et al. [11] also simulated the sorption of metal ions on chelant-impregnated activated carbons based on three modeling scenarios, namely (i) pore and surface diffusion in parallel, (ii) pore diffusion alone, and (iii) surface diffusion alone, and found that surface diffusion alone provided reasonably good predictions of the column dynamics.

However, the ion-exchange/adsorption processes over zeolites can be complicated because two distinct types of pore structures exist in most of the zeolite adsorbents, i.e., micropores within the crystals and macropores among the crystals. For adsorption on solids with a bimodal pore system like zeolite pellets, a heterogeneous model (also known as a macro–micro model) [5], [12], which considers both macropore and micropore diffusion resistances, should be used. However, because of the complexity of the model, only one diffusion resistance (either the micropore or macropore resistance) is considered, thus simplifying the modeling [5]. For example, it has been demonstrated that a two-phase homogeneous model (TPHDM) is sufficient for predicting the adsorption behaviors of zeolites toward various metal ions [5], [12], [13], assuming that (i) the metal ion concentration in the pore liquid is in instantaneous equilibrium with that on the solid surface, and (ii) the diffusion resistance in the micropores is negligible.

ETS-10, a zeolitic material [14] constituted from SiO₄ tetrahedra and TiO₆ octahedra, possesses a high cation-exchange capacity [15], [16] because of the presence of tetravalent Ti in an octa-coordinated state, which generates two negative charges balanced by alkali cations [17], namely Na⁺ and K⁺. In this work, the breakthrough behaviors of Pb²⁺ ions on ETS-10 pellets in a fix-bed column were experimentally measured and theoretically simulated. Since the ETS-10 particles used for the fixed-bed adsorption possess a bimodal pore system with both intracrystal micropores and intercrystal macropores, the TPHDM [5] was employed to predict and optimize the breakthrough curves. The values of the model parameters, including liquid film mass-transfer coefficient ( $k_{f}$ ), axial dispersion coefficient ( $D_{L}$ ), and effective macropore diffusivity ( $D_{e}$ ), were optimized and validated by comparing the model predictions with the experimental data.

Section snippets

Materials and methods

The ETS-10 nanocrystals, whose synthesis procedures were described in a previous study [18], were used without any chemical pretreatment in this study. The as-synthesized powdery solid was grounded and sieved using U.S. standard screens to obtain pellet particles of 40–60 meshes. By assuming that the particles are spherical in shape, the average diameter of the particles was estimated to be around $3.5 \times 10^{−4} m$ . The physical properties of the adsorbent are reported in Table 1.

The adsorption

Adsorption isotherm

Although the assumptions of the Langmuir isotherm cannot be applicable to the process of ion exchange, the sorption of heavy metal ions on ETS-10 has been previously observed to follow the Langmuir isotherm [16], [19], $q = \frac{q_{m} b C_{e}}{1 + b C_{e}},$ where b (1/mM) is the adsorption affinity, q (mmol/g) is the amount adsorbed, $C_{e}$ (mM) is the bulk concentration, and $q_{m}$ (mmol/g) is the maximum adsorption capacity. Therefore, the use of the Langmuir model to present the adsorption isotherm of Pb²⁺ ions onto ETS-10

Equilibrium isotherms

Fig. 2 presents the isotherm data (dots) of Pb²⁺ adsorption on ETS-10 particles at 298 K and the optimal fitting (solid line) from the Langmuir isotherm. The isotherm parameters are also listed in the figure. The fitting is seen to be reasonably good, which is in agreement with the experimental data [16], [19]. However, the maximum adsorption capacity ( $q_{m}$ ) was found to be 1.71 mmol/g, which is close to the value obtained by Choi et al. [22], but slightly higher than that determined

Summary

A two-phase homogeneous diffusion model (TPHDM) has been successfully used to describe and predict breakthrough curves for the fixed-bed sorption of lead ions onto microporous titanosilicate ETS-10 particles. Three important model parameters, namely the external mass-transfer coefficient ( $k_{f}$ ), effective macropore diffusivity ( $D_{e}$ ), and axial dispersion coefficient ( $D_{L}$ ) have been optimally extracted by using Genetic Algorithm. Compared to the empirical correlations of the three parameters, the

Acknowledgments

The authors thank NUS for financial support. L.L. thanks Singapore Millennium Foundation (SMF) for offering a SMF Postdoctoral Fellowship.

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Citation Excerpt :
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Modeling of the adsorption breakthrough behaviors of Pb2+ in a fixed bed of ETS-10 adsorbent

Abstract

Graphical abstract

Introduction

Section snippets

Materials and methods

Adsorption isotherm

Equilibrium isotherms

Summary

Acknowledgments

J. Hazard. Mater.

J. Hazard. Mater.

Water Res.

Micropor. Mesopor. Mater.

Electrochim. Acta

Ind. Eng. Chem. Res.

Ion Exchanger

Ind. Eng. Chem. Res.

AIChE J.

AIChE J.

Ind. Eng. Chem. Res.

Ind. Eng. Chem. Res.

AIChE J.

AIChE J.

Ind. Eng. Chem. Res.

Modeling of the adsorption breakthrough behaviors of Pb²⁺ in a fixed bed of ETS-10 adsorbent