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Modelling urban stormwater treatment—A unified approach
e c o l o g i c a l e n g i n e e r i n g 2 7 ( 2 0 0 6 ) 58–70
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Modelling urban stormwater treatment—A unified approach Tony H.F. Wong a,b,c , Tim D. Fletcher a,b,∗ , Hugh P. Duncan a,b,d , Graham A. Jenkins b,e a
Department of Civil Engineering (Institute for Sustainable Water Resources), Monash University, Vic. 3800, Australia b Cooperative Research Centre for Catchment Hydrology, Australia c Ecological Engineering P/L, 28 St. Edmonds Rd, Prahran, Vic. 3181, Australia d Melbourne Water Corporation, 100 Wellington Parade, East Melbourne, Vic. 3001, Australia e School of Environmental Engineering, Griffith University, Nathan, Qld. 4111, Australia
a r t i c l e
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a b s t r a c t
Article history:
To protect receiving waters from stormwater pollution, stormwater managers need to be
Received 22 November 2004
able to predict the performance of proposed stormwater treatment measures, under variable
Received in revised form 12
operating conditions. This paper describes the development of a model, capable of predicting
October 2005
the performance of stormwater wetlands, ponds, vegetated swales, sediment basins and
Accepted 24 October 2005
biofilters, with a single algorithm. The model describes two principal processes: (a) water quality behaviour and (b) hydrodynamic behaviour. Water quality is described by a first-order kinetic decay model (named the “k–C*” model,
Keywords:
after its two parameters, the decay rate, k, and equilibrium concentration, C*). However, since
Stormwater treatment model
pollutant removal depends on flow behaviour, the continuously stirred tank reactor (CSTR)
First-order kinetic decay
concept is used to account for the hydrodynamics within a treatment device. Where the
Hydrodynamics
device has a high degree of turbulence or short-circuiting (such as in a sediment basin), the
k–C*
k–C* model is applied through a small number of CSTRs in series, whereas a well-designed
CSTRs
wetland with even flow distribution is modelled by a high number of CSTRs. The unified model has been successfully tested on a series of treatment measures—a wetland, pond, swale, grass filter, gravel filter, and large lake. Necessary research to address limitations and assumptions of the model is described. © 2005 Elsevier B.V. All rights reserved.
1.
Introduction
The impacts of urban stormwater on receiving waters are well known, and include water quality degradation, flow-induced erosion, and habitat loss (House et al., 1993; Marsalek, 1991; Novotny and Witte, 1997; Rutherfurd and Ducatel, 1994; Walsh, 2000). In recent years, many government and community organizations have placed increasing emphasis on developing and implementing strategies to reduce urban stormwater pollution (Maksimovic and Tejada-Guibert, 2001; Roesner, 1999; U.S.
∗
Corresponding author. Tel.: +61 3 9905 2599; fax: +61 3 9905 5033. E-mail address: tim.fl[email protected] (T.D. Fletcher).
0925-8574/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.ecoleng.2005.10.014
Environmental Protection Agency, 1994; Victoria Stormwater Committee, 1999). Design and implementation of stormwater treatment strategies often involve a substantial investment in the construction of stormwater treatment measures. Several stormwater treatment measures are used (e.g., ponds, wetlands, swales, infiltration systems), depending on the nature of the stormwater pollutants being targeted, and on scale and available space. In many cases, a sequence (often called a “treatment train”) of measures may be used. For example, lin-
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ear infiltration or biofiltration systems may be placed within the urban streetscape, and may convey water to a sedimentation basin and constructed wetland, before discharging to an ornamental pond (Lloyd et al., 2001). In order to prioritize the implementation of stormwater treatment measures, urban waterway managers need to be able to predict and assess their performance, both individually and in various combinations. There is thus a strong demand for predictive models, that can be applied across a range of locations and conditions, to predict the general performance of a range of stormwater treatment measures (Phillips and Thompson, 2002). In response to this need, stormwater modelling software such as AQUALM (and its varieties) and SWMM (and its varieties) has been developed (Phillips and Thompson, 2002; US EPA, 1994; Wong et al., 2002). Many of these models provide sophisticated descriptions of pollutant generation behaviour and of hydraulic behaviour, but their descriptions of treatment behaviour are limited by available underlying treatment algorithms and by the range of treatment measures to which they can be applied. For example, XP-AQUALM provides a sedimentation model for ponds, as well as user-defined retention curves. For most other treatments, the software requires userdefined retention curves (McAlister et al., 2003). Similarly, the basis of SWMM’s stormwater treatment prediction is based on the choice of a user-defined first-order decay rate, or sedimentation theory with particle-size specific settling velocity distributions for pollutants (Huber et al., 1987; McAlister et al., 2003). SWMM also utilizes user-input as to whether flow is completely mixed, or plug flow, to predict the overall level of treatment for a pollution control pond. Ideally, an integrated stormwater model would utilize a consistent framework for modelling the majority of stormwater treatment measures. Such a model would be able to describe pollutant behaviour through an individual event, as well as through a long continuous run of events and interevent periods. Despite a substantial effort in monitoring of stormwater treatment measures around the world (Duncan, 1997a; Gamble and Walker, 1995; Krejcik et al., 1999; Urbonas, 1995), few of these data have been used effectively to provide reliable predictions of treatment performance (Strecker et al., 2001). A number of authors have developed algorithms using deterministic or pseudo-deterministic approaches, which can describe well the detailed behaviour of a specific stormwater treatment measure (e.g., Deletic, 2001; Lee et al., 1989), in some cases for a limited range of operating conditions. There are many such models, with diverse objectives, assumptions, and applications. At the other end of the scale, some researchers have taken a statistical approach, relating observed performance at a range of temporal scales to parameters which describe the treatment measure, its catchments, or the relationship between them (e.g., Duncan, 1997a, 1997b; Reckhow and Qian, 1994; Strecker et al., 2001). However, the relationships utilized in this approach are generally very noisy, and thus do not account adequately for the observed variability. Neither approach has quite met the requirements for integrated stormwater management modelling. The mechanisms involved in the removal of stormwater pollutants encompass physical, chemical, and biological pro-
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cesses. Whilst the detailed long-term behaviour may be very complex (Kadlec and Knight, 1996), the processes associated with sedimentation and filtration (through vegetation or a filtration medium) are dominant in the initial interception of stormwater contaminants during a storm event. In this paper, it is proposed that the overall behaviour of pollutants as they pass through a range of treatment measures can be described by a unified model, based on a simple first-order kinetic decay algorithm, coupled to an existing model of flow hydrodynamic behaviour. Common stormwater treatment measures—vegetated swales, wetlands, ponds, sedimentation basins, and infiltration systems are considered to be a single continuum of treatment based around two fundamental processes operating during the passage of a storm event through these measures, i.e., (i) flow attenuation and detention and (ii) particle sedimentation and filtration. In this context, a vegetated swale is just an ephemeral vegetated wetland usually operating at a higher hydraulic loading than a constructed wetland. Similarly, ponds are modified wetlands characterized by deeper open water and fringing vegetation. Hydraulic loading, vegetation density and areal coverage, hydraulic efficiency, and the characteristics of the target pollutants (e.g., particle-size distribution and contaminant speciation) largely influence their differences in performance. In the same way, infiltration systems simply use vertical filtration processes, instead of the horizontal filtration processes, which occur in swales and wetlands. Despite their apparent differences, the basic physical processes occurring in each of these stormwater treatment measures are the same. Consequently, it is proposed that these processes can be modelled using a unified approach. Obviously, chemical and biological processes also contribute to pollutant removal, and so the unified model needs to describe the overall pollutant removal behaviour. The objective of a unified modelling approach is to provide an efficient, reliable, and widely applicable model for predicting pollutant removal from a range of stormwater treatment measures. The model has been incorporated into a software package called Model for Urban Stormwater Improvement Conceptualization (MUSIC) (Cooperative Research Centre for Catchment Hydrology, 2005), which is used by urban water managers to evaluate and prioritize stormwater treatment strategies based on predicted hydrologic and water quality outcomes. This paper: (i) outlines the conceptual basis behind the proposed unified stormwater treatment model, and (ii) presents tests of its application to a range of stormwater treatment measures.
2.
Background theory
Modelling stormwater treatment requires simulation of the two principal processes, which influence the degree of pollutant removal from stormwater treatment measures: (a) water quality behaviour, and (b) flow hydrodynamic behaviour.
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2.1. Water quality behaviour—the first-order kinetic decay (k–C*) model A simple model describing pollutant removal is a twoparameter first-order decay function (Eq. (1)), which expresses the rate at which pollutant concentration moves towards an equilibrium or background concentration (C*), with distance along the treatment measure, as a linear function of the concentration (Kadlec, 2000; Kadlec and Knight, 1996): q
dC = −k(C − C∗ ) dx
(1)
where q is the hydraulic loading rate (m/year), defined as the ratio of the inflow and the surface area of the system, x is the fraction of distance from inlet to outlet, C is the concentration of the water quality parameter, C* is the background concentration of the water quality parameter, and k is the areal decay rate constant (m/year). The parameters k and C* are lumped parameters representing the combined effects of a number of pollutant removal mechanisms. A high value of k results in a rapid approach to the equilibrium concentration C*, and hence a higher treatment capacity (provided that C* is less than the inflow concentration). We contend here that this model, known as the “k–C* model”, can be applied to a wide range of pollutants, including total suspended sediment (TSS), total phosphorus (TP) and total nitrogen (TN). We also demonstrate its application for predicting treatment of biochemical oxygen demand (BOD) and turbidity through a treatment system. The behaviour of heavy metals in previously published studies (e.g., Scott and Fulton, 1978) suggests that it could also be useful for predicting their treatment behaviour. We hypothesise that the k–C* model acts to describe the overall movement towards an equilibrium. Therefore, it can describe the overall movement towards the physical equilibrium in particle sedimentation or filtering, or the complex biochemical equilibrium in treatment of nitrogen. Our hypothesis is that the model can describe the overall behaviour in most cases. The k–C* model assumes steady and plug-flow conditions, and has been widely used (e.g., Mitsch et al., 1995; Upton and Green, 1995), particularly in predicting water quality improvement in wastewater treatment wetlands. Departure from the assumed plug-flow conditions of the k–C* model is considered to be amongst the most significant factors influencing the accuracy of the model. Plug-flow conditions rarely, if ever, occur in the field; some degree of dispersion and mixing usually occur. Coupling of the k–C* model with a flowhydrodynamic model (see next section) goes some way to accounting for the variable conditions observed in stormwater treatment facilities.
2.2. Flow hydrodynamic behaviour—the continuously stirred tank reactor (CSTR) model The treatment effectiveness of a stormwater treatment measure depends upon the flow behaviour in that system. The most effective treatment will occur where the entire treatment surface area is engaged, and there are no stagnant zones,
Fig. 1 – Examples of distribution of tracer concentration over time (V, volume; Q, discharge; V/Q, theoretical detention time) (Persson et al., 1999).
nor flow short-circuiting through preferential flow paths. Flow conditions approaching plug flow will be conducive to effective treatment, since all ‘parcels’ of inflow will be subject to equal detention time. This behaviour is explained by Kadlec and Knight (1996), who introduce the retention time distribution (RTD) function to describe how hydraulic residence time varies. For example, consider the situation where a parcel of water, dosed briefly with a conservative tracer, flows through a detention system such as a wetland (Fig. 1). Under idealised plug-flow conditions, the concentration–time distribution of the tracer is a spike with a very small deviation about the mean residence time. In this case, each parcel of tracer entering the wetland experiences a similar period of detention. Poor flow distribution conditions (see Fig. 1) are akin to the fully-mixed (often called ‘continuously stirred’) flow conditions. The concentration–time distribution takes the form of an exponential decay function. This flow condition can be modelled as a single continuously stirred tank reactor, where the effect of flow dilution in steady flow conditions progressively reduces the tracer concentration at the outflow. Idealised plug-flow conditions can be simulated by representing the detention storage as a large number of CSTRs in series. The degree to which flow hydrodynamic conditions in a stormwater treatment measure depart from an idealised plugflow condition can be modelled by appropriate selection of the number of CSTRs. A single CSTR (such as a small pond with low aspect ratio) will result in a pollutant hydraulic residence time distribution represented by an exponential decay function (strongly right-skewed), where the peak discharge concentration occurs almost immediately after dosing, and concentration then reduces with the effects of dilution. Conversely, as the number of CSTRs in series increases, the residence time distribution becomes more like plug flow (such as may be observed in a long vegetated swale), and the time-lag of the peak discharge concentration is closer to the nominal detention time (given by volume/discharge). Persson et al. (1999) introduced a quantitative measure of flow hydrodynamics in stormwater to enable easy comparison of detention systems of different shape and inlet/outlet locations. This measure is referred to as hydraulic efficiency (), designed to reflect (i) the effective volume of the storage, and (ii) the hydraulic residence time distribution (Eq. (2)). The effec-
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Fig. 2 – Hydraulic efficiency (), effective volume ratio (ev ) and the number of CSTRs (N), for hypothetical stormwater treatment systems (A–M), showing the appropriate number of CSTRs (after Persson et al., 1999). Arrows show inflow and outflow; circles (case K and L) show islands. Multiples arrows (case E) show distributed inflow, whilst barriers show berms to elongate flow path (case F) and porous wall to spread flow (case M).
tive volume represents the proportion of the storage actively engaged by the flow path (to account for zones of zero flow or recirculation, such as fringing vegetation areas). The values of hydraulic efficiency range between 0 and 1, with near zero values reflecting poor flow hydrodynamic conditions and values close to unity representing near plug-flow conditions. Persson et al. (1999) demonstrate that hydraulic efficiency is equivalent to the ratio of the peak of the hydraulic residence time distribution to the nominal residence time (given by V/Q in Fig. 1). The number of continuously stirred tanks (NCSTR ) can be related to the hydraulic efficiency of the treatment facility (Eq. (2)) (Persson et al., 1999).
= ev 1 −
1 N
=
t p
tn
‘parcels’ of more and less treated water move through it. To describe water quality behaviour completely, it is therefore necessary to consider both the pollutant depletion and the flow hydrodynamics simultaneously. The k–C* model must be applied to notionally discrete batches of water. The CSTR model provides notional batches of this form. Hence, the k–C* model can be applied to each of these notional batches in series. In practice, the n notional batches (or ‘notional storages’) are assumed to have 1/nth of the volume of the (real) overall storage. The k–C* model and the flow-hydrodynamics model are therefore linked by the representation of treatment systems in terms of their number of CSTRs, and the application of the k–C* model to each of the CSTRs in turn.
(2)
where is the hydraulic efficiency (ratio ranging from 0 to 1) of the system, ev the effective volume (ratio ranging from 0 to 1, defined by the proportion of the storage actively engaged by the flow path), N the number of continuously stirred tank reactors, tp the time of the peak of the hydraulic residence time distribution, and tn the time of the nominal residence time distribution (defined by the ratio of storage volume to discharge rate). In design, it is possible to estimate the hydraulic efficiency and effective volume of a proposed stormwater treatment measure and use these to determine the appropriate number of CSTRs to account for the effects of shape, inlet and outlet locations, bathymetry, and vegetation characteristics on hydrodynamic behaviour. This is illustrated in Fig. 2, adapted from Persson et al. (1999), which shows a range of shapes, their respective hydraulic efficiencies, effective volume ratios, and equivalent number of CSTRs. In modelling, each case is used with the number of CSTRs rounded to the nearest integer (as explained below). During unsteady flows (i.e., real stormwater systems), water quality varies throughout the storage volume, as
2.3. Testing the applicability of the first-order kinetic decay (k–C*) model Application of the first-order kinetic decay (k–C*) model was tested on a range of stormwater treatment facilities: (a) ponds and wetlands, (b) vegetated swales and filter strips, and (c) gravel filters. For each application, the methods of monitoring and analysis are briefly described in the following sections, and the observed results are compared with those predicted from the model. The purpose of testing described here is not to report appropriate values of k and C* for a given treatment type or site, but rather to assess whether the first-order kinetic decay model adequately describes observed pollutant behaviour. The testing utilized both existing data reported in the literature, and new data collected by the authors. In each case, the k–C* model is fitted to observed data using the objective function of minimizing the root mean square error (RMSE) (Eq. (3)). The methods and results of each of these applications are
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Fig. 3 – Experimental channel layout in Hallam Valley wetland, with dosing inlet shown (inset).
presented and discussed in the following sections
n 1 2 RMSE = (Oi − Pi ) n
(3)
i=1
where RMSE is the root mean square error, Oi the observed value of a water quality measure, Pi the predicted or modelled value, and n is the number of sampling points.
2.3.1.
using Standard Methods (Greenberg et al., 1999). Event-mean concentrations were calculated for each sampling location, and the first-order decay model fitted by minimising the RMSE (Eq. (3))
Ponds and wetlands
Field experiments were carried out in the Hallam Valley stormwater treatment wetland in Melbourne, Australia (Wong et al., 2000). The wetland is approximately 18 ha in total area, comprising various cells of open water, deep marsh and shallow marsh. Two parallel experimental channels were established within the wetland (Fig. 3). Each channel was 3 m wide, 20 m long and 250 mm deep. One was densely vegetated with Eleocharis acuta (Slender spikerush), whilst the other was open water with all vegetation removed. The channels were separated from each other and the surrounding wetland by 300 mm diameter plastic tubes filled with water. The vegetated channel was unlined, whilst the unvegetated channel was lined with plastic sheeting. An inlet and mixing box (see inset in Fig. 3), supplied by a constant-head tank, was used to discharge flow evenly into the upstream end of each channel. A dye, conservative tracer (NaBr) and known concentrations of TSS were added to the inlet boxes under steady flow conditions. Two hydraulic load rates (Eq. (4)) were used and two input particle-size distributions were used, described as either clay dominant (a fine mix with d50 of 20 m) or sand dominant (with d25 of 20 m). Samples were taken manually with a sampling rod, connected to an intake tube, connected to an autosampler pump. Samples were taken at a frequency ranging from 2 to 10 min, matched to timing of the pollutograph at each site. From the data, the pollutograph was constructed over a period of 1 h (for the high flow rate) or 2 h (for the low flow rate), at six equidistant locations along the 20 m long channel, and analysed for TSS concentration. Samples were analysed in the laboratory,
q=
Q 31536A
(4)
where q is the hydraulic loading (m/year), Q the flow rate (L/s), and A is the area of the experimental channel (m2 ). TSS concentrations measured at points along the two channels are shown (by the symbols) in the typical examples in Figs. 4 and 5, together with the predicted concentrations using k–C* models (lines). The root mean square error is low in nearly all cases (ranging from 1.9 to 8.6 mg/L) (Table 1). The average RMSE for the vegetated channel was 5.9, and 4.2 mg/L in the open channel; not statistically different (t-test) at p = 0.05. However, it is apparent that TSS concentration in the vegetated channel decays to a significantly (t-test, p = 0.02) lower equilibrium concentration (mean C* = 32.7 mg/L) than in the open water (mean C* = 59.9 mg/L). This difference reflects the ability of vegetation to facilitate sedimentation, and to reduce re-suspension, through the effects of wind protection and flow calming. The decay rate (k) was also greater in the vegetated channel (mean = 7813 m/year) than in the open water (mean = 5892 m/year), although the difference was not significant.
2.3.2.
Vegetated swales and filter strips
Testing of the applicability of the k–C* model for vegetated swales and filter strips was undertaken using previously conducted experiments on (a) stormwater treatment by a grass swale within a flume, and (b) field experiments on a grass filtration treatment of wastewater. Researchers at the University of Texas (Barrett et al., 1998; Walsh et al., 1997) used a 40 m × 0.75 m flume to create a swale, at an average slope of 0.44%, with soil and grass overlying a layer of gravel. A constant-head tank discharged to an initial mixing basin, where known concentrations of pollutants were added. The experiments used a cocktail of pollutants
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Fig. 4 – Observed and modelled TSS concentrations at Hallam Valley wetland vegetated experimental section (key to legend: V, vegetated; flow, Low or High; sediment mix, Coarse or Fine; refer to Table 1).
Fig. 5 – Observed and modelled TSS concentrations at Hallam Valley wetland open water experimental section; O, open water; flow, Low or High; sediment mix, Coarse or Fine; refer to Table 1).
Table 1 – Summary of RMSE for all runs at Hallam Valley wetland Label
Vegetation
Flow (high/low)
Sediment mix
Flow (L/s)
Hydraulic loading (m/year)
RMSE (mg/L)
VHC1 VHC2 VHF1 VHF2 VLC1 VLC2 VLF1 VLF2 OHC1 OHC2 OHF1 OHF2 OLC1 OLC2 OLF1 OLF2
Vegetated Vegetated Vegetated Vegetated Vegetated Vegetated Vegetated Vegetated Open Open Open Open Open Open Open Open
High High High High Low Low Low Low High High High High Low Low Low Low
Coarse Coarse Fine Fine Coarse Coarse Fine Fine Coarse Coarse Fine Fine Coarse Coarse Fine Fine
2.85 2.65 2.90 2.73 1.40 1.65 1.46 1.54 2.90 2.75 2.78 2.86 1.35 1.51 1.39 1.46
1498 1393 1524 1435 736 867 767 809 1524 1445 1461 1503 710 794 731 767
5.4 7.6 5.2 5.9 8.6 4.1 4.1 6.5 6.6 5.2 6.7 5.1 3.2 2.0 1.9 3.2
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Fig. 6 – Best and worst-case examples of k–C* model application to swale performance data from Walsh et al. (1997).
collected from a sediment pond, with synthetic pollutants added where necessary to match typical stormwater quality characteristics (Walsh et al., 1997). Water quality samples were taken using dedicated sampling tubes located every 10 m along the swale, and from the downstream discharge weir. We fitted a k–C* model to the published results of these experiments. The best and worst cases for TSS, TP and TN are shown in Fig. 6, along with the RMSE of the model fit. For each parameter, the best case provides an excellent fit to the observed data, and in most cases, the RMSE is much closer to the best case than the worst case (Table 2). For TSS, there is very little difference between the best and worst case: the model seems capable of describing the behaviour very well in every case.
Another published study of vegetated filters was undertaken at the Western Treatment Plant, in Melbourne, Australia, which treats sewage by a combination of primary settlement, land filtration, grass filtration, and lagoons (Scott and Fulton, 1978). In the grass filtration process, settled sewage flows through irrigation bays. The bays were 10 m wide, with slopes of 0.1 to 0.4%, and planted with grass. Scott and Fulton (1978) described a measurement program, which took water quality samples at 50 m intervals in four parallel bays over one winter irrigation season. Measured concentrations of TSS and BOD5 at each distance, averaged over the four bays, are shown in Fig. 7, together with fitted curves of the k–C* form. Scott and Fulton (1978) present results for 19 water quality parameters, and the great majority exhibit behaviour of the form shown. For example, total organic
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Table 2 – Root mean square error (RMSE, in mg/L) of model fits to Texas swale data; best (B) and worst fit cases (W) are highlighted Case
Hydraulic loading (m/year)
B C D E F G H I J K Average
19917 13693 13693 13693 4564 4564 13693 13693 19917 19917
RMSE TSS
TP
TN
2.8 (W) 14.5 6.0 4.0 10.4 4.7 10.9 (B) 2.3 6.3 n/a 6.9
0.010 0.009 0.017 0.073 (B) 0.001 0.042 (W) 0.084 0.004 0.037 0.015 0.029
0.04 (W) 0.14 0.08 (B) 0.01 0.12 0.08 0.06 0.10 0.05 n/a 0.08
Case A was excluded due to concerns about experimental conditions during this sampling run.
Fig. 7 – TSS and BOD5 concentrations in Grass Filtration Bays (after Scott and Fulton (1978)), showing model fits and RMSE in mg/L.
carbon, chromium, copper, lead, nickel, zinc and Methylene Blue active substances (MBAS) all show behaviour that is well-described by the k–C* model. The behaviour of nitrogen and phosphorus species, as well as iron and cadmium, are more erratic.
2.3.3.
Gravel filters
Sivakumar (1980) described a program of laboratory measurements of turbidity in a horizontal flow gravel filter. The filter comprised a rectangular box 1.8 m long, 400 mm wide, and 500 mm deep with an overflow set at 450 mm depth. The box was filled with gravel ranging from 2 to 12 mm in diameter. Tests were carried out for several flow rates, and for both high and low input turbidity. All results were presented by Sivakumar in terms of percent removal. Sivakumar (1980) fitted turbidity reductions as a power function of flow rate, input turbidity, depth of measurement, and length of filter. However, if the fitted results are expressed as output percent (i.e., turbidity not removed), which is more analogous to output concentration, the data can again be closely fitted by a curve of the k–C* form as shown in Fig. 8.
2.4. Case study: application of the unified CSTR and k–C* model—Blackburn Lake Having demonstrated the ability of the k–C* model to describe water quality processes within a range of stormwater treatment facilities, we undertook a case study of the combined application of the k–C* algorithm with the adopted number of CSTRs being based on the procedure of Persson et al. (1999), to describe flow behaviour and its influence on contaminant routing, and thus overall treatment performance.
2.4.1.
Site details
Blackburn Lake is located in the eastern suburbs of Melbourne, Australia, and was constructed in 1888 for agricultural water supply purposes. Its history and characteristics, along with the monitoring methodology, are described in detail by RossRakesh et al. (1999), but are summarised briefly here. The lake has an estimated permanent pool volume of 57,000 m3 and a surface area of 27,000 m2 for the permanent pool. The catchment area is 296 ha, with a mix of urban land uses (48% residential, 40% industrial, 10% open space), with total fraction imperviousness of 58% (Fig. 9).
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Fig. 8 – Turbidity in a gravel filter (after Sivakumar (1980)).
Fig. 9 – Map of Blackburn Lake catchment.
There are five inlets to the lake. The primary spillway is via a 1.9 m (inside diameter) circular spillway, whilst the low flow outlet is a rectangular orifice (cut into the side of the glory hole), with a height of 0.38 m and width of 0.76 m, giving an extended detention depth of 1.8 m.
2.4.2.
Flow and water quality monitoring
Rainfall (6 min timestep) was monitored from three sites within and around the catchment, and then distributed across the sub-catchments by Thiessen polygons (RossRakesh et al., 1999). Continuous (2 min) inflows were measured at four of the inlets (and modelled for the remaining small inlet), with discharge calculated from stage readings. Water quality sampling was undertaken during both dry weather and storm events. Manual grab sampling at the main inlet (which accounts for more than 80% of inflow to the lake), and at the outlet, was undertaken on a fortnightly basis. Wetweather sampling utilized automatic samplers at the main inlet and at the outlet. The wet-weather sampling frequency was matched to the hydrograph, with more intensive sampling during the first part of an event. At the inlet, samples were taken every 10 min for the first hour, and hourly thereafter. For most of the shorter events, the scheme was mod-
ified to collect more samples (12) at the 10 min frequency. Due to its attenuated flows, the outlet sampling had a lower frequency—set to take samples every 20 min for the first 2 h, and hourly thereafter (RossRakesh et al., 1999). Two events with good water quality data throughout the event – one in February 1996 and one in June 1996 – were used for detailed analysis in developing the unified approach to modelling stormwater treatment.
2.4.3.
Data analysis and model testing
For the examples shown below, the observed flow and concentration data have been reformatted into equal hourly timesteps, by combining readings as necessary (during events), or interpolating between readings (during inter-event periods). The combined k–C* and CSTR modelling calculations are then performed using a spreadsheet approach. Where two CSTRs are used, they are assumed to be of equal volume. Inflow to the first (or only) CSTR is the observed inflow to the lake. Inflow to the second of two CSTRs is proportioned between the observed inflow and the calculated outflow from the lake. This calculation can readily be extended to more than two CSTRs. At the start of a timestep, new water is introduced from inflow or a previous cell and the dilution effects calcu-
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Fig. 10 – TSS concentration over time in Blackburn Lake, for event of February 1996. Modelled results show calibration using 1 and 2 CSTRs.
Fig. 11 – TSS concentration over time in Blackburn Lake, for event of June 1996. Modelled results show calibration using 1 and 2 CSTRs.
lated. At the end of the timestep the decay of concentrations towards background levels is calculated for all cells. The curve fits have been optimised using the root mean square error and an iterative approach. In practice, since N must be an integer, only a small number of trials for N will be needed. In this example, k and C* have been optimised for N = 1 and 2, using the same k and C* values for both storm events. The RMSE is considerably lower when N = 2.
2.4.4.
Case study results
The observed and modelled data for the two events are shown in Figs. 10 and 11. Model results are shown both for a single CSTR and for two CSTRs, with k and C* optimised separately for each value of N. The difference in lag and curve shape can be clearly seen. N = 1 describes a single well-mixed reactor, and gives an immediate and rapid increase in simulated concentration at the start of the event, whilst N = 2 gives a smoother and more attenuated curve. There is perhaps an indication from the graphs that the observed output lies somewhere between that predicted by the k–C* model with one and two CSTRs. The general shape of Blackburn Lake suggests a width to length ratio of about one in four and hydraulic behaviour like that of
Case I in Fig. 2 ( = 0.41; N = 1.7 from Eq. (2)). Whilst interpolation between simulations utilizing one and two CSTRs would be theoretically possible, this would be computationally demanding in ‘real-world applications’, where the model would be used for long-duration, short timestep simulations. In Fig. 11, it can be seen that the ‘second peak’ (which occurs at around the 120 h mark) results in very little response from the model. This is expected, given the very small size of that event (the peak flow is 537 kL/h, compared with 6166 kL/h for the first peak). In this very large storage, such a small event would likely be fully treated by the lake. However, one can see some response in the measured points. This anomaly occurs because of inflows from sub-catchment A (Fig. 9), which effectively ‘short-circuit’ the lake’s storage given their proximity to the outlet. Additionally, calibration of the k and C* parameters has been undertaken on a lumped basis for both events (Figs. 10 and 11), with weighting of the objective function (RMSE) given to the larger events, which carry the majority of the pollutant load. Results from this case study suggest that the combined application of the CSTR and k–C* models can predict pollutant behaviour through a large ‘real-world’ stormwater treatment
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pond, which has highly variable flow rates and inflow concentrations.
3.
Discussion
Application of the first-order kinetic decay (k–C*) model to a range of stormwater treatment measures—wetlands, ponds, swales and filtration systems – has demonstrated its potential for providing an efficient modelling framework for stormwater quality improvement processes. In most cases presented in this paper, the k–C* model was able to describe the observed behaviour quite closely. The results suggest that there is an underlying similarity of overall behaviour, suggesting an underlying unity of the net effect of a number of complex processes. It must be noted that the model is intended as a conceptual analysis and design tool, and that detailed analysis may be needed for specific situations, and for detailed design. Combining the k–C* algorithm with the CSTR algorithm is an important requirement, to account for the effect of treatment design on flow hydrodynamics. The combination has demonstrated its effectiveness for a large system, with variable inflow rates and concentrations. It allows one model to be used to describe a range of stormwater treatment facilities, by changing the model parameters to reflect differences in hydraulic loading and behaviour, and pollutant characteristics. There are clear advantages in being able to describe water quality treatment across a range of different treatment measures using a unified approach. It provides computational and model-development efficiency, allowing models of different treatment measures to be developed simply by changing the input conditions (e.g., hydraulic loading and input concentration) and model parameters (decay rate, background concentration and hydraulic efficiency), without needing to create a different model structure. Use of the three-parameter (k, C* and NCSTR ) model minimizes the number of parameters to be calibrated. This is important if urban waterway managers are able to apply such
models across a range of catchments and treatment types. However, the tradeoff between model accuracy and calibration data requirements is a difficult one. The most reliable prediction of pollutant removal for a given event will be provided by a more detailed or sophisticated model, but often at the expense of prohibitive calibration requirements. Perhaps most importantly, the use of such a unified approach provides a well-defined focus for future research to enhance the model. The first priority for such research is to apply the combined CSTR and k–C* models to a range of other ‘real-world’ stormwater treatments, using monitored storm event data. One assumption underlying the first-order decay model is that of constancy of the model parameters – decay rate (k) and background concentration (C*) (Kadlec, 2000). Our own research (e.g., Deletic and Fletcher, 2004; Fletcher et al., 2002; Wong et al., 2000; Wong et al., 1999) and that of others (Kadlec, 2000) suggests that this is not really the case. The influence of hydraulic loading and inflow concentration on the model parameters (k and C*) is unclear, as shown in the examples for the University of Texas swale data (Walsh et al., 1997) (Figs. 12 and 13); however both k and C* show some tendency to increase at higher hydraulic loading rates. At high inflow concentrations, C* and k are also high, but the relationships are again quite inconsistent. It is evident that further research is needed to examine how k and C* vary with these factors. Given the importance of physical processes in removing many stormwater pollutants, the influence of particle-size and settling velocity distributions also require investigation. Further refinements to the model could incorporate a more explicit accounting for this, for example using the particle fall number approach described by Deletic (1999, 2001). To date, this approach has been used to provide ‘pseudo-calibration’ of the k–C* model for swales (Deletic and Fletcher, 2004), and is now being tested for wetlands (Fletcher et al., 2004). Research to date (and that presented in this paper) has primarily focussed on water quality behaviour during and soon after storm events. Future research will also need to investigate the fate of pollutants after the initial interception and treatment. The role of biological and chemical processes in the
Fig. 12 – Relationships between model parameters (k and C*) and hydraulic loading for TSS in Texas swale data (after Walsh et al. (1997).
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Fig. 13 – Relationships between model parameters (k and C*) and inflow concentration for TSS in Texas swale data (after Walsh et al. (1997).
subsequent transformation and removal of pollutants could be important, particularly for nitrogen (Fletcher et al., 2004). This is particularly the case for treatment measures which utilize significant storage and detention times; in these measures the inter-event (i.e., dry weather) processes may substantially influence the long-term water quality performance (Fletcher et al., 2004; Kasper and Jenkins, 2003).
4.
Conclusions
The proposal that a range of stormwater treatment measures – including wetlands, ponds, infiltration systems and vegetated swales – can be described using a unified stormwater treatment model is supported by a range of experimental data. Using this approach, differences between the various treatment facilities are accommodated by changing the model parameters to match the characteristics of the facility, rather than by changing the overall model structure. The unified stormwater treatment model provides an efficient means of predicting and assessing the performance of stormwater treatment measures. It by no means provides a complete answer to the problem of predicting stormwater treatment (because k and C* are shown to vary with changes in operating conditions). However, the model does provide a very efficient lumped approach to describing the overall water quality processes in treatment, and a useful focus for ongoing research to refine and quantify understanding of factors that influence stormwater treatment performance.
Acknowledgements The authors express their appreciation to the comments provided by Jane Catford, Barry Hart, Sally Taylor, Marie Keatley and three anonymous reviewers. Melbourne Water’s support of the experimental program is acknowledged with gratitude.
references
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RossRakesh, S., Gippel, C., Chiew, F.H.S., Breen, P.F., 1999. Blackburn Lake discharge and water quality monitoring program: data summary and interpretation. Technical Report No. 99/13. Cooperative Research Centre for Catchment Hydrology, Melbourne. Rutherfurd, I.D., Ducatel, L.R., 1994. Impact of urbanisation on natural streams. Water (AWWA J.) (April), 12–16. Scott, T.M., Fulton, P.M., 1978. Removal of pollutants in the overland flow (grass filtration) system. In: Paper presented at the International Conference on Developments in Land Methods of Wastewater Treatment and Utilization, Melbourne. Sivakumar, M., 1980. Design of a prefilter to reduce turbidity for the artificial recharge of groundwater. In: Paper presented at the AWRC Groundwater Recharge Conference, Townsville, Queensland, pp. 142–151. Strecker, E.W., Quigley, M.M., Urbonas, B.R., Jones, J.E., Clary, J.K., 2001. Determining urban storm water BMP effectiveness. J. Water Resour. Plan. Manage. 127 (3), 144–149. U.S. Environmental Protection Agency, 1994. National Pollutant Discharge Elimination Systems Watershed Strategy (No. 833R96002). EPA, US. Upton, J., Green, M.B., 1995. A successful strategy for small treatment plants. Water Qual. Int. 4, 12–14. Urbonas, B.R., 1995. Recommended parameters to report with BMP monitoring data. J. Water Resour. Plan. Manage. 121 (1), 23–34. US EPA, 1994. Storm Water Management Model (SWMM) (Version 4.3). EPA, US. Victoria Stormwater Committee, 1999. Urban Stormwater: Best Practice Environmental Management Guidelines. CSIRO, Melbourne. Walsh, C.J., 2000. Urban impacts on the ecology of receiving waters: a framework for assessment, conservation and restoration. Hydrobiologia 431 (2), 107–114. Walsh, P.M., Barrett, M.E., Malina, J.F., Charbeneau, R.J., 1997. Use of vegetative controls for treatment of highway runoff. Retrieved 17th September, 2004. from http://www.crwr.utexas.edu/reports/1997/rpt97-5.shtml. Wong, T.H.F., Breen, P.F., Lloyd, S.D., Walker, T., Dahnke, B., Wootton, R., 2000. Suspended solids removal in stormwater wetlands: quantifying the role of aquatic macrophytes. In: Paper presented at the Seventh International Conference on Wetlands for Water Pollution Control, Florida, pp. 1545–1552. Wong, T.H.F., Fletcher, T.D., Duncan, H.P., Coleman, J.R., Jenkins, G.A., 2002. A model for urban stormwater improvement conceptualisation. In: Paper presented at the Ninth International Conference on Urban Drainage, Portland, Oregon, September 9–12th. Wong, T.H.F., Rodder, A., Geiger, W.F., 1999. Predicting the performance of a constructed combined sewer overflow wetland. In: Paper presented at the Eighth International Conference on Urban Storm Drainage, Sydney, Australia, 30 August–3 September, pp. 1947–1954.
available at www.sciencedirect.com
journal homepage: www.elsevier.com/locate/ecoleng
Modelling urban stormwater treatment—A unified approach Tony H.F. Wong a,b,c , Tim D. Fletcher a,b,∗ , Hugh P. Duncan a,b,d , Graham A. Jenkins b,e a
Department of Civil Engineering (Institute for Sustainable Water Resources), Monash University, Vic. 3800, Australia b Cooperative Research Centre for Catchment Hydrology, Australia c Ecological Engineering P/L, 28 St. Edmonds Rd, Prahran, Vic. 3181, Australia d Melbourne Water Corporation, 100 Wellington Parade, East Melbourne, Vic. 3001, Australia e School of Environmental Engineering, Griffith University, Nathan, Qld. 4111, Australia
a r t i c l e
i n f o
a b s t r a c t
Article history:
To protect receiving waters from stormwater pollution, stormwater managers need to be
Received 22 November 2004
able to predict the performance of proposed stormwater treatment measures, under variable
Received in revised form 12
operating conditions. This paper describes the development of a model, capable of predicting
October 2005
the performance of stormwater wetlands, ponds, vegetated swales, sediment basins and
Accepted 24 October 2005
biofilters, with a single algorithm. The model describes two principal processes: (a) water quality behaviour and (b) hydrodynamic behaviour. Water quality is described by a first-order kinetic decay model (named the “k–C*” model,
Keywords:
after its two parameters, the decay rate, k, and equilibrium concentration, C*). However, since
Stormwater treatment model
pollutant removal depends on flow behaviour, the continuously stirred tank reactor (CSTR)
First-order kinetic decay
concept is used to account for the hydrodynamics within a treatment device. Where the
Hydrodynamics
device has a high degree of turbulence or short-circuiting (such as in a sediment basin), the
k–C*
k–C* model is applied through a small number of CSTRs in series, whereas a well-designed
CSTRs
wetland with even flow distribution is modelled by a high number of CSTRs. The unified model has been successfully tested on a series of treatment measures—a wetland, pond, swale, grass filter, gravel filter, and large lake. Necessary research to address limitations and assumptions of the model is described. © 2005 Elsevier B.V. All rights reserved.
1.
Introduction
The impacts of urban stormwater on receiving waters are well known, and include water quality degradation, flow-induced erosion, and habitat loss (House et al., 1993; Marsalek, 1991; Novotny and Witte, 1997; Rutherfurd and Ducatel, 1994; Walsh, 2000). In recent years, many government and community organizations have placed increasing emphasis on developing and implementing strategies to reduce urban stormwater pollution (Maksimovic and Tejada-Guibert, 2001; Roesner, 1999; U.S.
∗
Corresponding author. Tel.: +61 3 9905 2599; fax: +61 3 9905 5033. E-mail address: tim.fl[email protected] (T.D. Fletcher).
0925-8574/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.ecoleng.2005.10.014
Environmental Protection Agency, 1994; Victoria Stormwater Committee, 1999). Design and implementation of stormwater treatment strategies often involve a substantial investment in the construction of stormwater treatment measures. Several stormwater treatment measures are used (e.g., ponds, wetlands, swales, infiltration systems), depending on the nature of the stormwater pollutants being targeted, and on scale and available space. In many cases, a sequence (often called a “treatment train”) of measures may be used. For example, lin-
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ear infiltration or biofiltration systems may be placed within the urban streetscape, and may convey water to a sedimentation basin and constructed wetland, before discharging to an ornamental pond (Lloyd et al., 2001). In order to prioritize the implementation of stormwater treatment measures, urban waterway managers need to be able to predict and assess their performance, both individually and in various combinations. There is thus a strong demand for predictive models, that can be applied across a range of locations and conditions, to predict the general performance of a range of stormwater treatment measures (Phillips and Thompson, 2002). In response to this need, stormwater modelling software such as AQUALM (and its varieties) and SWMM (and its varieties) has been developed (Phillips and Thompson, 2002; US EPA, 1994; Wong et al., 2002). Many of these models provide sophisticated descriptions of pollutant generation behaviour and of hydraulic behaviour, but their descriptions of treatment behaviour are limited by available underlying treatment algorithms and by the range of treatment measures to which they can be applied. For example, XP-AQUALM provides a sedimentation model for ponds, as well as user-defined retention curves. For most other treatments, the software requires userdefined retention curves (McAlister et al., 2003). Similarly, the basis of SWMM’s stormwater treatment prediction is based on the choice of a user-defined first-order decay rate, or sedimentation theory with particle-size specific settling velocity distributions for pollutants (Huber et al., 1987; McAlister et al., 2003). SWMM also utilizes user-input as to whether flow is completely mixed, or plug flow, to predict the overall level of treatment for a pollution control pond. Ideally, an integrated stormwater model would utilize a consistent framework for modelling the majority of stormwater treatment measures. Such a model would be able to describe pollutant behaviour through an individual event, as well as through a long continuous run of events and interevent periods. Despite a substantial effort in monitoring of stormwater treatment measures around the world (Duncan, 1997a; Gamble and Walker, 1995; Krejcik et al., 1999; Urbonas, 1995), few of these data have been used effectively to provide reliable predictions of treatment performance (Strecker et al., 2001). A number of authors have developed algorithms using deterministic or pseudo-deterministic approaches, which can describe well the detailed behaviour of a specific stormwater treatment measure (e.g., Deletic, 2001; Lee et al., 1989), in some cases for a limited range of operating conditions. There are many such models, with diverse objectives, assumptions, and applications. At the other end of the scale, some researchers have taken a statistical approach, relating observed performance at a range of temporal scales to parameters which describe the treatment measure, its catchments, or the relationship between them (e.g., Duncan, 1997a, 1997b; Reckhow and Qian, 1994; Strecker et al., 2001). However, the relationships utilized in this approach are generally very noisy, and thus do not account adequately for the observed variability. Neither approach has quite met the requirements for integrated stormwater management modelling. The mechanisms involved in the removal of stormwater pollutants encompass physical, chemical, and biological pro-
59
cesses. Whilst the detailed long-term behaviour may be very complex (Kadlec and Knight, 1996), the processes associated with sedimentation and filtration (through vegetation or a filtration medium) are dominant in the initial interception of stormwater contaminants during a storm event. In this paper, it is proposed that the overall behaviour of pollutants as they pass through a range of treatment measures can be described by a unified model, based on a simple first-order kinetic decay algorithm, coupled to an existing model of flow hydrodynamic behaviour. Common stormwater treatment measures—vegetated swales, wetlands, ponds, sedimentation basins, and infiltration systems are considered to be a single continuum of treatment based around two fundamental processes operating during the passage of a storm event through these measures, i.e., (i) flow attenuation and detention and (ii) particle sedimentation and filtration. In this context, a vegetated swale is just an ephemeral vegetated wetland usually operating at a higher hydraulic loading than a constructed wetland. Similarly, ponds are modified wetlands characterized by deeper open water and fringing vegetation. Hydraulic loading, vegetation density and areal coverage, hydraulic efficiency, and the characteristics of the target pollutants (e.g., particle-size distribution and contaminant speciation) largely influence their differences in performance. In the same way, infiltration systems simply use vertical filtration processes, instead of the horizontal filtration processes, which occur in swales and wetlands. Despite their apparent differences, the basic physical processes occurring in each of these stormwater treatment measures are the same. Consequently, it is proposed that these processes can be modelled using a unified approach. Obviously, chemical and biological processes also contribute to pollutant removal, and so the unified model needs to describe the overall pollutant removal behaviour. The objective of a unified modelling approach is to provide an efficient, reliable, and widely applicable model for predicting pollutant removal from a range of stormwater treatment measures. The model has been incorporated into a software package called Model for Urban Stormwater Improvement Conceptualization (MUSIC) (Cooperative Research Centre for Catchment Hydrology, 2005), which is used by urban water managers to evaluate and prioritize stormwater treatment strategies based on predicted hydrologic and water quality outcomes. This paper: (i) outlines the conceptual basis behind the proposed unified stormwater treatment model, and (ii) presents tests of its application to a range of stormwater treatment measures.
2.
Background theory
Modelling stormwater treatment requires simulation of the two principal processes, which influence the degree of pollutant removal from stormwater treatment measures: (a) water quality behaviour, and (b) flow hydrodynamic behaviour.
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2.1. Water quality behaviour—the first-order kinetic decay (k–C*) model A simple model describing pollutant removal is a twoparameter first-order decay function (Eq. (1)), which expresses the rate at which pollutant concentration moves towards an equilibrium or background concentration (C*), with distance along the treatment measure, as a linear function of the concentration (Kadlec, 2000; Kadlec and Knight, 1996): q
dC = −k(C − C∗ ) dx
(1)
where q is the hydraulic loading rate (m/year), defined as the ratio of the inflow and the surface area of the system, x is the fraction of distance from inlet to outlet, C is the concentration of the water quality parameter, C* is the background concentration of the water quality parameter, and k is the areal decay rate constant (m/year). The parameters k and C* are lumped parameters representing the combined effects of a number of pollutant removal mechanisms. A high value of k results in a rapid approach to the equilibrium concentration C*, and hence a higher treatment capacity (provided that C* is less than the inflow concentration). We contend here that this model, known as the “k–C* model”, can be applied to a wide range of pollutants, including total suspended sediment (TSS), total phosphorus (TP) and total nitrogen (TN). We also demonstrate its application for predicting treatment of biochemical oxygen demand (BOD) and turbidity through a treatment system. The behaviour of heavy metals in previously published studies (e.g., Scott and Fulton, 1978) suggests that it could also be useful for predicting their treatment behaviour. We hypothesise that the k–C* model acts to describe the overall movement towards an equilibrium. Therefore, it can describe the overall movement towards the physical equilibrium in particle sedimentation or filtering, or the complex biochemical equilibrium in treatment of nitrogen. Our hypothesis is that the model can describe the overall behaviour in most cases. The k–C* model assumes steady and plug-flow conditions, and has been widely used (e.g., Mitsch et al., 1995; Upton and Green, 1995), particularly in predicting water quality improvement in wastewater treatment wetlands. Departure from the assumed plug-flow conditions of the k–C* model is considered to be amongst the most significant factors influencing the accuracy of the model. Plug-flow conditions rarely, if ever, occur in the field; some degree of dispersion and mixing usually occur. Coupling of the k–C* model with a flowhydrodynamic model (see next section) goes some way to accounting for the variable conditions observed in stormwater treatment facilities.
2.2. Flow hydrodynamic behaviour—the continuously stirred tank reactor (CSTR) model The treatment effectiveness of a stormwater treatment measure depends upon the flow behaviour in that system. The most effective treatment will occur where the entire treatment surface area is engaged, and there are no stagnant zones,
Fig. 1 – Examples of distribution of tracer concentration over time (V, volume; Q, discharge; V/Q, theoretical detention time) (Persson et al., 1999).
nor flow short-circuiting through preferential flow paths. Flow conditions approaching plug flow will be conducive to effective treatment, since all ‘parcels’ of inflow will be subject to equal detention time. This behaviour is explained by Kadlec and Knight (1996), who introduce the retention time distribution (RTD) function to describe how hydraulic residence time varies. For example, consider the situation where a parcel of water, dosed briefly with a conservative tracer, flows through a detention system such as a wetland (Fig. 1). Under idealised plug-flow conditions, the concentration–time distribution of the tracer is a spike with a very small deviation about the mean residence time. In this case, each parcel of tracer entering the wetland experiences a similar period of detention. Poor flow distribution conditions (see Fig. 1) are akin to the fully-mixed (often called ‘continuously stirred’) flow conditions. The concentration–time distribution takes the form of an exponential decay function. This flow condition can be modelled as a single continuously stirred tank reactor, where the effect of flow dilution in steady flow conditions progressively reduces the tracer concentration at the outflow. Idealised plug-flow conditions can be simulated by representing the detention storage as a large number of CSTRs in series. The degree to which flow hydrodynamic conditions in a stormwater treatment measure depart from an idealised plugflow condition can be modelled by appropriate selection of the number of CSTRs. A single CSTR (such as a small pond with low aspect ratio) will result in a pollutant hydraulic residence time distribution represented by an exponential decay function (strongly right-skewed), where the peak discharge concentration occurs almost immediately after dosing, and concentration then reduces with the effects of dilution. Conversely, as the number of CSTRs in series increases, the residence time distribution becomes more like plug flow (such as may be observed in a long vegetated swale), and the time-lag of the peak discharge concentration is closer to the nominal detention time (given by volume/discharge). Persson et al. (1999) introduced a quantitative measure of flow hydrodynamics in stormwater to enable easy comparison of detention systems of different shape and inlet/outlet locations. This measure is referred to as hydraulic efficiency (), designed to reflect (i) the effective volume of the storage, and (ii) the hydraulic residence time distribution (Eq. (2)). The effec-
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Fig. 2 – Hydraulic efficiency (), effective volume ratio (ev ) and the number of CSTRs (N), for hypothetical stormwater treatment systems (A–M), showing the appropriate number of CSTRs (after Persson et al., 1999). Arrows show inflow and outflow; circles (case K and L) show islands. Multiples arrows (case E) show distributed inflow, whilst barriers show berms to elongate flow path (case F) and porous wall to spread flow (case M).
tive volume represents the proportion of the storage actively engaged by the flow path (to account for zones of zero flow or recirculation, such as fringing vegetation areas). The values of hydraulic efficiency range between 0 and 1, with near zero values reflecting poor flow hydrodynamic conditions and values close to unity representing near plug-flow conditions. Persson et al. (1999) demonstrate that hydraulic efficiency is equivalent to the ratio of the peak of the hydraulic residence time distribution to the nominal residence time (given by V/Q in Fig. 1). The number of continuously stirred tanks (NCSTR ) can be related to the hydraulic efficiency of the treatment facility (Eq. (2)) (Persson et al., 1999).
= ev 1 −
1 N
=
t p
tn
‘parcels’ of more and less treated water move through it. To describe water quality behaviour completely, it is therefore necessary to consider both the pollutant depletion and the flow hydrodynamics simultaneously. The k–C* model must be applied to notionally discrete batches of water. The CSTR model provides notional batches of this form. Hence, the k–C* model can be applied to each of these notional batches in series. In practice, the n notional batches (or ‘notional storages’) are assumed to have 1/nth of the volume of the (real) overall storage. The k–C* model and the flow-hydrodynamics model are therefore linked by the representation of treatment systems in terms of their number of CSTRs, and the application of the k–C* model to each of the CSTRs in turn.
(2)
where is the hydraulic efficiency (ratio ranging from 0 to 1) of the system, ev the effective volume (ratio ranging from 0 to 1, defined by the proportion of the storage actively engaged by the flow path), N the number of continuously stirred tank reactors, tp the time of the peak of the hydraulic residence time distribution, and tn the time of the nominal residence time distribution (defined by the ratio of storage volume to discharge rate). In design, it is possible to estimate the hydraulic efficiency and effective volume of a proposed stormwater treatment measure and use these to determine the appropriate number of CSTRs to account for the effects of shape, inlet and outlet locations, bathymetry, and vegetation characteristics on hydrodynamic behaviour. This is illustrated in Fig. 2, adapted from Persson et al. (1999), which shows a range of shapes, their respective hydraulic efficiencies, effective volume ratios, and equivalent number of CSTRs. In modelling, each case is used with the number of CSTRs rounded to the nearest integer (as explained below). During unsteady flows (i.e., real stormwater systems), water quality varies throughout the storage volume, as
2.3. Testing the applicability of the first-order kinetic decay (k–C*) model Application of the first-order kinetic decay (k–C*) model was tested on a range of stormwater treatment facilities: (a) ponds and wetlands, (b) vegetated swales and filter strips, and (c) gravel filters. For each application, the methods of monitoring and analysis are briefly described in the following sections, and the observed results are compared with those predicted from the model. The purpose of testing described here is not to report appropriate values of k and C* for a given treatment type or site, but rather to assess whether the first-order kinetic decay model adequately describes observed pollutant behaviour. The testing utilized both existing data reported in the literature, and new data collected by the authors. In each case, the k–C* model is fitted to observed data using the objective function of minimizing the root mean square error (RMSE) (Eq. (3)). The methods and results of each of these applications are
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Fig. 3 – Experimental channel layout in Hallam Valley wetland, with dosing inlet shown (inset).
presented and discussed in the following sections
n 1 2 RMSE = (Oi − Pi ) n
(3)
i=1
where RMSE is the root mean square error, Oi the observed value of a water quality measure, Pi the predicted or modelled value, and n is the number of sampling points.
2.3.1.
using Standard Methods (Greenberg et al., 1999). Event-mean concentrations were calculated for each sampling location, and the first-order decay model fitted by minimising the RMSE (Eq. (3))
Ponds and wetlands
Field experiments were carried out in the Hallam Valley stormwater treatment wetland in Melbourne, Australia (Wong et al., 2000). The wetland is approximately 18 ha in total area, comprising various cells of open water, deep marsh and shallow marsh. Two parallel experimental channels were established within the wetland (Fig. 3). Each channel was 3 m wide, 20 m long and 250 mm deep. One was densely vegetated with Eleocharis acuta (Slender spikerush), whilst the other was open water with all vegetation removed. The channels were separated from each other and the surrounding wetland by 300 mm diameter plastic tubes filled with water. The vegetated channel was unlined, whilst the unvegetated channel was lined with plastic sheeting. An inlet and mixing box (see inset in Fig. 3), supplied by a constant-head tank, was used to discharge flow evenly into the upstream end of each channel. A dye, conservative tracer (NaBr) and known concentrations of TSS were added to the inlet boxes under steady flow conditions. Two hydraulic load rates (Eq. (4)) were used and two input particle-size distributions were used, described as either clay dominant (a fine mix with d50 of 20 m) or sand dominant (with d25 of 20 m). Samples were taken manually with a sampling rod, connected to an intake tube, connected to an autosampler pump. Samples were taken at a frequency ranging from 2 to 10 min, matched to timing of the pollutograph at each site. From the data, the pollutograph was constructed over a period of 1 h (for the high flow rate) or 2 h (for the low flow rate), at six equidistant locations along the 20 m long channel, and analysed for TSS concentration. Samples were analysed in the laboratory,
q=
Q 31536A
(4)
where q is the hydraulic loading (m/year), Q the flow rate (L/s), and A is the area of the experimental channel (m2 ). TSS concentrations measured at points along the two channels are shown (by the symbols) in the typical examples in Figs. 4 and 5, together with the predicted concentrations using k–C* models (lines). The root mean square error is low in nearly all cases (ranging from 1.9 to 8.6 mg/L) (Table 1). The average RMSE for the vegetated channel was 5.9, and 4.2 mg/L in the open channel; not statistically different (t-test) at p = 0.05. However, it is apparent that TSS concentration in the vegetated channel decays to a significantly (t-test, p = 0.02) lower equilibrium concentration (mean C* = 32.7 mg/L) than in the open water (mean C* = 59.9 mg/L). This difference reflects the ability of vegetation to facilitate sedimentation, and to reduce re-suspension, through the effects of wind protection and flow calming. The decay rate (k) was also greater in the vegetated channel (mean = 7813 m/year) than in the open water (mean = 5892 m/year), although the difference was not significant.
2.3.2.
Vegetated swales and filter strips
Testing of the applicability of the k–C* model for vegetated swales and filter strips was undertaken using previously conducted experiments on (a) stormwater treatment by a grass swale within a flume, and (b) field experiments on a grass filtration treatment of wastewater. Researchers at the University of Texas (Barrett et al., 1998; Walsh et al., 1997) used a 40 m × 0.75 m flume to create a swale, at an average slope of 0.44%, with soil and grass overlying a layer of gravel. A constant-head tank discharged to an initial mixing basin, where known concentrations of pollutants were added. The experiments used a cocktail of pollutants
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Fig. 4 – Observed and modelled TSS concentrations at Hallam Valley wetland vegetated experimental section (key to legend: V, vegetated; flow, Low or High; sediment mix, Coarse or Fine; refer to Table 1).
Fig. 5 – Observed and modelled TSS concentrations at Hallam Valley wetland open water experimental section; O, open water; flow, Low or High; sediment mix, Coarse or Fine; refer to Table 1).
Table 1 – Summary of RMSE for all runs at Hallam Valley wetland Label
Vegetation
Flow (high/low)
Sediment mix
Flow (L/s)
Hydraulic loading (m/year)
RMSE (mg/L)
VHC1 VHC2 VHF1 VHF2 VLC1 VLC2 VLF1 VLF2 OHC1 OHC2 OHF1 OHF2 OLC1 OLC2 OLF1 OLF2
Vegetated Vegetated Vegetated Vegetated Vegetated Vegetated Vegetated Vegetated Open Open Open Open Open Open Open Open
High High High High Low Low Low Low High High High High Low Low Low Low
Coarse Coarse Fine Fine Coarse Coarse Fine Fine Coarse Coarse Fine Fine Coarse Coarse Fine Fine
2.85 2.65 2.90 2.73 1.40 1.65 1.46 1.54 2.90 2.75 2.78 2.86 1.35 1.51 1.39 1.46
1498 1393 1524 1435 736 867 767 809 1524 1445 1461 1503 710 794 731 767
5.4 7.6 5.2 5.9 8.6 4.1 4.1 6.5 6.6 5.2 6.7 5.1 3.2 2.0 1.9 3.2
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Fig. 6 – Best and worst-case examples of k–C* model application to swale performance data from Walsh et al. (1997).
collected from a sediment pond, with synthetic pollutants added where necessary to match typical stormwater quality characteristics (Walsh et al., 1997). Water quality samples were taken using dedicated sampling tubes located every 10 m along the swale, and from the downstream discharge weir. We fitted a k–C* model to the published results of these experiments. The best and worst cases for TSS, TP and TN are shown in Fig. 6, along with the RMSE of the model fit. For each parameter, the best case provides an excellent fit to the observed data, and in most cases, the RMSE is much closer to the best case than the worst case (Table 2). For TSS, there is very little difference between the best and worst case: the model seems capable of describing the behaviour very well in every case.
Another published study of vegetated filters was undertaken at the Western Treatment Plant, in Melbourne, Australia, which treats sewage by a combination of primary settlement, land filtration, grass filtration, and lagoons (Scott and Fulton, 1978). In the grass filtration process, settled sewage flows through irrigation bays. The bays were 10 m wide, with slopes of 0.1 to 0.4%, and planted with grass. Scott and Fulton (1978) described a measurement program, which took water quality samples at 50 m intervals in four parallel bays over one winter irrigation season. Measured concentrations of TSS and BOD5 at each distance, averaged over the four bays, are shown in Fig. 7, together with fitted curves of the k–C* form. Scott and Fulton (1978) present results for 19 water quality parameters, and the great majority exhibit behaviour of the form shown. For example, total organic
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Table 2 – Root mean square error (RMSE, in mg/L) of model fits to Texas swale data; best (B) and worst fit cases (W) are highlighted Case
Hydraulic loading (m/year)
B C D E F G H I J K Average
19917 13693 13693 13693 4564 4564 13693 13693 19917 19917
RMSE TSS
TP
TN
2.8 (W) 14.5 6.0 4.0 10.4 4.7 10.9 (B) 2.3 6.3 n/a 6.9
0.010 0.009 0.017 0.073 (B) 0.001 0.042 (W) 0.084 0.004 0.037 0.015 0.029
0.04 (W) 0.14 0.08 (B) 0.01 0.12 0.08 0.06 0.10 0.05 n/a 0.08
Case A was excluded due to concerns about experimental conditions during this sampling run.
Fig. 7 – TSS and BOD5 concentrations in Grass Filtration Bays (after Scott and Fulton (1978)), showing model fits and RMSE in mg/L.
carbon, chromium, copper, lead, nickel, zinc and Methylene Blue active substances (MBAS) all show behaviour that is well-described by the k–C* model. The behaviour of nitrogen and phosphorus species, as well as iron and cadmium, are more erratic.
2.3.3.
Gravel filters
Sivakumar (1980) described a program of laboratory measurements of turbidity in a horizontal flow gravel filter. The filter comprised a rectangular box 1.8 m long, 400 mm wide, and 500 mm deep with an overflow set at 450 mm depth. The box was filled with gravel ranging from 2 to 12 mm in diameter. Tests were carried out for several flow rates, and for both high and low input turbidity. All results were presented by Sivakumar in terms of percent removal. Sivakumar (1980) fitted turbidity reductions as a power function of flow rate, input turbidity, depth of measurement, and length of filter. However, if the fitted results are expressed as output percent (i.e., turbidity not removed), which is more analogous to output concentration, the data can again be closely fitted by a curve of the k–C* form as shown in Fig. 8.
2.4. Case study: application of the unified CSTR and k–C* model—Blackburn Lake Having demonstrated the ability of the k–C* model to describe water quality processes within a range of stormwater treatment facilities, we undertook a case study of the combined application of the k–C* algorithm with the adopted number of CSTRs being based on the procedure of Persson et al. (1999), to describe flow behaviour and its influence on contaminant routing, and thus overall treatment performance.
2.4.1.
Site details
Blackburn Lake is located in the eastern suburbs of Melbourne, Australia, and was constructed in 1888 for agricultural water supply purposes. Its history and characteristics, along with the monitoring methodology, are described in detail by RossRakesh et al. (1999), but are summarised briefly here. The lake has an estimated permanent pool volume of 57,000 m3 and a surface area of 27,000 m2 for the permanent pool. The catchment area is 296 ha, with a mix of urban land uses (48% residential, 40% industrial, 10% open space), with total fraction imperviousness of 58% (Fig. 9).
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Fig. 8 – Turbidity in a gravel filter (after Sivakumar (1980)).
Fig. 9 – Map of Blackburn Lake catchment.
There are five inlets to the lake. The primary spillway is via a 1.9 m (inside diameter) circular spillway, whilst the low flow outlet is a rectangular orifice (cut into the side of the glory hole), with a height of 0.38 m and width of 0.76 m, giving an extended detention depth of 1.8 m.
2.4.2.
Flow and water quality monitoring
Rainfall (6 min timestep) was monitored from three sites within and around the catchment, and then distributed across the sub-catchments by Thiessen polygons (RossRakesh et al., 1999). Continuous (2 min) inflows were measured at four of the inlets (and modelled for the remaining small inlet), with discharge calculated from stage readings. Water quality sampling was undertaken during both dry weather and storm events. Manual grab sampling at the main inlet (which accounts for more than 80% of inflow to the lake), and at the outlet, was undertaken on a fortnightly basis. Wetweather sampling utilized automatic samplers at the main inlet and at the outlet. The wet-weather sampling frequency was matched to the hydrograph, with more intensive sampling during the first part of an event. At the inlet, samples were taken every 10 min for the first hour, and hourly thereafter. For most of the shorter events, the scheme was mod-
ified to collect more samples (12) at the 10 min frequency. Due to its attenuated flows, the outlet sampling had a lower frequency—set to take samples every 20 min for the first 2 h, and hourly thereafter (RossRakesh et al., 1999). Two events with good water quality data throughout the event – one in February 1996 and one in June 1996 – were used for detailed analysis in developing the unified approach to modelling stormwater treatment.
2.4.3.
Data analysis and model testing
For the examples shown below, the observed flow and concentration data have been reformatted into equal hourly timesteps, by combining readings as necessary (during events), or interpolating between readings (during inter-event periods). The combined k–C* and CSTR modelling calculations are then performed using a spreadsheet approach. Where two CSTRs are used, they are assumed to be of equal volume. Inflow to the first (or only) CSTR is the observed inflow to the lake. Inflow to the second of two CSTRs is proportioned between the observed inflow and the calculated outflow from the lake. This calculation can readily be extended to more than two CSTRs. At the start of a timestep, new water is introduced from inflow or a previous cell and the dilution effects calcu-
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Fig. 10 – TSS concentration over time in Blackburn Lake, for event of February 1996. Modelled results show calibration using 1 and 2 CSTRs.
Fig. 11 – TSS concentration over time in Blackburn Lake, for event of June 1996. Modelled results show calibration using 1 and 2 CSTRs.
lated. At the end of the timestep the decay of concentrations towards background levels is calculated for all cells. The curve fits have been optimised using the root mean square error and an iterative approach. In practice, since N must be an integer, only a small number of trials for N will be needed. In this example, k and C* have been optimised for N = 1 and 2, using the same k and C* values for both storm events. The RMSE is considerably lower when N = 2.
2.4.4.
Case study results
The observed and modelled data for the two events are shown in Figs. 10 and 11. Model results are shown both for a single CSTR and for two CSTRs, with k and C* optimised separately for each value of N. The difference in lag and curve shape can be clearly seen. N = 1 describes a single well-mixed reactor, and gives an immediate and rapid increase in simulated concentration at the start of the event, whilst N = 2 gives a smoother and more attenuated curve. There is perhaps an indication from the graphs that the observed output lies somewhere between that predicted by the k–C* model with one and two CSTRs. The general shape of Blackburn Lake suggests a width to length ratio of about one in four and hydraulic behaviour like that of
Case I in Fig. 2 ( = 0.41; N = 1.7 from Eq. (2)). Whilst interpolation between simulations utilizing one and two CSTRs would be theoretically possible, this would be computationally demanding in ‘real-world applications’, where the model would be used for long-duration, short timestep simulations. In Fig. 11, it can be seen that the ‘second peak’ (which occurs at around the 120 h mark) results in very little response from the model. This is expected, given the very small size of that event (the peak flow is 537 kL/h, compared with 6166 kL/h for the first peak). In this very large storage, such a small event would likely be fully treated by the lake. However, one can see some response in the measured points. This anomaly occurs because of inflows from sub-catchment A (Fig. 9), which effectively ‘short-circuit’ the lake’s storage given their proximity to the outlet. Additionally, calibration of the k and C* parameters has been undertaken on a lumped basis for both events (Figs. 10 and 11), with weighting of the objective function (RMSE) given to the larger events, which carry the majority of the pollutant load. Results from this case study suggest that the combined application of the CSTR and k–C* models can predict pollutant behaviour through a large ‘real-world’ stormwater treatment
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pond, which has highly variable flow rates and inflow concentrations.
3.
Discussion
Application of the first-order kinetic decay (k–C*) model to a range of stormwater treatment measures—wetlands, ponds, swales and filtration systems – has demonstrated its potential for providing an efficient modelling framework for stormwater quality improvement processes. In most cases presented in this paper, the k–C* model was able to describe the observed behaviour quite closely. The results suggest that there is an underlying similarity of overall behaviour, suggesting an underlying unity of the net effect of a number of complex processes. It must be noted that the model is intended as a conceptual analysis and design tool, and that detailed analysis may be needed for specific situations, and for detailed design. Combining the k–C* algorithm with the CSTR algorithm is an important requirement, to account for the effect of treatment design on flow hydrodynamics. The combination has demonstrated its effectiveness for a large system, with variable inflow rates and concentrations. It allows one model to be used to describe a range of stormwater treatment facilities, by changing the model parameters to reflect differences in hydraulic loading and behaviour, and pollutant characteristics. There are clear advantages in being able to describe water quality treatment across a range of different treatment measures using a unified approach. It provides computational and model-development efficiency, allowing models of different treatment measures to be developed simply by changing the input conditions (e.g., hydraulic loading and input concentration) and model parameters (decay rate, background concentration and hydraulic efficiency), without needing to create a different model structure. Use of the three-parameter (k, C* and NCSTR ) model minimizes the number of parameters to be calibrated. This is important if urban waterway managers are able to apply such
models across a range of catchments and treatment types. However, the tradeoff between model accuracy and calibration data requirements is a difficult one. The most reliable prediction of pollutant removal for a given event will be provided by a more detailed or sophisticated model, but often at the expense of prohibitive calibration requirements. Perhaps most importantly, the use of such a unified approach provides a well-defined focus for future research to enhance the model. The first priority for such research is to apply the combined CSTR and k–C* models to a range of other ‘real-world’ stormwater treatments, using monitored storm event data. One assumption underlying the first-order decay model is that of constancy of the model parameters – decay rate (k) and background concentration (C*) (Kadlec, 2000). Our own research (e.g., Deletic and Fletcher, 2004; Fletcher et al., 2002; Wong et al., 2000; Wong et al., 1999) and that of others (Kadlec, 2000) suggests that this is not really the case. The influence of hydraulic loading and inflow concentration on the model parameters (k and C*) is unclear, as shown in the examples for the University of Texas swale data (Walsh et al., 1997) (Figs. 12 and 13); however both k and C* show some tendency to increase at higher hydraulic loading rates. At high inflow concentrations, C* and k are also high, but the relationships are again quite inconsistent. It is evident that further research is needed to examine how k and C* vary with these factors. Given the importance of physical processes in removing many stormwater pollutants, the influence of particle-size and settling velocity distributions also require investigation. Further refinements to the model could incorporate a more explicit accounting for this, for example using the particle fall number approach described by Deletic (1999, 2001). To date, this approach has been used to provide ‘pseudo-calibration’ of the k–C* model for swales (Deletic and Fletcher, 2004), and is now being tested for wetlands (Fletcher et al., 2004). Research to date (and that presented in this paper) has primarily focussed on water quality behaviour during and soon after storm events. Future research will also need to investigate the fate of pollutants after the initial interception and treatment. The role of biological and chemical processes in the
Fig. 12 – Relationships between model parameters (k and C*) and hydraulic loading for TSS in Texas swale data (after Walsh et al. (1997).
ecological engineering
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Fig. 13 – Relationships between model parameters (k and C*) and inflow concentration for TSS in Texas swale data (after Walsh et al. (1997).
subsequent transformation and removal of pollutants could be important, particularly for nitrogen (Fletcher et al., 2004). This is particularly the case for treatment measures which utilize significant storage and detention times; in these measures the inter-event (i.e., dry weather) processes may substantially influence the long-term water quality performance (Fletcher et al., 2004; Kasper and Jenkins, 2003).
4.
Conclusions
The proposal that a range of stormwater treatment measures – including wetlands, ponds, infiltration systems and vegetated swales – can be described using a unified stormwater treatment model is supported by a range of experimental data. Using this approach, differences between the various treatment facilities are accommodated by changing the model parameters to match the characteristics of the facility, rather than by changing the overall model structure. The unified stormwater treatment model provides an efficient means of predicting and assessing the performance of stormwater treatment measures. It by no means provides a complete answer to the problem of predicting stormwater treatment (because k and C* are shown to vary with changes in operating conditions). However, the model does provide a very efficient lumped approach to describing the overall water quality processes in treatment, and a useful focus for ongoing research to refine and quantify understanding of factors that influence stormwater treatment performance.
Acknowledgements The authors express their appreciation to the comments provided by Jane Catford, Barry Hart, Sally Taylor, Marie Keatley and three anonymous reviewers. Melbourne Water’s support of the experimental program is acknowledged with gratitude.
references
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