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Applying a framework for calibrating a biofilm-reactor model:a full-scale moving-bed biofilm reactor active in
nitrification
Doris Brockmann, Joshua P. Boltz, Eberhard Morgenroth, Glen T. Daigger, Mogens Henze, Bruce Rittmann, Kim H. Sorensen, Imre Takács, Peter A.
Vanrolleghem, Mark van Loosdrecht
To cite this version:
Doris Brockmann, Joshua P. Boltz, Eberhard Morgenroth, Glen T. Daigger, Mogens Henze, et al..
Applying a framework for calibrating a biofilm-reactor model:a full-scale moving-bed biofilm reactor active in nitrification. 9. International Conference on Biofilm Reactors, International Water Associa- tion (IWA). INT., May 2013, Paris, France. �hal-02748421�
Applying a framework for calibrating a biofilm-reactor model:
a full-scale moving-bed biofilm reactor active in nitrification
Doris Brockmann 1, Joshua P. Boltz 2, Eberhard Morgenroth 3, Glen T. Daigger 4, Mogens Henze 5, Bruce Rittmann 6, Kim H. Sørensen 7, Imre Takács 8, Peter A. Vanrolleghem 9, Mark van Loosdrecht 10
1 INRA, UR0050, Laboratoire de Biotechnologie de l’Environnement, Avenue des Etangs, Narbonne, F-11100, France (E-mail: doris.brockmann@supagro.inra.fr), 2 CH2M HILL, Tampa, FL, USA (Email:
jboltz@CH2M.com), 3 Eawag/ETH Zürich, (Email: Eberhard.Morgenroth@eawag.ch), 4 CH2M HILL, 5 TU Denmark, 6 Arizona State University, Tempe, USA, 7 Veolia Water Technical Direction, 1,rue G.B. Pirelli 94410 St. Maurice France, 8 Dynamita, France, 9 modelEAU, Université Laval, Québec, QC, Canada (E-mail:
Peter.Vanrolleghem@gci.ulaval.ca), 10 Dept. Biotechnology, Delft Univ. of Technology Abstract
Many wastewater treatment plant (WWTP) simulators include biofilm reactor modules, enabling a more widespread application of biofilm models in engineering practice. To increase acceptance, and promote proper and effective biofilm model use in practice, a framework for biofilm reactor model calibration and application is needed. A step-wise calibration approach for biofilm reactor models was presented at WWTmod 2012. The proposed calibration framework was used in this study to calibrate a biofilm reactor model for a full-scale tertiary nitrification moving-bed biofilm reactor (MBBR). Steady-state model calibration was based on monitoring data for effluent NH4-N, NO3-N and TSS concentrations, along with measured biofilm biomass averaged over five years.
Three parameters, detachment rate, biofilm biomass concentration, and mass transfer boundary layer thickness, were adjusted to fit steady-state model results to measured data. Dynamic simulation with the calibrated model showed a poor representation of the timely evolution of the biofilm biomass, which did not negatively influence the prediction of nitrification rates. For dynamic calibration, however, a question needs to be addressed: How can we deal with the fact that the timely evolution of the biofilm biomass may not be described mechanistically well enough by biofilm models (as in this study).
Keywords
Biofilm, reactor, calibration, good modeling practice, full-scale, MBBR, modeling
INTRODUCTION
Most wastewater treatment plant (WWTP) simulators include one-dimensional biofilm models that are configured to describe some biofilm reactors (Boltz et al. 2010). The broader availability of biofilm models in WWTP simulation tools enables an increased application of biofilm modeling in engineering practice. A more widespread application of biofilm models in practice is welcome, but guidance for model calibration is needed to allow for increased acceptance, including appropriate and effective use of biofilm models in engineering design (Morgenroth et al. 2000; Boltz et al.
2010). At WWTmod 2012, Boltz et al. (2012) presented a framework for biofilm reactor model calibration. The authors based the calibration framework on the recommendations and the structured framework for the use of activated sludge models in practice presented by Rieger et al.
(2012), and they discussed differences between calibrating biofilm reactor models and activated sludge models. A step-wise calibration approach for biofilm reactor models was proposed that covers relevant steps to be considered when calibrating a biofilm reactor model (Boltz et al. 2012).
In addition, relevant parameters and processes were indicated.
The goal of this study is to present a first application of the proposed framework for calibrating biofilm-reactor models. The step-wise calibration approach was applied to calibrate a biofilm reactor model of a full-scale tertiary nitrification moving-bed biofilm reactor (MBBR).
MATERIALS AND METHODS Full-scale tertiary nitrification MBBR
The calibration framework was tested using data from the full-scale MBBR nitrification process at the Moorhead, Minnesota Wastewater Treatment Facility (Minnesota, USA). The MBBR began operation in 2003. The MBBR reactor has a volume of 2970 m3 and is filled to 32% (v/v) with free moving plastic biofilm carriers (Zimmerman et al. 2005). The Hydroxyl-Pac media has an effective specific surface area of 388 m2/m3 of filled volume (Bjornberg et al. 2009) or 124 m2/m3 reactor volume. Based on tracer studies with biofilm present, the full-scale MBBR can be modeled as two equal-volume CSTRs in series plus "dead" volume that is a function of the influent flow rate (Zimmerman et al. 2005). The effluent of the MBBR is discharged to a polishing pond (Zimmerman et al. 2005).
Daily monitoring data were available for effluent flow (Q), airflow rate, and air pressure. Influent and effluent temperature, dissolved oxygen (DO) concentration, pH, and NH3-N concentration were measured three times a week. Influent and effluent concentrations of five-day carbonaceous biochemical demand (CBOD5), soluble CBOD5 (only influent), total Kjeldahl nitrogen (TKN), nitrite-nitrogen (NO2-N), nitrate-nitrogen (NO3-N), alkalinity, and total suspended solids (TSS), as well as biofilm biomass on the carriers were measured once a week. Table 1 summarizes the wastewater characterization averaged over the years 2007-2011.
Table 1 : Wastewater characterization averaged over the years 2007-2011, with standard deviation in parentheses.
Parameter Unit value
Qin m3/d 17,691 (± 6,056)
CBOD5 g BOD/m3 6.8 (± 3.5)
sol CBOD5 g BOD/m3 4.0 (± 2.0)
TSS g TSS/m3 6.8 (± 3.2)
TKN g N/m3 27.0 (± 9.8)
NH3-N g N/m3 25.2 (± 9.4)
NO2-N g N/m3 0.9 (± 1.1)
NO3-N g N/m3 1.7 (± 0.8)
Alkalinity mol HCO3-/m3 6.5 (± 1.4)
Mathematical model
In a first step, the full-scale nitrifying MBBR was modeled as a single CSTR to take into account that the biofilm biomass within an MBBR is well mixed. The modeled MBBR had an "active"
volume of 77% and a "dead" volume of 23% at an average influent flow rate of 18,000 m3/d, based on the linear relation between influent flow rate and “dead” volume presented by Zimmerman et al.
(2005). In a second step, the full-scale nitrifying MBBR was modeled as two equal-volume CSTRs in series to account for the mixing conditions of the bulk liquid observed by Zimmerman et al.
(2005). Biochemical conversion processes were modeled using the Activated Sludge Model No. 3 (ASM3), but storage of readily biodegradable substrate was not modeled (Boltz et al. 2011). The rate of biofilm detachment was described as a function of the biofilm thickness (rdet = kdet · LF).
The biofilm was discretized into 10 equally sized layers. The effluent TSS concentration was equal to the TSS concentration in the second CSTR because suspended solids were not specifically retained in the MBBR. Simulations were carried out using AQUASIM (Reichert 1998).
Influent wastewater characterization with respect to state variables
The influent wastewater characterization with respect to nitrogenous compounds and alkalinity was straight forward: NH4-N was attributed to SNHx, NO2-N+NO3-N was attributed to SNOx. In contrast, the characterization with respect to organic compounds was more complicated. All soluble CBOD5
was attributed to readily biodegradable substrate (SB). All particulate CBOD5 (CBOD5 - soluble
CBOD5) contributes to slowly biodegradable substrate (XCB), heterotrophic bacteria (XOHO), and autotrophic nitrifiers (XANO) according to equation (1).
( + ) 1 − _ , . + 1 − _ , = − (1)
where fXU_Bio,end.resp is the production of particulate undegradable organics (XU) in endogenous respiration, and fSU_XCB,hyd is the production of soluble undegradable organics (SU) in hydrolysis. It was assumed that the biodegradable COD was equal to the CBOD5. The proportion of XANO:XOHO:XCB (0.02:0.23:0.75) was equal to the proportion for the tertiary nitrifying MBBR in Boltz et al. (2011). XU was derived from equation (2).
= 0.75( + ) + 0.9( + ) (2)
Calibration
The steady-state calibration of the biofilm reactor model followed the iterative approach proposed by Boltz et al. (2012). A detailed presentation of the calibration framework is given in Boltz et al.
(2013). The calibration was based on monitoring data for effluent NH4-N, NOx-N, and TSS concentrations, along with measured biofilm biomass per m2 of effective specific surface area of biofilm carriers. Statistical analysis and density plots of the monitoring data showed that the distributions of the effluent concentrations and the biofilm biomass were skewed, except for the effluent nitrate concentrations, which were almost normally distributed. Consequently, steady-state calibration was based on the medians of the monitoring data (2007-2011) and not on the means.
Approximate standard errors of the parameter estimates were calculated from the estimated covariance matrix of the estimates (Dochain & Vanrolleghem 2001).
For dynamic simulation of MBBR operation of the years 2007-2011, the goodness-of-fit of the calibration was evaluated using different quantitative quality criteria (Hauduc et al. 2011): the mean absolute error (MAE), the root mean square error (RMSE), the median of the absolute relative error expressed in percentage (MdAPE), and the percent bias (PBIAS). The quality criteria are calculated by equations (3) to (6).
=1
, − , (3)
= 1
, − , (4)
= , − ,
, ∙ 100 (5)
= 100 ∙ , − , / , (6)
Sensitivity analysis
A local sensitivity analysis of the calibrated model was carried out with respect to calibrated parameters and organic substrate characterization. Sensitivity with regard to organic substrate characterization was evaluated because the influent characterization of organic substrate could only be based on total and soluble CBOD5 influent data. For the calculation of a sensitivity measure δ, local sensitivity values were scaled to include information on the uncertainty range of the parameters. The sensitivity measure δ is given by (Brun et al. 2001):
= 1
, ℎ , =∆
∙ (7)
where Δpj is the uncertainty range of parameter pj, sci is a scale factor, and n is the number of model outputs considered. Biokinetic and biofilm parameters were assigned to the same uncertainty classes as in Boltz et al. (2011). Influent SB, XCB, and XU concentrations were assigned to uncertainty class 3 (uncertainty range: 50% of the parameter value) to account for limited information with regard to organic substrate characterization.
The software package R (R Development Core Team 2010) was used for data processing and calculation of quality criteria, sensitivity measure δ, and standard error of the estimates.
RESULTS AND DISCUSSION Steady-state calibration
Following the calibration framework, first the detachment rate (kdetach) was adjusted to fit the model-predicted biofilm biomass of the MBBR, modeled as single CSTR, to the measured values.
Then, the biofilm biomass concentration (BBC) was adjusted to obtain a reasonable biofilm thickness in the model (184 μm). Because the biofilm biomass concentration influences the biofilm biomass and the detachment rate influences the biofilm thickness, several iterations are necessary at this point of the model calibration to fit model outputs to experimental data. In a third step, the modeled effluent TSS concentration was fitted to measured data by decreasing the XU concentration in the influent from 5.6 g COD/m3 to 4 g COD/m3. Then, the mass transfer boundary layer thickness (LL) was adjusted to fit model outputs for SNHx and SNOx concentrations to experimental data. As reducing LL to 0 μm did still result in an overestimation of the effluent SNHx concentration, also the values of the half-saturation constants KNHx,ANO, KO2,ANO, KO2,OHO, and KSB,OHO were reduced. To account at least for some external mass transfer resistance, LL was set to a value as high as possible (30 μm), while still matching effluent SNHx concentrations. The increased biofilm biomass production resulting from the low values for LL and the half-saturation constants required an iteration of the calibration steps. Table 3 presents initial and calibrated parameter values as well as the standard error of the parameter estimates.
Table 2 : Initial and calibrated parameter values for a single CSTR (after steady-state calibration).
Description Symbol Unit initial calibrated Standard error*
absolute relative
Detachment rate kdetach d-1 0.2 0.013 ±0.003 0.25 Biofilm biomass concentration BBC g COD/m3 50,000 100,000 ±7.9e-8 7.9e-13
Mass-transfer boundary layer
thickness LL μm 100 30 ±99 3.3
Half-saturation constant of heterotrophs for SB
KSB,OHO g COD/m3 4 0.1 0.023 0.23
Half-saturation constant of heterotrophs for SO2
KO2,OHO g O2/m3 0.1 0.05 2.0e-4 0.004
Half-saturation constant of nitrifiers for SNHx
KSB,ANO g N/m3 0.7 0.05 0.16 3.29
Half-saturation constant of nitrifiers for SO2
KO2,ANO g O2/m3 0.8 0.05 0.001 0.021
* Standard errors of the parameter estimates could only be calculated with the Moore-Penrose generalized inverse of a matrix as the sensitivity matrix was singular.
The calibration of the single CSTR resulted in low errors between steady-state model outputs and measured data (median) (SNHx: 0.0%; SNOx: 12.5%; TSS: 2.0%; biofilm biomass: 3.6%). However, an unreasonable low value for LL and modification of half-saturation constants were necessary to adjust for an inadequate representation of the mixing conditions of the liquid phase. As a consequence, the model representation of the MBBR was changed to two equal-volume CSTRs in series to account for the observed mixing conditions. To calibrate the model with two CSTRs in series, only the detachment rate (0.012 d-1), the biofilm biomass concentration (100 kg COD/m3),
and the mass transfer boundary layer thickness (100 μm) needed to be adjusted. The model- predicted biofilm biomass and biofilm thickness of the MBBR were calculated as means of the model-predicted biofilm biomass and biofilm thickness in the two CSTRs, respectively. With a calibrated BBC of 100 kg/m3, a reasonable mean biofilm thickness of 183 μm was obtained. The calibrated BBC is high compared to a typical range of 40-60 kg/m3, but in agreement with measured values. Bjornberg et al. (2009) reported BBCs ranging from 90 kg/m3 at a biofilm thickness of 200 μm to 110 kg/m3 at a biofilm thickness of 100 μm. Initial and calibrated parameter values as well as the standard error of the parameter estimates for the model with two CSTRs in series are summarized in Table 3. The calibrated value for LL has a large standard error, while the standard errors of the calibrated values for kdetach and BBC are small. The calculated correlation matrix of the calibrated parameters revealed a high correlation of BBC and kdetach, and confirmed the observation during the calibration procedure (iterations needed for calibrating kdetach and BBC).
Table 3 : Initial and calibrated parameter values for two CSTRs in series (after steady-state calibration).
Description Symbol Unit initial calibrated Standard error*
absolute relative
Detachment rate kdetach d-1 0.2 0.012 ±0.003 0.25 Biofilm biomass concentration BBC g COD/m3 50,000 100,000 ±2.3e-11 2.3e-16
Mass-transfer boundary layer
thickness LL μm 100 100 ±81 0.81
* Standard errors of the parameter estimates could only be calculated with the Moore-Penrose generalized inverse of a matrix as the sensitivity matrix was singular.
Steady-state model calibration resulted in good agreement between steady-state model outputs and measured data (median) for effluent ammonium and alkalinity concentrations, as well as biofilm biomass (Table 4). The model slightly over-predicted the steady-state effluent nitrate and TSS concentrations with respect to the median. A better match of the effluent TSS concentration can be obtained by reducing the XU influent concentration.
Table 4: Average monitoring data (2007-2011) and steady state model outputs for two CSTRs in series.
Parameter Unit measured model error*
mean (± std.dev.) median
TSS g TSS/m3 10.5 (±4.3) 9.8 10.9 11.2 %
Biofilm biomass g TSS/m2 16.8 (±10.7) 14.0 14.3 2.1 %
Ammonium g N/m3 2.1 (±3.7) 0.4 0.4 0.0 %
Nitrate g N/m3 23.5 (±6.4) 24.0 26.8 11.7 %
Alkalinity mol HCO3-/m3 3.5 (± 1.7) 3.0 3.0 0.0 %
*The error was calculated with respect to the median.
Sensitivity analysis
A local sensitivity analysis was carried out with respect to calibrated parameters of the model with two CSTRs in series (BBC, LL, and kdetach) and SB, XCB, and XU influent concentrations. The sensitivity results were compared to sensitivity results for maximum growth rates of heterotrophic and autotrophic bacteria (μOHO,Max, μANO,Max), substrate affinity constants (KSB.OHO, KNHx,ANO), and oxygen affinity constants (KO2,OHO, KO2,ANO) for heterotrophic and autotrophic bacteria, respectively. Error! Reference source not found. presents sensitivity measures δ for steady-state effluent SNHx, SNOx, and TSS concentrations, and mean biofilm biomass.
The effluent SNHx, SNOx, and TSS concentrations and the biofilm biomass were most sensitive to changes in LL. The low sensitivities of effluent SNHx and SNOx concentrations to changes in the organic substrate characterization show that nitrification in the full-scale MBBR was not impacted by influent organic substrate. This is expected and consistent with full-scale tertiary nitrifying
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in the ammonium effluent concentration are not well represented by the model, but evaluation of the model fit for low ammonium effluent concentrations is difficult on a visual basis. However, the model was not able to adequately describe the timely evolution of the biofilm biomass. This is not surprisingly because the biofilm biomass evolution is not properly, mechanistically described in the model. The poor representation of the biofilm biomass, however, did not negatively influence the prediction of nitrification rates, because the ratio of maximum biomass growth rate to maximum substrate transport rate was mostly above 1 in the first CSTR (82% of the simulation period), where on average 84% of the ammonium was removed. Calculation of approximate standard errors of the parameter estimates based on dynamic simulation results led to decreased errors (relative standard errors: kdetach 0.31%; BBC 0.07%; LL 11.5%).
Figure 2: Measured and predicted ammonium, nitrate and TSS effluent concentrations, and mean biofilm biomass.
Table 5: Calculated quality criteria for ammonium and nitrate effluent concentrations, TSS bulk phase concentration, biofilm biomass, and all four target constituents simultaneously.
Quality criteria Target value Ammonium Nitrate TSS Biofilm biomass Overall
MAE 0 1.62 5.26 3.41 7.61 3.29
RMSE 0 3.39 7.34 5.60 11.27 6.03
MdAPE 0 76.57% 17.30% 22.22% 40.79% 45.69%
PBIAS 0 58.34% -7.52% 12.74% 29.98% 13.27%
MAE: mean absolute error; RMSE: root mean square error; MdAPE: median of the absolute percent error; PBIAS:
percent bias
In addition to visual evaluation of the goodness-of-fit, quantitative quality criteria (Table 5) were calculated for an objective assessment of the calibration quality. The high values calculated for the MdAPE and the PBIAS for the effluent ammonium concentration result from the underestimation of the peaks. The higher values calculated for the MAE and the RMSE for the effluent nitrate concentration show that the goodness-of-fit is not as good as it seems based on a visual evaluation.
The negative value of the PBIAS indicates that the model overestimates the effluent nitrate concentration. An MdAPE of 22% calculated for the bulk phase TSS concentrations shows that the agreement between model outputs and measured data is not as good as it seems based on a visual
evaluation. The differences between model results and measured data, mainly at the end of the simulation period, are probably due to an inaccurate influent characterization with respect to particulate undegradable organic substrate.
CONCLUSIONS
A previously proposed framework for biofilm reactor calibration was used for steady-state calibration of a biofilm reactor model for a full-scale tertiary nitrifying MBBR. Consequently, not all steps of the step-wise approach were covered by the presented calibration exercise. The calibration exercise showed that an adequate representation of the mixing conditions in the bulk phase is important to obtain reasonable parameter estimates. For the model with two CSTRs in series, steady-state calibration of three parameters, kdetach, BBC, and LL, resulted in an adequate goodness-of-fit for steady-state effluent SNHx and SALK concentrations, and biofilm biomass.
Effluent SNOx and TSS concentrations were slightly overestimated by the model. Local sensitivity analysis showed that a good wastewater characterization with respect to organic substrate is important for modeling nitrifying biofilm reactors in order to adequately represent effluent TSS concentrations and biofilm biomass. In addition, for dynamic calibration, a question needs to be addressed: How can we deal with the fact that the timely evolution of the biofilm biomass may not be described mechanistically well enough by biofilm models (as in this study).
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