Application of equilibrium and mass transfer models to dynamic removal of Cr(VI) ions by Chitin in packed column reactor

Process Biochemistry 36 (2001) 1187– 1197 www.elsevier.com/locate/procbio

Application of equilibrium and mass transfer models to dynamic removal of Cr(VI) ions by Chitin in packed column reactor Yes¸im Sag˘ *, Yu¨cel Aktay Department of Chemical Engineering, Faculty of Engineering, Hacettepe Uni6ersity, 06532 Beytepe, Ankara, Turkey Received 7 November 2000; received in revised form 6 February 2001; accepted 13 February 2001

Abstract The dynamic removal of hexavalent chromium by chitin flakes was studied in a packed column reactor. The values of column parameters were predicted as a function of flow rate, bed depth, particle size and inlet metal ion concentration. On evaluating the breakthrough curves, sorption isotherms were obtained and modelled according to the Langmuir, the Redlich– Peterson and the Freundlich models. Kinetic and mass transfer aspects of the dynamic removal of Cr(VI) ions by chitin were investigated using several mathematical models. Column studies showed a good correlation between the experimental data and the calculated breakthrough curves obtained by the Adams–Bohart or the Wolborska models and the Clark model. The simulation of the whole breakthrough curve was effective with the Clark model, but the breakthrough was best predicted by Adams– Bohart, or related derived models. © 2001 Elsevier Science Ltd. All rights reserved. Keywords: Sorption; Chitin; Chromium; Packed column reactor; Equilibrium isotherms; Mass transfer models

1. Introduction Environmental conservation is of increasing social and economic importance. A particularly intractable pollution problem is that of the contamination of waters by heavy metals. Chromium is of great concern. It is used in a variety of industrial applications, including electroplating, leather tanning, textile dying and the metal finishing industry. In aqueous systems, chromium occurs in both trivalent and hexavalent forms, the latter being of particular concern because of its greater toxicity. Conventional processes used to remove hexavalent chromium are adsorption on activated carbon, reverse osmosis, or chemical processes such as reduction of hexavalent chromium into trivalent chromium, then its precipitation as chromium hydroxide [1]. Sorption, however, seems a good alternative. Many sorbents have been tested for the sorption of hexavalent chromium including activated carbon, tailored zeolites, hematite, fly ash, composed primarily of silica and alumina, moss * Corresponding author. Tel.: + 90-312-2977444; fax: +90-3122992124. E-mail address: [email protected] (Y. Sag˘).

peat, composed of lignin and cellulose, and corncob [2–5]. The abilities of microorganisms to remove hexavalent chromium in solution have also been extensively studied [6–9]. In fact, the overall sorption is located in the cell wall of microorganisms, through passive phenomena, which include sorption, complexation or precipitation processes. In the case of fungal biomasses the cell wall mainly consists of an association of glycoproteins, glucans and chitin or chitosan [10]. Chitin, a biopolymer consisting of b-(1-4)-2-acetamido-2-deoxy-D-glucose units, is the second most abundant polysaccharide occurring in nature, after cellulose. Although this polysaccharide is structurally similar to cellulose, it has less chemical versatility because of its strong crystal structure, and hence research on chitin is limited. One of the most attractive characteristics of chitin is the ability to absorb metal ions. During the past 20 years, great efforts have been made to apply this feature in chemical engineering and biomedical applications, including waste water treatment, metal accumulation and recovery, as well as functional membranes, and the control of necessary metal elements in the human body [11]. However, there is little known about the mecha-

0032-9592/01/$ - see front matter © 2001 Elsevier Science Ltd. All rights reserved. PII: S 0 0 3 2 - 9 5 9 2 ( 0 1 ) 0 0 1 5 0 - 9

Y. Sag˘, Y. Aktay / Process Biochemistry 36 (2001) 1187–1197

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nisms of metal uptake by chitin, both the physical or chemical reactions between the metal ions and chitin and the resultant structures of the formed aggregates or complexes. The different models for the metal sorption by chitin include: (1) formation of metal aggregates; (2) complexation; and (3) simple sorption [12– 15]. The aim of this study was to understand the mechanisms that govern chromium removal, and to find an appropriate model for the kinetics and mass transfer of removal in a packed column reactor.

influent was introduced by a upflow of varying volumetric flow rate Q (from 2.5 to 10 ml min − 1), giving a linear flow rate U0 between 0.66 and 2.65 m h − 1. The effluent samples were taken at 5 min intervals at the beginning of column operation and at 30 min intervals after reaching equilibrium. Experiments were terminated when the chitin bed was saturated with Cr(VI) ions.

2.4. Analysis of Cr(VI) ions The Cr(VI) content in the column outflow was determined spectrophotometrically at 540 nm using diphenyl carbazide as the complexing agent [17].

2. Materials and methods

2.1. Materials Chitin prepared from crab shells (poly(N-acetyl-1,4b-D-glucopyranosamine)] (C8H13NO5)n (Fluka 22720) was used for chromium removal. Before utilisation of the sorbent, the raw chitin was ground and sieved into two fractions as a function of particle diameter dp (mm) — 420B dp B 595 and 595Bdp B841. Before and after sorption experiments, the chitin particles were weighed and no weight loss of the sorbent was observed. The degree of deacetylation (DD) of the chitin flakes was determined by a Fourier transform infrared (FTIR) spectroscope (Shimadzu 8100) using the following equation [16]:

  

Degree od deacetylation (%) = 1−

n

A1655 1 × ×100 A3450 1.33

(1)

where A1655 and A3450 are absorbency values at 1655 and 3450 cm − 1 for carbonyl and hydroxyl peaks, respectively. Acetylation analysis gives a 27.2% DD.

2.2. Preparation of Cr(VI) solutions The stock solution of Cr(VI) (1.0 g l − 1) was prepared by dissolving a weighed quantity of potassium dichromate (K2Cr2O7) in distilled water. The range of concentrations of prepared metal solutions varied between 0.962 and 4.808 mmol l − 1. The chosen inlet metal ion concentration range corresponds to 50– 250 mg l − 1 on the basis of weight. The pH of each was adjusted to the required value for the biosorption of Cr(VI) ions, by adding 1 mol l − 1 of H2SO4.

2.3. Column studies Identical packed columns, 2.5 cm in diameter and 3.25 and 6.0 cm in height, were used in the sorption studies. Packed bed experiments were carried out at 25°C. The masses of sorbent are set at 1.5 and 2.75 g for depths (Z) of 3.25 and 6.0 cm, respectively. The

3. Evaluation of breakthrough curves and mathematical models applied to equilibrium and mass transfer in packed column The breakthrough curves for the sorption of Cr(VI) ions onto chitin were measured as a function of flow rate, particle size, bed depth, amount of chitin in the column and inlet metal ion concentration. The results are given in terms of the maximum (equilibrium) capacity of the column, Cmax (mmol), the amount of metal loading onto chitin, qeq (mmol g − 1), and the adsorption yield (adsorbed metal percentage), %Y. The maximum (equilibrium) capacity of the column for a given feed concentration is equal to the area under the plot of the adsorbed metal ion concentration Cads (mmol l − 1) versus time (min) or the area behind the breakthrough curve. The amount of metal that remains in the effluent, Ceq (mmol l − 1), is the area under the breakthrough curve. Cmax = Q

&

a

0

C0t− Ceq =

(2)

Cads dt

&

a

Cads dt

0

t

or Ceq =

W−qeqX Qt

(3)

The amount of metal loading onto chitin is calculated from the weight of metal adsorbed per unit dry weight of chitin in the column (that is, the ratio of the maximum capacity of the column to the amount of chitin in the column). qeq =

Cmax X

(4)

The adsorption yield is the ratio of the maximum capacity of the column to the amount of metal loading into the column, W (mg) [18,19]. Y=

Cmax ×100 W

(5)

Y. Sag˘ , Y. Aktay / Process Biochemistry 36 (2001) 1187–1197

W = C0Qt.

(6)

The mass transfer between the solution and the liquid phase is modelled by several equations or concepts in both static and dynamic contact. Sorption isotherms show the distribution of solute between the liquid and solid phases. This relation is used in several models of dynamic studies for the prediction of breakthrough curves. In this study, the equilibrium isotherms were analysed using the Langmuir, the Freundlich and the Redlich– Peterson sorption models. The main models explained in this paper are briefly described in this part.

3.1. Sorption isotherms The most widely used isotherm equation for modeling the biosorption equilibrium data is the Langmuir equation [20,21]. The Langmuir model suggests that uptake occurs on an homogeneous surface by monolayer sorption without interaction between sorbed molecules. This model is described by the equation. qeq =

a Ceq 1+ b Ceq

(7)

Where Ceq is the metal concentration in solution, qeq the adsorbed metal ion quantity per unit weight of dried biomass at equilibrium and a = qsb. The constants a and b are the characteristics of the Langmuir equation and can be determined from a linearised form of Eq. (7). The Langmuir equation obeys Henry’s Law at low concentrations. The Freundlich model proposes a monolayer sorption with a heterogeneous energetic distribution of active sites, and with interactions between sorbed molecules, as described by the following equation [20,21]. qeq = KFC 1/n eq

(8)

where KF and 1/n are the Freundlich constants. A further empirical isotherm has been developed by Redlich and Peterson (RP), incorporating three parameters [22]: qeq =

KRCeq 1+ aR C ieq

(9)

where the exponent i, lies between 0 and 1. When i = 1, the Redlich– Peterson equation reduces to the Langmuir equation. When i = 0, Henry’s law form results. The dynamic removal of Cr(VI) by chitin was studied in fixed columns with both the Adams– Bohart and Clark models.

3.2. The Adams–Bohart and Wolborska models Analysis of biosorption-column performance has been attempted by means of the conventional Adams–

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Bohart sorption model, which was developed for sorption to granulated activated carbon; this model assumes that the adsorption rate is proportional to both the residual capacity of the activated carbon and the concentration of the sorbing species. The Adams–Bohart model is used for the description of the initial part of the breakthrough curve [23]. The mass transfer rates obey the following equations: #q = − kqC (t

(10)

(C k = − qC (Z U0

(11)

where q is the metal ion content in the sorbent at t, C the solute concentration in solution, Z the column depth, k the kinetic constant and U0 the linear flow rate. Some assumptions are made for the solution of the differential equation system: (i) the concentration field is considered to be low, e.g. effluent concentration Cs B 0.15C0; (ii) for t “ , qz “ N0, z is the apparent volumic mass of the sorbent in the packed bed and N0 the saturation concentration. The following equation is obtained, with parameters k and N0 [24]: ln

Cs Z = kC0 t− kN0 C0 U0

(12)

The Wolborska model is also used for the description of adsorption dynamics in the range of the low-concentration breakthrough curve [25]. The mass transfer in the fixed bed sorption is described by the following system of equations: the balance equation of process dynamics:

       

(C (C (q ( 2C + U0 + =D (t (Z (t (Z 2 (q (q = −6 = ia (C−Ci ), (t (z

(13) (14)

where q is the solute concentration in the solid phase, Ci the solute concentration at the solid/liquid inrterface, D the axial diffusion coefficient, w the migration rate and ia the kinetic coefficient of the external mass transfer. With some assumptions previously described by Wolborska: Ci  C, w U0 and axial diffusion negligible D “ 0 as t “ 0, the solution can be approximated to: ln

Cs iaC0 iZ = t− a C0 N0 U0

with ia =

U 2o 2D

'

1+

4i0D −1 U 20

(15)



(16)

where io is the external mass transfer coefficient with a negligible axial dispersion coefficient D. The migration velocity of the steady-state front satisfies the relation, known as Wicke’s law:

Y. Sag˘ , Y. Aktay / Process Biochemistry 36 (2001) 1187–1197

1190

6=

U0C0 N0 +C0

(17)

The expression of the Wolborska solution is equivalent to the Adams –Bohart relation if the coefficient k is equal to ia /N0. So the drawing of ln Cs /C0 versus t would give information on both models [24].

3.3. Clark model Clark modelization associates the Freundlich equation and the mass transfer concept according to Eqs. (8) and (18): U0

dC =kT (C− Ceq), dZ

(18)

where kT is the mass transfer rate coefficient. Clark resolved this system and obtained the following solution [26]:



C n0 − 1 1+ [(C n0 − 1/C nb − 1 −1)ertb ]e − rt

or



C no − 1 1+ Ae − rt





1/n − 1

=Cs

(19)

1/n − 1

where



(20)

=Cs

4.1. Effect of flow rate



C n0 − 1 −1 ertb A= C nb − 1

(21)

and R(n− 1) = r

R=

particular species is dependent upon chromium concentration and pH. A lower pH will cause the functional groups of chitin to be protonated to a higher extent and result in a stronger attraction for a negatively charged ion in the solution. Since the Cr(VI) ions in the solution are present in the form of dichromate ions which are negatively charged, they are attracted by the protonated amino groups of the chitin. In a previous study, Cr(VI) ions were shown to be best adsorbed onto chitin at pH 2.0 in batch stirred reactor [27]. In this study, crab shell chitin with a 27.2% deacetylation degree (DD) was used. The number of Cr(VI) ions sorbed onto chitin is reported to increase with the increase of the DD. This is mainly due to the increase of − NH+ groups in 3 chitin with a high DD and the low pH of the system. However, a high DD of chitosan brings an instability in acidic solutions owing to the increased solubility. Metal-containing industrial waste waters are strongly acidic and this restricts the use of chitosan as a metal scavenger, especially in the case of chromium. For that reason, chitin was chosen as sorbent in this study, and the sorption of Cr(VI) ions onto chitin in packed column reactors was performed at pH 2.0.

kT 6 U0

(22)

Eq. (20) is the generalized logistic function. 6, n, Cb and tb are the migration velocity, the Freundlich constant, the concentration at breakthrough, and the time at breakthrough, respectively.

4. Results and discussion Chromium forms stable complexes such as Cr2O27 − , 2− and HCr2O− HCrO− 4 , CrO4 7 and the fraction of any Table 1 Effect of flow rate and bed depth on the sorption of Cr(VI) ions by chitin Flow rate (ml min−1)

Bed depth (cm)

W (mmol)

qeq ( mmol g−1)

Y (%)

2.5 5.0 10.0 2.5 5.0 10.0

3.25 3.25 3.25 6 6 6

0.540 0.756 0.877 1.260 1.477 1.448

0.051 0.048 0.047 0.081 0.060 0.045

14.28 9.50 8.01 17.62 11.20 8.57

To investigate the effect of flow rate on the sorption of Cr(VI) ions by chitin, the inlet metal concentration in the feed was held constant at 1.923 mmol l − 1 while the flow rate was changed from 2.5 to 10 ml min − 1 for bed depths (Z) of 6.0 and 3.25 cm. Maximum column capacity is generally expected to increase with increasing flow rates because of high metal loading. However, the longer the contact time between metal solution and sorbent in packed column reactor the greater the amount of metal adsorbed. For Cr(VI) sorption onto chitin, the amount of metal loading on the sorbent surface decreased with increasing flow rate and maximum sorption yields were obtained at a flow rate of 2.5 ml min − 1 (Table 1).

4.2. Effect of particle size and initial metal ion concentration on equilibrium parameters for the sorption of Cr(VI) ions onto chitin Various mechanisms have been proposed for the sorption of heavy metal ions onto chitin/chitosan. For example, the formation of a coordination complex between the metal and the chitin nitrogen or oxygen has been suggested. Ion exchange has also been suggested as a process that may be active in the uptake of certain metals by chitin or chitosan, however, the chitin/chitosan-metal biosorption mechanism has not been fully explained [10,15]. Sorption of chromium appears to occur by precipitation onto chitin with the formation of nodules of metal, a mechanism referred to the Eiden-

Y. Sag˘ , Y. Aktay / Process Biochemistry 36 (2001) 1187–1197

Fig. 1. The breakthrough curves of Cr(VI) obtained at increasing Cr(VI) ion concentrations in the 0.920 –5.055 mmol l − 1 range (flow rate, 2.5 ml min − 1; bed depth, 6 cm). Table 2 Effect of particle size on the sorption isotherm coefficients of the Langmuir model (flow rate, 2.5 ml min−1; bed depth, 6 cm) Particle size (mm)

qs (mmol g−1)

b (l mmol−1)

a (l g−1)

R

420–595 595–841

0.154 0.160

0.634 0.422

0.098 0.067

0.994 0.983

Table 3 Effect of particle size on the sorption isotherm coefficients of the Redlich–Peterson model (flow rate, 2.5 ml min−1; bed depth, 6 cm) Particle size (mm)

KR (l g−1)

aR mmoli+1 g−1 l−i

i

R

420–595 595–841

0.102 0.074

0.742 0.582

0.957 0.902

0.997 0.983

Table 4 Effect of particle size on the sorption isotherm coefficients of the Freundlich model (flow rate, 2.5 ml min−1; bed depth, 6 cm) 0

0

Particle size (mm)

KF (mmol1−b g−1lb )

1/n

R

420–595 595–841

0.059 0.047

0.494 0.601

0.980 0.966

Jewell effect [28]. This possible mechanism implies a multilayer sorption, or heterogenous sorption induced by variation in sorption energies on various sites or by several different sorbed species. It would be interesting to model sorption isotherms and to determine which

1191

out of the Langmuir and Freundlich theories equations is the better predicting (Eqs. (7) and (8)). The sorption of Cr(VI) ions onto chitin flakes having a size distribution varying between 420 and 595, and 595 and 841 mm in the packed column reactor was investigated as a function of metal ion concentrations in the feed solutions. For determination of the sorption characteristics of Cr(VI) ions in the packed column, the inlet concentrations of Cr(VI) ions were varied between 0.920 and 5.055 mmol l − 1. In all the breakthrough curves the normalized concentration, defined as the measured concentration divided by the inlet concentration, is plotted against volumes of synthetic aqueous solutions treated. The general position of the breakthrough curve along the volume axis depends on the capacity of the column with respect to the feed concentration. This is set by the equilibrium. By comparing the breakthrough curves in Fig. 1, it is seen that decreasing the feed concentration increases the volume of the feed that can be processed and shifts the breakthrough curve to the right. As the concentration of Cr(VI) ions increases in the feed, the breakthrough curves become steeper. Much sharper breakthrough curves and higher sorption capacities for Cr(VI) ions were obtained at higher concentrations of Cr(VI) ions. The breakthrough curves were evaluated. The equilibrium sorption data of Cr(VI) ions by chitin in the packed column reactor were analyzed using the Langmuir, the Redlich–Peterson and the Freundlich sorption models. The sorption constants calculated according to the Langmuir, the Redlich–Peterson and the Freundlich sorption models are listed in Tables 2–4, respectively. The Langmuir equation was linearised by plotting 1/qeq versus 1/Ceq to determine the Langmuir constants from the slope 1/a and the intercept b/a. The amount of adsorbate per unit weight of adsorbent to form a complete monolayer on the surface is qs and b is the ratio of adsorption/desorption rates and a large value of b implies strong bonding. The three parameters, aR, KR and i, given by the Redlich– Peterson sorption model were estimated from the equilibrium sorption data of Cr(VI) ions using an MS Excel 7.0 computer program. Finally, the intercept of the linearised Freundlich equation, KF, is an indication of the sorption capacity of the sorbent; the slope, 1/n, indicates the effect of concentration on the sorption capacity and represents the sorption intensity. The correlation coefficients (R) were generally very high for the various models. Intraparticle diffusion coefficients determined in batch stirred reactor indicated a poor intraparticular diffusion of Cr(VI) ions into the chitin or into the pores [27]. Since the poor diffusion in the solid, or the limitation of diffusion to a thin layer, implies that good overall sorption is possibly due to multilayer sorption, the BET model describing multilayer sorption was also applied to sorption equilibrium data of Cr(VI) ions onto chitin. However, the BET equation was not

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Y. Sag˘ , Y. Aktay / Process Biochemistry 36 (2001) 1187–1197

satisfactory to correlate the experimental isotherms obtained in packed column reactor, as also previously observed in batch stirred reactor [27]. Tables 2–4 also illustrate the effect of particle size on the modelling of sorption isotherms. The equilibrium uptake was influenced by the size distribution of sorbent particles. Maximum uptake was a function of the specific area or external surface of the sorbent. Thus, the smaller the particle, the larger the surface area. It is clear that the Langmuir constants, qs and b, the Redlich –Peterson constants, KR and aR, and the Freundlich constant, a 0, decreased with increase in mean chitin diameter, suggesting that the smaller particles tend to have a higher capacity for Cr(VI). If the sorption capacity is independent of the particle size, it would indicate that all the sorbent mass was saturated; the solute is able to diffuse even at the centre of the particle. On the other hand, a large size of Cr(VI) ions could explain a restriction in the diffusion of solute. The solute required more time to diffuse to the interior of the particle. The values of various isotherm constants for Cr(VI) sorption onto chitin were also determined in batch stirred reactor [27]. The Langmuir constants, qs and b, at pH 2.0 and in a particle size range 420–595 mm were 1.816 mmol g − 1 and 0.252 l mmol − 1, respectively. The Redlich– Peterson coefficients estimated from the sorption data of Cr(VI) ions were KR = 0.682 l g − 1, aR =1.008 mmoli + 1 g − 1 l − i, and i = 0.256. The Freundlich constants, KF and 1/n, 0 0 were determined as 0.347 mmol 1 − b g − 1 lb and 0.866, respectively. For all the sorption models examined, the values of isotherm constants obtained in the packed column were considerably lower than those obtained in the batch stirred reactor, as also expected. The static

Fig. 3. Comparison of the experimental values (symbols) and those predicted by the Adams – Bohart model (lines). (Bed depth, 3.25 cm; C0, 1.923 mmol l − 1; Q, 2.5 ml min − 1;dp, 420 – 595 mm).

studies allow the experimental conditions to be optimized, and the mechanisms to be interpreted. These experimental data are generally used in further studies concerning the dynamic sorption of solute in column studies, for the prediction of the breakthrough curves. However, it is important to note that the values of sorption constants obtained in batch stirred reactor show the maximum values of these constants for the sorption of Cr(VI) ions onto chitin, when the flow rate of the solution is zero, that is, the contact time between the metal solution and chitin flakes approximates infinite. For that reason, sorption isotherms and constants should be re-determined in a packed column reactor evaluating the breakthrough curves in order to model such a system mathematically or predict the scaling-up of a unit plant.

4.3. Application of the Adams–Bohart and Wolborska models on the sorption of Cr(VI) ions by chitin

Fig. 2. The breakthrough curve of Cr(VI) sorption by chitin with the Adams– Bohart model. The Adams–Bohart model profile is presented in full lines, the symbol denotes experimentally obtained values (C0, 2.952 mmol l − 1; flow rate, 2.5 ml min − 1; bed depth, 6.0 cm; particle size, 420 –595 mm).

Adams –Bohart, and related models, allow some mass transfer coefficients to be estimated, particularly the kinetic constant k. According to the Adams–Bohart model, the breakthrough curves were linearized by plotting ln Cs /C0 versus t to determine the column parameters, the kinetic constant, k (l mmol − 1 min − 1), from the slope and the saturation concentration, N0 (mmol l − 1), from the intercept. For breakthrough curves, linearization was carried out using the least squares method in a given range of effluent concentrations. The values of the Adams–Bohart and Wolborska model parameters corresponding to experimental conditions and the correlation coefficients (R) are given in Table 5. The simulated breakthrough curve at an inlet Cr(VI) ion concentration of 2.952 mmol l − 1 and in a particle size range 420–595 mm for 6 cm bed depth is given in Fig. 2. This figure shows the superposition of experimental results (points) and theoretical calculated points

Table 5 Adams–Bohart and Wolborska model parameters corresponding to experimental conditions Experimental parameters Z (cm)

Adams–Bohart model

Wolborska model

U0 (m h−1)

C0 (mmol l−1)

N0 (mmol l−1)

k×103 (l mmol−1 min−1)

ia (h−1) 6×102 (m h−1)

R

2.5 5.0 10.0 2.5 5.0 10.0

0.66 1.32 2.65 0.66 1.32 2.65

1.965 2.017 2.193 1.902 2.110 2.069

48.99 41.94 53.81 19.72 25.99 27.79

4.3 8.1 14.1 21.5 25.6 28.8

12.64 20.38 45.52 25.44 39.92 48.02

2.55 6.06 10.38 5.81 9.91 18.36

0.895 0.894 0.872 0.911 0.800 0.861

2.5 2.5 2.5 2.5 2.5

0.66 0.66 0.66 0.66 0.66

0.920 1.902 2.952 3.961 5.055

10.29 19.72 29.95 37.87 46.57

32.1 21.5 9.5 8.0 6.9

19.82 25.44 17.07 18.18 19.28

5.42 5.81 5.92 6.25 6.46

0.906 0.911 0.928 0.913 0.944

2.5 2.5 2.5 2.5 2.5

0.66 0.66 0.66 0.66 0.66

1.003 2.037 3.046 3.732 4.925

12.35 23.66 33.15 36.05 46.53

16.7 10.2 5.8 8.1 6.2

12.38 14.48 11.54 17.52 17.31

4.96 5.23 5.55 6.19 6.32

0.927 0.958 0.953 0.937 0.953

Effect of flow rate 3.25 3.25 3.25 6 6 6 a Effect of inlet metal ion concentration in a particle size range 420–595 mm 6 6 6 6 6 Effect of inlet metal ion concentration in a particle size range 595–841 mm 6 6 6 6 6

Y. Sag˘ , Y. Aktay / Process Biochemistry 36 (2001) 1187–1197

Q (ml min−1)

1193

Y. Sag˘ , Y. Aktay / Process Biochemistry 36 (2001) 1187–1197

1194

to experimental data than for other conditions. Increasing flow velocity induced an increase of ia, k and 6. These results are consistent with previous study on uranium sorption onto silica gel [24]. The kinetic constant k varied between 4.3×10 − 3 (0.83× 10 − 4) and 32.1× 10 − 3 l mmol − 1 min − 1 (6.17× 10 − 4 l mg − 1 min − 1). These values are compatible with the kinetic constant k previously estimated in the range 1.2× 10 − 4 –2.5×10 − 3 l mg − 1 min − 1 for the sorption of uranium by silica gel in column studies [24]. The migration velocity 6 was calculated by the Wolborska method and the values are set between 2.55× 10 − 2 and 18.36× 10 − 2 m h − 1 and the mass transfer coefficient ia between 11.54 and 48.02 h − 1. ia is an effective coefficient which reflects the effect of both mass transfer in the liquid phase and axial diffusion. Wolborska observed that in short beds or at high flow rates of solution through the bed, the axial diffusion is negligible and ia = i0, the external mass transfer coefficient [25]. As seen from Table 4, particle size influences the sorption rate. As the particle size is decreased, the external surface of the chitin flakes increased, and the values of the kinetic constant k also increased. This decrease in the particle size decreased the external mass transfer resistance. The external dif-

Fig. 4. Comparison of the experimental values (symbols) and those predicted by the Adams –Bohart model (lines). (Bed depth, 6.0 cm; C0, 1.923 mmol l − 1; Q, 2.5 ml min − 1;dp, 420–595 mm).

(lines). It appears that the breakthrough is well predicted by Adams –Bohart, or derived models, whereas the whole breakthrough curve can not be defined. Effect of flow rate on the breakthrough curve of Cr(VI) sorption by chitin with the Adams– Bohart model for 3.25 and 6.0 cm bed depths is given in Figs. 3 and 4, respectively. For the highest flow rates and column heights the Adams modelization corresponds less well Table 6 Clark model parameters corresponding to experimental conditionsa Experimental parameters

Clark model

Z (cm) Effect of flow rate

Q (ml min−1)

U0 (m h−1)

C0 (mmol l−1)

ln A

A

r×102 (min−1)

RPEa(%)

3.25 3.25 3.25 6 6 6

2.5 5.0 10.0 2.5 5.0 10.0

0.66 1.32 2.65 0.66 1.32 2.65

1.965 2.017 2.193 1.902 2.110 2.069

0.1658 0.1739 1.1701 2.8233 3.1033 2.8178

1.1803 1.1899 3.2224 16.8325 22.2702 16.7396

4.77 10.94 42.68 8.86 25.68 62.10

2.9 4.2 2.4 11.7 7.2 5.8

Effect of inlet metal ion concentration in a particle size range 420–595 mm 6 6 6 6 6

2.5 2.5 2.5 2.5 2.5

0.66 0.66 0.66 0.66 0.66

0.920 1.902 2.952 3.961 5.055

2.1569 2.8233 1.9106 2.0184 1.9250

8.6443 16.8325 6.7569 7.5263 6.8552

8.33 8.86 8.04 9.30 8.03

10.5 11.7 7.5 8.1 6.5

Effect of inlet metal ion concentration in a particle size range 595–841 mm 6 6 6 6 6

2.5 2.5 2.5 2.5 2.5

0.66 0.66 0.66 0.66 0.66

1.003 2.037 3.046 3.732 4.925

0.2116 0.3935 0.1904 1.9972 1.4363

1.2357 1.4822 1.2097 7.3681 4.2050

0.38 1.22 2.57 10.76 8.02

20.3 17.4 15.0 12.0 12.6

a

Relative percentage error (RPE) between the experimental and predicted values. % [ (qi, eq)predicted−(qi, eq)experimental /(qi,eq)experimental]×100

RPE(%)= N, number of experimental data.

N

.

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fusion rate (ia, h − 1) was increased by lowering the particle size of the sorbent. The increased particle size will introduce a higher external mass transfer and will therefore have a lower external mass transfer coefficient. Increasing the flow rate from 2.5 to 10 ml min − 1 increased the ia value; this was not unexpected as increased turbulence reduces the film boundary layer surrounding the chitin particle. Although the Adams – Bohart model provides a simple and comprehensive approach to running and evaluating sorption-column tests, its validity is limited to the range of conditions used. For example, the model assumes the presence of only one contaminant in the waste water. Since it was developed for sorption to granulated activated carbon, the fundamental difference between ion exchange, an effective mechanism in biosorption, and sorption on activated carbon limits the use of this model in biosorption. For example, the Adams– Bohart model cannot predict the important effects on column performance of changes in pH, ionic forms of the biosorbent and feed composition.

4.4. Application of the Clark model on the sorption of Cr(VI) ions by chitin Column parameters for the Clark model given by Eq. 19. were estimated from the column sorption data of Cr(VI) by using an MS Excel 7.0 computer program. The simulated breakthrough curves were plotted using 45–330 points for a simulation period of 45– 330 min with respect to column saturation time. The characteristics of the Clark model are compiled in Table 6. The simulated breakthrough curve at an inlet Cr(VI) ion concentration of 0.920 mmol l − 1 and in a particle size range 420– 595 mm for 6 cm bed depth is given in Fig. 5. For this breakthrough curve, the best fit equation is Cs =



C 1.02 0 ) 1+8.64e − 0.0833t



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to the mass transfer varied between 0.38×10 − 2 and 62.1× 10 − 2 min − 1. The value of this coefficient approximated a mean value of 8.51×10 − 2 min − 1 at optimum values of all the parameters examined (at 2.5 ml min − 1 flow rate, 0.920–5.055 mmol l − 1 inlet metal ion concentration range, 6 cm bed depth and 250–420 mm particle size range). 5. Conclusion In this study, the kinetics and mass transfer for the sorption of Cr(VI) ions onto chitin were modelled by several equations or concepts in dynamic contact.The kinetics were studied paying special interest to the effect of flow rate, bed depth, particle size and inlet metal ion concentration. Breakthrough curves were plotted. Several models were applied to simulate the breakthrough curves in order to predict the scaling-up of a unit plant. The distribution of the Cr(VI) ions between the liquid phase and the solid phase was described by several mathematical relationships such as the Langmuir, the Redlich–Peterson and the Freundlich models. The characteristic sorption parameters for each isotherm were determined. Several models such as the Adams– Bohart, and derived forms, or the Clark, were applied to experimental data obtained from dynamic studies performed on fixed columns. These models gave good approximations of experimental behaviour. The initial segment of the breakthrough curve was defined by the Adams –Bohart model, while the whole breakthrough curve was well predicted by the Clark model. Adams–

0.977

(23)

The effect of flow rate on the breakthrough curve of Cr(VI) sorption by chitin with the Clark model for 3.25 and 6.0 cm bed depths is given in Figs. 6 and 7, respectively. It appears that the simulation of the whole breakthrough curve is effective with the Clark model. For higher column height, lower inlet Cr(VI) ion concentrations and larger particle size, the correlation between the experimental and the predicted values using the Clark model deviated slightly. Guibal et al. reported r coefficients changing between 1.18× 10 − 2 and 14.94×10 − 2 min − 1 with experimental parameters for uranium sorption by silica gel at similar column heights and flow rates [24]. The same order of magnitude for the r coefficient was obtained for Cr(VI) sorption by chitin in this study. The r coefficient related

Fig. 5. The breakthrough curve of Cr(VI) sorption by chitin with the Clark model. The Clark model profile is presented in full lines, the symbol denotes experimentally obtained values (C0, 0.920 mmol l − 1; flow rate, 2.5 ml min − 1; bed depth, 6.0 cm; particle size, 420 –595 mm).

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References

Fig. 6. Comparison of the experimental values (symbols) and those predicted by the Clark model (lines). (Bed depth, 3.25 cm; C0, 1.923 mmol l − 1; Q, 2.5 ml min − 1; dp, 420–595 mm).

Fig. 7. Comparison of the experimental values (symbols) and those predicted by the Clark model (lines). (Bed depth, 6.0 cm; C0, 1.923 mmol l − 1; Q, 2.5 ml min − 1; dp, 420–595 mm).

Bohart and Wolborska models allowed some mass transfer coefficients to be estimated, the kinetic constant, k, the saturation concentration, N0, the kinetic coefficient of the external mass transfer, ia, and the migration velocity, 6. The generalized logistic functions of the breakthrough curves and the coefficient related to the mass transfer were obtained by using the Clark model.

Acknowledgements The authors wish to thank TU8 BI: TAK, the Scientific and Technical Research Council of Turkey, for the partial financial support of this study (Project No: YDABC ¸ AG, 199Y095).

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