Acclimatization model of an aerobic bioreactor for ... - Semantic Scholar
Simulation Modelling Practice and Theory 17 (2009) 680–691
Contents lists available at ScienceDirect
Simulation Modelling Practice and Theory journal homepage: www.elsevier.com/locate/simpat
Acclimatization model of an aerobic bioreactor for the treatment of toxic wastewater Manuel J. Betancur a,*, Fajith Martínez a, Carlos Ocampo b, Jaime A. Moreno c, Germán Buitrón d, Iván Moreno-Andrade d a
A+D Universidad Pontificia Bolivariana, Cq. 1#70-01, of 11-259, Medellín, Colombia CIBIOT, Universidad Pontificia Bolivariana, Cq. 1#70-01, of 11-259, Medellín, Colombia c Automation Department, Engineering Institute, Universidad Nacional Autónoma de México, Cd. Universitaria, 04510 Coyoacán, México DF, Mexico d Laboratory for Research on Advanced Processes for Water Treatment, Engineering Institute, Campus Juriquilla, Querétaro, Universidad Nacional Autónoma de México, Blvd. Juriquilla 3001, Querétaro 76230, Mexico b
a r t i c l e
i n f o
Article history: Received 4 April 2008 Received in revised form 3 October 2008 Accepted 4 December 2008 Available online 16 December 2008
Keywords: Acclimatization Bioreactor Mathematical model SBR Wastewater treatment
a b s t r a c t This work proposes a mathematical model for the acclimatization process of a bioreactor treating toxic wastewater. Experimental data was used to identify the changing kinetic parameters of the model as acclimatization progresses. It was found that only one key parameter, the specific biomass growth rate function, changed during the acclimatization process. Therefore, an acclimatization model was proposed to explain the changes of this parameter. Ó 2008 Elsevier B.V. All rights reserved.
1. Introduction Many processes in the chemical, pharmaceutical, plastic, petrochemical industries, etc., generate WW which contains organic toxic compounds. The treatment and reutilization of such WW is an option in areas where water resources are scarce, hence the importance for the improvement of the WW treatment technologies. The utilization of biological treatments is based on the capacity of microorganisms, specifically bacteria, to degrade a great quantity of toxic substances. The pollutants are treated as food by the bacteria and these, while feeding, increase their population at the same time as the water gets treated. Some microorganisms perform the treatment process in the presence of oxygen and others in its absence [1]. For the aerobic reactions the oxygen is dissolved in the water by means of aerator systems. A tank, within which the proper conditions for the bio-reaction to take place are guaranteed, on a large scale basis, is called a bioreactor [2]. The SBR have an increased efficiency and flexibility compared to continuous reactors. For such a reason the term SBR is used as a synonym for WWTP technology where the volume in the reactor tank is variable in time[3–5]. The processes that occur in a SBR are identical to those of a conventional continuous activated sludge. Nevertheless an important difference exists between both. In a SBR system all the stages of the process are performed in the same reactor, with different phases separated in time[6], whereas in the continuous processes the different stages are performed simultaneously, in different tanks or tank sections [6]. * Corresponding author. Tel.: +57 4 4159020x9584. E-mail address: [email protected] (M.J. Betancur). 1569-190X/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.simpat.2008.12.001
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Nomenclature 4CP B COD DO DOC K1 K2 KI KLa KS KW MC n O Osat Q S S* Si Sm S0 SBR TSS V Ve Vf V0 VSS W WW WWTP X
l l(S) l l*
lmax
4-chlorophenol specific endogenous respiration rate (h1) chemical oxygen demand (mg/L) dissolved oxygen (mgDO/L) dissolved organic carbon (mg/L) biomass/substrate yield coefficient (mg4CP/mgTSS) biomass/oxygen yield coefficient (mgDO/mgTSS) inhibition coefficient (mg4CP/L) oxygen mass transfer coefficient (h1) Michaelis–Menten saturation constant (mg4CP/L) half acclimatization constant model candidate exponent constant dissolved oxygen concentration (mgDO/L) dissolved oxygen concentration at saturation (mg/L) inflow volumetric flow (L/h) substrate concentration (mg/L) substrate concentration at which the biomass growth rate reaches its maximum value (mg/L) toxic concentration in the influent (mg/L) substrate concentration for medium Biomass growth rate (mg/L) initial substrate concentration in the affluent (mg/L) sequencing batch reactor total solid suspended (mg/L) volume level of the liquid in the SBR exchange volume (L) final volume (L) inicial volume (L) volatile suspended solids (mg/L) total mass of processed substrate (mg4CF) wastewater wastewater treatment plant active biomass concentration (mgTSS/L) specific biomass growth rate (h1) specific biomass growth rate in function of S (h1) ideal maximum value, for the non-inhibited case only, of the specific biomass growth rate (h1) maximum value, for a given inhibiting batch reaction, of the specific biomass growth rate (h1) maximum value of l* (h1) during acclimatization
The stages that are required to carry out an operative cycle in a SBR are[5] shown in Fig. 1: filling, where there is admitted a volume of WW into the SBR; reaction, where biomass is mixed and put in contact with the toxic WW and, if the biomass is aerobic, air is injected to allow the biochemical reaction that transforms the toxic substrate; settle, where the aeration and the agitation systems are suspended to allow the biomass to settle at the bottom of the SBR; draw, where the supernatant (treated water) is evacuated, and dead time. Due to its toxicity, biological treatment of WW containing a toxic substrate is difficult, since the microorganisms are initially not able to treat that substance. Therefore, the first step to make a SBR operative is the acclimatization, i.e., the adaptation of the microorganisms to a particular toxic substrate. Different mechanisms have been described to explain the process of acclimatization. Wiggings et al. [7] suggested that during this process there is a selection and a multiplication of specialized microorganisms and physiological transformations occur in the metabolic system of the microorganisms, i.e., alterations at the enzymatic level, regulation and production, mutations, etc. When the biomass is aerobic, the acclimatization periods range from hours to days, depending on the characteristics of the WW, temperature, pH, substrate type and concentration, etc. Once acclimatized, an appropriate control strategy of the SBR may avoid the negative impact of the inhibition caused by the excess of toxic substrate and maintain a high sludge activity of the biomass [8,9]. However, the initial acclimatization of biomass, when the SBR is inoculated for the first time, or after a failure of the system, still has to be manually controlled. The automation of the acclimatization process of a SBR would allow the operation in the WWTP to be more reliable and more optimal. Therefore, a model of the acclimatization process is necessary. Buitrón and Moreno[10] proposed such a model for a SBR treating 4CP as model substrate. They assumed that the acclimatization effect is reflected in the change of l(S),
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Fig. 1. Operation phases of a SBR.
which in turn can be modeled using the Haldane Law, which describes the behavior of l depending on S. However, the identificability of the parameters of l, using the measurements of S with batch experiments, is very poor [10,11]. In this work we propose an improved mathematical acclimatization model. It uses, besides the substrate kinetics, the on line measurement of the DO to determine the changes of the kinetic parameters of l during acclimatization. Thus the proposed model not only explains the evolution of the S over time but also the evolution of the DO. The introduction of the DO measurements improves the model identificability because the DO measurement can be done on line, generating samples qualitatively and quantitatively more reliable than those of S, which usually have to be processed manually and so they are more prone to experimental error. The objective of this work is to identify and validate a mathematical model of the acclimatization of microorganisms to inhibitory compounds, using 4CP as a model compound, in a SBR used for the treatment of toxic WW. Section 2 describes the methodology. Section 3 introduces the mathematical model of bio-reaction. The acclimatization experimental results are presented in Section 4. Section 5 describes the sensitivity analysis of the parameters of l for any given single batch. In Section 6 two model candidates are proposed. Finally some conclusions are presented. 2. Methodology An aerobic automated SBR system with a capacity of 7 L and an exchange volume of 57% (4 L) was used. The airflow rate was 1.5 L/min and the temperature within the SBR was controlled at 20 °C. The DO was measured on line using an industrial polarographic sensor and transmitter (Hendress + Hauser model COS41 and Liquisys-M COM223-DX1105). The fill and draw flows were controlled by peristaltic pumps (Cole–Palmer model 752350 (0–100 rpm) and 523-40 (0–600 rpm) series Masterflex, respectively). The reactor was inoculated with microorganisms from a municipal activated sludge WWTP. The biomass concentration was set to 2000 mgVSS/L. A synthetic WW containing 4CP, as a toxic model compound, was used as the sole source of carbon and energy. Nutrients such as nitrogen, phosphorus, and oligoelements were added following the techniques recommended by AFNOR [12]. The SBR was operated under the following batch strategy: pre-aeration time 15 min (aeration after the draw phase, before the next filling phase, in order to begin each new degradation cycle with a not limiting oxygen concentration), filling time 12.6 min, reaction time (variable depending on the necessary time to reach 99% of removal efficiency of 4CP), settling time 12 to 30 min, and draw time 1 min. Degradation time, for the 4CP, is the filling time plus the reaction time. The end of the degradation time was indirectly determined using the dynamics of the O present in the reactor [13]. In this work two sets of experiments, for the acclimatization of the biomass, were performed for two different substrate concentrations, one with S0 = 50 mg4CP/L and the other one for 100 mg4CP/L. The acclimatization model identification was performed using the first set, S0 = 100 mg4CP/L, and the second set, S0 = 50 mg4CP/L, was used for validation. The acclimatization began with fresh, not acclimatized, sludge from a nearby WWTP. In both cases sequencing batch reactions were cyclically performed, keeping the same biomass in the reactor, until reaction times became approximately constant, i.e., until the biomass was finally acclimatized. It is important to note that during the acclimatization to 4CP, the microorganisms increase the degradation rate and the activity. Due to this, the performance of the bioreactor is better as the acclimatization takes place, even if the biomass concentration is kept at the preset value.
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The acclimatization of bacteria to 4CP substrate must be performed for relatively low concentrations. For high values of S the acclimatization may not be possible. Moreno-Andrade and Buitrón[14] observed that this inhibition is not only a function of the initial concentration of the toxic compound, but also of the initial biomass concentration. A low biomass concentration may produce a high degree of inhibition. For this reason a low value (under 0.4) for the substrate/biomass concentrations relation is recommended. 4CP concentration (as total phenol concentration) was measured taking samples and processing them offline using the colorimetric technique of 4-aminoantipyrine according to APHA [15]. TSS and VSS were determined according to the APHA Standard Methods [15]. DOC was determined with a Shimadzu TOC-5050 and COD according to the APHA Standard Methods [15]. These analyses were performed to evaluate 4CP mineralization. 3. Mathematical model of the bio-reaction A key parameter of the reaction model is l(S), as it directly influences both S and DO dynamics. All of the other bio-reaction model parameters, i.e. with the exception of l related parameters, are supposed invariable during the acclimatization process. Therefore, to understand how l parameters evolve in the time, depending on the exposure of the biomass to the toxic substance, seems to be the key for the modeling of the acclimatization process. In a SBR, the filling and reaction phases can be described by the differential equations set [8–10]
Q X_ ¼ lðSÞX X ; V
ð1Þ
Q S_ ¼ k1 lðSÞX þ ðSi SÞ ; V
ð2Þ
Q O_ ¼ ðk2 lðSÞ þ bÞX þ kL aðOsat OÞ O ; V V_ ¼ Q
ð3Þ ð4Þ
assuming that O is not a limiting reactive, i.e., when it can be supposed that both l and b are not a function of O.For inhibitory substrates, l may be described using the Haldane law (see Fig. 2)
lðSÞ ¼
l0 S 2
K S þ S þ SK I
;
ð5Þ
which is valid when the oxygen is not a limiting reactant, i.e., for normal operation conditions. An alternate, equivalent, parameterization of the Haldane model was used [8,9] (see Fig. 2), defined as
S ¼
pffiffiffiffiffiffiffiffiffiffi KIKS
ð6Þ
for the substrate concentration value that generates the maximum biomass growth rate,
l ¼
l0
1 þ 2K S =S
for the above mentioned maximum rate, and
Fig. 2. Model Law of Haldane. l* = 0.0098 (h1), S* = 15 mg4CP/L, Sm = 60 mg4CP/L equivalents to l = 0.0885, KI = 3.7500, KS = 59.9995.
ð7Þ
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Sm ¼
K 2I þ 4S þ
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi K 2I þ 8K I S þ 12S2 2
ð8Þ
for the substrate concentration at which inhibition is 50%. This new set of parameters, described in (6)–(8), do have a better graphical (see Fig. 2), and physical, interpretation than the classical ones in (5).
4. Acclimatization experiments For both sets of acclimatization experiments, the acclimatized states were reached after 10 batches, i.e., after the 10th batch the 4CP degradation time did not diminish appreciably. For the 50 mg4CP/L case the degradation time diminished gradually from 40.21 h to 1.21 h, from cycles 1 to 10, respectively. For the 100 mg4CP/L case, also, 10 batches were required to obtain the acclimatization, in which process the degradation time was reduced from 52.21 h to 1.37 h. In Figs. 3 and 4 it is possible to observe the degradation time for S0 = 100 mg4CP/L and S0 = 50 mg4CP/L, respectively. Both figures show that the first batch was rather slow but, as more batches are executed, the degradation becomes more rapid, evidencing that the acclimatization is taking place. As the aerobic bacteria degrade the substrate present in the WW, they consume oxygen in order to cover for metabolic needs and also to produce new cells. (Fig. 5) shows the DO evolution during the acclimatization of the biomass to S0 = 100 mg4CP/L. For every batch it can be seen a time for which DO is established in a maximum value, near to saturation, just after having passed a valley where it exhibited its minimal value. Such a time is at the end of the reaction, i.e., the time were the substrate is been depleted and thus no more oxygen is needed for processing it. The minimal value of the valley, related to the maximum oxygen consumption, tends to diminish in every new batch during the acclimatization, and becomes stable finally after the 10th batch (not shown). Such a behavior is the motivation to try and model the process of acclimatization of the biomass using also the DO kinetics variations.
5. Sensitivity analysis of the kinetic parameters The initial hypothesis is that changes of l(S) parameters (6)–(8) during the first successive reactions, explain the evolution of the model of the SBR during the acclimatization, and hence explain the changes in the DO as well as the substrate kinetics. Nevertheless, during every particular batch, the whole model is supposes to be invariant, i.e., l* (6), S* (7) and Sm (8) may change only from one batch to the next. Two alternatives were studied for the identification of the model parameters: one using only the experimental information of S kinetics, and the other one using both the experimental information of S and that of the DO. Fig. 6 shows the simulation, for a single batch, of the model response with the identified parameters. A better fit for S is obtained when only the experimental data of S is used. Nevertheless, for the DO kinetics, the best fit is found when the experimental data of both S and DO are used. As the future and final objective of our work is to design a control law able to automate the acclimatization process, based only on the online measurement of DO, then including the experimental data of DO for the identification is justified.
Fig. 3. Kinetic of degradation of 4CP during the acclimatization to S0 = 100 mg4CP/L.
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Fig. 4. Kinetic of degradation of 4CP during the acclimatization to S0 = 50 mg4CP/L.
Fig. 5. Evolution of the DO during the acclimatization to S0 = 100 mg4CP/L (filling and draw phases time are not included in the graphs).
The identification of the parameters l* (6), S* (7), and Sm (8), was done for each single batch (1)–(10), for both experimental data sets. The identification software was developed using Matlab’s Optimization Toolbox, in particular the lsqnonlinear function set to the Levenberg–Marquardt method. Fig. 7 shows the identification results for both experimental sets. Fig. 7a shows the evolution of l* as the acclimatization progresses. Note that its final value is different for both acclimatization runs. On the other hand, for S* and Sm, Fig. 7b and c, respectively, their values are very similar and their variations during each run are minimal. This leads to assume that S* and Sm exhibit low sensitivity to the acclimatization process, hence it is reasonable to characterize them as constants for all batches. Under these assumptions, the graphic of l(S) retains the exact same shape during the whole acclimatization process, changing only its height l*. Such changes in l* from one batch to the next are, therefore, considered to be the effect of the acclimatization process. Hence, a model of such a change will explain the
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Fig. 6. Model simulation of filling and reaction, for batch 7S0 = 100 mg4CP/L: (a) continuous line: model identified using S and DO. S* = 15.0660, Sm = 60.2778, l* = 0.0124; (b) dotted line: model identified using S only S* = 23.9867, Sm = 48.1241, l* = 0.0172; (c) circles: experimental data.
associated evolution of (5) in order to allow the fill and reaction model in (1)–(4) to be used for any given batch during the acclimatization process. 6. Mathematical model of the acclimatization The growth of l, from one batch to the next, during the experimental acclimatization process, exhibited an s-shaped form. Hence, we proposed two mathematical model candidates (MC) for comparison, including the logistic generalized equation, which is often used by biologists to describe and predict population growth, choosing the cumulative total amount of substrate processed, W, as the independent variable:
lMC1 ðWÞ ¼ lMC2 ðWÞ ¼
lmax lmin
1þ
W K W Si
n þ lmin ;
ð9Þ
þ lmin ;
ð10Þ
lmax lmin
1þe
K W S þn W i
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Fig. 7. Identification of the kinetic parameters; (a) l, (b) S*, (c) Sm; during acclimatization to S0 = 50 and 100 mg4CP/L.
where W = jSiVe is equivalent to the number of batches already performed multiplied by Si and by the total affluent volume fed to the reactor in each batch, Ve = Vf V0 = 4 L.In order to identify the parameters in (9) and (10), the minimization of the Total Squared Error (TSE) criteria was used, i.e., to find the parameter set that minimizes
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TSEðlmax ; lmin ; n; K W Þ ¼
X ðlExp lMC Þ2 ; j
where j represents the batch number during a given acclimatization run, lMC are the l* values found using the model candidate being identified, and lexp corresponds to the l* value individually identified for each batch using its own experimental data. Table 1 Experimental vs. model candidates results for l*(W). S0 (mg4CP/L)
50
100
j Batch
1 2 4 7 8 10 1 4 6 7 10
W (mg4CP)
200 400 800 1400 1600 2000 400 1600 2400 2800 4000
l*(h1)
lExp
lMC1
lMC2
0.00030 0.00090 0.00250 0.00530 0.00480 0.00970 0.00250 0.00870 0.01190 0.01150 0.03280
0.00030 0.00031 0.00082 0.00560 0.00716 0.00878 0.00250 0.00418 0.01327 0.01958 0.02984
0.00042 0.00055 0.00133 0.00537 0.00700 0.00892 0.00289 0.00583 0.01329 0.01884 0.03030
Fig. 8. Acclimatization model candidate 1 (Eq. (9)) of l as a function of W with n = 5.52079 and KW = 26.732: (a) identification using S0 = 100 mg4CP/L; (b) validation using S0 = 50 mg4CP/L.
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Fig. 9. Acclimatization model candidate 2 (Eq. (10)), of l as a function of W with n = 5.090 and KW = 5.3323: (a) identification using S0 = 100 mg4CP/L; (b) validation using S0 = 50 mg4CP/L.
Table 1 presents the comparison between experimental results and both model candidate predictions. In graphical form, Fig. 8a and b shows the identification (using the first experiments set) and validation (using the second experiments set), respectively, of the Model candidate 1 (9). Fig. 9a and b shows the same situation but for the Model candidate 2 (10). Both model candidates present similar responses. To determine which model provides a better fit with respect to the experimental data, the Correlation Coefficient (R), the Determination Coefficient (R2) and the Total Squared Error (TSE) were computed and are presented in Table 2, showing that the candidate which presents a better fit to experimental data is the Model 2 (10). Then, using this model, the simulation of the acclimatization was performed for S0 = 100 mg4CP/L, for each of the monitored batches. Results appear in Fig. 10a. Note that Fig. 5 is repeated in Fig. 10b in order to allow for a direct comparison between the experimental data and the simulation when the proposed acclimatization model is used. It can be seen that the simulation reflects accurately the shape, the timing, and, particularly, as shown in Fig. 11, the minimum values of DO during the experimental results. The previous results suggest that the proposed mathematical model for l*, as a function of the total amount of substrate processed and of the input substrate concentration, allows to describe sufficiently well the experimental DO kinetics during the acclimatization.
Table 2 Statistical parameters of the model candidates. Model Candidate
R
R2
TSE
MC1 (Eq. (9)) MC2 (Eq. (10))
0.938 0.954
0.879 0.911
4.219 105 2.457 105
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Fig. 10. Evolution of DO kinetic during the acclimatization to S0 = 100 mg4CP/L: (a) simulation; (b) experimental.
7. Conclusions A mathematical model was presented that explains the evolution of l during the acclimatization of aerobic biomass to an inhibitory toxic substrate. The method used for the model identification included the use of the experimental data of DO, thus allowing the model to predict the effects of the acclimatization in the behavior of the DO, a variable which, unlike S, is possible to be reliably measured online. The Haldane law was used as the model of l(S), but expressed as a function of l*, S* and Sm. These parameters exhibit a more direct physical meaning than the original KI, KS, l0. The results of the identification show that, for the objectives at hand, S* and Sm exhibit low sensitivity to the acclimatization process. The opposite is true for l*, which increases from an initial minimum up to reaching a maximum when the biomass already is acclimatized, following an s-shape pattern as a function of the total amount of substrate treated during the acclimatization batches. Two model candidates were proposed to explain such an increase. It was found that the generalized logistic curve fits best the experimental results. The model identification was performed using the results of the acclimatization to S0 = 100 mg4CP/L and the validation used the results of the acclimatization to S0 = 50 mg4CP/L.
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Fig. 11. Minimal value of the DO during the acclimatization.
The proposed model is the first step to set the bases of future works in search of a final objective: design a control law, for automating the acclimatization process, based on the online measurement of the DO concentration. Acknowledgments The CIDI-UPB is gratefully acknowledged for the financing of the project # 957-11/06-28. Fajith Martínez thanks UPB for their internship offered during his Master of Engineering studies. The authors acknowledge also CONACYT projects 46093Y and 51244; DGAPA-UNAM project PAPIIT IN112207. Thanks to Jaime Perez, at UNAM, for his technical assistance. References [1] S. Venkata Mohan, P.N. Sarma, Advanced Bioremediation Processes in Chemical Industries, Scientific and Technical Report (10), IWA Publishing, London, 2001. p. 76. [2] M. Levin, M. Gealt, Biotreatment of Industrial and Hazardous Waste, McGraw-Hill, New York, USA, 1993. [3] P.A. Wilderer, R.L. Irvine, M.C. Goronszy, Sequencing batch reactor technology, Chemical Business 5 (2006). April. [4] M.J. Palma_Acosta, J. Manga Certain, Simulación de un sistema de fangos activados en discontinuo (SBR) para el tratamiento de aguas residuales con altos contenidos de nitrógeno, ingeniería & Desarrollo 18 (julio-Diciembre) (2005) 61–71. [5] I. García Expósito, El sistema SBR en la industria agroalimenticia, Tecnología del Agua 23 (234) (2003) 62–69. [6] R. Herrera, Reactor biológico secuenciado (SBR), Tecnología del Agua 21 (219) (2001) 68–72. [7] B.A. Wiggings, S.H. Jones, M.A. Alexander, Explanations for the acclimation period preceding the mineralization of organic chemicals in aquatic environments, Applied and Environmental Microbiology 53 (4) (1987) 791–796. [8] M.J. Betancur, J.A. Moreno, I. Moreno-Andrade, G. Buitrón, Practical optimal control of fed-batch bioreactors for the waste water treatment, International Journal of Robust and Nonlinear Control 16 (3) (2005) 173–190. [9] I. Moreno-Andrade, G. Buitrón, M.J. Betancur, J.A. Moreno, Optimal degradation of inhibitory wastewaters in a fed-batch bioreactor, Journal of Chemical Technology and Biotechnology 81 (4) (2006) 713–720. [10] G. Buitrón, J.A. Moreno, Modeling of the acclimation/deacclimation process of a mixed culture degrading 4-chlorophenol, Water Science and Technology 49 (1) (2004) 79–86. [11] A. Holmberg, On the practical identifiability of microbial growth models incorporating Michaelis–Menten type nonlinearities, Mathematical Bioscience 62 (1982) 23–42. [12] AFNOR, Evaluation en mileu aqueux de la biodegradabilité aérobie ‘‘ultime” des produits organiques solubles, Normalisation française, (1985) NFT 90– 312. [13] G. Buitron, M-E. Schoeb, J. Moreno, Automated sequencing batch bioreactor under extreme peaks of 4-chlorophenol, Water Science and Technology 47 (10) (2003) 175–181. [14] I. Moreno-Andrade, G. Buitrón, Influence of the initial substrate to microorganisms ratio on the anaerobic inhibition test, Water Science and Technology 48 (6) (2003) 17–22. [15] APHA, Standard methods for the examination of water and wastewater. A.D. Eaton, A.E. Clesceri, E.W. Rice, A.E. Greenberg (Eds), APHA, AWWA and WPCF, 21th ed., Port City Press, Baltimore, Maryland, 2005.
Contents lists available at ScienceDirect
Simulation Modelling Practice and Theory journal homepage: www.elsevier.com/locate/simpat
Acclimatization model of an aerobic bioreactor for the treatment of toxic wastewater Manuel J. Betancur a,*, Fajith Martínez a, Carlos Ocampo b, Jaime A. Moreno c, Germán Buitrón d, Iván Moreno-Andrade d a
A+D Universidad Pontificia Bolivariana, Cq. 1#70-01, of 11-259, Medellín, Colombia CIBIOT, Universidad Pontificia Bolivariana, Cq. 1#70-01, of 11-259, Medellín, Colombia c Automation Department, Engineering Institute, Universidad Nacional Autónoma de México, Cd. Universitaria, 04510 Coyoacán, México DF, Mexico d Laboratory for Research on Advanced Processes for Water Treatment, Engineering Institute, Campus Juriquilla, Querétaro, Universidad Nacional Autónoma de México, Blvd. Juriquilla 3001, Querétaro 76230, Mexico b
a r t i c l e
i n f o
Article history: Received 4 April 2008 Received in revised form 3 October 2008 Accepted 4 December 2008 Available online 16 December 2008
Keywords: Acclimatization Bioreactor Mathematical model SBR Wastewater treatment
a b s t r a c t This work proposes a mathematical model for the acclimatization process of a bioreactor treating toxic wastewater. Experimental data was used to identify the changing kinetic parameters of the model as acclimatization progresses. It was found that only one key parameter, the specific biomass growth rate function, changed during the acclimatization process. Therefore, an acclimatization model was proposed to explain the changes of this parameter. Ó 2008 Elsevier B.V. All rights reserved.
1. Introduction Many processes in the chemical, pharmaceutical, plastic, petrochemical industries, etc., generate WW which contains organic toxic compounds. The treatment and reutilization of such WW is an option in areas where water resources are scarce, hence the importance for the improvement of the WW treatment technologies. The utilization of biological treatments is based on the capacity of microorganisms, specifically bacteria, to degrade a great quantity of toxic substances. The pollutants are treated as food by the bacteria and these, while feeding, increase their population at the same time as the water gets treated. Some microorganisms perform the treatment process in the presence of oxygen and others in its absence [1]. For the aerobic reactions the oxygen is dissolved in the water by means of aerator systems. A tank, within which the proper conditions for the bio-reaction to take place are guaranteed, on a large scale basis, is called a bioreactor [2]. The SBR have an increased efficiency and flexibility compared to continuous reactors. For such a reason the term SBR is used as a synonym for WWTP technology where the volume in the reactor tank is variable in time[3–5]. The processes that occur in a SBR are identical to those of a conventional continuous activated sludge. Nevertheless an important difference exists between both. In a SBR system all the stages of the process are performed in the same reactor, with different phases separated in time[6], whereas in the continuous processes the different stages are performed simultaneously, in different tanks or tank sections [6]. * Corresponding author. Tel.: +57 4 4159020x9584. E-mail address: [email protected] (M.J. Betancur). 1569-190X/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.simpat.2008.12.001
M.J. Betancur et al. / Simulation Modelling Practice and Theory 17 (2009) 680–691
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Nomenclature 4CP B COD DO DOC K1 K2 KI KLa KS KW MC n O Osat Q S S* Si Sm S0 SBR TSS V Ve Vf V0 VSS W WW WWTP X
l l(S) l l*
lmax
4-chlorophenol specific endogenous respiration rate (h1) chemical oxygen demand (mg/L) dissolved oxygen (mgDO/L) dissolved organic carbon (mg/L) biomass/substrate yield coefficient (mg4CP/mgTSS) biomass/oxygen yield coefficient (mgDO/mgTSS) inhibition coefficient (mg4CP/L) oxygen mass transfer coefficient (h1) Michaelis–Menten saturation constant (mg4CP/L) half acclimatization constant model candidate exponent constant dissolved oxygen concentration (mgDO/L) dissolved oxygen concentration at saturation (mg/L) inflow volumetric flow (L/h) substrate concentration (mg/L) substrate concentration at which the biomass growth rate reaches its maximum value (mg/L) toxic concentration in the influent (mg/L) substrate concentration for medium Biomass growth rate (mg/L) initial substrate concentration in the affluent (mg/L) sequencing batch reactor total solid suspended (mg/L) volume level of the liquid in the SBR exchange volume (L) final volume (L) inicial volume (L) volatile suspended solids (mg/L) total mass of processed substrate (mg4CF) wastewater wastewater treatment plant active biomass concentration (mgTSS/L) specific biomass growth rate (h1) specific biomass growth rate in function of S (h1) ideal maximum value, for the non-inhibited case only, of the specific biomass growth rate (h1) maximum value, for a given inhibiting batch reaction, of the specific biomass growth rate (h1) maximum value of l* (h1) during acclimatization
The stages that are required to carry out an operative cycle in a SBR are[5] shown in Fig. 1: filling, where there is admitted a volume of WW into the SBR; reaction, where biomass is mixed and put in contact with the toxic WW and, if the biomass is aerobic, air is injected to allow the biochemical reaction that transforms the toxic substrate; settle, where the aeration and the agitation systems are suspended to allow the biomass to settle at the bottom of the SBR; draw, where the supernatant (treated water) is evacuated, and dead time. Due to its toxicity, biological treatment of WW containing a toxic substrate is difficult, since the microorganisms are initially not able to treat that substance. Therefore, the first step to make a SBR operative is the acclimatization, i.e., the adaptation of the microorganisms to a particular toxic substrate. Different mechanisms have been described to explain the process of acclimatization. Wiggings et al. [7] suggested that during this process there is a selection and a multiplication of specialized microorganisms and physiological transformations occur in the metabolic system of the microorganisms, i.e., alterations at the enzymatic level, regulation and production, mutations, etc. When the biomass is aerobic, the acclimatization periods range from hours to days, depending on the characteristics of the WW, temperature, pH, substrate type and concentration, etc. Once acclimatized, an appropriate control strategy of the SBR may avoid the negative impact of the inhibition caused by the excess of toxic substrate and maintain a high sludge activity of the biomass [8,9]. However, the initial acclimatization of biomass, when the SBR is inoculated for the first time, or after a failure of the system, still has to be manually controlled. The automation of the acclimatization process of a SBR would allow the operation in the WWTP to be more reliable and more optimal. Therefore, a model of the acclimatization process is necessary. Buitrón and Moreno[10] proposed such a model for a SBR treating 4CP as model substrate. They assumed that the acclimatization effect is reflected in the change of l(S),
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Fig. 1. Operation phases of a SBR.
which in turn can be modeled using the Haldane Law, which describes the behavior of l depending on S. However, the identificability of the parameters of l, using the measurements of S with batch experiments, is very poor [10,11]. In this work we propose an improved mathematical acclimatization model. It uses, besides the substrate kinetics, the on line measurement of the DO to determine the changes of the kinetic parameters of l during acclimatization. Thus the proposed model not only explains the evolution of the S over time but also the evolution of the DO. The introduction of the DO measurements improves the model identificability because the DO measurement can be done on line, generating samples qualitatively and quantitatively more reliable than those of S, which usually have to be processed manually and so they are more prone to experimental error. The objective of this work is to identify and validate a mathematical model of the acclimatization of microorganisms to inhibitory compounds, using 4CP as a model compound, in a SBR used for the treatment of toxic WW. Section 2 describes the methodology. Section 3 introduces the mathematical model of bio-reaction. The acclimatization experimental results are presented in Section 4. Section 5 describes the sensitivity analysis of the parameters of l for any given single batch. In Section 6 two model candidates are proposed. Finally some conclusions are presented. 2. Methodology An aerobic automated SBR system with a capacity of 7 L and an exchange volume of 57% (4 L) was used. The airflow rate was 1.5 L/min and the temperature within the SBR was controlled at 20 °C. The DO was measured on line using an industrial polarographic sensor and transmitter (Hendress + Hauser model COS41 and Liquisys-M COM223-DX1105). The fill and draw flows were controlled by peristaltic pumps (Cole–Palmer model 752350 (0–100 rpm) and 523-40 (0–600 rpm) series Masterflex, respectively). The reactor was inoculated with microorganisms from a municipal activated sludge WWTP. The biomass concentration was set to 2000 mgVSS/L. A synthetic WW containing 4CP, as a toxic model compound, was used as the sole source of carbon and energy. Nutrients such as nitrogen, phosphorus, and oligoelements were added following the techniques recommended by AFNOR [12]. The SBR was operated under the following batch strategy: pre-aeration time 15 min (aeration after the draw phase, before the next filling phase, in order to begin each new degradation cycle with a not limiting oxygen concentration), filling time 12.6 min, reaction time (variable depending on the necessary time to reach 99% of removal efficiency of 4CP), settling time 12 to 30 min, and draw time 1 min. Degradation time, for the 4CP, is the filling time plus the reaction time. The end of the degradation time was indirectly determined using the dynamics of the O present in the reactor [13]. In this work two sets of experiments, for the acclimatization of the biomass, were performed for two different substrate concentrations, one with S0 = 50 mg4CP/L and the other one for 100 mg4CP/L. The acclimatization model identification was performed using the first set, S0 = 100 mg4CP/L, and the second set, S0 = 50 mg4CP/L, was used for validation. The acclimatization began with fresh, not acclimatized, sludge from a nearby WWTP. In both cases sequencing batch reactions were cyclically performed, keeping the same biomass in the reactor, until reaction times became approximately constant, i.e., until the biomass was finally acclimatized. It is important to note that during the acclimatization to 4CP, the microorganisms increase the degradation rate and the activity. Due to this, the performance of the bioreactor is better as the acclimatization takes place, even if the biomass concentration is kept at the preset value.
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The acclimatization of bacteria to 4CP substrate must be performed for relatively low concentrations. For high values of S the acclimatization may not be possible. Moreno-Andrade and Buitrón[14] observed that this inhibition is not only a function of the initial concentration of the toxic compound, but also of the initial biomass concentration. A low biomass concentration may produce a high degree of inhibition. For this reason a low value (under 0.4) for the substrate/biomass concentrations relation is recommended. 4CP concentration (as total phenol concentration) was measured taking samples and processing them offline using the colorimetric technique of 4-aminoantipyrine according to APHA [15]. TSS and VSS were determined according to the APHA Standard Methods [15]. DOC was determined with a Shimadzu TOC-5050 and COD according to the APHA Standard Methods [15]. These analyses were performed to evaluate 4CP mineralization. 3. Mathematical model of the bio-reaction A key parameter of the reaction model is l(S), as it directly influences both S and DO dynamics. All of the other bio-reaction model parameters, i.e. with the exception of l related parameters, are supposed invariable during the acclimatization process. Therefore, to understand how l parameters evolve in the time, depending on the exposure of the biomass to the toxic substance, seems to be the key for the modeling of the acclimatization process. In a SBR, the filling and reaction phases can be described by the differential equations set [8–10]
Q X_ ¼ lðSÞX X ; V
ð1Þ
Q S_ ¼ k1 lðSÞX þ ðSi SÞ ; V
ð2Þ
Q O_ ¼ ðk2 lðSÞ þ bÞX þ kL aðOsat OÞ O ; V V_ ¼ Q
ð3Þ ð4Þ
assuming that O is not a limiting reactive, i.e., when it can be supposed that both l and b are not a function of O.For inhibitory substrates, l may be described using the Haldane law (see Fig. 2)
lðSÞ ¼
l0 S 2
K S þ S þ SK I
;
ð5Þ
which is valid when the oxygen is not a limiting reactant, i.e., for normal operation conditions. An alternate, equivalent, parameterization of the Haldane model was used [8,9] (see Fig. 2), defined as
S ¼
pffiffiffiffiffiffiffiffiffiffi KIKS
ð6Þ
for the substrate concentration value that generates the maximum biomass growth rate,
l ¼
l0
1 þ 2K S =S
for the above mentioned maximum rate, and
Fig. 2. Model Law of Haldane. l* = 0.0098 (h1), S* = 15 mg4CP/L, Sm = 60 mg4CP/L equivalents to l = 0.0885, KI = 3.7500, KS = 59.9995.
ð7Þ
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Sm ¼
K 2I þ 4S þ
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi K 2I þ 8K I S þ 12S2 2
ð8Þ
for the substrate concentration at which inhibition is 50%. This new set of parameters, described in (6)–(8), do have a better graphical (see Fig. 2), and physical, interpretation than the classical ones in (5).
4. Acclimatization experiments For both sets of acclimatization experiments, the acclimatized states were reached after 10 batches, i.e., after the 10th batch the 4CP degradation time did not diminish appreciably. For the 50 mg4CP/L case the degradation time diminished gradually from 40.21 h to 1.21 h, from cycles 1 to 10, respectively. For the 100 mg4CP/L case, also, 10 batches were required to obtain the acclimatization, in which process the degradation time was reduced from 52.21 h to 1.37 h. In Figs. 3 and 4 it is possible to observe the degradation time for S0 = 100 mg4CP/L and S0 = 50 mg4CP/L, respectively. Both figures show that the first batch was rather slow but, as more batches are executed, the degradation becomes more rapid, evidencing that the acclimatization is taking place. As the aerobic bacteria degrade the substrate present in the WW, they consume oxygen in order to cover for metabolic needs and also to produce new cells. (Fig. 5) shows the DO evolution during the acclimatization of the biomass to S0 = 100 mg4CP/L. For every batch it can be seen a time for which DO is established in a maximum value, near to saturation, just after having passed a valley where it exhibited its minimal value. Such a time is at the end of the reaction, i.e., the time were the substrate is been depleted and thus no more oxygen is needed for processing it. The minimal value of the valley, related to the maximum oxygen consumption, tends to diminish in every new batch during the acclimatization, and becomes stable finally after the 10th batch (not shown). Such a behavior is the motivation to try and model the process of acclimatization of the biomass using also the DO kinetics variations.
5. Sensitivity analysis of the kinetic parameters The initial hypothesis is that changes of l(S) parameters (6)–(8) during the first successive reactions, explain the evolution of the model of the SBR during the acclimatization, and hence explain the changes in the DO as well as the substrate kinetics. Nevertheless, during every particular batch, the whole model is supposes to be invariant, i.e., l* (6), S* (7) and Sm (8) may change only from one batch to the next. Two alternatives were studied for the identification of the model parameters: one using only the experimental information of S kinetics, and the other one using both the experimental information of S and that of the DO. Fig. 6 shows the simulation, for a single batch, of the model response with the identified parameters. A better fit for S is obtained when only the experimental data of S is used. Nevertheless, for the DO kinetics, the best fit is found when the experimental data of both S and DO are used. As the future and final objective of our work is to design a control law able to automate the acclimatization process, based only on the online measurement of DO, then including the experimental data of DO for the identification is justified.
Fig. 3. Kinetic of degradation of 4CP during the acclimatization to S0 = 100 mg4CP/L.
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Fig. 4. Kinetic of degradation of 4CP during the acclimatization to S0 = 50 mg4CP/L.
Fig. 5. Evolution of the DO during the acclimatization to S0 = 100 mg4CP/L (filling and draw phases time are not included in the graphs).
The identification of the parameters l* (6), S* (7), and Sm (8), was done for each single batch (1)–(10), for both experimental data sets. The identification software was developed using Matlab’s Optimization Toolbox, in particular the lsqnonlinear function set to the Levenberg–Marquardt method. Fig. 7 shows the identification results for both experimental sets. Fig. 7a shows the evolution of l* as the acclimatization progresses. Note that its final value is different for both acclimatization runs. On the other hand, for S* and Sm, Fig. 7b and c, respectively, their values are very similar and their variations during each run are minimal. This leads to assume that S* and Sm exhibit low sensitivity to the acclimatization process, hence it is reasonable to characterize them as constants for all batches. Under these assumptions, the graphic of l(S) retains the exact same shape during the whole acclimatization process, changing only its height l*. Such changes in l* from one batch to the next are, therefore, considered to be the effect of the acclimatization process. Hence, a model of such a change will explain the
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Fig. 6. Model simulation of filling and reaction, for batch 7S0 = 100 mg4CP/L: (a) continuous line: model identified using S and DO. S* = 15.0660, Sm = 60.2778, l* = 0.0124; (b) dotted line: model identified using S only S* = 23.9867, Sm = 48.1241, l* = 0.0172; (c) circles: experimental data.
associated evolution of (5) in order to allow the fill and reaction model in (1)–(4) to be used for any given batch during the acclimatization process. 6. Mathematical model of the acclimatization The growth of l, from one batch to the next, during the experimental acclimatization process, exhibited an s-shaped form. Hence, we proposed two mathematical model candidates (MC) for comparison, including the logistic generalized equation, which is often used by biologists to describe and predict population growth, choosing the cumulative total amount of substrate processed, W, as the independent variable:
lMC1 ðWÞ ¼ lMC2 ðWÞ ¼
lmax lmin
1þ
W K W Si
n þ lmin ;
ð9Þ
þ lmin ;
ð10Þ
lmax lmin
1þe
K W S þn W i
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Fig. 7. Identification of the kinetic parameters; (a) l, (b) S*, (c) Sm; during acclimatization to S0 = 50 and 100 mg4CP/L.
where W = jSiVe is equivalent to the number of batches already performed multiplied by Si and by the total affluent volume fed to the reactor in each batch, Ve = Vf V0 = 4 L.In order to identify the parameters in (9) and (10), the minimization of the Total Squared Error (TSE) criteria was used, i.e., to find the parameter set that minimizes
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TSEðlmax ; lmin ; n; K W Þ ¼
X ðlExp lMC Þ2 ; j
where j represents the batch number during a given acclimatization run, lMC are the l* values found using the model candidate being identified, and lexp corresponds to the l* value individually identified for each batch using its own experimental data. Table 1 Experimental vs. model candidates results for l*(W). S0 (mg4CP/L)
50
100
j Batch
1 2 4 7 8 10 1 4 6 7 10
W (mg4CP)
200 400 800 1400 1600 2000 400 1600 2400 2800 4000
l*(h1)
lExp
lMC1
lMC2
0.00030 0.00090 0.00250 0.00530 0.00480 0.00970 0.00250 0.00870 0.01190 0.01150 0.03280
0.00030 0.00031 0.00082 0.00560 0.00716 0.00878 0.00250 0.00418 0.01327 0.01958 0.02984
0.00042 0.00055 0.00133 0.00537 0.00700 0.00892 0.00289 0.00583 0.01329 0.01884 0.03030
Fig. 8. Acclimatization model candidate 1 (Eq. (9)) of l as a function of W with n = 5.52079 and KW = 26.732: (a) identification using S0 = 100 mg4CP/L; (b) validation using S0 = 50 mg4CP/L.
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Fig. 9. Acclimatization model candidate 2 (Eq. (10)), of l as a function of W with n = 5.090 and KW = 5.3323: (a) identification using S0 = 100 mg4CP/L; (b) validation using S0 = 50 mg4CP/L.
Table 1 presents the comparison between experimental results and both model candidate predictions. In graphical form, Fig. 8a and b shows the identification (using the first experiments set) and validation (using the second experiments set), respectively, of the Model candidate 1 (9). Fig. 9a and b shows the same situation but for the Model candidate 2 (10). Both model candidates present similar responses. To determine which model provides a better fit with respect to the experimental data, the Correlation Coefficient (R), the Determination Coefficient (R2) and the Total Squared Error (TSE) were computed and are presented in Table 2, showing that the candidate which presents a better fit to experimental data is the Model 2 (10). Then, using this model, the simulation of the acclimatization was performed for S0 = 100 mg4CP/L, for each of the monitored batches. Results appear in Fig. 10a. Note that Fig. 5 is repeated in Fig. 10b in order to allow for a direct comparison between the experimental data and the simulation when the proposed acclimatization model is used. It can be seen that the simulation reflects accurately the shape, the timing, and, particularly, as shown in Fig. 11, the minimum values of DO during the experimental results. The previous results suggest that the proposed mathematical model for l*, as a function of the total amount of substrate processed and of the input substrate concentration, allows to describe sufficiently well the experimental DO kinetics during the acclimatization.
Table 2 Statistical parameters of the model candidates. Model Candidate
R
R2
TSE
MC1 (Eq. (9)) MC2 (Eq. (10))
0.938 0.954
0.879 0.911
4.219 105 2.457 105
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Fig. 10. Evolution of DO kinetic during the acclimatization to S0 = 100 mg4CP/L: (a) simulation; (b) experimental.
7. Conclusions A mathematical model was presented that explains the evolution of l during the acclimatization of aerobic biomass to an inhibitory toxic substrate. The method used for the model identification included the use of the experimental data of DO, thus allowing the model to predict the effects of the acclimatization in the behavior of the DO, a variable which, unlike S, is possible to be reliably measured online. The Haldane law was used as the model of l(S), but expressed as a function of l*, S* and Sm. These parameters exhibit a more direct physical meaning than the original KI, KS, l0. The results of the identification show that, for the objectives at hand, S* and Sm exhibit low sensitivity to the acclimatization process. The opposite is true for l*, which increases from an initial minimum up to reaching a maximum when the biomass already is acclimatized, following an s-shape pattern as a function of the total amount of substrate treated during the acclimatization batches. Two model candidates were proposed to explain such an increase. It was found that the generalized logistic curve fits best the experimental results. The model identification was performed using the results of the acclimatization to S0 = 100 mg4CP/L and the validation used the results of the acclimatization to S0 = 50 mg4CP/L.
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Fig. 11. Minimal value of the DO during the acclimatization.
The proposed model is the first step to set the bases of future works in search of a final objective: design a control law, for automating the acclimatization process, based on the online measurement of the DO concentration. Acknowledgments The CIDI-UPB is gratefully acknowledged for the financing of the project # 957-11/06-28. Fajith Martínez thanks UPB for their internship offered during his Master of Engineering studies. The authors acknowledge also CONACYT projects 46093Y and 51244; DGAPA-UNAM project PAPIIT IN112207. Thanks to Jaime Perez, at UNAM, for his technical assistance. References [1] S. Venkata Mohan, P.N. Sarma, Advanced Bioremediation Processes in Chemical Industries, Scientific and Technical Report (10), IWA Publishing, London, 2001. p. 76. [2] M. Levin, M. Gealt, Biotreatment of Industrial and Hazardous Waste, McGraw-Hill, New York, USA, 1993. [3] P.A. Wilderer, R.L. Irvine, M.C. Goronszy, Sequencing batch reactor technology, Chemical Business 5 (2006). April. [4] M.J. Palma_Acosta, J. Manga Certain, Simulación de un sistema de fangos activados en discontinuo (SBR) para el tratamiento de aguas residuales con altos contenidos de nitrógeno, ingeniería & Desarrollo 18 (julio-Diciembre) (2005) 61–71. [5] I. García Expósito, El sistema SBR en la industria agroalimenticia, Tecnología del Agua 23 (234) (2003) 62–69. [6] R. Herrera, Reactor biológico secuenciado (SBR), Tecnología del Agua 21 (219) (2001) 68–72. [7] B.A. Wiggings, S.H. Jones, M.A. Alexander, Explanations for the acclimation period preceding the mineralization of organic chemicals in aquatic environments, Applied and Environmental Microbiology 53 (4) (1987) 791–796. [8] M.J. Betancur, J.A. Moreno, I. Moreno-Andrade, G. Buitrón, Practical optimal control of fed-batch bioreactors for the waste water treatment, International Journal of Robust and Nonlinear Control 16 (3) (2005) 173–190. [9] I. Moreno-Andrade, G. Buitrón, M.J. Betancur, J.A. Moreno, Optimal degradation of inhibitory wastewaters in a fed-batch bioreactor, Journal of Chemical Technology and Biotechnology 81 (4) (2006) 713–720. [10] G. Buitrón, J.A. Moreno, Modeling of the acclimation/deacclimation process of a mixed culture degrading 4-chlorophenol, Water Science and Technology 49 (1) (2004) 79–86. [11] A. Holmberg, On the practical identifiability of microbial growth models incorporating Michaelis–Menten type nonlinearities, Mathematical Bioscience 62 (1982) 23–42. [12] AFNOR, Evaluation en mileu aqueux de la biodegradabilité aérobie ‘‘ultime” des produits organiques solubles, Normalisation française, (1985) NFT 90– 312. [13] G. Buitron, M-E. Schoeb, J. Moreno, Automated sequencing batch bioreactor under extreme peaks of 4-chlorophenol, Water Science and Technology 47 (10) (2003) 175–181. [14] I. Moreno-Andrade, G. Buitrón, Influence of the initial substrate to microorganisms ratio on the anaerobic inhibition test, Water Science and Technology 48 (6) (2003) 17–22. [15] APHA, Standard methods for the examination of water and wastewater. A.D. Eaton, A.E. Clesceri, E.W. Rice, A.E. Greenberg (Eds), APHA, AWWA and WPCF, 21th ed., Port City Press, Baltimore, Maryland, 2005.
