Immobilized cell fixed-bed bioreactor for wastewater decolorization

Immobilized cell fixed-bed bioreactor for wastewater decolorization

Process Biochemistry 40 (2005) 3434–3440 www.elsevier.com/locate/procbio Immobilized cell fixed-bed bioreactor for wastewater decolorization Bor-Yann...

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Process Biochemistry 40 (2005) 3434–3440 www.elsevier.com/locate/procbio

Immobilized cell fixed-bed bioreactor for wastewater decolorization Bor-Yann Chen a, Shan-Yu Chen b, Jo-Shu Chang b,* a

Department of Chemical and Materials Engineering, National I-Lan University, I-Lan 260, Taiwan b Department of Chemical Engineering, National Cheng Kung University, Tainan 701, Taiwan

Abstract Fixed-bed bioreactors using gel-entrapped cells of Pseudomonas luteola were utilized for azo-dye decolorization in continuous mode. The decolorization performance of the fixed-bed decolorizers was examined to investigate the effect of bed length, volumetric flow rate, dye loading rate, dye concentration in the feed, as well as the characteristics of matrix (i.e., calcium alginate (CA) and polyacrylamide (PAA)) for cell immobilization. With a constant feeding dye concentration of 50 mg/l, the beds with CA-immobilized cells had an optimal volumetric decolorization rate (nv,dye) of 30.6 mg/h/l and a specific decolorization rate (ns,dye) of 2.61 mg/g cell/h when HRT and dye loading rate was 1.12 h and 2.25 mg/h, respectively. In contrast, the beds with PAA cells reached an optimal nv,dye and ns,dye of 7.12 mg/h/l and 1.70 mg/g cell/ h, respectively, at a much longer HRT (8.0 h) due to diffusion-control mechanism for decolorization. For CA-cell beds, the dependence of specific decolorization rate on feeding dye concentration (0–200 mg/l) could be described by typical Monod-type kinetics, while for those with PAA cells, the relationship eventually followed first-order kinetics. This apparent first-order kinetics of PAA-cell systems is very likely due to mass transfer resistance of entrapped cells. At approximately same biomass loading, the beds with CA cells seem to be more economically feasible than those with PAA cells due to significantly less mass transfer resistance and higher volumetric decolorization rates. # 2005 Elsevier Ltd. All rights reserved. Keywords: Azo dye; Decolorization; Pseudomonas luteola; Immobilized cells; Fixed-bed bioreactor; Calcium alginate; Polyacrylamide

1. Introduction It has been a great challenge to decolorize wastewater bearing with recalcitrant synthetic dye compounds released from industrial effluents [1–5]. Azo dye is the most frequently used synthetic dye (ca. >60%) in Taiwan, and thus in particular requires to be cleaned up to mitigate the impact on the environment since itself or its derived metabolic intermediates are potentially carcinogenic or mutagenic [6]. Mineralization of azo dyes by bacterial species is often triggered by an enzymatic decolorization step, leading to reduction of azo bond(s) by oxygensensitive azoreductase under anaerobic environments [1]. The decolorized metabolites can be further degraded via a sequence of aerobic or anaerobic pathways [4,7]. Although literature [2,8] have demonstrated that bacterial decolorization of azo dyes may become a potential alternative to conventional wastewater decolorization * Corresponding author. Tel.: +886 6 2757575x62651; fax: +886 6 2344496. E-mail address: [email protected] (J.-S. Chang). 1359-5113/$ – see front matter # 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.procbio.2005.04.002

approaches, there is still few economically-effective examples demonstrating the bacterial method being applied in practical wastewater decolorization processes [9]. For a more viable application of the bacterial decolorization system, it is crucial to select appropriate types of biocatalyst (suspended or immobilized cells) and bioreactor operation (e.g., CSTR, batch, fed-batch cultures) [10,11]. Due to non-growth associated characteristics of dye decolorization, using suspended cultures is not technically feasible for long-term continuous operation due to total washout of non-growing cells. This suggests the technique of cell immobilization as one of viable alternatives for dye decolorization. In fact, it has been demonstrated that immobilized microbial systems greatly improve bioreactor efficiency; for instance, increasing process stability and tolerance to shock loadings, allowing higher treatment capacity per unit biomass and generating relatively less biological sludge [12]. Previous study [10] also confirmed such economic feasibility and technical effectiveness of using immobilized cells of a wild-type bacterium (Pseudomonas luteola) in batch operations

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for azo-dye decolorization; for example, the stability, mechanical strength, and reusability of the immobilized biocatalyst were significantly enhanced as compared with suspended cells. In addition, biocatalyst immobilization could significantly increase the entrapped biomass concentration, and thereby reduces the bioreactor volume to satisfy a critical criterion in practical uses. Cell immobilization with gel entrapment holds an extra benefit of creating a local anaerobic environment, which is particularly suitable for oxygen-sensitive bacterial decolorization [10]. Therefore, it seems promising to use immobilizedcell system to develop decolorization bioprocesses. However, to our knowledge immobilized-cell-based continuous processes (such as fixed-bed bioreactors) for longterm decolorization operation has not been investigated yet and part of operation criteria from industrial perspectives still requires clarification. Therefore, the goal of this follow-up study is to clearly reveal such figures to assess the economic and technical feasibility of the system for on site or/and in situ practical applications. In the present work, fixed-bed processes containing gelentrapped P. luteola cells were used for continuous decolorization. The fixed-bed decolorizers were conducted under different feeding conditions (e.g., volumetric flow rate, dye loading concentration, etc.) and bed characteristics (e.g., gel-strength, bed-length and the limitation of mass transfer resistance). The results obtained from this study are expected to provide information regarding the effect of operation parameters and bed characteristics on the performance of bacterial decolorization and also to demonstrate feasible operation strategies to utilize the immobilized-cell fixed beds for efficient decolorization of dye-laden wastewaters.

2. Materials and methods 2.1. Microorgansim and cultivation P. luteola was predominately isolated from an activatedsludge system for treatment of dye-bearing wastewater [13]. The strain is capable of efficiently expressing azoreductase activity to decolorize myriads of azo dyes via cometabolism initiated by azo bond reduction [13,14]. The P. luteola strain was cultivated aerobically at 28 8C with Luria-Bertani (LB) broth or yeast extract-glucose (YG) medium [14], typically containing 1.25 g/l of glucose (Difco) and 3.0 g/l of yeast extract (Difco). 2.2. Measurement of dye concentration The model azo dye used in this study was C.I. Reactive Red 22, which was obtained from Sumitomo, Inc. (Tokyo, Japan). The concentration of the azo dye in samples was determined by measuring the absorbance of the supernatant at 510 nm as described elsewhere [15].

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2.3. Cell immobilization method 2.3.1. Immobilization with calcium alginate (CA) A cell solution of ca. 25 g/l was mixed with sodium alginate (Sigma) at a 2% weight to volume (w/v) ratio. The mixture was dropped into 0.1 M CaCl2 solution through a syringe to form particles of approximately 2.5–3.0 mm in diameter. The particles were suspended in the CaCl2 solution for 12 h to enhance their mechanical stability. The average biomass content per unit volume of the CA beads was 36 mg/cm3. 2.3.2. Immobilization with polyacrylamide (PAA) Detailed procedures were described elsewhere [10,14]: In general, 15 ml of the prepared cell solution (ca. 25 g/l) was rapidly mixed with a solution containing 1.81 g of acrylamide monomer, 0.9 g of N,N0 -methylene-bisacrylamide, 0.09 ml of potassium persulfate (5%, w/v), and 0.8 ml of 3-(dimethylamino) propionitrile (2.5%, w/v) on a shallow plate. All the chemical reagents used in the study were purchased from Sigma. After completion of polymerization (ca. 10 min), the resulted gel-like slice was cut into 3 mm cubes, which were rinsed with deionized and distilled water prior to further decolorization operations. The average biomass content per unit volume of the PAA beads was 22 mg/cm3. 2.4. Operations of fixed-bed decolorizers The immobilized cells were stacked into glass columns (ca. 2.2 cm in diameter) with the bed length in the range of 13 to 40 cm. The feeding stream containing nutrient medium (0.5% yeast extract) and azo-dye substrate (C.I. Reactive Red 22 at 25–200 mg/l) was continuously pumped upward from the bottom into the column to avoid channeling effects and increase retention time. To maintain the mechanical stability of CA beads, 0.01 M CaCl2 was supplemented into the feeding stream for conditioning during the operation of CA columns. The volumetric feeding rate was ranged from 15 to 60 ml/h. The porosity of the beds with PAAimmobilized cells was approximately 54%, while for beds packed with CA-immobilized cells was ca. 65%. Samples were collected from the effluent at designated time intervals to measure the residual dye concentration. The effectiveness of the fixed-bed decolorizer is evaluated by the specific decolorization rate (ns,dye; mg dye/g cell/h), overall decolorization rate (no,dye; mg dye/h) and volumetric decolorization rate (nv,day; mg dye/h/l). These decolorization rates were determined from elution curves and physical properties of the bed according to the following equations. Z t 1 ns;dye ¼ FðC0  Cout Þ dt X0 t 0 Z no;dye 1 t no;dye ¼ FðC0  Cout Þ dt; nv;day ¼ t 0 V where, X0 denotes biomass loading in the fixed bed (g/l), t denotes operation time (h), F denotes volumetric flow rate

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(l/h), and C0 and Cout represent inlet and outlet concentration of dye (mg/l), respectively. To investigate the effect of cell-free matrix on decolorization, blank experiments were conducted using fixed-bed columns packed with a desired amount of cell-free matrix beads. The volumetric feeding rate and the dye concentration in feed were 30 ml/h and 50 mg/L, respectively. The residual dye concentration in the effluent was monitored at designated time spans.

dye removal capacity per volume of immobilized bead than PAA cells did. This is most likely due to higher biomass loading per unit matrix (mentioned earlier) and less mass transfer resistance (to be discussed later) in CA-immobilized cells. 3.2. The effect of bed-length on fixed-bed decolorization

As the matrices used for cell immobilization may contribute to decolorization via abiotic process (such as adsorption), color-removal experiments with fixed beds solely containing cell-free matrix beads (calcium alginate and polyacrylamide) were conducted for control comparison. The size and the amount of the matrix beads in the columns were approximately identical to those used in the beds packed with immobilized cells. As shown in Fig. 1, color removal by cell-free beads at an inlet dye concentration of 50 mg/l and a volumetric flow rate of 30 ml/h was very limited, especially for the bed with CA-beads. The cellfree CA and PAA matrix could only account for 1.9 and 8.4% of total decolorization of fixed beds containing immobilized cells (Fig. 1). The low dye removal capacity of the matrices can be attributed to due to low dye adsorption capacity of the matrices, as indicated in our previous work [10], showing that PAA matrix had a maximal adsorption capacity of 9 mg dye/cm3, while the adsorption by CA matrix was much lower (ca. 0.9 mg dye/cm3). These results indicate that the decolorization contributed by matrix adsorption of dye is negligible in a continuous flow fixedbed process. Fig. 1 also shows that CA cells attained higher

A higher bed length (L) with similar particle size and bed porosity represents a higher biomass loading. The overall decolorization rate is considered to be positively proportional to biomass loading. Fig. 2 and Table 1 show that the overall decolorization rate (no,dye) of fixed beds containing CA-immobilized cells essentially increased with an increase in bed-length for L = 13–40 cm, but there was only tiny difference in no,dye between the fixed bed with L = 30 and 40 cm. During steady-state operation, the dye concentration in the exiting stream (Ce,dye) was ca. 60–65% and 35–40% of that in the influent (C0,dye) for fixed bed with bed length of 13 and 20 cm, respectively. However, the Ce,dye/C0,dye ratio decreased to 10–15% (i.e., 85–90% conversion) for the bed with L = 30 and 40 cm. It seems that a bed length of 30 cm was enough to attain a nearly complete conversion, so it is not surprised to observe similar overall decolorization performance for the bed with L = 30 and 40 cm. However, the specific decolorization rate was lower for L = 40 cm (Table 1) due to higher biomass loading in the bed with L = 40 cm. Table 1 also shows that the volumetric decolorization rate (nv,dye) was similar for L = 13 and 20 cm, but sharply decreased as the bed length was increased to 30 and 40 cm. This seems to suggest that the effect of mass transfer on the efficiency of decolorization may become important for L > 30 cm, as the decrease in nv,dye for beds with longer L might be associated with less efficient mass transfer. The mass transfer resistance at longer bed length was observed via significant CO2 sparging within the column for the fixed bed with L = 40 cm, causing the

Fig. 1. Time course of cumulative color removal (per unit volume of immobilized bead) for fixed beds containing immobilized Pseudomonas luteola cells and cell-free matrices (CA: calcium alginate; PAA: polyacrylamide). Operation conditions: volumetric flow rate = 30 ml/h, dye concentration in the feed = 50 mg/l.

Fig. 2. Dependence of cumulative decolorization profiles on bed length for fixed beds containing calcium alginate-immobilized cells of Pseudomonas luteola. Operation conditions: volumetric flow rate = 30 ml/h, dye concentration in the feed = 50 mg/l.

3. Results and discussion 3.1. Fixed-bed decolorization with cell-free matrices

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Table 1 The effect of bed length on the performance of decolorization in fixed beds containing calcium alginate-immobilized cells of P. luteola Bed length (cm)

Biomass loading X0 (g)

Bed porosity (%)

Overall decolorization rate, no,dye (mg/h)

Specific decolorization rate, ns,dye (mg/g cell/h)

Volumetric decolorization rate, nv,dye (mg/h/l)

13 20 30 40

0.35 0.59 1.21 1.43

69.7 67.5 60.4 64.1

0.71 1.14 1.41 1.42

2.02 1.93 1.17 0.99

21.5 22.7 16.6 12.3

formation of dead zones with poor mass transfer efficiency. In addition, the higher pressure drop due to increase in bed length may also influence the decolorization efficiency. 3.3. The effect of volumetric feeding rate on fixed-bed decolorization Decolorization performance of fixed beds (ca. biomass loading of 0.54  0.04 g) operated at different volumetric feeding rates is shown in Fig. 3 and Table 2. At a constant feeding dye concentration of 50 mg/l, the optimal volumetric decolorization rate was achieved at a volumetric feeding rate of 45 ml/h (i.e., nv,dye = 30.6 mg/h/l) and 15 ml/ h (i.e., nv,dye = 7.12 mg/h/l), respectively, for fixed beds containing CA- and PAA-immobilized cells. A higher volumetric feeding rate led to a higher dye-loading rate, but would lower the hydraulic retention time (HRT) (Table 2). Previous study [10] revealed that in suspended batch cultures the maximal decolorization rate of PAA and CA cells would not achieve unless dye concentration exceeded 500 and 3000 mg/l, respectively. This implies that for a feeding dye concentration of 50 mg/l, a high dye-loading rate should still favor efficient decolorization due to the absence of inhibitory threat to cell survival and azoreduction capacity. However, despite a positive effect of higher dye loading rates on volumetric decolorization rate according to reaction kinetics, the optimal performance did not occur at the highest volumetric feeding rate of 60 ml/h. Apparently, a sufficient retention time was essential for an effective decolorization, in particular for PAA-immobilized cells, whose preferable decolorization rates took place at lower

volumetric feeding rates (i.e., higher HRTs) than that of CA cells (Fig. 3, Table 2). Aware that this retention time should at least exceed the minimum time required for dye molecules diffusing into intraparticle phase for reaction and intermediary products out of outer boundary layer of entrapped cells. This retention time depends upon such factors as (1) rate of dye adsorption of gels; (2) rate to transport from the bulk fluid to surface of entrapped cell ‘‘pellets’’; (3) rate to external diffusion and reaction on the entrapped cells and (4) the tendency of the dye and its intermediate either to be held for a period of time in gels for degradation or ‘‘absorptive storage’’ [15–18]. Thus, the results shown in Fig. 3 and Table 2 seem to imply that the effect of mass transfer on decolorization in PAA-immobilized cells was more significant than in CA-immobilized cells, since PAA cells required a longer retention time to reach optimal decolorization. The higher mass transfer restriction in PAA cells can be ascribed to their higher dye adsorption ability [10] and smaller pore size indicated by analysis with scanning electron microscopy (SEM) (data not shown) than those of CA beads. The results also suggest that both dye loading rate and retention time are significant to determine an economically feasible operation for the fixed-bed decolorizers. 3.4. The effect of feeding dye concentration on fixed-bed decolorization Fixed-bed decolorization experiments at different feeding concentrations were carried out at a constant volumetric flow rate of 30 ml/h (i.e., HRT = 1.68 h) and biomass loading of 0.55  0.05 g to exclude the confounding effect of retention time. Fig. 4a shows that fixed beds containing CA cells exhibited Monod-type kinetics (Eq. (1)) and the kinetic constants, ns,dye,max and Kdye, were ca. 4.13 mg/g cell/h and 69.3 mg/l, respectively. ns;dye ¼

Fig. 3. Dependence of volumetric decolorization rate on volumetric feeding rate for fixed beds containing calcium alginate (CA)- and polyacrylamide (PAA)-immobilized cells of Pseudomonas luteola. Operation conditions: dye concentration in the feed = 50 mg/l, biomass loading = 0.54 g.

ns;dye;max Cdye Kdye þ Cdye

(1)

where ns,dye,max denotes the maximum specific decolorization rate (mg/g cell/h) and Kdye denotes apparent Monod constant (mg/l). In contrast, as indicated in Fig. 4b, the beds with PAA cells exhibited a different dependence of decolorization rate on the dye concentration (Cdye), in particular for Cdye > 100 mg/l. Unlike the beds with CA cells, the specific decolorization rate of PAA-cell beds essentially increased linearly with an increase in the dye concentration (Fig. 4b). The first-order kinetics for the correlation between

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Table 2 The effects of volumetric feeding rate on the performance of fixed-bed decolorizers containing calcium alginate (CA) and polyacrylamide (PAA) immobilized cells of P. luteola (feeding concentration of dye = 50 mg/L) Type of immobilized cells in the bed

Volumetric feeding rate (ml/h)

HRT (h)

Dye loading rate (mg/h)

Volumetric decolorization rate (mg/h/l)

Specific decolorization rate (mg/g cell/h)

CA-cells

15 30 45 60

3.4 1.7 1.1 0.8

0.75 1.5 2.3 3.0

15.5 19.7 30.6 5.57

1.44 1.68 2.61 0.47

PAA-cells

15 30 45 60

8.0 4.0 2.7 2.0

0.75 1.5 2.3 3.0

7.12 6.45 6.37 5.95

1.70 1.54 1.52 1.45

ns,dye and Cdye implies that PAA cells may have a much larger Kdye value over the feeding dye concentrations used (Kdye  Cdye), such that Eq. (1) can be simplified as ns,dye = kdyeCdye (i.e., kdye ffi ns,dye,max/Kdye = 0.026 l/g cell/ h). This is consistent with our previous findings with batch experiments [10], showing that the Kdye value of PAAimmobilized cells was ca. 1000 mg/l, nearly five-fold higher than that obtained for CA-cells. This is primarily due to mass transfer restriction and dye adsorption ability of the PAA cells. Hence, the different decolorization kinetics for PAA cells may be attributed to the mass transfer effect controlling the rate of decolorization rate of PAA cells, which required a longer HRT (lower volumetric flow rate) to reach an optimal

Fig. 4. Dependence of specific decolorization rate on dye concentration in the feed for fixed beds containing Pseudomonas luteola cells immobilized by (a) calcium alginate and (b) polyacrylamide (PAA) matrix. Operation conditions: volumetric flow rate = 30 ml/h, biomass loading = 0.54 g.

decolorization performance (Fig. 3). The mass transfer issues on PAA cells is addressed in Appendix A, where mass transfer equations were derived for fixed beds containing PAA-immobilized cells. The derivation (Eq. (A.12)) shows that PAA-immobilized cell systems required longer retention times (smaller nx in (A.12)) to achieve better decolorization performances. 3.5. Comparison of decolorization performance of fixed beds with CA and PAA cells Among the rate parameters used in this study, the volumetric decolorization rate (nv,dye) is apparently a better performance index for practical evaluation to overall decolorization efficiency of fixed-bed bioreactors containing immobilized cells at similar biomass loading. Fig. 5 shows that the nv,dye value obtained from the bed containing CA cells was always substantially higher than that from the bed packed with PAA cells. This is due primarily to a more efficient mass transfer in CA cells and also a higher immobilized biomass density (ca. 36 mg cell/cm3 bead) in CA immobilized cells, as compared to 22 mg cell/cm3 bead in PAA cells. It appears that the beds packed with CA cells may be more technically favorable than those with PAA cells in practical applications.

Fig. 5. Dependence of volumetric decolorization rate on dye concentration in the feed for fixed beds containing calcium alginate (CA)- and polyacrylamide (PAA)-immobilized cells of Pseudomonas luteola. Operation conditions: volumetric flow rate = 30 ml/h, biomass loading = 0.54 g.

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and the equation of continuity for component A (i.e., azo dye) as

4. Conclusions This study demonstrates the feasibility of using gelentrapped cells of P. luteola for continuous decolorization of dye-laden influents using fixed-bed bioreactors. The decisive factors of operation conditions and bed characteristics to determine the performance of the fixed-bed decolorization were bed length (equivalent to biomass loading), dye loading rate, and the retention time. Optimal operation conditions and decolorization performance were also strongly dependent upon the characteristics of microbial cells, matrix property, bioactivity, the limitation of mass transfer resistance. At a fixed feeding concentration of dye (50 mg/l), the best decolorization rate did not occur at the fastest dye loading rate, but was strongly dependent on the hydraulic retention time due to mass transfer diffusion limitation. The optimal volumetric and specific decolorization rates for the beds with CA-immobilized cells occurred when HRT and dye loading rate was 1.12 h and 2.25 mg/h, respectively, while for beds with PAA cells the optimal performance occurred at a much longer HRT (ca. 8 h), indicating that mass transfer associated with PAA cells was less efficient (Appendix A). The PAA cells had better specific decolorization rate than the CA cells did when the feeding dye concentration was higher than 100 mg/l. The beds with CA cells achieved better overall decolorization activity (in terms of nv,dye), and thereby are more economically feasible to be used in practical wastewater decolorization treatments. Acknowledgements The authors gratefully acknowledge financial supports (NSC-89-2214-E-035-015, NSC 90-2214-E-197-003, and NSC 93-2214-E-197-002) of National Science Council of Republic of China. Some significant conclusions were initiated while one of the authors (BYC) was a research associate with the National Research Council (NRC), USA working in the National Risk Management Research Laboratory (NRMRL), US Environmental Protection Agency (EPA), Cincinnati, Ohio, USA. Appendix A. The differential equation of mass transfer According to the equation of continuity for the mixture [19], the one-dimensional differential equation of mass transfer can be derived as @r ~  r~ r vþ ¼ 0; @t

(A.1)

or Dr ~ ~ þ rr v ¼ 0; Dt

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(A.2)

@r ~ ~ r nA þ A þ rA ¼ 0; @t

(A.3)

where ~ nA denotes the mass flux vector of component A; r and rA are mass densities of total mixture and species A, respectively. In addition, rA is biochemical formation rate in the units (mass of A produced)/(volume)(time). By substitution of the mass flux ~ nA relative to a fixed spatial coordinate system for a binary system, we obtain ~ A þ vA ð~ ~ nA þ ~ nB Þ; nA ¼ rDAB rv

(A.4)

~ nA ¼ rA~ nA ;

(A.5)

~ nA ¼ rB~ nB ;

(A.6)

where vA is the mass fraction of species A (=rA/r). If the density r and the diffusion coefficient DAB are assumed constant, Eq. (A.3) becomes ~ 2 rA þ rA r ~ ~ ~ A þ @rA þ rA DAB r n þ~ n  rr @t ¼ 0:

(A.7)

Eliminating the second term in (A.7) and introducing rA = RA (i.e., decay rate of dye A), one may rewrite (A.7) as @CA ~ A  RA : ~ 2 CA  ~ ¼ DAB r n  rC @t

(A.8)

Considering mass transfer differential equation only in longitudinal direction (i.e., neglecting transfer contributions in radical direction) at steady state with first-order decay kinetics (i.e., RA = kCA as Ks  CA in Monod kinetics), we can rewrite (A.8) as d2 CA dCA  bCA ¼ 0; a dx2 dx 0  CA ðx ! 1Þ < þ 1

CA ðx ¼ 0Þ ¼ C0 ; (A.9)

where parameters a and b are a = nx/DAB and b = k/DAB and nx is the velocity in longitudinal direction. The particular solution of (A.9) is then obtained as sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi! ) ( vx 4kDAB CA ¼ C0 exp 1 1þ x : (A.10) 2DAB v2x Using p binomial ffiffiffiffiffiffiffiffiffiffiffiffiffi expansion, one may reformulate (A.10) for nx  4kDAB as    k k2 DAB 2k3 D2AB CA ¼ C0 exp  þ  þ ... x : nx n3x n5x (A.11) If mass diffusion coefficient DAB and decolorization decay constant k are relatively smaller than square of

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longitudinal velocity n2x, Eq. (A.11) can be approximately approached as   k (A.12) CA ffi C0 exp  x : nx If diffusion coefficient assumes as a ‘‘weak function’’ of longitudinal velocity nx [20] in an empirical expression DAB ¼ ax nx ;

(A.13)

one may also obtain an almost identical expression as shown in (A.12). The most significant of (A.12) is to uncover design criteria of minimum bed length to attain desired treatment performance (e.g., 5% residual dye). Eq. (A.12) indicates that, to reach same decolorization performance, the smaller longitudinal velocity nx (i.e., higher HRT) at the same longitudinal position (e.g., x = L) in different immobilized cell columns should show a lower decay rate constant k. In addition, this equation also reveals a relationship between decolorization performance and operation parameters (e.g., k and nx) at various longitudinal position. According to Eq. (A.12), the decay rate constant (k) at longitudinal position of 40 cm at steady state (ca. 40–100 h) for feeding rates of 15, 30, 45 and 60 ml/h (i.e., nx = 4.77, 9.55, 14.3, and 19.1 m/h) are estimated as 0.404, 0.155, 0.110 and 0.093 h1, respectively. The dependence of k value on volumetric feeding rate appeared to follow similar trend as the decolorization rates shown in Table 2. This result implies that a mass transfer-controlled system inevitably requires a longer retention time to reach better decolorization performance. Note that the assumption of mass diffusion resistance as a sole control mechanism may not be appropriate to describe CA-cell systems due to its non-monotonic concavity of decolorization performance (Table 2; Fig. 3).

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