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.

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.

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.

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.

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.