Modeling Mass Removal and Sediment Deposition in Stormwater Ponds Using Floating Treatment Islands: A Computational Approach

doi:10.21203/rs.3.rs-3140335/v1

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Modeling Mass Removal and Sediment Deposition in Stormwater Ponds Using Floating Treatment Islands: A Computational Approach

https://doi.org/10.21203/rs.3.rs-3140335/v1

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published 13 Oct, 2023

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Floating Treatment Islands (FTIs) offers effective solutions for stormwater management, providing flood attenuation and pollutant removal capabilities. However, there remains a knowledge gap concerning their performance, specifically in terms of pollutant removal and sediment deposition. To address this gap, the present study employs Computational Fluid Dynamics (CFD) modeling to investigate the intricate interactions within FTI systems. Various FTI configurations are analyzed, considering mass removal through FTIs and sediment deposition. The findings demonstrate that FTIs have a significant influence on flow patterns and mass removal. Notably, FTIs enhance mass removal compared to the control case, with larger sediment particles exhibiting higher removal rates. The correlation between the short-circuit index and sedimentation in FTI ponds highlights the potential of FTIs as indicators of treatment efficiency. Furthermore, the study focuses on mass removal exclusively through the FTI root zones. The positioning of FTIs within the pond has a considerable impact, resulting in differences of up to 20% in mass removal. Moreover, the FTI configuration exerts a more pronounced influence on mass removal through FTIs than through sediment deposition alone. In cases where both processes occur simultaneously, the presence of FTIs lead to higher mass removal, primarily attributed to the FTIs themselves, particularly in the initial segment. Remarkably, certain FTI configurations enable mass removal exceeding 70% for large sediment particles, even with a pond length less than half of the original.

Computational Fluid Dynamics

Settling Velocity

Floating Treatment Islands

Wetlands

Sedimentation

Water Treatment

Shear Stress

Floods represent significant climate-related disasters, with approximately 58 million people worldwide being exposed to river flood events annually. These events result in approximately 5,700 fatalities and $145 billion in losses each year (Dottori et al., 2018). Moreover, the impacts of floods on the economy and public health are expected to increase due to climate change and the intensification of extreme rainfall events (Alfieri et al., 2016; Yin et al., 2018). Under an optimistic scenario of a global temperature increase of 1.5°C, human losses from flooding could rise by 70–83%, direct flood damage by 160–240%, and relative welfare reduction could range from 0.23 to 0.29% (Dottori et al., 2018).

The global trend of urbanization is another factor that contributes to the flood risk. By 2030, it is estimated that nearly 5 billion people, accounting for 60% of the world's population, will reside in cities (UN, 2012). Urbanization brings about changes in the natural landscape, such as alterations in land use, land cover, and increased impermeable surfaces (Satterthwaite, 2011). Consequently, the urban land area exposed to floods is projected to increase by more than 250% by 2030 (Güneralp et al., 2015). Urbanization also leads to changes in the quality of runoff water, as various pollutants originating from urban activities accumulate on urban surfaces (Sadeghi et al., 2018). During storm events, these pollutants, including nutrients like phosphorus and nitrogen, as well as sediments, metals, oil and grease, and bacteria, are washed off and transported to water bodies such as rivers, lakes, and estuaries, causing their degradation. Therefore, it is essential to divert urban stormwater runoff to stormwater management facilities to reduce peak flows and treat the water before it reaches receiving bodies of water.

Constructed wetlands with surface flow, dominated by sediment-rooted emergent aquatic macrophytes, have gained significant acceptance as urban stormwater management facilities in recent years (Headley and Tanner, 2012). Their popularity stems from their ability to attenuate peak flood flows, provide a relatively passive, low-cost, and low-maintenance stormwater treatment solution, and offer recreational, aesthetic, and ecological benefits by creating novel urban landscapes (Headley and Tanner, 2012; Lucke et al., 2019; Guzman et al., 2018). However, these wetlands are limited in their capacity to tolerate deeper water depths and are susceptible to chronic die-back if inundated beyond certain thresholds (Headley and Tanner, 2012). As a result, they require either larger areas to accommodate vegetation growth and flood attenuation or bypass flows during heavy rainfall events, leading to compromised stormwater treatment (Headley and Tanner, 2012).

To overcome these limitations, floating treatment islands (FTIs) have emerged as a promising solution. FTIs utilize emergent macrophytes that grow on a floating mat at the water's surface (Headley and Tanner, 2012). The roots of these plants hanging beneath the floating mat help reduce flow velocities, facilitating the entrapment and sedimentation of suspended particles (Lucke et al., 2019). Additionally, the plant roots provide a large surface area for the growth of biofilms, promoting the biological uptake of nutrients (Nichols et al., 2016; Lucke et al., 2019). Due to the greater available surface area for biofilm growth compared to sediment-rooted wetlands, FTIs have a higher potential for pollutant removal per unit area (Nichols et al., 2016). Unlike sediment-rooted wetlands, the floating vegetation in FTIs allows them to tolerate a wider range of water levels, enabling increased water depth and retention time during flood events (Headley and Tanner, 2012). FTIs can also be integrated into existing retention ponds to enhance water quality, aesthetics, and habitat.

Despite the potential advantages of FTIs, there are still gaps and weaknesses in the existing literature regarding their performance and functioning, as highlighted by Lucke et al. (2019) in a recent review. Firstly, many researchers have positioned FTIs randomly within ponds, failing to maximize the flow through the FTWs and treating them as passive systems. Secondly, the evaluation of FTI performance would benefit from including a control pond (traditional treatment pond) in the study. Lastly, determining the specific contribution of FTIs to nutrient removal, distinct from the overall performance of the ponds themselves, remains challenging. Therefore, understanding the hydraulic performance of FTIs is crucial, and considering computational modeling with full-scale ponds is a promising avenue for further investigation (Lucke et al., 2019).

Within this context, several studies have addressed some of the points raised by Lucke et al. (2019), including Xavier et al. (2018), Liu et al. (2019), Waite et al. (2021), Yamasaki et al. (2022), Wang et al. (2022), and Nuruzzaman et al. (2023). Xavier et al. (2018), in particular, utilized Computational Fluid Dynamics (CFD) to address the significance of FTI positioning and quantifying the mass removal achieved by each FTI. By investigating various FTI configurations, Xavier et al. demonstrated that the wake generated by upstream FTIs had a negative impact on the mass removal efficiency of downstream FTIs. As a result, segmenting a single large FTI into multiple smaller ones in series did not improve overall nutrient removal. However, segmenting a single FTI into a pair of parallel FTIs resulted in enhanced nutrient removal, making it the optimal configuration at the pond scale.

Building upon the findings of Xavier et al. (2018), our study expands the investigation by considering the mass removal achieved through sediment deposition. This refinement is crucial as both processes—sediment deposition and FTI-mediated removal—contribute to pollutant removal within FTI systems. The flow regime that optimizes pollutant removal by FTIs may not necessarily be conducive to sediment deposition-based removal. Therefore, understanding the interaction between these two processes is pivotal in establishing design guidelines for FTIs. In this study, we employed a CFD model to examine the removal of pollutants by FTIs and sediment deposition, as well as to assess how different FTI configurations influence both processes. By incorporating a control system, we aimed to showcase the advantages of FTI systems over traditional stormwater retention systems. This comprehensive approach allows us to gain insights into the complex dynamics of pollutant removal in FTI systems and provides valuable information for the development of effective FTI design guidelines.

The geometry of the stormwater pond was selected to replicate the pond described in Khan et al. (2013). The pond consisted of a rectangular tank with sloping sides in a 2:1 ratio (horizontal:vertical), with top dimensions of length, width, and depth measuring 41.0 m, 15.0 m, and 2.3 m, respectively. The inlet and outlet pipes had diameters of 450 mm and 1050 mm, respectively, which corresponded to the dimensions presented in Xavier et al. (2018). The geometric specifications for all FTI configurations are presented in Table 1 and visually depicted in Fig. 1. In each case, the total volume occupied by the root zone was maintained at 11% of the overall pond volume.

Table 1

Dimensions of the root zones (length, width, depth) given in meters.
	FTI 1	FTI 2	FTI 3	FTI 4	FTI 5 and FTI 6
Case 1	6.0, 7.7, 1.05	6.0, 7.7, 1.05	-	-	-
Case 2	3.0, 8.0, 2.0	3.0, 8.0, 2.0	-	-	-
Case 3	3.0, 7.7, 1.05	3.0, 4.9, 1.05	3.0, 4.9, 1.05	3.0, 7.7, 1.05	3.0, 4.9, 1.05
Case 4	12,7.7,1.05	-	-	-	-
Case 5	15.4, 3.0, 1.05	15.4, 3.0, 1.05	-	-	-

FIGURE 1.

To analyze the flow field within the pond, the computational fluid dynamics (CFD) software ANSYS CFX® 17.0 was employed. A three-dimensional transient simulation was conducted using the Shear Stress Transport (SST) Reynolds-Averaged Navier-Stokes (RANS) turbulence model. Detailed information about the model and its validation can be found in Xavier et al. (2018). The evolution of the concentration field, C, was described using conservation of mass,

$$\frac{\partial C}{\partial t}+{U}_{j}\frac{\partial C}{\partial {x}_{i}}=\frac{\partial }{\partial {x}_{i}}\left(D\frac{\partial C}{\partial {x}_{i}}-\stackrel{-}{{u}_{i}c}\right)+{S}_{C}$$

with turbulent Schmidt number, Sc = ν/D_T = 1 (D_T is the turbulent diffusivity), which falls within the range of measured values (e.g., Gualtieri et al., 2017). To assess the relative contributions of the sediment deposition at the bottom of the pond and the FTWs upon the mass removal, multiple simulations were run for each case.

First, the removal achieved through FTIs was calculated by conducting the tracer simulation (Eq. 1) with the removal term (Sc) activated exclusively for the FTIs. Specifically, within the FTI region, mass removal was represented by a first-order decay reaction (Sc = -krC), while outside the FTI, Sc was set to zero. Xavier et al. (2018) estimated a removal rate (kr) of 0.0071/s for total nitrogen, derived from measured removal within mesocosms conducted by Chang et al. (2012) and Chua et al. (2012). The water surface and all solid surfaces were modeled with a no-flux boundary condition.

One significant difference from the setup employed by Xavier et al. (2018) lies in the modeling of the tracer. In this case, two materials were created for this purpose. The first material, referred to as "Sed," shared the same characteristics as water except for its density, which was set to 2150 kg/m³ and 2190 kg/m³ for the simulations involving the original and larger sediments, respectively. These values were chosen based on the median particle diameter and density reported by Zanders (2004), who focused on sediments from road runoff. The second material, named "watersed," represented a variable composition mixture consisting of water and the "Sed" material. This approach allowed for the separate insertion of the tracer into the water, resembling the methodology employed by Xavier et al. (2018). However, it is important to note that the hydrodynamics of the tracer differed due to its higher density.

The removal achieved through sedimentation was determined by conducting the tracer simulation with the removal mechanism activated solely for sedimentation. The sedimentation rate was estimated using the equation proposed by Einstein and Krone (1962):

$${S}_{C}=\left\{\begin{array}{c}0, \tau >{\tau }_{c}\\ \frac{{w}_{s}rC}{\varDelta z}\left(1-\frac{\tau }{{\tau }_{c}}\right), \tau <{\tau }_{c}\end{array}\right.$$

where w_s is the settling velocity, r is an empirical coefficient set equal to 2 (Parker et al., 1987), τ_c is the shear stress below which the sediment deposits, C is the sediment concentration, and Δz is the height of the computational grid elements attached to the bottom of the pond. The critical shear stress can be approximated as follows (Julien, 2010):

$$\frac{{\tau }_{c}}{\left({\rho }_{p}-{\rho }_{w}\right)g{d}_{p}}={\tau }_{*c}=0.25{d}_{*}^{-0.6}\text{tan}\varphi$$

where

$${d}_{*}={\left[\frac{\left({\rho }_{p}-{\rho }_{w}\right)g}{{\rho }_{w}{\nu }^{2}}\right]}^{\frac{1}{3}}{d}_{p}$$

where ρ_p is the density of the particle; ρ_w is the density of the fluid; g is the gravitational acceleration (9.8 m/s²); ν is the kinematic viscosity, φ is the angle of repose, and d_p is the diameter of the particle. Eq. 2 is valid for 0.3 < d_* < 19. The settling velocity is equal to (Cheng, 1997):

$${w}_{s}=\frac{\nu }{{d}_{p}}{\left(\sqrt{25+1.2{d}_{*}^{2}}-5\right)}^{1.5}$$

Two particle diameters were tested in this study, namely d_p = 44 and 112 µm, which correspond to the median particle diameter observed at two distinct road sites in North Carolina (Winston and Hunt, 2017). These values also fall within the range of median particle diameters measured at commercial parking lots and residential basins (Selbig et al., 2016). Additionally, the tested particle diameters ranged from 11 to 150 µm, which encompasses sediments known to carry nutrients such as phosphorus and nitrogen in stormwater (Vaze and Chiew, 2004). The particle density was assumed to be 2.65 g/cm³, a value consistent with reported values from various stormwater runoff studies (ranging from 2.1 to 2.9 g/cm³; Ferreira and Stenstrom, 2013). For particles with rounded shapes within the range of diameters considered in this study, the angle of repose was approximately 30 degrees (Simons, 1957). The water density and kinematic viscosity were taken as 10³ kg/m³ and 10^− 6 m²/s, respectively. Based on the data obtained, the critical shear stress for mass removal was determined to be 0.072 Pa for the original sediment and 0.108 Pa for the larger sediment.

The third run for each case encompassed the implementation of Eq. 1, wherein the removal mechanism was activated for both FTIs and sedimentation. To accurately determine the amount of mass removed, a mass balance analysis was conducted by quantifying the mass passing through planes strategically positioned within the pond. These planes, illustrated in Fig. 2, spanned the complete vertical range of the channel, stretching from its bottom to its surface. By employing this approach, we obtained valuable insights into the spatial distribution of removed mass, facilitating a comprehensive understanding of the removal dynamics within the system.

FIGURE 2.

The findings presented in Fig. 3 provide an insightful analysis of the velocity vectors and contour map at the bottom of the pond. Notably, the inlet jet experienced a deflection towards one side of the pond, reattaching at the wall. Upstream of this reattachment point, a small circulation zone emerged. Subsequently, the flow proceeded towards the opposite wall, wherein a portion of it was redirected towards the upstream side, resulting in the formation of a substantial circulation zone. Interestingly, in the ponds equipped with FTIs, the longitudinal elongation of the upstream large recirculation zone was observed, contrasting the pond without FTI.

As the downstream flow progressed, it underwent a bifurcation, giving rise to two distinct pathways. The first pathway contributed to the emergence of an additional recirculation zone, while the second pathway followed the sidewall until reaching the pond outlet. The extent of the downstream recirculation zone exhibited variations among the experimental cases. In the control case (Control), the recirculation zone occupied the entire area, whereas in Cases 1 to 3 (with the core positioned upstream of the second FTI), it encompassed approximately half of the area. Remarkably, in Cases 4 and 5, the recirculation zone covered less than one-third of the area. This reduction in size can be attributed to the presence of FTIs, which effectively mitigated the downstream recirculation zone, facilitating a more homogeneous lateral distribution of the flow towards the end of the pond. Importantly, this observed flow pattern demonstrated consistency across different heights, thereby corroborating the findings reported by Nuruzzaman et al. (2023). Their study highlighted the advantageous role of placing a FTI near the inlet in promoting enhanced flow uniformity within the pond compared to other FTI configurations. Consequently, the presence of FTIs fosters a more uniform spreading of the flow across the width of the pond, resembling a plug flow. Plug flow, characterized by uniform velocity profiles, offers particular benefits for mass removal within the pond, encompassing processes such as sedimentation and microbial activity (Andradóttir, 2017). However, it is important to clarify that mass removal through microbial activity falls outside the scope of this study.

Furthermore, it is worth noting that small recirculation zones were observed in the corners of the pond, albeit their characteristics varied depending on the height and specific case studied.

FIGURE 3.

The sedimentation dynamics in this study are governed by Eq. 2, which incorporates the influence of bottom shear stress on sediment deposition. Therefore, analyzing the shear stress contour map at the pond bottom provides valuable insights into the role of FTIs in sedimentation processes. To illustrate this, Fig. 4 presents a visual representation of the shear stress distribution for the original sediment. In accordance with Eq. 2, sedimentation gradually decreases as bottom shear stress increases until a critical threshold is reached, beyond which no further sedimentation occurs (indicated by the white areas in Fig. 4). In the larger sediment tests (not shown here, it was observed that the white zone decreased in size due to the increase in critical shear stress.

FIGURE 4.

The shear stress distribution at the bottom of the pond reveals several significant observations. Primarily, higher magnitudes of bottom shear stress are observed along the path of the primary jet. In the absence of FTIs (Control), the primary jet extends its reach to more distant regions from the pond inlet, resulting in elevated bottom shear stress levels in those areas. However, in the presence of FTIs, particularly near the inlet, the normal trajectory of the jet is disrupted, leading to a redirection of a portion of the incoming flow beneath the FTIs (Fig. 4). This diversion intensifies the bottom shear stress and reduces the available area for sediment deposition compared to the control case. Remarkably, the region beneath the first FTI exhibits an overwhelming exceedance of the critical bottom shear stress, resulting in a substantial reduction in sediment deposition. As the flow approaches the outlet, the bottom shear stress gradually decreases, approaching a value close to zero (approximated by 1 - τ/τc ≈ 1 in Eq. 2), allowing for a greater extent of sediment deposition. In tests involving larger sediment sizes, the white zone indicating non-sediment deposition decreases in size due to the increase in critical shear stress.

However, a notable exception is observed in Case 2, where the extension of the sediment deposition area decreases compared to the control case (Fig. 4). This can be attributed to the greater depth of the root zone in the FTI of Case 2 relative to the other cases. The deeper root zone significantly obstructs the longitudinal flow (Fig. 5), causing a substantial portion of the flow to be diverted along the lateral sides of the FTI. Consequently, the depth of the root zone reduces the bottom shear stress, limiting the extent of non-sediment deposition (white area) in the longitudinal direction.

FIGURE 5.

In addition to the significance of bottom shear stress, tracer concentration emerged as a crucial factor influencing sedimentation dynamics, as highlighted by Eq. 2. Interestingly, while the potential for sediment deposition increased as we approached the outlet due to reduced bottom shear stress, a contrasting trend was observed with tracer concentration. As the tracer traveled from the inlet to the pond outlet, its concentration gradually decreased, indicating a decreased likelihood of sediment deposition according to Eq. 2. In the absence of FTIs (Control), where the jet remained unobstructed, the decline in tracer concentration was relatively moderate, as the high-concentration jet flowed more directly towards regions farther from the inlet. However, in the presence of FTIs, where a portion of the jet was hindered, a fraction of the concentrated tracer was redirected upstream of the FTIs, while another fraction continued downstream. Notably, Case 2 exhibited a significant obstruction of the jet by the FTI, resulting in a reversal of flow back towards the pond inlet. Consequently, the high tracer concentration predominantly localized in regions characterized by elevated bottom shear stress at the pond bottom, with implications for the amount of sediment deposited.

When examining mass retention within the pond, it is important to consider the scenario where sedimentation is the sole mechanism of mass retention (Fig. 6). The presence of FTIs had a noticable impact on increasing mass retention through sedimentation compared to the control case. The relative differences between the configurations with FTIs and the control case (e.g., (Case 1 - Control) x 100 / Control) ranged from 9.1–17.3% for the original sediment and from 6.9–9.6% for the larger sediment. These findings indicate that while FTIs do not directly remove mass through their root zone, they contribute significantly to enhancing sediment deposition. On average, the relative difference in mass deposition for the larger sediment was 24.8% higher compared to the original sediment.

The impact of FTIs on the total mass removal varied among the different configurations, with a more pronounced effect observed for the original sediment compared to the larger sediment. The maximum relative difference among cases for the original sediment was 7.5%, whereas for the larger sediment it was 2.6%. This discrepancy can be attributed to the settling velocity of the sediments. In the case of the larger sediment, the settling velocity exceeded the critical velocity, determined by the water depth and the inflow time through the pond (hL/U), except for Cases 0 and 5 (Camp, 1946). Conversely, all cases involving the original sediment exhibited settling velocities lower than the critical velocity. Another factor explaining the greater influence of the configuration on the behavior of the original sediment was the larger difference in deposition area among the configurations compared to the larger sediment. These factors collectively account for the enhanced significance of the FTI configuration in relation to the original sediment compared to the larger sediment. Nonetheless, Cases 1 and 2 consistently demonstrated the highest effectiveness in sediment retention within the pond, surpassing the other configurations.

FIGURE 6.

The relationship between the mass retained through sedimentation and the short-circuit index, q₁₀, is depicted in Fig. 7. The short-circuit index, defined as q₁₀ = t₁₀/T_n, represents the dimensionless time required for the first 10% of tracer mass to exit the pond (where T_n is the nominal residence time, and t₁₀ is the time at which 10% of the injected mass has exited the basin). Hydraulic short-circuiting presents a prevalent challenge in pond hydraulics, as it circumvents the treatment process, particularly the sediment deposition that contains pollutants, when stormwater takes a direct path through the pond. The correlation observed between the short-circuit index and sedimentation in ponds with FTIs implies its potential as a robust indicator. The introduction of FTIs demonstrated a notable reduction in short-circuiting when compared to the control pond. Alongside FTIs, various other solutions have been proposed by engineers to mitigate short-circuiting, including the implementation of long aspect ratios, sinuous channels, baffles, and deep zones. Additionally, the utilization of islands (not FTIs) as a measure to redirect inflow and optimize circulation within treatment wetlands and ponds has been suggested (Guzman et al., 2018). Our findings underscore the critical significance of meticulous basin design and effective flow control mechanisms in mitigating short-circuiting and enhancing treatment efficiency.

FIGURE 7.

When examining mass retention solely through the root zones of FTIs, without considering sedimentation, the sequence of configurations with the highest efficiency was as follows: Case 1 > Cases 4 and 5 > Case 3 > Case 2 (Fig. 6). The relative difference between Case 1 (worst) and Case 2 (best) was approximately 20%. This highlights that the influence of FTI configuration is more significant for mass removal through the FTIs than through sediment deposition. A more comprehensive discussion on the impact of different configurations on mass removal solely through the FTIs can be found in Xavier et al. (2018), whose objective was to evaluate mass removal exclusively through FTIs. However, it is important to note that overall pond hydraulics usually fail to capture mass removal occurring solely within the FTIs. For instance, Nuruzzaman et al. (2023) demonstrated that indicators of overall pond hydraulic performance (e.g., short-circuiting) do not establish a clear relationship with pollutant mass removal. Nonetheless, treatment efficiency is highly dependent on the hydraulic behavior within the FTIs (e.g., residence time).

Finally, when considering mass removal through both FTIs and sedimentation to the bed, the overall mass removal was significantly enhanced compared to the control case, as depicted in Fig. 6. The relative difference between the configurations with FTIs and the control case (e.g., (Case 1 - Control) x 100 / Control) ranged from 26.2–33.3% for the original sediment and from 9.2–11.9% for the larger sediment. On average, the relative difference in mass deposition for the larger sediment was 12.6% higher than that of the original sediment. Therefore, the presence of FTIs substantially increased mass removal when compared to the control pond configuration.

Among the different configurations, Case 1 demonstrated the highest efficiency, closely followed by Case 2, while Cases 3, 4, and 5 exhibited nearly identical overall performance. The maximum relative difference between the cases with FTIs was low (less than 6.0%). When both processes, namely FTIs and sedimentation, were responsible for mass removal, the individual retention capacities of each process were lower compared to when only the individual processes were involved in mass removal. This suggests that the sedimentation occurring upstream of the FTIs reduced the mass received by them, subsequently decreasing their mass removal efficiency. Similarly, the mass removed by the FTIs reduced the quantity of mass available for deposition downstream of the FTIs.

Although it is intriguing to evaluate the influence of different configurations on overall mass removal, it is also essential to examine how mass removal occurs within the pond (Fig. 8). Let's consider the example of the large sediment, where the absence of FTIs (Control) led to a higher sediment accumulation in the initial 7.0 meters of the pond compared to the configurations with FTIs. In this upstream section of the FTIs, their impact has already been observed, as the presence of FTIs decelerated the flow velocity upstream of the leading edge of the FTIs near the water surface and increased it around and below the FTIs (Fig. 5), thereby reducing sediment deposition.

FIGURE 8.

Beyond this initial segment, the configurations with FTIs exhibited enhanced mass removal compared to Control. This improvement can be primarily attributed to the mass removal facilitated by the FTIs themselves, with a smaller contribution from sediment deposition. The ratio between the change in mass removal and the change in longitudinal distance experienced a significant increase at the beginning of the FTI. Notably, in Case 2, featuring the deepest FTI among all cases, the presence of the FTI resulted in a gradient exceeding 400% (observe the change in slope in Fig. 8 from longitudinal distance 5.5 m to 11.5 m). As mentioned earlier, this increase in mass removal is predominantly due to the FTIs and not sedimentation.

Furthermore, once the 15.0-meter mark was reached, all configurations incorporating FTIs demonstrated higher mass removal compared to the pond without FTIs. When FTIs were positioned in series, the magnitude of the ratio between the change in mass removal and the change in longitudinal distance increment was considerably reduced for the second FTI. In Case 1, for example, this gradient exceeded 170% for the first FTI, while it was approximately 35% for the second FTI. Hence, despite the observed influence of the second FTI on mass removal in cases where FTIs were arranged in series, its effect was notably more modest compared to the first FTI. This reduced mass removal in the downstream FTI has previously been linked by Xavier et al. (2018) to a lower proportion of inflow entering the downstream FTI. In other words, if less flow enters the FTI, there is a decrease in mass removal. When comparing the different configurations with FTIs in series, in line with the observations made by Xavier et al. (2018), the mass removal by the second FTI in Case 2 was lower than in Cases 1 and 3, as the inflow of mass was reduced.

In the latter portion of the pond, the differences in mass removal among the configurations with FTIs diminished, reaching less than 5.0%. For the ponds with FTIs, the slope at which the mass removal increased declined with increasing longitudinal distance because, as the mass removal increased, the available tracer concentration diminished, resulting in less tracer concentration available to be removed and thus slowing down the rate of mass removal (see Eq. 2). However, since there was still a significant distance remaining until the end of the pond, the configurations that still had a higher tracer concentration experienced a greater mass removal, whether through FTIs or sedimentation. This finding suggests that the configuration primarily influences mass removal from the first FTI to the midpoint of the pond.

Figure 9 offers an additional perspective on the findings discussed earlier, providing a visual representation of the pond length required to achieve specific levels of mass removal. For instance, in Case 4, a length of 15.0 meters is necessary to achieve a 60% mass removal. This figure holds practical implications, as it allows us to extract valuable insights. Taking Case 2 as an example, which requires a shorter pond length compared to the other configurations to achieve a mass removal of 70%, the primary contribution to mass removal occurs due to the presence of the first FTI. The second FTI contributes minimally to mass removal; in fact, from the second FTI to the end of the pond, there is only a gradual increase in mass removal through sediment deposition. Thus, if a 70% removal is desired, a significantly shorter pond length of approximately 15.0 meters might be sufficient for Case 2. It is important to emphasize that this reduced length would also alter the hydrodynamics of the pond, potentially influencing mass removal. Nonetheless, similar practical implications can be deduced from the graph presented in Fig. 8.

FIGURE 9.

The study revealed that the introduction of FTIs had a notable impact on flow patterns and sediment removal. Without FTIs, the primary jet extended further into the pond, leading to elevated bottom shear stress levels in distant regions. However, the presence of FTIs disrupted the normal trajectory of the jet, diverting a portion of the flow beneath the FTIs. This diversion increased bottom shear stress and reduced the area available for sediment deposition compared to the control case without FTIs. The depth of the root zone within the FTIs also played a role in sediment deposition. A deeper root zone obstructed the longitudinal flow, redirecting a substantial portion of the flow along the lateral sides of the FTI. This, in turn, reduced bottom shear stress and limited non-sediment deposition in the longitudinal direction.

Regarding mass retention, the study demonstrated that FTIs significantly enhanced sediment deposition, leading to increased mass removal compared to the control case without FTIs. The relative difference in mass deposition was higher for larger sediment particles than for the original sediment. The short-circuit index exhibited a correlation with sedimentation in ponds with FTIs. The presence of FTIs reduced short-circuiting compared to the control pond configuration, indicating the potential of FTIs as a robust indicator for enhancing treatment efficiency.

In terms of mass removal exclusively through the root zones of FTIs, the positioning of FTIs inside the pond resulted in differences of up to 20% in mass removal. The influence of FTI configuration was more pronounced for mass removal solely through the FTIs than through sediment deposition alone. When removal occurred through both sediment deposition and FTIs, the presence of FTIs led to higher mass removal, particularly in the initial segment where the change in mass removal was primarily attributed to the FTIs rather than sedimentation. The effect of the second FTI in cases with FTIs arranged in series was more modest compared to the first FTI. Depending on the FTI configuration, the pond could be less than half its length and still provide a mass removal of over 70% (for large sediment particles).

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Authors Contributions

All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by Manoel Lucas Machado Xavier, Johannes Gerson Janzen and Heidi Nepf. The first draft of the manuscript was written by Manoel Lucas Machado Xavier and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

Funding

The authors declare that no funds, grants, or other support were received during the preparation of this manuscript.

Competing Interests

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.

-Availability of data and materials

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Modeling Mass Removal and Sediment Deposition in Stormwater Ponds Using Floating Treatment Islands: A Computational Approach

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