Elsevier

Water Research

Volume 209, 1 February 2022, 117965
Water Research

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

https://doi.org/10.1016/j.watres.2021.117965Get rights and content

Abstract

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.

Introduction

As a unit operation (UO), clarification basins are widely implemented to sequester particulate matter (PM) as well as PM-bound chemicals and pathogens, whether for storm-, waste- or potable water treatment. In recent decades, there has been a worldwide increase in the implementation of clarification basins (wet detention or retention) as a type of green water infrastructure for urban water management (Beckingham, Callahan, Vulava, 2019, Silverman, Sedlak, Nelson, 2019). Across North America, clarification basins are one of the most ubiquitous and visible forms of green infrastructure for diffuse or nonpoint source pollution (NPS) control (National Research Council, 2008). In many situations of urban land development, construction of a clarification basin is a requirement and a presumptive best management practice (BMP) by regulatory agencies (Li, Spelman, Sansalone, 2021, St. Johns River Water Management District, 2018). Renwick et al. (2006) estimated that the number of constructed basins by 2006 ranged from 2.6 to 9 million in the United States (US), with a spatial number density of at least 5/km2 for urban/suburban areas in Florida and Louisiana. Such a number of constructed basins modifies rainfall-runoff phenomena with the potential benefit to urban water clarification, human and ecological habitat interaction with urban water, and the potential as a reclaimed water (Beckingham, Callahan, Vulava, 2019, Li, Spelman, Sansalone, 2021, Luthy, Wolfand, Bradshaw, 2020).

There has been a long history of research to quantify clarification benefits facilitated by basins, hydrologic benefits notwithstanding, and to improve the economy of basin designs. Over 100 years of research has been devoted to elucidate clarification functionality and developing indices and models for basin design and regulation. Early studies have proposed semi-empirical models based on data and physical indices from basins (Brune, 1953, Chen, 1975, Hazen, 1904, Heinemarm, 1981, Nix, 1982, Rausch, Schreiber, 1981, Verstraeten, Poesen, 2000). In particular, the model proposed by Brune (1953) for PM separation (or trap efficiency [TE]) based on capacity-inflow ratio (analogous to mean residence time [RT]) was widely adopted. Later, with the application of digital computers, basin functionality was examined with numerical models (Dhamotharan et al., 1981). Based on reactor theory and assumption of idealized flow hydrodynamics (i.e., complete-mixing flow or plug flow), Huber (1984); Huber et al. (2006); Nix et al. (1988) developed process-based (lumped) dynamics model for basin clarification process such as continuous stirred-tank reactor (CSTR) models. Such dynamic models constitute the theoretical foundation for the current, most prominent and leading urban water simulation tool, the Storm Water Management Model (SWMM) (Rossman, 2015).

As computational resources continue to increase, more recent studies have built upon this foundation with models such as SWMM and moved towards hydrodynamic-resolving computational fluid dynamics (CFD) simulations (Gao, Stenstrom, 2018, Zhang, Tejada-Martínez, Zhang, Lei, 2014). A range of CFD tools for basin clarification simulation have been developed such as the shallow water equation (SWE) (Guan, Ahilan, Yu, Peng, Wright, 2018, Hinterberger, Fröhlich, Rodi, 2007, Li, Spelman, Sansalone, 2021, Nadaoka, Yagi, 1998), Reynolds-averaged Navier-Stokes equations (RANS) (Liu, García, 2011, Sonnenwald, Guymer, Stovin, 2018, Spelman, Sansalone, 2017, Stovin, Saul, 1996, Yan, Lipeme Kouyi, Gonzalez-Merchan, Becouze-Lareure, Sebastian, Barraud, Bertrand-Krajewski, 2014), large-eddy simulation (LES) (Hinterberger, Fröhlich, Rodi, 2007, Li, Balachandar, Sansalone, 2021). Compared to early empirical indices, semi-empirical models and more recent processed-based model, these CFD tools demonstrate further improved predictive capability for basin hydrodynamics (turbulence) with coupled clarification and water chemistry functionality (Liu, Zhang, Nielsen, Cataño-Lopera, 2020, Spelman, Sansalone, 2017).

In contrast to almost a half-century of clarification modeling progress, decades of regulatory, design, and management guidance for clarification basins have been and are still based on empirical techniques and lumped indices that were postulated in the 1960s (Brune, 1953, New Jersey Department of Environmental Protection, 2021, Nix, Heaney, Huber, 1988). Specifically, presumptive criteria based on RT (or hydraulic RT, HRT) to achieve a level of PM separation, for example 80%, are still widely adopted by regulatory agencies (California Stormwater Quality Association, 2003, Clar, Barfield, O’Connor, 2004, Florida Administration Code, United States Environmental Protection Agency, 2009, Vijay, Barbara). The definition of RT, while variable (e.g., mean annual RT), is typically defined as the ratio between permanent pool volume (also known as water quality volume) and mean (wet season) flowrate (Atlanta Regional Commission, 2016, Minnesota Pollution Control Agency, St. Johns River Water Management District, 2018). Design guidance based on RT also varies. Some agencies suggest basins should be sized with an RT from many days to several weeks (Tennessee Department of Environment and Conservation, 2014, United States Environmental Protection Agency, 1999, Virginia Department of Environmental Quality, 2015), while others require a minimum 14 day RT (Massachusetts Department of Environmental Protection, Management, Massachusetts Office of Coastal Zone, 1997, North Carolina Department of Environmental Quality, 2020, St. Johns River Water Management District, 2018). In some cases, with protected water bodies, an additional 50% permanent pool volume and a minimum RT of 21 days are required (St. Johns River Water Management District, 2018).

Notwithstanding the widespread adoption of RT to index basin clarification, the basis for RT from first principles to scale basin clarification is unclear and potentially not robust. There is significant documentation to illustrate the substantial influence of system configuration, loading conditions, hydrodynamics and PM granulometry on basin clarification of PM (Guzman, Cohen, Xavier, Swingle, Qiu, Nepf, 2018, Krajewski, Sikorska, Banasik, 2017, Persson, Somes, Wong, 1999, Sonnenwald, Guymer, Stovin, 2018, Verstraeten, Poesen, 2000). Yet, the RT index is agnostic to all of these input parameters. Therefore, the robustness of RT to scale basin PM separation performance requires examination over a wide range of system geometrics, PM granulometry, and loading conditions. This examination is critical from an economic perspective considering the significant basin land and construction cost (hundreds of thousands to tens of millions USD, as shown in Fig. S1) that result from current RT-based regulation criteria. Such an effort was, and remains, a critical need as identified several decades ago and more recently Beckingham et al. (2019); Verstraeten and Poesen (2000). Without a clear illustration of predictive capability or potential liability of RT criteria, basin design will continue to be guided by potentially less robust methods or indices, hindering the effort and progress towards economical basin design and sustainable urban water management.

On the order hand, advanced basin design and regulation tools such as CFD, while providing capability and accuracy, do require that the stakeholder, whether as industry, planning, management or regulatory, to have or redevelop knowledge and skills for such tools as compared to existing RT criteria. The hesitancy to more frequently apply CFD has historically posed a challenge for wider implementation and regulatory acceptance of CFD for urban water systems, despite the existence of decades of practice-based implementation in chemical, mechanical and aeronautical engineering. Indeed, Liu et al. (2020) concludes that CFD is deployed to a lesser extent by civil and environmental professionals. Such a lack of deployment and demand for CFD may also be responsible for the previously illustrated gap between research and empirically-based engineering practice for basin design, retrofits and regulation. To reduce such a gap and accelerate the translation of research outcomes to practice-based planning and engineering, a method is critically needed to leverage the robust predictive capability of CFD models while provides user-friendly basin design experience; implementable outcomes from CFD as provided by current digital tools (e.g., spreadsheets) are needed for basins as a sustainable and resilient urban water management unit.

Artificial intelligence (AI) and machine learning (ML) can potentially provide such a solution. ML offers a wide range of techniques to analyze information, identify patterns from data and has been applied to diverse disciplines such as image recognition, language processing, autonomous vehicles, medicine, real-time flooding control (Bartos, Kerkez, 2021, Kerkez, Gruden, Lewis, Montestruque, Quigley, Wong, Bedig, Kertesz, Braun, Cadwalader, Poresky, Pak, 2016, Mullapudi, Lewis, Gruden, Kerkez, 2020), and new physics discoveries (Cranmer et al., 2020). ML models such as artificial neural network (ANN) are able to learn the multi-dimensional and non-linear correlations between input features and output labels from data, as supervised learning (Brunton, Noack, Koumoutsakos, 2020, Steven L. Brunton, 2019). In this respect, ML models can be similarly developed to approximate the mapping relation between basin geometric parameters (features) and basin clarification or water chemistry functionality (labels), for example based on the higher-fidelity CFD simulations of PM transport and fate. Compared with the empirical and lumped models, such trained ML models preserve the dependence of PM separation to detailed system geometrics, loading condition, and PM granulometry. Compared with the higher-fidelity CFD models, trained ML models obviate the time-consuming CFD computation and facilitate a simple and efficient examination of basin geometrics, retrofit of impaired basins and regulation for practical application.

This research enhances and extends the existing research of urban water clarification basin design and regulation by developing a CFD-augmented ML model for PM separation. A novel approach hybridizing CFD and ML models (i.e., decision tree, random forest, ANN, and symbolic regression) is proposed to facilitate robust and simple basin analysis and geometric design. The objectives are (1) examine the system PM separation with a validated CFD model over a range of common design geometrics (e.g., basin aspect ratio, depth, inlet and outlet locations), PM characteristics (PM density, particle size distribution [PSD]), and loading condition (e.g., mean wet season flowrate) (2) examine the robustness of RT as an index to characterize and scale basin PM separation performance (3) assess the dependence of basin PM separation performance on various nondimensional groups based on dynamic similarity, and (4) develop a CFD-augmented ML model for urban water clarification basin analysis, design and regulation, in part, as a tool for creating physically-based, generalizable and simple algebraic expressions to map the functionality of basin inputs through basin parameters to basin outputs of interest, in this case basin PM separation.

Section snippets

Materials and methods

The background information on current basin design and regulatory presumptive guidance based on RT is introduced in the subsection of Background for basin geometrics and regulation. The CFD methodology for basin PM separation simulation is provided in the subsection of CFD simulation of PM transport and fate. The last subsection of Data-driven ML models for PM separation describes the ML model selection, development, training, and test.

RT As a scaling index for separation of PM and total PM

Fig. 5 illustrates the dependence of PM separation on the basin RT index in plot (a) for different PM settling velocity (function of PM diameters, PM density). Also shown in plot (b) is the predictive capability of an RT-based empirical model of Harper and Baker (2003) that Florida regulatory agencies currently adopt for evaluating basin PM separation (St. Johns River Water Management District, 2018). The expression for the Harper and Baker (2003) model is provided in Table S2.

Fig. 5

Pareto frontier and the economy of basin design

The observed scaling behavior with respect to separation of PM and also total PM has critical implications for the economy of basin design and urban water management, as highlighted in the following case. Fig. 12 illustrates the basin design economy by a Pareto frontier diagram for an example site in southwest Florida with a mean wet season flowrate of 0.1m3/s and coarser heterodisperse influent PSD. These site hydrological conditions and PM loading characteristics are measured from a 12-month

Conclusions

This study examines the robustness of residence time (RT) and also of nondimensional groups of geometric and dynamic similarity as potential indices to scale clarification basin performance (as PM and total PM separation). CFD simulation of PM transport and fate for a wide range of basin configuration, loading conditions, and PM characteristics are carried out with a total number of parametric combinations of 1.6×105. CFD results agree well with the basin field monitoring data and physical

Acknowledgment

This work was partially funded by the Florida Water Resources Research Center under a grant from the U.S. Department of Interior U.S. Geological Survey.

Supplemental materials

Figs. S1-S8 and Tables S1-S3 are available online.

Declaration of Competing Interest

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.

References (107)

  • United States Environmental Protection Agency

    Storm Water Technology Fact Sheet Wet Detention Ponds

    Technical Report

    (1999)
  • B.J. Ward et al.

    Predictive models using ǣcheap and easyǥ field measurements: can they fill a gap in planning, monitoring, and implementing fecal sludge management solutions?

    Water Res.

    (2021)
  • B.M. Adams et al.

    Dakota, A Multilevel Parallel Object-Oriented Framework for Design Optimization, Parameter Estimation, Uncertainty

    Technical Report

    (2020)
  • Atlanta Regional Commission

    Georgia Stormwater Management Manual

    Technical Report

    (2016)
  • S. Balachandar et al.

    Turbulent dispersed multiphase flow

    Annu Rev Fluid Mech

    (2010)
  • G.I. Barenblatt

    Scaling, self-similarity, and intermediate asymptotics

    (2014)
  • M. Bartos et al.

    Pipedream: an interactive digital twin model for natural and urban drainage systems

    Environmental Modelling & Software

    (2021)
  • B. Beckingham et al.

    Stormwater ponds in the southeastern u.s. coastal plain: hydrogeology, contaminant fate, and the need for a social-Ecological framework

    Front. Environ. Sci.

    (2019)
  • S.L. Brunton et al.

    Machine learning for fluid mechanics

    Annu Rev Fluid Mech

    (2020)
  • S.L. Brunton et al.

    Discovering governing equations from data by sparse identification of nonlinear dynamical systems

    (2016)
  • California Stormwater Quality Association

    Stormwater best management practice hand book

    Technical Report

    (2003)
  • C.-N. Chen

    Design of sediment retention basins

    Proceedings of the National Symposium on Urban Hydrology and Sediment Control

    (1975)
  • V.T. Chow

    Open-channel hydraulics

    (2008)
  • M.L. Clar et al.

    Stormwater Best Management Practice Design Guide Volume 3: Basin Best Management Practices

    Technical Report

    (2004)
  • Cranmer, M., Sanchez-Gonzalez, A., Battaglia, P., Xu, R., Cranmer, K., Spergel, D., Ho, S., 2020. Discovering Symbolic...
  • S. Dhamotharan et al.

    Unsteady one-dimensional settling of suspended sediment

    Water Resour Res

    (1981)
  • S. Elghobashi

    Particle-laden turbulent flows: direct simulation and closure models

    Appl. Sci. Res.

    (1991)
  • Florida Administration Code, 2005. 62-40.432 Water Resource Implementation Rule: Surface Water Management Regulation....
  • Florida Department of Transportation

    Technical report on the water management performance of the FAA pond at Naples Municipal Airport

    Technical Report

    (2016)
  • J.H. Friedman et al.

    The elements of statistical learning

    (2017)
  • H. Gao et al.

    Evaluation of three turbulence models in predicting the steady state hydrodynamics of a secondary sedimentation tank

    Water Res.

    (2018)
  • C.M. García et al.

    Turbulence measurements with acoustic doppler velocimeters

    J. Hydraul. Eng.

    (2005)
  • M. Garcia et al.

    Entrainment of bed sediment into suspension

    J. Hydraul. Eng.

    (1991)
  • G. Garofalo et al.

    Urban drainage clarifier load-response as a function of flow, unsteadiness, and baffling

    J. Environ. Eng.

    (2018)
  • D.E. Goldberg

    Genetic algorithms in search, optimization, and machine learning

    (1989)
  • M. Guan et al.

    Numerical modelling of hydro-morphological processes dominated by fine suspended sediment in a stormwater pond

    J Hydrol (Amst)

    (2018)
  • C.B. Guzman et al.

    Island topographies to reduce short-circuiting in stormwater detention ponds and treatment wetlands

    Ecol Eng

    (2018)
  • H.H. Harper et al.

    Evaluation of Alternative Stormwater Regulations for Southwest Florida

    Technical Report

    (2003)
  • H.H. Harper et al.

    Evaluation of current stormwater design criteria within the state of Florida

    Technical Report

    (2007)
  • A. Hazen

    On sedimentation

    Transactions of the American Society of Civil Engineers

    (1904)
  • H.G. Heinemarm

    A new sediment trap efficiency curve for small reservoirs

    J. Am. Water Resour. Assoc.

    (1981)
  • R. Huang et al.

    Machine learning in natural and engineered water systems

    Water Res.

    (2021)
  • W.C. Huber

    Stormwater management model, users manual, version III

    Technical Report

    (1984)
  • W.C. Huber et al.

    BMP modeling concepts and simulation

    Technical Report

    (2006)
  • Y. Jia et al.

    Water quality modeling in sewer networks: review and future research directions

    Water Res.

    (2021)
  • Karniadakis, G. E., Kevrekidis, I. G., Lu, L., Perdikaris, P., Wang, S., Yang, L., 2021. Physics-informed machine...
  • B. Kerkez et al.

    Smarter stormwater systems

    Environ. Sci. Technol.

    (2016)
  • S. Khan et al.

    Retrofitting a stormwater retention pond using a deflector island

    Water Sci. Technol.

    (2011)
  • H. Li et al.

    Large-eddy simulation of flow turbulence in clarification systems

    Acta Mech

    (2021)
  • H. Li et al.

    Benchmarking reynolds-Averaged navierstokes turbulence models for water clarification systems

    J. Environ. Eng.

    (2021)
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