Ionic strength effect on copper biosorption by Sphaerotilus natans: equilibrium study and dynamic modelling in membrane reactor

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40 (2006) 144– 152

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Ionic strength effect on copper biosorption by Sphaerotilus natans: equilibrium study and dynamic modelling in membrane reactor F. Beolchinia,, F. Pagnanellib, L. Torob, F. Veglio`c a

Dipartimento di Scienze del Mare, Universita` Politecnica delle Marche, Via Brecce Bianche, Ancona, Italy Dipartimento di Chimica, Facolta` di S.M.F.N., Universita` degli Studi ‘‘La Sapienza’’, P.le A. Moro, 5, 00185 Roma, Italy c Dipartimento di Chimica, Ingegneria Chimica e Materiali, Universita` degli Studi di L’Aquila, 67040 Monteluco di Roio, L’Aquila, Italy b

ar t ic l e i n f o

A B S T R A C T

Article history:

Biosorption of copper by Sphaerotilus natans in different conditions of ionic strength and pH

Received 14 February 2005

was studied by performing sorption tests in batch and membrane reactors. Equilibrium

Received in revised form

batch tests evidenced the negative effect of ionic strength and the positive effect of pH on

26 October 2005

biosorption performances: the highest determined value for copper specific uptake, q, was

Accepted 27 October 2005

about 60 mg/g at pH 6 and about 15 mg/g at pH 4. A competitive equilibrium model was

Available online 6 December 2005

successfully fitted to experimental data at different ionic strength levels to account for

Keywords:

copper–sodium competition. In membrane reactor tests, experimental profiles of copper

Copper

concentration in the permeate vs. time did not evidence a significant effect of ionic

Biosorption

strength at low pH values (4 and 5). On the other hand a more remarkable effect of ionic

Membrane

strength on copper concentration in the permeate was observed at pH 6. Experimental

Equilibrium

profiles of continuous biosorption in the membrane reactors were successfully simulated

Kinetics

by developing a dynamic model accounting for Cu–Na competition and for binding ability

Modelling

of cells fragments. & 2005 Elsevier Ltd. All rights reserved.

1.

Introduction

Biosorption of heavy metals is an alternative technology to ion exchange and active carbon sorption, aimed at the treatment of industrial wastewaters by using wastes from agricultural and industrial activities, seaweed and specially propagated biomasses of bacteria, yeast and fungi as alternative sorbent materials (Veglio` and Beolchini, 1997). Investigation of the physico-chemical mechanisms involved in metal removal (such as physical adsorption, ion exchange, surface complexation and surface micro-precipitation) is a fundamental step for the optimization of the operating conditions, product development and process design. MeCorresponding author. Tel.: +39 071 2204225; fax: +39 071 2204650.

E-mail address: [email protected] (F. Beolchini). 0043-1354/$ - see front matter & 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.watres.2005.10.031

chanistic equilibrium models accounting for the effect of the operating conditions (such as pH and ionic strength) (Volesky, 2001) can be fundamental for mechanism investigation but also as constitutive equations in the development of dynamic models in continuous biosorption processes. Biosorbent can be generally used in fixed bed columns only after preliminary immobilization in polymeric matrixes (because of the little dimensions and low mechanical strength of the particles) leading to additional costs for the adsorbent preparation and increasing mass transfer resistance. An alternative configuration can be considered using directly free cells in continuous biosorption processes by the application of a tangential flow filtration device to retain the cells in the

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145

Abbreviations and notations

KNa (L/meq) Na binding reaction equilibrium constant,

b (L/mg) Langmuir model parameter Ceq (mg/L, meq/L) copper equilibrium concentration

q (mg/g, meq/g) copper specific uptake qmax (mg/g) Langmuir model parameter Stot (meq/g) total active sites concentration on the

competitive model parameter

in solution

CIN (meq/L) copper concentration in the inlet stream CNa (meq/L) Na concentration in solution COUT (meq/L) copper concentration in the outlet stream

CRET (meq/L) copper concentration inside the reactor F (L/h) permeate (and inlet) flow rate KMe (L/meq) metal binding reaction equilibrium con-

V (L) WSP X (g/L) s

biomass, competitive model parameter reaction volume water soluble polymers biomass concentration copper retention coefficient

stant, competitive model parameter

system (Brady et al., 1976; Tanaka et al., 1994; Bayhan et al., 2001; Chang and Chen, 1999; Veglio` et al., 2000). This configuration using free cells ensures not only good contact and a continuous separation among solid particles and solute in the liquid but also allows working at high fluxes over prolonged time periods. The economic feasibility of the process is further improved if biosorbents are regenerated by means of acid solutions (Vijayaraghavan et al., 2005) and reused in subsequent sorption/desorption cycles. The interpretation and representation of experimental data by dynamic models can help to investigate about the different physico-chemical phenomena occurring in the system and to have a deeper understanding of biosorption mechanisms operating in metal removal. Dynamic models accounting for the effect of the operating conditions are then fundamental mathematical tools in process development and design. Previous works have demonstrated the ability of Sphaerotilus natans to adsorb efficiently toxic metals, such as copper and cadmium (Esposito et al., 2001) and the equilibrium of biosorption has been modeled in single and multimetal systems (Pagnanelli et al., 2002). Dynamic modelling was previously performed (Beolchini et al., 2004, 2005) considering the unsteady mass balances of the metal in the system and the equilibrium parameters obtained by biosorption batch tests using Langmuir models. The proposed dynamic models developed for single metal and binary biosorption in membrane reactors gave an improved representation of experimental data with respect to simple simulations by introducing a minimum number of adjustable parameters (either one or two). Nevertheless, a comparison among data and model predictions denoted that those models were not a perfect representation of the experimental trend, systematically underestimating or overestimating the data (Beolchini et al., 2005). In this work the effect of ionic strength on copper biosorption by Sphaerotilus natans is investigated by performing equilibrium sorption tests in batch systems and continuous biosorption tests in membrane reactors at different salt levels. An original model accounting for the effect of the ionic strength in batch tests was successfully developed and used as constitutive equilibrium equation for dynamic simulation of continuous biosorption tests in membrane reactors at different salt levels.

2.

Materials and methods

2.1.

Microorganisms

Sphaerotilus natans is a Gram-negative bacterium isolated from the waste streams of a water purification plant where is generally present and responsible for bulking phenomena. The cultivation medium consists of meat peptone (7.5 g/L) and yeast extract (7.5 g/L) and the operating conditions are 25 1C and 1 atm with an air flux rate of 0.5 vvm in a bioreactor vessel of 3 L. The biomass produced was separated by centrifugation, washed by distilled water, lyophilized and stored (Esposito et al., 2001).

2.2.

Experimental tests and analytical determinations

Each equilibrium test at a specific condition of pH and ionic strength was carried out by using an experimental procedure named as ‘‘Subsequent Addition Method’’ (S.A.M.) (Pagnanelli et al., 2000), which allows the whole sorption isotherm to be obtained at a constant equilibrium pH by using only one sample, saving time, reagents and biomass. The experimental procedure consists of successive spikes of a heavy metal concentrated solution to 100 mL of a cellular suspension (3 g/L) kept in a 250 mL shaken flask under magnetic stirring. For each metal addition, residual metal concentration was determined on samples collected after the system had reached equilibrium conditions (30 min). Some tests without biomass were also performed in order to evaluate the possible contribution of the precipitation mainly for high pH values. Metal specific uptake q (mg/g of lyophilized biomass) was calculated by the mass balance of the metallic ion in the system. Membrane biosorption tests were performed as follows: a suspension of the biomass (3 g/L) was introduced in a temperature-controlled glass reactor (liquid volume 100 mL, temperature 30 1C, ionic strength as specified) and fed through a membrane module by a peristaltic pump (tangential velocity 0.3 m/s; transmembrane pressure 200 kPa). Figure 1 shows a schematic diagram of the employed system. Further details about experimental apparatus can be found elsewhere (Beolchini et al., 2001). A polysulfone membrane was used with 100,000 Da molecular weight cut off (MWCO) and a total area of 36 cm2. The mixing in the reactor was

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Feed Co (mg/L)

40 (2006) 144– 152

Table 1 – Factors and levels investigated

Retentate

Factor

Levels

x (g/L) CSTR

pH NaNO3

UF/MF

Permeate C (mg/L) Figure 1 – Schematic diagram of the membrane biosorption apparatus.

ensured both by a magnetic stirrer placed into the reactor and by the recirculation flow of the retentate stream. Consequently the reactor can be assumed to be as a continuous stirred tank reactor (CSTR) (Beolchini et al., 2001). The copper solution (CuSO4, Cu 100 mg/L) was then fed to the reactor by a peristaltic pump, paying attention to control its flow rate: this was always equal to the permeate flow rate produced in the membrane module. This control was necessary because the permeate flux in general decreases during time due to the fouling characteristics of the suspension, as already reported for this cells harvesting system (Cheryan, 1998). The flux decreasing (F) was monitored during time and in this way the reactor worked at a constant volume. pH was controlled at a fixed value, according to operating conditions. Different samples of permeate and retentate were collected during time and copper was determined by a Varian atomic absorption spectrophotometer (Varian SPECTRA 2000). In the case of permeate, no cell harvesting was needed because all cells were completely retained by the membrane. In the case of retentate, cells were previously separated by centrifugation at 8000 g for 10 min.

3.

Results and discussion

Table 1 shows factors and levels investigated both for equilibrium and for membrane reactor tests. pH and ionic strength are among the most influential factors affecting biosorption performances because of the nature of the active sites of biomasses and the type of interactions among these active sites and ionic species in solution. The active sites involved in biosorption of heavy metals can be extremely heterogeneous according to the wide variety of biosorbents used for these applications. Wastes from agriculture, wood and paper industry are mainly made up of cellulose and lignin containing different kinds of polyphenolic and polyhydroxyl groups, which are active in metal removal (Bailey et al., 1999; Williams et al., 1998). Bacterial biomasses are characterized by carboxylic, phosphordiesters, phosphoric, amines and hydroxyl sites that are typical of the peptidoglycan, teichoic and teichuronic acids of the membrane cell wall (Cox et al., 1999; Pagnanelli et al., 2004). Seaweed and especially brown seaweed containing high amount of alginate (polymer mannuronic and guluronic acids) are rich of carboxylic, amines, phosphates, hydroxyl and sulphate groups (Chen et al., 1997). Weakly acidic groups can be dissociated or not (and then available for metal binding by surface complexation

4 No

5 0.1 M

6 0.2 M

mechanism) according to the equilibrium pH conditions of the aqueous suspension. On the other side, strong acid sites (binding heavy metals especially by ion exchange reactions) are significantly affected by concentration in solution of other ubiquitous ionic species such as sodium reducing heavy metal removal for competition effects (Schiewer and Wong, 2000). As shown in Table 1, pH ranged from 4 to 6. These levels were suggested by previous results (Esposito et al., 2001) which evidenced that biosorption increased with pH. Obviously no experiments were performed at pH higher than 6, in order to avoid precipitation phenomena which might be confounded with biosorption. As concerns ionic strength levels, three different values were chosen (Table 1): the first one, with no addition of NaNO3, was considered as a low ionic strength level, the other two were relatively high (0.1 and 0.2 M) in order to simulate many typical wastewater (Schiewer and Wong, 2000). Regarding copper speciation, in the investigated pH range it is mainly present in the form of Cu2+ and its speciation is not significantly influenced by the presence of NaNO3 (prediction of Medusa Software (2001) by Ignasi Puigdomenech).

3.1.

Equilibrium

The present equilibrium study was performed in order not only to characterize Sphaerotilus natans equilibrium behavior in different pH and ionic strength conditions, but also to find equilibrium parameters which are fundamental for the further dynamic simulation in the membrane process. Figure 2 shows experimental data for copper sorption equilibrium by Sphaerotilus natans for different pH and ionic strength levels (Table 1). It can be observed, as expected, the positive effect of pH on biosorption performances: the highest copper specific uptake (q ffi 60 mg=g) was obtained at pH 6 without NaNO3 addition, while a dramatic reduction (to 15 mg/g) was observed at pH 4. The relatively high copper specific uptake (q ffi 60 mg=g ffi 1 mmol=g) confirms the good sorption abilities of Sphaerotilus, as it comes out from a comparison with literature (Table 2). As concerns the effect of pH, the observed profiles confirm previous results (Esposito et al., 2001): acidic sites of the biosorbent are more available for copper complexation, due to a major dissociation at pH 6 rather than pH 4. The analysis of the data at each pH without NaNO3, with NaNO3 0.1 M and with NaNO3 0.2 M, denoted that there is not a significant difference among the chosen salt levels. Consequently, considering the negligible effect of NaNO3 addition in the investigated range, experimental values obtained in the presence of NaNO3 (any concentration) were all grouped in one series of data, named high ionic strength. On the other hand, data obtained with no NaNO3 added were named low ionic strength.

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70 no NaNO3 0.1 M NaNO3 0.2 M NaNO3

0.5 low ionic strength high ionic strength

60

0.4

0 0

20

40

(a)

60 80 Ceq (mg/L)

100

120

qma 40

0.3

30

0.2

20

no NaNO3 0.1 M NaNO3 0.2 M NaNO3

0.1

b

10

30

20

b (L/mg)

50

10 qmax (mg/g)

q (mg/g)

20

q (mg/g)

147

40 (20 06) 14 4 – 152

0

0 3

4

5 pH

6

7

Figure 3 – Estimated values for Langmuir model parameters (experimental data in Fig. 1).

10

0 0

20

(b)

40 60 Ceq (mg/L)

80

100

60

q (mg/g)

50 40 30

no NaNO3 0.1 M NaNO3 0.2 M NaNO3

20 10 0 0

(c)

50

100 150 Ceq (mg/L)

200

250

Figure 2 – Experimental data for copper sorption equilibrium by Sphaerotilus natans at different pH and different ionic strength levels. Lines were calculated by Langmuir model.

Table 2 – Uptake capacities for copper(II) of various biosorbents Adsorbent

Lignite S.fluitans A.nodosum C.vulgaris R.arrhizus P.aeruginosa A.oryzae Schizophyllum commune P. pulmonarius CCB019 Arthrobacter sp.

Maximum q (mmol/g)

Reference

0.1 0.96 0.99 0.67 0.25 0.3 0.07 0.025

Kaewsarn, 2002 Kaewsarn, 2002 Kaewsarn, 2002 Kaewsarn, 2002 Kaewsarn, 2002 Kaewsarn, 2002 Kaewsarn, 2002 Veit et al., 2005

0.1

Veit et al., 2005

0.16

Veglio` et al., 1998

tion at pH 4 in the case of high ionic strength (both concentrations of NaNO3) with respect to low ionic strength (no NaNO3 added). On the other hand, this reduction is less remarkable (even if it is always present) at pH 6. Sodium was reported to interact and compete with metals for electrostatic binding to biomass active sites (Schiewer and Wong, 2000). The interaction pH-ionic strength can be then explained considering a constant sorption decrease due to ionic strength (which interact with ion-exchange sites) over a pHdepending metal binding (complexation) due to site dissociation. The decrease of copper specific uptake due to ionic strength effect can be estimated as about 6–8 mg/g for any pH value: this is obviously very significant when the overall copper specific uptake is lower than 20 mg/g (pH 4), and it is poorly remarkable when compared with a specific uptake of about 60 mg/g (pH 6). According to this interpretation the unrevealed difference among the two salt levels can be due to a complete saturation of active sites for ion exchange even for the lower salt level (NaNO3 0.1 M). A preliminary approach in equilibrium data modeling was performed by fitting Langmuir adsorption model (Langmuir, 1918) to experimental data: q¼

As concerns the effect of ionic strength for the different pH levels, an interaction seems to occur among these operating factors. Figure 2(a) shows a significant reduction of biosorp-

qmax bCeq . 1 þ bCeq

(1)

Lines in Fig. 1 were calculated by Langmuir model (Eq. (1)); Fig. 3 shows the estimated values for parameters qmax and b at different pH (3, 4 and 5) and ionic strength (high ionic strength and low ionic strength). Figure 3 denotes the steep increase of maximum metal specific uptake (parameter qmax) as pH increases. This enhancement in the maximum biosorption abilities with pH is probably due to a major dissociation of biosorbent’s acidic sites, that are available for biosorption. It is also possible to observe that ionic strength especially acts on the equilibrium constant (parameter b) rather than on qmax. An analogy with inhibition of enzymatic reactions (Bailey and Ollis, 1986) led us to suppose a competitive mechanism: only the affinity constant (corresponding to parameter b) is modified by the presence of a competitive inhibitor. According to a competitive mechanism, the following equation can be written for the

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1.5

1

0.5

0 0

0.5 1 1.5 experimental q (meq/g)

2

Figure 4 – Scatter diagram of calculated (by Eq. (2)) vs. experimental values of copper specific uptake.

2.0

3.2.

1.0

Figures 6–8 show copper concentration in the permeate (named as COUT) under different conditions of pH and ionic strength (experimental design in Table 1). Simulations performed in the case of no biomass in the reactor, blank simulation, (Beolchini et al., 2001) are also reported as a dotted line in order to evaluate the effectiveness of

0.0 3

4

5 pH

6

7

3

4

5 pH

6

7

(a) 2.0 KMe (L/meq)

Dynamics modeling in membrane reactor

1.5 1.0 0.5 0.0

0.020 KNa (L/meq)

COUT F

2 COUT (meq/L)

(b)

0.2

2.5

0.015 0.010 0.005

1.5

0.12

1

0.08

0.5

0.04

0

0.000 3

4

(c)

5 pH

6

7

0

0.5

(a)

Figure 5 – Competitive sorption model parameters (Eq. (2)).

q¼

COUT (meq/L)

Stot KMe Ceq , 1 þ KMe Ceq þ KNa Cna

(2)

where all quantities are expressed in equivalents of metal per gram of biomass (q) and per liter of suspension (Ceq). Eq. (2) was fitted to experimental data obtained at different levels of NaNO3 concentration, previously reported in Fig. 2. Figure 4 shows the calculated vs. experimental values for copper specific uptake in order to check the ability of Eq. (2) to fit the obtained experimental data. Figure 5 reports the estimated values for Eq. (2) parameters together with

1 1.5 time (h)

2

2.5

0.16

1.5

0.12

1

0.08

0.5

0.04

0 0 (b)

0 2.5

0.2 COUT F

2 metal specific uptake as a function of metal and sodium concentration:

0.16 F (L/h)

Stot (meq/g)

3.0

standard errors, as a function of solution pH. It can be observed that parameter STOT increases with pH. This course is in agreement with previously observed profiles of maximum metal uptake vs. pH, considering that STOT represents the total concentration of active sites on the biosorbent (Bailey and Ollis, 1986). Parameters KMe and KNa represent the equilibrium constants of the reactions for the formation of complexes metal-biosorbent and sodium-biosorbent, respectively (Bailey and Ollis, 1986). Figure 5 shows that while KMe increases with pH, KNa decreases. This means that an increase in pH is favorable for the metal complexation and unfavorable for sodium complexation. This is in agreement with previously observed results: an increase in the ionic strength at low pH (pH 4) affects copper biosorption at a greater extent with respect to the same increase at high pH (pH 6). The good agreement between experimental and calculated values (Fig. 4) and the relatively low error on parameters estimates (Fig. 5) confirm the suitability of the competitive model (Eq. (2)) to represent experimental sorption data at different levels of ionic strength.

0.5

1 1.5 time (h)

2

F (L/h)

calculated q (meq/g)

2

40 (2006) 144– 152

0 2.5

Figure 6 – Experimental (points) and predicted by Eq. (9) (continuous line) values for copper concentration in the permeate, for low (a) and high (b) ionic strength, at pH 4. Dotted values represent the calculated values in a blank simulation (no X). Stars represent permeate flowrate vs. time profile.

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2

0.16

1.5

0.12

1

0.08

0.5

0.04

0 0

0.5

(a)

1 1.5 time (h)

2

COUT F

2



0.16

1.5

0.12

1

0.08

0.5

0.04

0 0

0.5

(b)

1 1.5 time (h)

2



0 2.5



Figure 7 – Experimental (points) and predicted by Eq. (9) (continuous line) values for copper concentration in the permeate, for low (a) and high (b) ionic strength, at pH 5. Dotted values represent the calculated values in a blank simulation (no X). Stars represent permeate flowrate vs. time profile.

0.2

2 1.5

0.12

1

0.08

0.5

0.04

0 0

0.5

(a)

1 1.5 time (h)

2

2.5 COUT (meq/L)

0.16

0 2.5 0.2

COUT F

2.0

0.16

1.5

0.12

1.0

0.08

0.5

0.04

0.0 0.0

F (L/h)

COUT F

0.5

1.0 1.5 time (h)

2.0

F (L/h)

COUT (meq/L)

2.5

(b)

 A comparison with the blank simulation confirms the

0.2

2.5 COUT (meq/L)

0 2.5

0 2.5

Figure 8 – Experimental (points) and predicted by Eq. (9) (continuous line) values for copper concentration in the permeate, for low (a) and high (b) ionic strength, at pH 6. Dotted values represent the calculated values in a blank simulation (no X). Stars represent permeate flowrate vs. time profile.

149

biosorption. Furthermore, permeate flow-rate (equal to the inlet one, in order to have a constant volume) vs. time profile is also shown for each test. A first analysis of the reported data suggests the following remarks:

F (L/h)

COUT (meq/L)

0.2

COUT F

F (L/h)

2.5

40 (20 06) 14 4 – 152

effectiveness of Sphaerotilus natans as biosorbent in membrane processes, as already demonstrated in previous works (Beolchini et al., 2004). The effect of pH is very important also for membrane processes: very low concentrations (near to zero) of copper in the outlet stream were obtained under pH 6 (Fig. 8), while higher profiles can be observed at pH 4 and 5 (Figs. 6 and 7). This behavior confirms the positive effect of pH on Sphaerotilus sorption ability, as already observed from equilibrium tests. The effect of ionic strength is less significant as pH decreases while it is particular evident at pH 6 (Fig. 8) where COUT profile for high ionic strength is over than that at low ionic strength for each time (meaning lower metal removal for high ionic strength). A comparison with Italian legislation limits for copper concentration in wastewater (that is 1 mg/L ¼ 0:016 meq=L) evidences that permeate quality respects legislation limits within the first hour processing only in tests at pH 6 and low ionic strength (Fig. 8a). In this case further tests should be performed enhancing the biosorbent concentration, in order to optimize the wastewater treatment process.

This opposite effect with respect to batch tests (where the effect of ionic strength is less significant at pH 6 than at lower pH) can be explained by hypothesizing a partial biomass degradation in membrane reactors. Previous works using a different specially propagated biomass (Arthrobacter sp.) (Pagnanelli et al., 2000) denoted that there is a partial cell disruption due to high shear stress conditions in the membrane apparatus. In addition it was also observed that this effect was more significant for increasing pH values in the range 3–6. This was explained by considering a combined chemical degradation occurring near neutral pH which emphasizes mechanical stress effects (this was partially verified by performing discontinuous experiments in test tubes simulating continuous biosorption in membrane reactors in milder mechanical stress conditions). It is reasonable to assume that also in this system there is a correlation among pH and cell degradation so that a larger amount of cell fragment is present in the reactor at pH 6. This hypothesis is confirmed by copper retention coefficient vs. time profile monitored for any investigated condition (Fig. 9) and calculated according to the following equation: s¼1

COUT , CRET

(3)

where COUT and CRET were experimentally determined during time. It is evident that metal retention is not equal to zero (as it happens without biomass in the membrane module considering that membrane pores dimension is significantly higher than copper ion species in aqueous solutions). Non ideal behavior denoted in Fig. 9 (i.e. not zero metal retention) might be due to the presence of biomass fragments which led

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Table 3 – Eq. (10) parameters for sigma vs. time profile

1

pH

low ionic strength high ionic strength

0.8 sigma

40 (2006) 144– 152

4 5 6, low ionic strength 6, high ionic strength

0.6 0.4

sa

sb

sc

0 0 0.65 0.26

0.45 0.78 0.42 0.84

0.98 0.83 9.7 7.1

0.2 0 0

0.5

1

(a)

1.5 time (h)

2

2.5

3

1

0.6

no more significant at high ionic strength. In fact, as the biomass in batch systems, cell fragments present lower copper binding ability for high ionic strength level (Rivas et al., 2003) and, as a consequence, s profile in this case tends to quite ideal values around 0.2. On the other side for low ionic strength the binding capacity of cell fragments are maximized and the metal retention coefficient at pH 6 presents quite constant values around 0.6–0.7 (far away from the ideal zero value). In analogy with studies reported in the literature on water soluble polymers (WSP) complexes with metals, that are retained by ultrafiltration membrane (Rivas et al., 2003; Rivas and Villoslada, 2000; Villoslada and Rivas, 2003), the following equation was used to fit metal retention vs. time experimental profile:

0.4

s ¼ sa þ sb expðsc tÞ,

0.2

where parameters sa, sb and sc, estimated by non linear regression procedures (Himmelblau, 1978), are reported in Table 3. Considering that no significant effect of ionic strength on s can be remarked at pH 4 and 5, data obtained at different levels of ionic strength (and at constant pH) were grouped in single series; on the other hand, two separate regressions were performed for data at different ionic strength and pH 6. Equilibrium model accounting for ionic strength level and s profiles are included in the dynamic simulation of biosorption in membrane reactor developed according to the following general assumptions (Beolchini et al., 2001, 2004):

low ionic strength high ionic strength

sigma

0.8 0.6 0.4 0.2 0 0

0.5

1

(b)

1.5 time (h)

2

2.5

3

1 low ionicstrength high ionic strength

sigma

0.8

0 0 (c)

0.5

1

1.5 time (h)

2

2.5

3

Figure 9 – Copper retention coefficient vs. time profile for different pH and ionic strength. Points were calculated from experimental data by Eq. (3), lines were calculated by Eq. (4) (parameters in Table 3).

both to a partial pore occlusion causing permeate flux decline (Figs. 6–8) and to copper binding by soluble macromolecules (released by biomass due to the shear stress). In this case it can be hypothesized that copper bound to soluble macromolecules is still in solution, but it is retained by the ultrafiltration membrane since copper complexes might be larger than membrane pores. Retention coefficient profiles observed for pH 4 and 5 for both ionic strength levels are quite similar (Fig. 9a and b), while a strong detachment can be observed at pH 6 (Fig. 9c). A comparison between all sigma profiles at a low ionic strength level (Fig. 9) evidences that a remarkable difference can be observed at pH 6 with respect to pH 4 and 5. This might be due to the previously mentioned biomass disruption more significant at pH 6 than at pH 4 and 5. Copper complexation (and hence its retention) increases with the presence of cell’s macromolecules. On the other hand, when ionic strength is high (Fig. 9c) such macromolecules interact also with sodium, reducing available macromolecule sites for copper complexation. As a consequence, the remarkable effect of pH observed at low ionic strength is

(4)

 perfect mixing (as verified in the case of control tests without biomass);

 biosorption as an equilibrium process (metal uptake rate being faster than the residence time in the reactor);

 no transport resistance in the bulk solution: metal





concentration in the bulk solution is assumed equal to the one near the solid adsorbent according to the good mixing conditions ensured by magnetic stirring and retentate recycle in the reactor; metal retention coefficient vs. time profile as given by Eq. (4), adopted on the basis of experimental data in analogy with studies on WSP complexes with metals, that are retained by ultrafiltration membrane (Rivas et al., 2003; Rivas and Villoslada, 2000; Villoslada and Rivas, 2003); constant reaction volume (since the inlet flow-rate was adjusted according to the outlet flow-rate).

Dynamic simulations were developed by considering the unsteady mass balance of the metal in the reactor (C)

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assuming that copper concentration in the reactor and in the retentate are the same: FCIN  FC  V

d dC ðqXÞ ¼ V . dt dt

(5)

In this equation a general approach is performed, where biomass concentration is not supposed as a constant. According to equilibrium hypothesis, metal concentration on the solid, q, is given by q¼

Stot KMe COUT . 1 þ KMe COUT þ KNa CNa

(6)

Eq. (6) corresponds to Eq. (2), where the equilibrium concentration is the one in the permeate instead of the concentration in the reactor (C). The most simple approach would lead us to assume that the equilibrium concentration is the one inside the reactor, and not in the permeate; nevertheless we suppose (and s profiles previously shown confirm this hypothesis) that not all copper in solution inside the reactor is available for biosorption, since it is bound to macromolecules. Consequently, equilibrium copper concentration is assumed to be the one in the permeate (and not the one in the retentate), since copper available for biosorption is solely the one that is not complexed, that is also the only one passing through the membrane and found in the permeate. This last assumption along with the analysis of ionic strength effect represent the most significant novelty of dynamic simulations presented in this paper with respect to previous works (Beolchini et al., 2001, 2004). Considering that metal is partially retained by the membrane, copper concentration in the retentate (and then in the reactor, C) can be expressed as a function of metal retention, s (Eq. (10)) and copper concentration in the outlet stream, COUT, from Eq. (3): CðtÞ ¼

COUT ðtÞ . 1  sðtÞ

(8)

where parameters a, b and g were estimated by fitting to experimental data (Figs. 6–8). Coupling Eqs. (5)–(7) and rearranging yields the following equation for copper concentration in the permeate during time: FðtÞ STOT KMe COUT dX COUT ds ðCIN  COUT Þ   ð1 þ KMe COUT þ KNa CNa Þ dt ð1  sðtÞÞ2 dt V dCOUT ¼ 1 XðtÞSTOT KMe ð1 þ KNa CNa Þ dt þ 1  sðtÞ ð1 þ KMe COUT þ KNa CNa Þ2

(9) to be integrated with initial conditions: COUT ¼ 0 for t ¼ 0. Eq. (9) was integrated by Runge–Kutta algorithms for all the investigated conditions reported in Figs. 6–8, under the hypothesis of constant biomass concentration and equal to the initial value (consequently dX=dt ¼ 0). The obtained data are represented by continuous lines showed in the same figures. A very good agreement between experimental and calculated results can be observed, especially considering that no data fitting but just a prediction was performed on the

151

basis of equilibrium study performed in batch tests also accounting for the previously hypothesized complexing ability of cell fragments denoted by non ideal s profiles during time. Furthermore, the hypothesis of constant biomass concentration might be reasonable, considering that biosorption mechanism is not dependent on biomass metabolism but it is just due to chemico-physical interactions. Consequently, even if shear stress reduces biomass cells integrity, its effect on cell wall active groups might be not significant.

4.

Conclusions

This work concerns copper biosorption by Sphaerotilus natans. An improvement on already published data was performed considering the following aspects:

 the effect of ionic strength coupled with pH on the process

 

(7)

Furthermore permeate flow-rate vs. time profile can be described by the following equation, which takes into account permeate flux decline (Cheryan, 1998): FðtÞ ¼ a  btg ,

40 (20 06) 14 4 – 152



was evidenced. Both the factors prove to be fundamental when considering real wastewaters. Equilibrium tests evidenced the negative effect of ionic strength and the positive effect of pH on biosorption performance. In membrane reactor tests, experimental profiles of copper concentration in the permeate vs. time did not evidence a significant effect of ionic strength, at low pH values (4 and 5). On the other hand a more remarkable effect of ionic strength on copper concentration in the permeate was observed at pH 6; equilibrium data in batch mode were successfully fitted by a competitive equilibrium model; dynamic data in the membrane process were successfully predicted by a mathematical model developed according to a mechanistic approach accounting for copper–sodium competition; complexing ability of macromolecules generated by cell fragments was accounted for by considering metal concentration in the permeate instead of the one in the reactor as a corrected concentration of free metal ions available for biosorption.

This dynamic model was an improvement on the previously published models, which still had a partially empirical character containing one or two parameters to be estimated during integration by fitting procedures. In this case Eq. (9) can be used to predict the biosorption-ultrafiltration integrated process: the only data that are necessary (that are equilibrium constants) can be achieved from equilibrium tests. Further work is in progress aimed at verifying the ability of Eq. (9) to predict previously published data of the same and other authors.

Acknowledgements The authors are grateful to Mr. Marcello Centofanti and Mrs. Lia Mosca for their helpful collaboration in the experimental work.

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