A CFD-ML augmented alternative to residence time for clarification basin scaling and design
Graphical abstract
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 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 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 . 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.
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2022, Water ResearchCitation Excerpt :A critical factor that escalates basin cost is the current adoption of presumptive basin performance based on residence time (RT, or hydraulic residence time [HRT]) or surface overflow rate (SOR) models (Li and Sansalone, 2022a; Spelman and Sansalone, 2021). To provide a model alternative, a more robust algebraic model for basin clarification has recently been proposed based on symbolic regression (SR) and computational fluid dynamics (CFD) simulations (Li and Sansalone, 2022a). However, this model did not address (1) basin geometrics (e.g. horizontal aspect ratio, baffle geometry) or (2) geometric optimization for basin planning or retrofit.
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2022, Water ResearchCitation Excerpt :In particular, the impacts and consequences resulted from the presumptions required of analytical models in practical engineering design and regulatory guidance, require interrogation and elucidated. Without a clear illustration of the applicability and elucidation of generality, clarification system design and regulation can be potentially mis-represented by methods that are not as robust and economic (Li and Sansalone, 2022; Li et al., 2021c). This study interrogates common analytical models representing clarification by common UO systems for their predictive capability and generalizability with attention to applications of PM and PM-partitioned constituents clarification in the urban water cycle.