- Email: [email protected]
Modelling of the growth of a methanotrophic biofilm
8)
Pergamon
J. pp. 199-204. 1997. C 1997 IAWQ. Published by Elsevier Science Ud Pnnted an Great Bnuun. 0273-1223197 $17'00 + &00
WQr. Sc,. rICh. Vol. 36, No.
PH: S0273-1223(97)OO353-3
MODELLING OF THE GROWTH OF A METHANOTROPHIC BIOFILM Jean-Pierre Arcangeli and Erik Arvin Department of Environmental Science and Engineering. The Techflical University of Denmark, Building J15. DK·2800 Lyngby. Denmark
ABSTRACT A model describing the growth of a methanolfOphlc blOfilm IS presented. This model involves simultaneous growth of methanotrophs. heterotrophs and mtnfiers. Heterotrophic biomass grows on soluble polymers which arise from the hydrolysis of dead biomass entrapped in the blOfilm. Nitrifiers develop because of the presence of ammonia in the mineral medium. A comparIson of this model with experimental data showed that the biofilm growth. methane removal. oxygen consumption. product formation and biofilm detachment could be filled well. Parameter estimation yielded a maximum growth rate for melhanolrophs. 11m • of 1.17 ± 0.2 d· l • at 20"C. a decay rate, bm, of 0.34 ± 0.06 d-I. a half-saluraloon constant. K S(CH4)' of 0.08 ± 0.05 mg CH411. and a yield coeffiCIent. YCH4' of 0.21 ± 0.03 g X CODlg CH4 COD. In addItion. a senSItivity analysis has been performed for thIS model. 11 mdlcated that the most inOuentinl factors were those relnted to the biofilm (I.e. density; solid volume fraction: thickness). TIus suggeslS thnt in order to improve the model. funher research is needed in the field of blofilm structure and composition. Ie> 1997 IAWQ. Published by Elsevier Science Ltd.
KEYWORDS AQUAS1M; biodegradation; biofilm; growth; kinetics; methane; modelling. INTRODUCTION Chlorinated aliphatic hydrocarbons (CAHs) are widely used in industry as solvents for degreasing and dry cleaning. The compounds migrate quickly through soils. and several are persistent in certain environments. Consequently, it is not surprising that CAHs are often found in hazardous waste sites and contaminated groundwater. Nowadays, it has become evident that the methanotrophic bacteria are able to co-metabolize CAHs (Wilson and Wilson. 1985; Tsien et al., 1989). Consequently, knowledge of the kinetics of growth of these bacteria is essential for the design of treatment processes for contaminated water containing CAHs compounds. Although the kinetics of growth of methanotrophic bacteria is well established for suspended culture cultures (e.g. Oldenhuis et ai., 1991; Alvarez-Cohen and McCarty, 1991; Broholm et ai., 1992), comparatively little is known about the kinetics of growth of these bacteria in biofilm systems (Bilbo et ai., 1992; Anderson and McCarty. 1994). Therefore, it was the purpose of this study to present a biological model able to simulate the growth of a methanotrophic biofilm. It was also the purpose to discuss the variability of the parameter estimates. MATERIALS AND METHODS The biofilm reactor used is a so-called Biodrum system (Kristensen and Jansen, 1980). It consists of two Plexiglas cylinders, one rotating inside the other with the biomass growing on the surfaces of both the rotator 199
200
J.·P. ARCANGELI and E. ARVIN
and the stator. The volume of the reactor is approx. 0.96 litre. the surface area 0.16 m 2. The rotation (2t rpm) and the recycling system (50 11h) ensure nearly total mixing of the bulk liquid providing a relative uniform biofilm growth in the reactor. Methane and oxygen were dissolved in the inflow stream al thereafter supplied in the reactor (Fig. \, Items 2 and 4). The reactor was inoculated with a mixed cultu obtained from a waterworks treating methane containing groundwater (Nyk0bing Sjrelland. Denmark). T biofilm grew aerobically with methane as the sole carbon source under non-sterile conditions. Biofil growth. methane degradation. oxygen consumption. detachment, and product formation were monitor throughout the experiments. Analytical methods and inoculation procedure are given in Arcangeli et , (1996). The experimental results were used to establish a cumulative chemical oxygen (COD) balance I the entire biofilm growth. This allowed us to determine the stoichiometry of the reaction. Thereafter, t experimental data were modelled with the computer program AQUASIM developed by EAWAG Switzerland (Reichert. 1994). AQUAS 1M is an interactive program for the identification and simulation aquatic systems. The biofilm model used in this program is based on the formulation described by Wanr and Reichert (1996).
Y 9)
,,
5)
6)
,, 7):
8)
FIgure I. Experimenlal sci-Up. (I) melhane supply (®Tedlar hag); (2) melhane huhhle column; (3) oxygen supply (l!CJTedlar hag); (4) oxygen huhhle column; (5) mineral medium; (6) inlel sampling pon; (7) hiofilm rcaclor; (X) recirculalion 1001'. (9) oUllel.
RESULTS AND DISCUSSION COp balance The cumulative COD balance illustrated in Figure 2 shows that the production of soluble polym (polysaccharide) accounts for 2 t03 % of the total methane degraded. It also shows a very high oXYI1 consumption of 3.3 mg 02lmg CH 4 degraded (average value). However. a more detailed measurement the specific oxygen consumption showed that this value increased with increasing biofilm thickness: fre 3.1 to 3.7 mg 02/mg CH 4 degraded. This extra oxygen demand was the result of the growth of heterotroI and nitrifiers in the biofilm. Heterotrophic biomass grew on soluble polymers which arose from 1 hydrolysis of dead biomass entrapped in the biofilm. Nitrifiers developed because of the presence ammonia in the mineral medium (nitrate and nitrite were detected in the outlet of the reactor).
201
Melhanotrophic biolilm
12000
(mg COD)
10000 8000
6000 4000 2000 In
10
out
In
-
c:::::J Methane
18
out
~
In
out
In
29 39 Time (days)
Oxygen consumption
Detached biomass
(In the outlet)
-
out
c=
In
54
out
In
66
oul
Soluble polymers
Attached bIomas.
Figure 2. Cumulative COD balance relalive 10 the growlh of a melhanotrophic biolilm. For each lime step Iwo hislograms are indicaled: the firsl gives the cumulated melhane inpul in the reactor, the second Jives the cumulated oulput.
Biochemjcal model The following biological model is proposed. Three groups of active bacteria are considered: methanotrophs.
heterotrophs and nitrifiers. These active biomasses are growing on methane. soluble polymers. and ammonia. Active bacteria decay into inert and biodegradable biomass. The biodegradable biomass hydrolyses into soluble polymers which are degraded by heterotrophs. In addition. extracellular polymeric substances (EPS) holding the bacteria together are produced by active bacteria. The biofilm detachment is assumed to be a function of the biofilm thickness growth velocity. Finally. nitrification is also carried out by methanotrophs: a cross-competitive inhibition governs the biodegradation rate of methane and ammonia. The experimental data was modelled with the computer programme AQUASIM developed by EAWAG in Switzerland (Reichert. 1994). AQUAS1M is an interactive program for the identification and simulation of aquatic systems. The biofilm model used in this program is based on the formulation described by Wanner and Reichert (1996). Parameter estimation The comparison between model and experimental data is shown in Figure 3. In general. the agreement is good. Parameters and their individual standard deviations were determined by fitting the model to the experimental data using the estimation routine included in AQUAS1M. Table I summarises the estimated parameters. In general. an individual standard deviation of 20-30% was found for most of the model parameters. The methane yield coefficient displayed the smallest standard deviation. whereas the standard deviation reached 50% for the half-saturation constants and for the coefficients controlling the hydrolysis of biodegradable biomass. Concerning the parameters governing the growth of the heterouophs and nitrifiers. a minor modifICation of the values recommended by Henze et al. (1995) was necessary (see Table I). Nitrification was carried out in the biofilm by both nitrifiers and methanotrophs. Model simulations showed that nitrifiers developed in the biofilm several weeks after the reactor was inoculated. Consequently. for shon-term experiments nitrifiers could not develop. In these cases. nitrification was accomplished by rnethanotrophs. However. it was
202
l.-P ARCANGELI and E. ARVIN
observed that ammonia inhibited competitively the methane oxidation. This is in agreement with other work (Le. Whittenbury et al., 1970; Bedard and Knowles, 1989). The estimated I!Nm is high consIdering that the maximum nitrification rate determined for methanotrophs is still more than 20 times higher than one of the lowest rates reported for an ammonia oxidiser (Bedard and Knowles, 1989).
Time (days) Figure 3. Modelling of the methane removal rate and the blOfilm growth. Measured data: (0) Model: Solid hne. Vanabllity zone: dashed hnes.
(a)
Table 1. Kinetic and stoichiometric parameters used in the model. Data are expressed in COD units. Fixed parameters (not calibrated). Values in parenthesis are those recommended by Henze et al. (1995). Parameters Maximum specific growth rate for methanotrophs, I-Im Maximum specific nitrification rate for methanotrophs, IlNm Maximum decay rate for methanotrophs, bm Methane half-saturation constant, KS(CH', Yield for methanotrophs, YCH, Maximum specIfic growth rate for OItrifiers, I-IN Maximum decay rate for nitrifiers, bN Ammonia half-saturation constant, KS(NH'" Yield for nitrifiers and for methanotrophs growing on NH, YNH' Oxygen half-saturation constant, KS(Ol" . • Oxygen half-saturation constant for nitrifiers, KS(02 ..", Yield for heterotrophs, Y H Maximum specific growth rate for heterotrophs, ~IH Maximum decay rate for heterotrophs, b" Polymers half-saturation constant Ks(sp) Biofilm (Biodegradable biomass) hydrolysis rate, kll EPS formation coefficient, a Detachment rate, del.
unit
Estimate
(d") (d")
1.17 ± 0.2 ("0.001 0.34 ± 0.06 0.08 ± 0.05 0.21 ± 0.03 ("1 (I) ("0.15 (0.15) (,'2 (I) (0)0.24(0.24) ("0.2 (0.2) ("0.5 (0.5) ("0.5 (0.63) ("6 (6) ("0.4 (0.4)
(d") (glm') (gXlgS) (d") (d· l ) (mg NH,-N/L) (gXN/gNH,-N) (glm') (g/m') (gXH/gS p )
(d")
(d") (glm') (d· l )
(d")
("6 1.4 ± 0.8
0.94 ± 0.3 0.1 ± 0.02
Methanolrophlc blOfilm
203
Varjabjhtyanalysis A sensitivity test was performed for the biochemical model. It consists of altering independently various parameters used in the model and assessing how much these variations affect the modelled curves. Such a task can be performed automatically by AQUAS 1M. The results summarised in Table 2 indicate that the most influential factors are the biofilm parameters, namely the biomass density, the initial biomass volume fractions, the detachment, and the biofilm thickness. The kinetic and the stoichiometric parameters related to the methanotrophic bacteria also have strong effect on the variability of the model, especially on the simulation of the methane and the oxygen consumption. The parameters controlling the hydrolysis of the biodegradable biomass and the growth of heterotrophs affect the modelling of the polymers' production. The diffusivity of soluble components has a very small impact of the variability of the model. Altogether, the variability range of the model is shown in Figure 3: the envelope defined by dashed lines describes the maximum variation of the model using the parameters and their respective standard deviations. It appears that the variability of the model is more significant for the simulation of the biofilm growth than for the simulation of the methane removal. Table 2. Sensitivity analysis. Effect of different groups of parameters on the simulation of: the biofilm thickness (a); methane removal (b); oxygen consumption (c); polymers' production (d); detachment (e) and nitrification (0 Parameters related to:
U
Methanotrophs Nitrifiers Heterotrophs Biofilm parameters Hydrolysis Diffusivity
(.)Thickness
(b/CH4
1')02
(Jipoly.
(O)Detach.
('Nitrif.
++ + + +++
+++
++/+++ + + +++
++
++ + + +++
++ +++ + +++
+ + +++
+++ +++ ++
+ -/+
-/+
-; insignificant effect; + moderate effect; ++ significant effect; +++: very strong effect.
The variability of the model ranges from 10 to 20% for the modelling of the methane removal and the oxygen consumption. Still, the variability of the model is high for the modelling of biofilm growth, the nitrification, the detachment and the polymers' production. It should be pointed out, however, that the experimental data are within the confidence interval defined by the model, Furthermore, the trend of the model is in agreement with the experimental data. Consequently, this model is of interest for the design of treatment units involving methanotrophic bacteria. Nevertheless, the significant confidence interval generated for the biofilm thickness denotes the lack of reliable data on the biofilm composition and structure, and how to integrate this information into the model. This is the subject of further research (Bishop and Rittmann, 1995). CONCLUSION The model presented here could predict well the consumption of methane and oxygen, the production of polymers. the detachment and the biofilm growth. The model requires three types of active biomass: methanotrophs. heterotrophs and nitrifiers. The parameters in the model were estimated from experimental results, from calibration. and from literature values. The modelling of experimental data combined with a sensitivity analysis allowed us to define a zone of variability of the model. Most of the measured data were inside this variability zone suggesting that the model is valid. However, more research is needed in relation to the biofilm structure and composition in order to improve the modelling of the biofilm growth. ACKNOWLEDGEMENT This study was funded by the Commission of the European Communities. Contract EV5V-CT92-0239; BIODEC project.
J.-P. ARCANGELI and E. ARVIN
204
REFERENCES Alvarez-Cohen, L. and McCany, P. L. (1991). Product toxicity and cometabolic competilive inhibllion modelhng of chloroform and lrichloroelhylene lransfonnation by melhanolrophic resting cells. Appl. Enviran. Microbwl.. 57,1031-1037. Anderson, J. E. and McCany. P. L. (1994). Model for treatment of trichloroelhylene by melhanotrophic btofilms. J. Environ. Eng., 120, 379-400. Arcangeli, J. P., Mm, E., Mejlhede, M. and Lauritsen, F. R. (1996). Biodegradation of cis-I,2-dichloro-ethylene al low concentralions wIth methane-oxidising bacteria in a biofilm reactor. Wat. Res., 30, 1885-1893. Bedard, C. and Knowles, R. (1989). Physiology, biochemistry, and specific inhlbllors of CH4' NH 4+, and CO oxidalion by melhanolrophs and nitrifiers. Microbial. Rev., 53, 68-84. Bilbo, C. M., Arvm, E.. Holsl, H. and Spliid, H. (1992). Modelling lhe growth of methane-oxIdising bacleria in a fixed biofilm. Wal. Res., 26, 301-309. Bishop, P. L. and Ritlmann, B. E. (1995) Modelling heterogeneity in biofilms: report of the discussion session. Wal. Sci. Tech., 32(8),263-265. Henze. M.. Gujer, W., Mino, T, Matsuo, T.• Wenlzel, M. C. and Marais, G. v. R. (1995). AClivaled Sludge Model No.2. London. IAWQ SCientific and Technical Repon No.3. Kr,stensen, G. H. and Jansen, J. \a Cour (1980). Fixed Film Kinetics. Description of laboratory equipment. Departmenl of Environmental Engineering. Technical Universily of Denmark. Oldenhuls, R., Oedzes, J. Y., Van der Waarde, J. J. and Janssen, D. B. (1991). Kinetics of chlorinated hydrocarbon degradation by Melh)'losinus Irichosporium OB3b and loxicity of lrichloroethylene. Appl. Environ. MIcrobial.. 57, 7-14. Relchen, P. (1994). AQUASIM - a tool for simulallon and data analysis of aquatic syslems. Wal. Sci. Tech., 30(2), 21-30. Tsien, H. C., Brusseau, G. A., Hanson, R. S. and Wackelt, L. P. (1989). BIodegradation of trichloroethylene by Melhylosinus Irichosporlum OB3b. Appl. Environ. Microbiol .• 55. 3155-3161. Wanner. O. and Reichen. P. (1996). Mathemalical modelling of mixed·culture biofilms. Biolechnology and Bioengineering 49, 172-184. Whittenbury, R.. Phillips. K. C. and Wilkinson, J. F. (1970). Enrichment, Isolalion and some propenies of methane.utilising baclena. J. Gen. Microbial., 61, 205·218. Wilson, J. T. and Wilson, B. H. (1985). Biodegradalion of trichloroethylene in soil. Appl. Environ. Microbial.. 49, 242-243.
Pergamon
J. pp. 199-204. 1997. C 1997 IAWQ. Published by Elsevier Science Ud Pnnted an Great Bnuun. 0273-1223197 $17'00 + &00
WQr. Sc,. rICh. Vol. 36, No.
PH: S0273-1223(97)OO353-3
MODELLING OF THE GROWTH OF A METHANOTROPHIC BIOFILM Jean-Pierre Arcangeli and Erik Arvin Department of Environmental Science and Engineering. The Techflical University of Denmark, Building J15. DK·2800 Lyngby. Denmark
ABSTRACT A model describing the growth of a methanolfOphlc blOfilm IS presented. This model involves simultaneous growth of methanotrophs. heterotrophs and mtnfiers. Heterotrophic biomass grows on soluble polymers which arise from the hydrolysis of dead biomass entrapped in the blOfilm. Nitrifiers develop because of the presence of ammonia in the mineral medium. A comparIson of this model with experimental data showed that the biofilm growth. methane removal. oxygen consumption. product formation and biofilm detachment could be filled well. Parameter estimation yielded a maximum growth rate for melhanolrophs. 11m • of 1.17 ± 0.2 d· l • at 20"C. a decay rate, bm, of 0.34 ± 0.06 d-I. a half-saluraloon constant. K S(CH4)' of 0.08 ± 0.05 mg CH411. and a yield coeffiCIent. YCH4' of 0.21 ± 0.03 g X CODlg CH4 COD. In addItion. a senSItivity analysis has been performed for thIS model. 11 mdlcated that the most inOuentinl factors were those relnted to the biofilm (I.e. density; solid volume fraction: thickness). TIus suggeslS thnt in order to improve the model. funher research is needed in the field of blofilm structure and composition. Ie> 1997 IAWQ. Published by Elsevier Science Ltd.
KEYWORDS AQUAS1M; biodegradation; biofilm; growth; kinetics; methane; modelling. INTRODUCTION Chlorinated aliphatic hydrocarbons (CAHs) are widely used in industry as solvents for degreasing and dry cleaning. The compounds migrate quickly through soils. and several are persistent in certain environments. Consequently, it is not surprising that CAHs are often found in hazardous waste sites and contaminated groundwater. Nowadays, it has become evident that the methanotrophic bacteria are able to co-metabolize CAHs (Wilson and Wilson. 1985; Tsien et al., 1989). Consequently, knowledge of the kinetics of growth of these bacteria is essential for the design of treatment processes for contaminated water containing CAHs compounds. Although the kinetics of growth of methanotrophic bacteria is well established for suspended culture cultures (e.g. Oldenhuis et ai., 1991; Alvarez-Cohen and McCarty, 1991; Broholm et ai., 1992), comparatively little is known about the kinetics of growth of these bacteria in biofilm systems (Bilbo et ai., 1992; Anderson and McCarty. 1994). Therefore, it was the purpose of this study to present a biological model able to simulate the growth of a methanotrophic biofilm. It was also the purpose to discuss the variability of the parameter estimates. MATERIALS AND METHODS The biofilm reactor used is a so-called Biodrum system (Kristensen and Jansen, 1980). It consists of two Plexiglas cylinders, one rotating inside the other with the biomass growing on the surfaces of both the rotator 199
200
J.·P. ARCANGELI and E. ARVIN
and the stator. The volume of the reactor is approx. 0.96 litre. the surface area 0.16 m 2. The rotation (2t rpm) and the recycling system (50 11h) ensure nearly total mixing of the bulk liquid providing a relative uniform biofilm growth in the reactor. Methane and oxygen were dissolved in the inflow stream al thereafter supplied in the reactor (Fig. \, Items 2 and 4). The reactor was inoculated with a mixed cultu obtained from a waterworks treating methane containing groundwater (Nyk0bing Sjrelland. Denmark). T biofilm grew aerobically with methane as the sole carbon source under non-sterile conditions. Biofil growth. methane degradation. oxygen consumption. detachment, and product formation were monitor throughout the experiments. Analytical methods and inoculation procedure are given in Arcangeli et , (1996). The experimental results were used to establish a cumulative chemical oxygen (COD) balance I the entire biofilm growth. This allowed us to determine the stoichiometry of the reaction. Thereafter, t experimental data were modelled with the computer program AQUASIM developed by EAWAG Switzerland (Reichert. 1994). AQUAS 1M is an interactive program for the identification and simulation aquatic systems. The biofilm model used in this program is based on the formulation described by Wanr and Reichert (1996).
Y 9)
,,
5)
6)
,, 7):
8)
FIgure I. Experimenlal sci-Up. (I) melhane supply (®Tedlar hag); (2) melhane huhhle column; (3) oxygen supply (l!CJTedlar hag); (4) oxygen huhhle column; (5) mineral medium; (6) inlel sampling pon; (7) hiofilm rcaclor; (X) recirculalion 1001'. (9) oUllel.
RESULTS AND DISCUSSION COp balance The cumulative COD balance illustrated in Figure 2 shows that the production of soluble polym (polysaccharide) accounts for 2 t03 % of the total methane degraded. It also shows a very high oXYI1 consumption of 3.3 mg 02lmg CH 4 degraded (average value). However. a more detailed measurement the specific oxygen consumption showed that this value increased with increasing biofilm thickness: fre 3.1 to 3.7 mg 02/mg CH 4 degraded. This extra oxygen demand was the result of the growth of heterotroI and nitrifiers in the biofilm. Heterotrophic biomass grew on soluble polymers which arose from 1 hydrolysis of dead biomass entrapped in the biofilm. Nitrifiers developed because of the presence ammonia in the mineral medium (nitrate and nitrite were detected in the outlet of the reactor).
201
Melhanotrophic biolilm
12000
(mg COD)
10000 8000
6000 4000 2000 In
10
out
In
-
c:::::J Methane
18
out
~
In
out
In
29 39 Time (days)
Oxygen consumption
Detached biomass
(In the outlet)
-
out
c=
In
54
out
In
66
oul
Soluble polymers
Attached bIomas.
Figure 2. Cumulative COD balance relalive 10 the growlh of a melhanotrophic biolilm. For each lime step Iwo hislograms are indicaled: the firsl gives the cumulated melhane inpul in the reactor, the second Jives the cumulated oulput.
Biochemjcal model The following biological model is proposed. Three groups of active bacteria are considered: methanotrophs.
heterotrophs and nitrifiers. These active biomasses are growing on methane. soluble polymers. and ammonia. Active bacteria decay into inert and biodegradable biomass. The biodegradable biomass hydrolyses into soluble polymers which are degraded by heterotrophs. In addition. extracellular polymeric substances (EPS) holding the bacteria together are produced by active bacteria. The biofilm detachment is assumed to be a function of the biofilm thickness growth velocity. Finally. nitrification is also carried out by methanotrophs: a cross-competitive inhibition governs the biodegradation rate of methane and ammonia. The experimental data was modelled with the computer programme AQUASIM developed by EAWAG in Switzerland (Reichert. 1994). AQUAS1M is an interactive program for the identification and simulation of aquatic systems. The biofilm model used in this program is based on the formulation described by Wanner and Reichert (1996). Parameter estimation The comparison between model and experimental data is shown in Figure 3. In general. the agreement is good. Parameters and their individual standard deviations were determined by fitting the model to the experimental data using the estimation routine included in AQUAS1M. Table I summarises the estimated parameters. In general. an individual standard deviation of 20-30% was found for most of the model parameters. The methane yield coefficient displayed the smallest standard deviation. whereas the standard deviation reached 50% for the half-saturation constants and for the coefficients controlling the hydrolysis of biodegradable biomass. Concerning the parameters governing the growth of the heterouophs and nitrifiers. a minor modifICation of the values recommended by Henze et al. (1995) was necessary (see Table I). Nitrification was carried out in the biofilm by both nitrifiers and methanotrophs. Model simulations showed that nitrifiers developed in the biofilm several weeks after the reactor was inoculated. Consequently. for shon-term experiments nitrifiers could not develop. In these cases. nitrification was accomplished by rnethanotrophs. However. it was
202
l.-P ARCANGELI and E. ARVIN
observed that ammonia inhibited competitively the methane oxidation. This is in agreement with other work (Le. Whittenbury et al., 1970; Bedard and Knowles, 1989). The estimated I!Nm is high consIdering that the maximum nitrification rate determined for methanotrophs is still more than 20 times higher than one of the lowest rates reported for an ammonia oxidiser (Bedard and Knowles, 1989).
Time (days) Figure 3. Modelling of the methane removal rate and the blOfilm growth. Measured data: (0) Model: Solid hne. Vanabllity zone: dashed hnes.
(a)
Table 1. Kinetic and stoichiometric parameters used in the model. Data are expressed in COD units. Fixed parameters (not calibrated). Values in parenthesis are those recommended by Henze et al. (1995). Parameters Maximum specific growth rate for methanotrophs, I-Im Maximum specific nitrification rate for methanotrophs, IlNm Maximum decay rate for methanotrophs, bm Methane half-saturation constant, KS(CH', Yield for methanotrophs, YCH, Maximum specIfic growth rate for OItrifiers, I-IN Maximum decay rate for nitrifiers, bN Ammonia half-saturation constant, KS(NH'" Yield for nitrifiers and for methanotrophs growing on NH, YNH' Oxygen half-saturation constant, KS(Ol" . • Oxygen half-saturation constant for nitrifiers, KS(02 ..", Yield for heterotrophs, Y H Maximum specific growth rate for heterotrophs, ~IH Maximum decay rate for heterotrophs, b" Polymers half-saturation constant Ks(sp) Biofilm (Biodegradable biomass) hydrolysis rate, kll EPS formation coefficient, a Detachment rate, del.
unit
Estimate
(d") (d")
1.17 ± 0.2 ("0.001 0.34 ± 0.06 0.08 ± 0.05 0.21 ± 0.03 ("1 (I) ("0.15 (0.15) (,'2 (I) (0)0.24(0.24) ("0.2 (0.2) ("0.5 (0.5) ("0.5 (0.63) ("6 (6) ("0.4 (0.4)
(d") (glm') (gXlgS) (d") (d· l ) (mg NH,-N/L) (gXN/gNH,-N) (glm') (g/m') (gXH/gS p )
(d")
(d") (glm') (d· l )
(d")
("6 1.4 ± 0.8
0.94 ± 0.3 0.1 ± 0.02
Methanolrophlc blOfilm
203
Varjabjhtyanalysis A sensitivity test was performed for the biochemical model. It consists of altering independently various parameters used in the model and assessing how much these variations affect the modelled curves. Such a task can be performed automatically by AQUAS 1M. The results summarised in Table 2 indicate that the most influential factors are the biofilm parameters, namely the biomass density, the initial biomass volume fractions, the detachment, and the biofilm thickness. The kinetic and the stoichiometric parameters related to the methanotrophic bacteria also have strong effect on the variability of the model, especially on the simulation of the methane and the oxygen consumption. The parameters controlling the hydrolysis of the biodegradable biomass and the growth of heterotrophs affect the modelling of the polymers' production. The diffusivity of soluble components has a very small impact of the variability of the model. Altogether, the variability range of the model is shown in Figure 3: the envelope defined by dashed lines describes the maximum variation of the model using the parameters and their respective standard deviations. It appears that the variability of the model is more significant for the simulation of the biofilm growth than for the simulation of the methane removal. Table 2. Sensitivity analysis. Effect of different groups of parameters on the simulation of: the biofilm thickness (a); methane removal (b); oxygen consumption (c); polymers' production (d); detachment (e) and nitrification (0 Parameters related to:
U
Methanotrophs Nitrifiers Heterotrophs Biofilm parameters Hydrolysis Diffusivity
(.)Thickness
(b/CH4
1')02
(Jipoly.
(O)Detach.
('Nitrif.
++ + + +++
+++
++/+++ + + +++
++
++ + + +++
++ +++ + +++
+ + +++
+++ +++ ++
+ -/+
-/+
-; insignificant effect; + moderate effect; ++ significant effect; +++: very strong effect.
The variability of the model ranges from 10 to 20% for the modelling of the methane removal and the oxygen consumption. Still, the variability of the model is high for the modelling of biofilm growth, the nitrification, the detachment and the polymers' production. It should be pointed out, however, that the experimental data are within the confidence interval defined by the model, Furthermore, the trend of the model is in agreement with the experimental data. Consequently, this model is of interest for the design of treatment units involving methanotrophic bacteria. Nevertheless, the significant confidence interval generated for the biofilm thickness denotes the lack of reliable data on the biofilm composition and structure, and how to integrate this information into the model. This is the subject of further research (Bishop and Rittmann, 1995). CONCLUSION The model presented here could predict well the consumption of methane and oxygen, the production of polymers. the detachment and the biofilm growth. The model requires three types of active biomass: methanotrophs. heterotrophs and nitrifiers. The parameters in the model were estimated from experimental results, from calibration. and from literature values. The modelling of experimental data combined with a sensitivity analysis allowed us to define a zone of variability of the model. Most of the measured data were inside this variability zone suggesting that the model is valid. However, more research is needed in relation to the biofilm structure and composition in order to improve the modelling of the biofilm growth. ACKNOWLEDGEMENT This study was funded by the Commission of the European Communities. Contract EV5V-CT92-0239; BIODEC project.
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