Environ. Sci. Technol. 2007, 41, 5875-5881
Predicting the Accumulation of Harmful Metabolic Byproducts During the Treatment of VOC Emissions in Suspended Growth Bioreactors S. BORDEL, R. MUN ˜ OZ, L. F. DIAZ, AND S. VILLAVERDE* Valladolid University, Department of Chemical Engineering and Environmental Technology, Paseo del Prado de la Magdalena, s/n, E-47005 Valladolid, Spain
A predicting model is proposed to evaluate metabolic byproducts accumulation and process performance in suspended growth reactors treating air emissions contaminated with volatile organic compounds (VOCs). The model presented integrates a multistep kinetic model and a general mechanistic model describing bioreactor operation. This integrated model is based on general equations modeling, both mass transport and the mechanisms underlying pollutant biotransformation and byproducts accumulation, and can be applied to a wide range of operating conditions (VOC substrate, O2, and nutrients limitation) The model was tested for predicting benzyl alcohol (BA) accumulation in a chemostat reactor treating toluene. BA accumulates in Pseudomonas putida F1 cultures degrading toluene as a result of methyl monooxygenation reaction parallel to the main TOD degradation pathway. The operational conditions leading to BA accumulation are evaluated through simulations assays. Simulation results indicate that BA accumulation occurs when other substrates rather than toluene are limiting. Therefore, operation under toluene limitation is highly recommended to ensure not only the detoxification goals but also to avoid potential mutagenic effects of BA over the microbial culture.
Introduction Operational problems derived from the accumulation of harmful metabolites represent a serious limitation to the implementation of biological methods for the off-gas treatment of volatile organic contaminants (VOCs) (1-3). These metabolites are often produced during the aerobic biodegradation of VOCs or during the cometabolic conversion of chlorinated VOCs, and they can be even more toxic than their parent compounds (4-7). Bacteria can contain more than one pathway for the degradation of the VOC derivatives (4, 8, 9). These pathways, and each conversion step within the pathways, are modulated by a number of factors such as the concentration of enzymes, substrates, and cosubstrates (such as O2 and/or an electron carrier). Any difference on the rate at which each conversion step takes place may render the accumulation of metabolic * Corresponding author phone: +34983423656; fax: +34983423013; e-mail:
[email protected]. 10.1021/es070365k CCC: $37.00 Published on Web 07/12/2007
2007 American Chemical Society
intermediates in the main degradation pathway (10), which are commonly found during episodes of high loading rates (3, 5, 11). In other cases, metabolic byproducts accumulate as a result of the activation/inactivation of specific enzymes under different conditions. These metabolic byproducts are not formed in the main degradation pathway. For instance, Yu and co-workers (6) reported the accumulation of cresol and phenol in PpF1 cultures degrading toluene and benzene under O2 limiting conditions, respectively. A similar scenario can be found in the cometabolic conversion of toxic VOCs such as chlorinated ethenes (CE), wherein CE conversion metabolites might accumulate. These metabolic byproducts do not support bacterial growth but often inactivate the enzymatic machinery of bacteria, with the consequent decrease in biodegradation performance (4, 12). Bordel and co-workers (13) reported benzyl alcohol (BA) accumulation into the culture broth as a result of a sidechain monooxygenation of toluene in PpF1. This accumulation had no apparent effects on the overall process as BA did not support significant PpF1 growth nor inhibit toluene biodegradation (13). However, BA was previously reported as responsible for the loss of the toluene degradation capacity in Pseudomonas putida 54G. Its mutagenic properties triggered the growth of mutants incapable to degrade toluene (14-15). Therefore, the accumulation of BA in Pseudomonas cultures must be followed and controlled to avoid any potential mutagenic effects. This requires the development of mathematical models for predicting the accumulation of these harmful metabolitc byproducts. To the best of our knowledge, the mathematical modeling of the accumulation of metabolic byproducts, formed in parallel reactions to the main catabolic pathway, has never been reported. Few kinetic models describing the accumulation of metabolic intermediates are available (10, 16, 17). These models predicted the overall biodegradation rate by calculating the consumption rate of the metabolic intermediate accumulating into the system (10). Nevertheless, the modeling of processes where metabolic byproducts accumulate must take into account the degradation rate of both the main VOC fraction following the natural degradation pathway (TOD for toluene in PpF1) and the small VOC fraction bioconverted in side reactions (BA in PpF1) (Figure 1). In this work, a previously described multistep kinetic model (17) was adapted to predict the accumulation of BA, during the degradation of toluene in PpF1 cultures. The multistep model was integrated within a mechanistic model for predicting the performance of suspended growth bioreactors (SGRs) (18). The aim was to build a holistic model capable of predicting the accumulation of BA together with the toluene removal rate and biomass production in SGRs. The system modeled was a PpF1 culture growing in a chemostat operated either under toluene, oxygen, or nitrogen limitation.
Theoretical Aspects Metabolic Byproduct Accumulation Model. Multistep kinetic models are necessary when accumulating extracellular metabolites support biomass growth since Monod or Andrews-Haldane equations are not capable of modeling these processes (10, 16). These multikinetic models aimed at describing the metabolic fluxes of carbon and/or electrons throughout the degradation pathways, and at determining the stoichiometries and energy yields for biomass growth (11, 19, 20). VOL. 41, NO. 16, 2007 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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The fact that BA accumulation rate was constant during bioreactor start-up (13) indicated that BA concentration (i.e., its external flux Jex i , see SI) did not significantly affect its consumption rate. Therefore, η can be considered as zero. In this context, eqs 1 and 2 can be combined as follows.
kS JBAfX+CO2 ) kBA kS + k/BA
FIGURE 1. Alternative biodegradation pathways for toluene by PpF1 that render 3 methyl cathecol through the main TOD pathway (solid arrow), and benzyl alcohol in a side methyl monooxygenation reaction (dotted arrow). Based on the concept of synthesizing unit (SU) proposed by Kooijman (21), Bordel and co-workers (17) successfully developed a multistep kinetic model to describe the accumulation of catechol during benzene biodegradation by a PpF1. Kooijman defined SU as a generalized enzyme governed by classical association-dissociation kinetics (22). SU kinetics is thus based on arrival rates rather than on concentrations, which is particularly useful in heterogeneous environments inside the cell, where the concentration concept is not easy to apply. Details on the mathematical formulation of the sequence of biotransformations followed by the VOC substrate can be found in the Supporting Information (SI) section and in previous work (17). During toluene (S) biodegradation by PpF1 no accumulation of metabolic intermediates of the TOD pathway, such as 3-methyl catechol, was recorded in the cultivation (13). However, toluene monooxygenation into benzyl alcohol (BA) did occur in a side-chain reaction (Figure 1). The multistep kinetic model was thus tailored to describe the accumulation of BA, a side-chain byproduct of toluene biodegradation. The molar production and consumption of benzyl alcohol (BA) can be described by eqs 1 and 2, respectively.
CS JSfBA ) kS * KS + CS
(1)
where CS represents toluene concentration and kS equals k1e1 (see SI).
JSfBA + ηCBA JBAfX+CO2 ) kBA / kBA + JSfBA + ηCBA
(2)
where CBA represents BA concentration, η is a proportionality constant, and kBA and k*BA are equal to k2e2t and ki/γipi in eq 5, SI, respectively. Oxygen limitation is likely to occur during toluene biodegradation, and in this particular case, BA formation and its subsequent mineralization to CO2 and biomass (X) becomes a function of O2 concentration. Therefore, eqs 1 and 2 must be modified to take episodes of O2 limitation into account.
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COx kS ) kS0 COx + KSOx
(3)
COx kBA ) kBA0 COx + KBAOx
(4)
(5)
/
CS +
k/BAK kS +
S k/BA
where BA consumption is modulated by a saturation-like function (kS/(kS + k/BA)), whose value depends on the molar BA production rate per unit of biomass (kS) and a kinetic constant (k/BA) that, by analogy to saturation functions, was named half saturation BA consumption rate constant. Summarizing, the mass of byproduct accumulating per unit of time and biomass can be obtained from equation 5, where νBA is the molar weight of BA.
rBA ) νBA(JSfBA - JBAfCO2+X)
(6)
SGR Operational Model. SGRs are a reliable technology in processes operated at high VOC loadings rates, where byproduct accumulation is likely to occur or, during the degradation of chlorinated VOCs, where medium acidification severely reduces process performance (3, 7, 23). Despite being an effective alternative to biofiltration processes, the development of mechanistic models for predicting SGRs performance is scarce. A mechanistic model describing BTEX removal in an activated sludge process has been reported in the literature (24). Lee and co-workers (23) modeled the cometabolic degradation of TCE using phenol as growth substrate. However, no accumulation of metabolic byproducts resulting from TCE oxidation was reported. The accumulation of metabolic byproducts in SGRs was here addressed by coupling the above-described byproduct accumulation model and a mechanistic model devised to describe the performance of SGRs during the degradation of VOCs (18). This model can be applied to a wide variety of real scenarios where VOC, oxygen, or nutrient supply can limit the biodegradation process. It was capable of accurately describing steady-state VOC elimination rates (RS) and biomass concentrations in SGRs together with the concentrations of VOC, oxygen, and nitrogen (18). This mechanistic model was here adapted for predicting the performance of a chemostat treating toluene where BA accumulation occurred. A mass balance of BA in a chemostat suspended growth bioreactor allowed for estimation of the concentration of this mutagenic byproduct in the reactor effluent.
CBA )
rBA X D
(7)
where D is the dilution rate. The model was thus used to obtain biomass (X) and toluene concentration (rBA ) f(Cs), eq 5) in the reaction medium, which are then employed as input data on the multikinetic model previously described. Microbial growth rate was initially modeled using the SKIP approach proposed by Reardon and co-workers (5) considering the contributions of toluene (S) and BA to microbial growth.
[
µ ) µSmax
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CS
CS + CS + KS + IBA,SCBA µBAmax
]
CBA (8) CBA + KBA + IS,BACS
where Ci, Ki and Ii,j stand for concentration, half saturation constant, and interaction parameter, respectively. The Ii,j parameters are inhibition coefficients that inform on the inhibition exerted by a certain substrate “i” on the consumption of substrate “j”. In a previous work, Bordel and co-workers (13) reported that toluene consumption was not inhibited by BA in PpF1 cultures, which translated into a very low value for the IBA,S coefficient. On the other hand, BA degradation did not significantly occur until toluene was depleted from the media, which implied high values for the IS,BA coefficient. Moreover, although PpF1 was capable of utilizing BA as a sole carbon and energy source, it supported much lower growth rate than toluene or 3-methyl catechol, the most common metabolic intermediate of the TODpathway (13). This, in terms of specific growth rates, implied µBAmax values 2-3 times lower than µSmax. In consequence, the second term of the SKIP equation was negligible and toluene was considered as the sole substrate supporting microbial growth. This is in agreement with the assumption of zeroing the parameter η of eq 2 in the byproduct accumulation model, as the external flux of BA (Jex i , see SI) did not significantly contribute to its consumption rate. The growth eq 8 was then simplified into a Monod eq 9 wherein two saturation functions for O2 and nitrogen limitation were added. The use of a Monod equation instead of the previously described Haldane-Andrews eq 13 was justified by the low concentration range used in this work. Gas toluene concentrations (CginS) from 3.3 to 20.2 × 10-3 kg m-3 rendered liquid toluene concentrations from 14.5 to 89 × 10-3 kg m-3, which are far below the inhibitory constant (KI of 753 × 10-3 kg m-3) reported by Bordel and co-workers (13).
µ ) µmax
CS Cox CN CS + KS Cox + Kox CN + KN
(9)
The pollutant elimination rate (RS) per volume unit is a function of the specific growth rate, the substrate yield coefficient (YX/S), the maintenance coefficient (bS), and the biomass concentration (X).
RS ) qSX )
(
)
µ + bS X YX/S
(10)
where qS represent the specific toluene consumption rate. Oxygen and nutrients consumption rates can be represented using similar equations. At steady state, the elimination rate equals the pollutant transport from the gas to the reaction medium.
RS )
Qg β (Cgin - mSCS) Vr S S
(11)
with
(
βS ) 1 - exp -
)
klaSVr m S Qg
(12)
where Qg is the gas flow, Vr is the reactor volume, Cgin S is the inlet gaseous toluene concentration, and βS is a transport parameter that strongly depends on the volumetric mass transfer coefficient (klaS), and the adimensional Henry constant for the target pollutant (mS). Oxygen transfer can be described by similar equations. Nutrients such as nitrogen or phosphorus are introduced in the mineral salt medium and its consumption rate can be obtained from a simple mass balance. In addition, for a chemostat operating at steady state, the biomass growth rate equals the dilution rate.
D)µ
(13)
The resulting system of eight nonlinear equations necessary to describe the continuous operation of SGRs can be solved simultaneously using a vector-based approach (18). Thus, once the volumetric elimination rate (Rs) is determined, the liquid concentration of toluene can be obtained transforming eq 11 into eq 14. Likewise, O2 concentration can be obtained in a similar equation. Once X, CS and COx are obtained, CBA is directly obtained from equation 7.
CS )
(
)
1 gin RSVr C mS S Qg β S
(14)
Experimental Section Culture Conditions and Microorganisms. A Pseudomonas putida F1 strain [DSMZ 6899] was selected for toluene biodegradation. A modified Brunner medium (MBM) was used for bacterial cultivation. The medium was prepared with 1 kg m-3 of (NH4)2SO4 instead of 0.5 kg m-3 as described in the original medium. Inocula preparation was carried out according to Bordel and co-workers (13). Experimentation. The experiments were carried out under sterile conditions in a magnetically stirred 1 L glass bioreactor (Afora S.A, Spain) operated in chemostat mode at 25 ×C and 500 rpm. Process start-up was carried out according to Bordel and co-workers (13). Toluene was continuously supplied in the gaseous phase through a stone sparger located at the bottom of the bioreactor. Its concentration was regulated by mixing a toluene-saturated stream with a toluene-free air stream at different proportions. The total toluene-laden air flow rate was 1.8 × 10-5 m3 s-1. For a more detailed description of the experimental setup see Bordel and co-workers (13). BA accumulation during continuous operation was monitored at five steady states under D ranging from 3 × 10-5 to 7.5 × 10-5 s-1 (0.11 to 0. 27 h-1) and CSgin from 3.3 to 20.2 × 10-3 kg m-3. These steady states were used to fit the multistep kinetic parameters governing BA production under oxygen limiting conditions (KSOx and KBAOx). Each steady state was maintained for approx one week with daily bioreactor sampling. Process monitorization involved the determination of both toluene and BA concentrations in the gaseous and aqueous phases, respectively, and the absorbance at 650 nm. Besides KSOx and KBAOx, another four parameters of the byproduct accumulation model (ks0, kAB0, KS* and kBA*) were fitted. This was done using experimental data obtained by following the biodegradation process start-up at different gas toluene concentrations (CSgin) as described in Bordel and co-workers (13). Analytical Procedures. Toluene and benzyl alcohol were analyzed according to Bordel and co-workers (13). Toluene analysis was performed in a gas chromatograph (HewlettPackard 5890, Palo Alto, CA) coupled with a mass spectrometer detector (Hewlett-Packard 5973 MSD) and a HP5MS fused silica capillary column (Agilent Technologies, Santa Clara, CA). Benzyl alcohol was quantified by HPLCUV using a WATERS 515 HPLC pump coupled with UV1000 SPECTRASERIESDetector (Thermo separation Products, CA) and a Supelcosil LC-PAH column (Supelco, Bellefonte, PA). External standards were used to enable quantitative determination. Absorbance at 650 nm was used as an indicator of microbial growth and measured using a HITACHI U200 UV/ visible spectrophotometer (Hitachi Ltd, Tokyo, Japan). A correlation between absorbance (A) at 650 nm and biomass dry weight (DW) was performed rendering a linear function VOL. 41, NO. 16, 2007 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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FIGURE 2. Experimental (symbols) and model (solid line) results for the net specific accumulation rate of BA at different toluene concentrations in the liquid phase. with a regression coefficient of 0.995, valid for A values ranging from 0.2 and 0.7.
Results Model Validation and Parameter Fitting. A set of five experimental steady states and six batch experiments was used to correlate the integrated model. Six parameters of the byproduct accumulation model (Table 1) were adjusted by nonlinear regression using the Solver tool of Excel (Microsoft Corp.). This model provided a reasonable good correlation (average relative error of 6%) of the increase of BA production rates with increasing toluene concentrations under nonoxygen limiting conditions (Figure 2). In Table 2, the experimental and predicted values for the concentration of BA are presented at all steady-state experiments conducted together with the removal efficiency (RE) of the system. The average error in the estimation of BA concentrations within the five experimental steady states tested was 17%. At high pollutant concentrations (CSgin of 11.7 × 10-3 and 20.3 × 10-3 kg m-3) the process was limited by O2 mass transport as shown by the low O2 concentrations predicted (COx of 0.8 × 10-3 and 0.7 × 10-3 kg m-3, respectively) and BA accumulated at high concentrations (53 ( 13 × 10-3, 48 ( 8 × 10-3 kg m-3) (Table 2). When toluene was supplied from 3.3 to 6.0 × 10-3 kg m-3, CS remained below 1.5 × 10-3 kg m-3, which indicated that process operated under toluene limiting conditions. Under these conditions CBA remained below 5 × 10-3 kg m-3 (Table 2). The RE ranged between 41 and 89% of toluene removal depending on the operational conditions.
FIGURE 3. Influence of toluene gas inlet concentration (Csgin) on toluene elimination rate, (RS) (solid line), BA (dashed line), and toluene (dotted line) liquid concentrations (CS and CBA, respectively). Simulations done at D ) 5.6 × 10-5 s-1 (0.2 h-1), Qg) 1.8 × 10-5 m3s-1, and klaOx ) 4.2 × 10-2 s-1. Simulation Tool. The coupling of the byproduct accumulation model and the SGR operational model allowed prediction of the toluene removal rate, biomass concentration, and the liquid concentrations of toluene (S), BA, O2, and nitrogen during steady-state operation. To illustrate the potential of this modeling approach, the influence of toluene inlet concentration (CSgin), dilution rate (D), and mass transfer coefficient (klaOx) on BA accumulation and toluene removal rate was evaluated. The simulations assays here reported were done under similar conditions than those presented in Bordel and co-workers (18) to highlight the significance of BA accumulation episodes under the different operational conditions tested. At low toluene concentrations, where the process was limited by toluene supply, BA concentrations remained below 5 × 10-3 kg m-3 (Figure 3). However, at high toluene concentrations (CSgin > 6 × 10-3 kg m-3), nitrogen availability became the limiting factor, resulting in no further increase in the toluene RS and in increasing toluene liquid concentration. This increase in CS was concomitant with an increase in CBA as predicted by eq 6. Therefore, process operation under toluene limiting conditions was highly recommended as it allowed the complete destruction of the target pollutant and avoids the accumulation of toxic and mutagenic metabolic byproducts.
TABLE 1. Parameters of the Byproduct Accumulation Model Fitted by Nonlinear Regression Using Solver (Microsoft Corp.). kS0 × 1010 (mol kg-1s-1)
kBA0 × 1010 (mol kg-1s-1)
KS* × 103 (kg m-3)
kAB* × 1010 (mol kg-1s-1)
KSOx × 103 (kg m-3)
KBAOx × 103 (kg m-3)
7.72
58.3
9.3
58.3
0.92
0.03
TABLE 2. Experimental and Predicted Concentration Values Using the Integrated Model D × 105 (s-1)
3 Cgin S × 10 (kg m-3)a
CS × 103 (kg m-3)b
COx × 103 (kg m-3)b
CN × 103 (kg m-3)b
CBA × 103 (kg m-3)b
CBA × 103 (kg m-3)c
RE (%)e
7.5 7.5 6.5 6.5 3.05
20.2 11.7 6.0 5.4 3.3
47.5 16.2 1.5 1.3 0.4
0.7 0.8 2.5 3.0 4.7
14.4 16.9 52.8 66.4 47.4
56.8 38.9 4.6 3.5 1.5
48 ( 8 53 ( 13 5(1 3(1 d
67 41 88 89 83
a Measured toluene gas concentration. b Model predicted values for the liquid concentrations of S, O , nitrogen, and BA. c Measured BA 2 concentration in the culture broth. d Under the HPLC-UV detection limit (>1 × 10-3 kg m-3). e RE stands for removal efficiency calculated as (CSgin. CSgout)100/Cgin S
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∆CBA/CBA SR ) 100 ∆P/P
(17)
The obtained results for fitted parameters of the byproduct accumulation model, indicated that model predictions were sensitive to the maximum BA production rate per biomass unit (kS0) (SR ) 189%), the maximal BA consumption rate per biomass unit (kBA0) (SR ) 622%), and the half saturation BA consumption rate (kBA*) (SR ) 610%). These rates are of special relevance for evaluating the production and consumption of BA according to eqs 1-6. The fitted parameters corresponding to the substrate semisaturation constant for the reaction of BA formation (KS*) (SR ) 35%), the O2 semisaturation constant in BA production reactions (KSOx) (SR ) 46%), and the oxygen semisaturation constant in BA consumption reactions (KBAOx) (SR ) 46%), did not cause significant changes of BA concentration.
Discussion
FIGURE 4. Influence of the oxygen mass transport coefficient (klaOx) on the toluene elimination rate (RS) (solid line), and BA liquid concentration CBA (dashed line) (upper graph), and toluene CS (dotted line) and oxygen COx (continuous line) liquid concentrations (lower s graph). Simulations done at Cgin ) 5 × 10-3 kg m-3, D ) 5.6 × 10-5 s-1 (0.2 h-1), and Qg) 1.8 × 10-5 m3s-1. BA concentration steadily decreased with increasing D being this decrease concomitant with a decrease in Cs (see Figure 1, SI) as a consequence of the higher nitrogen suppy (which was limiting for low D) (18). At dilution rates higher than 4.16 × 10-5 s-1 (0.15 h-1) toluene supply turned into the limiting factor (Cs ≈ 0 × 10-3 kg m-3) and BA concentration became negligible. In Figure 4 the influence of mass transport coefficient klaOx on the BA accumulation together with the elimination capacity (RS) and the concentrations of toluene and O2 were simulated. BA accumulated initially at low klaOx values up to a maximum for klaOx of 1.5 × 10-2 s-1 as a result of the oxygen limitation. Further increases of klaOx caused CBA to decrease concomitantly with the decrease in the toluene concentration as the production of BA started to be limited by toluene. Toluene removal rate, RS, increased linearly with increasing klaOx to reach its highest value for a klaOx of 3.33 × 10-2 s-1. At that point toluene concentration decreased to values close to KS (1.8 × 10-3 kg m-3) and started to control the biodegradation process. Further increases in klaOx did not cause any changes on the RS as the system had reached the highest removal capacity. Sensitivity Analysis. The sensitivity of the predicted CBA to variations in the byproduct accumulation model parameters was investigated under the following operational conditions: D ) 6.67 × 10-5 s-1 (0.24 h-1), klaOx ) 4.2 × 10-2 s-1, Qg ) 1.8 × 10-5 m3 s-1 and CSgin ) 6 × 10-3 kg m-3. The sensitivity analysis was performed using the ratio between the relative variation of CBA and the relative variation of the target parameter as response variable. Thus, the sensitivity ratio (SR) for a generic parameter P was defined as follows:
The accumulation of metabolic byproducts during continuous process operation is of great importance as these metabolites can be even more toxic than the initial parent VOCs and its accumulation can seriously affect process performance (4-6, 25). The holistic model here presented integrates two previously reported models: (1) a multistep kinetic model developed to describe the accumulation of cathecol during benzene degradation (13), and (2) a mechanistic operational model capable to describe the performance of SGRs (18). This operational model was tailored considering the contribution of all organic substrates supporting growth using the SKIP approach of Reardon and co-workers (5). In our particular case, BA was formed in a side reaction wherein a fraction of the C-source deviated from the TOD pathway, the only catabolic pathway reported for toluene degradation in PpF1 (26). The microbial growth eq 8 included the contribution of toluene and BA to microbial growth since none of the intermediates of the TOD pathway accumulated in the system. Experimental observations allowed simplifying the eqs 2 and 8 of the byproduct accumulation and SGR operational models into eqs 5 and 9, respectively. Although BA did not contribute to microbial growth, its accumulation must be carefully monitored due to its potential mutagenic effects on the culture (14). This has been hypothesized as one of the causes triggering process instability due to the loss of the elimination capacity in toluene biodegradation processes (15, 25). In this regard, the new holistic model herein presented was capable of accurately predict the concentration of metabolic byproducts that might severely limit process performance. Given the merits of this approach, the new model constitutes a very useful tool in the design and operation of biological VOCs treatment process wherein metabolic byproducts usually accumulate. It must be also pointed out that some of the fitted values of the model (Table 1) appeared to be contradictory. The KBAOx (≈ 0.03 × 10-3 kg m-3) and KSOx (≈ 0.92 × 10-3 kg m-3) values of Table 1 might suggest that low O2 concentrations limited BA production rather its consumption (KBAOx much lower than KSOx) while in reality BA accumulated at low O2 concentrations (Figure 4). However, these KBAOx and KSOx values inserted into eqs 3 and 4 and substituted into eqs 1 and 5 showed that other mechanisms controlled BA consumption. Equation 5 shows that the consumption rate of BA is heavily controlled by its production with a saturationlike function (kS/(kS + kBA*)). This function reached its highest value (0.12) for the highest (kS) value, i.e., the maximum benzyl alcohol production rate per biomass unit (kS0 ≈ 7.7 × 10-10 mol kg-1s-1), considering the value of the half saturation benzyl alcohol consumption rate (kBA* ≈ 58.3 × 10-10 mol kg-1s-1). Consequently, despite the fact that KBAOx is much VOL. 41, NO. 16, 2007 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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KS
Substrate semi-saturation constant for the TOD pathway (kg m-3)
K S*
Substrate semi-saturation constant for the reaction of BA formation (kg m-3)
KOx
Oxygen semi-saturation constant (kg m-3)
KN
Nutrients semi-saturation constant (kg m-3)
KSOx
Oxygen semi-saturation constant in BA production reactions (kg m-3)
KBAOx
Oxygen semi-saturation constant in BA consumption reactions (kg m-3)
mS
Henry constant for the substrate (dimensionless)
mOx
Henry constant for the oxygen (dimensionless)
Qg
Gas flow rate (m3 s-1)
qS
Substrate consumption rate per biomass unit (s-1)
RS
Volumetric VOC substrate removal rate (kg m-3 s-1)
ROx
Volumetric oxygen removal rate (kg m-3 s-1)
rBA
Specific benzyl alcohol accumulation rate (s-1)
t
Time (s)
Vr
Reactor volume (m3)
X
Biomass concentration (kg m-3)
Nomenclature
YX/S
Biomass-substrate yield factor (dimensionless)
a
Interfacial area per volume unit or specific area (m-1)
YX/Ox
Biomass-oxygen yield factor (dimensionless)
bS
Substrate maintenance consumption rate per biomass unit (s-1)
βS
Maximal substrate fraction transportable from the gas stream to the liquid
Cgin S
Toluene gas inlet concentration (kg m-3)
βOx
Maximal oxygen fraction transportable from the gas stream to the liquid
gin COx
Oxygen gas inlet concentration (kg m-3)
h
Proportionality constant (m3 kg-biomass-1 s-1)
m
Biomass specific growth rate (s-1)
µmax
Maximal biomass specific growth rate (s-1)
νi
Molar weight of metabolite i (kg mol-1)
lower than KSOx, the consumption of BA was always much lower than its production even at low O2 concentrations. The effect of these regulatory mechanisms can be observed in Figure 4 where BA accumulated at low klaOx values, wherein O2 concentration limited toluene degradation (with an oxygen semisaturation constant of KOx ≈ 1.0 × 10-3 kg m-3; 18). Under these conditions BA was formed faster than it was consumed. This BA accumulation increased concomitantly with increasing values of klaOx while oxygen concentration was the limiting substrate and toluene was in excess. However, as a result of the increase in O2 supply, BA formation was further limited by toluene due to the high substrate semisaturation constant for the reaction of BA formation (KS* ≈ 9.2 × 10-3 kg m-3). This provoked CBA to decrease over klaOx values of 1.5 × 10-2 s-1 as toluene concentration dropped to KS* values (Figure 4). In general, BA was formed in situations of toluene overflow in the TOD pathway. This overflow situation was caused by either directly a high inlet concentration of toluene or a limiting concentration of O2 or nitrogen (i.e., high CSgin, low D or low klaOx), which made toluene to be in excess. This means that methyl-monooxygenation of toluene is likely to occur when toluene is not the limiting substrate. Once BA was formed its consumption was negatively modulated by its own production. BA accumulated into the system since its consumption was always lower than its production. Therefore, to keep BA concentration at low values, the reactor must be operated under toluene limiting conditions.
m-3)
CS
Toluene liquid concentration (kg
CSi
Concentration of the intermediate i (kg m-3)
COx
Oxygen liquid concentration (kg
m-3) m-3)
CN
Nutrients liquid concentration (kg
D
Dilution rate (s-1)
Dg
Gas dilution rate (s-1)
Ii,j
Inhibition coefficient in the SKIP equation (dimensionless)
This research was supported by the Spanish Ministry of Education and Science (PPQ2006-08230 and JCI-2005-1881-5 contracts).
JSfBA
Molar production of BA (mol kg-biomass-1 s-1)
Supporting Information Available
JBAfCO2+X Molar consumption of BA (mol kg-biomass-1 s-1) kBA
BA consumption rate per biomass unit (mol kgbiomass-1 s-1)
kBA0
Maximum BA consumption rate per biomass unit (mol kg-biomass-1 s-1)
kBA*
Half saturation BA consumption rate constant (mol kg-biomass-1 s-1)
klaOx
Oxygen transport coefficient at the liquid (s-1)
klaS
Substrate transport coefficient at the liquid (s-1)
kS
BA production rate per biomass unit (mol kgbiomass-1 s-1)
kS0
Maximum BA production rate per biomass unit (mol kg-biomass-1 s-1)
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Acknowledgments
Byproduct accumulation model: The mathematical formulation describing the sequence of biotransformations, followed by the VOC substrate through the catabolic pathway is presented. Figure 1: Influence of dilution rate on toluene elimination rate, BA and toluene liquid concentrations during process operation. This material is available free of charge via the Internet at http://pubs.acs.org.
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Received for review February 13, 2007. Revised manuscript received May 9, 2007. Accepted May 18, 2007. ES070365K
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