Towards good modelling practice for parallel hybrid models for wastewater treatment processes.

This study explores various approaches to formulating a parallel hybrid model (HM) for Water and Resource Recovery Facilities (WRRFs) merging a mechanistic and a data-driven model. In the study, the HM is constructed by training a neural network (NN) on the residual of the mechanistic model for effluent nitrate. In an initial experiment using the Benchmark Simulation Model no. 1, a parallel HM effectively addressed limitations in the mechanistic model's representation of autotrophic bacteria growth and the data-driven model's incapability to extrapolate. Next, different versions of a parallel HM of a large pilot-scale WRRF are constructed, using different calibration/training datasets and different versions of the mechanistic model to investigate the balance between the calibration effort for the mechanistic model and the compensation by the NN component. The HM can improve predictions compared to the mechanistic model. Training the NN on an independent validation dataset produced better results than on the calibration dataset. Interestingly, the best performance is achieved for the HM based on a mechanistic model using default (uncalibrated) parameters. Both long short-term memory (LSTM) and convolutional neural network (CNN) are tested as data-driven components, with a CNN HM (root-mean-squared error (RMSE) = 1.58 mg NO3-N/L) outperforming an LSTM HM (RMSE = 4.17 mg NO3-N/L).

A full-scale operational digital twin for a water resource recovery facility-A case study of Eindhoven Water Resource Recovery Facility.

Digital transformation for the water sector has gained momentum in recent years, and many water resource recovery facilities modelers have already started transitioning from developing traditional models to digital twin (DT) applications. DTs simulate the operation of treatment plants in near real time and provide a powerful tool to the operators and process engineers for real-time scenario analysis and calamity mitigation, online process optimization, predictive maintenance, model-based control, and so forth. So far, only a few mature examples of full-scale DT implementations can be found in the literature, which only address some of the key requirements of a DT. This paper presents the development of a full-scale operational DT for the Eindhoven water resource recovery facility in The Netherlands, which includes a fully automated data-pipeline combined with a detailed mechanistic full-plant process model and a user interface co-created with the plant's operators. The automated data preprocessing pipeline provides continuous access to validated data, an influent generator provides dynamic predictions of influent composition data and allows forecasting 48 h into the future, and an advanced compartmental model of the aeration and anoxic bioreactors ensures high predictive power. The DT runs near real-time simulations every 2 h. Visualization and interaction with the DT is facilitated by the cloud-based TwinPlant technology, which was developed in close interaction with the plant's operators. A set of predefined handles are made available, allowing users to simulate hypothetical scenarios such as process and equipment failures and changes in controller settings. The combination of the advanced data pipeline and process model development used in the Eindhoven DT and the active involvement of the operators/process engineers/managers in the development process makes the twin a valuable asset for decision making with long-term reliability. PRACTITIONER POINTS: A full-scale digital twin (DT) has been developed for the Eindhoven WRRF. The Eindhoven DT includes an automated continuous data preprocessing and reconciliation pipeline. A full-plant mechanistic compartmental process model of the plant has been developed based on hydrodynamic studies. The interactive user interface of the Eindhoven DT allows operators to perform what-if scenarios on various operational settings and process inputs. Plant operators were actively involved in the DT development process to make a reliable and relevant tool with the expected added value.

An improved 1D reactive Bürger-Diehl settler model for secondary settling tank denitrification.

An improved 1D reactive settler model is pursued in order to increase the understanding of reactive settling processes and obtain a better prediction of the nitrogen mass balance in wastewater treatment systems. The developed model is based on the 1D Bürger-Diehl settler model with compression function and the Activated Sludge Model No. 1 biological reactions. Specific attention was paid in the model development phase to optimal selection of settling velocity functions and integration of the correct clarifier geometry. A unique measurement campaign was carried out with different operational scenarios to quantify the denitrification in a secondary settling tank. A detailed step-wise calibration effort demonstrated that by choosing an appropriate settling velocity function (power-law structure) and considering the true clarifier geometry allows to accurately capture the biomass concentration profile, total sludge mass, sludge blanket height, and the reaction rates. The resulting model is able to accurately describe total suspended solids (TSS) and nitrate concentration profiles throughout a settling tank under different operational conditions. As such the model can be applied in further scenario analysis and system optimization. PRACTITIONER POINTS: A unique measurement campaign was carried out to obtain detailed data for a reactive settler model development. A 1-D reactive settler model is developed based on the Bürger-Diehl framework including ASM1 biokinetics and the clarifier geometry. An extensive calibration and model selection effort was performed. The model accurately predicts measured concentration profiles in the settling tank. The developed model can be integrated in a plant-wide model to properly calculate the nitrogen mass balance of a WRRF.

In silico assessment of household level closed water cycles: Towards extreme decentralization.

Water management in most of the developed world is currently practiced in a highly centralized manner, leading to major infrastructure and energy costs to transport water. To decrease the impacts of water scarcity and climate change, the decentralization of water can increase local robustness. In extremis, decentralization can involve building or house level water supply and treatment. Here, we constructed a MATLAB/Simulink model for two decentralized water management configurations at the household level, assuming the socio-environmental setting of Flanders, Belgium. Independence from the potable water grid and sewer system was pursued through rainwater harvesting, reuse of wastewater streams fit-for-purpose, and discharge via infiltration. The mass balance for water was calculated over the system boundaries showing high potential for independence from the grid with a reasonable treatment train and storage options. Next, the risk of contaminant accumulation within the circular system was assessed, showing a key limitation on decentralized system performance necessitating a system purge. Up to 59% of system rainwater usage was due to the replacement of this purge. Employing treatment units with high (95%) contaminant rejection efficiencies eliminated contaminant accumulation issues. The raw model output was quantitatively assessed by constructing four newly proposed key performance indicators (KPIs), quantifying system independence, circularity, drought tolerance and local water body recharge, which allowed for facilitated system comparison and communication to stakeholders. A sensitivity analysis was performed in which the effect of input parameter variability and uncertainty on system performance was quantified. The sensitivity analysis showed the importance of water recovery and contaminant removal efficiencies of the applied treatment technologies on system performance when contaminant accumulation in the system forms an issue. In systems not severely affected by pollutant accumulation, parameters such as inhabitant number and roof surface had the largest effect. As a whole, this work shows the potential of extreme decentralization of water systems and addresses the obstacle towards implementation formed by the accumulation of contaminants due to system circularity. Additionally, this study provides a framework for operational and technological decision support of decentralized household-scale water systems and, by extension, for future water policy-making.

The transition of WRRF models to digital twin applications.

Digital Twins (DTs) are on the rise as innovative, powerful technologies to harness the power of digitalisation in the WRRF sector. The lack of consensus and understanding when it comes to the definition, perceived benefits and technological needs of DTs is hampering their widespread development and application. Transitioning from traditional WRRF modelling practice into DT applications raises a number of important questions: When is a model's predictive power acceptable for a DT? Which modelling frameworks are most suited for DT applications? Which data structures are needed to efficiently feed data to a DT? How do we keep the DT up to date and relevant? Who will be the main users of DTs and how to get them involved? How do DTs push the water sector to evolve? This paper provides an overview of the state-of-the-art, challenges, good practices, development needs and transformative capacity of DTs for WRRF applications.

Hybrid modelling of water resource recovery facilities: status and opportunities.

Mathematical modelling is an indispensable tool to support water resource recovery facility (WRRF) operators and engineers with the ambition of creating a truly circular economy and assuring a sustainable future. Despite the successful application of mechanistic models in the water sector, they show some important limitations and do not fully profit from the increasing digitalisation of systems and processes. Recent advances in data-driven methods have provided options for harnessing the power of Industry 4.0, but they are often limited by the lack of interpretability and extrapolation capabilities. Hybrid modelling (HM) combines these two modelling paradigms and aims to leverage both the rapidly increasing volumes of data collected, as well as the continued pursuit of greater process understanding. Despite the potential of HM in a sector that is undergoing a significant digital and cultural transformation, the application of hybrid models remains vague. This article presents an overview of HM methodologies applied to WRRFs and aims to stimulate the wider adoption and development of HM. We also highlight challenges and research needs for HM design and architecture, good modelling practice, data assurance, and software compatibility. HM is a paradigm for WRRF modelling to transition towards a more resource-efficient, resilient, and sustainable future.

Mainstream short-cut N removal modelling: current status and perspectives.

This work gives an overview of the state-of-the-art in modelling of short-cut processes for nitrogen removal in mainstream wastewater treatment and presents future perspectives for directing research efforts in line with the needs of practice. The modelling status for deammonification (i.e., anammox-based) and nitrite-shunt processes is presented with its challenges and limitations. The importance of mathematical models for considering N2O emissions in the design and operation of short-cut nitrogen removal processes is considered as well. Modelling goals and potential benefits are presented and the needs for new and more advanced approaches are identified. Overall, this contribution presents how existing and future mathematical models can accelerate successful full-scale mainstream short-cut nitrogen removal applications.

Hybrid differential equations: Integrating mechanistic and data-driven techniques for modelling of water systems.

Mathematical modelling is increasingly used to improve the design, understanding, and operation of water systems. Two modelling paradigms, i.e., mechanistic and data-driven modelling, are dominant in the water sector, both with their advantages and drawbacks. Hybrid modelling aims to combine the strengths of both paradigms. Here, we introduce a novel framework that incorporates a data-driven component into an existing activated sludge model of a water resource recovery facility. In contrast to previous efforts, we tightly integrate both models by incorporating a neural differential equation into an existing mechanistic ODE model. This machine learning component fills in the knowledge gaps of the mechanistic model. We show that this approach improves the predictive capabilities of the mechanistic model and is able to extrapolate to unseen conditions, a problematic task for data-driven models. This approach holds tremendous potential for systems that are difficult to model using the mechanistic paradigm only.

Assessing the effects of non-pharmaceutical interventions on SARS-CoV-2 transmission in Belgium by means of an extended SEIQRD model and public mobility data.

We present a compartmental extended SEIQRD metapopulation model for SARS-CoV-2 spread in Belgium. We demonstrate the robustness of the calibration procedure by calibrating the model using incrementally larger datasets and dissect the model results by computing the effective reproduction number at home, in workplaces, in schools, and during leisure activities. We find that schools and home contacts are important transmission pathways for SARS-CoV-2 under lockdown measures. School reopening has the potential to increase the effective reproduction number from Re=0.66±0.04 (95 % CI) to Re=1.09±0.05 (95 % CI) under lockdown measures. The model accounts for the main characteristics of SARS-CoV-2 transmission and COVID-19 disease and features a detailed representation of hospitals with parameters derived from a dataset consisting of 22 136 hospitalized patients. Social contact during the pandemic is modeled by scaling pre-pandemic contact matrices with Google Community Mobility data and with effectivity-of-contact parameters inferred from hospitalization data. The calibrated social contact model with its publically available mobility data, although coarse-grained, is a cheap and readily available alternative to social-epidemiological contact studies under lockdown measures, which were not available at the start of the pandemic.

The future of WRRF modelling - outlook and challenges.

The wastewater industry is currently facing dramatic changes, shifting away from energy-intensive wastewater treatment towards low-energy, sustainable technologies capable of achieving energy positive operation and resource recovery. The latter will shift the focus of the wastewater industry to how one could manage and extract resources from the wastewater, as opposed to the conventional paradigm of treatment. Debatable questions arise: can the more complex models be calibrated, or will additional unknowns be introduced? After almost 30 years using well-known International Water Association (IWA) models, should the community move to other components, processes, or model structures like 'black box' models, computational fluid dynamics techniques, etc.? Can new data sources - e.g. on-line sensor data, chemical and molecular analyses, new analytical techniques, off-gas analysis - keep up with the increasing process complexity? Are different methods for data management, data reconciliation, and fault detection mature enough for coping with such a large amount of information? Are the available calibration techniques able to cope with such complex models? This paper describes the thoughts and opinions collected during the closing session of the 6th IWA/WEF Water Resource Recovery Modelling Seminar 2018. It presents a concerted and collective effort by individuals from many different sectors of the wastewater industry to offer past and present insights, as well as an outlook into the future of wastewater modelling.

Experimental assessment and validation of quantification methods for cellulose content in municipal wastewater and sludge.

Cellulose, mostly in the form of toilet paper, forms a major component of the particulates in raw municipal wastewater, which could lead to significant consequences due to the potential accumulation of cellulosic fibers and slow biodegradability. Despite the sparse reports on cellulose content and degradation in wastewater and sludge, an accurate and validated method for its quantification in such matrices does not exist. In this paper, four different methods were compared including dilute acid hydrolysis, concentrated acid hydrolysis, enzymatic hydrolysis, and the Schweitzer reagent method. The Schweitzer reagent method, applied to municipal wastewater and sludge, was found to be a very robust and reliable quantification method in light of its reproducibility, accuracy, and ideal (100%) recovery. The determination of cellulose content is critical to understand its fate in wastewater treatment plants as well as improve sludge management and enhance resource recovery.

Predicting the fate of micropollutants during wastewater treatment: Calibration and sensitivity analysis.

The presence of micropollutants in the environment and their toxic impacts on the aquatic environment have raised concern about their inefficient removal in wastewater treatment plants. In this study, the fate of micropollutants of four different classes was simulated in a conventional activated sludge plant using a bioreactor micropollutant fate model coupled to a settler model. The latter was based on the Bürger-Diehl model extended for the first time to include micropollutant fate processes. Calibration of model parameters was completed by matching modelling results with full-scale measurements (i.e. including aqueous and particulate phase concentrations of micropollutants) obtained from a 4-day sampling campaign. Modelling results showed that further biodegradation takes place in the sludge blanket of the settler for the highly biodegradable caffeine, underlining the need for a reactive settler model. The adopted Monte Carlo based calibration approach also provided an overview of the model's global sensitivity to the parameters. This analysis showed that for each micropollutant and according to the dominant fate process, a different set of one or more parameters had a significant impact on the model fit, justifying the selection of parameter subsets for model calibration. A dynamic local sensitivity analysis was also performed with the calibrated parameters. This analysis supported the conclusions from the global sensitivity and provided guidance for future sampling campaigns. This study expands the understanding of micropollutant fate models when applied to different micropollutants, in terms of global and local sensitivity to model parameters, as well as the identifiability of the parameters.

Concentration-driven models revisited: towards a unified framework to model settling tanks in water resource recovery facilities.

A new perspective on the modelling of settling behaviour in water resource recovery facilities is introduced. The ultimate goal is to describe in a unified way the processes taking place both in primary settling tanks (PSTs) and secondary settling tanks (SSTs) for a more detailed operation and control. First, experimental evidence is provided, pointing out distributed particle properties (such as size, shape, density, porosity, and flocculation state) as an important common source of distributed settling behaviour in different settling unit processes and throughout different settling regimes (discrete, hindered and compression settling). Subsequently, a unified model framework that considers several particle classes is proposed in order to describe distributions in settling behaviour as well as the effect of variations in particle properties on the settling process. The result is a set of partial differential equations (PDEs) that are valid from dilute concentrations, where they correspond to discrete settling, to concentrated suspensions, where they correspond to compression settling. Consequently, these PDEs model both PSTs and SSTs.

On constitutive functions for hindered settling velocity in 1-D settler models: Selection of appropriate model structure.

Advanced 1-D models for Secondary Settling Tanks (SSTs) explicitly account for several phenomena that influence the settling process (such as hindered settling and compression settling). For each of these phenomena a valid mathematical expression needs to be selected and its parameters calibrated to obtain a model that can be used for operation and control. This is, however, a challenging task as these phenomena may occur simultaneously. Therefore, the presented work evaluates several available expressions for hindered settling based on long-term batch settling data. Specific attention is paid to the behaviour of these hindered settling functions in the compression region in order to evaluate how the modelling of sludge compression is influenced by the choice of a certain hindered settling function. The analysis shows that the exponential hindered settling forms, which are most commonly used in traditional SST models, not only account for hindered settling but partly lump other phenomena (compression) as well. This makes them unsuitable for advanced 1-D models that explicitly include each phenomenon in a modular way. A power-law function is shown to be more appropriate to describe the hindered settling velocity in advanced 1-D SST models.

Dynamic modelling of solids in a full-scale activated sludge plant preceded by CEPT as a preliminary step for micropollutant removal modelling.

The presence of micropollutants in the environment has triggered research on quantifying and predicting their fate in wastewater treatment plants (WWTPs). Since the removal of micropollutants is highly related to conventional pollutant removal and affected by hydraulics, aeration, biomass composition and solids concentration, the fate of these conventional pollutants and characteristics must be well predicted before tackling models to predict the fate of micropollutants. In light of this, the current paper presents the dynamic modelling of conventional pollutants undergoing activated sludge treatment using a limited set of additional daily composite data besides the routine data collected at a WWTP over one year. Results showed that as a basis for modelling, the removal of micropollutants, the Bürger-Diehl settler model was found to capture the actual effluent total suspended solids (TSS) concentrations more efficiently than the Takács model by explicitly modelling the overflow boundary. Results also demonstrated that particular attention must be given to characterizing incoming TSS to obtain a representative solids balance in the presence of a chemically enhanced primary treatment, which is key to predict the fate of micropollutants.

Population balance models: a useful complementary modelling framework for future WWTP modelling.

Population balance models (PBMs) represent a powerful modelling framework for the description of the dynamics of properties that are characterised by distributions. This distribution of properties under transient conditions has been demonstrated in many chemical engineering applications. Modelling efforts of several current and future unit processes in wastewater treatment plants could potentially benefit from this framework, especially when distributed dynamics have a significant impact on the overall unit process performance. In these cases, current models that rely on average properties cannot sufficiently capture the true behaviour and even lead to completely wrong conclusions. Examples of distributed properties are bubble size, floc size, crystal size or granule size. In these cases, PBMs can be used to develop new knowledge that can be embedded in our current models to improve their predictive capability. Hence, PBMs should be regarded as a complementary modelling framework to biokinetic models. This paper provides an overview of current applications, future potential and limitations of PBMs in the field of wastewater treatment modelling, thereby looking over the fence to other scientific disciplines.

A consistent modelling methodology for secondary settling tanks: a reliable numerical method.

The consistent modelling methodology for secondary settling tanks (SSTs) leads to a partial differential equation (PDE) of nonlinear convection-diffusion type as a one-dimensional model for the solids concentration as a function of depth and time. This PDE includes a flux that depends discontinuously on spatial position modelling hindered settling and bulk flows, a singular source term describing the feed mechanism, a degenerating term accounting for sediment compressibility, and a dispersion term for turbulence. In addition, the solution itself is discontinuous. A consistent, reliable and robust numerical method that properly handles these difficulties is presented. Many constitutive relations for hindered settling, compression and dispersion can be used within the model, allowing the user to switch on and off effects of interest depending on the modelling goal as well as investigate the suitability of certain constitutive expressions. Simulations show the effect of the dispersion term on effluent suspended solids and total sludge mass in the SST. The focus is on correct implementation whereas calibration and validation are not pursued.