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Modeling and parameter estimation of two-phase endogenous respirograms and COD measurements during aerobic digestion of biological sludge
Accepted Manuscript Modeling and parameter estimation of two-phase endogenous respirograms and COD measurements during aerobic digestion of biological sludge C. Fall, J.A. Rogel-Dorantes, E.L. Millán-Lagunas, C.G. Martínez-García, B.C. Silva-Hernández, F.S. Silva-Trejo PII: DOI: Reference:
S0960-8524(14)01379-0 http://dx.doi.org/10.1016/j.biortech.2014.09.120 BITE 14010
To appear in:
Bioresource Technology
Received Date: Revised Date: Accepted Date:
20 July 2014 21 September 2014 23 September 2014
Please cite this article as: Fall, C., Rogel-Dorantes, J.A., Millán-Lagunas, E.L., Martínez-García, C.G., SilvaHernández, B.C., Silva-Trejo, F.S., Modeling and parameter estimation of two-phase endogenous respirograms and COD measurements during aerobic digestion of biological sludge, Bioresource Technology (2014), doi: http:// dx.doi.org/10.1016/j.biortech.2014.09.120
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1 Modeling and parameter estimation of two-phase endogenous respirograms and COD measurements during aerobic digestion of biological sludge Fall C.1*, Rogel-Dorantes J.A.1, Millán-Lagunas E.L.1, Martínez-García C.G.1 Silva-Hernández B.C.1 and Silva-Trejo F.S.1 1
Centro Interamericano de Recursos del Agua (CIRA), Universidad Autónoma del Estado de México (UAEM), Apdo postal 367, Toluca, C.P. 50091, México. * Corresponding author: [email protected]; Tel +52 722 2965550.
ABSTRACT Long-term aerobic digestion batch tests were performed on a sludge that contained mainly two fractions, a heterotrophic biomass XH and its endogenous residues XP, which were cultivated in conditions known to favor bio-storage (XSto). The objective was to model the stabilization of the sludge and determine the parameters of the endogenous decay processes, based on simultaneous measurements of the chemical oxygen demand (COD) and oxygen uptake rates (OUR). The respirograms were shown to have a two-phase structure that was describable with activated sludge model 3 (ASM3), but not with ASM1. Comparing the information from the COD and OUR data suggested the presence of two different groups of heterotrophs (XHa and XHb), one that decays with oxygen consumption and another without using O2. A modified ASM3 model was proposed, which was able to fit the OUR and COD data from the digesters, as well as cases from the literature.
KEYWORDS: accumulating organisms; aerobic digestion; endogenous respirograms; parameter identifiability; storage.
1. INTRODUCTION Aerobic digestion is one of the most commonly used sludge stabilization processes. The
2 development of descriptive models for this process is important for multiple reasons. It allows simulating and predicting the stabilization of biological sludge (Marais and Ekama, 1976). Also, batch digestion tests are very often used to estimate the parameters of the decay processes included in activated sludge models (ASMs) (Henze et al., 2000).
Current aerobic digestion models (Marais and Ekama, 1976; Gomez et al., 2007) utilize the concept of biomass loss by endogenous respiration. The active biomass is combined in one heterotroph-dominant group (XH) that follows a first-order decay rate law (dXH/dt = bHXH), where bH is the first-order decay rate constant (d-1).
The decay process by endogenous respiration and its modified version (death-regeneration) are also used in the dynamic activated sludge models (mainly ASM1, ASM2d, and ASM3; Henze et al., 2000). The ASMs include several decay processes related to each of the active biomass components and internal storage compounds, e.g. the heterotrophs (XH) and the stored polymers (XSto). Some aerobic digestion models were developed by simplifying the ASM1 model and including or no a slow biodegradation process for the endogenous residues, XP (Ramdani et al., 2010; Özdemir et al., 2014).
In the past, mainly two experimental methods were developed for estimating the bH constant. One was by monitoring the oxygen uptake rates (OUR) and the other was by measuring the volatile (or total) suspended solids (VSS and TSS), in aerobic digestion tests (Marais and Ekama, 1976; Van Haandel et al., 1998). There was no formal update of the bH estimation methods in regard to the ASM3 and ASM2d models. The latter models consider other types of microorganisms, in particular ones that are capable of storing the substrate as biopolymers.
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A wide interval of bH values is reported in the literature, without clear reasons for such dispersion. The accepted default value for bH is 0.2 d-1 at 20°C (Henze et al., 2000; Ramdani et al., 2010). However, many other values have been reported, from 0.06 to 0.5 d-1 (Friedrich and Takáks, 2013). Many factors can explain the wide divergence between the reported values of the 20°C heterotrophic decay constant. Friedrich and Takáks (2013) pointed out the type of data gathered (VSS or OUR) and the quality of the mathematical regressions performed to estimate the parameters (identifiability issues). The identifiability issues may add to the confusion by enlarging the intervals of bH values reported in the literature. A high coefficient of correlation (R2) is not enough to justify the representativeness of a regression constant. It is imperative to test the identifiability or the uniqueness of the estimated parameters sets (Koch et al., 2000; Insel et al., 2002; Sin et al., 2005; Guisasola et al., 2005). AQUASIM is one of the modeling software known to perform this task very well (Reichert, 1998; Fall et al., 2007).
Another important factor that has not been scrutinized enough is the exact nature of the biomass for which the decay rates are reported. The biomass in treatment plants is not just ordinary heterotrophic organisms (OHOs). Other types of bacteria can form an important part of the sludge. This is the case of phosphorus- and glycogen-accumulating microorganisms (PAOs and GAOs) in enhanced biological phosphorus removal plants (EBPR) (Lu et al., 2007; Wang et al., 2012). Among other aspects, PAOs and GAOs differ from OHOs in two essential points regarding digestion. First, their decay constant is much lower (0.03-0.04 d-1; Lu et al., 2007 and Wentzel et al., 1989a), which extends the treatment times to stabilize the sludge. Secondly, the presence of stored material in the biomass can affect the shape of the endogenous respirograms and its interpretation.
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In some studies, such as in Van Haandel et al. (1998) and Ramdani et al. (2010), there were no differences between the decay constants obtained by the traditional VSS and OUR bH methods. In these cases however, it was clearly about OHOs (bH =0.2 d-1). Results from both methods diverged clearly in Özdemir et al. (2013) for a biomass that was apparently storagecapable bacteria (bH of 0.21 d-1 by VSS versus 0.06 d-1 by the OUR). In a study that involucrated many sludge from different EBPR plants (Friedrich and Takáks, 2013), the authors decided not to run the VSS-based method in parallel to the OUR method. However, the study revealed a shape of the endogenous respirograms (two-phases) that was very different from typical one for OHOs (one phase). The first and fast step was attributed to decay of the stored compounds (XSto), while the second slower phase was associated to decay of the heterotrophs (XH). Some data from Friedrich and Takáks (2013) as well as Özdemir et al. (2013) will be used latter to test the models and programs developed in the present study.
Based on the aforementioned findings (dispersion of the bH values and the need to take into account other types of sludge), it is pertinent to revisit the methods used to determine the decay parameters, as well as reevaluate the behavior of aerobic digestion in bacterial cultures not dominated by OHOs. This is in accordance with the position adopted by the Good Modelling Practices (GMP) group, who recommended that the characterization methods used in active sludge models be rethought (Choubert et al., 2013).
The objective of the research was to model the stabilization of storing-biomass sludge and determine the parameters of the endogenous decay processes, based on simultaneous measurements of the chemical oxygen demand (COD) and oxygen uptake rates (OUR). To be
5 able to adequately estimate the model parameters, it is important to avoid most of the confounding factors (e.g., the type of biomass and the parameter identifiability issues). In consequence, the study was performed with a sludge model that contained only two main components, the heterotrophic fraction XH and its endogenous residues XP. The sludge was cultivated in conditions known to favor the bio-storage (XSto). Aerobic digestion experiments were performed while the endogenous respirograms and the COD profiles were fit separately, and then simultaneously, with ASM3 and ASM1 derived sub-models.
2. MATERIALS AND METHODS
2.1 Cultivation of the sludge model The sludge used latter to perform the digestion tests, was produced by operating an activated sludge system in the laboratory, which was fed with synthetic wastewater based on acetate. Two 30 L sequential batch reactors (SBRs) were used, operated at solids retention time of 15 d. As in previous works (Giraldo et al., 2007; López-Vázquez et al., 2007; Ramdani et al., 2010), it was a strategy of this research to base the study on a type of biological sludge with not very complex characteristics and a relatively constant composition in time (sludge model). The nominal composition of the synthetic wastewater was previously reported (MartinezGarcia et al., 2014), having a total chemical oxygen demand (COD) of 500 mg/L and an approximate COD/N/P ratio of 100/5/0.5. Under these conditions, the sludge produced in the reactors was expected to contain only two to three fractions: mainly, the heterotrophic biomass (XH) and the endogenous residues (XP) coming from bacterial lysis, and eventually stored polymer components (XSto). Allylthiourea was added to inhibit the development of autotrophic bacteria (5 mg/L ATU, Henze et al., 2000; López-Vázquez et al., 2007).
6
The SBR were operated in anaerobic-aerobic reaction phases and under alternated conditions of starvation and abundance of food (feast/famine). This was a way to favor bioaccumulation mechanisms in the heterotrophic bacteria and a strategy to overcome some sludge bulking problems that were occurring earlier in the research. The 30 L SBR operation cycle was as follows: - 2 L purge of mixed liquor, sedimentation for 1 h; - pouring of 20 L of treated supernatant (approximately 10 min); - feeding of 2 L of concentrated fresh medium (in less than 1 min); - mechanical mixing in non-aerated phase for 1 h, before adding 18 L of tap water to complete the influent; - airing and reaction at 20 ± 2°C for the rest of the day. The medium was prepared in concentrated form to yield the nominal 500 mg/L COD, when 2 L of it was diluted with 18 L of tap water.
2.2 Aerobic digestion of the sludge To estimate the decay parameters via the VSS-COD and OUR methods (Van Haandel et al., 1998), several aerobic digestion tests were performed (20°C) once the SBRs were stabilized. In each run, 4 L of mixed liquor purged from the SBRs were concentrated and transferred to a small digester-reactor operated in batch (1.7 L). The particulate COD and the endogenous OURs (or rO2) of the digesters were monitored for several days, up to 20 days by respirometry and more than 40 days with Hach COD kits. Regularly, the evaporated water from the digesters was replaced with distilled water, before performing the COD and rO2 measurements.
Total and soluble COD (1.2 µm filters) analyses were carried out in triplicate with Hach reactive kits at the 150 and 1500 mg/L ranges, and with strict control on the practices when homogenizing, micro-pipetting (cut-off tips), and diluting the solids. All along the text, the
7 COD data reported (and used in the models) are particulate COD (total COD - soluble COD). The soluble COD contents of the sludge were generally very low (< 60 mg/L). Routine checks were made (VSS/TSS and VSS/COD ratios, temperature, pH, etc.), in accordance with standard methods (APHA, 2005).
2.3 Respirometric measurements Closed Winkler BOD bottles were used to measure the OUR (or rO2), daily and in duplicate, to avoid errors that could occur when using respirometers that are open to the atmosphere. The bottles were filled to the top with O2 pre-saturated sludge from the digesters. Then, a magnetic bar and a conical BOD probe (YSI 5750, YSI inc., Ohio, USA) were inserted to close the respirometer and collect the OUR daily. The temperature was kept constant (20 ± 0.5°C) by immersing the bottles in a temperature-controlled bath. After the first 3 to 5 days, the OUR only decreased slightly (< 1 mg/L.d, daily), so it was then measured in longer intervals of days to properly detect the drops. The oxygen meter (YSI 57) was connected to a computer via an automatic data logger (5 s intervals) and a software (Windmill 3.0, Manchester, UK).
2.4 Modeling and parameter estimation ASM3 and ASM1 reduced to their decay processes were used to model the digested sludge. For greater simplicity, these are referred to throughout the text as ASM1 and ASM3, with the understanding that here they refer to the simplified or modified versions of the models, limited to the decay processes. The model matrix is shown in Table 1, where only the first process is considered for ASM1, while for ASM3, the two processes described are considered (decay of XH vs. of XSto).
8 Table 1 Even though the autotrophic biomass was ignored as a sludge component (as it is small with respect to the total COD), in terms of rO2, the endogenous nitrification has to be taken into account where it was not voluntarily inhibited with ATU. This will be the case when modeling data collected by Friedrich and Takáks (2013). The nitrification of the ammonium released by the lysis of the heterotrophic bacteria (fN = 0.063 mgN per mgCOD of XH) increases the OUR during digestion, which is considered when defining the stoichiometric coefficient for oxygen, SO (constant C, process 1, Table 1). It is important to highlight that including the nitrification process would not affect the bH estimations (Wentzel, 1989b; van Haandel et al., 1998); it would only modify the estimation of the amount of initial active biomass (iniXH).
According to the matrix, the COD and OUR of the sludge in digestion can be calculated using ASM3, based on Equations 1 and 2, which were used to fit the data. When using ASM1, the terms related to the component XSto were eliminated from Equations 1 and 2. COD (t ) mod el =
r
O2
X H + X P + X Sto
(t ) mod el = (1 − fp ) C b H X H + b Sto X Sto
(1) (2)
The modeling, the parameter estimation and the sensitivity analyses were performed using AQUASIM (Reichert, 1998). The estimated parameters were iniXSto, iniXH, iniXP, bSto and bH, representing the initial concentrations of the stored products, aerobic heterotrophic biomass and endogenous residues (mg/L COD), respectively, and the decay kinetic constants (d-1). Identifiability analyses were performed by interpreting the profiles of the absolute-relative sensitivity functions (δ or SensAR) defined by Equation 3. The variable y is the response (rO2 or COD) over which the impact of each of the parameters p (bH, iniXH, etc.) is evaluated.
9
δ ya,,pr =
p
∂y ∂p
(3)
3. RESULTS AND DISCUSSION
3.1 Characteristics and modeling of the respirograms When the sludge model was digested, the endogenous respirograms showed atypical behavior. For ordinary heterotrophic organisms (OHOs), a single exponential phase (ASM1) is typically expected, but this was not the case in this study. On the contrary, as observed also by Friedrich and Takáks (2013), all the obtained rO2 curves showed a two-phase structure. The first phase, attributed to XSto, was a rapid decay that lasted between 2 and 4 days, while the second phase related to XH was very slow throughout the remaining time (Figs 1a, 1b, 1c). More than 20 runs were performed, including at other temperatures, and they all showed the same behavior. --> Figure 1
When the monitoring time was short, as in run #1 (Figure 1a), the decay slope in the second phase was not always clearly evident, because the variations of rO2 from one day to the next were very small (< 0.5 mg/L·h). Another particular characteristic was the low magnitude of the respiration rates, mainly during the second phase (< 3 mg O2/g VSS·h).
The OUR profiles obtained in this study were similar to the respirograms shown by Wentzel et al. (1989a), for cultures enriched with PAOs, and by Friedrich and Takáks (2013), when studying the sludge of an EBPR plant (Fig. 1d). In a related previous study, Martínez-García et al. (2014) determined that, due to the reactor operation procedure, the sludge model used in
10 the present research was most likely enriched with bacteria capable of storing acetate in the form of biopolymers (Xsto).
In some of the runs (one-tenth), an unexpected OUR peak was observed at some moment during the second phase of the respirograms. This irregularity was also observed by Wentzel et al. (1989a), as well as by Friedrich and Takáks (2013), approximately at day 10. This phenomenon does not have a clear explanation. One of the hypotheses suggested by the previous authors is a greater predator activity that occurs latter in the process. Other advanced reason is the acclimatization of the bacteria to the famine conditions, after some days of digestion. More research is needed in this regard.
The decay respirograms were modeled based on both ASM1 and ASM3. As shown in Figs 1a and 1b, it was not possible to fit the respirograms to ASM1: the data in the second decay phase fell outside the model line. In contrast, the model derived from ASM3 perfectly fitted all the data series, in both phase 1 and phase 2 (Figs. 1a, 1b, 1c and 1d). In particular, Figs 1c and 1d also visualize the contributions attributed to the decay of the components XSto and XH, and to the nitrification of the ammonium released by lysis (where applicable, Fig. 1d).
Friedrich and Takáks (2013) obtained two-phase respirograms (Fig. 1d, with nitrification). Without necessarily referring to ASM3, these authors used a non-linear regression method to estimate the values of the slopes (bH and bSto) for each of the phases of the respirogram. Using AQUASIM with the simplified matrix of Table 1 (including nitrification) led to the same result (Fig. 1d), as this approach was able to fit the data of the authors (graph 3 of the cited authors). The parameters estimated using this fit are included in Table 2. On one hand, the
11 above confirms the capacity of the sub-model derived from ASM3 to represent two-phase decay respirograms, either with or without nitrification. On the other hand, it shows that the proposal of Friedrich and Takáks (2013), presented as a new way of interpreting two-phase decay respirograms, can be derived from ASM3.
In summary, the endogenous respirograms (aerobic digestion) showed a particular structure that clearly comprises two phases, which are describable with ASM3, but not with ASM1.
3.2 Sensitivity analysis and estimation of the parameters from the respirograms Figure 2 shows the behavior of the sensitivity functions of the endogenous OUR (SensAR rO2), for the ASM3-based model. The concerned five parameters are iniXSto, iniXH, iniXP, bSto and bH. --> Figure 2
As expected, the sensitivity functions show that the concentration of the endogenous residues, iniXP, cannot
be estimated using only respirometric data. The rO2 has zero sensitivity with
respect to iniXP. On the other hand, at some point, the absolute values of the SensAR functions were relatively high for the remaining four parameters. In addition, no symmetry or parallelism was detected between the different profiles (Insel et al., 2002). This demonstrates that the four remaining parameters (iniXSto, iniXH, bSto and bH) are identifiable from the respirograms.
The estimated values of the parameters and their standard deviations are shown in Table 2. This is for a number of runs selected from the present research, as well as for two runs taken
12 from the literature (graph 2 of Friedrich and Takáks, 2013, and graph 5 of Özdemir et al., 2013). In both cases, an adequate description of the foreign data was achieved with the proposed model. This made it possible to check the correct implementation of the ASM3 based model in AQUASIM, using a series of independent data. Table 2
To accurately extract the ASM3 parameters, respirograms with enough data points and with good resolution in the two regions are required. This was not the case in the short runs. For these runs, even when the ASM3-based model gave a good fit (Fig. 1a, run #1), the sensitivity analysis showed that bH and iniXH were not identifiable. As shown on Table 2, the fit of run #1 gave an inflated iniXH value (7000 mg/L COD) and a too-small bH of 0.007 d-1.
Table 2 shows that the initial amount of stored polymer in the sludges varied between 20 and 182 mg/L COD (< 2% of the COD of the sludge, runs #1 to #7), compared to 11-225 mg/L (< 3% of the COD) in the study by Friedrich and Takáks (2013). The values estimated from the endogenous respiration tests of Wentzel et al. (1989b), for cultures enriched with PAOs, fell in the same ranges. Therefore, iniXSto contributed in a negligible manner (< 3%) to the total COD of the cultivated sludge. Despite its small COD fraction, XSto had a substantial impact on the respiration rates, being responsible of 40 to 75% of the initial OUR. It is important to notice that the low XSto values are a reflect of the small quantities of polymer that remain in the culture reactors (or in the EBPR processes), after their aerobic phase. Lopez et al. (2006) reported levels of approximately 18 mg of PHA and 189 mg of glycogen per gram of VSS, at the end of the aeration phase of an EBPR plant. In the case of Özdemir et al. (2013) presented in Table 2, the samples contained a greater amount of iniXSto.
13 The polymer decay constant (bSto) varied between 0.71 and 1.62 d-1 (runs #1 vs. #6), which is clearly much higher than the value suggested by default in ASM3 and ASM2d (0.2 d-1). The high value found in the present study is in accord with the those measured in experiments using similar sludge, up to 3 d-1, as observed by Wentzel et al. (1989b), and from 0.8 to 6 d-1, as observed by Friedrich and Takáks (2013).
Another particularity observed in the studied sludge was the slow decay of the heterotrophic biomass (bH < 0.1 d-1, Table 2), compared to 0.2 d-1, which is the commonly accepted value for OHOs. Other sludge from EBPR plants, as studied by Giraldo et al. (2007) and Friedrich and Takáks (2013), were in the same ranges (bH as low as 0.07 d-1). In a previous related study, Martínez-García et al. (2014) determined that the identity of the dominant heterotrophs in the sludge under study was not ordinary (non-OHOs), but more probably PAOs or GAOs, identified by their low decay rate (0.03-0.04 d-1, Wentzel et al., 1989b; Vargas et al., 2013).
The fourth and last parameter shown in Table 2 (iniXH) provides additional information of great interest. The values obtained are relatively low compared to the total COD (run #1 excluded). As estimated from the reprograms, the initial active fraction Fa (= iniXH / sludge total COD) was between 16 and 41%. This is apparently low compared to the commonly expected range of 65% or more (Ramdani et al., 2010). In addition, anticipating the next section, the active fractions measured by respirometry were far lower than the Fa values determined by monitoring the CODs over the digestion time. Given this observation, it was postulated that the fraction of active biomass measured by respirometry only represents the portion of biomass that consumes oxygen, but not necessarily all the groups of microorganisms.
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Table 2 also presents the modeling results of an endogenous respirogram from Özdemir et al. (2013), now by using the ASM3-based model. In the original work (graph 6 of the cited paper), the authors modeled the respirograms as a single phase (as in ASM1), obtaining a bH of 0.21 d-1, which was contradicting their other value (0.06 d-1) measured via the VSS method. Here, by refitting those foreign data with ASM3, the bH obtained is 0.05 d-1 (Table 2), which is now in accordance with the value estimated by the VSS method (0.06 d-1). On the other hand, the value of the aerobically active fraction (iniXH) was re-estimated as 1767 ± 160 mg/L COD (Table 2), which is 38% of the total COD. This shows that here also, the value of iniXH measured by the aerobic activity was potentially inferior to the total active biomass.
In summary, the sensitivity analysis of the ASM3 model could be used to determine the validity conditions of the parameters estimated from the respirograms. The accuracy of the program used was validated using a series of foreign data. The decay constant bH was lower than the default value for OHOs, while the bsto values measured in the sludge model (and in the foreign sludge contents) were higher than the values cited in some references. The iniXH fraction contributed slightly to the total COD of the sludge content (< 3%) but was responsible of a good part of the endogenous rO2 (40 to 75% at the beginning). Apparently, the respirometry tests only detect the aerobically active fraction of the biomass.
3.3 Modeling of sludge decay through COD measurements Both ASM3 and ASM1 have been evaluated to model the decay of solids based on COD. ASM1 was tested because the contribution of XSto in terms of COD was low. Figure 3 shows
15 the fits and the sensitivity functions (SensAR-COD). The results shown correspond to digestion test #6, but illustrate in general the behavior of all runs. The fit obtained was good for both models (ASM1 and ASM3, Fig. 3a); however, as established by the outputs of the sensitivity analysis (Fig. 3b), it was not possible to identify a unique set of parameters when modeling the COD data with ASM3. There was a dependency between iniXH and bH (almost parallel traces) and more, the sensitivity of iniXP was almost null. This means that, even when the ASM3 fit is excellent, the estimations of iniXH, iniXP and bH provided by the regression are inaccurate (Table 3, run #6). --> Figure 3
Regarding the ASM1 model, the sensitivity analysis results are shown in Fig. 3c, for run #6. In general, the model for COD is sensitive to all the parameters (bH, iniXP and more for iniXH), which were perfectly identifiable.
When iniXSto is small, the ASM3 and ASM1 models are equivalent in terms of predicting the COD of the digested sludge over time (this is not the case when predicting the OUR). However, only the ASM1 parameters can be identified from the COD data, not those of the ASM3. Thus, the ASM1-COD fit is a good way to approximate some of the ASM3 parameters (bH, iniXHtotal, iniXP) that are non-identifiable from the COD-ASM3 fit. Table 3 shows the values of the estimated parameters and their standard deviations when modeling the COD decay with ASM1. Measured through the COD, the tendency of low bH values was confirmed in the sludge model, as well as in the foreign sludge (0.02 to 0.1 d-1, versus 0.2 d-1 in ASM3). Table 3
16 Another important observation that stands out from Table 3 is the new estimation of the active biomass (iniXH and Fa). The values obtained based on the respirograms (Table 2, Fa = 16-41 %) were much lower than from the COD measurements (Table 3, Fa = 66-77 %). This suggests a scenario in which two groups of heterotrophic microorganisms are considered (XHa and XHb), instead of only one (XH). The decay of XHa would be accompanied by oxygen consumption, unlike XHb, whose decay does not consume oxygen. The modeling of the data on this basis is carried out in the sections 3.4 and 3.5.
Table 3 also shows the fits of the VSS data of Özdemir et al. (2013) (graph 6 of the cited author, reconverted into COD), arriving at the same value of bH as in the original publication. What stands out is that the iniXH estimated through VSS measurements (3456 mg/L COD, approx. 2430 mg/L VSS) was also greater than the amount of initial biomass estimated using the aerobic activity (respirometry, 1767 mg/L COD, see Table 2 above).
In summary, the sensitivity analysis showed that the decay parameters are not identifiable when fitting the COD data with ASM1, when iniXSto is small (although it has an important influence on the rO2). In this case, the parameters bH, iniXHtotal and iniXP for ASM3 are better estimated from the ASM1-COD fit. On the other hand, this confirms the need to modify the model (two heterotrophs groups, XHa vs. XHb, instead of one).
3.4 Proposal of model modifications and parameter estimation method There are different modeling concepts and approaches that could be compatible with the observed behavior (aerobically active fraction < total active fraction). However, considering
17 two groups of heterotrophs with different metabolic pathways is a more plausible hypothesis. In many plants, different heterotrophs groups such as PAOs, GAOs and OHOs coexist (Crocetti et al., 2002; Flowers et al., 2013; Weissbrodt et al., 2013). Different strains of PAOs and GAOs that have denitrification capacity (D-PAOs and D-GAOs) were also identified, which use NO3 instead of oxygen (Hu et al., 2002; Acevedo et al., 2012; Tian et al., 2013). Adding to the complexity, a novel heterotrophic nitrifying bacterium was recently isolated from activated sludge. The strain exhibited efficient heterotrophic nitrification as well as aerobic denitrification ability (Yong-Xiang et al., 2014; Soda and Ishikawa, 2014). In addition, decay is active in all the types of environment (aerobic, anaerobic or anoxic) (Lu et al., 2007; Lopez et al., 2006).
With respect to the operation mode of the XHb group (which decays without O2) in the aerobic environment of the digester, there are two possibilities. A first hypothesis would be that they are located in regions inside the flocs that are not exposed to oxygen due to diffusion limitations. In this case, the decay of XHb may occur in anaerobic or anoxic environments. A typical example is the simultaneous nitrification-denitrification occurring in floc cores with high O2 gradients in aerated activated sludge tanks (Downing et al., 2010) and in aerobic digesters (Zhang et al., 2013). A second hypothesis would be that the XHb group is in contact with the O2 but has developed another metabolic process for decay or maintenance that does not involve oxygen. Allylthiourea was added only at small dose during the culture of the biomass (5 mg/L ATU in the SBRs, based on López-Vázquez et al., 2007). Compared to 20 mg/L ATU suggested by Henze et al. (2000), lower doses may limit the autotrophs in the SBR culture, however, a slow (but sufficient) nitrification may take place in the digesters that have a higher solid content (concentrated sludge). More research is required to determine the
18 metabolic pathways of the XHb fraction. Meanwhile, a predictive model is proposed, postulating the existence of two groups of dominant heterotrophic bacteria in the system: one that decays using O2 and another that decays without the presence of oxygen (XHa and XHb). Table 4
The relevant modifications proposed in the ASM3 model, with respect to the decay processes, are described in the matrix shown in Table 4. Because the metabolic pathways are not totally known, no matrix column is shown for the counterpart component of XHb, which may be NO3, as an electron acceptor. However, this information is not necessary at all, to be able to fit the OUR data. According to the model, the COD and rO2 of the sludge, during the aerobic digestion, are given by Equations 4 and 5. These expressions would also serve as a basis for fitting the COD and OUR data, to estimate the proposed modified-ASM3 decay parameters. COD (t ) mod el =
r
O2
X Ha + X Hb + X P + X Sto
(4)
(t ) mod el = (1 − fp ) C b H X Ha + bSto X Sto
(5)
The six parameters to be estimated are bSto, bH, iniXHa, iniXHb, iniXP and iniXSto.
3.5 Simultaneous fit of the COD and OUR data to the proposed model Before performing the simultaneous fit, it is important to show how the information from the separate ASM1-COD and ASM3-OUR fits can be integrated, to obtain the decay parameters for the proposed modified-ASM3 model. The fit of the respirograms with ASM3 directly provides the final estimations (“integrated values”, Table 5) of iniXSto, bSto and iniXHa, while the fit of the COD with ASM1 gives the total biomass, iniXHtotal. Table 5
19
The other three parameters, whose values are shadowed in Table 5 (bH, iniXP and iniXHb), may be obtained by combining the results of the two fits. iniXHb is the difference between iniXHtotal and iniXHa, while the initial concentration of XP is calculated by subtracting the amount iniXSto from the value of iniXP initially obtained from the ASM1-COD fit. The bH obtained from the fit of the respirogram is only relevant to the first biomass fraction (XHa), while the value of bH obtained from the fit of the COD is essentially a weighted average applicable to the sum of the two biomass communities (XHa + XHb). For the sludge under study, the two decay constant values were similar (Table 5), so a single bH parameter was used for the two communities of bacteria (averaging).
The reasoning utilized to obtain the data shown in Table 5, that is, the determination of parameters using both the COD-ASM1 and OUR-ASM3 regressions, is only acceptable when the set of parameters of each regression is perfectly identifiable. One of the advantages of this reasoning is its didactic character. Alternatively, there is a better way to obtain a final set of parameters from the ASM3-modified model that lacks the previous limitation; the COD and OUR data can be simultaneously fitted, directly with the ASM3-modified model. To do this, the matrix of the model (Table 4) was implemented in a program run in AQUASIM. The simultaneous fit of different experiments, or of different kinds of measurements, (e.g., COD and rO2) is known to be a practice for improving the parameter estimation process (Reichert, 1998; Sin et al., 2005).
AQUASIM contains algorithms for non-linear regression, where the convergence criterion is the minimization of the sum of squared errors between the model output and the data (χ2). It is
20 important to prevent the software from focusing only on fitting the COD data, to the detriment of the OUR data; this is because the order of magnitude of the COD (thousands of mg/L) and its χ2 is much higher than for the rO2 (< 10 mg/L·h). One way to avoid this type of bias is to perform a simultaneous fit based on the relative values, normalized with the initial values at t = 0 (i.e., the ratios COD (t) / CODinitial and rO2 (t) / rO2 initial). Figure 4 and Table 6 show the results of the simultaneous fits of COD and OUR and their sensitivity analysis. These results concern two long-term digestion runs performed in the present research (run #6 and #7, carried out at different periods), and a foreign run, whose data were taken from the literature. --> Figure 4
The proposed model was very well able to fit the COD and OUR data simultaneously for each of the runs (Fig. 4a and b, run #7; Fig. 4c and d, data from Özdemir et al., 2013). The simulated profiles of COD and rO2 for the different sludge components (XHa, XHb, XSto, XP) are presented in the Figures. The simultaneous fitting graphs corresponding to run #6 are not shown because they are, other than a few minor details, very similar to those shown previously in Figures 1a and 2a (rO2 vs. COD fit).
All the parameters were sufficiently sensitive, with respect to at least one of the response variables (Figs. 4e and 4f). In addition, there was no symmetry or parallelism between the profiles of the SensAR functions (Reichert, 1998; Insel et al., 2002). This confirms that the simultaneous fitting process provides a unique set of parameters that is perfectly identifiable for each digestion run. While the estimation of iniXP and iniXHb comes exclusively from the monitoring of the COD (Fig. 4e), iniXSto and bSto are mainly extracted from the respirogram (Fig. 4f). On the contrary, the estimations of iniXHa and bH can come from either the
21 respirogram or the COD measurements. Exceptionally, for the case shown in Fig. 4e (based in the run by Özdemir et al., 2013), the SensAR function showed some capacity of the COD data to participate in the estimation of iniXSto and bSto. This is due to the greater amount of XSto apparently present in this sludge at the time of its harvest (695 mg/L, compared to 125 mg/L in run #6, Table 6). For this same reason, the duration of the influence zone of iniXSto and bSto in Figure 4f was longer compared to that in run #6 (see Fig. 2 above).
The sets of parameters estimated from the simultaneous fits are presented in Table 6, along with the standard deviations (Std dev). First, the values obtained with the simultaneous fit were very similar to the previous values obtained by integration from the separated fits (CODASM1 vs. OUR-ASM3, Table 5 previously shown above). This confirms and validates that the analysis of the COD data with ASM1 is an adequate means of simplification to identify some of the parameters of the ASM3-modified model, where iniXSto is low. Table 6
Second, the tendencies observed and discussed in the previous sections are confirmed with the simultaneous fits: a) A low decay constant (bH of 0.032 to 0.096 d-1). b) The total active biomass was re-estimated between 60 and 72%, which includes a fraction that decays without consuming oxygen from the aerobic digester (26% in run #6 and 47% in the sample of Özdemir et al.) and another fraction whose decay can be detected through respirometric tests. c) A small initial amount of stored polymer (< 2%) compared to the total COD. d) A decay constant (bSto = 0.71 to 1.62 d-1) similar to the ranges measured in other works (Wentzel et al., 1989b; Friedrich and Takáks, 2013) but greater than the value suggested by “default” in ASM3 and ASM2d (0.2 d-1).
22
In summary, the modified model derived from ASM3 adequately represented the aerobic digestion data. All 6 parameters (bSto, bH, iniXHa, iniXHb, iniXP and iniXSto) were identifiable from the simultaneous fit of the long-term COD-time data and endogenous respiration. The decay constant of the stored products (bSto), as measured in the present study, ranged from 0.71 to 1.62 d-1, much higher than the value suggested by default in ASM3 and ASM2d.
4. CONCLUSIONS
The endogenous respirograms of the digested sludge had a two-phase structure that was describable with ASM3, and not with ASM1. The amount of stored polymers was low (<3% of the COD), but it was responsible of 40 to 75% of OUR. The parallel monitoring of the COD and the OUR revealed the presence of two groups of heterotrophs in the sludge, one decaying with, and another without O2 use. A modified model from ASM3 was proposed. All 6 parameters of the ASM3-modified sub-model were identifiable by performing a simultaneous fit of the COD and the OUR data.
ACKNOWLEDGMENTS Many thanks to “Consejo Nacional de Ciencias y Tecnología”, CONACYT Mexico, who financially supported this study through the project # CB152943.
23 REFERENCES 1. Acevedo B., Oehmen A., Carvalho G., Seco A., Borrás L. And Barat R. (2012). Metabolic shift of polyphosphate-accumulating organisms with different levels of polyphosphate storage. Water Research 46, 1889-1900. 2. APHA (2005), Standard Methods for the Examination of Water and Wastewater, 29th ed., American Public Health Association (APHA, AWWA and WPCF), Washington DC. 3. Choubert JM., Rieger L., Shaw A. Copp J., Spérandio M., Sørensen K., Rönner-Holm S., Morgenroth E., Melcer H. and Gillot S. (2013). Rethinking wastewater characterization methods for activated sludge systems - a position paper. Water Science & Technology . 67 (11), 2363-73. 4. Crocetti G.R., Banfield J.F. Séller J., Bond P.L. and Blackall L.L. (2002). Glycogenaccumulating organisms in laboratory-scale and full-scale wastewater treatment processes. Microbiology 148, 3353–3364. 5. Downing L., Boksiner G., Juarez R., and Young M. (2010). Accounting for nitrogen losses in a large-scale municipal WWTP. 2nd IWA-WEF Wastewater Treatment Modelling Seminar, Mont-Sainte-Anne (Qc) Canada, 28-31 March 2010, Conference Proceedings, 203-209. 6. Fall C. and Loaiza-Navia J. (2007). Design of a Tracer Test Experience and Dynamic Calibration of the Hydraulic Model for a Full-scale WWTP by Use of AQUASIM. Water Environ. Res., 79 (8), 893-900. 7. Flowers J.J., Cadkin T.A. and McMahon K.D. (2013). Seasonal bacterial community dynamics in a full-scale enhanced biological phosphorus removal plant. Water Research 47, 7019-7031. 8. Friedrich M. and Takács I. (2013). A new interpretation of endogenous respiration profiles for the evaluation of the endogenous decay rate of heterotrophic biomass in activated sludge. Water Res. 47(15), 5639-46. 9. Giraldo E., Goel R. y Noguera D, (2007). Modeling Microbial Decay in a Cannibal™ Sludge Minimization Process. Proceedings WEFTEC 2007, 22-27 oct., San Diego. 10. Gomez J., de Gracia M., Ayesa E. and Garcia-Heras J.L. (2007). Mathematical modelling of autothermal thermophilic aerobic digesters. Water Res., 41, 959-68. 11. Guisasola A., Sin G., Baeza J., Carrera J. and Vanrolleghem P. A. (2005). Limitations of ASM1 and ASM3: A comparison based on batch oxygen uptake rate profiles from different full-scale wastewater treatment plants. Wat. Sci. Technol., 52(10-11), 69-77. 12. Henze M., Gujer W., Mino T. y Van Loosdrecht M. V. (2000). Activated sludge models, ASM1, ASM2, ASM2d and ASM3. IWA Publishing, London, UK, 130p. 13. Hu Z.R. Wentzel M.C. and Ekama G.A. (2002). Anoxic growth of phosphateaccumulating organisms (PAOs) in biological nutrient removal activated sludge systems. Water Research 36, 4927-4937. 14. Insel G., Gül O.K., Orhon D., Vanrolleghem P.A. and Henze M. (2002). Important limitations in the modeling of activated sludge: biased calibration of the hydrolysis process. Water Science and Technology 45 (2), 23–36.
24 15. Koch G., Kuhni M., Gujer W. and Siegrist H. (2000). Calibration and validation of Activated Sludge Model No. 3 for Swiss municipal wastewater. Water Res., 34 (14), 35803590. 16. Lopez C., Pons M.N. and Morgenroth E. (2006). Endogenous processes during long-term starvation in activated sludge performing enhanced biological phosphorus removal. Water Res. 40, 1519-1530. 17. López-Vázquez C.M., Song Y.I., Hooijmans C.M., Brdjanovic D., Moussa M.S., Gijzen H.J. and Van Loosdrecht M.C.M. (2007). Short-term temperature effects on the anaerobic metabolism of Glycogen Accumulating Organisms. Biotechnol Bioeng. 97(3), 483-495. .18. Lu H., Keller J. and Yuan Z. (2007). Endogenous metabolism of Candidatus Accumulibacter Phosphatis under various starvation conditions. Water Res. 41, 4646-4656. 19. Marais G.v.R. and Ekama G.A. (1976). The activated sludge process: steady stat behavior. Water SA, 12 (4), 163-200. 20. Martínez-García C.G., Olguín M.T. and Fall C. (2014). Aerobic stabilization of biological sludge characterized by an extremely low decay rate: Modeling, identifiability analysis and parameter estimation. Bioresource Technol. 166, 112-119. 21. Özdemir S., Uçar D., Çokgör E.U. and Orhon D. (2013). Extent of endogenous decay and microbial activity in aerobic stabilization of biological sludge. Desalination and Water Treatment, 2013, 1-7. 22. Özdemir S., Çokgör E.U. and Orhon D. (2014). Modeling the fate of particulate components in aerobic sludge stabilization – Performance limitations. Bioresource Technol. 164, 315–322. 23. Ramdani A., Dold P., Déléris S., Lamarre D., Godbout A. and Comeau Y. (2010). Biodegradation of the endogenous residue of activated sludge. Water Res. 44, 2179-2188. 24. Reichert P. (1998). AQUASIM 2.0. User Manual. Swiss Federal Institute for Environmental Science and Technology (EAWAG), Switzerland, 219 p. 25. Shoda, M. and Ishikawa Y. (2014). Heterotrophic nitrification and aerobic denitrification of high-strength ammonium in anaerobically digested sludge by Alcaligenes faecalis strain No.4. J. of Bioscience and Bioeng. 117 (6), 737–741. 26. Sin G., Guisasola A., De Pauw D., Baeza J., Carrera J. and Vanrolleghem P. A. (2005). A new approach for modelling simultaneous storage and growth processes for activated sludge systems under aerobic conditions. Biotechnol. Bioeng. 92, 600-613. 27. Tian W.D., López-Vázquez C.M., Li W.G., Brdjanovic D. and Van Loosdrecht M.C.M. (2013). Occurrence of PAO-I in a low temperature EBPR system. Chemosphere 92, 1314– 1320. 28. Van Haandel A.C., Catunda, P.F.C. and Araujo L.S. (1998). Biological sludge stabilisation: Part 1. Kinetics of aerobic sludge digestion. Water SA, 24 (3), 223-230. 29. Vargas M., Yuan Z. and Pijuan M. (2013). Effects of long-term starvation conditions on poly-phosphate and glycogen-accumulating organisms. Bioresource Technol. 127, 126-131. 30. Wang Y., Geng J., Peng Y., Wang C., Guo G. and Liu S. (2012). A comparison of
25 endogenous processes during anaerobic starvation in anaerobic end sludge and aerobic end sludge from anaerobic/aerobic/oxic sequencing batch reactor performing denitrifying phosphorus removal. Bioresource Technol. 104, 19-27. 31. Weissbrodt D.G., Schneiter G.S., Furbringer J.M. and Holliger C. (2013). Identification of trigger factors selecting for polyphosphate- and glycogen-accumulating organisms in aerobic granular sludge sequencing batch reactors. Water Res. 47, 7006-18. 32. Wentzel M.C., Ekama G.A., Loewenthal R.E., Dold P.L. and Marais G.v.R. (1989a). Enhanced polyphosphate organism cultures in activated sludge systems. Part II: Experimental behaviour. Water SA, 15 (2), 71-88. 33. Wentzel M.C., Dold P.L., Ekama G.A. and Marais G.v.R. (1989b). Enhanced polyphosphate organism cultures in activated sludge systems. Part III: Kinetic model. Water SA, 15 (2), 89-102. 34. Yong-Xiang R., Lei Y. and Xian L. (2014). The characteristics of a novel heterotrophic nitrifying and aerobic denitrifying bacterium, Acinetobacter junii YB. Bioresource Technol. 171, 1–9. 35. Zhang X., Peng D., Guo Y., Yang C. and Wang B. (2013). Rate control-based strategy to enhance biological nitrogen removal during anoxic/oxic sludge digestion. Desalination and Water Treatment, Published online 16 Dec 2013.
FIGURE CAPTIONS Figure 1: Endogenous respirograms: structure and modeling (ASM1 vs. ASM3 fit). Figure 2: Sensitivity analysis of the model derived from the ASM3 (run #6) Figure 3: Fit of the COD data and sensitivity analysis (run #6): a) fit with the ASM1 and ASM3 models; b) SensAR functions of ASM3; c) SensAR functions of ASM1; d) total COD, XH and XP simulated based on ASM1. Figure 4: Simultaneous fit and simulation of the COD and OUR of run #7 (a and b); of the run by Özdemir et al., 2013 (c and d); and of the sensitivity functions (SensAR, e and f).
26
Table 1: Matrix representation of decay processes in ASM1 ( line 1) and ASM3 (1 + 2) Components Processes ↓ 1. Decay of XH 2. Decay of XSto
XSto
SO
XP
XH
Rates
-(1-fp) C -1
fp
-1
-1
bH XH bSto XSto
Components: stored compound (XSto, mg/L COD); dissolved oxygen (SO, mg/L O2); endogenous residues (XP, mg/L COD); heterotrophs (XH, mg/L COD). Parameters: fp = 0.2, fraction of biomass converted in Xp (Henze et al., 2000); bH and bSto, 1st order decay constants. C = 1, without nitrification vs. C = (1+4.57*fN) with nitrif., where fN = 0.063.
27
Table 2: ASM3 parameters as estimated from the OUR data only Sludge
Run #
total COD (mg/L)
#1 #4 #6
#7
Estimated values iniXH
iniXSto
bH
bSto (d-1)
(mg/L COD)
8457 ± 260 5331 ± 90
7000 2218 ± 885
182 ± 33 75 ± 33
0.0072 0.71 ±0.37 0.060 1.27 ± 0.03 ± 0.37
6381 ± 120 5660 ± 63
1009 ± 65 986 ± 60 1595 ± 60
125 ±10 20 ±5 204 ± 38
0.097 1.62 ±0.011 ± 0.09 0.081 1.60 ±0.008 ± 0.30 0.15 1.27 ±0.02 ± 0.14
Friedrich and Takáks, (2013), as recalculated Özdemir et al., 2013, as recalculated
1767 899 ± 159 ± 173
0.05 ±0.02
0.30 ± 0.03
28
Table 3: ASM1 (and ASM3) parameters as estimated from the COD data only
Sludge
Run #
Total COD (mg/L)
#5
#6 #7
3527 ± 62 6381 ± 120 5660 ± 63
Özdemir et al. (2013), as Recalculated in Aquasim
Estimated values iniXH
iniXP
(mg/L COD)
2740 ± 88 4717 ± 220 3641 ± 286 3456 ± 160
756 ± 93 1666 ± 180 1988 ±308 957 ± 98
bH
Fa
-1
(%)
(d )
0.022 ±0.002 0.10 ± 0.01 0.026 ±0.004 0.066 ±0.008
77% 74% 65% 75%
29
Table 4: Peterson Matrix of the modified-ASM3 sub-model Processes ↓ Decay of XHa Decay of XHb Decay of XSto
XSto
SO -(1-fp) C
-1
-1
XP fp fp
XHa -1
XHb -1
Rates bH XHa bH XHb bSto XSto
Components: stored compounds (XSto, mg/L COD); dissolved oxygen (SO, mg/L O2); endogenous residues (XP, mg/L COD); heterotrophs ( XHa and XHb, mg/L COD). Parameters: fp = 0.2, fraction of biomass converted in Xp; bH and bSto 1st order decay constants. C = 1, without nitrification vs. C = (1+4.57*fN) with nitrif., where fN = 0.063.
30
Table 5: Integration of the information from the separate fits of the COD and OUR data COD fit OUR fit Parameters (ASM1) (ASM3) bH (d-1) 0.100 0.097 bSto (d-1) 1.625 iniXSto (mg/L) 125 iniXP (mg/L) 1666 IniXHa (mg/L) 1010 IniXHb (mg/L) IniXH total 4717
Integrated values 0.098 1.626 125 1541 1010 3707 4717
31
Table 6: Estimated parameters of the proposed model (COD and rO2) Runs Parameters bH (d-1) bSto (d-1) iniXSto (mg/L) iniXP (mg/L) iniXHa (mg/L) iniXHb (mg/L) Total COD
#6 Estimated Std dev. values ± 0.009 0.096 ± 0.20 1.63 ± 18 125 ± 154 1651 ± 82 1018 ± 182 3630 6424 -
#7 Estimated Std dev. values ± 0.007 0.032 ± 0.11 0.70 ± 14 70 ± 354 2324 ± 330 1827 ± 177 1487 5709 -
Özdemir et al. * Estimated Std dev. values ± 0.010 0.054 ± 0.07 0.35 ± 213 695 ± 122 1006 ± 386 2143 ± 322 750 4594 -
* : Özdemir et al., (2013), data from authors graphs 5 and 6 were fit with the modified model
32
Figure 1: Endogenous respirograms: structure and modeling (ASM1 vs. ASM3 fit).
33
Figure 2: Sensitivity analysis of the model derived from the ASM3 (run #6)
34
Figure 3: Fit of the COD data and sensitivity analysis (run #6): a) fit with the ASM1 and ASM3 models; b) SensAR functions of ASM3; c) SensAR functions of ASM1; d) total COD, XH and XP simulated based on ASM1.
35
Figure 4: Simultaneous fit and simulation of the COD and OUR of run #7 (a and b); of the run by Özdemir et al., 2013 (c and d); and of the sensitivity functions (SensAR, e and f).
36
HIGHLIGHTS
1. Sludge digestion respirograms had two phases describable with ASM3, not with ASM1. 2. Storage was < 3% of the biomass COD but accounted up to 75% of the O2 uptake rate. 3. 2 groups of storing bacteria was detected, one decaying using O2 and the other no. 4. The modified ASM3 model proposed was able to predict the COD and OUR of digesters. 5. The parameters of the model are identifiable by fitting the COD and OUR together.
S0960-8524(14)01379-0 http://dx.doi.org/10.1016/j.biortech.2014.09.120 BITE 14010
To appear in:
Bioresource Technology
Received Date: Revised Date: Accepted Date:
20 July 2014 21 September 2014 23 September 2014
Please cite this article as: Fall, C., Rogel-Dorantes, J.A., Millán-Lagunas, E.L., Martínez-García, C.G., SilvaHernández, B.C., Silva-Trejo, F.S., Modeling and parameter estimation of two-phase endogenous respirograms and COD measurements during aerobic digestion of biological sludge, Bioresource Technology (2014), doi: http:// dx.doi.org/10.1016/j.biortech.2014.09.120
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1 Modeling and parameter estimation of two-phase endogenous respirograms and COD measurements during aerobic digestion of biological sludge Fall C.1*, Rogel-Dorantes J.A.1, Millán-Lagunas E.L.1, Martínez-García C.G.1 Silva-Hernández B.C.1 and Silva-Trejo F.S.1 1
Centro Interamericano de Recursos del Agua (CIRA), Universidad Autónoma del Estado de México (UAEM), Apdo postal 367, Toluca, C.P. 50091, México. * Corresponding author: [email protected]; Tel +52 722 2965550.
ABSTRACT Long-term aerobic digestion batch tests were performed on a sludge that contained mainly two fractions, a heterotrophic biomass XH and its endogenous residues XP, which were cultivated in conditions known to favor bio-storage (XSto). The objective was to model the stabilization of the sludge and determine the parameters of the endogenous decay processes, based on simultaneous measurements of the chemical oxygen demand (COD) and oxygen uptake rates (OUR). The respirograms were shown to have a two-phase structure that was describable with activated sludge model 3 (ASM3), but not with ASM1. Comparing the information from the COD and OUR data suggested the presence of two different groups of heterotrophs (XHa and XHb), one that decays with oxygen consumption and another without using O2. A modified ASM3 model was proposed, which was able to fit the OUR and COD data from the digesters, as well as cases from the literature.
KEYWORDS: accumulating organisms; aerobic digestion; endogenous respirograms; parameter identifiability; storage.
1. INTRODUCTION Aerobic digestion is one of the most commonly used sludge stabilization processes. The
2 development of descriptive models for this process is important for multiple reasons. It allows simulating and predicting the stabilization of biological sludge (Marais and Ekama, 1976). Also, batch digestion tests are very often used to estimate the parameters of the decay processes included in activated sludge models (ASMs) (Henze et al., 2000).
Current aerobic digestion models (Marais and Ekama, 1976; Gomez et al., 2007) utilize the concept of biomass loss by endogenous respiration. The active biomass is combined in one heterotroph-dominant group (XH) that follows a first-order decay rate law (dXH/dt = bHXH), where bH is the first-order decay rate constant (d-1).
The decay process by endogenous respiration and its modified version (death-regeneration) are also used in the dynamic activated sludge models (mainly ASM1, ASM2d, and ASM3; Henze et al., 2000). The ASMs include several decay processes related to each of the active biomass components and internal storage compounds, e.g. the heterotrophs (XH) and the stored polymers (XSto). Some aerobic digestion models were developed by simplifying the ASM1 model and including or no a slow biodegradation process for the endogenous residues, XP (Ramdani et al., 2010; Özdemir et al., 2014).
In the past, mainly two experimental methods were developed for estimating the bH constant. One was by monitoring the oxygen uptake rates (OUR) and the other was by measuring the volatile (or total) suspended solids (VSS and TSS), in aerobic digestion tests (Marais and Ekama, 1976; Van Haandel et al., 1998). There was no formal update of the bH estimation methods in regard to the ASM3 and ASM2d models. The latter models consider other types of microorganisms, in particular ones that are capable of storing the substrate as biopolymers.
3
A wide interval of bH values is reported in the literature, without clear reasons for such dispersion. The accepted default value for bH is 0.2 d-1 at 20°C (Henze et al., 2000; Ramdani et al., 2010). However, many other values have been reported, from 0.06 to 0.5 d-1 (Friedrich and Takáks, 2013). Many factors can explain the wide divergence between the reported values of the 20°C heterotrophic decay constant. Friedrich and Takáks (2013) pointed out the type of data gathered (VSS or OUR) and the quality of the mathematical regressions performed to estimate the parameters (identifiability issues). The identifiability issues may add to the confusion by enlarging the intervals of bH values reported in the literature. A high coefficient of correlation (R2) is not enough to justify the representativeness of a regression constant. It is imperative to test the identifiability or the uniqueness of the estimated parameters sets (Koch et al., 2000; Insel et al., 2002; Sin et al., 2005; Guisasola et al., 2005). AQUASIM is one of the modeling software known to perform this task very well (Reichert, 1998; Fall et al., 2007).
Another important factor that has not been scrutinized enough is the exact nature of the biomass for which the decay rates are reported. The biomass in treatment plants is not just ordinary heterotrophic organisms (OHOs). Other types of bacteria can form an important part of the sludge. This is the case of phosphorus- and glycogen-accumulating microorganisms (PAOs and GAOs) in enhanced biological phosphorus removal plants (EBPR) (Lu et al., 2007; Wang et al., 2012). Among other aspects, PAOs and GAOs differ from OHOs in two essential points regarding digestion. First, their decay constant is much lower (0.03-0.04 d-1; Lu et al., 2007 and Wentzel et al., 1989a), which extends the treatment times to stabilize the sludge. Secondly, the presence of stored material in the biomass can affect the shape of the endogenous respirograms and its interpretation.
4
In some studies, such as in Van Haandel et al. (1998) and Ramdani et al. (2010), there were no differences between the decay constants obtained by the traditional VSS and OUR bH methods. In these cases however, it was clearly about OHOs (bH =0.2 d-1). Results from both methods diverged clearly in Özdemir et al. (2013) for a biomass that was apparently storagecapable bacteria (bH of 0.21 d-1 by VSS versus 0.06 d-1 by the OUR). In a study that involucrated many sludge from different EBPR plants (Friedrich and Takáks, 2013), the authors decided not to run the VSS-based method in parallel to the OUR method. However, the study revealed a shape of the endogenous respirograms (two-phases) that was very different from typical one for OHOs (one phase). The first and fast step was attributed to decay of the stored compounds (XSto), while the second slower phase was associated to decay of the heterotrophs (XH). Some data from Friedrich and Takáks (2013) as well as Özdemir et al. (2013) will be used latter to test the models and programs developed in the present study.
Based on the aforementioned findings (dispersion of the bH values and the need to take into account other types of sludge), it is pertinent to revisit the methods used to determine the decay parameters, as well as reevaluate the behavior of aerobic digestion in bacterial cultures not dominated by OHOs. This is in accordance with the position adopted by the Good Modelling Practices (GMP) group, who recommended that the characterization methods used in active sludge models be rethought (Choubert et al., 2013).
The objective of the research was to model the stabilization of storing-biomass sludge and determine the parameters of the endogenous decay processes, based on simultaneous measurements of the chemical oxygen demand (COD) and oxygen uptake rates (OUR). To be
5 able to adequately estimate the model parameters, it is important to avoid most of the confounding factors (e.g., the type of biomass and the parameter identifiability issues). In consequence, the study was performed with a sludge model that contained only two main components, the heterotrophic fraction XH and its endogenous residues XP. The sludge was cultivated in conditions known to favor the bio-storage (XSto). Aerobic digestion experiments were performed while the endogenous respirograms and the COD profiles were fit separately, and then simultaneously, with ASM3 and ASM1 derived sub-models.
2. MATERIALS AND METHODS
2.1 Cultivation of the sludge model The sludge used latter to perform the digestion tests, was produced by operating an activated sludge system in the laboratory, which was fed with synthetic wastewater based on acetate. Two 30 L sequential batch reactors (SBRs) were used, operated at solids retention time of 15 d. As in previous works (Giraldo et al., 2007; López-Vázquez et al., 2007; Ramdani et al., 2010), it was a strategy of this research to base the study on a type of biological sludge with not very complex characteristics and a relatively constant composition in time (sludge model). The nominal composition of the synthetic wastewater was previously reported (MartinezGarcia et al., 2014), having a total chemical oxygen demand (COD) of 500 mg/L and an approximate COD/N/P ratio of 100/5/0.5. Under these conditions, the sludge produced in the reactors was expected to contain only two to three fractions: mainly, the heterotrophic biomass (XH) and the endogenous residues (XP) coming from bacterial lysis, and eventually stored polymer components (XSto). Allylthiourea was added to inhibit the development of autotrophic bacteria (5 mg/L ATU, Henze et al., 2000; López-Vázquez et al., 2007).
6
The SBR were operated in anaerobic-aerobic reaction phases and under alternated conditions of starvation and abundance of food (feast/famine). This was a way to favor bioaccumulation mechanisms in the heterotrophic bacteria and a strategy to overcome some sludge bulking problems that were occurring earlier in the research. The 30 L SBR operation cycle was as follows: - 2 L purge of mixed liquor, sedimentation for 1 h; - pouring of 20 L of treated supernatant (approximately 10 min); - feeding of 2 L of concentrated fresh medium (in less than 1 min); - mechanical mixing in non-aerated phase for 1 h, before adding 18 L of tap water to complete the influent; - airing and reaction at 20 ± 2°C for the rest of the day. The medium was prepared in concentrated form to yield the nominal 500 mg/L COD, when 2 L of it was diluted with 18 L of tap water.
2.2 Aerobic digestion of the sludge To estimate the decay parameters via the VSS-COD and OUR methods (Van Haandel et al., 1998), several aerobic digestion tests were performed (20°C) once the SBRs were stabilized. In each run, 4 L of mixed liquor purged from the SBRs were concentrated and transferred to a small digester-reactor operated in batch (1.7 L). The particulate COD and the endogenous OURs (or rO2) of the digesters were monitored for several days, up to 20 days by respirometry and more than 40 days with Hach COD kits. Regularly, the evaporated water from the digesters was replaced with distilled water, before performing the COD and rO2 measurements.
Total and soluble COD (1.2 µm filters) analyses were carried out in triplicate with Hach reactive kits at the 150 and 1500 mg/L ranges, and with strict control on the practices when homogenizing, micro-pipetting (cut-off tips), and diluting the solids. All along the text, the
7 COD data reported (and used in the models) are particulate COD (total COD - soluble COD). The soluble COD contents of the sludge were generally very low (< 60 mg/L). Routine checks were made (VSS/TSS and VSS/COD ratios, temperature, pH, etc.), in accordance with standard methods (APHA, 2005).
2.3 Respirometric measurements Closed Winkler BOD bottles were used to measure the OUR (or rO2), daily and in duplicate, to avoid errors that could occur when using respirometers that are open to the atmosphere. The bottles were filled to the top with O2 pre-saturated sludge from the digesters. Then, a magnetic bar and a conical BOD probe (YSI 5750, YSI inc., Ohio, USA) were inserted to close the respirometer and collect the OUR daily. The temperature was kept constant (20 ± 0.5°C) by immersing the bottles in a temperature-controlled bath. After the first 3 to 5 days, the OUR only decreased slightly (< 1 mg/L.d, daily), so it was then measured in longer intervals of days to properly detect the drops. The oxygen meter (YSI 57) was connected to a computer via an automatic data logger (5 s intervals) and a software (Windmill 3.0, Manchester, UK).
2.4 Modeling and parameter estimation ASM3 and ASM1 reduced to their decay processes were used to model the digested sludge. For greater simplicity, these are referred to throughout the text as ASM1 and ASM3, with the understanding that here they refer to the simplified or modified versions of the models, limited to the decay processes. The model matrix is shown in Table 1, where only the first process is considered for ASM1, while for ASM3, the two processes described are considered (decay of XH vs. of XSto).
8 Table 1 Even though the autotrophic biomass was ignored as a sludge component (as it is small with respect to the total COD), in terms of rO2, the endogenous nitrification has to be taken into account where it was not voluntarily inhibited with ATU. This will be the case when modeling data collected by Friedrich and Takáks (2013). The nitrification of the ammonium released by the lysis of the heterotrophic bacteria (fN = 0.063 mgN per mgCOD of XH) increases the OUR during digestion, which is considered when defining the stoichiometric coefficient for oxygen, SO (constant C, process 1, Table 1). It is important to highlight that including the nitrification process would not affect the bH estimations (Wentzel, 1989b; van Haandel et al., 1998); it would only modify the estimation of the amount of initial active biomass (iniXH).
According to the matrix, the COD and OUR of the sludge in digestion can be calculated using ASM3, based on Equations 1 and 2, which were used to fit the data. When using ASM1, the terms related to the component XSto were eliminated from Equations 1 and 2. COD (t ) mod el =
r
O2
X H + X P + X Sto
(t ) mod el = (1 − fp ) C b H X H + b Sto X Sto
(1) (2)
The modeling, the parameter estimation and the sensitivity analyses were performed using AQUASIM (Reichert, 1998). The estimated parameters were iniXSto, iniXH, iniXP, bSto and bH, representing the initial concentrations of the stored products, aerobic heterotrophic biomass and endogenous residues (mg/L COD), respectively, and the decay kinetic constants (d-1). Identifiability analyses were performed by interpreting the profiles of the absolute-relative sensitivity functions (δ or SensAR) defined by Equation 3. The variable y is the response (rO2 or COD) over which the impact of each of the parameters p (bH, iniXH, etc.) is evaluated.
9
δ ya,,pr =
p
∂y ∂p
(3)
3. RESULTS AND DISCUSSION
3.1 Characteristics and modeling of the respirograms When the sludge model was digested, the endogenous respirograms showed atypical behavior. For ordinary heterotrophic organisms (OHOs), a single exponential phase (ASM1) is typically expected, but this was not the case in this study. On the contrary, as observed also by Friedrich and Takáks (2013), all the obtained rO2 curves showed a two-phase structure. The first phase, attributed to XSto, was a rapid decay that lasted between 2 and 4 days, while the second phase related to XH was very slow throughout the remaining time (Figs 1a, 1b, 1c). More than 20 runs were performed, including at other temperatures, and they all showed the same behavior. --> Figure 1
When the monitoring time was short, as in run #1 (Figure 1a), the decay slope in the second phase was not always clearly evident, because the variations of rO2 from one day to the next were very small (< 0.5 mg/L·h). Another particular characteristic was the low magnitude of the respiration rates, mainly during the second phase (< 3 mg O2/g VSS·h).
The OUR profiles obtained in this study were similar to the respirograms shown by Wentzel et al. (1989a), for cultures enriched with PAOs, and by Friedrich and Takáks (2013), when studying the sludge of an EBPR plant (Fig. 1d). In a related previous study, Martínez-García et al. (2014) determined that, due to the reactor operation procedure, the sludge model used in
10 the present research was most likely enriched with bacteria capable of storing acetate in the form of biopolymers (Xsto).
In some of the runs (one-tenth), an unexpected OUR peak was observed at some moment during the second phase of the respirograms. This irregularity was also observed by Wentzel et al. (1989a), as well as by Friedrich and Takáks (2013), approximately at day 10. This phenomenon does not have a clear explanation. One of the hypotheses suggested by the previous authors is a greater predator activity that occurs latter in the process. Other advanced reason is the acclimatization of the bacteria to the famine conditions, after some days of digestion. More research is needed in this regard.
The decay respirograms were modeled based on both ASM1 and ASM3. As shown in Figs 1a and 1b, it was not possible to fit the respirograms to ASM1: the data in the second decay phase fell outside the model line. In contrast, the model derived from ASM3 perfectly fitted all the data series, in both phase 1 and phase 2 (Figs. 1a, 1b, 1c and 1d). In particular, Figs 1c and 1d also visualize the contributions attributed to the decay of the components XSto and XH, and to the nitrification of the ammonium released by lysis (where applicable, Fig. 1d).
Friedrich and Takáks (2013) obtained two-phase respirograms (Fig. 1d, with nitrification). Without necessarily referring to ASM3, these authors used a non-linear regression method to estimate the values of the slopes (bH and bSto) for each of the phases of the respirogram. Using AQUASIM with the simplified matrix of Table 1 (including nitrification) led to the same result (Fig. 1d), as this approach was able to fit the data of the authors (graph 3 of the cited authors). The parameters estimated using this fit are included in Table 2. On one hand, the
11 above confirms the capacity of the sub-model derived from ASM3 to represent two-phase decay respirograms, either with or without nitrification. On the other hand, it shows that the proposal of Friedrich and Takáks (2013), presented as a new way of interpreting two-phase decay respirograms, can be derived from ASM3.
In summary, the endogenous respirograms (aerobic digestion) showed a particular structure that clearly comprises two phases, which are describable with ASM3, but not with ASM1.
3.2 Sensitivity analysis and estimation of the parameters from the respirograms Figure 2 shows the behavior of the sensitivity functions of the endogenous OUR (SensAR rO2), for the ASM3-based model. The concerned five parameters are iniXSto, iniXH, iniXP, bSto and bH. --> Figure 2
As expected, the sensitivity functions show that the concentration of the endogenous residues, iniXP, cannot
be estimated using only respirometric data. The rO2 has zero sensitivity with
respect to iniXP. On the other hand, at some point, the absolute values of the SensAR functions were relatively high for the remaining four parameters. In addition, no symmetry or parallelism was detected between the different profiles (Insel et al., 2002). This demonstrates that the four remaining parameters (iniXSto, iniXH, bSto and bH) are identifiable from the respirograms.
The estimated values of the parameters and their standard deviations are shown in Table 2. This is for a number of runs selected from the present research, as well as for two runs taken
12 from the literature (graph 2 of Friedrich and Takáks, 2013, and graph 5 of Özdemir et al., 2013). In both cases, an adequate description of the foreign data was achieved with the proposed model. This made it possible to check the correct implementation of the ASM3 based model in AQUASIM, using a series of independent data. Table 2
To accurately extract the ASM3 parameters, respirograms with enough data points and with good resolution in the two regions are required. This was not the case in the short runs. For these runs, even when the ASM3-based model gave a good fit (Fig. 1a, run #1), the sensitivity analysis showed that bH and iniXH were not identifiable. As shown on Table 2, the fit of run #1 gave an inflated iniXH value (7000 mg/L COD) and a too-small bH of 0.007 d-1.
Table 2 shows that the initial amount of stored polymer in the sludges varied between 20 and 182 mg/L COD (< 2% of the COD of the sludge, runs #1 to #7), compared to 11-225 mg/L (< 3% of the COD) in the study by Friedrich and Takáks (2013). The values estimated from the endogenous respiration tests of Wentzel et al. (1989b), for cultures enriched with PAOs, fell in the same ranges. Therefore, iniXSto contributed in a negligible manner (< 3%) to the total COD of the cultivated sludge. Despite its small COD fraction, XSto had a substantial impact on the respiration rates, being responsible of 40 to 75% of the initial OUR. It is important to notice that the low XSto values are a reflect of the small quantities of polymer that remain in the culture reactors (or in the EBPR processes), after their aerobic phase. Lopez et al. (2006) reported levels of approximately 18 mg of PHA and 189 mg of glycogen per gram of VSS, at the end of the aeration phase of an EBPR plant. In the case of Özdemir et al. (2013) presented in Table 2, the samples contained a greater amount of iniXSto.
13 The polymer decay constant (bSto) varied between 0.71 and 1.62 d-1 (runs #1 vs. #6), which is clearly much higher than the value suggested by default in ASM3 and ASM2d (0.2 d-1). The high value found in the present study is in accord with the those measured in experiments using similar sludge, up to 3 d-1, as observed by Wentzel et al. (1989b), and from 0.8 to 6 d-1, as observed by Friedrich and Takáks (2013).
Another particularity observed in the studied sludge was the slow decay of the heterotrophic biomass (bH < 0.1 d-1, Table 2), compared to 0.2 d-1, which is the commonly accepted value for OHOs. Other sludge from EBPR plants, as studied by Giraldo et al. (2007) and Friedrich and Takáks (2013), were in the same ranges (bH as low as 0.07 d-1). In a previous related study, Martínez-García et al. (2014) determined that the identity of the dominant heterotrophs in the sludge under study was not ordinary (non-OHOs), but more probably PAOs or GAOs, identified by their low decay rate (0.03-0.04 d-1, Wentzel et al., 1989b; Vargas et al., 2013).
The fourth and last parameter shown in Table 2 (iniXH) provides additional information of great interest. The values obtained are relatively low compared to the total COD (run #1 excluded). As estimated from the reprograms, the initial active fraction Fa (= iniXH / sludge total COD) was between 16 and 41%. This is apparently low compared to the commonly expected range of 65% or more (Ramdani et al., 2010). In addition, anticipating the next section, the active fractions measured by respirometry were far lower than the Fa values determined by monitoring the CODs over the digestion time. Given this observation, it was postulated that the fraction of active biomass measured by respirometry only represents the portion of biomass that consumes oxygen, but not necessarily all the groups of microorganisms.
14
Table 2 also presents the modeling results of an endogenous respirogram from Özdemir et al. (2013), now by using the ASM3-based model. In the original work (graph 6 of the cited paper), the authors modeled the respirograms as a single phase (as in ASM1), obtaining a bH of 0.21 d-1, which was contradicting their other value (0.06 d-1) measured via the VSS method. Here, by refitting those foreign data with ASM3, the bH obtained is 0.05 d-1 (Table 2), which is now in accordance with the value estimated by the VSS method (0.06 d-1). On the other hand, the value of the aerobically active fraction (iniXH) was re-estimated as 1767 ± 160 mg/L COD (Table 2), which is 38% of the total COD. This shows that here also, the value of iniXH measured by the aerobic activity was potentially inferior to the total active biomass.
In summary, the sensitivity analysis of the ASM3 model could be used to determine the validity conditions of the parameters estimated from the respirograms. The accuracy of the program used was validated using a series of foreign data. The decay constant bH was lower than the default value for OHOs, while the bsto values measured in the sludge model (and in the foreign sludge contents) were higher than the values cited in some references. The iniXH fraction contributed slightly to the total COD of the sludge content (< 3%) but was responsible of a good part of the endogenous rO2 (40 to 75% at the beginning). Apparently, the respirometry tests only detect the aerobically active fraction of the biomass.
3.3 Modeling of sludge decay through COD measurements Both ASM3 and ASM1 have been evaluated to model the decay of solids based on COD. ASM1 was tested because the contribution of XSto in terms of COD was low. Figure 3 shows
15 the fits and the sensitivity functions (SensAR-COD). The results shown correspond to digestion test #6, but illustrate in general the behavior of all runs. The fit obtained was good for both models (ASM1 and ASM3, Fig. 3a); however, as established by the outputs of the sensitivity analysis (Fig. 3b), it was not possible to identify a unique set of parameters when modeling the COD data with ASM3. There was a dependency between iniXH and bH (almost parallel traces) and more, the sensitivity of iniXP was almost null. This means that, even when the ASM3 fit is excellent, the estimations of iniXH, iniXP and bH provided by the regression are inaccurate (Table 3, run #6). --> Figure 3
Regarding the ASM1 model, the sensitivity analysis results are shown in Fig. 3c, for run #6. In general, the model for COD is sensitive to all the parameters (bH, iniXP and more for iniXH), which were perfectly identifiable.
When iniXSto is small, the ASM3 and ASM1 models are equivalent in terms of predicting the COD of the digested sludge over time (this is not the case when predicting the OUR). However, only the ASM1 parameters can be identified from the COD data, not those of the ASM3. Thus, the ASM1-COD fit is a good way to approximate some of the ASM3 parameters (bH, iniXHtotal, iniXP) that are non-identifiable from the COD-ASM3 fit. Table 3 shows the values of the estimated parameters and their standard deviations when modeling the COD decay with ASM1. Measured through the COD, the tendency of low bH values was confirmed in the sludge model, as well as in the foreign sludge (0.02 to 0.1 d-1, versus 0.2 d-1 in ASM3). Table 3
16 Another important observation that stands out from Table 3 is the new estimation of the active biomass (iniXH and Fa). The values obtained based on the respirograms (Table 2, Fa = 16-41 %) were much lower than from the COD measurements (Table 3, Fa = 66-77 %). This suggests a scenario in which two groups of heterotrophic microorganisms are considered (XHa and XHb), instead of only one (XH). The decay of XHa would be accompanied by oxygen consumption, unlike XHb, whose decay does not consume oxygen. The modeling of the data on this basis is carried out in the sections 3.4 and 3.5.
Table 3 also shows the fits of the VSS data of Özdemir et al. (2013) (graph 6 of the cited author, reconverted into COD), arriving at the same value of bH as in the original publication. What stands out is that the iniXH estimated through VSS measurements (3456 mg/L COD, approx. 2430 mg/L VSS) was also greater than the amount of initial biomass estimated using the aerobic activity (respirometry, 1767 mg/L COD, see Table 2 above).
In summary, the sensitivity analysis showed that the decay parameters are not identifiable when fitting the COD data with ASM1, when iniXSto is small (although it has an important influence on the rO2). In this case, the parameters bH, iniXHtotal and iniXP for ASM3 are better estimated from the ASM1-COD fit. On the other hand, this confirms the need to modify the model (two heterotrophs groups, XHa vs. XHb, instead of one).
3.4 Proposal of model modifications and parameter estimation method There are different modeling concepts and approaches that could be compatible with the observed behavior (aerobically active fraction < total active fraction). However, considering
17 two groups of heterotrophs with different metabolic pathways is a more plausible hypothesis. In many plants, different heterotrophs groups such as PAOs, GAOs and OHOs coexist (Crocetti et al., 2002; Flowers et al., 2013; Weissbrodt et al., 2013). Different strains of PAOs and GAOs that have denitrification capacity (D-PAOs and D-GAOs) were also identified, which use NO3 instead of oxygen (Hu et al., 2002; Acevedo et al., 2012; Tian et al., 2013). Adding to the complexity, a novel heterotrophic nitrifying bacterium was recently isolated from activated sludge. The strain exhibited efficient heterotrophic nitrification as well as aerobic denitrification ability (Yong-Xiang et al., 2014; Soda and Ishikawa, 2014). In addition, decay is active in all the types of environment (aerobic, anaerobic or anoxic) (Lu et al., 2007; Lopez et al., 2006).
With respect to the operation mode of the XHb group (which decays without O2) in the aerobic environment of the digester, there are two possibilities. A first hypothesis would be that they are located in regions inside the flocs that are not exposed to oxygen due to diffusion limitations. In this case, the decay of XHb may occur in anaerobic or anoxic environments. A typical example is the simultaneous nitrification-denitrification occurring in floc cores with high O2 gradients in aerated activated sludge tanks (Downing et al., 2010) and in aerobic digesters (Zhang et al., 2013). A second hypothesis would be that the XHb group is in contact with the O2 but has developed another metabolic process for decay or maintenance that does not involve oxygen. Allylthiourea was added only at small dose during the culture of the biomass (5 mg/L ATU in the SBRs, based on López-Vázquez et al., 2007). Compared to 20 mg/L ATU suggested by Henze et al. (2000), lower doses may limit the autotrophs in the SBR culture, however, a slow (but sufficient) nitrification may take place in the digesters that have a higher solid content (concentrated sludge). More research is required to determine the
18 metabolic pathways of the XHb fraction. Meanwhile, a predictive model is proposed, postulating the existence of two groups of dominant heterotrophic bacteria in the system: one that decays using O2 and another that decays without the presence of oxygen (XHa and XHb). Table 4
The relevant modifications proposed in the ASM3 model, with respect to the decay processes, are described in the matrix shown in Table 4. Because the metabolic pathways are not totally known, no matrix column is shown for the counterpart component of XHb, which may be NO3, as an electron acceptor. However, this information is not necessary at all, to be able to fit the OUR data. According to the model, the COD and rO2 of the sludge, during the aerobic digestion, are given by Equations 4 and 5. These expressions would also serve as a basis for fitting the COD and OUR data, to estimate the proposed modified-ASM3 decay parameters. COD (t ) mod el =
r
O2
X Ha + X Hb + X P + X Sto
(4)
(t ) mod el = (1 − fp ) C b H X Ha + bSto X Sto
(5)
The six parameters to be estimated are bSto, bH, iniXHa, iniXHb, iniXP and iniXSto.
3.5 Simultaneous fit of the COD and OUR data to the proposed model Before performing the simultaneous fit, it is important to show how the information from the separate ASM1-COD and ASM3-OUR fits can be integrated, to obtain the decay parameters for the proposed modified-ASM3 model. The fit of the respirograms with ASM3 directly provides the final estimations (“integrated values”, Table 5) of iniXSto, bSto and iniXHa, while the fit of the COD with ASM1 gives the total biomass, iniXHtotal. Table 5
19
The other three parameters, whose values are shadowed in Table 5 (bH, iniXP and iniXHb), may be obtained by combining the results of the two fits. iniXHb is the difference between iniXHtotal and iniXHa, while the initial concentration of XP is calculated by subtracting the amount iniXSto from the value of iniXP initially obtained from the ASM1-COD fit. The bH obtained from the fit of the respirogram is only relevant to the first biomass fraction (XHa), while the value of bH obtained from the fit of the COD is essentially a weighted average applicable to the sum of the two biomass communities (XHa + XHb). For the sludge under study, the two decay constant values were similar (Table 5), so a single bH parameter was used for the two communities of bacteria (averaging).
The reasoning utilized to obtain the data shown in Table 5, that is, the determination of parameters using both the COD-ASM1 and OUR-ASM3 regressions, is only acceptable when the set of parameters of each regression is perfectly identifiable. One of the advantages of this reasoning is its didactic character. Alternatively, there is a better way to obtain a final set of parameters from the ASM3-modified model that lacks the previous limitation; the COD and OUR data can be simultaneously fitted, directly with the ASM3-modified model. To do this, the matrix of the model (Table 4) was implemented in a program run in AQUASIM. The simultaneous fit of different experiments, or of different kinds of measurements, (e.g., COD and rO2) is known to be a practice for improving the parameter estimation process (Reichert, 1998; Sin et al., 2005).
AQUASIM contains algorithms for non-linear regression, where the convergence criterion is the minimization of the sum of squared errors between the model output and the data (χ2). It is
20 important to prevent the software from focusing only on fitting the COD data, to the detriment of the OUR data; this is because the order of magnitude of the COD (thousands of mg/L) and its χ2 is much higher than for the rO2 (< 10 mg/L·h). One way to avoid this type of bias is to perform a simultaneous fit based on the relative values, normalized with the initial values at t = 0 (i.e., the ratios COD (t) / CODinitial and rO2 (t) / rO2 initial). Figure 4 and Table 6 show the results of the simultaneous fits of COD and OUR and their sensitivity analysis. These results concern two long-term digestion runs performed in the present research (run #6 and #7, carried out at different periods), and a foreign run, whose data were taken from the literature. --> Figure 4
The proposed model was very well able to fit the COD and OUR data simultaneously for each of the runs (Fig. 4a and b, run #7; Fig. 4c and d, data from Özdemir et al., 2013). The simulated profiles of COD and rO2 for the different sludge components (XHa, XHb, XSto, XP) are presented in the Figures. The simultaneous fitting graphs corresponding to run #6 are not shown because they are, other than a few minor details, very similar to those shown previously in Figures 1a and 2a (rO2 vs. COD fit).
All the parameters were sufficiently sensitive, with respect to at least one of the response variables (Figs. 4e and 4f). In addition, there was no symmetry or parallelism between the profiles of the SensAR functions (Reichert, 1998; Insel et al., 2002). This confirms that the simultaneous fitting process provides a unique set of parameters that is perfectly identifiable for each digestion run. While the estimation of iniXP and iniXHb comes exclusively from the monitoring of the COD (Fig. 4e), iniXSto and bSto are mainly extracted from the respirogram (Fig. 4f). On the contrary, the estimations of iniXHa and bH can come from either the
21 respirogram or the COD measurements. Exceptionally, for the case shown in Fig. 4e (based in the run by Özdemir et al., 2013), the SensAR function showed some capacity of the COD data to participate in the estimation of iniXSto and bSto. This is due to the greater amount of XSto apparently present in this sludge at the time of its harvest (695 mg/L, compared to 125 mg/L in run #6, Table 6). For this same reason, the duration of the influence zone of iniXSto and bSto in Figure 4f was longer compared to that in run #6 (see Fig. 2 above).
The sets of parameters estimated from the simultaneous fits are presented in Table 6, along with the standard deviations (Std dev). First, the values obtained with the simultaneous fit were very similar to the previous values obtained by integration from the separated fits (CODASM1 vs. OUR-ASM3, Table 5 previously shown above). This confirms and validates that the analysis of the COD data with ASM1 is an adequate means of simplification to identify some of the parameters of the ASM3-modified model, where iniXSto is low. Table 6
Second, the tendencies observed and discussed in the previous sections are confirmed with the simultaneous fits: a) A low decay constant (bH of 0.032 to 0.096 d-1). b) The total active biomass was re-estimated between 60 and 72%, which includes a fraction that decays without consuming oxygen from the aerobic digester (26% in run #6 and 47% in the sample of Özdemir et al.) and another fraction whose decay can be detected through respirometric tests. c) A small initial amount of stored polymer (< 2%) compared to the total COD. d) A decay constant (bSto = 0.71 to 1.62 d-1) similar to the ranges measured in other works (Wentzel et al., 1989b; Friedrich and Takáks, 2013) but greater than the value suggested by “default” in ASM3 and ASM2d (0.2 d-1).
22
In summary, the modified model derived from ASM3 adequately represented the aerobic digestion data. All 6 parameters (bSto, bH, iniXHa, iniXHb, iniXP and iniXSto) were identifiable from the simultaneous fit of the long-term COD-time data and endogenous respiration. The decay constant of the stored products (bSto), as measured in the present study, ranged from 0.71 to 1.62 d-1, much higher than the value suggested by default in ASM3 and ASM2d.
4. CONCLUSIONS
The endogenous respirograms of the digested sludge had a two-phase structure that was describable with ASM3, and not with ASM1. The amount of stored polymers was low (<3% of the COD), but it was responsible of 40 to 75% of OUR. The parallel monitoring of the COD and the OUR revealed the presence of two groups of heterotrophs in the sludge, one decaying with, and another without O2 use. A modified model from ASM3 was proposed. All 6 parameters of the ASM3-modified sub-model were identifiable by performing a simultaneous fit of the COD and the OUR data.
ACKNOWLEDGMENTS Many thanks to “Consejo Nacional de Ciencias y Tecnología”, CONACYT Mexico, who financially supported this study through the project # CB152943.
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FIGURE CAPTIONS Figure 1: Endogenous respirograms: structure and modeling (ASM1 vs. ASM3 fit). Figure 2: Sensitivity analysis of the model derived from the ASM3 (run #6) Figure 3: Fit of the COD data and sensitivity analysis (run #6): a) fit with the ASM1 and ASM3 models; b) SensAR functions of ASM3; c) SensAR functions of ASM1; d) total COD, XH and XP simulated based on ASM1. Figure 4: Simultaneous fit and simulation of the COD and OUR of run #7 (a and b); of the run by Özdemir et al., 2013 (c and d); and of the sensitivity functions (SensAR, e and f).
26
Table 1: Matrix representation of decay processes in ASM1 ( line 1) and ASM3 (1 + 2) Components Processes ↓ 1. Decay of XH 2. Decay of XSto
XSto
SO
XP
XH
Rates
-(1-fp) C -1
fp
-1
-1
bH XH bSto XSto
Components: stored compound (XSto, mg/L COD); dissolved oxygen (SO, mg/L O2); endogenous residues (XP, mg/L COD); heterotrophs (XH, mg/L COD). Parameters: fp = 0.2, fraction of biomass converted in Xp (Henze et al., 2000); bH and bSto, 1st order decay constants. C = 1, without nitrification vs. C = (1+4.57*fN) with nitrif., where fN = 0.063.
27
Table 2: ASM3 parameters as estimated from the OUR data only Sludge
Run #
total COD (mg/L)
#1 #4 #6
#7
Estimated values iniXH
iniXSto
bH
bSto (d-1)
(mg/L COD)
8457 ± 260 5331 ± 90
7000 2218 ± 885
182 ± 33 75 ± 33
0.0072 0.71 ±0.37 0.060 1.27 ± 0.03 ± 0.37
6381 ± 120 5660 ± 63
1009 ± 65 986 ± 60 1595 ± 60
125 ±10 20 ±5 204 ± 38
0.097 1.62 ±0.011 ± 0.09 0.081 1.60 ±0.008 ± 0.30 0.15 1.27 ±0.02 ± 0.14
Friedrich and Takáks, (2013), as recalculated Özdemir et al., 2013, as recalculated
1767 899 ± 159 ± 173
0.05 ±0.02
0.30 ± 0.03
28
Table 3: ASM1 (and ASM3) parameters as estimated from the COD data only
Sludge
Run #
Total COD (mg/L)
#5
#6 #7
3527 ± 62 6381 ± 120 5660 ± 63
Özdemir et al. (2013), as Recalculated in Aquasim
Estimated values iniXH
iniXP
(mg/L COD)
2740 ± 88 4717 ± 220 3641 ± 286 3456 ± 160
756 ± 93 1666 ± 180 1988 ±308 957 ± 98
bH
Fa
-1
(%)
(d )
0.022 ±0.002 0.10 ± 0.01 0.026 ±0.004 0.066 ±0.008
77% 74% 65% 75%
29
Table 4: Peterson Matrix of the modified-ASM3 sub-model Processes ↓ Decay of XHa Decay of XHb Decay of XSto
XSto
SO -(1-fp) C
-1
-1
XP fp fp
XHa -1
XHb -1
Rates bH XHa bH XHb bSto XSto
Components: stored compounds (XSto, mg/L COD); dissolved oxygen (SO, mg/L O2); endogenous residues (XP, mg/L COD); heterotrophs ( XHa and XHb, mg/L COD). Parameters: fp = 0.2, fraction of biomass converted in Xp; bH and bSto 1st order decay constants. C = 1, without nitrification vs. C = (1+4.57*fN) with nitrif., where fN = 0.063.
30
Table 5: Integration of the information from the separate fits of the COD and OUR data COD fit OUR fit Parameters (ASM1) (ASM3) bH (d-1) 0.100 0.097 bSto (d-1) 1.625 iniXSto (mg/L) 125 iniXP (mg/L) 1666 IniXHa (mg/L) 1010 IniXHb (mg/L) IniXH total 4717
Integrated values 0.098 1.626 125 1541 1010 3707 4717
31
Table 6: Estimated parameters of the proposed model (COD and rO2) Runs Parameters bH (d-1) bSto (d-1) iniXSto (mg/L) iniXP (mg/L) iniXHa (mg/L) iniXHb (mg/L) Total COD
#6 Estimated Std dev. values ± 0.009 0.096 ± 0.20 1.63 ± 18 125 ± 154 1651 ± 82 1018 ± 182 3630 6424 -
#7 Estimated Std dev. values ± 0.007 0.032 ± 0.11 0.70 ± 14 70 ± 354 2324 ± 330 1827 ± 177 1487 5709 -
Özdemir et al. * Estimated Std dev. values ± 0.010 0.054 ± 0.07 0.35 ± 213 695 ± 122 1006 ± 386 2143 ± 322 750 4594 -
* : Özdemir et al., (2013), data from authors graphs 5 and 6 were fit with the modified model
32
Figure 1: Endogenous respirograms: structure and modeling (ASM1 vs. ASM3 fit).
33
Figure 2: Sensitivity analysis of the model derived from the ASM3 (run #6)
34
Figure 3: Fit of the COD data and sensitivity analysis (run #6): a) fit with the ASM1 and ASM3 models; b) SensAR functions of ASM3; c) SensAR functions of ASM1; d) total COD, XH and XP simulated based on ASM1.
35
Figure 4: Simultaneous fit and simulation of the COD and OUR of run #7 (a and b); of the run by Özdemir et al., 2013 (c and d); and of the sensitivity functions (SensAR, e and f).
36
HIGHLIGHTS
1. Sludge digestion respirograms had two phases describable with ASM3, not with ASM1. 2. Storage was < 3% of the biomass COD but accounted up to 75% of the O2 uptake rate. 3. 2 groups of storing bacteria was detected, one decaying using O2 and the other no. 4. The modified ASM3 model proposed was able to predict the COD and OUR of digesters. 5. The parameters of the model are identifiable by fitting the COD and OUR together.