Methods to model particulate matter clarification of unit operations subject to unsteady loadings

A novel method for identifying aerobic granular sludge state using sorting, densification and clarification dynamics during the settling process

Aerobic granular sludge is one of the most promising biological wastewater treatment technologies, yet maintaining its stability is still a challenge for its application, and predicting the state of the granules is essential in addressing this issue. This study explored the potential of dynamic texture entropy, derived from settling images, as a predictive tool for the state of granular sludge. Three processes, traditional thickening, often overlooked clarification, and innovative particle sorting, were used to capture the complexity and diversity of granules. It was found that rapid sorting during settling indicates stable granules, which helps to identify the state of granules. Furthermore, a relationship between sorting time and granule heterogeneity was identified, helping to adjust selection pressure. Features of the dynamic texture entropy well correlated with the respirogram, i.e., R2 were 0.86 and 0.91 for the specific endogenous respiration rate (SOURe) and the specific quasi-endogenous respiration rate (SOURq), respectively, providing a biologically based approach for monitoring the state of granules. The classification accuracy of models using features of dynamic texture entropy as an input was greater than 0.90, significantly higher than the input of conventional features, demonstrating the significant advantage of this approach. These findings contributed to developing robust monitoring tools that facilitate the maintenance of stable granular sludge operations.

Implementing machine learning to optimize the cost-benefit of urban water clarifier geometrics

Clarification basins are ubiquitous water treatment units applied across urban water systems. Diverse applications include stormwater systems, stabilization lagoons, equalization, storage and green infrastructure. Residence time (RT), surface overflow rate (SOR) and the Storm Water Management Model (SWMM) are readily implemented but are not formulated to optimize basin geometrics because transport dynamics remain unresolved. As a result, basin design yields high costs from hundreds of thousands to tens of million USD. Basin optimization and retrofits can benefit from more robust and efficient tools. More advanced methods such as computational fluid dynamics (CFD), while demonstrating benefits for resolving transport, can be complex and computationally expensive for routine applications. To provide stakeholders with an efficient and robust tool, this study develops a novel optimization framework for basin geometrics with machine learning (ML). This framework (1) leverages high-performance computing (HPC) and the predictive capability of CFD to provide artificial neural network (ANN) development and (2) integrates a trained ANN model with a hybrid evolutionary-gradient-based optimization algorithm through the ANN automatic differentiation (AD) functionality. ANN model results for particulate matter (PM) clarification demonstrate high predictive capability with a coefficient of determination (R²) of 0.998 on the test dataset. The ANN model for total PM clarification of three (3) heterodisperse particle size distributions (PSDs) also illustrates good performance (R²>0.986). The proposed framework was implemented for a basin and watershed loading conditions in Florida (USA), the ML basin designs yield substantially improved cost-effectiveness compared to common designs (square and circular basins) and RT-based design for all PSDs tested. To meet a presumptive regulatory criteria of 80% PM separation (widely adopted in the USA), the ML framework yields 4.7X to 8X lower cost than the common basin designs tested. Compared to the RT-based design, the ML design yields 5.6X to 83.5X cost reduction as a function of the finer, medium, and coarser PSDs. Furthermore, the proposed framework benefits from ANN's high computational efficiency. Optimization of basin geometrics is performed in minutes on a laptop using the framework. The framework is a promising adjuvant tool for cost-effective and sustainable basin implementation across urban water systems.

Interrogating common clarification models for unit operation systems with dynamic similitude

Surface overflow rate (SOR), plug flow reactor (PFR) and continuously stirred tank reactor (CSTR) are common models for clarification unit operations (UO). With wide deployment in engineering practice and regulation, through tools from spreadsheets to complex numerical codes, these models are formulated based upon conceptualized system geometry (e.g., rectangular channel) and idealized hydrodynamics (plug flow or well-mixed conditions). Yet the hydrodynamics and geometry of actual UO systems can be complex and substantially different from these assumptions. As a result, the applicability and generalizability of these models require critical and systematic interrogation. This study examines the predictive capability and generalizability of these common models for a hydrodynamic separator (HS), tanks, rectangular clarifiers and an urban drainage basin based on physical model data and high-fidelity large-eddy simulation (LES). Moreover, this study presents a novel application of dynamic similitude to developing a more generalized and physically interpretable model based on the hypothesis that PM and PM-partitioned constituent separation in a UO can be approximated solely through the dimensionless settling velocity W (Hazen number). Based on this hypothesis and dynamic similitude, a similarity modified gamma model (SMG) is proposed and tested. With dynamic similitude and W, results show common models are not robust and generalizable for predicting PM separation with error ranging from 30 to 50% and can significantly oversize a clarifier up to 904%. The non-linear characteristics of PM separation are shown to have a critical role in clarifications system design scalability and economics. In contrast, the SMG model is robust and generalizes the PM separation for geometrically similar systems, irrespective of particle density, particle size distribution (PSD), and loading conditions. The developed theory and proposed SMG model also can simplify and reduce the effort as well as expense of physical model testing while serving as an adjuvant for numerical simulations of clarification systems. Results also reveal commercial HS systems do not outperform simple plain tank geometries. The complex turbulence vortical structures pose significant challenges for UO system analysis and design.

A CFD-ML augmented alternative to residence time for clarification basin scaling and design

Particulate matter (PM), while not an emerging contaminant, remains the primary labile substrate for partitioning and transport of emerging and known chemicals and pathogens. As a common unit operation and also green infrastructure, clarification basins are widely implemented to sequester PM as well as PM-partitioned chemicals and pathogens. Despite ubiquitous application for urban drainage, stormwater clarification basin design and optimization lacks robust and efficient design guidance and tools. Current basin design and regulation primarily adopt residence time (RT) as presumptive guidance. This study examines the accuracy and generalizability of RT and nondimensional groups of basin geometric and dynamic similarity (Hazen, Reynolds, Schmidt numbers) to scale clarification basin performance (measured as PM separation and total PM separation). Published data and 160,000 computational fluid dynamics (CFD) simulations of basin PM separation over a wide range of basin configurations, loading conditions, and PM granulometry (particle size distribution [PSD], density) are examined. Based on the CFD database, a novel implementation of machine learning (ML) models: decision tree (DT), random forest (RF), artificial neural networks (ANN), and symbolic regression (SR) are developed and trained as surrogate models for basin PM separation predictions. Study results indicate that: (1) Models based solely on RT are not accurate or generalizable for basin PM separation, with significant differences between CFD and RT models primarily for RT < 200 hr, (2) RT models are agnostic to basin configurations and PM granulometrics and therefore do not reproduce total PM separation, (3) Trained ML models provide high predictive capability, with (R2) above 0.99 and prediction for total PM separation within ±15%. In particular, the SR model distilled from CFD simulations is entirely defined by only two compact algebraic equations (allowing use in a spreadsheet tool). The SR model has a physical basis and indicates PM separation is primarily a function of the Hazen number and basin horizontal and vertical aspect ratios, (4) With common presumptive guidance of 80% for PM separation, a Pareto frontier analysis indicates that the CFD-ML augmented SR model generates significant economic benefit for basin planning/design, and (5) CFD-ML models show that enlarging basin dimensions (increasing RT) to address impaired behavior can result in exponential cost increases, irrespective of land/infrastructure adjacency conflicts. CFD-ML applications can extend to intra-basin retrofits (permeable baffles) to upgrade impaired basins.

Settling characteristics of nonspherical porous sludge flocs with nonhomogeneous mass distribution

The paper reports on the development of an advanced Lagrangian particle tracking model of sludge flocs that takes into account its nonspherical shape, the internal porosity and permeability, as well as the nonhomogenous mass distribution. The floc shapes, sizes and free settling velocities are determined based on the experimental measurement of settling sludge flocs originating from a wastewater treatment plant. Based on the floc shape characterization, a prolate axisymmetric ellipsoid is selected as the modelled sludge particle. In order to determine the main particle characteristics, e.g. the internal porosity, the density and the flow permeability, a Lagrangian particle tracking model is developed based on Brenner's drag model for a prolate axisymmetric ellipsoid and a buoyancy force model for a porous particle. The model is implemented for numerical simulations of the free settling process. The obtained floc characteristics are presented in the form of a two-part polynomial fitting curve, which can be used to model floc characteristics. The values of settling velocities of flocs computed by the model show very good agreement with experimental results. Futhermore, as the internal structure of a floc is seldom uniform, the nonhomogeneous mass distribution is considered, influencing the rotational and translational motions of the settling flocs. The nonhomogeneous mass distribution is introduced into the floc settling model. The parametric analyses of different barycentre offsets and shear rates are performed, and their influences on the free settling velocity are evaluated. The presented modelling approach can also be applied to flocculent settling of alum and other flocs in drinking water treatment plants. The developed Lagrangian model is suitable for use as a point source within the framework of Eulerian flow computations, and is solved as a two-phase flow model with a suitable Computational Fluid Dynamics code.