Derivation and application of a new model for ... - Semantic Scholar

Water Research 36 (2002) 1313–1323

Derivation and application of a new model for heavy metal biosorption by algae Karina Yew-Hoong Gina, Ying-Zhong Tanga,*, M.A. Azizb a b

Tropical Marine Sciences Institute (TMSI), National University of Singapore, 14 Kent Ridge Road, 119223 Singapore Department of Civil Engineering, National University of Singapore, E1A-07-03, 1 Engineering Drive 2, 117576 Singapore Received 30 October 2000; received in revised form 28 May 2001; accepted 2 July 2001

Abstract An equilibrium model for describing the relationships between important parameters for heavy metal sorption by algae was derived through a thermodynamics approach. In this model, both the removal efficiency of heavy metal and metal adsorption per unit algal biomass are considered to be simple functions of the ratio of algal biomass concentration to the initial metal concentration for selected conditions, i.e. as at constant pH and temperature. The model was found to fit the experimental results well (judged by the correlation–regression coefficient, R2 ), for the adsorption of cadmium, copper, lead and zinc by two algal species, Oocystis sp. (both living and non-living) and Chlorococcum sp. The applicability of the model was also supported by the reprocessed results of experimental data given in the literature, i.e. for the metal species, Cd, Pb, Cu and Ag, the algal species, Chlorella vulgaris, Scenedesmus quadricauda and Cladophora crispata, and both batch and continuous fixed-bed reactors. It was also demonstrated that the model could be applied over a broad range of pH for cadmium and copper adsorption by Oocystis sp. However, the model was not applicable at very low and high pH levels, due to negligible adsorption and precipitation, respectively. r 2002 Elsevier Science Ltd. All rights reserved. Keywords: Heavy metal; Biosorption; Algal biomass; Equilibrium model; Cadmium (Cd); Copper (Cu)

1. Introduction With increasing generation of heavy metals for technological activities, many aquatic environments face metal concentrations that exceed water quality criteria designed to protect the environment, animals and humans. In response to increasing metal toxicity concerns, new technologies involving the use of microalgae [1–5] potentially offer a more economical treatment alternative [6] because many features of algae make them potentially good candidates for heavy metal removal [3,1,7]. From the viewpoint of application, it is important to develop an appropriate mathematical model for describ-

*Corresponding author. Tel.: +65-7749882. E-mail addresses: [email protected] (K.Y.-H. Gin), tmstyz @nus.edu.sg (Y.-Z. Tang), [email protected] (M.A. Aziz).

ing the equilibrium behavior of an algae–metal system (either batch or continuous system) in order to guide the process design and screening of algal strains. The most widely used models to describe the equilibrium behavior of metal uptake are the well-known Langmuir and Freundlich sorption isotherms [8–23]. The two equations can be expressed as follows: Freundlich sorption isotherm: x ð1Þ ¼ Kf Ce1=n : m Langmuir sorption isotherm: x bCe ðx=mÞmax ; ¼ 1 þ bCe m

ð2Þ

where x=m is the solute (metal) concentration in the sorbent (algae), Ce the equilibrium concentration of solute in the solution, Kf a constant, ðx=mÞmax the maximum solute concentration in the sorbent, and b and

0043-1354/02/$ - see front matter r 2002 Elsevier Science Ltd. All rights reserved. PII: S 0 0 4 3 - 1 3 5 4 ( 0 1 ) 0 0 3 3 2 - 3

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K.Y.-H. Gin et al. / Water Research 36 (2002) 1313–1323

M=C0

Nomenclature C0 Ce Ce =C0 DG0 ; DG00 ; DG M

initial metal concentration, mg/l equilibrium metal concentration in solution, mg/l ratio of the equilibrium metal concentration to the initial metal concentration change of reaction free energy concentration of algal biomass, mg/l

n are constants related to the energy of sorption. However, in quantifying the differences between two different sorption systems, it is necessary that the evaluation be carried out at the same equilibrium (final, residual) concentration. Any other comparison carries an inherent error and can only serve as a qualitative comparison [5]. The Langmuir model was originally formulated based on theoretical assumptions: (1) the sorption reaction can be represented as a coordination reaction with 1 : 1 stoichiometry (i.e. monolayer sorption); (2) the activities of the surface sites are proportional to their concentration and (3) the number of sorption sites is fixed [24]. On the other hand, the Freundlich model has generally been considered an empirical relationship and has been used widely to fit experimental data [16,17,19,10,14,24]. Recently, it has also been shown that the Freundlich isotherm can be derived theoretically to some extent based on the assumption that the free energy of the sorption reaction increases linearly with the log-concentration of adsorbate (i.e. the equilibrium concentration of metal in the metal–algae system) [24]. In terms of fitting the models to experimental data, it was found that the Freundlich model generally gave a better fit for higher equilibrium metal (Cd) concentrations [19]. In addition, it has been shown that, while both models can be used to fit the experimental data of Cd, Cu and Pb sorption by Chlorella fusca, the Freudlich model has a wider range of application in terms of metal concentration [16]. However, the application of these two models in interpreting metal sorption by algae has met with some problems. For example, Hashim et al. [25] reported that a unique isotherm equation could not be obtained if different initial metal concentrations and algal dosage were used for the same set of experiments. This makes it difficult to quantitatively compare two sorption systems with different initial metal and algal concentrations. A review of the experimental procedures for those studies where the sorption isotherm equations were used to fit experimental data showed that the experiments were, in fact, conducted with either constant algal biomass concentration [10,12–

X x=m ðx=mÞc ; ðM=C0 Þc ðx=mÞmax a; b

ratio of the algal biomass to the initial metal concentration concentration of metal adsorbed by algae, mg/l adsorbed-metal content per unit algal biomass, mg/g critical value of x=m and M=C0 maximum of x=m in the present model coefficients in the present model

15,18,19,21–23] or constant initial metal concentration [10]. Recently, as a result of mounting evidence supporting the ion-exchange mechanism for metal adsorption by algal biomass (non-living biomass, in particular), new isotherm models have been recommended, in place of the Langmuir and Freundlich isotherms [26–28]. One of these models, called the ion-exchange isotherm, was developed from a general ion-exchange reaction between metal species, M1 and M2 (originally bound to the algal biomass) [28]. The model can be summarized as follows: ion-exchange reaction nM1þm þ mM2þn 2nM1þm þ mM2þn ; equilibrium constant m qn CfM2 KM1M2 ¼ M1 m n : qM2 Cfm2 ion-exchange isotherm Q ; qM1 ¼ 1 þ CfM2 =KM1M2 Cfm1 qM2 ¼

Q ; 1 þ CfM1 =KM1M2 CfM2

ð3Þ

ð4aÞ ð4bÞ

where M1 and M2 are the targeted heavy metal and the ion originally bound to the algal biomass (e.g. Ca2+, K+, H+, etc.); m and n the valence of M1 and M2; respectively; Q represents the total concentration of binding sites in the algal biomass; CfM1 and CfM2 are the equilibrium concentrations of M1 and M2 in solution, respectively; qM1 and qM2 the contents of M1 and M2 in the algal biomass. A significant development of the model is that the proton concentration (pH) can be incorporated into the equation as an independent variable if the algal biomass is pre-protonated, i.e. M2 is replaced by H+. However, this model still did not account for how the changes in initial heavy metal and algal biomass concentrations affect the equilibrium metal concentration in the solution and the metal content adsorbed on the algal biomass. Instead, as already seen in the Langmuir isotherm, the equilibrium concentrations of both the displaced and targeted metals


in solution are treated as independent parameters, which are determined by the initial concentrations of algal biomass and the targeted heavy metal. Furthermore, it will be difficult to apply the model when considering more than one species of ion bound to the sites on the algal biomass, as the number of constants in this models will increase accordingly. In retrospect, all the above equilibrium models may be viewed as ‘‘descriptive’’ rather than ‘‘predictive’’ models, i.e. they describe the relationships between the equilibrium parameters, rather than predict the equilibrium state according to the initial conditions for a particular algae–metal system. In the present study, we derive a new equilibrium model which describes the relationships between the equilibrium concentrations of metal, metal sorption per unit algal biomass and the most important factors affecting these two parametersFthe concentration of algal biomass and initial metal concentration. The model was applied to experiments on Cd, Cu, Pb and Zn uptake by two tropical, unicellular algal species, Oocystis sp. and Chlorococcum sp. In addition, the effects of pH on the application of the model were also explored.

2. Theoretical derivation of model The model derived in this study was obtained using thermodynamics as an overall approach to the system. The basic equation of the model is: Ce M : ð5Þ ¼ a exp b C0 C0 In deriving the above equation, first consider the sorption reaction as a simple change in the state of the heavy metal solution: M

C0 - Ce ;

00

DG ;

where C0 is the initial concentration of heavy metal in solution, Ce the equilibrium concentration of metal in solution after sorption, M the concentration of algal 0 biomass and DG0 is the effective free energy change, which changes with the proceeding of the adsorption reaction. The total free energy change of the sorption reaction, DG; can thus be expressed as a function of C0 and Ce : Ce 0 ð6Þ DG ¼ DG0 RT ln C0 which is analogous to the expression for the free energy change of an ideal gas at constant temperature, DG ¼ nRT lnðp2 =p1 Þ; where p2 and p1 are the final and initial pressures, respectively, [29]. In fact, as pointed out by Morel and Hering [24], Eq. (6) can be rationally extended from the above expression of the free energy

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change of ideal gas by application of Raoult’s and Henry’s laws for the equilibrium between the concentrations of solvent and solutes and their vapor pressures. From the viewpoint of statistical mechanics, Eq. (6) can be considered similar to the Maxwell–Boltzmann distribution law [24]. It should be noted that the symbol ‘‘minus’’ is used in the above equation because sorption is not a spontaneous reaction, i.e. the metal solution will not shift automatically from state C0 to state Ce without the addition of energy. Consider the empirical facts that if the ratio, Ce =C0; decreases for increasing M at constant C0 and increases for increasing C0 at constant M; the sorption reaction must become more favorable under con0 ditions of higher M and lower C0 ; i.e. DG0 must decrease (or increase negatively) for increasing M and decreasing C0 : There are obviously many alternative 0 formulations to account for a negative increase in DG0 for the sorption reaction, as seen in the Langmuir and Freundlich sorption isotherms. We assume that the free energy change of sorption decreases linearly with the concentration of algal biomass (M) and with the reciprocal of the initial heavy metal concentration (C0 ), then M 00 0 ðbo0Þ; ð7Þ DG ¼ DG þ bRT C0 where b is a negative constant and DG0 the standard free energy change. Note that b should be less than zero, otherwise the reaction cannot proceed. At equilibrium, Eqs. (6) and (7) can be combined. Assuming DG ¼ 0; M Ce DG ¼ 0 ¼ DG0 þ bRT RT ln ; ð8Þ C0 C0 ln

Ce C0

¼

DG0 M þb : RT C0

0 Ce DG M þb ; ¼ exp C0 C0 RT 0 DG bM exp : ¼ exp C0 RT

ð9Þ

By defining a ¼ expðDG0 =RTÞ; the expression (5) can be obtained. Note that DG0 is a function of temperature only [29]. Under normal experimental conditions, the difference in temperature between the beginning and end of an experiment is not significant, therefore DG0 can be taken as zero. Consequently, the constant, a; is equal to 1 (under experimental conditions, a may take on other values less than or larger than 1, as shown and discussed later). Now consider the situation when the sorption system is not in equilibrium, i.e. DGa0: In turn, we can obtain another expression from Eqs. (6) and (7)

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Since the absolute value of b is small, the difference between b0 M=C00 and bM=C0 is negligible. Hence,

as follows: 0 Ce DG DG bM þ ; ¼ exp RT C0 C0 0 DG DG M : ¼ exp exp b RT C0

ð90 Þ 0

Again, after defining a ¼ expðDG DG=RTÞ; an expression can be obtained, of the same form as Eq. (5). This implies that the application of Eq. (5) to fit experimental data does not depend on whether the system is in equilibrium or not; the difference is simply reflected in the value of the coefficient, a: Now, consider a closed algae–metal system, where the mass balance equation for heavy metal is as follows: C0 ¼ Ce þ X;

ð10Þ

where X is the sorbed heavy metal calculated as weight per volume (mg/l). After substituting Eq. (5) into Eq. (10) and defining x=m ¼ X=M; the expression for the metal content per unit algal biomass, x=m; as a function of M=C0 is x 1 a expðbM=C0 Þ : ¼ m M=C0

ð11Þ

By combining Eqs. (5) and (11), the relationship between the metal content per unit algal biomass (x=m) and the ratio, Ce =C0 ; can be derived as follows: x 1 Ce =C0 ¼b : m lnðCe =aC0 Þ

ð12Þ

Eq. (12) shows clearly an important difference from the widely used Freundlich and Langmuir sorption isotherms. In this equation, the metal content per unit algal biomass is expressed as a function of both the equilibrium and initial metal concentrations rather than a function of the equilibrium metal concentration alone, as expressed in the isotherm equations. The model has the advantage of being simple in form and can be applied to a set of experimental data under both equilibrium and non-equilibrium conditions. The value of b reflects the metal sorption ability of algae. The higher the absolute value of b; the bigger the slope of the curve for Eq. (5), and the higher the sorption ability. As shown from Eq. (5), the constant, a; should take a value of 1 under ideal conditions. However, a; may also take on values either larger or smaller than 1 under actual experimental conditions. In the case where a is greater than 1, it can be demonstrated mathematically that this is due to a constant mass loss of metal, g (e.g. during any rinsing procedures where samples are filtered and/or sorption of metal to the flask wall). Consider Eq. (5) and let C00 ¼ C0 g: Then, Eq. (5) can be written as Ce Ce 0M 0 ¼ exp b ¼ a : C00 C00 C0 g

Ce Ce Ce ¼ ¼ 0 aC0 a0 C00 a ðC0 gÞ and Ce Ce : o C0 C0 g Thus, it can be deduced that a0 > a ¼ 1: It is interesting to point out that, when the value of a is greater than 1, a non-monotone relationship for x=m vs. M=C0 and for x=m vs. Ce =C0 can be predicted by Eqs. (11) and (12). Also if a > 1; by differentiating Eqs. (11) and (12), an expression of the maximum for x=m can be obtained: x b ¼ m max 1 bðM=C0 Þc M ð13Þ ¼ a bexp b C0 c when M 1 a exp b ¼ ; C0 c 1 bðM=C0 Þc

ð14Þ

where ðM=C0 Þc is the critical value of M=C0 : However, if a > 1; the value of x=m calculated from Eqs. (11) and (12) may take on negative values when M=C0 o lnðaÞ=b: This represents a limit for the application of this model. On the other hand, a may also take on values much lower than 1. One possible reason is that the actual initial metal concentrations (C0 ) in the algae–metal system are lower than the predesigned values due to errors in solution preparation or precipitation of metals. Another possible reason is that a set of relatively high values of M=C0 (either very high M or very low C0 ) was used in fitting the model.

3. Materials and methods A series of experiments were designed to test the model for the sorption of Cd, Cu, Pb and Zn using living or heat-treated algal biomass. The algal strains used were tropical fresh-water species, acclimatized by exposure to various concentrations of Cd and Cu. The species were identified as Oocystis sp. (about 5 mm 7 mm) and Chlorococcum sp. (average diameter of 5 mm). The algae were cultured at a light intensity of 5000 Lux and room temperature (about 281C), with the composition of culture media following that of Ting et al. [30]. The heavy metals were used in the form of chloride salts (CdCl2 . 1.5H2O, CuCl2 . 2H2O, PbCl2 . H2O, ZnCl2).

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K.Y.-H. Gin et al. / Water Research 36 (2002) 1313–1323 Table 1 Experimental conditions of the batch tests for metal sorption Test

Algae

Metal

pH

Metal concentration (mg/l)

Biomass concentration (mg/l)

na

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

Oocystis Oocystisb Oocystis Oocystis Oocystisb Oocystis Oocystis Oocystis Oocystis Oocystis Chlorococcum Chlorococcum Chlorococcum Chlorococcum Chlorococcum Chlorococcum Chlorococcum

Cd Cd Cd Cu Cu Cu Pb Pb Zn Zn Cd Cu Cu Pb Pb Zn Zn

7.5 7.5 7.5 5.5 5.5 5.5 5.5 6.5 5.5 7.0 7.5 3.5 5.5 3.5c 4.5c 4.5 6.5

5 10 0.5–35 10 10 0.5–25 20 10, 20, 30 20 2, 5, 8, 10, 12 2, 5, 8, 10 5.5, 3.5 5, 10, 15 5, 10 5, 10 1, 3, 5, 10 5, 10

2–171 6.5–345 28, 51 2.5–304 6–338.5 4.5, 60 2.5–80.5 16–80 0.5–157.5 6, 30, 140, 100 10–60 12, 25, 73, 143 13, 26, 77, 154 14, 48, 79, 105 11–225 33, 100, 170 8.5–130

12 7 21 10 7 10 12 9 11 13 12 8 12 8 12 12 12

a

Sample number. Heat-treated algal biomass was used. c The pH were adjusted separately before mixing algal suspension with metal solution. b

Table 2 Experimental conditions of batch tests to determine the effect of pH on the model using the fresh biomass of Oocysis sp. Test

Metal

pH

Metal concentration (mg/l)

Biomass concentration (mg/l)

Sample number

18 19 20 21 22 23 24 25 26 27

Cd Cd Cd Cd Cd Cu Cu Cu Cu Cu

4.5 6.0 7.5 9.0 10.5 2.5 3.5 4.5 5.5 7.0

2 2 2 2 2 10 2, 5, 8, 10 2, 5, 8, 10 0.5–35 10

7–104.5 7.5–99 1.0–179 7–134 8–58 8.0–249 7, 41.5, 200 1.0, 20, 115 44 23.5–373

7 9 8 7 6 9 12 11 10 9

The batch experiments were divided into two parts. In the first part, 17 tests were carried out at a selected initial pH, as given in Table 1. In the second part, 10 additional tests were carried out to test the effects of pH on the applicable range of the model (Table 2). Algal cultures were first harvested by centrifugation or filtration (0.45 mm membrane). The biomass was then rinsed with deionized distilled water (DDW) three times and then adjusted to a certain volume. For experiments conducted with heat-treated biomass, the collected fresh algae were treated by heating in an oven (1031C) for 3 h. The dried algae were then re-suspended by ultrasonic treatment (microscope examination showed that the

algal cells were still intact). A certain amount of algal biomass was then added to a series of flasks containing a nutrient-free solution of heavy metal. The pH for all these bottles were eventually adjusted to the desired level, except for the two experiments in which the pH were adjusted separately for algal and metal solutions before mixing (Tests 14 and 15, refer to Table 1). The bottles were then placed on a shaker with rotating velocity 60–80 rpm for 72 h at room temperature (B281C). After the incubation, the algae were filtered onto 0.45 mm filter membrane, and the algae-free solution (filtrate) was collected for measurement.

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pH values were measured using a digital Horiba F-22 pH meter. Algal biomass was measured as follows: the samples were filtered onto pre-weighed 0.45 mm membrane, dried at 1031C for 24 h, cooled in a desiccator for 24 h, and weighed to obtain the dry weight of algae. Metal concentration was measured using a AA-6701F SHIMADZU Atomic Absorption Spectrophotometer (flame continuous mode). For measurement of metal concentration in the algae sample, the filter membrane containing algae was digested with concentrated nitrate acid on an electrothermal plate till the sample solution became colorless (modified from that in Ref. [30]). The digested samples were then diluted with DDW so as to allow the concentration of metals to be within the measuring range of the instrument. For measurement of metal in solution, the algae-free samples were measured directly with F-AAS or measured after dilution. Correlation–regression analysis was conducted with Microsoft Excel 97.

4. Results and discussion 4.1. Application of the model The experiments conducted were initially focused on Cd and Cu sorption. From the results, it can be seen that the exponential equation (Eq. (5)), Ce =C0 ¼ a expðbM=C0 Þ; is able to fit the experimental data reasonably well for the sorption of Cd and Cu by the algal biomass of both Oocystis sp. and Chlorococcum sp. (either in living or dead form) at different pH (Figs. 1a, 2a, 3a and 4a). The experiments conducted with both different initial metal concentrations and biomass concentrations (Tests 3, 6, 11–13, refer to Table 1) test the applicability of the model (Figs. 3a and 4a). The results of metal content per unit algal biomass, x=m (calculated with Eqs. (11) or (12) according to the values of a and b obtained from fitting Eq. (5)) are also consistent with the experimental data, particularly for higher values of M=C0 ; where the effect of mass loss is less significant (Figs. 1b and c, 2b and c, 3b and c, 4b and c). (Note that because of the more significant effects of mass loss and experimental errors at lower values of M; the calculated values of x=m deviated from the experimental data more significantly for lower values of M=C0 ; compared to higher values.) Furthermore, nonmonotone curves for the relationships of x=m vs. M=C0 and x=m vs. Ce =C0 were also observed for the experiments conducted with the same initial cadmium concentrations, as shown in Figs. 1b and c. However, these non-monotone characteristics were not observed for other experiments (Tests 3, 4, 6 and 7). Some possible explanations for this are as follows: (1) for the experiments conducted with different initial metal and biomass concentrations (i.e. Tests 3, 6, 10–17), the value

Fig. 1. Experimental data of cadmium sorption by fresh or heat-treated biomass of Oocystis sp. with the same initial metal concentration at an initial pH of 7.5 (Tests 1 and 2, refer to Table 1): (a) relationship between Ce =C0 vs. M=C0 ; (b) relationship between x=m vs. M=C0 ; (c) relationship between x=m vs. Ce =C0 :

of M=C0 were often higher than the critical value, ðM=C0 Þc and (2) the non-monotone characteristics may be shaded or blurred by the variation in metal mass loss, as different C0 and M were used. From the viewpoint of application of the model, this problem can be lessened by limiting the mass loss as much as possible, or by using only the experimental data corresponding to the right side of the maximum value of x=m in the curves for x=m vs. M=C0 : From Eq. (12), it can be seen that x=m is expressed as a function of both Ce and C0 in the model, and is basically determined by the ratio of algal biomass to initial metal concentration, as shown in Eq. (11). We also attempted to fit the experimental data to the Freudlich and Langmuir isotherms. However, except for some experiments (i.e. those with the same C0 or same M), these two isotherms were unable to fit the data well for the experiments conducted with both different C0 and M: From Fig. 5, it can be seen that the plots for x=m vs. Ce do not show a monotone functional relationship whereas plots for x=m vs. Ce =C0 do show a functional


Fig. 2. Experimental data of copper sorption by fresh or heattreated biomass of Oocystis sp. with the same initial metal concentration at an initial pH of 5.5 (Tests 4 and 5, refer to Table 1): (a) relationship between Ce =C0 vs. M=C0 ; (b) relationship between x=m vs. M=C0 ; (c) relationship between x=m vs. Ce =C0 :

relationship. In fact, Hashim et al. [25] also found that a unique isotherm equation could not be obtained if different initial metal concentrations and algal biomass dosage were used for the same set of experiments. These results show that there is a limit to the application of the Freundlich and Langmuir isotherms. Mathematically, the expressions for the ratio of Ce =C0 ; derived from the Freundlich and Langmuir isotherms, can be obtained, respectively, as follows: Ce M Ce1=n ; ¼ 1 Kf ð15Þ C0 C0 Ce ðx=mÞmax bCe M ¼1 : C0 1 þ bCe C0

ð16Þ

Note that Eqs. (15) and (16) are expressed in terms of both Ce and M=C0 ; whereas Eq. (5) is a function of M=C0 only.

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Fig. 3. Experimental data of cadmium and copper sorption by fresh biomass of Oocystis sp. with different initial metal and algal concentrations at a constant initial pH (Tests 3 and 6, refer to Table 1): (a) relationship between Ce =C0 vs. M=C0 ; (b) relationship between x=m vs. M=C0 ; (c) relationship between x=m vs. Ce =C0 :

The fact that the model could also be used to fit the data of both Cd and Cu sorption by heat-treated Oocystis sp. (refer to Figs. 1 and 2) demonstrates that the model does not depend on whether the algae are living or dead. This implies that the metal sorption by Oocystis sp. is based on some physical–chemical mechanisms, such as ion exchange [31]. In addition, the model was able to fit the data for Pb and Zn sorption by both the biomass of Oocystis sp. and Chlorococcum sp. (the exception is for Pb sorption conducted at pH 6.5 due to precipitation) (Table 3), showing that the model is not metal-species specific nor algal-species specific. However, whether it can be applied to the sorption/ uptake of metals existing in the form of negative ions (e.g. UO2 2 ) is still open to question. From Table 3, it can be seen that the absolute values of b at higher pH were larger than those at lower pH for both Pb and Zn adsorption by Oocystis sp. and Chlorococcum sp. This reflects the higher metal adsorption ability of algal

1320


Fig. 5. The different scatter lines for the relationships for x=m vs. Ce and x=m vs. Ce =C0 when both different initial metal and algal biomass concentrations were applied. The experiment was conducted with 5, 10, and 15 mg/l for the initial Cu concentrations and 13, 25, 75, and 155 mg/l of Chlorococcum sp. at pH 5.5.

Fig. 4. Experimental data of cadmium and copper sorption by fresh biomass of Chlorococcum sp. with different initial metal and algal concentrations at a constant initial pH (Tests 11–13, refer to Table 1): (a) relationship between Ce =C0 vs. M=C0 ; (b) relationship between x=m vs. M=C0 ; (c) relationship between x=m vs. Ce =C0 :

biomass at higher pH levels, as pointed out previously in the derivation of the model. The model is also supported by the re-processed results of experimental data given by other researchers [32,10,33] (Table 4). In these studies, different metals (Pb, Ag, Cu and Cd) and different algae (Chlorella vulgaris, Scenedesmus quadricauda, and Cladophora crispata) were used, together with much higher ranges of initial metal concentrations (3.75–200 mg/l) and algal biomass (3.0– 6000 mg/l). Furthermore, according to the model fit to data obtained from experiments on a continuous fixedbed reactor with different detention time of metals (Table 4), it can be seen that the application of the model does not depend on whether sorption is at equilibrium, as already shown theoretically in the derivation of the model.

Table 3 Correlation–regression analysis using Eq. (5) for the experimental data of Pb and Zn sorption by fresh algal biomass of Oocysis sp. and Chlorococcum sp. Testa

Metal

pH

a

b

R2

nb

7c 8c 9c 10c 14d 15d 16d 17d

Pb Pb Zn Zn Pb Pb Zn Zn

5.5 6.5 5.5 7.0 3.5 4.5 4.5 6.5

0.9827 F 0.9973 0.9169 0.9949 0.9684 0.9821 0.9361

0.0688 F 0.0086 0.0173 0.0026 0.0138 0.0020 0.0195

0.9615 0.1378 0.9988 0.9641 0.9208 0.9522 0.8928 0.9188

12 9 11 11 8 12 12 12

a

The initial metal concentrations and the concentrations of algal biomass are given in Table 1. Sample number. c Conducted with the alga, Oocystis sp. d Conducted with the alga, Chlorococcum sp. b

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Table 4 Reprocessed experimental results of batch or continuous fixed-bed reactor for metal sorption by dried algal biomass from Aksu and Kutsal [10], Harris and Remelow [32] and Aksu et al. [33]. The pH for all experiments was 5.0. Data were fitted with Eq. (5) Algae

Metal

C0 (mg/l)

M (mg/l)

R2

n

Ref.

Chlorella vulgaris C. vulgaris C. vulgaris C. vulgaris C. vulgaris C. vulgaris Scenedesmus quadricauda S. quadricauda Cladophora crispatac C. crispatac C. crispatac C. crispatac

Pb Pb Pb Pb Ag Cu Ag Cu Cd Cd Cd Cd

50 100 200 F 3.75 5 3.75 5 25, 175 25, 175 25, 175 25–175

250–1000 250–1000 250–1000 F 1000–6000 1000–6000 1000–6000 1000–6000 2.89–52 2.89–52 3.35–54 2.89–52

0.9950 0.9904 0.9960 0.9222a

6 6 6 18 6 6 6 6 18 18 18 39

(1) (1) (1) (1) (2) (2) (2) (2) (3) (3) (3) (3)

b

0.9971 0.9498 0.9293 0.9243d 0.8940d 0.8315d 0.9393e

a

Reprocessed data from the three preceding batches. Not applicable due to the high ratio of M=C0 (1600) where the removals of almost all samples were close to 100%. c Conducted in a continuous fixed-bed column. The residual concentrations of Cd in the effluent were calculated according to the removal efficiencies. d Integrated processed results of two experimental runs with flow rates of 3.2, 6.0 and 9.0 ml/min, respectively. e Integrated processed results of five experimental runs with flow rate of 3.2 ml/min. (1)FAksu and Kutsal [10]. (2)FHarris and Ramelow [32]. (3)FAksu et al. [33]. b

Table 5 Correlation–regression analysis in fitting the experimental data of Cd and Cu sorption by fresh algal biomass of Oocysis sp. at different pH levels with Eq. (5)a Tests

Metal

pH

a

b

R2

nb

18 19 20 21 22 23 24 25 26 27

Cd Cd Cd Cd Cd Cu Cu Cu Cu Cu

4.5 6.0 7.5 9.0 10.5 2.5 3.5 4.5 5.5 7.0

1.3925 1.1497 0.9117 0.937 0.6594 F 0.9994 0.9970 0.9668 F

0.0302 0.0326 0.0253 0.0350 0.0465 F 0.0004 0.0035 0.0158 F

0.8666 0.9783 0.9748 0.9599 0.9631 0.5431c 0.9869 0.9609 0.9802 0.0006c

7 9 8 7 6 9 12 11 10 9

a

For Tests 18–22 (Table 2), the initial Cd concentrations for all experiments were 2 mg/l while the concentrations of algal biomass varied between samples. For Tests 23–27, the initial Cu concentrations were constant while the concentrations of algal biomass varied between samples (Table 2). b Sample number. c Failed in fitting the model.

4.2. Effect of pH on the model In order to test whether the model can be applied to other pH conditions, a series of experiments (experiments 18–27, Table 2) were conducted with the live algal biomass of Oocystis sp. for Cd and Cu sorption at different initial pH levels. In general, the model could be applied to a broad range of pH levels (Table 5), as

reflected by the values of R2 : However, the applicable ranges of pH were different for Cd and Cu, with Cd having a wider range than Cu. For Cd, the values of R2 were still satisfactory at pH values where precipitation might occur (e.g. pH 10.5). However, for low values of pH, the value of R2 decreased significantly, e.g. at pH 4.5, R2 ¼ 0:8666: For Cu, the model could be applied satisfactorily within the pH range from 3.5 to 5.5, but

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the values of R2 decreased drastically when the initial pH was as low as 2.5 (R2 ¼ 0:5431) or as high as 7.0 (R2 ¼ 0:0006) (Table 5). Note that the model failed for Pb sorption by Oocystis sp. at pH 6.5 (Table 3) and for Zn sorption by Chlorococcum sp. at pH 7.0 (data not shown). From the above results, the applicable range of pH for the model depends on the specific combination of metal and algal species. In general, the pH range has two limits: a ‘‘lower point’’ and a ‘‘higher point’’. The ‘‘lower point’’ may be reasonably assumed to be the ‘‘inflection point’’ of zeta potential where the algal cell surface carries an approximate zero net charge [25]. When the pH is lower than the ‘‘inflection point’’, the sorption of metal can be negligible (or is very low if it still occurs due to ‘‘entrapment’’ or some other physical mechanism). The low sorption of metals at low pH is also reflected by the small absolute value of the coefficient b; as observed in Table 3 and Fig. 4 (for Cu). This is consistent with other researchers’ results [32,12,25,34]. The ‘‘higher point’’ depends mostly on the solubility of the specific metal in water. However, it may also depend on the affinity of a specific algal species to a specific metal, and the experimental conditions (e.g. ion intensity, temperature, chelatins). When precipitation plays a more important role than sorption by algae, the model is no longer applicable. Nevertheless, the model can still be used to fit a set of experimental data when the pH is quite high, as long as the initial metal concentration is within its solubility, as shown by the results for Cd sorption by Oocystis sp. at pH 10.5 when C0 was 2.0 mg/l (Table 5).

5. Conclusions *

*

*

The developed model has the following advantages: (a) simplicity of form, (b) theoretical derivation and (c) it can be applied to a set of experimental data under both equilibrium and non-equilibrium conditions. From this study, it was found that the model gave a good fit to the data for sorption of Cd, Cu, Pb and Zn by both living and heat-treated biomass of Oocystis sp. and Chlorococcum sp. at fixed pH levels. The robustness of the model was also demonstrated by the re-processed results of experimental data given in the literature. It was also shown that the model could be applied to a broad range of pH for Cd and Cu sorption by algae, although the range depended on the species of metal and algae present. As this model was derived through a thermodynamics approach, it does not provide any information on the actual sorption mechanism. Further studies to derive this model based on assumptions of

mechanisms, such as ion exchange and Coulombic attraction, would be useful. In addition, the model is limited because it does not specifically consider the effect of pH (or concentration of protons). (This could be incorporated, for example, by quantifying the relationship between the coefficients of the model and pH.) Nevertheless, as the model stands, it can be used to predict the heavy metal concentration in solution and the metal sorption capacity of algae for both batch and continuous algae–metal systems within the range of pH most possibly used in practice.

Acknowledgements The authors gratefully acknowledge the technical assistance from Seet Joo Luang, S.G. Chandrasegaran, Choy Moon Nien, Chong-Teo Beng Lay, Liang Choon Chuan and Yong Tat Fah. This study was funded by the National University of Singapore.

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