water Article
Empirical Sewer Water Quality Model for Generating Influent Data for WWTP Modelling Jeroen Langeveld 1,2, * , Petra Van Daal 2,3 , Remy Schilperoort 1 , Ingmar Nopens 4 Tony Flameling 5 and Stefan Weijers 5 1 2 3 4 5
*
,
Partners4UrbanWater, Javastraat 104a, Nijmegen 6524 MJ, The Netherlands;
[email protected] Section Sanitary Engineering, Department of Water Management, Delft University of Technology, P.O. Box 5048, Delft 2628 CD, The Netherlands;
[email protected] Witteveen+Bos, P.O. Box 233, Deventer 7400 AE, The Netherlands BIOMATH, Department of Mathematical Modelling, Statistics and Bioinformatics, Ghent University, Coupure Links 653, Gent 9000, Belgium;
[email protected] Waterschap De Dommel, P.O. Box 10.001, Boxtel 5280 DA, The Netherlands;
[email protected] (T.F.);
[email protected] (S.W.) Correspondence:
[email protected]; Tel.: + 31-6-1897-6283
Received: 30 March 2017; Accepted: 30 June 2017; Published: 5 July 2017
Abstract: Wastewater treatment plants (WWTP) typically have a service life of several decades. During this service life, external factors, such as changes in the effluent standards or the loading of the WWTP may change, requiring WWTP performance to be optimized. WWTP modelling is widely accepted as a means to assess and optimize WWTP performance. One of the challenges for WWTP modelling remains the prediction of water quality at the inlet of a WWTP. Recent applications of water quality sensors have resulted in long time series of WWTP influent quality, containing valuable information on the response of influent quality to e.g., storm events. This allows the development of empirical models to predict influent quality. This paper proposes a new approach for water quality modelling, which uses the measured hydraulic dynamics of the WWTP influent to derive the influent water quality. The model can also be based on simulated influent hydraulics as input. Possible applications of the model are filling gaps in time series used as input for WWTP models or to assess the impact of measures such as real time control (RTC) on the performance of wastewater systems. Keywords: sewer system; empirical model; influent generator; influent modelling; gap filling
1. Introduction Modelling of wastewater treatment plants (WWTPs) using activated sludge models (ASM) has become a standard in both industry and academia for a range of objectives, amongst others WWTP design [1,2], operation [3], and control [4,5]. Especially the latter objective, developing control strategies and assessing the performance of control strategies requires high frequency influent data [6]. In a comprehensive review, [7] discussed the available approaches for generating influent data. The approaches range from (1) data driven methods based on creating databases with monitoring and experimental data and derived models using the data; (2) very simple models based on harmonic functions; and (3) phenomenological models [8,9]. The data driven methods comprise two different approaches. The first method [10] uses pollutant release patterns derived from literature to generate dynamic influent data aggregating the punctual emissions from the database. The second method [11] interpolates available influent data at e.g., a daily timescale to e.g., hourly dynamics. Water 2017, 9, 491; doi:10.3390/w9070491
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The simple models based on harmonic functions are very well suited for the analyses of dry weather flow (DWF) situations, but less so for wet weather flow (WWF) situations [7]. The phenomenological models are the most detailed influent models, that can give a phenomenological representation of dynamics of WWTP influent, including diurnal patterns, weekend, seasonal, and holiday variations as well as rain events [7,8]. Despite being labelled as ‘promising’ [7], todays phenomenological models cannot adequately reproduce the dynamics in WWTP influent during wet weather due to a relatively poor representation of the build-up and wash off of urban pollutants. This is also true for the most recently published influent generator by [12], who use a mix of statistical and conceptual modelling techniques for synthetic generation of influent time series. The limitations associated with the use of influent generators are not surprising given the state of the art knowledge on the physical-chemical, biological and transport processes occurring in sewer systems [13–17]. Sediment transport especially is not very well understood and not very successfully reproduced in deterministic sewer models. This is partly due to the fact that it is currently not possible to get enough data on the initial sewer sediment conditions throughout an entire sewer network. It is interesting to note that the developers of influent generators, showing many similarities with simplified or parsimonious sewer models [18,19], are facing the same issues as sewer modelers in the past, i.e., how to incorporate the contribution of in-sewer stocks during storm events to the outflow of sewers via either combined sewer overflow (CSO) or WWTP influent. In order to overcome the limitations of deterministic sewer models, regression models have been proposed, which are validated against monitoring data. A recent successful example of this approach is given by [20], who developed an empirical model for storm water total suspended solids (TSS), event mean concentrations with rainfall depth, and antecedent dry weather period as input variables. These empirical relations, that are valid at a CSO or storm sewer outfall (SSO), however, are not suitable for the prediction of WWTP influent quality, as these models do not predict the influent quality during DWF. For WWTP influent modelling, the empirical model described by [21], relates the influent concentration to the daily flows. A weak point of this approach is the impossibility to account for the dynamics during storm events. This is a major drawback, as storm events typically do not last a full day. Recent applications of water quality sensors have resulted in the availability of long time series of WWTP influent quantity and quality [22,23]. These time series contain a lot of information on the response of influent quality to storm events and the contribution of in-sewer stocks to WWTP influent [24]. In this study, time series analysis is used to understand the dynamics of WWF related variations in WWTP influent quality and to relate the variation in influent quality to influent hydraulics. This allowed the development of an empirical model based on understanding of the underlying physical processes. The paper is organized as follows: first, the available data set of WWTP Eindhoven is described. Second, the model development and calibration method are presented. Next, the calibration results, model results and the transferability of the concept are presented, discussed, and finally, some foreseen applications of the model are introduced. 2. Materials and Methods 2.1. System Description: The Dommel River IUWS The Dommel river is relatively small and sensitive to loadings from CSOs and WWTP effluent. The river flows through the city of Eindhoven (the Netherlands) from the Belgian border (south) into the River Meuse (north). The Dommel receives discharges from the 750,000 people equivalent (PE) WWTP of Eindhoven and from over 200 CSOs in 10 municipalities. In summer time, the base flow in the river just downstream of the WWTP comprises 50% of WWTP effluent, increasing to 90% during small storm events. The Dommel River does not yet meet the requirements of the European
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Union Water The water qualitynutrient issues toconcentration be addressed are dissolved oxygen (DO)Framework depletion, Directive ammonia(WFD) peaks [25]. and seasonal average levels [26,27]. oxygen (DO) depletion, ammonia peaks and seasonal average nutrient concentration levels [26,27]. Earlier research within the KALLISTO project [18,25] demonstrated that the WWTP effluent is the Earlier research the KALLISTO project demonstrated that thethe WWTP effluentpeaks is the in main main source forwithin the toxic ammonia peaks in [18,25] the Dommel river and that ammonium the source for the toxic ammonia peaks in the Dommel river and that the ammonium peaks in the WWTP WWTP effluent can be significantly reduced by applied integrated real time control (RTC). In [28], effluent can be significantly applied integrated realand time control (RTC). In [28], use the use of RTC by activating reduced in-sewerby storage volume to reduce delay the hydraulic peak the loading of activating in-sewer to shown reduce and delay the hydraulic peak Reference loading of the ofRTC the by WWTP during storm storage events volume has been to be an effective measure. [29] WWTP during storm events has been shown to be an effective measure. Reference [29] introduced a introduced a new RTC concept: the smart buffer, which minimizes the peak load to the biology at new RTCEindhoven concept: the buffer, which minimizes the peak load to the biology WWTP WWTP bysmart applying the aforementioned RTC combined with usingat only one Eindhoven of the three by applying the aforementioned RTC combined with using only one of the three primary clarifiers primary clarifiers (PC) during dry weather (DWF) and using the other two PCs only during storm (PC) during dry weather (DWF) and using the other two PCs only during storm events. events. The The10 10municipalities municipalitiescontributing contributingto tothe theWWTP WWTPinfluent influentare aredivided dividedover overthree threecatchment catchmentareas areas that are very different in size and character, each having a separate inflow to the WWTP (see Figure 1). that are very different in size and character, each having a separate inflow to the WWTP (see Figure Wastewater from Eindhoven Stad (ES, municipality of Eindhoven) accounts for approximately 50% 1). Wastewater from Eindhoven Stad (ES, municipality of Eindhoven) accounts for approximately (in practice ranging between 14,000 and and 17,000 m3 /h) of of thethe hydraulic 50% (in practice ranging between 14,000 17,000 m3/h) hydrauliccapacity capacityand andisisdischarged discharged directly to the WWTP. The other nine (much smaller) municipalities are each connected directly to the WWTP. The other nine (much smaller) municipalities are each connectedto toone oneof ofthe the two one to to the thenorth north(Nuenen/Son (Nuenen/Sonoror NS, 7 km length) and to twowastewater wastewater transport transport mains, mains, one NS, 7 km in in length) and oneone to the 3 /h) and 43% the south (Riool Zuid or RZ, 32 km in length), accounting for respectively 7% (3000 m 3 south (Riool Zuid or RZ, 32 km in length), accounting for respectively 7% (3000 m /h) and 43% (in 3 (in practice ranging from 14,000 15,000 of the hydraulic capacity. elaborate description of practice ranging from 14,000 to to 15,000 m3m /h)/h) of the hydraulic capacity. AnAn elaborate description of the the studied wastewater system found in [23]. studied wastewater system cancan be be found in [23].
catchment area: Nuenen/Son Eindhoven Stad Riool-Zuid
Closing section river
ps Son ps Nederwetten ps Gerwen ps Nuenen cs rwzi wwtp ps Eeneind Eindhoven
ps Wintelre
Veldhoven ps Knegsel
ps Mierlo sludge proc. inst.
Geldrop
cs de Meren
ps Aalst Aalst
ps Heeze
ps Waalre
ps Steensel
cs Valkenswaard ps Eersel ps Riethoven
ps Duizel
Bergeijk
ps Sterksel
Valkenswaard
ps Leende
ps Westerhoven
wwtp Eindhoven free flow conduits pressure mains pumping stations control stations sludge proc. inst.
ps Weebosch ps Borkel Luijksgestel 0
3
6
N
9 km
Figure1.1.Wastewater Wastewatersystem systemof ofEindhoven Eindhoven(Left) (Left)and andits itsreceiving receivingstreams streamsand andschematic schematiclay layout outof of Figure the wastewater system; (Right) Figure reproduced with permission from [23]. the wastewater system; (Right) Figure reproduced with permission from [23].
2.2. Monitoring Network and Data Validation 2.2. Monitoring Network and Data Validation At each of the three inflows into the WWTP (locations ‘A’ in Figure 1 at the right) on-line At each of the three inflows into the WWTP (locations ‘A’ in Figure 1 at the right) on-line spectroscopy sensors (UV-VIS) have been installed that measure equivalent concentration values of spectroscopy sensors (UV-VIS) have been installed that measure equivalent concentration values of wastewater quality parameters: total suspended solids (TSS), chemical oxygen demand (COD), and wastewater quality parameters: total suspended solids (TSS), chemical oxygen demand (COD), and filtered COD (CODf), i.e., the dissolved fraction of COD, at an interval of 2 min. In addition, flow is filtered COD (CODf), i.e., the dissolved fraction of COD, at an interval of 2 min. In addition, flow is recorded every minute at these locations and ammonium (NH4, using Hach Lange Amtax sensors) at recorded every minute at these locations and ammonium (NH4 , using Hach Lange Amtax sensors) the Eindhoven Stad and Riool Zuid catchments. In this study, monitoring data for the year 2012 was at the Eindhoven Stad and Riool Zuid catchments. In this study, monitoring data for the year 2012 used. was used. The monitoring data were validated manually, focusing on obtaining reliable data for calibration The monitoring data were validated manually, focusing on obtaining reliable data for calibration of of wet weather flow processes. Figure 2 shows an example of data and their evaluation. After wet weather flow processes. Figure 2 shows an example of data and their evaluation. After validation, validation, only 38.5% of the data was considered to have an acceptable quality during the condition required. This percentage of data perceived ‘good enough’ after validation may seem relatively low.
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only 38.5% of the data was considered to have an acceptable quality during the condition required. During earlier research (2007–2008) at WWTP UV-VIS thelow. percentage This percentage of dataprojects perceived ‘good enough’ afterEindhoven validationon may seem sensors, relatively During of ‘good enough’ data after data validation ranged between 50% and 75%, despite very intensive earlier research projects (2007–2008) at WWTP Eindhoven on UV-VIS sensors, the percentage of ‘good maintenance and data surveillance [23] and between without 50% restrictions the influent conditions. WWTP enough’ data after validation ranged and 75%,ondespite very intensive maintenance influent has shown be without a very difficult medium waterconditions. quality monitoring. The dataset after and surveillance [23]toand restrictions on thefor influent WWTP influent has shown validation comprises approximately 30 storm events with good data for each calibration performed. to be a very difficult medium for water quality monitoring. The dataset after validation comprises In the model calibration, thesewith events, the antecedent dry day and following dry approximately 30 storm events goodincluding data for each calibration performed. Inseveral the model calibration, days, were used. In Figure 2, and all other Figures, the datafollowing used for calibration is represented by the these events, including the antecedent dry day and several dry days, were used. In Figure 2, dark grey bullets, data not used for calibration with light grey bullets. An assessment of routine h and all other Figures, the data used for calibration is represented by the dark grey bullets, data24 not water quality samples of WWTP influent showed that the DWF does not show a noticeable seasonal used for calibration with light grey bullets. An assessment of routine 24 h water quality samples of pattern. WWTP influent showed that the DWF does not show a noticeable seasonal pattern.
Figure 2. Example of quality evaluation of monitoring data.
2.3. Data 2.3. Data Analysis Analysis In earlier earlier work work [16], [16], a a part part of of this this data data set set was was used used to to study study the the dynamics dynamics of of wastewater wastewater In composition. Thisresulted resulted in well described typical diurnal patterns during DWF and typical composition. This in well described typical diurnal patterns during DWF and typical dynamics dynamics during WWF (Figure 3). during WWF (Figure 3).
Figure 3. Wet weather flow flow (WWF) (WWF) dynamics dynamics during storm event 2008 in Figure 3. Wet weather during the the stages stages of of aa storm event on on 12 12 June June 2008 in Eindhoven Stad catchment. Eindhoven Stad catchment.
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For WWF, it has been observed that the concentration levels of the wastewater show a typical For WWF, beenevent: observed thatperiod the concentration levels of storm the wastewater show typical pattern duringitahas storm a short called ‘onset’ of the event, with an aincreased pattern during a storm event: a short period called ‘onset’ of the storm event, with an increased concentration level for particulate matter but not for dissolved matter, a longer period called concentration level dilution for particulate matter but notand for dissolved periodand called ‘dilution’,a ‘dilution’, where of both dissolved particulatematter, mattera longer takes place, ‘recovery’, where of both dissolved and particulate matterreturn takes to place, ‘recovery’, a period where perioddilution where dissolved and particulate matter slowly DWFand levels. dissolved and particulate matter slowly return to DWF levels. 2.4. Model Development 2.4. Model Development The general idea behind the model development is that the measured hydraulic influent data, The idealevel behind theinfluent model pumping development is that measured hydraulic influent data, i.e., flowgeneral and water in the station, canthe be used to make a distinction between i.e., waterDWF, level onset in theof influent station,WWF can be used to make a distinction between theflow four and patterns: WWF, pumping dilution during and recovery after WWF. Each of these the four patterns: DWF, onset of WWF, dilution during WWF and recovery after WWF. Each of these patterns is denoted as a system state, during which a certain relation between flow and concentration patterns is denoted as a system state, during which a certain relation between flow and concentration level applies. This allows the incorporation of the contribution of in-sewer stocks on top of the mixing level applies. This allows the incorporation of the The contribution in-sewer stocks of the mixing process between wastewater and stormwater. latter is of a common featureonoftop influent models process between wastewater and stormwater. The latter is a common feature of influent models applied applied to simulate both dry and wet periods, while explicitly accounting for the contribution of intosewer simulate both dry and wetthe periods, while explicitly accounting for the of in-sewer stocks circumventing relatively limited knowledge associated incontribution sewer processes. stocksThe circumventing theaverage relatively knowledge associated in core sewer water quality drylimited weather diurnal pattern is the ofprocesses. the model. As long as the The water quality average dry weather diurnal pattern is the core of the model. Asdata longisasused, the system state is ‘DWF’, the average dry weather diurnal pattern based on monitoring system state is the ‘DWF’, the average dry weather diurnal based on monitoring used, together with measured flow data. The average drypattern weather diurnal pattern has data beenisderived together with the measured flow data. The average dry weather diurnal pattern has been derived from flow monitoring data by averaging the monitoring data of 10 dry days over 5 min intervalsfrom with flow monitoring data by averaging the monitoring data of 10 dry days over 5 min intervals with the the same timestamp. same timestamp. During wet weather, the model superimposes a number of processes on the DWF pattern for During wet the model superimposes a number on(NH the 4DWF pattern water quality to weather, mimic onset, dilution, and recovery. The typeofofprocesses parameter or COD) andfor the water quality to mimic onset, dilution, and recovery. The type of parameter (NH or COD) and the 4 applied. The type type of event (small, medium or large) determine which of these processes is to be type of event (small, medium or large) determine of these processes to be applied. of event is used as characteristic of a storm event,which as it was found that the is relation betweenThe flowtype and ofconcentration event is used levels as characteristic of a storm event, as it was found that the relation between flow and differs very much between small, medium, and large storm events. The concentration levels differs very much andinfluent large storm events.station, The measured measured hydraulics, in this case thebetween flow andsmall, watermedium, level in the pumping are used hydraulics, in this case the flow and water level in the influent pumping station, are used to determine to determine which of the described processes should be activated in the model, using the scheme of which Figureof4.the described processes should be activated in the model, using the scheme of Figure 4. yes
DWF, process 1 no yes
DWF, process 1 no
∩
yes small event, process 6 dilution and restoration
no
∩
yes
medium event, process 2 dilution, process 3 dilution during onset, process 5 first flush during onset (for COD only) and process 4 recovery
no
yes
large event, process 2 dilution, process 3 dilution during onset, process 5 first flush during onset (for COD only) and process 4 recovery
Figure 4. Selection of water quality processes to be superimposed on process 1 during dry weather Figure 4. Selection of water quality processes to be superimposed on process 1 during dry weather (DWF), using information on hydraulics. The abbreviation Th in the figure is short for threshold. (DWF), using information on hydraulics. The abbreviation Th in the figure is short for threshold.
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As indicated in Figure 4, two conditions have to be met to change from DWF to WWF. The first is that the upper limit for dry weather conditions (QDWF , set at the 95th percentile of the flow values collected during dry weather at a specific timestamp) has to be exceeded, the second that the volume should exceed a certain threshold (set at 5000 m3 ). The second condition is added to exclude apparent events in the data caused by interference of the pump operation due to for example to maintenance. The value of 5000 m3 , equivalent to the volume of 2 h of DWF, shown to be sufficient to filter flow values exceeding QDWF due to operational issues during DWF. A small storm event is defined as an event for which the water level in the influent chamber does not rise above the DWF threshold value (set at 11.30 m AD) and the flow exceeds the 95 percentile DWF value with less than a threshold set at 4000 m3 /h These events are very small storm events, where the inflow is less than 0.2 mm/h or 2 m3 /ha). Medium events are defined as events where the water level in the influent chamber does not exceed the DWF threshold value, but the flow exceeds the 95 percentile DWF value with more than the threshold. These events are typically relatively small, low intensity storm events, where the inflow is less than the available pumping capacity (which is equal to an interceptor capacity of 0.7 mm/h or 7 m3 /ha). Large storm events are defined as events during which not only flow increases, but also the water level in the influent pumping station increases above the DWF threshold value. This occurs only if the sewer system starts filling during bigger storm events exceeding the pumping capacity of the WWTP. The processes applied in the model are: Process 1 the basic process for all parameters, is the DWF pattern for water quality. It is derived from high-frequency monitoring data collected during multiple dry weather days, by averaging over the same time stamps. Process 2 mimics dilution and is based on the ratio between the actual flow (Qactual ) and the upper limit for the flow during DWF at that time of the day at the location of the WWTP inlet works (QDWF ). The wastewater concentration is calculated using Formula (1): CWWF (t) = CDWF (t) (a1 QDWF (t)/Qactual (t) − a1 + 1)
(1)
With CWWF = calculated concentration during wet weather, and CDWF = the concentration during DWF conditions at that time of the day. The dilution factor a1 (-) is introduced to allow adjustment to the dilution rate if necessary. A value of 1 for factor a1 indicates that the dilution is exactly inverse to the increase in flow. A value of a1 smaller than 1 would impose an increase in pollutant loads during the event, which could be necessary to account for pollutant contributions originating from in-sewer stocks. A value of a1 larger than 1 would impose a decrease in pollutant loads during the event, which could be expected for a compound where in-sewer stocks are zero and a part of the pollutants would be discharged via a CSO. For low dilution ratios, i.e., QDWF (t)/Qactual (t) being close to 1, the factor a1 has a limited influence, for higher dilution ratios, the factor a1 contributes to a larger extent. Process 3 accounts for dilution during the onset of storm events. Process 3 is described by a parabolic function, valid for the period between the start of the storm event and the moment of the maximum dilution. The length of this period, the duration of the onset a3 , is determined during model calibration. This process is necessary to account for the delayed dilution observed in the monitoring data, see Figure 5. During the first part of the event on 28 July 2012, the influent flow increased rapidly to the maximum flow rate of 14,000 m3 /h, while the NH4 concentration gradually reduced to a minimum of 5 mg NH4 /l. Using Formula (1) during the onset of the storm event, would result in an overestimation of the dilution. Instead, Formula (3) applies during the onset of the storm event: CWWF (t) = CDWF (t) × (dilution depth/a2 2 ) × (t − tend onset )2 - dilution depth + 1
(2)
where a2 = duration of onset and dilution depth = the minimal ratio CDWF (t)/CWWF (t) during the onset of the storm event. Figure 5 shows how the parameters in the parabolic function of Formula (2) are defined.
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Figure 5. Parameters of parabolic function that describes the delayed dilution of the quality Figure 5. Parameters of parabolic function that describes the delayed dilution of the quality parameters parameters compared tocompared the flow. to the flow.
Process 4 reproduces restoration, which describes the gradual return of concentration values to Process 4 reproduces restoration, which describes the gradual return of concentration values to DWF values after the storm event. Based on the analysis of the available data set, restoration can be DWF values after the storm event. Based on the analysis of the available data set, restoration can be assumed to be a linear process at rate a3 (mg/(L·s)) until the concentration returns to the DWF value. assumed to be a linear process at rate a3 (mg/(L·s)) until the concentration returns to the DWF value. During the restoration phase, the concentration is calculated by: During the restoration phase, the concentration is calculated by: CWWF(t + 1) = CWWF(t) (1 + a3) dt. (3) CWWF (t + 1) = CWWF (t) (1 + a3 ) dt. (3) Process 5 describes a first flush in concentration levels of particulate material (see Figure 3), it is thus not valid for soluble substances. This initial peak increases the concentrations during the first Process 5 describes a first flush in concentration levels of particulate material (see Figure 3), it stage of storm events, before dilution becomes the dominant process. Process 5 is modeled as a is thus not valid for soluble substances. This initial peak increases the concentrations during the triangle that causes an instant increase of the COD concentration of a4 mg/l at the onset of the event, first stage of storm events, before dilution becomes the dominant process. Process 5 is modeled as a decreasing with a fixed rate a5 (mg/(L·s)). triangle that causes an instant increase of the COD concentration of a4 mg/l at the onset of the event, Process 6 regards dilution and restoration for small events. Process 6 describes the concentration decreasing with a fixed rate a5 (mg/(L·s)). profile as a fixed-shape triangle, where dilution takes place at a fixed rate a6 (mg/(L·s)) during x h and Process 6 regards dilution and restoration for small events. Process 6 describes the concentration recovery at the same rate a6 (mg/L/s) during the next x h. In the case of Eindhoven Stad and Riool profile as a fixed-shape triangle, where dilution takes place at a fixed rate a6 (mg/(L·s)) during x h and Zuid a duration of 13 h proved to be a good estimate of the duration of process 6. recovery at the same rate a6 (mg/L/s) during the next x h. In the case of Eindhoven Stad and Riool Zuid a duration of 13 h proved to be a good estimate of the duration of process 6. 2.5. Model Calibration 2.5. Model In thisCalibration study the differential evolution adaptive metropolis (DREAM) algorithm is the method [30,31] applied to calibrate the parameters of the empirical model to(DREAM) find the minimal difference In this study the differential evolution adaptive metropolis algorithm is the between the empirical model output and the monitoring data. The effectiveness of DREAM in water method [30,31] applied to calibrate the parameters of the empirical model to find the minimal difference related model calibration has output been demonstrated in manydata. previous studies, e.g.,of [32–34]. between the empirical model and the monitoring The effectiveness DREAM in water Table 1 shows the model parameters, units and the searching range for the calibration related model calibration has been demonstrated in many previous studies, e.g., [32–34]. procedure. The threshold values selecting the type of and event derived during data analysis procedure. before the Table 1 shows the for model parameters, units thewere searching range for the calibration calibration of the model and were consequently not included theanalysis model calibration. The threshold values for parameters selecting the type of event were derived during in data before the Future users of the model on other catchments may include these parameters as part ofcalibration. the model calibration of the model parameters and were consequently not included in the model calibration. of clarity, these parameters listed here: Future usersFor of reasons the model on other catchments mayare include these parameters as part of the model V Th: threshold value for making distinction between real storm events and irregularities in the calibration. For reasons of clarity, these parameters are listed here: DWFVdue to operational issues. In this study set at equivalent of 2 h of DWF. Th : threshold value for making distinction between real storm events and irregularities in the Th: threshold value to distinguish medium from small storm events. Set in this study at an DWFQdue to operational issues. In this study set at equivalent of 2 h of DWF. equivalent of 0.2 mm/h of runoff. QTh : threshold value to distinguish medium from small storm events. Set in this study at an h Th: threshold value to distinguish large from medium storm events. Set in this study at 0.30 m equivalent of 0.2 mm/h of runoff. above the setpoint of the frequency controlled pumps. hTh : threshold value to distinguish large from medium storm events. Set in this study at 0.30 m x: duration of dilution and restoration for small events: Set in this study at 13 h. above the setpoint of the frequency controlled pumps. x: duration of dilution and restoration for small events: Set in this study at 13 h.
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Table 1. Model parameters, units, and search range. COD = chemical oxygen demand. Model Parameter
Abbreviation
Unit
Search Range
dilution factor a1 0–2 dilution delay factor a2 minutes 0–600 recovery factor a3 mg/(L·s) 0–0.01 Water 2017, 9, 491 peak first flush concentration a4 mg/l 0–2000 recovery factor first flush a mg/(L·s) 0–10 Table 1. Model parameters, 5units, and search range. COD = chemical oxygen demand. recovery factor small events a6 mg/(L·s) 0–0.01
Parameter NH4 , COD NH4 , COD NH4 , COD 8 of 18 COD COD NH4 , COD
Abbreviation Unit Search Range Parameter Model Parameter dilution factor a1 0–2 NH4, COD delay factor a2 minutes 0–600 4, COD The calibration isdilution performed using 5000 iterations in DREAM for the CODNH model and 2500 for the recovery factor a3 mg/(L·s) 0–0.01 NH4, COD NH4 model, as it peak wasfirst found from test runs that the cumulative density functions of the parameters mg/l 0–2000 COD flush concentration a4 0–10 iterations. COD recovery first flush stability)a5after a mg/(L·s) do not change (within thefactor parameter few thousand The last 50% of the recovery factor small events a6 mg/(L·s) 0–0.01 NH4, COD
iterations are used for further analysis: the optimal parameter set and model output are derived, and the model is run all these parameter determine the 95% confidence intervals Thewith calibration is performed usingsets 5000to iterations in DREAM for the COD model and 2500 for for the NH4 the NH4 model, as it was found from test runs that the cumulative density functions of the parameters and COD concentrations. do not change (within the parameter stability) after a few thousand iterations. The last 50% of the are used for further analysis: the optimal parameter set and model output are derived, and 3. Results iterations and Discussion the model is run with all these parameter sets to determine the 95% confidence intervals for the NH4
This section an overview of the model results, a discussion of their quality and the and CODpresents concentrations. transferability of the model concept. The model was first developed, tested and calibrated on data of 3. Results and Discussion Eindhoven Stad only and the data from the subcatchment Riool Zuid were used to be able to discuss This section presents an overview of the model results, a discussion of their quality and the the transferability of the concept. 3.1.
transferability of the model concept. The model was first developed, tested and calibrated on data of Eindhoven Stad only and the data from the subcatchment Riool Zuid were used to be able to discuss Calibration Results the transferability of the concept.
The DREAM algorithm was applied with a total of 5000 iterations for the COD model and 2500 3.1. Calibration Results for the NH4 model. The algorithm uses 2 × n Markov Chains, with n being the number of model The DREAM algorithm was applied with a total of 5000 iterations for the COD model and 2500 parametersforbeing evaluated. This resulted in 312 iterations for the COD model and 208 iterations for the NH4 model. The algorithm uses 2 × n Markov Chains, with n being the number of model the NH4 model. Figure 6 shows theThis variation model parameter values during theiterations calibration parameters being evaluated. resulted in in 312 iterations for the COD model and 208 for process the NH Figure 6 shows the variation inStad model during the calibration for the model for4 model. NH4 for catchment Eindhoven forparameter the firstvalues Markov Chain of each iteration. for the model for NH 4 for catchment Eindhoven Stad for the first Markov Chain of each Parametersprocess concerning medium and large storm events are denoted in Figure 6 as subscripts M and iteration. Parameters concerning medium and large storm events are denoted in Figure 6 as respectively. The value of each of the model parameters is relatively stable during the calibration L subscripts M and L respectively. The value of each of the model parameters is relatively stable during process, showing that the number of that iterations wasofsufficient to converge. the calibration process, showing the number iterations was sufficient to converge.
Figure 6. Parameter values during model calibration. For each iteration, only the first Markov Chain
Figure 6. Parameter values during model calibration. For each iteration, only the first Markov Chain of of the parameter set is shown. the parameter set is shown. The correlation between the model parameters was found to be limited from Figure 7, showing a high identifiability of the model parameters.
The correlation between the model parameters was found to be limited from Figure 7, showing a high identifiability of the model parameters.
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Figure 7. 7. Posterior Posterior distribution distribution of of model model parameters parameters a11 to a66 for the NH44 model for catchment Eindhoven Stad based on the second 50% of the the iterations. iterations. The histograms represent the posterior distribution ofindividual individualmodel model parameters the scatter represent the relationships for distribution of parameters andand the scatter plots plots represent the relationships for various combinations of parameters. various combinations of parameters.
The model parameter parameter values values are are shown shown in in Table Table 22 for for the theNH NH4 and and COD COD model. model. For For the the NH NH4 The model 4 4 model, there there is is no no strong need to to make and medium storms, as as the model, strong need make aa distinction distinction between between large large and medium storms, the model model parameters are are rather rather similar. similar. For For COD, COD, however, the model model parameters parameters differ differ strongly strongly for for large large and and parameters however, the medium storm events. A value of 1 of the dilution factor would mean no contribution of in-sewer medium storm events. A value of 1 of the dilution factor would mean no contribution of in-sewer stocks and and only values below below 11 would of in-sewer in-sewer stocks. stocks. The stocks only perfect perfect dilution, dilution, values would indicate indicate aa contribution contribution of The values for the dilution factor for NH 4 are just below 1, indicating that for NH4 the contribution of in values for the dilution factor for NH4 are just below 1, indicating that for NH4 the contribution of sewer stocks is relatively limited. ForFor thethe COD, however, thethe values of aof 1 are quite low. A value for in sewer stocks is relatively limited. COD, however, values a1 are quite low. A value a 1 of approximately 0.5 leads to CWWF = 0.57 × CDWF based on Formula (1) and the maximum ratio for a1 of approximately 0.5 leads to CWWF = 0.57 × CDWF based on Formula (1) and the maximum between Qactual Q and QDWF (15,000/2100 = 7.1). This means that at a flow of 15,000 m3/h, the concentration 3 ratio between actual and QDWF (15,000/2100 = 7.1). This means that at a flow of 15,000 m /h, the in the WWTP in influent is stillinfluent 0.57 × Cis DWF. Consequently, the influent load at that moment will be concentration the WWTP still 0.57 × CDWF . Consequently, the influent load at that approximately 4 (7.1 × 0.57) times the DWFtimes load.the This peak loadThis factor was observed regularly in moment will be approximately 4 (7.1 × 0.57) DWF load. peak load factor was observed monitoring data for this catchment [23]. regularly in monitoring data for this catchment [23]. Table 2. 2. Model Model parameters parameters values values for for NH NH4 and COD model for Eindhoven Stad Catchment. Subscript Table 4 and COD model for Eindhoven Stad Catchment. Subscript M and L in model parameters denote medium and large storm events. M and L in model parameters denote medium and large storm events. Abbreviation NH4 Model Model Parameter Model Parameter Abbreviation NH4 Model dilution factor, large storms a1,L 0.95 (-) dilution factor, largelarge storms a1,L 0.95 dilution delay factor, storms a2,L 123 (-) (min) dilution delay factor, large storms a2,L 123 (min) 0.82 (-) dilution factor, medium storms a1,M dilution factor, medium storms a1,M 0.82 (-) dilution factor,medium medium storms a2,M 115 (min) dilution delay delay factor, storms a2,M 115 (min) 0.00025 (mg/(L·s)) recoveryfactor factor recovery a3 a3 0.00025 (mg/(L ·s)) peak first a4 a4 Not Notapplicable applicable peak firstflush flushconcentration concentration recovery factor flush a5 a5 Not recovery factorfirst first flush Notapplicable applicable recovery factor small events a6 0.00059 (mg/(L·s)) 0.00059 (mg/(L·s)) recovery factor small events a6
COD Model 0.63 (-) 0.63(min) (-) 342 342 (min) 0.47 (-) 0.47 (-) 589 (min) 589 (min) 0.00014(mg/(L (mg/(L·s)) 0.00014 ·s)) 48 ·s)) 48(mg (mgCOD/(L COD/(L·s)) 0.19 ·s)) 0.19(mg (mgCOD/(L COD/(L·s)) 0.00017 (mg/(L·s)) 0.00017 (mg/(L·s)) COD Model
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3.2. Model Results 3.2. Model Model Results Results 3.2. Figure 8 shows the resulting predicted water quality and the measured water quality for NH4 in Figureinfluent showsfor theEindhoven resulting predicted predicted waterquality qualityand andthe the measured measuredwater waterquality qualityfor forNH NH4 in in the WWTP Stad. Figure 88 shows the resulting water 4 the WWTP influent for Eindhoven Stad. the WWTP influent for Eindhoven Stad.
Figure 8. Model vs. monitoring data: NH4 concentration in the wastewater treatment plant (WWTP) Figure Modelvs.vs. monitoring NH4 concentration in the wastewater treatment plant Figure 8. Model monitoring data:data: NH4 concentration in the wastewater treatment plant (WWTP) influent. (WWTP) influent. influent.
The results show that the dynamics in the model (solid black line) and the monitoring data (grey The results show that that the the dynamicsinin interms the model model (solid black black line) and and the monitoring monitoring data (grey results show dynamics the (solid the data (grey dots)The show an overall good agreement of dynamics and line) values during wet weather during dots) show an overall overall good agreement in terms of of dynamics dynamics and values values during wet weather during dots) show an good terms and wet weather the large events of 28 and 29agreement July. In thein monitoring data, dilution starts aduring little bit earlier thanduring in the the large events of 28 and 29 July. In the monitoring data, dilution starts a little bit earlier than in (25 the the large eventsthe of medium 28 and 29 July.on In31 the monitoring starts aDuring little bitdry earlier than in model. During event July, the modeldata, fit isdilution less satisfying. weather model. During the medium event on 31 July, the model fit is less satisfying. During dry weather (25 the model. During medium event on 31 July, the concentration model fit is less During dry weather July till 28 July), thethe daily variation in the measured of satisfying. NH4 is represented well by the JulyJuly tillThe 28 28 July), thethe daily variation inin the by the the (25 till July), daily variation themeasured concentration ofNH NH44isisrepresented represented well by model. remaining differences are due tomeasured the fact concentration that the DWF of dynamics in the modelwell represent model. The remaining differences are due to the fact that the DWF dynamics in the model represent model. The remaining differences levels are dueand to the thatvaries the DWF themean modelsquared represent the the average DWF concentration thefact DWF per dynamics day. The in root error the average DWF and the DWF varies perThe day. rootsquared mean squared error average DWF concentration levelslevels andthe the DWF varies percalibration day. root mean error (RMSE) (RMSE) for the NHconcentration 4 model based on data used in the isThe 6.3 mg NH 4/l, or nearly 16% (RMSE) the NHbased 4 model based on the data used in the calibration is 6.3 mg NH4/l, or nearly 16% for the NH the data used in the9calibration 6.3 mg NHcumulative 16% related to related tofor the mean DWF on concentration. Figure shows the is normalized density function 4 model 4 /l, or nearly related to the mean DWF concentration. Figurethe 9 shows the4normalized cumulative density function the mean DWF concentration. 9 shows normalized cumulative density function of (CDF) of the model results andFigure the monitoring data for NH and COD. Both the RMSE and (CDF) the CDF (CDF) of the model results and used the monitoring dataand for COD. NHincludes 4 and COD. Both the RMSE and the CDF the model results and the monitoring datamodelling, for NH Both the the with CDF are based are based on the entire dataset for allRMSE stormand events sufficient 4 which are based on the entire dataset used for modelling, which includes all storm events with sufficient on thequality entire dataset modelling, which allthe storm events withAs sufficient data quality data and theused dry for days preceding and includes following storm event. expected, the high datathe quality and the dry and following the expected, the high and dry days preceding andpreceding following thenot storm event. Asstorm expected, high concentrations, concentrations, which occurdays during DWF, are captured very wellevent. due the toAs the daily variation in concentrations, which occur during DWF, are not captured very well due to the daily variation in which occur during DWF, are not captured very well due to the daily variation in DWF concentrations. DWF concentrations. At lower concentration levels, the agreement between model and monitoring DWF concentrations. At lower concentration levels, the agreement between model and monitoring At lower concentration levels, the agreement between model and monitoring data is reasonable. data is reasonable. data is reasonable.
Figure 9. CDFs Figure 9. CDFs of of model model results results and and measurements measurements for for NH NH44 and and COD COD in in WWTP WWTP influent influent for for the the Figure 9. CDFs of model results and measurements for NH4 and COD in WWTP influent for the Eindhoven Stad (ES) catchment. Eindhoven Stad (ES) catchment. Eindhoven Stad (ES) catchment.
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The COD CODmodel modelalso alsoincorporates incorporates process process 55describing describing the the peak peak first firstflush flushconcentration concentrationthat that The wasobserved observed in inthe themonitoring monitoringdata, data,see seeFigure Figure3.3. The The model model results results for for the the COD COD model model for for the the was Eindhoven Stad catchment are shown in Figure 10. As expected, the model fit is not as good as the Eindhoven Stad catchment are shown in Figure 10. As expected, the model fit is not as good as the modelfitfitforfor NH 4, which is partly due the difference in theofquality of the monitoring data, model NH is partly due to theto difference in the quality the monitoring data, illustrated 4 , which illustrated by the outliers in the monitoring shown10inand Figure 10 due and to partly duethat to the fact that by the outliers in the monitoring data showndata in Figure partly the fact modelling modelling suspended solids is much morethan difficult than modelling solutes. Thefor RMSE for the COD suspended solids is much more difficult modelling of solutes.ofThe RMSE the COD model modelon based on monitoring data in the calibration is 109 mg COD/l, equivalent with of the based monitoring data used in used the calibration is 109 mg COD/l, equivalent with 18% of18% the mean meanconcentration. DWF concentration. This RMSE forisCOD is in relative terms comparable to the RMSE DWF This RMSE for COD in relative terms comparable to the RMSE for NHfor 4 . NH4.
Figure 10. Model vs. monitoring data: CODtotal in the WWTP influent for Eindhoven Stad. The small Figure 10. Model vs. monitoring data: CODtotal in the WWTP influent for Eindhoven Stad. The small peaks in influent concentration (typically referred to as ‘first flush’) at the beginning of storm events peaks in influent concentration (typically referred to as ‘first flush’) at the beginning of storm events on on 4 June, 6 June and 8 June are adequately represented by the model. 4 June, 6 June and 8 June are adequately represented by the model.
The influent model has been developed to be used to deliver input for WWTP models that is The influenttomodel beenperformance developed to beto used to deliver input for WWTPsuch models that is reliable enough assesshas WWTP and assess the impact of measures, as real time reliable enough to assess WWTP performance and to assess the impact of measures, such as real control (RTC) in wastewater systems. An earlier version of this influent model presented has already time (RTC) in wastewater systems. An earlieratversion of thisDe influent model presented has beencontrol used for this purpose in the KALLISTO project water board Dommel [26,28]. The current already used for this assessment purpose in of thethe KALLISTO project at water Dommel version been is applied in the performance of the smartboard bufferDeconcept at [26,28]. WWTP The current version is applied in the assessment of the performance of the smart buffer concept at Eindhoven [29]. The values for the RMSE for NH4 just meet the quality requirements for WWTP WWTP [29]. RMSE NHmeet meetrequirements. the quality requirements for 4 justthese influentEindhoven data derived byThe [35],values while for for the COD they for easily This shows that WWTP influent data derived by [35], while for COD they easily meet these requirements. This shows the influent model is sufficiently good for the described modelling purposes. that the influent model is sufficiently good for the described modelling purposes. 3.3. Transferability of the Concept 3.3. Transferability of the Concept The structure of the influent model was developed for the catchment Eindhoven Stad (ES) only. The structure of the influent model was developed for the catchment Eindhoven Stad (ES) only. The data from the catchment Riool Zuid (RZ) were used to verify the concept, using the same routines The data from the catchment Riool Zuid (RZ) were used to verify the concept, using the same routines for calibration. With respect to the transferability, it has to be noted that the subcatchments ES and for calibration. With respect to the transferability, it has to be noted that the subcatchments ES and RZ RZ are independent catchments, allowing the transferability of the concept to be tested. are independent catchments, allowing the transferability of the concept to be tested. The model parameters are shown in Table 3. For catchment RZ, the model parameters for The model parameters are shown in Table 3. For catchment RZ, the model parameters for medium medium and large storms are very similar for both the NH4 and COD model, showing that this and large storms are very similar for both the NH4 and COD model, showing that this distinction distinction between large and medium events is not necessary for this catchment. The model between large and medium events is not necessary for this catchment. The model parameter values for parameter values for the dilution factor a1 for the RZ catchment show a strong similarity with the the dilution factor a1 for the RZ catchment show a strong similarity with the model parameters for the model parameters for the ES catchment. For NH4, the dilution during the storm event, calculated by ES catchment. For NH4 , the dilution during the storm event, calculated by Formula (1), remains nearly Formula (1), remains nearly reciprocal to the increase in influent flow during the storm event. This reciprocal to the increase in influent flow during the storm event. This indicates that during the storm indicates that during the storm event, nearly all nitrogen in the WWTP influent stems from the event, nearly all nitrogen in the WWTP influent stems from the wastewater, with only very limited wastewater, with only very limited contributions from the rainfall runoff and the in-sewer stocks. contributions from the rainfall runoff and the in-sewer stocks.
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Table 3. Model parameters values for NH4 and COD model for Riool Zuid Catchment. Subscript M and L in model parameters denote medium and large storm events. Table 3. Model parameters values for NH4 and COD model for Riool Zuid Catchment. Subscript M and LModel in model parameters denote Abbreviation medium and large stormNH events. Parameter 4 Model COD Model dilution factor, large storms Model Parameter dilution delay factor, large storms dilution factor, medium storms dilution factor, large storms dilutiondelay delay factor, factor, large storms dilution medium dilution factor, medium storms storms dilution delay factor, medium storms recovery factor recovery factor peak first flush concentration peak first flush concentration recovery factorfirst firstflush flush recovery factor recovery factor small events recovery factor small events
a1,L Abbreviation a2,L
a1,Ma1,L a2,L a2,Ma1,M a2,M a3 a 3 a 4 a4 a5 a5 a6 a6
0.96 (-) NH4(min) Model 373 0.98 0.96(-) (-) 373 (min) 4270.98 (min) (-) 427 (min) 0.00033 0.00033(mg/(L·s)) (mg/(L·s)) Not Notapplicable applicable Notapplicable applicable Not 0.00027 (mg/(L·s)) 0.00027 (mg/(L·s))
0.49 (-) COD 590Model (min)
0.49 0.49 (-)(-) 590 (min) 548 (-) (min) 0.49 548 (min) 0.00034 (mg/(L·s)) 0.00034 (mg/(L ·s)) (mg COD/(L·s)) 6060(mg COD/(L ·s)) 0.06 COD/(L ·s)) 0.06(mg (mg COD/(L·s)) 0.00002 (mg/(L · s)) 0.00002 (mg/(L·s))
For the COD, the dilution factor of a11 of of 0.49 0.49 results results in in COD COD concentration concentration levels during the high flow period of storm events of between 250 and 300 300 mg mg COD/L COD/L and, and, as as aa consequence, consequence, high influent peak loads. loads.This Thisadditional additional load arriving viainfluent the influent at the WWTP a storm event load arriving via the at the WWTP during aduring storm event originates originates mainly from the in-sewer stocks [15], given the fairly low COD concentration in Dutch mainly from the in-sewer stocks [15], given the fairly low COD concentration in Dutch stormwater of stormwater of 61 mg COD/L [36]. 61 mg COD/L [36]. The overall overallmodel model performance for RZ thecatchment, RZ catchment, expressed terms is ofcomparable RMSE, is performance for the expressed in terms in of RMSE, comparable with the performance for the ES catchment. The RMSE amounts to 8.9 mg NH 4/L, with the performance for the ES catchment. The RMSE amounts to 8.9 mg NH4 /L, equivalent with equivalent with 22% ofvalue the mean DWF forand the to NH 4 model and to 126 mg COD/L, 22% of the mean DWF for the NHvalue 126 mg COD/L, equivalent with equivalent 25% of the 4 model with 25% of the mean DWF value for the COD model. As for Eindhoven Stad, the cumulative density mean DWF value for the COD model. As for Eindhoven Stad, the cumulative density function for function for model results and monitoring data show reasonable agreement for both NH 4 and COD, model results and monitoring data show reasonable agreement for both NH4 and COD, see Figure 11, see 11, with again the biggest differences being in the higher (DWF) concentration ranges. withFigure once again theonce biggest differences being in the higher (DWF) concentration ranges.
4 and COD in WWTP influent for the Figure 11. CDFs CDFs of ofmodel modelresults resultsand and measurements measurements forfor NHNH COD in WWTP influent for the Riool 4 and Zuid (RZ) Riool Zuidcatchment. (RZ) catchment.
As need to to change change the the model model structure, structure, it As there there was was no no need it was was concluded concluded that that the the model model is is in in principle transferable to other catchments, provided that the dynamics during WWF show similar principle transferable to other catchments, provided that the dynamics during WWF show similar patterns described in Figure 3. 3. Literature patterns as as described in Figure Literature confirms confirms these these patterns patterns to to be be fairly fairly general general [37,38], [37,38], A A number of distinct phases in the influent pollutograph are defined during storm events: number of distinct phases in the influent pollutograph are defined during storm events: Phase 1) increase increaseofof flow rate and subsequently increase of the load arriving at the WWTP to Phase 1) flow rate and subsequently anan increase of the load arriving at the WWTP duedue to the the ‘push’ of wastewater with concentration DWF concentration levels. This phasedistinct is more the more ‘push’ of wastewater with DWF levels. This phase is more thedistinct more wastewater wastewater is stored downstream in either large interceptor sewers or rising mains. is stored downstream in either large interceptor sewers or rising mains. Phase increasedconcentration concentrationof ofsuspended suspendedsolids solids as as eroded eroded sewer sewer sediments sediments start start to to arrive arrive at Phase 2) 2) increased at the the WWTP. These sediments are usually transported with a velocity lower than the fluid velocity [14]. WWTP. These sediments are usually transported with a velocity lower than the fluid velocity [14]. Phase arrivalofofdiluted dilutedwastewater wastewateratatthe theWWTP. WWTP. Phase 3) 3) arrival Phase 4) return to DWF equilibrium. Equilibrium for dissolved compounds will be reached as soon as all remaining storm runoff has been transported (pumped) towards the WWTP. Reaching
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Phase 4) return to DWF equilibrium. Equilibrium for dissolved compounds will be reached as soon as all remaining storm runoff has been transported (pumped) towards the WWTP. Reaching equilibrium for suspended solids may last longer since it takes time before all depressions within the sewer system are filled again with sediment. Phases 1 and 2 are both part of the onset of the storm event, phase 3 is similar to the dilution stage, while phase 4 relates closely to the stage of recovery after the storm events. Despite the need of further research on the transferability, the similarities in system dynamics strongly indicate a wider applicability of the model then just for Eindhoven Stad and Riool Zuid. The consistency in the dilution factors for NH4 and COD for Eindhoven Stad and Riool Zuid (with dilution factors for NH4 just a little smaller than 1, indicating a small contribution of in-sewer stocks and dilution factors for COD around 0.5, indicating a large contribution of in-sewer stocks) demonstrate that the empirical model is able to capture the contribution of in-sewer stocks during the dilution phase of the event adequately. This is an important benefit of the model compared with influent generators reviewed by [7]. The differences in model parameters related to the first flush and recovery after the event seem to be linked to the differences in lay out of the sewer system. Future research is necessary to further elaborate on the relation between parameter values and physical characteristics of the catchment. The amount of in-sewer storage relative to the pumping capacity of the WWTP will likely be related to the length of the recovery period, as these characteristics determine the emptying time of the sewer system, which will be related to the length of the recovery. The differences in performance, although relatively small, can be attributed to the different characteristics of the RZ catchment and possibly also to the limited quality of the sensor data. This is illustrated by Figures 12 and 13. In Figure 12, the results for NH4 are shown for the RZ catchment for the week after 16 July and in Figure 13 for the first two weeks of December 2012. During the events of 17 July and 21 July, the monitoring data show two distinct dilution phases during the events. One dilution phase occurs at the beginning of the storm event and one at the end. This phenomenon does not occur during the storm events of 2 and 4 December, but to a lesser extent on 10 December. The Riool Zuid catchment (the light grey catchments in Figure 1, left) has a very different structure compared with ‘Eindhoven Stad’ (the dark colored central catchment in Figure 1, left). While the ES catchment is a gravity system draining to one central point, the RZ catchment is 32 km long with a number of subcatchments of various sizes at different distances. It is assumed that the double dip is caused by a difference in transport times for two main areas in this catchment, which causes the concentrations to drop for a second time during a storm event. The double dilution dip is of course driven by rainfall and as a result, the spatial variation in the rainfall is the main explanatory factor for the differences per event. In the model, this effect could be mimicked by dividing the Riool Zuid catchment into two catchment basins, with a cut at pumping station Aalst, see Figure 1 (left), and to add the transport time in the transport sewer to one of the basins. However, as the error made in the model results is relatively small due to the low influent flows, this adjustment was not considered necessary at this moment. The base line of the model consists of the mean DWF concentration. Data analysis of available 24 h composite samples of the WWTP influent showed that there was no seasonal trend for NH4 and COD. Despite the absence of a seasonal trend, the mean DWF concentration varied during the monitoring period. Due to a lack of sampling data, it could not be determined whether changes in this DWF concentration level were due to real changes or due to e.g., a temporary drift of the sensor. Differences in the main DWF concentration levels were observed for NH4 , e.g., compare the concentration levels on 16 July in Figure 12 (around 40 mg/L) and 1 December in Figure 13 (around 55 mg/L). This difference is even bigger for COD, see Figure 14. The mean DWF, derived from monitoring data, is nearly 500 mg COD/L, while the monitoring data on 2 June are nearly 700 mg COD/L. In this study, the model has been calibrated using the mean DWF derived from all available monitoring data during DWF.
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Figure 12. Model vs. monitoring data: NH Figure 12. Model concentration in theWWTP WWTPinfluent influentcatchment catchmentRiool-Zuid Riool-Zuid concentration in the WWTP influent catchment Riool-Zuid Figure 12. Model vs. monitoring data: NH concentrationin inthe the WWTP influent catchment Riool-Zuid Figure 12. Modelvs. vs.monitoring monitoringdata: data:NH NH4444concentration between 16 July and 23 July. ‘Double’ dilution dips at 17 July around noon and 18 July between 16 July and 23 July. ‘Double’ dilution dips occur July around noon and 18 July around between 16 July and 23 July. ‘Double’ dilution dips occur at 17 July around noon and 18 July around between 16 July and 23 July. ‘Double’ dilution dips occur at 17 July around noon and 18 Julyaround around midnight and on 21 July at 2:00 a.m. and 12:00 a.m. midnight and on 21 July at 2:00 a.m. and 12:00 a.m. midnight and on 21 July at 2:00 a.m. and 12:00 a.m. midnight and on 21 July at 2:00 a.m. and 12:00 a.m.
Figure 13. Model vs. monitoring data: NH Figure 13. Model concentration in theWWTP WWTPinfluent influentcatchment catchmentRiool-Zuid Riool-Zuid Figure 13. Model vs. monitoring data: NH concentration in the WWTP influent catchment Riool-Zuid Figure 13. Modelvs. vs.monitoring monitoringdata: data:NH NH4444concentration concentrationin inthe the WWTP influent catchment Riool-Zuid between 1 December and 15 December. between 1 December and 15 December. between 1 December and 15 December. between 1 December and 15 December.
Figure 14. Model vs. monitoring data: COD concentration Figure 14. Model vs. WWTP influentcatchment catchmentRiool-Zuid. Riool-Zuid. Figure 14. Model vs. monitoring data: COD in WWTP influent catchment Riool-Zuid. Figure 14. Model vs.monitoring monitoringdata: data:COD CODconcentration concentrationin inWWTP WWTPinfluent catchment Riool-Zuid.
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Finally, the results shown in this paper are based on NH4 and COD only, where NH4 is representative for solutes predominantly derived from wastewater and COD for parameters for which the in-sewer stocks, i.e., sediment and biofilm, contribute significantly to the pollutant load in the influent during storm events [24]. For WWTP modelling other parameters, such as phosphorous, also need to be taken into account. Total phosphorous is known to exert similar behavior as the COD and consequently, the COD model may be used to recalculate the total phosphorous concentration. Ortho-phosphate, on the other hand, is dissolved and behaves in the sewer like NH4 [37] and consequently, the NH4 model may be used. 3.4. Applications: Influent Generation, Surveillance of Monitoring Equipment and Gap Filling The influent model as described in this paper generates influent water quality dynamics using measured influent hydraulics as input. This application was used in [29] to evaluate the performance of integrated RTC for urban wastewater system Eindhoven. Another application of the influent model is described in [28], where (an earlier version of) the influent model was implemented in the WEST software [28] to generate influent water quality dynamics based on the simulated influent water quantity by the sewer sub model. In this application, a representative DWF curve based on monitoring data was used [28]. It would also have been possible to use harmonic functions for DWF and to use the influent model to complement the time series with WWF dynamics. In other words, the influent model can be applied on measured or simulated hydraulics and may also be applied in combination with the harmonic functions described in the introduction. Moreover, as the empirical influent model is developed to adequately mimic WWF dynamics, it might be included in the phenomenological influent pollutant disturbance scenario generator [9], which is the latest version of the phenomenological model developed by [8], replacing the relatively weak sewer model module of this model. The influent model can also be used for surveillance of monitoring equipment at the inlet of the WWTP. e.g., earlier research has shown that the hydraulic monitoring data at WWTP Eindhoven is very reliable with over 99% good data [23]. Running the influent model continuously on measured hydraulic data and comparing raw monitoring data of the influent water quality with the simulated influent water quality data would allow easy detection of anomalies in the monitoring data. This could be used to alarm operators to check the monitoring equipment. Early detection of problems with sensors will possibly result in a higher yield of good quality data. A final application of the influent model discussed in this paper is gap filling in time series [39]. Figure 15 shows an example of the application of gap filling. The dots show the measured NH4 concentration in the influent of WWTP Eindhoven. The dark grey dots are data that could be used e.g., for assessing the performance of the influent model, the light grey dots show data that are rejected during the validation. The black line shows the simulated concentrations by the influent model. By applying gap filling a continuous time series is generated, the final time series is composed of the dark grey dots and where these are missing data are filled in using the influent model results. For some of the potential applications of the model, such as gap filling or data validation, it is advisable to regularly check the absolute value of the sensor data during DWF to ascertain whether changes in the DWF concentration level are due to real changes or due to a sensor drift. In case these are due to e.g., seasonal variation in the influent concentration levels during DWF, this should be accounted for when applying the influent model. The routine 24-h samples typically available for WWTP influent may be used to check for a seasonal pattern.
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Figure Gap filling influent model. NH4 ininfluent WWTPcatchment influent in WWTP Figure 15. Gap filling withwith the the influent model. ExampleExample for NH4 for catchment Eindhoven. Eindhoven.
4. Conclusions Conclusions and and Outlook Outlook 4. Modelling of of influent influent quality quality is is an an increasingly increasingly important important tool tool to to enable enable WWTP WWTP models models to to Modelling optimize the the performance performance of of WWTPs WWTPs during during wet wet weather. weather. The The main main issue issue in in modelling modelling wastewater wastewater optimize quality during during storm storm events events is is to to account account for for in-sewer in-sewer stocks, stocks, which which have have aa varying varying contribution contribution to to quality the wastewater wastewater quality. quality. Neither traditional traditional sewer water water quality quality models models nor nor the the available available influent influent the generators are are capable capable of of adequately adequately addressing addressing this this issue. issue. The The proposed proposed empirical empirical model model is is based based generators on aa detailed detailed study study of of the the observed observed water water quality quality and and predicts predicts itit by by combining combining aa number number of of actual actual on processessuch suchas asDWF, DWF,dilution, dilution,restoration, restoration,and and first flush. Overall, model shows that is able processes first flush. Overall, thethe model shows that it isitable to to reasonably predict NH 4 concentration, which is a solute substance, as well as to reasonably predict reasonably predict NH4 concentration, which is a solute substance, as well as to reasonably predict COD concentration, concentration, which whichis is to toaalarge largeextent extentassociated associatedwith withparticles. particles. COD The model model structure structure was was demonstrated demonstrated to to be be transferable transferable to to aa catchment catchment with with different different The characteristics. Eindhoven Stad is a large catchment with the WWTP located near the center, characteristics. Eindhoven Stad is a large catchment with the WWTP located near the center, Riool Riool Zuid Zuid comprises of ainterceptor long interceptor the wastewater frommunicipalities seven municipalities comprises of a long sewer,sewer, which which drains drains the wastewater from seven with a with aofrange of catchment sizes. Due to variation spatial variation of the and rainfall and variation travel times, range catchment sizes. Due to spatial of the rainfall variation in travelin times, ‘double ‘double dilution’ may occur in thecoming influentfrom coming Zuid. Despite thesedynamics different dilution’ dips maydips occur in the influent Rioolfrom Zuid.Riool Despite these different dynamics and characteristics, there no need to adjust the model the empirical and characteristics, there was no needwas to adjust the model structure of thestructure empiricalofinfluent model. influent model. Future research in catchments in sewer systems with less in-sewer storage volume is Future research in catchments in sewer systems with less in-sewer storage volume is needed to further needed the to further explore of thethe transferability of the model concept. explore transferability model concept. The model modelconcept conceptisisused usedininongoing ongoingresearch researchtototest testthe the performance RTC smart buffers The performance of of RTC of of smart buffers at at WWTP Eindhoven [28]. The model concept could also be used to fill gaps in time series for influent WWTP Eindhoven [28]. The model concept could also be used to fill gaps in time series for influent water quality quality and and be be used used for for advanced advanced data data validation validation to to detect detect outliers outliers and and drift drift of of water water quality quality water sensors, as as these these sensors sensors are arestill stillvery veryvulnerable vulnerableand anddata dataquality qualitycontrol controlremains remainsaadifficult difficultissue. issue. sensors, Acknowledgments: project is funded KRW-innovation subsidy from AgentschapNL (www.agentschapnl. Acknowledgments: The The project is byfunded by KRW-innovation subsidy from AgentschapNL nl). The Dutch Foundation forDutch Applied Water Research (STOWA) engaged (STOWA) in the project to communicate and (www.agentschapnl.nl). The Foundation for Applied WaterisResearch is engaged in the project publish the research results. to communicate and publish the research results. Author Contributions: Jeroen Langeveld and Remy Schilperoort developed the influent model, Petra Van Daal Author Contributions: Jeroen Langeveld and Remy Schilperoort developed the influent model, Daal improved the model structure and performed the model calibration, while Tony Flameling and Petra StefanVan Weijers improved the model structure and of performed model calibration, while Tony Flameling and Stefan Weijers were involved in the development the modelthe and provision of data. Ingmar Nopens contributed to the gap filling. Jeroen Langeveld wrote the paper. were involved in the development of the model and provision of data. Ingmar Nopens contributed to the gap filling. Jeroen Langeveld thedeclare paper.no conflict of interest. Conflicts of Interest: The wrote authors
Conflicts of Interest: The authors declare no conflict of interest.
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