Kinetic modeling of growth and biodegradation of phenol and m-cresol using Alcaligenes faecalis

Process Biochemistry 42 (2007) 510–517 www.elsevier.com/locate/procbio

Kinetic modeling of growth and biodegradation of phenol and m-cresol using Alcaligenes faecalis Jing Bai a,b,*, Jian-Ping Wen a, Hong-Mei Li a,d, Yan Jiang a,c a

Department of Biochemical Engineering, School of Chemical Engineering and Technology, Tianjin University, Tianjin 300072, PR China b Institute of Modern Physics, Chinese Academy of Science, Lanzhou 730000, PR China c School of Life Sciences and chemistry, Harbin college, Harbin 150016, PR China d Yancheng Textile Vocational and Technical College, Yancheng 224005, PR China Received 12 May 2006; received in revised form 20 August 2006; accepted 1 October 2006

Abstract A phenol-degrading microorganism, Alcaligenes faecalis, was used to study the substrate interactions during cell growth on phenol and mcresol dual substrates. Both phenol and m-cresol could be utilized by the bacteria as the sole carbon and energy sources. When cells grew on the mixture of phenol and m-cresol, strong substrate interactions were observed. m-Cresol inhibited the degradation of phenol, on the other hand, phenol also inhibited the utilization of m-cresol, the overall cell growth rate was the co-action of phenol and m-cresol. In addition, the cell growth and substrate degradation kinetics of phenol, m-cresol as single and mixed substrates for A. faecalis in batch cultures were also investigated over a wide range of initial phenol concentrations (10–1400 mg L1) and initial m-cresol concentrations (5–200 mg L1). The single-substrate kinetics was described well using the Haldane-type kinetic models, with model constants of mm1 = 0.15 h1, KS1 = 2.22 mg L1 and Ki1 = 245.37 mg L1 2 for cell growth on phenol and mm2 = 0.0782 h1, KS2 = 1.30 mg L1 and Ki2 = 71.77 mgL1, K 0i2 ¼ 5480 ðmg L1 Þ for cell growth on m-cresol. Proposed cell growth kinetic model was used to characterize the substrates interactions in the dual substrates system, the obtained parameters representing interactions between phenol and m-cresol were, K = 1.8  106, M = 5.5  105, Q = 6.7  104. The results received in the experiments demonstrated that these models adequately described the dynamic behaviors of phenol and m-cresol as single and mixed substrates by the strain of A. faecalis. # 2006 Elsevier Ltd. All rights reserved. Keywords: Alcaligenes faecalis; Biodegradation; Phenol; m-Cresol; Inhibition; Kinetics

1. Introduction Phenol, a compound regarded as a priority contaminant by the Chinese Environmental Protection Agency, is a characteristic pollutant in wastewaters and effluents from crude oil and coal conversion processes and has been detected recently in river water and in effluents from wastewater treatment plants [1–3]. Its methylated derivative o-, m- and p-cresol has been detected not only in leachate from creosote sites, and as such, has given rise to groundwater pollution, but has also been found in a huge range of industrial effluents. Due to the toxic properties of both phenol and cresol, the efficient removal of these compounds by microorganisms is of great importance. * Corresponding author at: Department of Biochemical Engineering, School of Chemical Engineering and Technology, Tianjin University, Tianjin 300072, PR China. Tel.: +86 22 27890492; fax: +86 22 27890492. E-mail address: [email protected] (J. Bai). 1359-5113/$ – see front matter # 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.procbio.2006.10.004

To treat phenolic compounds, biological methods are preferable because this is economical, and there is a low possibility of the production of byproducts. The biodegradation of phenol have been widely examined in the past three decades and different microorganisms were used by different researchers in this kind of study [4–7]. Several other studies have shown that cresols can be degraded by a wide variety of microorganisms [8– 10]. The microorganisms used are usually aerobes because the aerobes are efficient at degrading toxic compounds and usually transform the organic compounds into inorganic compounds (CO2, H2O). As phenol and cresol are most important components in phenolic wastewater; recently, the inhibitions of cresol on aerobic biodegradation of phenol have been investigated. Kar et al. [11] observed that phenol and p-cresol mutually inhibited each other; the inhibition of p-cresol to phenol degradation was stronger than reverse, but o-cresol enhanced phenol degradation marginally. Paraskevi et al. [12] demonstrated that the addition of o-cresol strongly inhibited phenol

J. Bai et al. / Process Biochemistry 42 (2007) 510–517

transformation in respect to the strong competitive inhibition between the substrates. Perron and Welander [13] paid attention on the interaction of phenol and cresol when they were degraded at low temperatures. However, their researches focused on the substrate interactions during phenol biodegradation in the cresol–phenol mixtures only qualitatively and hitherto, no other reports were found on the substrate interaction kinetics during phenol degradation. Knowledge of the kinetics of biodegradation is important for the evaluation of the persistence of organic pollutant and the design of biodegradation facilities [14]. Therefore, further detailed research is needed to quantify these substrate interactions in the degradation of phenol and m-cresol mixtures. The aim of our present work is to investigate and quantify the kinetics of cell growth and biodegradation of phenol and m-cresol as the single and mixed substrates using Alcaligenes faecalis.

2.1. Cell growth on phenol and m-cresol

kþ2

kþ3

X 0 þ S1 , X 0 S1 k3 kþ4

X 0 þ S2 , X 0 S2 k4

kþ5

X 0 S1 þ S2 , X 0 S1 S2 k5 kþ6

X 0 S2 þ S2 , X 0 S22 k6

k0þ3

X 00 S2 X 00 þ S2 , 0

(7)

k3 k0þ4

X 00 S1 X 00 þ S1 , 0

(8)

k4

k0þ5

X 00 S2 þ S2 , X 00 S22 0

(9)

k5 k0þ6

X 00 S2 þ S1 , X 00 S2 S1 0

(10)

k6 k0þ7

(11)

k0þ8

X 00 S21 X 00 S1 þ S1 , 0

(12)

k8

Eqs. (1), (2), (6), (7) and (9) represent substrate-inhibition of phenol and m-cresol, respectively. The cross-inhibition between phenol and m-cresol is represented by Eqs. (3)–(5), (8) and (10)–(12). By considering the above mechanism and assuming pseudosteady state for formation of the cellular intermediates, the cell growth equation, for the mixed two growth substrates (phenol and m-cresol), can be obtained. Cellular intermediates in this mechanism are X0 , X0 S1, X0 S2, X0 S1S2, X 0 S22 , X00 , X00 S2, X00 S1, X 00 S22 and X 00 S21 . From Eqs. (1) to (5), dX 0 ¼ kþ1 XS1  k1 X 0  kþ2 X 0 þ kþ3 X 0 S1  k3 ½X 0 S1  dt þ kþ4 X 0 S2  k4 ½X 0 S2  þ kþ5 ½X 0 S1 S2  k5 ½X 0 S1 S2  þ kþ6 ½X 0 S2 S2  k6 ½X 0 S22  ¼ 0

On the basis of the experimental results (that both substrates exerted substrate-inhibition on the cells and cross-inhibition occurred between phenol and m-cresol) and considering that the inhibitory effects of m-cresol on the cell growth behaviors are larger than those of phenol, the following sequences of reactions based on enzymatic reactions are proposed: k1

(6)

k1

k7

In our work, as the flasks were covered with six layer gauzes, it was presumed that the aeration provided by shaking the flasks was sufficient to keep the oxygen concentration constant and not limited, the influence of oxygen was not considered. Thus, the A. faecalis growth rate and substrate degradation rate were only limited by substrate concentration at fixed initial pH, temperature and shaking rate. To develop the cell growth kinetics model in binary substrates system, our strategy is first to specify the cell growth model for cells acting on phenol and m-cresol alone, and then to quantify the substrates interactions. Because of the inhibition of high phenol or m-cresol concentration on the cell growth, the Haldane type kinetic models [15] were selected for assessing the dynamic behavior of A. faecalis growth on phenol or m-cresol alone.

kþ1

k0þ2

X 00 !2X X þ S2 , 0

X 00 S1 þ S2 , X 00 S1 S2 0

2. Kinetics models

X þ S1 , X 0 !2X

k0þ1

511

(13a)

Eqs. (2)–(5) will provide d½X 0 S1  ¼ kþ3 X 0 S1  k3 ½X 0 S1  ¼ 0 dt

(13b)

d½X 0 S2  ¼ kþ4 X 0 S2  k4 ½X 0 S2  ¼ 0 dt

(13c)

(1)

d½X 0 S1 S2  ¼ kþ5 ½X 0 S1 S2  k5 ½X 0 S1 S2  ¼ 0 dt

(13d)

(2)

d½X 0 S22  ¼ kþ6 ½X 0 S2 S2  k6 ½X 0 S22  ¼ 0 dt

(13e)

(3)

By solving Eqs. (13a)–(13e) and (14a)–(14e) can be obtained:

(4)

X0 ¼

(5)

½X 0 S1  ¼

kþ1 XS1 k1 þ kþ2 kþ3 kþ1 XS2 k3 k1 þ kþ2 1

(14a) (14b)

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½X 0 S2  ¼

kþ4 kþ1 XS1 S2 k4 k1 þ kþ2

(14c)

kþ5 kþ3 kþ1 XS2 S2 ½X 0 S1 S2  ¼ k5 k3 k1 þ kþ2 1 ½X 0 S22  ¼

(14d)

kþ6 kþ4 kþ1 XS1 S22 k6 k4 k1 þ kþ2

(14e)

and dX T dX ¼ g X1 þ g X2 ¼ dt dt

(18)

g X1 ¼ kþ2 X 0

(19)

mX1 ¼

Similarly, we can also obtain from Eqs. (6) to (12)): 00

X ¼

k0þ1

¼ XS2

(15a)

½X 00 S2  ¼

k0þ3 k0þ1 XS2 0 0 k3 k1 þ k0þ2 2

(15b)

½X 00 S1  ¼

k0þ4 k0þ1 XS2 S1 k04 k01 þ k0þ2

(15c)

½X 00 S22  ¼

k0þ5 k0þ3 k0þ1 XS3 0 0 0 k5 k3 k1 þ k0þ2 2

(15d)

k01 þ k0þ2

½X 00 S2 S1  ¼

k0þ6 k0þ3 k0þ1 XS2 S1 k06 k03 k01 þ k0þ2 2

(15e)

k0 k0þ4 k0þ1 ½X S1 S2  ¼ þ7 XS1 S22 k07 k04 k01 þ k0þ2

(15f)

X T ¼ X þ X 0 þ X 00 þ ½X 0 S1  þ ½X 00 S2  þ ½X 00 S22  þ ½X 0 S2  þ ½X 00 S1  þ ½X 0 S1 S2  þ ½X 0 S22  þ ½X 00 S2 S1  þ ½X 00 S1 S2  XS1 XS2 XS21 XS22 þ þ þ K S1 K S2 K i1 K S1 K i2 K S2 XS32 XS1 S2 XS1 S2 XS21 S2 XS1 S22 þ 0 þ þ 0 þ þ K i2 K S2 mK S1 m K S2 nK i1 K S1 gmK S1 XS22 S1 XS1 S2 XS2 S2 þ 0 0 2 þ 0 01 hK i2 K S2 g m K S2 n m K S2

(16)

Here, k0 1 ¼ 0 þ1 0 ; K S2 k1 þ kþ2 k0þ5 k0þ3 1 0 ¼ 0 K i2 k5 k03 1 kþ5 ¼ ; n k5

1 k0þ7 ¼ ; g0 k07

1 k0þ6 ¼ h k06

dX T X T dt

g X2 k0þ2 X 00 ¼ XT XT mm2 S2 K S2 þ S2 þ

þ

S32 K 0i2

þ Sf1 þ

S21 fK i1 þ 1f

þ 1f KS1 S2

(21)

MS21 S2 þ 1f QS1 S22

where mm2 ¼ k0þ2 Based on Eqs. (20) and (21) above, the specific growth rate can be obtained as (22)

(mm1, KS1, Ki1) and (mm2, KS2, Ki2, K 0i2 ) can be obtained separately from the kinetics of individual cell growth on phenol alone or m-cresol alone, respectively. Although f is derived as the ratio of KS1 and KS2, it should be determined as an independent parameter from fitting experimental data due to the complexity of the system [16].

Analyzing the utilization of the substrate in cells in more detail, the consumption of substrate for cell growth and for maintenance and also, for product formation if possible has to be considered [17]. The substrate consumption rate of substrate biodegradation is:

1 kþ4 ¼ ; m k4

1 k0þ8 ¼ ; n0 k08

S22 K i2

2.2. Substrates degradation kinetics model

1 kþ3 ¼ ; K i1 k3

1 kþ6 ¼ ; g k6

rS ¼

1 Y X=S

r X þ mc X þ

1 Y P=S

rP

(23)

where rP = arX + bX is the product formation rate and because YX/S, mc, YP/S, a, b are all constants, Eq. (23) can be reduced to

The specific growth rate is defined as mX ¼

mX2 ¼

mX ¼ mX1 þ mX2

þ ½X 00 S21  ¼ X þ

k0þ4 1 ¼ ; m0 k04

þ QS1 S22

Similarly,

(15g)

Therefore, the total cell mass can be represented as follows:

k0 1 ¼ þ3 ; K i2 k03

(20)

  K S1 1 K S1 þ f ¼ ; mm1 ¼ kþ2 ; K¼ ; m K S2 m0 K S2   1 K S1 M¼ þ 0 0 ; nK i1 n m K S2   1 K S1 K S1 þ Q¼ þ gm hK i2 KS2 g0 m0 K S2

¼

k0 k0þ4 k0þ1 ½X 00 S21  ¼ þ8 XS2 S2 0 0 0 k8 k4 k1 þ k0þ2 1

1 kþ1 ¼ ; K S1 k1 þ kþ2

K S1 þ

mm1 S1 2 S1 þ S1 =K i1 þ fS2 þ fS22 =K i2 þ fS32 =K 0i2 þ KS1 S2 þ MS21 S2

where

00

þ

g X1 kþ2 X 0 ¼ XT XT

(17)

r S ¼ Ar X þ BX

(24)

J. Bai et al. / Process Biochemistry 42 (2007) 510–517

or mS ¼ Amx þ B

(25)

where A = (1/YX/S + a/YP/S) and B = (mc + b/YP/S) are all kinetic constants and they were regressed using Matlab based on the experimental data. Thus, the specific degradation rates of phenol and m-cresol in dual substrates system can be represented as follows: mS1 ¼

dS1 ¼ A1 mX1 þ B1 X T dt

(26)

mS2 ¼

dS2 ¼ A2 mX2 þ B2 X T dt

(27)

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plotting dry weight of biomass per liter against optical density. Dry weight was determined by filtering a specific volume of suspended culture through preweighted 0.45 mm pore size filters, drying the cells at 105 8C until the weight were constant. Phenol and m-cresol concentrations were quantified by high performance liquid chromatography (HPLC). Immediately after the measurements of optical density, aqueous samples of suspended culture were centrifuged at 7500 rpm for 10 min. Then the cells free supernatants were used for determining the residual phenolic concentrations in the solution. HPLC was performed on a reverse phase C18 column (250 mm  4.6 mm, LabAlliance, U.S.A.) with a methanol/ water (400/300, v/v) mobile phase at a flow rate of 1.0 mL min1, and detection was realized with a UV detector (Model 500, LabAlliance, U.S.A.) at 280 nm. The retention time for phenol was 4.89 min and for m-cresol was 6.12 min.

3.4. Statistics All experiments were repeated three times. The data shown in the corresponding figures in Section 4 were the mean values of the experiments.

3. Materials and methods

4. Results and discussion

3.1. Microorganism and culture conditions

4.1. Biodegradation on single growth substrate

A. faecalis was isolated in this lab from acclimated activated sludge collected from a municipal gasworks in China and identified based on physiological and biochemical tests and 16SrDNA by the Institute of Microbiology, Chinese Academy of Sciences. Stork culture of this strain was maintained by periodic sub transfer on nutrient agar slants and stored at 4 8C. Pure culture of this microorganism was used throughout our work. The liquid mineral salt medium (MSM) used in this study has a composition as follows (g L1): 0.4 K2HPO4, 0.2 KH2PO4, 0.1 NaCl, 0.1 MgSO4, 0.01 MnSO4H2O, 0.01 Fe2(SO4)3H2O, 0.01 Na2MoO42H2O, 0.4 (NH4)2SO4. Phenol and/or m-cresol were added to the medium before inoculation [18,19]. The initial pH value of the medium was adjusted to 7.2 with 30% NaOH before autoclaving.

3.2. Biodegradation experiments The startup of the experiments was obtained by inoculating 10 mL LB medium with microbial strain from nutrient agar slant stored in 4 8C refrigerator, in sterile conditions. After 18 h of incubation at 30 8C, subculture was carried out by inoculating 2 mL of the cell culture to 100 mL fresh LB medium at initial pH of 7.2. Then 2.5 mL of the cells at late exponential growth phase (OD600 around 1.2 absorbance units) were transferred into the MSM as inoculation. The biodegradation experiments were conducted in a series of 250 mL sterile shaking flasks. Each flask contained 50 mL sterile mineral salt medium (MSM) with various phenol or m-cresol concentrations. When they were used as the sole carbon source and energy, phenol concentrations varied from 10 to 1400 mg L1, and m-cresol concentrations varied from 5 to 200 mg L1 were investigated. To determine the interactions between the mixed substrates, batch experiments were also performed in MSM with both phenol and m-cresol were existed. The used phenol concentrations were ranging from 10 to 1400 mg L1 (10, 50, 100, 150, 200, 300, 500, 800, 1000, 1200, 1400), and at each phenol concentration 5–200 mg L1 (5, 10, 30, 50, 80, 100, 150, 200) m-cresol were added to the medium. The sub cultivated cells at late exponential phase were also used to inoculation. Five milliliters samples were periodically removed from the medium for analysis of cell density and residual phenolic concentrations. All of above experiments were carried out at the initial pH of 7.2 and 30 8C in an orbital shaker at 200 rpm.

Batch cultures of A. faecalis were conducted in media containing either phenol or m-cresol as the sole carbon source. Substrate of high concentrations can exhibit inhibitions on cell growth and its own degradation [14], the inhibitions of phenol on cell growth and substrate degradation were widely observed by some other researchers [21–23]. Fig. 1 depicted the comparison of cell growth and substrate degradation at the initial phenol or m-cresol concentration of 100 mg L1. It was very impressive for 100 mg L1 phenol to be entirely degraded within 10 h. This was 22 h less than that for 100 mg L1 mcresol. It can still be seen from the cell growth curves that there is hardly any lag phase can be observed when cell grow on phenol, but when used the same amount of m-cresol as sole substrate, 12 h lag phase appeared. And the cell growth rate and the ultimate cell concentration were higher than that on mcresol alone. It may be attributed to the fact that m-cresol was more toxic than phenol, it exhibit larger inhibitory effects on the cell growth behaviors. In order to obtain the cell growth and degradation kinetic model parameters of single substrate, cell and substrate

3.3. Analytical methods Cell density was determined with a UV spectrophotomer (Lingguang Shanghai analysis equipment factory, Shanghai) by measuring the absorbance of the microorganism at the wavelength of 600 nm [20]. Then OD600 was converted to dry cell weight by a calibration curve, which was obtained by

Fig. 1. Comparison of cell growth and substrates degradation at the initial phenol or m-cresol concentration of 100 mg L1.

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J. Bai et al. / Process Biochemistry 42 (2007) 510–517

concentrations were measured with time for different initial liquid substrate concentrations of phenol (10–1400 mg L1) alone and m-cresol (5–200 mg L1) alone. Model parameters were estimated by curve-fitting based on non-linear least squares of residuals. Non-linear regression analysis was performed using Matlab software employing a hybrid of the Gauss–Newton and steepest descent techniques to solving non-linear equations. And the following model equations and their regression coefficients were obtained for phenol alone and m-cresol alone: For phenol alone: m0X1 ¼

mm1 S1 0:15S1 ¼ 2 K S1 þ S1 þ S1 =K i1 2:22 þ S1 þ S21 =245:37

ðR2 ¼ 0:992Þ m0S1 ¼ A01 m0X1 þ B01 ¼ 0:7575m0X1 þ 0:1132

(28) ðR2 ¼ 0:987Þ (29)

For m-cresol alone: mm2 S2 K S2 þ S2 þ S22 =K i2 þ S32 =K 0i2 0:0782S2 ¼ 1:30 þ S2 þ S22 =71:77 þ S32 =5480

m0X2 ¼

ðR2 ¼ 0:995Þ m0S2 ¼ A02 m0X2 þ B02 ¼ 1:6848m0X2 þ 0:0177

(30) ðR2 ¼ 0:985Þ (31)

Fig. 3. Dependence of specific growth rate and specific degradation rate of m-cresol alone at different initial m-cresol concentrations.

the simulated values of cell growth and degradation kinetic models agreed well with the experimental data. Comparing Fig. 2 with Fig. 3, we found that both the specific cell growth rates and the specific degradation rates in phenol solution were much higher than that in m-cresol solution, which indicated that the strain was inclined to utilize more phenol than m-cresol. It might be result from the fact that strain A. faecalis was separated from the acclimated activated sludge using phenol as sole carbon and energy source and it was easy for it to adjust to the environment with phenol. 4.2. Biodegradation on dual growth substrates

The dependences of A. faecalis specific growth rate and degradation rate on the initial concentrations of phenol and mcresol alone are shown in Figs. 2 and 3. It can be seen that the maximum specific growth and degradation rates both occurred at low substrate concentration. And with further increase of initial substrate concentration, much lower values of the specific growth and degradation rates were obtained. The phenomenon was substantially result from intense substrate inhibition at high substrate concentration. And the higher the substrate concentration in the medium was, the stronger the substrate inhibition displayed. In addition, it was also noted that

A series of biodegradation experiments with media containing both phenol and m-cresol at different concentrations were performed. Examinations were varied widely (phenol concentration from 10 to 1400 mg L1 and m-cresol concentration from 5 to 200 mg L1) so as to validate the general application of these models. As the presence of interaction between phenol and m-cresol dual substrates, the behavior of cell growth and substrate degradation might differ greatly from the single substrate system.

Fig. 2. Influence of the initial phenol concentration alone on the specific growth rate and specific degradation rate.

Fig. 4. Experimental data and model simulation for cell growth at initial total phenolic concentration of 200 mg L1. The lines represent model simulation.

J. Bai et al. / Process Biochemistry 42 (2007) 510–517

Fig. 5. Experimental data and model simulation of phenol and m-cresol degradation at initial total phenolic concentration of 200 mg L1. The lines represent model simulation.

Examples of the overall cell concentrations and substrates degradation at the initial total phenolic concentration (sum of phenol and m-cresol) of 200 mg L1 are shown in Figs. 4 and 5, respectively. The cell growth curves at initial phenol or mcresol concentration of 200 mg L1 are presented to Fig. 4 so as to see the inhibition effects of the second component in detail. It can be observed from Fig. 4 that the overall cell growth rates on the dual substrates were higher than these of m-cresol alone and smaller than these of phenol alone and the total cell growth was the co-action of phenol and m-cresol. It was clear that the overall cell growth rates decreased with the increased m-cresol concentration in the medium (Fig. 4). It may due to the added m-cresol enhance the substrate inhibition of the mixed system on cell growth, however, the substrates interactions may be another important reason. We can see from Fig. 5 that both phenol and m-cresol could be consumed simultaneously, but the presence of m-cresol decreased the degradation rate of phenol. At the same time, phenol also exerted strong inhibition on m-cresol transformation; it was observed that rapid removal of m-cresol occurred only near the depletion of phenol. Kinetics of overall cell growth on phenol in the presence of m-cresol was modeled by Eq. (22). Using the determined parameters for cells grown on phenol (mm1, KS1, Ki1) and m-cresol (mm2, KS2, Ki2, K 0i2 ) alone, coupled with experimental data obtained from cells grown on the dual growth substrates, the parameters representing interactions between phenol and m-cresol including f, K, M, Q were determined, and f = 2.46  0.12, K = 1.8  0.36  106, M = 5.5  0.74  105, Q = 6.7  0.53  104. As shown in Fig. 4, the model fitted the experimental data well with R2 = 0.996.

515

The specific degradation rates of phenol and m-cresol on the dual substrates system were modeled by Eqs. (26) and (27), respectively. Based on the experimental data of biodegradation and calculated mX1 and mX2 with time according to Eqs. (20) and (21), the model parameters of phenol and m-cresol obtained for the substrates degradation kinetics in the dual substrates system were shown in Table 1. Fig. 5 also shows the comparisons of the predictions of these degradation kinetic models and the experimentally determined degradation data of phenol and m-cresol on the dual substrates system at the initial total phenolic concentrations of 200 mg L1. Obviously, the simulated values of the degradation kinetics of phenol and m-cresol in the dual substrates system agreed well with the experimental data. Comparison between experimental results and model simulation of cell growth and substrates degradation in dual substrates system in all other experiments were also performed, the outcome showed that the experimental data and model prediction were in good agreement with R2  0.95. 5. Comparison with the other model The kinetics of cell growth on multiple growth substrates in biodegradation reaction has been widely studied by some other researchers. The most widely used model was the crossinhibition equation proposed by Yoon et al. [16], Abuhamed et al. [24] modified this model to determine the interactions between benzene, toluene and phenol under the substrate inhibition effects. The model equation used by Abuhamed et al. were also adopted to simulate the overall cell growth data of our research, and Eqs. (26) and (27) were still used to model phenol and m-cresol degradation, respectively. The obtained models were: For overall cell growth: mX ¼

0:15S1 2:22 þ S1 þ S21 =245:37 þ 4:82S2 þ

1:3 þ S2 þ

0:0782S2 þ S32 =5480 þ 4:126S1

S22 =71:768

(32)

Table 1 Summary of the model parameters for specific degradation kinetics in the dual substrates system Phenol

m-Cresol 1

B2 (h1)

A1

B1 (h )

A2

3.3171  0.1547

0.0029  0.00051

0.8593  0.0478 2

0.0057  0.0012

Correlation coefficients of phenol and m-cresol are R = 0.992 and R2 = 0.991, respectively.

Fig. 6. Comparison of our model and model used by Abuhamed et al. on simulation of cell growth in mixed substrates system, initial phenol concentration of 150 mg L1 and m-cresol concentration of 50 mg L1.

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Acknowledgements The authors wish to acknowledge the financial support provided by the Key National Natural Science Foundation of China (No. 20336030), Key Natural Science Foundation of Tianjin (No. 05YFJZJC 00500), Program for New Century Excellent Talents in University and Program for Changjiang Scholars and Innovative Research Team in University. Appendix A A B Fig. 7. Comparison of our model and model used by Abuhamed et al. on simulation of substrates degradation in mixed substrates system, initial phenol concentration of 150 mg L1 and m-cresol concentration of 50 mg L1.

f g g0 h kj

For phenol degradation in the dual substrates system: mS1 ¼ 2:4175mX1 þ 0:0025

(33)

For m-cresol degradation in the dual substrates system: mS2 ¼ 1:192mX1 þ 0:0079

k0j

(34)

Curve fitting at different initial phenol and m-cresol concentration was carried out, typical example of cell growth and substrates degradation at initial phenol concentration of 150 mg L1 and m-cresol concentration of 50 mg L1 are plotted in Figs. 6 and 7, respectively. For comparison, our model simulation is also presented. It can be seen that the fit of the model used by Abuhamed et al. was not as good as the models used in our work, especially during the substrates degradation course. So we can conclude that our model was better to depict our experimental results. 6. Conclusions Biological degradations of phenol and m-cresol as the single and mixed substrates by a bacterial strain of A. faecalis in the liquid mineral salt medium (MSM) were carried out in shakeflask experiments at 30 8C and the initial pH of approximately 7.2. The cells were able to consume phenol and m-cresol alone completely. When cells grew on the mixture of phenol and mcresol, strong substrate interactions were observed. The kinetics of phenol and m-cresol as the single and mixed substrates by A. faecalis were investigated at the initial phenol concentrations varied from 10 to 1400 mg L1, the initial mcresol concentrations varied from 5 to 200 mg L1, the temperature of 30 8C and the initial pH of 7.2. The kinetic models for the specific growth rate and the specific degradation of phenol and m-cresol as the single and mixed substrates were proposed, and the simulated values of these models agreed well with the experimental data. It is our view that the above information would be useful for modeling and designing the units treating phenol- and m-cresol-contaminate wastewaters.

K, M, Q KS1 KS2 Ki1 Ki2 K 0i2 m m0 mc n n0 Rm S t YX/S YP/S X

growth associated constant for substrate consumption non-growth associated constant for substrate consumption (h1) substrate interaction coefficient ratio of k6 to k+6 (mg L1) ratio of k07 to k0þ7 (mg L1) ratio of k06 to k0þ6 (mg L1) (j = + 1, 1, +2, +3, 3, +4, 4, +5, 5, +6, 6) reaction rate constants shown in Eqs. (1)–(5) (units: k+1, k+3, k+4, k+5, k+6 ((mg L1)1 h1); k1, k2, k1, k4, k5, k6 (h1)) (j = +1,1, +2, +3, 3, +4, 4, +5, 5, +6, 6, +7, 7. +8, 8) reaction rate constants shown in Eqs. (6)–(12) (units: k0þ1 , k0þ3 , k0þ4 , k0þ5 , k0þ6 , k0þ7 , k0þ8 ((mg L1)1 h1); k01 , k02 , k03 , k04 , k05 , k06 , k07 , k08 (h1)) substrate interaction coefficient ((mg L1)1) saturation constant for cell growth on phenol (mg L1) saturation constant for cell growth on m-cresol (mg L1) self-inhibition constant of phenol (mg L1) self-inhibition constant of m-cresol (mg L1) self-inhibition constant of m-cresol ((mg L1)2) ratio of k4 to k+4 (mg L1) ratio of k04 to k0þ4 (mg L1) maintenance energy coefficient (h1) ratio of k5 to k+5 (mg L1) ratio of k08 to k0þ8 (mg L1) initial m-cresol holdup initial substrate concentration (mg L1) time (h) cell yield coefficient on substrate product yield coefficient on substrate biomass concentration (mg L1)

Greek letters a growth associated constant for product formation b non-growth associated constant for product formation (h1) gS substrate degradation rate (mg L1 h1) mX overall specific growth rate in dual substrates (h1) mX1 specific growth rate on phenol in dual substrates (h1)

J. Bai et al. / Process Biochemistry 42 (2007) 510–517

mX2 mm mS mS1 mS2

specific growth rate on m-cresol in dual substrates (h1) maximum specific cell growth rate on phenol (mm1) or on m-cresol (mm2) (h1) specific substrate degradation rate (h1) specific degradation rate of phenol in dual substrates (h1) specific degradation rate of m-cresol in dual substrates (h1)

Superscript 0 single growth substrate Subscripts 1 growth substrate, phenol 2 growth substrate, m-cresol

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