Removal of nickel(II) ions from aqueous solution by biosorption in a fixed bed column: Experimental and theoretical breakthrough curves

Biochemical Engineering Journal 30 (2006) 184–191

Removal of nickel(II) ions from aqueous solution by biosorption in a fixed bed column: Experimental and theoretical breakthrough curves C.E. Borba a,∗ , R. Guirardello a , E.A. Silva b , M.T. Veit c , C.R.G. Tavares c a

School of Chemical Engineering, State University of Campinas, UNICAMP, University City Zeferino Vaz, P.O. Box 6066, CEP 13081-970 Campinas, SP, Brazil b Department of Chemical Engineering, West Parana State University, UNIOESTE, Faculty Street n. 2550, Garden La Salle, CEP 85903-000 Toledo, PR, Brazil c Department of Chemical Engineering, State University of Maringa, UEM, Av. Colombo 5790, CEP 87020-900 Maringa, PR, Brazil Received 8 November 2005; received in revised form 4 April 2006; accepted 5 April 2006

Abstract The nickel(II) ions biosorption process by marine algae Sargassum filipendula in a fixed bed column was investigated for the following experimental conditions: temperature = 30 ◦ C and pH 3.0. The experimental breakthrough curves were obtained for the following chosen flow rates 0.002, 0.004, 0.006, and 0.008 L/min. A mathematical model was developed to describe the nickel ion sorption in a fixed bed column. The model of three partial differential equations (PDE) has considered the hydrodynamics throughout the fixed bed column as well as the sorption process in the liquid and solid phases. The internal and external mass transfer limitations were considered, as well. The nickel ion sorption kinetics has been studied utilizing the Langmuir isotherm. The PDE of the system were discretized in the form of ordinary differential equations (ODE) and were solved for the given initial and boundary conditions using the finite volume method. A new correlation for external mass transfer coefficient was developed. Some of the model parameters were experimentally determined (ε, dp ) where the others such as (KF , KS ) were evaluated on the base of experimental data parameters. The identification procedure was based on the least square statistical method. The robustness and flexibility of the developed model was checked out using four sets of experimental data and the predictive power of the model was evaluated to be good enough for the all studied cases. The developed model can be useful tool for nickel ion removal process optimization and design of fixed bed columns using biomass of S. filipendula as a sorbent. © 2006 Elsevier B.V. All rights reserved. Keywords: Adsorption; Fixed bed; Nickel; Marine algae; Mass transfer; Modeling

1. Introduction Wastewater discharge from electroplating, electronics, and metal cleaning industries often contains high concentrations of nickel(II) ions and causes serious water pollution. The presence of nickel(II) ions above critical levels may cause various types of acute and chronic disorder in human health, such as severe damage of lungs and kidney, gastrointestinal distress (e.g. nausea, vomiting, and diarrhea), pulmonary fibrosis and renal edema, and skin dermatitis [1]. The conventional technologies of high concentration heavy metal ions removal from wastewater are the precipitation processes, membrane filtration, ion exchange, evaporation, electro-

∗

Corresponding author. Tel.: +55 45 3379 7092; fax: +55 19 3788 3910. E-mail address: [email protected] (C.E. Borba).

1369-703X/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.bej.2006.04.001

chemical processes, etc. The main disadvantages of mentioned technologies are the high cost of implantation and operations, for concentrations below 100 mg/L [2]. Hence, the new technologies with acceptable costs are necessary for reduction of the heavy metals concentration in industrial effluents. One of the promising alternatives is application of biosorption process that uses the living or dead organisms as an adsorbent such as fungus, bacteria, and seaweed [3,4]. The accumulated knowledge about biosorption mechanism is the base of the invention of new technologies to remove heavy metals from diluted solutions (1–100 mg/L) [5]. An additional advantage of the biosorption process is considered to be the low costs of used bioadsorbent, which can be obtained as a residue from bio-industries (fermentation bio-products) or biomass found in nature (marine algae) [6]. The biosorption mechanism, using as biosorbent marine algae, can involve the combination of one or more phenomena

C.E. Borba et al. / Biochemical Engineering Journal 30 (2006) 184–191

Nomenclature ae Ap As C C0 C|z=L CEXP Cmod dp DL Dm G JD kf K KF KS m ms NRe NSc q qmax Q t u0 VL VV z

mass transfer specific area (cm−1 ) external surface area of the particle of adsorbent (cm2 ) area of transversal section of the column (cm2 ) concentration of nickel(II) in the bulk fluid phase (meq/L) feed concentration of nickel(II) in the bulk fluid phase (meq/L) concentration of nickel(II) in the outlet the column (meq/L) experimental concentration of nickel in the effluent (meq/L) concentration of nickel(II) in the effluent calculated by the model (meq/L) equivalent diameter of the adsorbent particle (cm) axial dispersion coefficient in the fluid phase (cm2 /min) molecular diffusivity of nickel(II) (cm2 /min) mass flow (g/cm2 min) Chilton and Colburn factor mass transfer coefficient in the external liquid film (cm/min) Langmuir’s parameter (L/meq) mass transfer volumetric coefficient in the external liquid film (min−1 ) mass transfer coefficient in the adsorbent (min−1 ) experiments number biomass dry weight (g) Reynolds number Schmidt number average concentration of nickel(II) adsorbed in the algae (meq/) Langmuir isotherm parameter (meq/g) volumetric flow rate (cm3 /min) time (min) interstitial velocity of the fluid phase (cm/min) fixed bed volume (cm3 ) void bed (cm3 ) bed height (cm)

Greek letters ε Column void fraction µ viscosity of the fluid phase (g/(cm min)) ρF density of the fluid phase (g/cm3 ) ρL density of the bed (g/L)

such as ion exchange, complexation, physical and/or chemical adsorption, coordination, quelation, and inorganic microprecipitation. Among these unit processes, the ion exchange is considered to be the key one involved in the biosorption procedure [7]. Most separation and purification processes that use sorption technology involve continuous flow operations. In this operat-

185

ing mode, the saturated solid sorbent zone gradually extends throughout the column where the sorbate is adsorbed. The adsorption experimental data show a typical S-shaped curve where the slope is a result of three factors: the equilibrium sorption isotherm relationship, mass transfer effects throughout the sorbent in the column, and the influence of axial mixing, which determines deviation from the ideal plug-flow behavior [8]. Fixed bed columns systems with continuous flow allow the regenerating cycles operation. Using an appropriate eluent solution, the sorbent can be regenerate. The regeneration process liberates small volumes of concentrated metal solutions, which are more appropriate for conventional recovery processes [9]. To represent a dynamic heavy metals ions removal in fixed bed columns, a mathematical analysis of the system was performed and S-shaped experimental curves were evaluated. A typical breakthrough curve can be represented as a ratio of the effluent (C) and inlet concentration (C0 ) versus time. The efficiency of the adsorption process can be estimated by sharpness of the breakthrough curve. The correct design of a fixed bed column used for biosorption is not easy task and to reduce the costs of implementation of such equipment mathematical models have to be applied as the most robust and powerful tool. The model validation is performed on the bases of experimental data collected from laboratory scale, and statistical criterion is used during the non-linear parameter identification procedure. The developed models then may be applied for designing and process optimization in pilot plant and industrial scale [10]. The residence time is a key parameter in the design procedure of adsorption in fixed bed column [11]. When operating with low flow rates, the process is controlled by the external mass transfer (fluid around the particles surface) limitation. To avoid such a control, it is suggested for the process to operate in the range of higher flow rates. High flow rates may be applied in a process that is controlled by the internal mass transfer velocity (diffusion inside the particles). However, this will result in low residence times for adsorption and therefore, a decreasing of flow rates is suggested. It is obvious that the two effects are antagonistic and the optimal flow rate has to be searched in the intermediate region of flow rates [12]. Hence, the mass transfer coefficients have to be determined correctly to guarantee an optimal column design. The mathematical models used to describe the adsorption process can be divided in three categories: models of equilibrium stage, theory of the interference, and models of rate equation. The models of rate equation are more realistic compared to the others. These models are based on the species mass balances of interest in both, the fluid and the stationary phase (sorbent particles). They generally consider the effect of mass transfer in the liquid film, intraparticle diffusion, and equilibrium isotherms. Due to the complexity and non-linearity of these models, general analytical solutions are usually impossible to be achieved [13]. There are several mathematical models in the literature, which have been used to represent the dynamics of the fixed bed column. Models with analytical solutions [14,15] are often used for fitting the breakthrough curve. However, these mod-

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els need to be revised for mono-component systems; moreover, some assumptions are necessary to be made to achieve an analytical solution. Otero et al. [16] have investigated the phenol composite removal in fixed bed column. The applied model for the fixed bed adsorption has considered mass balance in the fluid phase, the adsorption equilibrium isotherm at the liquid/solid interface, and a linear driving force rate equation describing the diffusional mass transfer inside adsorbent particles. In this model, the ion diffusion limitation in the external film and the ion diffusion limitation in the adsorbent were connected to a global mass transfer coefficient. According to this author, the rate of adsorption is proportional to the driving force, which is the difference between the concentration in the adsorbed phase in equilibrium with the fluid phase bulk concentration and the average adsorbed concentration in the particle. Recently, several researchers [8,17–20] have used the linear driving force model to represent the rate equation. The most of the models consider only one limiting stage during the adsorption process. This assumption facilitates the resolution of the model, reducing the number of equations, which have to be solved. Mathematical models that incorporate mass transfer limitations can be used for prediction of the characteristic breakthrough curves. However, for accurate prediction, such models require reliable experimental data with respect to the feeding conditions and to the parameters associated with the mass transfer processes: diffusion limitation in the liquid film around the adsorbent particles and diffusion limitation of solute inside the adsorbent. A more sophisticated model considering double limitation effects to represent the adsorption dynamics in fixed bed was developed by Hsieh et al. [21]. A necessary, but not sufficient requirement for an adequate description of the sorption dynamics in fixed bed columns is for the mathematical formulas (adsorption isotherm, ion exchange isotherm, mass action law) to appropriately represent the equilibrium data among the phases in the column [10,22]. The ion exchange which has been identified as a main mechanism in the biosorption process and the equilibrium data are usually represented by adsorption isotherms such as: Langmuir, Freundlich, Sips, Redlich–Peterson. In the ion exchange isotherms, the effect of the released ion from the adsorbent is considered in the equations. It should be noted that, when the affinity of these ions is small compared with the metal uptake, this effect could be neglected. Usually, the Langmuir isotherm is used for the equilibrium description between the solid and liquid phases in an adsorption process. The constants in the Langmuir isotherm have physical meaning, where parameter (K) represents the ratio of adsorption and desorption rates. High values of this parameter indicate a strong affinity of the ion to the material sites. The parameter qmax represents the total number of available sites in the material adsorbent. Analyzing the results achieved in the area of heavy metal ion removal by biosorption, one can see that a challenging problem is the modeling of the fixed bed column containing biosorbent. The main objective of the present work was to develop a mathematical model for description of nickel(II) ion removal

dynamics in a fixed bed column, which was packed with the biomass of seaweed Sargassum sp. The mathematical model has to consider the adsorption process controlling steps such as the mass transfer limitation in the liquid film and in the adsorbent. In addition, the intention of this work was to develop a correlation between mass transfer coefficient in the external film and flow rate in the packed column. 2. Materials and methods 2.1. Biomass pre-treatment The brown seaweed (Sargassum filipendula) biomass was used as an adsorbent. The pre-treatment procedure was as follows: the seaweed were washed with tap water, rinsed with distilled water, and dried at 60 ◦ C for 24 h. The biomass was chemically pre-treated with calcium chloride (CaCl2 ·2H2 O), in a ratio of 25 g of native biomass per liter of calcium solution, following the method described elsewhere [23]. The biomass was placed in (0.2 mol/L CaCl2 ) solution and maintained under low agitation for 24 h. The pH initial solution was adjusted to 5.0 using 1.0N HCl solution, as described by authors [23–25]. At the end of the treatment process, the pre-treated biomass was rinsed three times with distilled water and dried at 60 ◦ C for 24 h, chopped and separated in different fraction sizes. For the sorption experiments in fixed bed column, the biomass particles with an average diameter of 2.2 mm were used. The particles were obtained after drying the biomass for 24 h at 105 ◦ C. 2.2. Nickel biosorption column preparation and operation The experimental module included a steel column with 2.8 cm internal diameter and 50 cm height connected with a peristaltic pump and a thermostatic bath, as shown in Fig. 1. The bed was packed distributing 8 g of pre-treated seaweed (dry base) along the column. The biomass was maintained in contact with deionized water for 12 h to complete the hydration process (volume expansion). Then, the residual water was drained and the bed height was fixed in 30.5 cm. The biosorbent material was washed with deionized water using continuous flow for 12 h in order to have the bed accommodation. After this procedure, the nickel solution (NiCl2 ·6H2 O) was fed to the column by peristaltic pump. The pH feed solution was adjusted to 3.0 with concentrated hydrochloric acid. The thermostatic bath was used to keep the feed solutions and the system at a constant temperature 30 ◦ C. The feed flow rates were used as follows: 0.002, 0.004, 0.006, and 0.008 L/min on ascending flow for nickel concentrations of 2.14, 2.11, 2.12, and 2.27 meq/L, respectively. Samples of nickel solution were collected at the column outlet for different time intervals and have been analyzed for nickel concentrations by using flame atomic absorption spectroscopy (“Varian Spectr AA-10 plus”). The samples were collected until the system reached steady state (column exhaustion) (where the nickel concentration in the liquid phase needs to be constant along the column and equal to feed concentration C = C* = C0 ).

C.E. Borba et al. / Biochemical Engineering Journal 30 (2006) 184–191

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Fig. 1. Scheme of the biosorption experimental module in fixed bed column.

2.3. Determination of the bed void fraction The total bed void fraction (ε) was determined at the end of each experiment, after the nickel solution was completely drained from the column bottom for 24 h. Then, deionized water was fed to the column until the bed was filled up. The amount of deionized water which was used to fill up the bed (VV ) was determined from the difference between the initial and the final volume in the recipient, and the bed void fraction (ε) was calculated as follows: VV ε= (1) VL 2.4. Calculation of the column biosorption capacity The amount of removed nickel ion by the pre-treated biomass was calculated from experimental breakthrough curve using the following formula: 
t 1 − C|z=L C0 Q VL εC0 ∗ q = (2) dt − 1000ms 0 C0 ms The integral part of Eq. (2) was solved numerically by the trapezoidal rule, using the experimental data from the breakthrough curve. 3. Mathematical modeling The mathematical modeling has a key role in the scale up procedure from laboratory experiments through pilot plant to industrial scale. The adequate models can help to analyze and to explain experimental data, to identify mechanisms relevant to the process, to predict changes due to different operating conditions and to optimize the process overall productivity. In this work, the process of nickel ion removal in fixed bed column was modeled using the following assumptions: • the hydrodynamics in the fixed bed column can be described using non-stationary state diffusion model; • the kinetics of nickel ions removal is based on the Langmuir isotherm, which represent the equilibrium on the solid/liquid interface;

• the description of the adsorption process has to considered the mass transfer limitation into the external liquid film around the adsorbent particles; • linear driving force is used to describe the concentration profile inside the particles; • isothermic and isobaric process conditions; • constant column void fraction; • constant physical properties of biomass (solid phase) and fluid phase; • negligible radial dispersion in the fixed bed column. Based on the mentioned above assumptions and mass balances for the liquid and solid phases in the fixed bed column the system equations can be written as follows. The mass balance of ion nickel concentration distribution and utilization in the fluid phase can be described by dispersion model: ∂C(t, z) ∂C(t, z) 1 ∂q(t, z) ∂2 C(t, z) = 0 (3) + ρL − DL + u0 ∂z ε ∂t ∂z2 ∂t The mass transfer equation for the ion concentration in the external liquid film is written: ∂q(t, z) KF ε (C(t, z) − C∗ ) = ∂t ρL

(4)

The mass transfer equation for the nickel ions on the solid particles is given by: ∂q(t, z) = −KS (q(t, z) − q∗ ) ∂t

(5)

where the initial condition for the model of the fluid phase is: C(0, z) = 0

(6)

The initial condition for the model of average concentration of the adsorbed nickel(II) ions in the algae (q) can be written as follows: q(0, z) = 0

(7)

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The boundary conditions are written as was suggested by the author [26]: DL

∂C(t, z) = u0 (C(t, 0) − C0 ) ∂z

∂C(t, z) =0 ∂z

at z = L

at z = 0

(8) (9)

where q* and C* are represented by the Langmuir isotherm. The mathematical expression of the Langmuir isotherm for a monocomponent system can be written as follows: q∗ =

qmax KC∗ 1 + KC∗

(10)

The mathematical model of the system is completed representing the dynamics of the nickel ions removal in a fixed bed column and it is built on the bases of Eqs. (3)–(5) and Eq. (10), with corresponding initial (6) and (7), and boundaries conditions (8) and (9). The model was solved using the finite volume method as was described by author [27]. The system of partial differential equations was discretized with respect to the space coordinate (z), resulting in a system of ordinary differential equations in time (t). The system of ordinary differential equations, with the initial and boundaries conditions, was solved by using the subroutine DASSL developed by Ref. [28], coded in FORTRAN. The mechanism for mass transfer in the adsorbent is through diffusion of the ions in the liquid solution inside the pores of the particles, and Fick’s law usually describes it. In order to facilitate the resolution of the resulting system of differential equations, some authors have proposed simpler expression [20]. Eq. (5) is an approximation that was originally proposed by Glueckauf and Coates [29]. Glueckauf [30] has shown that in certain conditions this expression can result in good approximations for the internal diffusion and adsorption modeling. This model is also called linear driving force (LDF) model. The mass transfer coefficient (kf ) in the external liquid film in fixed bed columns can be correlated with dimensionless groups characterized by the flow and geometry of the column. Dursun and Aksu have used the following correlation:  2/3 kf ρF µ = f (NRe ) (11) G ρF D m where

Authors

Correlation

Wilson and Geankoplis

JD =

McCune and Wilhelm

JD =

Chu et al.

JD =

Nath and Chand

JD =

QρF As ε

(12)

NRe

dp G = µ

(13)

In Eq. (11) the term inside parentheses represents the Schmidt number, and the term on the right hand side f(Re) represents the Chilton and Colburn factor JD in the following manner: kf ρF 2/3 N G Sc

JD =

For a large flat slab of side a, the surface area is defined by: (15)

(16)

Several correlations (see Table 1) have been used to calculate the mass transfer coefficient in the external liquid film of fixed bed columns, with the following generic formula: (n−1)

JD = WNRe

(17)

where W and n have received different values in each correlation. Substituting Eq. (17) in Eq. (16) results in: (n−1)

kf =

G NRe W 2/3 ρF N

(18)

Sc

Substituting the Reynolds and Schmidt’s numbers in Eq. (18) results in: kf =

W(dp /µ)n−1 Gn ρF (µ/ρF Dm )2/3

(19)

The mass transfer specific area ae can be defined as: ae =

6(1 − ε) dp

(20)

Multiplying both sides of Eq. (19) by the external specific area results in: KF = AGn

(21)

where ae W(dp /µ)n−1 ρF (µ/ρF Dm )2/3

KF = kf ae

and where dp is the equivalent diameter of the non-spherical particles, defined by the following equation:  (14) dp = 0.567 Ap

1.09 (−2/3) ε NRe (−0.507) 1.625NRe (−0.78) 5.7NRe (−0.59) 5.7NRe

Source: Ref. [31].

A=

G=

Ap = 2a2

Table 1 Correlations for the mass transfer coefficient in the liquid film in packed beds

(22) (23)

The axial dispersion coefficient can be estimated by using the following correlation [32]:   1 20 Dm DL + (24) = u 0 dp ε u0 dp 2 Two groups of model parameters can be recognized in the system Eqs. (1)–(24). The first group model parameters (ρL , ε, dp ) were measured during the experiments. The second group included the model parameters which values were estimated in

C.E. Borba et al. / Biochemical Engineering Journal 30 (2006) 184–191 Table 3 Experimental and calculated (Langmuir) nickel(II) uptake capacity

Table 2 Operating conditions and bed properties (pH 3.0; T = 30 ◦ C) Q (L/min)

C0 (meq/L)

ρL (g/L)

ε

0.002 0.004 0.006 0.008

2.140 2.110 2.120 2.270

41.359 41.361 41.537 41.791

0.875 0.870 0.876 0.880

the non-linear identification procedure using the experimental data and least square statistical method to form the objective function (criterion). The model parameters values of (KS , A, n) were obtained during the search of minimum of the following objective function: FOBJ =

n1 

2

(CiEXP − CiMOD ) +

j=1 nm  2 + (CiEXP − CiMOD )

n2 

189

Q (L/min)

C0 (meq/L)

q* (meq/g) experimental data

q* (meq/g) model

Deviationa (%)

0.002 0.004 0.006 0.008

2.140 2.110 2.120 2.270

1.468 1.350 1.174 1.369

1.234 1.223 1.225 1.269

15.97 9.41 4.37 7.28

a



Table 4 Evaluated parameter values of the model Parameter

Value

(min−1 )

2

(CiEXP − CiMOD ) + · · ·

j=1

(25)

j=1

where m is the number of experiments and all concentrations are considered at position z = L. In the search procedure, the optimization method of Nelder and Mead [33] was used. 4. Results and discussion The Langmuir isotherm was used in the model to describe a relationship between q* and C* . The parameters values used in Eq. (10) were qmax =2.49 ± 0.11 meq/g and K =0.46 ± 0.02 L/meq were experimentally obtained by Veit et al. [7] in the nickel ions removal process from solution using algae as an adsorbent in a fixed bed column. Four nickel(II) sorption experiments were performed in a fixed bed column. The experimental conditions, determining the values of feeding flow, ion concentration, porosity, and density of the bed are shown in Table 2. The predictive power of the model simulation of the adsorption column dynamics depends on the appropriate choice of the equilibrium isotherm [22]. Several researchers [34,35] have demonstrated the differences between the capacity of sorption process in continuous and in batch operations. These differences may be explained due to the required long time for batch experiments compared with continuous ones in columns. Other factors that may have an influence are the potential irreversibility of the adsorption process and different operating conditions of each system, such as the concentration in the fluid phase, which is continuously decreasing with time in a batch system, while it is continuously increasing in a continuous system [36]. Some ions attached to the adsorbent may be washed out from the system in a continuous column (open system), while in a batch system this effect does not exist. Based on the above-mentioned considerations, the parameters for the Langmuir isotherm were obtained from experimental data in a continuous column operation. Table 3 represents the values of the experimental capacity of biosorption, determined



∗ − q∗  /q∗ . Deviation 100 qexp exp mod

KS A (cm2 /g (cm2 min/g)n−1 ) n

0.030 0.215 0.682

by Eq. (2), and the values calculated by the Langmuir isotherm that best fitted the experimental data. The highest deviation was found for flow rate of 0.002 L/min, which also resulted in the highest difference between the experimental breakthrough curve and the simulated one (see Fig. 2). Ko et al. [36] has suggested for the processes on the macroscopic level, that if the flow rate increases, the residence time of the fluid in the bed decreases, resulting in a low use of the sorption capacity of the bed, and for the processes of microscopic level, the change of the volumetric flow rate affects only the diffusion of the ions in the liquid film, but not the one in the adsorbent. According to this author, high volumetric flow rates result in small resistances in the liquid film and high values of the external mass transfer coefficient. Based on these considerations, a constant mass transfer coefficient in the adsorbent was used for simulations of all data sets, while for the external mass transfer coefficient a correlation as a function of the Chilton–Colburn factor was developed resulting in Eq. (26). The identification of model parameters was performed fitting four experimental breakthrough curves (m = 4). In Table 4 the estimated values of the model parameters are shown. After determining the value of A, Eq. (22) was used to calculate the value of W, which value was found to be W = 4.25. The final correlation for JD can be written as follows: (−0.318)

JD = 4.25NRe

(26)

In the literature, some empirical correlations have been used to describe different systems and very different values for the external mass transfer coefficient were obtained. Even when applied to fixed bed columns with the same type of adsorbent, the correlations have shown errors up to 20%. The geometry and the rugosity of the adsorbent can be considered as relatively important factors to reliably estimate the external mass transfer coefficient in fixed bed column [37]. Hence, the importance of the developed correlation is to estimate the external mass transfer coefficient for the given experimental conditions in a fixed bed column where an adsorbent such as the marine algae biomass Sargassum sp. whit specific characteristics (geometry, rugosity, etc.) was used.

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Table 5 External mass transfer coefficient calculated for the new correlation and average value calculated by using the other correlations Q (L/min)

0.002 0.004 0.006 0.008

New correlation

Correlations average

kf (cm/min) Eq. (26)

KF (min−1 ) Eq. (23)

kf (cm/min)

KF (min−1 )

0.026 0.041 0.054 0.066

0.110 0.177 0.232 0.281

0.045 0.056 0.064 0.070

0.191 0.239 0.272 0.299

Table 6 Axial dispersion coefficient calculated by Eq. (24) Q (L/min)

u0 (cm/min)

DL (cm2 /min)

0.002 0.004 0.006 0.008

0.371 0.747 1.112 1.476

0.065 0.130 0.195 0.260

In Table 5 the values for the external mass transfer coefficient predicted by Eq. (26) are shown, and the average value calculated by the correlations is presented in Table 2. In Table 6 are given the values of the axial dispersion coefficient, calculated by Eq. (24), using the values of µ = 0.510 g/(cm min) and ρF = 1 g/cm3 . The molecular diffusivity value was Dm = 3.97 × 10−4 cm2 /min (source: Ref. [38]). The equivalent diameter was calculated considering the adsorbent particles as a flat slab of side a = 0.22 cm. It should be noted (see Table 6) that an increase of the volumetric flow rates promotes an increase in the axial dispersion inside the fixed bed column. The experimental breakthrough curves and the calculated ones are presented in Figs. 2–5. The effect of the feeding flow rate in the breakthrough curves was considered to be significant, where higher volumetric flow rates result in more inclined breakthrough curves and lower times of saturation.

Fig. 2. Experimental and calculated breakthrough curves for Q = 0.002 L/min (ρL = 41.359 g/L; ε = 0.870; C0 = 2.140 meq/L).

Fig. 3. Experimental and calculated breakthrough curves for Q = 0.004 L/min (ρL = 41.361 g/L; ε = 0.875; C0 = 2.110 meq/L).

Fig. 4. Experimental and calculated breakthrough curves for Q = 0.006 L/min (ρL = 41.537 g/L; ε = 0.876; C0 = 2.120 meq/L).

Fig. 5. Experimental and calculated breakthrough curves for Q = 0.008 L/min (ρL = 41.791 g/L; ε = 0.880; C0 = 2.270 meq/L).

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5. Conclusions The complex robust and flexible mathematical model describing the nickel(II) biosorption process in a fixed bed column filled up with marine algae S. filipendula, at temperature 30 ◦ C and pH 3.0 was developed. The following major results can be underlined: • the finite volumes numerical method was used to solve the system of three partial differential equations of the model; • a new correlation for the external mass transfer coefficient in the liquid film was developed: JD = 4.25(NRe )−0.318 , where kf is a function of the flow rates; • analyzing four sets of experimental data, the model was found to be robust and flexible enough in the representation of the adsorption dynamics in a fixed bed column for all the investigated cases; • based on the simulation analysis of the sorption process the authors believe that the developed model is very useful tool for phenomenological studies as well as for process optimization and a fixed bed column design, when a biomass adsorbent such as marine algae S. filipendula is used. Acknowledgement The authors gratefully acknowledge the financial support from Brazilian National Counsel of Technological and Scientific Development to conduct this work. References [1] N. Akhtar, J. Iqbal, M. Iqbal, Removal and recovery of nickel (II) from aqueous solution by loofa sponge-immobilized biomass of Chlorela sorokiniana: characterization studies, J. Hazard. Mater. B108 (2004) 85–94. [2] B. Volesky, Biosorption of Heavy Metals, CRC Press, Boston/Boca Raton, FL, 1990. [3] E.W. Wilde, J.R. Benemann, Bioremoval of heavy metals by use of microalgae, Biotechnol. Adv. 11 (1993) 781–812. [4] E. Sandau, P. Sandau, O. Pulz, Heavy metal sorption by microalgae, Acta Biotechnol. 16 (1996) 227–235. [5] K.H. Chong, B. Volesky, Description of two-metal biosorption equilibria by Langmuir type models, Biotechnol. Bioeng. 47 (1995) 451–460. [6] S. Schiewer, B. Volesky, Modelling multi-metal ion exchange in biosorption, Environ. Sci. Technol. 30 (1996) 2921–2927. [7] M.T. Veit, C.R.G. Tavares, E.A. Silva, Influence of pH and pre-treated biomass Sargassum filipendula in organic leaching, in: Anais do II Congresso Brasileiro de Termodinˆamica Aplicada, 2004 (In portuguese). [8] E.A. Silva, E.S. Cossich, C.R.G. Tavares, L. Cardozo, R. Guirardello, Modeling of copper (II) biosorption by marine alga Sargassum sp. in fixed bed column, Process Biochem. 38 (2002) 791–799. [9] D. Kratochvil, B. Volesky, Advanceds in biosorption of heavy metals, Trends Biotechnol. 16 (1998) 291–300. [10] E.A. Silva, C.R.G. Tavares, M.A.S.D. Barros, P.A. Arroyo, R.M. Schneider, M. Suszek, Modeling and experimental Cr+3 uptake using NaX zeolite, in: Sixth Italian Conference on Chemical and Process Engineering 2003, Pisa, Italy, Chem. Eng. Trans. 3 (2003) 303–308. [11] G. McKay, M.J. Bino, Fixed bed adsorption for the removal of pollutants from water, Environ. Pollut. 66 (1990) 33–53. [12] D.C.K. Ko, J.F. Poter, G. Mackay, Optimised correlations for the fixed bed adsorption of metal ions on bone char, Chem. Eng. Sci. 55 (2000) 5819–5829.

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