Real-time prediction of rain-impacted sewage flow for on-line control of chemical dosing in sewers
Graphical abstract
Introduction
Sewer networks are among the most critical urban infrastructures. They collect and transport domestic and industrial wastewater to wastewater treatment plants (WWTP) for treatment and disposal. Sewer systems are vulnerable to corrosion caused by hydrogen sulfide (H2S) generated in sewage under anaerobic conditions (Boon, 1995; Hvitved-Jacobsen et al., 2013). The emission of H2S and other odorous compounds also induce serious odour complaints and health hazards (Jiang et al., 2015).
To minimize the generation and emission of H2S in a whole network, a commonly used strategy is dosing of chemicals, such as oxygen (Gutierrez et al., 2008; Ochi et al., 1998), nitrate (Jiang et al., 2009; Yang et al., 2005), iron salts (Firer et al., 2008; Nielsen et al., 2005), and magnesium hydroxide (Mg(OH)2) (Gutierrez et al., 2009). The chemical dosing rate is critical to the sulfide control performance and the operational costs. The main dosing strategies include:
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Constant dosing with which the dosing rate is maintained at a constant value, without considering hydraulic or biological dynamics and variations of the wastewater characteristics.
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Flow-paced dosing, with the dosing rate proportional to the sewage flow rate.
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Profiled dosing, where the dosing rates are pre-defined in a profile which is established from empirical knowledge and typical hydraulic conditions (Ganigue et al., 2011). The dosing strategy may have satisfactory performance, when real conditions are similar to the designed ones. However, variable weather events induce changes to sewage hydraulics and characteristics, leading to non-optimal dosing.
Recently, an on-line control strategy of chemical dosing for sulfide mitigation was developed and applied to H2S control with Mg(OH)2 (Ganigué et al., 2016) and FeCl3 (Ganigué et al., 2018) dosing. One critical component of the control structures proposed was a feedforward controller that calculated the amount of Mg(OH)2 or FeCl3 required to balance acid or precipitate sulfide to be produced in the downstream pipes during sewage transport. As the acid/sulfide production mainly depends on the hydraulic retention time (HRT) of sewage in the pipe (Sharma et al., 2008a), the prediction of HRT is central for the control strategy (Sharma et al., 2008b). For a volume of sewage pumped into the pipe, it can be treated as a moving slug. The slug is pushed through the downstream pipe by the future sewage flow entering the sewer pipes. Due to this nature of sewage in sewers, the HRT of a sewage slug in the downstream pipe is unknown at the time when chemicals are dosed to the slug. Therefore, sewage flow has to be predicted several hours ahead in order to predict HRT of the current slug. The prediction horizon depends on the retention time of the slug in the pipe, generally in the order of hours.
An autoregressive model was developed for real-time prediction of future flow in sewers (Chen et al., 2014), which had been applied in the HRT-based on-line dosing control (Ganigué et al. 2016, 2018). The calibrated model could predict sewage flow up to six hours ahead with good accuracy during dry weather, providing critical inputs to the on-line controllers. The controller supported by the flow prediction reduced Mg(OH)2 consumption by 15% in comparison to flow-paced dosing strategy (Ganigué et al., 2016), and FeCl3 consumption by 31% (Ganigué et al., 2018) in real-sewer applications. In both cases, however, a delay of a few hours occurred between the real flows and predicted ones during wet weather. The delay was caused by the model not directly considering the rainfall in the catchment. Rainfall derived inflow and infiltration enter not only combined sewers, but also sanitary systems via cross-connection, defective pipes and joints, leaking manhole walls and covers or low disconnected traps (Butler and Davies, 2004). The additional flow shortens sewage HRT in the network, which affects the amount of chemicals required. Also, concentration of the chemical dosed is dramatically diluted by the increased flow. Both factors contribute to poorer control performance of sulfide in sewers (Jiang et al., 2013). Therefore, a methodology for flow prediction directly considering the impact of rainfalls is of great importance for the optimization of sulfide mitigation.
To develop a model for predicting the rain-impacted sewage flow, in a review of hydrological forecasting methods (O'Connell and Clarke, 1981), it was highlighted that a predicting model should be able to reflect the recently observed state, to provide immediate response to the time-varying series, and to compute efficiently. Bidwell (1971) predicted the stream flow out of a catchment, by considering the catchment as a discrete non-linear system with rainfall as the input. A certain memory period of rainfall values was determined by stepwise multiple regression. However, this method had low ability in accounting for evaporation, and caused over-estimation during long dry periods. In a study of hydrological runoff, the surface runoff and rainfall derived infiltration were separated based on unit hydrograph through ARMA (autoregressive moving average) transfer function modelling (Novotny and Zheng, 1989), but not as an exogenous input. In Novotny and Zheng (1989) and several other studies (Ding and Chen, 2005; Ding et al., 2006; Gelfan et al., 1999), several algorithms for model parameter estimation were introduced, and the impact of model structure, order and parameter values on the accuracy of prediction was analysed. These studies provided useful guidance on ARMA modelling. They showed that the accuracy of on-line flow prediction highly relied on the order of the model used. They also revealed that an increase of the model parameters can effectively improve the results for off-line prediction (Ding et al., 2006). However, the model cannot handle an entire non-stationary process and thus requires further study before being applied to predict sewage flow during wet weather.
This study aims to develop a methodology that is able to achieve real-time flow prediction of the sewage under variable weather conditions. This was achieved through fitting flows and rainfalls to an autoregressive moving average with exogenous inputs (ARMAX) model. The rainfall data was taken into consideration as an external input to improve the prediction accuracy by decreasing the delays. The calibration and validation of the model was conducted with data from two sewage pumping stations (SPSs) with different hydraulic characteristics and climatic conditions, collecting sewage in a small and a large catchment, respectively. The value of the models in supporting real-time chemical dosing control was then demonstrated through simulation studies.
Section snippets
Sewer systems and flow data
Two sewer systems, namely the UC09 SPS and the Bellambi SPS with different hydraulic characteristics and climatic conditions (see Fig. S1 in SI for their catchment maps), are used for the ARMAX model development and demonstration.
ARMAX model development
To construct an ARMAX model for accurate prediction, the development is an iterative process consisting of data pretreatment, order determination and parameter estimation (Brockwell and Davis, 2013).
Multi-step prediction of sewage flow rate
Sewage slugs carrying chemical typically have an HRT of hours. Therefore, it is essential to acquire flow information several hours ahead. In this light, the iterative multistep prediction approach is employed for real-time flow prediction in a horizon of several hours (Niu and Yang, 2009).
For a k-steps prediction, the forecasting value at time is calculated as follows:Where is iteratively sampled
Improvements achieved by the ARX model over an AR model
The present study illustrated the feasibility of using a simple yet effective approach for real-time future sewage flow prediction. Compared to the AR model, the ARX model significantly improved the prediction accuracy with a great decrease of the prediction delays, by taking rainfall into consideration as exogenous inputs, yielding excellent performance under both dry weather and wet weather conditions. The ARX model outperformed the AR model in wet weather when a longer prediction horizon is
Conclusions
A real-time prediction methodology for sewage flow was designed and implemented for on-line chemical dosing control for sulfide mitigation in sewers under variable weather conditions. The following conclusions are drawn:
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An ARX model involving the regression of historical sewage inflow with simultaneous consideration of rainfall data as an exogenous input was established, and was demonstrated to significantly improve the prediction accuracy in comparison to previously established AR models.
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ARX
Declaration of interests
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
The authors acknowledge the Network-wide Sewer Odour and Corrosion Management by Model Predictive Control Project LP160101040 funded by the Australian Research Council, City of Gold Coast, Queensland Urban Utilities and South Australian Water Corporation. Jiuling Li thanks the China Scholarship Council for Scholarship Support. Guangming Jiang is a recipient of the ARC Discovery Early Career Researcher Award Fellowship (DE170100694), and Zhiguo Yuan is an ARC Australian Laureate Fellow (
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