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A simplified steady-state model of a hybrid bioreactor composed of a bubble column bioreactor and biofilter compartments
Process Biochemistry 42 (2007) 554–560 www.elsevier.com/locate/procbio
A simplified steady-state model of a hybrid bioreactor composed of a bubble column bioreactor and biofilter compartments Sung Ho Yeom * Department of Environmental and Applied Chemical Engineering, Kangnung National University, Gangneung, Gangwondo 210-702, Republic of Korea Received 28 February 2006; received in revised form 26 September 2006; accepted 23 October 2006
Abstract In a previous study, a hybrid bioreactor comprised of a bubble column bioreactor section and a biofilter section was successfully applied to the treatment of benzene. In order to design and optimize the bioreactor system for actual use in the field, simple but effective mathematical models of the two-stage system were required. Since the liquid phase in the bubble column bioreactor section was well mixed, a CSTR (continuously stirred tank reactor) model was adopted for this section, with benzene removal by both air stripping and biodegradation being considered in the model equations. The gaseous benzene degradation in the biofilter section was described using a PFR (plug flow reactor) model. The combined model was validated through independent experiments, and the simulation results were in a good agreement with measured data. # 2006 Elsevier Ltd. All rights reserved. Keywords: Hybrid bioreactor; Modeling; Bubble column bioreactor; Biofilter; CSTR; PFR
1. Introduction It was shown that a hybrid bioreactor comprising of a bubble column bioreactor and a biofilter was a novel and excellent bioreactor system for the treatment of benzene, a volatile organic compound [1]. Recently, a Korean company tried to apply the hybrid bioreactor to actual wastewater treatment and needed simple but applicable mathematical models for the purpose of system design and optimization. Many mathematical analysis have been done on bubble column bioreactors and biofilters separately. In general, it is known to be very difficult to analyze bubble column bioreactor because the fluid dynamics of air bubbles and liquid phase in the bioreactor is very complex [2,3]. Therefore, experimental equations representing gas hold-up, mass transfer, liquid mixing and gas mixing are frequently used to establish models of bubble column bioreactor with many assumptions [4]. Hecht et al. [5], for example, developed a model of bubble column bioreactor containing immobilized microorganisms with following assumptions: (1) gas phase in plug flow, (2) wellmixed liquid phase, (3) quasi steady-state conditions for mass
* Tel.: +82 33 640 2406; fax: +82 33 641 2410. E-mail address: [email protected]. 1359-5113/$ – see front matter # 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.procbio.2006.10.012
transfer and reaction rates, (4) biomass concentration is an independent variable, (5) first order reaction with regard to biomass and substrate, zero order for oxygen, and (6) isobaric conditions. When the length of bubble column bioreactor is long enough compared with inner diameter of the column, a model equation representing pollutant concentration profile along the column is required to predict the pollutant degradation in a bubble column bioreactor [6,7]. However, if a pollutant concentration in effluent stream is the same as that in bubble column bioreactor (no concentration gradient along the column), complete mixing can be assumed, which makes mathematical model noticeably simple. In contrast to model of bubble column bioreactor, scientists and engineers have been trying to develop theoretical models of biofilter. Pioneering research in this area was conducted by Ottengraf and Van Den Oever [8] who considered the problem as composed of two phase: a bulk gas and a wet stagnant biolayer on the surface of solid particles in which contaminants are free to transfer from one to another. Based on this conceptual framework, they introduced a model in which a pair of equations, for each phase, accounts for diffusion and reaction in the biolayer, and advection in the vapor phase with equilibrium constraints at the interface. The same model, but with Haldane kinetics [9], was then applied by Shareefdeen and Baltzis [10] to predict methanol degradation. Hodge and
S.H. Yeom / Process Biochemistry 42 (2007) 554–560
Devinny [11] made the following modifications to the original model: (1) added dispersion to the gas phase, (2) ignored diffusion in the biofilm, and (3) took into account the presence of carbon dioxide. Even with the added features, some discrepancy still exists between the model predictions and the measured ethanol concentration along the biofilter. Another modification to the model was made with the incorporation of substrate adsorption and a rate expression suitable for twosubstrate systems [12,13]. As models become more refined, the more measurements which are necessary not only to validate the models but also to inspire modelling are required [2]. Although they have developed the models theoretically, many assumptions were still involved and many experimental data were required to get parameters. Shareefdeen and Baltzis [10] used 14 assumptions for the model development. Hodge and Devinny [11], Deshusses et al. [12], Zarook et al. [14] and Lu et al. [15] used 7, 10, 13 and 8 assumptions, respectively. Also, much time should be devoted to solve the partial differential equations suggested by them but the models did not show high accuracy in a wide experimental range. Therefore most of biofilter models were developed with the assumptions such as constant effective diffusivity, constant mass transfer rate, constant cell mass and thus quasi steady-state [11,16,17]. They supposed 1st-order degradation rate and the parameters contained in those models sometimes do not have clear physical or biological meanings. Although their simplified macro-kinetic models are very convenient to calculate removal efficiency at quasi steady state, they do not predict the behavior of pollutant precisely in the wide experimental range mainly because the rate of degradation is not necessarily 1st order [18]. In this study, the bubble column bioreactor and biofilter were mathematically described separately by adopting the simple concept of CSTR (continuously stirred tank reactor) and PFR (plug flow reactor), respectively. Each model required just 3–5 assumptions and 2–5 parameters to be determined. The models were validated through independent experiments and the simulation data were in a good agreement with measured ones.
2.3. Reactor design and operation conditions The hybrid bioreactor composed of a biofilter section and a bubble column bioreactor section was shown in Fig. 1. The diameter of a hybrid bioreactor was 6.0 cm. The working volume of bubble column bioreactor containing 100 mL of immobilized cells (beads) was 500 mL and that of the biofilter 760 cm3 (height, 27 cm). Four and one sampling ports were attached to the biofilter and bubble column bioreactor section, respectively. The hybrid bioreactor was installed in an exhaust hood and operated at 30 8C. To maintain the beads wet and to provide nutrient medium to microorganisms in the biofilter, 100 mL of medium was added from the top of the hybrid bioreactor every 10 h. The medium contained 2 g/L (NH4)2SO4, 0.3 g/L MgSO47H2O, 0.1 g/L K2HPO4, 0.1 g/L CaCl2 and 200 mL/L trace element. The trace element consisted of 16.2 g/L FeCl36H2O, 10.2 g/L CaCl22H2O, 0.22 g/L CoCl26H2O, 0.15 g/L CuSO45H2O, 0.13 g/L CrCl36H2O, 0.09 g/L NiCl36H2O and 40.0 g/L citric acid. The residence time was changed by manipulating the pumping rate of influent benzene solution. Air flow rate was changed by manipulating the air flow regulator attached to an air compressor.
2.4. Adaptation In order to eliminate adaptation time which alters the start point of degradation, microorganisms were fully adapted to benzene as follows. A 100 mL of beads were placed in a 500 mL flask containing 200 mL medium and cultured for 20 h at 30 8C. The medium also contained 120 mg/ L of benzene and inorganic nutrients of which composition was described above.
2.5. Assays The liquid benzene concentrations were analyzed by directly injecting 2 mL of the liquid sample into a gas chromatograph (HP 5890 II). To measure gas phase benzene, 1000 mL gas was directly withdrawn from off-gas port of biofilter section and injected into the GC. The detection limit of the GC was 0.05 mg/L. Cell mass in a bead was determined as follows. One hundred beads were dissolved in 7 mL of 65 mM phosphate buffer and sonicated. Cell free extract and alginate solution were separated by centrifugation. The total protein concentration in cell free extract was determined according to Bradford method [19] using a Bio-Rad protein assay kit with bovine albumin as a standard. The experiment showed that 1 g/L of cell mass corresponded to 0.47 g/L of protein.
2. Materials and methods 2.1. Microorganism Alcaligenes xylosoxidans Y234 isolated from crude oil-contaminated soil was used in this study. It can degrade benzene, toluene m-xylene and phenol [1]. A. xylosoxidans Y234 was precultured at 30 8C in a 500 mL flask containing 200 mL of medium (10 g/L glucose, 5 g/L yeast extract, 5 g/L (NH4)2SO4, 5 g/L KH2PO4 and 1 g/L MgSO7H2O).
2.2. Immobilization Sodium alginate was dissolved in hot distilled water to produce 5% solution. The microorganisms harvested from precultured solution by centrifugation (Hitachi, SCR 18B) were resuspended in distilled water and mixed with the same volume of sodium alginate solution to produce 5 g/L of cell mass. This mixture was extruded through a thin needle attached to a peristaltic pump into a 1% CaCl2 solution thus forming beads with a diameter of about 3 mm. After hardening for 1 h in this solution, the beads were washed several times with distilled water.
555
Fig. 1. Schematic diagram of the hybrid bioreactor.
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3. Results and discussions 3.1. Model of bubble column bioreactor section In this study, since only liquid benzene is fed to the bubble column bioreactor section, gas phase (air bubbles here) behavior is not considered. The model of the bubble column bioreactor was developed on the basis of following three assumptions. (1) Liquid phase is completely mixed, that is, benzene concentration is homogeneous throughout bubble column bioreactor. (2) Degradation rate of benzene is proportional to effective cell mass in the bioreactor described below. (3) The benzene degradation has a Monod-type dependency on benzene concentration. In the present study, since the column length was relatively short in comparison with the inner diameter of bubble column bioreactor (6 cm versus 17 cm) and the difference between benzene concentration in the effluent stream and that in the bubble column bioreactor was negligible (e.g., 2.16 mg/L versus 2.21 mg/L), the liquid phase in the bioreactor was supposed to be well mixed. Therefore, the model of the bubble column bioreactor can be expressed by adopting the concept of CSTR. The dissolved oxygen level was always above 23% of saturation value in the experimental ranges so only carbon source limitation is considered. Benzene was removed by both air injection and immobilized cells in the bubble column bioreactor. The decrease in benzene concentration by air injection in the bubble column bioreactor can be expressed as follows [1]. dC1 ¼ kC 1 dt
(1)
where C1 and k are liquid benzene concentration in the bubble column bioreactor section (mg/L) and benzene removal rate constant (L/min), respectively. The effect of airflow rate on the removal rate constant was shown in Fig. 2 and expressed as Eq. (2).
Fig. 2. The relationship between airflow rate and benzene removal constant in a bubble column bioreactor section. 1 vvm = 0.5 L/min.
benzene appeared almost constant. Although high cell mass loading is one of the main advantages of immobilization, cell mass above some level is not effective any more in terms of the degradation rate of benzene because of mass transfer limitation and reduction of available surface area. Similar phenomena were reported by other researchers [21–23]. Effective cell mass (Xeff) is now introduced to reflect those phenomena in this study. Effective cell mass is a hypothetical cell mass, which is calculated on the basis of degradation rate. That is, it is assumed that the same degradation rate means the same effective cell mass and that benzene degradation rate is directly proportional to effective cell mass throughout experimental range. Effective cell mass was calculated from benzene degradation rate as follows. The first effective cell mass was taken in the very lower region A (0.94 g/L here), and the effective cell mass was set to be the same as the real cell mass in a bead. The n-th effective
k ¼ f ðF air Þ 2 þ 1:823 105 F air þ 1:450 103 ¼ 3:657 108 Fair
(2) where F air is air flow rate (L/min) into the bubble column bioreactor section. Next, the benzene removal by immobilized cells was investigated. An alginate bead was considered as one catalyst of which ability to degrade benzene was proportional to the cell mass in a bead [20]. To investigate the dependency of degradation rate of benzene on the cell mass in a bead, the degradation rate of benzene was investigated changing cell mass in a bead. As shown in Fig. 3, as the cell mass increased in the range of 0–6 g/L (region A), so did the degradation rate of benzene linearly. However, in the range where the cell mass in a bead exceed that concentration (region B), degradation rate of
Fig. 3. The effect of cell mass on the benzene degradation rate.
S.H. Yeom / Process Biochemistry 42 (2007) 554–560
557
Table 1 Parameters for the simulation of a bubble column bioreactor section Parameter
Value
Remarks
k (mg/L) Kr (mg/L) N rmax (min1) Xeff (mg/bead) Yx/s
See Eq. (2) 55.97 3704 1.75 102 See Eq. (4) 0.33
Experimental Experimental Calculated Experimental Experimental Experimental
V
Fig. 4. Degradation of benzene by immobilized cells in a batch experiment.
cell mass is the product of first effective cell mass (or first actual cell mass) and the ratio of benzene degradation rate at n-th cell mass to that at first cell mass as shown in Eq. (3). Also, the ratio between any two degradation rates is equal to the ratio between the two effective cell masses. X eff; j-th ¼
degradation rate at X j-th ðX eff;1-st Þ degradation rate at X 1-st
(3)
where Xj-th represents the real cell mass and Xeff,j-th does effective cell mass at real cell mass Xj-th in a bead. The relationship between real cell mass and effective cell mass was correlated as an Eq. (4). X eff ¼
0:205X 0:090 þ X
(4)
The equation implies that the maximum effective cell mass is 0.205 mg/bead or 7593.2 mg/L. With this simplification, mass transfer of benzene from bulk liquid into a bead pore, benzene degradation by microorganisms and other physical and biological factors were lumped into effective cell mass. With the assumption (2), the degradation rate of benzene was proportional to total effective cell mass (XeffN, effective cell mass bead number) in the bubble column bioreactor. From the assumption (3), benzene degradation in a batch experiment can be expressed as Eq. (5) where gmax and Kr represent maximum specific degradation rate of benzene (min1) and half saturation constant (mg/L), respectively. Cell mass change was expressed as Eq. (6) and effective cell mass was calculated by combining Eqs. (4) and (6). The resulting integrated equation for the removal of benzene in the bubble column bioreactor is Eq. (7). V
dC 1 g C1 ¼ max X eff N dt K r þ C1
dX g C1 ¼ Y x=s max X eff dt K r þ C1
dC1 g C1 ¼ FC i FC 1 kC 1 max X eff N dt K r þ C1
(7)
where Yx/s, V, t, F and Ci denote cell yield (mg-cell/mgbenzene), working volume of bubble column bioreactor (L), time (min), flow rate of influent stream (L/min) and benzene concentration in influent stream (mg/L), respectively. To determine gmax and Kr, a batch experiment was conducted. One hundred benzene-adapted beads of which initial cell concentration was 2.54 102 mg/bead were put in a flask containing benzene and the behavior of benzene degradation was investigated as shown in Fig. 4. From the Lineweaver–Burk plot [24], rmax and Kr were determined to be 1.75 102 min1 and 55.97 mg/L, respectively. When suspended free cells were used, those values were 3.11 102 min1 and 33.54 mg/L, respectively [25]. The maximum specific degradation rate of benzene of suspended free cells was 1.8 times higher than that of immobilized cells and half saturation constant of the suspended free cells was lower than that of immobilized cells by 22.43 mg/L, which may be due to the mass transfer resistance of benzene from bulk liquid phase to cells in a bead. The parameters for the model equations of bubble column bioreactor section are listed in Table 1. In order to validate the model equations, an independent experiment was conducted as
(5)
(6)
Fig. 5. Comparison of simulation data with measured data in a bubble column bioreactor. Airflow rate = 1.0 vvm, benzene concentration = 45 mg/L, residence time = 15 min (a, *) and 60 min (b, &).
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Table 2 Comparison of simulation data with measured data for the removal efficiency of benzene in a bubble column bioreactor section Removal efficiency (%) a
Operation variables Benzene (mg/L)
Retention time (min)
Air flow rate (L/min)
Experiment (%)
Simulation (%)
Difference (%) (experiment simulation)
45 45 45
15 30 60
0.5 0.5 0.5
76.1 2.2 91.4 1.0 93.5 4.2
85.0 92.3 96.1
8.9 0.9 2.6
45 45 45
15 30 60
1.0 1.0 1.0
85.2 1.9 92.7 1.3 98.8 1.2
87.4 93.5 96.7
2.2 0.8 +2.1
75 75 75
15 30 60
0.5 0.5 0.5
76.1 3.2 91.6 2.7 94.7 0.8
84.1 92.0 96.0
8.0 0.4 1.3
75 75 75
15 30 60
1.0 1.0 1.0
83.6 2.6 94.3 1.8 95.1 1.3
86.9 93.3 96.7
3.3 +1.0 1.6
a
Removal efficiency = (removed benzene/influent benzene) 100.
shown in Fig. 5. The model equation well described time course of benzene degradation. The simulation data at various operation conditions were compared with duplicated experimental data at steady state in Table 2 and the difference of simulation data between them was less than 10%. 3.2. Model of a biofilter section In the hybrid bioreactor operation, inlet gaseous benzene concentration into the biofilter section was continuously varied, because stripped benzene concentration by air injection from the bubble column bioreactor section was continuously changed. That is, an initial condition (benzene concentration at the bottom of the biofilter) required to solve the conventional biofilter model equations also varied according to operation time. Thus, quasi steady state was assumed for convenience’s sake in the present study as many researchers did [10– 12,18,26]. According to Ottengraf [18], due to a small bead diameter (order of magnitude some millimeters) usually applied in biofilter and a generally low water solubility of the compounds to be transferred, the mass transfer resistance in the gas phase can generally be neglected. He also suggested that the compound concentrations in the wet biolayer at the interface are continuously in equilibrium with the respective concentrations in the bulk of the gas phase, thus continuous mass flow of the compounds from the gas to the wet biolayer maintains. Therefore, mass transfer resistance is not considered. In this study, the model of biofilter was developed with following five assumptions. (1) The concentration varies continuously in the axial direction through the biofilter. Consequently, the reaction rate will also vary axially. Therefore, the model of PFR (plug flow reactor) is used to express biofilter mathematically. PFR consists of a cylindrical column and is normally operated at steady state [27]. (2) Axial dispersion and diffusion of benzene in a air stream is negligible.
(3) The concentration of benzene in liquid phase is related to the benzene concentration in gas phase through the expression Cgas = HCliq, where H is Henry’s constant of benzene. (4) The specific degradation rate of benzene has a Monod-type dependency on benzene concentration in liquid phase. (5) Beads are hard (incompressible and non-swellable) sphere and distributed uniformly throughout the biofilter column. The system was schematically shown in Fig. 6 and the equation was derived just as the model of PFR was done. Mass balance over benzene in a biofilter column at quasi steady state with assumptions (1) and (2) can be expressed as Eq. (8) [27]. 0 ¼ F air2 C 2 jz F air2 C2 jzþDz r b DV
(8)
where DV, F air2, C2 and rb denotes control volume of biofilter (L), air flow rate (L/min) benzene concentration in biofilter (mg/L) and specific degradation rate of benzene in biofilter (mg/L min), respectively. From the assumption (3), specific degradation rate of benzene in a biofilter can be expressed as Eq. (9), where Cliq is the benzene concentration in liquid phase (mg/L) and can be converted to Cgas/H as mentioned in assumption (3). H was already measured to be 0.241 at 30 8C [1]. rb ¼
ymax Cliq X st K v þ C liq
(9)
Superficial airflow rate (yz) was airflow rate divided by cross sectional area of the biofilter as shown in Eq. (10) (Fig. 6). DV ¼ ADz;
yz ¼
F air F air ¼ 2 A pr
(10)
By substituting Eqs. (10) to (8) and approaching Dz ! 0, the resulting model equation of the biofilter section was obtained as Eq. (11). dC 2 1 ymax ðC 2 =HÞ ¼ X st yz K v þ ðC2 =HÞ dZ
(11)
S.H. Yeom / Process Biochemistry 42 (2007) 554–560
559
Fig. 6. Schematic diagram of PFR adopted for the mathematical analysis of biofilter section.
The advantage of this model is that only two parameters (ymax, Kv) are to be determined and this can be carried out by only one set of experiment at quasi steady-state. An experiment was performed with 1.4 mg/L of inlet benzene concentration and 0.35 m/min of superficial air flow rate (0.76 min of residence time). As time went, the benzene degradation profile changed from linear (zero order) to exponential (first order) behavior [1]. After 72-h operation, the benzene degradation profile following exponential behavior along the biofilter column maintained so it can be said that quasi steady-state was established in the biofilter. Constant cell mass (Xst) can be assumed at this stage [10,17,26] and it was measured to be 4.42 g/L. From the Lineweaver–Burk plot [23], ymax and Kv were determined to be 8.25 104 min1 and 0.98 mg/L, respectively. An independent experiment was conducted to validate the proposed model, which well described the degradation of benzene in the biofilter column at quasi steady-state in an independent experiments as shown in Fig. 7. To show the usefulness of the model firmly, the simulation data
Fig. 8. Comparison of simulation data with measured data with various inlet benzene concentrations in a biofilter section. Superficial air flow rate = 0.18 m/min.
for the effect of inlet benzene concentration on the removal efficiency were compared with the experimental data as shown in Fig. 8. As inlet benzene concentration was increased, the removal efficiency was decreased in both simulation and experimental results. The difference between them was negligible at high inlet benzene concentration. Due to detection limit of GC, a minor difference was shown at low inlet benzene concentration. 4. Conclusion In this study, simple but practical model equations were proposed to describe the degradation of benzene in both the bubble column bioreactor section and the biofilter section. The results showed that the CSTR concept was suitable for the bubble column bioreactor with well-mixed liquid and that the PFR concept was good for the biofilter operating at quasisteady state. In the further study, the effects of operation variables on the performance of each section will be investigated and optimization of the hybrid bioreactor be conducted. Acknowledgement This study was financially supported from Kangwon Regional Environmental Technology Development Center and the author thanks for the support. References
Fig. 7. Comparison of simulation data with measured data in a biofilter section. Superficial airflow rate = 0.18 m/min (*) and 0.35 m/min (&).
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A simplified steady-state model of a hybrid bioreactor composed of a bubble column bioreactor and biofilter compartments Sung Ho Yeom * Department of Environmental and Applied Chemical Engineering, Kangnung National University, Gangneung, Gangwondo 210-702, Republic of Korea Received 28 February 2006; received in revised form 26 September 2006; accepted 23 October 2006
Abstract In a previous study, a hybrid bioreactor comprised of a bubble column bioreactor section and a biofilter section was successfully applied to the treatment of benzene. In order to design and optimize the bioreactor system for actual use in the field, simple but effective mathematical models of the two-stage system were required. Since the liquid phase in the bubble column bioreactor section was well mixed, a CSTR (continuously stirred tank reactor) model was adopted for this section, with benzene removal by both air stripping and biodegradation being considered in the model equations. The gaseous benzene degradation in the biofilter section was described using a PFR (plug flow reactor) model. The combined model was validated through independent experiments, and the simulation results were in a good agreement with measured data. # 2006 Elsevier Ltd. All rights reserved. Keywords: Hybrid bioreactor; Modeling; Bubble column bioreactor; Biofilter; CSTR; PFR
1. Introduction It was shown that a hybrid bioreactor comprising of a bubble column bioreactor and a biofilter was a novel and excellent bioreactor system for the treatment of benzene, a volatile organic compound [1]. Recently, a Korean company tried to apply the hybrid bioreactor to actual wastewater treatment and needed simple but applicable mathematical models for the purpose of system design and optimization. Many mathematical analysis have been done on bubble column bioreactors and biofilters separately. In general, it is known to be very difficult to analyze bubble column bioreactor because the fluid dynamics of air bubbles and liquid phase in the bioreactor is very complex [2,3]. Therefore, experimental equations representing gas hold-up, mass transfer, liquid mixing and gas mixing are frequently used to establish models of bubble column bioreactor with many assumptions [4]. Hecht et al. [5], for example, developed a model of bubble column bioreactor containing immobilized microorganisms with following assumptions: (1) gas phase in plug flow, (2) wellmixed liquid phase, (3) quasi steady-state conditions for mass
* Tel.: +82 33 640 2406; fax: +82 33 641 2410. E-mail address: [email protected]. 1359-5113/$ – see front matter # 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.procbio.2006.10.012
transfer and reaction rates, (4) biomass concentration is an independent variable, (5) first order reaction with regard to biomass and substrate, zero order for oxygen, and (6) isobaric conditions. When the length of bubble column bioreactor is long enough compared with inner diameter of the column, a model equation representing pollutant concentration profile along the column is required to predict the pollutant degradation in a bubble column bioreactor [6,7]. However, if a pollutant concentration in effluent stream is the same as that in bubble column bioreactor (no concentration gradient along the column), complete mixing can be assumed, which makes mathematical model noticeably simple. In contrast to model of bubble column bioreactor, scientists and engineers have been trying to develop theoretical models of biofilter. Pioneering research in this area was conducted by Ottengraf and Van Den Oever [8] who considered the problem as composed of two phase: a bulk gas and a wet stagnant biolayer on the surface of solid particles in which contaminants are free to transfer from one to another. Based on this conceptual framework, they introduced a model in which a pair of equations, for each phase, accounts for diffusion and reaction in the biolayer, and advection in the vapor phase with equilibrium constraints at the interface. The same model, but with Haldane kinetics [9], was then applied by Shareefdeen and Baltzis [10] to predict methanol degradation. Hodge and
S.H. Yeom / Process Biochemistry 42 (2007) 554–560
Devinny [11] made the following modifications to the original model: (1) added dispersion to the gas phase, (2) ignored diffusion in the biofilm, and (3) took into account the presence of carbon dioxide. Even with the added features, some discrepancy still exists between the model predictions and the measured ethanol concentration along the biofilter. Another modification to the model was made with the incorporation of substrate adsorption and a rate expression suitable for twosubstrate systems [12,13]. As models become more refined, the more measurements which are necessary not only to validate the models but also to inspire modelling are required [2]. Although they have developed the models theoretically, many assumptions were still involved and many experimental data were required to get parameters. Shareefdeen and Baltzis [10] used 14 assumptions for the model development. Hodge and Devinny [11], Deshusses et al. [12], Zarook et al. [14] and Lu et al. [15] used 7, 10, 13 and 8 assumptions, respectively. Also, much time should be devoted to solve the partial differential equations suggested by them but the models did not show high accuracy in a wide experimental range. Therefore most of biofilter models were developed with the assumptions such as constant effective diffusivity, constant mass transfer rate, constant cell mass and thus quasi steady-state [11,16,17]. They supposed 1st-order degradation rate and the parameters contained in those models sometimes do not have clear physical or biological meanings. Although their simplified macro-kinetic models are very convenient to calculate removal efficiency at quasi steady state, they do not predict the behavior of pollutant precisely in the wide experimental range mainly because the rate of degradation is not necessarily 1st order [18]. In this study, the bubble column bioreactor and biofilter were mathematically described separately by adopting the simple concept of CSTR (continuously stirred tank reactor) and PFR (plug flow reactor), respectively. Each model required just 3–5 assumptions and 2–5 parameters to be determined. The models were validated through independent experiments and the simulation data were in a good agreement with measured ones.
2.3. Reactor design and operation conditions The hybrid bioreactor composed of a biofilter section and a bubble column bioreactor section was shown in Fig. 1. The diameter of a hybrid bioreactor was 6.0 cm. The working volume of bubble column bioreactor containing 100 mL of immobilized cells (beads) was 500 mL and that of the biofilter 760 cm3 (height, 27 cm). Four and one sampling ports were attached to the biofilter and bubble column bioreactor section, respectively. The hybrid bioreactor was installed in an exhaust hood and operated at 30 8C. To maintain the beads wet and to provide nutrient medium to microorganisms in the biofilter, 100 mL of medium was added from the top of the hybrid bioreactor every 10 h. The medium contained 2 g/L (NH4)2SO4, 0.3 g/L MgSO47H2O, 0.1 g/L K2HPO4, 0.1 g/L CaCl2 and 200 mL/L trace element. The trace element consisted of 16.2 g/L FeCl36H2O, 10.2 g/L CaCl22H2O, 0.22 g/L CoCl26H2O, 0.15 g/L CuSO45H2O, 0.13 g/L CrCl36H2O, 0.09 g/L NiCl36H2O and 40.0 g/L citric acid. The residence time was changed by manipulating the pumping rate of influent benzene solution. Air flow rate was changed by manipulating the air flow regulator attached to an air compressor.
2.4. Adaptation In order to eliminate adaptation time which alters the start point of degradation, microorganisms were fully adapted to benzene as follows. A 100 mL of beads were placed in a 500 mL flask containing 200 mL medium and cultured for 20 h at 30 8C. The medium also contained 120 mg/ L of benzene and inorganic nutrients of which composition was described above.
2.5. Assays The liquid benzene concentrations were analyzed by directly injecting 2 mL of the liquid sample into a gas chromatograph (HP 5890 II). To measure gas phase benzene, 1000 mL gas was directly withdrawn from off-gas port of biofilter section and injected into the GC. The detection limit of the GC was 0.05 mg/L. Cell mass in a bead was determined as follows. One hundred beads were dissolved in 7 mL of 65 mM phosphate buffer and sonicated. Cell free extract and alginate solution were separated by centrifugation. The total protein concentration in cell free extract was determined according to Bradford method [19] using a Bio-Rad protein assay kit with bovine albumin as a standard. The experiment showed that 1 g/L of cell mass corresponded to 0.47 g/L of protein.
2. Materials and methods 2.1. Microorganism Alcaligenes xylosoxidans Y234 isolated from crude oil-contaminated soil was used in this study. It can degrade benzene, toluene m-xylene and phenol [1]. A. xylosoxidans Y234 was precultured at 30 8C in a 500 mL flask containing 200 mL of medium (10 g/L glucose, 5 g/L yeast extract, 5 g/L (NH4)2SO4, 5 g/L KH2PO4 and 1 g/L MgSO7H2O).
2.2. Immobilization Sodium alginate was dissolved in hot distilled water to produce 5% solution. The microorganisms harvested from precultured solution by centrifugation (Hitachi, SCR 18B) were resuspended in distilled water and mixed with the same volume of sodium alginate solution to produce 5 g/L of cell mass. This mixture was extruded through a thin needle attached to a peristaltic pump into a 1% CaCl2 solution thus forming beads with a diameter of about 3 mm. After hardening for 1 h in this solution, the beads were washed several times with distilled water.
555
Fig. 1. Schematic diagram of the hybrid bioreactor.
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3. Results and discussions 3.1. Model of bubble column bioreactor section In this study, since only liquid benzene is fed to the bubble column bioreactor section, gas phase (air bubbles here) behavior is not considered. The model of the bubble column bioreactor was developed on the basis of following three assumptions. (1) Liquid phase is completely mixed, that is, benzene concentration is homogeneous throughout bubble column bioreactor. (2) Degradation rate of benzene is proportional to effective cell mass in the bioreactor described below. (3) The benzene degradation has a Monod-type dependency on benzene concentration. In the present study, since the column length was relatively short in comparison with the inner diameter of bubble column bioreactor (6 cm versus 17 cm) and the difference between benzene concentration in the effluent stream and that in the bubble column bioreactor was negligible (e.g., 2.16 mg/L versus 2.21 mg/L), the liquid phase in the bioreactor was supposed to be well mixed. Therefore, the model of the bubble column bioreactor can be expressed by adopting the concept of CSTR. The dissolved oxygen level was always above 23% of saturation value in the experimental ranges so only carbon source limitation is considered. Benzene was removed by both air injection and immobilized cells in the bubble column bioreactor. The decrease in benzene concentration by air injection in the bubble column bioreactor can be expressed as follows [1]. dC1 ¼ kC 1 dt
(1)
where C1 and k are liquid benzene concentration in the bubble column bioreactor section (mg/L) and benzene removal rate constant (L/min), respectively. The effect of airflow rate on the removal rate constant was shown in Fig. 2 and expressed as Eq. (2).
Fig. 2. The relationship between airflow rate and benzene removal constant in a bubble column bioreactor section. 1 vvm = 0.5 L/min.
benzene appeared almost constant. Although high cell mass loading is one of the main advantages of immobilization, cell mass above some level is not effective any more in terms of the degradation rate of benzene because of mass transfer limitation and reduction of available surface area. Similar phenomena were reported by other researchers [21–23]. Effective cell mass (Xeff) is now introduced to reflect those phenomena in this study. Effective cell mass is a hypothetical cell mass, which is calculated on the basis of degradation rate. That is, it is assumed that the same degradation rate means the same effective cell mass and that benzene degradation rate is directly proportional to effective cell mass throughout experimental range. Effective cell mass was calculated from benzene degradation rate as follows. The first effective cell mass was taken in the very lower region A (0.94 g/L here), and the effective cell mass was set to be the same as the real cell mass in a bead. The n-th effective
k ¼ f ðF air Þ 2 þ 1:823 105 F air þ 1:450 103 ¼ 3:657 108 Fair
(2) where F air is air flow rate (L/min) into the bubble column bioreactor section. Next, the benzene removal by immobilized cells was investigated. An alginate bead was considered as one catalyst of which ability to degrade benzene was proportional to the cell mass in a bead [20]. To investigate the dependency of degradation rate of benzene on the cell mass in a bead, the degradation rate of benzene was investigated changing cell mass in a bead. As shown in Fig. 3, as the cell mass increased in the range of 0–6 g/L (region A), so did the degradation rate of benzene linearly. However, in the range where the cell mass in a bead exceed that concentration (region B), degradation rate of
Fig. 3. The effect of cell mass on the benzene degradation rate.
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557
Table 1 Parameters for the simulation of a bubble column bioreactor section Parameter
Value
Remarks
k (mg/L) Kr (mg/L) N rmax (min1) Xeff (mg/bead) Yx/s
See Eq. (2) 55.97 3704 1.75 102 See Eq. (4) 0.33
Experimental Experimental Calculated Experimental Experimental Experimental
V
Fig. 4. Degradation of benzene by immobilized cells in a batch experiment.
cell mass is the product of first effective cell mass (or first actual cell mass) and the ratio of benzene degradation rate at n-th cell mass to that at first cell mass as shown in Eq. (3). Also, the ratio between any two degradation rates is equal to the ratio between the two effective cell masses. X eff; j-th ¼
degradation rate at X j-th ðX eff;1-st Þ degradation rate at X 1-st
(3)
where Xj-th represents the real cell mass and Xeff,j-th does effective cell mass at real cell mass Xj-th in a bead. The relationship between real cell mass and effective cell mass was correlated as an Eq. (4). X eff ¼
0:205X 0:090 þ X
(4)
The equation implies that the maximum effective cell mass is 0.205 mg/bead or 7593.2 mg/L. With this simplification, mass transfer of benzene from bulk liquid into a bead pore, benzene degradation by microorganisms and other physical and biological factors were lumped into effective cell mass. With the assumption (2), the degradation rate of benzene was proportional to total effective cell mass (XeffN, effective cell mass bead number) in the bubble column bioreactor. From the assumption (3), benzene degradation in a batch experiment can be expressed as Eq. (5) where gmax and Kr represent maximum specific degradation rate of benzene (min1) and half saturation constant (mg/L), respectively. Cell mass change was expressed as Eq. (6) and effective cell mass was calculated by combining Eqs. (4) and (6). The resulting integrated equation for the removal of benzene in the bubble column bioreactor is Eq. (7). V
dC 1 g C1 ¼ max X eff N dt K r þ C1
dX g C1 ¼ Y x=s max X eff dt K r þ C1
dC1 g C1 ¼ FC i FC 1 kC 1 max X eff N dt K r þ C1
(7)
where Yx/s, V, t, F and Ci denote cell yield (mg-cell/mgbenzene), working volume of bubble column bioreactor (L), time (min), flow rate of influent stream (L/min) and benzene concentration in influent stream (mg/L), respectively. To determine gmax and Kr, a batch experiment was conducted. One hundred benzene-adapted beads of which initial cell concentration was 2.54 102 mg/bead were put in a flask containing benzene and the behavior of benzene degradation was investigated as shown in Fig. 4. From the Lineweaver–Burk plot [24], rmax and Kr were determined to be 1.75 102 min1 and 55.97 mg/L, respectively. When suspended free cells were used, those values were 3.11 102 min1 and 33.54 mg/L, respectively [25]. The maximum specific degradation rate of benzene of suspended free cells was 1.8 times higher than that of immobilized cells and half saturation constant of the suspended free cells was lower than that of immobilized cells by 22.43 mg/L, which may be due to the mass transfer resistance of benzene from bulk liquid phase to cells in a bead. The parameters for the model equations of bubble column bioreactor section are listed in Table 1. In order to validate the model equations, an independent experiment was conducted as
(5)
(6)
Fig. 5. Comparison of simulation data with measured data in a bubble column bioreactor. Airflow rate = 1.0 vvm, benzene concentration = 45 mg/L, residence time = 15 min (a, *) and 60 min (b, &).
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Table 2 Comparison of simulation data with measured data for the removal efficiency of benzene in a bubble column bioreactor section Removal efficiency (%) a
Operation variables Benzene (mg/L)
Retention time (min)
Air flow rate (L/min)
Experiment (%)
Simulation (%)
Difference (%) (experiment simulation)
45 45 45
15 30 60
0.5 0.5 0.5
76.1 2.2 91.4 1.0 93.5 4.2
85.0 92.3 96.1
8.9 0.9 2.6
45 45 45
15 30 60
1.0 1.0 1.0
85.2 1.9 92.7 1.3 98.8 1.2
87.4 93.5 96.7
2.2 0.8 +2.1
75 75 75
15 30 60
0.5 0.5 0.5
76.1 3.2 91.6 2.7 94.7 0.8
84.1 92.0 96.0
8.0 0.4 1.3
75 75 75
15 30 60
1.0 1.0 1.0
83.6 2.6 94.3 1.8 95.1 1.3
86.9 93.3 96.7
3.3 +1.0 1.6
a
Removal efficiency = (removed benzene/influent benzene) 100.
shown in Fig. 5. The model equation well described time course of benzene degradation. The simulation data at various operation conditions were compared with duplicated experimental data at steady state in Table 2 and the difference of simulation data between them was less than 10%. 3.2. Model of a biofilter section In the hybrid bioreactor operation, inlet gaseous benzene concentration into the biofilter section was continuously varied, because stripped benzene concentration by air injection from the bubble column bioreactor section was continuously changed. That is, an initial condition (benzene concentration at the bottom of the biofilter) required to solve the conventional biofilter model equations also varied according to operation time. Thus, quasi steady state was assumed for convenience’s sake in the present study as many researchers did [10– 12,18,26]. According to Ottengraf [18], due to a small bead diameter (order of magnitude some millimeters) usually applied in biofilter and a generally low water solubility of the compounds to be transferred, the mass transfer resistance in the gas phase can generally be neglected. He also suggested that the compound concentrations in the wet biolayer at the interface are continuously in equilibrium with the respective concentrations in the bulk of the gas phase, thus continuous mass flow of the compounds from the gas to the wet biolayer maintains. Therefore, mass transfer resistance is not considered. In this study, the model of biofilter was developed with following five assumptions. (1) The concentration varies continuously in the axial direction through the biofilter. Consequently, the reaction rate will also vary axially. Therefore, the model of PFR (plug flow reactor) is used to express biofilter mathematically. PFR consists of a cylindrical column and is normally operated at steady state [27]. (2) Axial dispersion and diffusion of benzene in a air stream is negligible.
(3) The concentration of benzene in liquid phase is related to the benzene concentration in gas phase through the expression Cgas = HCliq, where H is Henry’s constant of benzene. (4) The specific degradation rate of benzene has a Monod-type dependency on benzene concentration in liquid phase. (5) Beads are hard (incompressible and non-swellable) sphere and distributed uniformly throughout the biofilter column. The system was schematically shown in Fig. 6 and the equation was derived just as the model of PFR was done. Mass balance over benzene in a biofilter column at quasi steady state with assumptions (1) and (2) can be expressed as Eq. (8) [27]. 0 ¼ F air2 C 2 jz F air2 C2 jzþDz r b DV
(8)
where DV, F air2, C2 and rb denotes control volume of biofilter (L), air flow rate (L/min) benzene concentration in biofilter (mg/L) and specific degradation rate of benzene in biofilter (mg/L min), respectively. From the assumption (3), specific degradation rate of benzene in a biofilter can be expressed as Eq. (9), where Cliq is the benzene concentration in liquid phase (mg/L) and can be converted to Cgas/H as mentioned in assumption (3). H was already measured to be 0.241 at 30 8C [1]. rb ¼
ymax Cliq X st K v þ C liq
(9)
Superficial airflow rate (yz) was airflow rate divided by cross sectional area of the biofilter as shown in Eq. (10) (Fig. 6). DV ¼ ADz;
yz ¼
F air F air ¼ 2 A pr
(10)
By substituting Eqs. (10) to (8) and approaching Dz ! 0, the resulting model equation of the biofilter section was obtained as Eq. (11). dC 2 1 ymax ðC 2 =HÞ ¼ X st yz K v þ ðC2 =HÞ dZ
(11)
S.H. Yeom / Process Biochemistry 42 (2007) 554–560
559
Fig. 6. Schematic diagram of PFR adopted for the mathematical analysis of biofilter section.
The advantage of this model is that only two parameters (ymax, Kv) are to be determined and this can be carried out by only one set of experiment at quasi steady-state. An experiment was performed with 1.4 mg/L of inlet benzene concentration and 0.35 m/min of superficial air flow rate (0.76 min of residence time). As time went, the benzene degradation profile changed from linear (zero order) to exponential (first order) behavior [1]. After 72-h operation, the benzene degradation profile following exponential behavior along the biofilter column maintained so it can be said that quasi steady-state was established in the biofilter. Constant cell mass (Xst) can be assumed at this stage [10,17,26] and it was measured to be 4.42 g/L. From the Lineweaver–Burk plot [23], ymax and Kv were determined to be 8.25 104 min1 and 0.98 mg/L, respectively. An independent experiment was conducted to validate the proposed model, which well described the degradation of benzene in the biofilter column at quasi steady-state in an independent experiments as shown in Fig. 7. To show the usefulness of the model firmly, the simulation data
Fig. 8. Comparison of simulation data with measured data with various inlet benzene concentrations in a biofilter section. Superficial air flow rate = 0.18 m/min.
for the effect of inlet benzene concentration on the removal efficiency were compared with the experimental data as shown in Fig. 8. As inlet benzene concentration was increased, the removal efficiency was decreased in both simulation and experimental results. The difference between them was negligible at high inlet benzene concentration. Due to detection limit of GC, a minor difference was shown at low inlet benzene concentration. 4. Conclusion In this study, simple but practical model equations were proposed to describe the degradation of benzene in both the bubble column bioreactor section and the biofilter section. The results showed that the CSTR concept was suitable for the bubble column bioreactor with well-mixed liquid and that the PFR concept was good for the biofilter operating at quasisteady state. In the further study, the effects of operation variables on the performance of each section will be investigated and optimization of the hybrid bioreactor be conducted. Acknowledgement This study was financially supported from Kangwon Regional Environmental Technology Development Center and the author thanks for the support. References
Fig. 7. Comparison of simulation data with measured data in a biofilter section. Superficial airflow rate = 0.18 m/min (*) and 0.35 m/min (&).
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