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A new settling velocity model to describe secondary sedimentation
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Available online at www.sciencedirect.com
ScienceDirect journal homepage: www.elsevier.com/locate/watres
A new settling velocity model to describe secondary sedimentation gner a, Lars Yde b, Philip J. Binning a, Elham Ramin a,*, Dorottya S. Wa sz a,* Michael R. Rasmussen c, Peter Steen Mikkelsen a, Benedek Gy. Plo a
Department of Environmental Engineering, Technical University of Denmark, Miljøvej, Building 113, 2800 Kgs. Lyngby, Denmark b DHI Water & Environment (S) Pte Ltd, Singapore 63714, Singapore c Department of Civil Engineering, Aalborg University, Sohngaardsholmsvej 57, 9000 Aalborg, Denmark
article info
abstract
Article history:
Secondary settling tanks (SSTs) are the most hydraulically sensitive unit operations in
Received 31 March 2014
biological wastewater treatment plants. The maximum permissible inflow to the plant
Received in revised form
depends on the efficiency of SSTs in separating and thickening the activated sludge. The
25 July 2014
flow conditions and solids distribution in SSTs can be predicted using computational fluid
Accepted 23 August 2014
dynamics (CFD) tools. Despite extensive studies on the compression settling behaviour of
Available online 3 September 2014
activated sludge and the development of advanced settling velocity models for use in SST simulations, these models are not often used, due to the challenges associated with their
Keywords:
calibration. In this study, we developed a new settling velocity model, including hindered,
Activated sludge
transient and compression settling, and showed that it can be calibrated to data from a
Compression
simple, novel settling column experimental set-up using the Bayesian optimization
Calibration
method DREAM(ZS). In addition, correlations between the Herschel-Bulkley rheological
Computational fluid dynamics
model parameters and sludge concentration were identified with data from batch rheo-
Rheology
logical experiments. A 2-D axisymmetric CFD model of a circular SST containing the new
Monte Carlo Markov Chain
settling velocity and rheological model was validated with full-scale measurements. Finally, it was shown that the representation of compression settling in the CFD model can significantly influence the prediction of sludge distribution in the SSTs under dry- and wetweather flow conditions. © 2014 Elsevier Ltd. All rights reserved.
1.
Introduction
In conventional wastewater treatment plants (WWTPs), bioreactors are connected to secondary settling tanks (SSTs) to separate the suspended biomass from treated water by means
of gravity sedimentation. The thickening and clarification efficiency of SSTs is significantly influenced by hydraulic disturbances during wet-weather flow conditions. This is of particular concern due to the increasing frequency of hydraulic shock-loads from urban run-offs to WWTPs associated with the effect of climate change on peak rainfall intensities
* Corresponding authors. Tel.: þ45 45 25 16 94. gner), [email protected] (L. Yde), [email protected] (P.J. E-mail addresses: [email protected] (E. Ramin), [email protected] (D.S. Wa sz). Binning), [email protected] (M.R. Rasmussen), [email protected] (P.S. Mikkelsen), [email protected] (B.Gy. Plo http://dx.doi.org/10.1016/j.watres.2014.08.034 0043-1354/© 2014 Elsevier Ltd. All rights reserved.
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sz et al., 2009). When examining SSTs (Larsen et al., 2009; Plo performance, it is important to consider the non-Newtonian (rheological) and settling behaviour of activated sludge because they have significant impacts on the overall transport and removal of solids (Ekama et al., 1997; Lakehal et al., 1999; De Clercq, 2003). To predict the internal flow field and solids distribution, complex computational fluid dynamics (CFD) models of SSTs have been developed (Larsen, 1977; Imam et al., 1983; Dahl, 1993). CFD models are based on the NaviereStokes equations and are computationally demanding. Nevertheless, they are cost effective because validated CFD models can be employed instead of field experiments to generate data for the calibration and validation of simpler one-dimensional (1-D) SST models for WWTP simulations under a range of boundary conditions (De Clercq, sz et al., 2007). 2003; Plo Since the first CFD model of an SST was developed by Larsen (1977), research has mostly aimed to improve the prediction accuracy of the CFD models by optimizing the mathematical structure of the turbulence and buoyant flow modelling components (Adams and Rodi, 1990; Bretscher et al., 1992; Lakehal et al., 1999; De Clercq, 2003; Weiss et al., 2007). Currently, despite significant advancements in the research on the settling and rheological characteristics of activated sludge, their representation in CFD models of SSTs is not well-established. Concerning the settling velocity models, the recent development of phenomenological sedimentation-consolidation theory has led to extensive studies on the compression settling behaviour of activated sludge, and has subsequently been expressed in settling velocity models (Bu¨rger, 2000; Kinnear, 2002; De Clercq et al., 2008). The proposed calibration methods for these models, however, require non-destructive monitoring of dynamic settling profiles during batch experiments such as radiotracer tests (De Clercq et al., 2005) and are not simple to do in practice. Therefore, the application of compression settling models is limited to a few cases of 1-D SST modelling (De Clercq et al., 2008; Bu¨rger et al., 2011). Most of the CFD studies consider only the hindered (and flocculent) settling cs et al. (1991). regimes using the empirical formulation of Taka To encourage a broader application of compression settling models for numerical modelling of SSTs, there is a need for a simple but robust experimental methodology. Regarding the rheological models for activated sludge, Ratkovich et al. (2013) were critical about the procedures currently used to select and calibrate them. They demonstrated the need for high quality measurements and stressed the importance of good modelling practice in rheological modelling. These factors need to be considered in CFD modelling of SSTs, where the rheological model of activated sludge plays an important role in accurate prediction of hydrodynamics in SSTs. This paper aims to (i) l set-up and use the obtained data to evaluate the accuracy of current settling velocity models and propose a new settling velocity model that describes the experimental observations more accurately; (ii) perform rheological measurements to obtain high quality data for selection and calibration of a rheological model for activated sludge, and establish correlations between rheological model parameters and sludge concentration; and finally, (iii)
perform simulations with a 2-D axisymmetric CFD model with the new settling and rheological models and validate the CFD model with full-scale measurements. In addition, an assessment is conducted of the influence of omitting the transient and compression settling from the CFD model cs hindered (and flocculent) settling velocity when using Taka model.
2.
Materials and methods
2.1.
Case study
The SST studied is located in Lundtofte WWTP (Lyngby, Denmark). It is a circular centre-feed conical tank. During the measurement campaign, the SST was operated with 100 m3/h average overflow rate, 1.45 recycle ratio, and 5.64 kg/ m3average feed sludge concentration. An activated sludge sample was collected from the combined recycle flow channel of Lundtofte WWTP on the day of the settling experiments. Sludge samples taken were aerated overnight with coarse air bubbles and the sampled effluent SST was stored at 4 C for the rheological experiments conducted on the following day. To validate the settling velocity model, another sludge sample was collected from a different WWTP (Lynetten). The description of the two WWTPs, the detailed design of the Lundtofte SST, and the list of corresponding experiments are given in Table 1.
2.2.
Experiments
2.2.1.
Settling column tests
We developed a simple laboratory set-up, consisting of a glass column (Fig. 1a) with a Solitax® total suspended solids (TSS)
Table 1 e The description of WWTPs and the list of corresponding experiments. Parameters a
PE SRT [d] SST type c DSVI [ml/g] SST design Clarifier diameter [m] Depth of outer wall [m] Bottom slope [%] Centre wall diameter [m] Centre wall depth [m] Inlet surface area [m2] Recycle surface area [m2] Tank surface area [m2] Sludge removal mechanism Experiments Settling Rheology Full-scale measurements b
a b c
Lundtofte WWTP
Lynetten WWTP
135,000 31 circular 125
750,000 29 rectangular 90
24.5 3.48 7.66 3 6.2 4.24 3.96 470 scraper
Not investigated
x x x
x e e
Population equivalent (design). Sludge retention time (design). Diluted sludge volume index of the sampled sludge.
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a
c
d
bubbles, no pre-shearing was applied to the sludge sample. The diluted sludge sample was replaced with a new aliquot for each experiment to minimize the uncertainty associated with the changes in sludge characteristics. By applying the decreasing shear stress mode in through consecutive experiments (starting from the maximum value corresponding to shear rate of around 250 s1 with the frequency of 10 points per decade on a logarithmic scale), we could minimize sludge settling. The flow in the gap was assumed laminar during the measurements. The conversion equations of torque and angular velocity to shear stress and shear rate, respectively, are described in the Supporting Information.
2.2.3.
b
Fig. 1 e Settling column (a), with a Solitax TSS sensor installed at the bottom of the column (b). Evolution of the sludge blanket height SBH (c), and the sludge concentration measured in the bottom of the column Xb (d), for different initial sludge concentrations (Lundtofte WWTP sludge).
sensor (Hach Lange, Germany) installed at the bottom (Fig. 1b). A series of batch settling tests were performed using the sludge samples diluted with SST effluent over a concentration range of 1.7e5.1 kg/m3, which is typical for feed concentration into SSTs. Before each settling test, the sludge sample was homogenized in the column with coarse air bubbles. The TSS sensor was validated in-situ by comparing the measured initial sludge concentration at the start of each test to the values obtained from gravimetric analysis. The evolution of sludge blanket height, SBH (Fig. 1c), and sludge concentration at the bottom, Xb (Fig. 1d) were recorded over the 60 min duration of each test.
2.2.2.
Rheological experiments
The non-Newtonian behaviour of the sampled sludge from the Lundtofte WWTP was studied using laboratory shear stress-controlled measurements in a rotational rheometer (AR 2000, TA Instruments, USA), with concentric conicalcylindrical geometry. To avoid breakage of flocs, the annular gap size was set to 5.92 mm, which is larger than the maximum floc size reported in literature (Li and Ganczarczyk, 1991). A Smart Swap™-based Peltier Plate temperature system was used to perform measurements under different isothermal conditions (10, 15, 20 C) typically observed at WWTPs under seasonal temperature variations. The sludge sample was diluted with SST effluent to 5e13 kg/m3 concentration range, which is typically found in the vicinity of the sludge blanket in SSTs where the rheological behaviour of sludge significantly impacts the flow field (Ratkovich et al., 2013). Besides the overnight aeration with the coarse air
449
Full-scale measurements
Full-scale measurements were performed at Lundtofte SST to validate the CFD model. The sludge concentration and velocity profiles were measured at four different radial distances from the centre of the tank using a Solitax® TSS sensor and a Vectrino® 3-D acoustic Doppler velocimeter (Nortek BV, the Netherlands) simultaneously (see Fig. S2 in the Supporting Information). The Vectrino® receivers were located 20 cm below the Solitax® sensor to avoid flow disturbance during velocity measurements.
2.3.
Calibration of the settling velocity models
To calibrate the selected settling velocity models (presented in section 3.1) to the settling measurements, they were imple sz mented in a dynamic 1-D model of the settling column (Plo et al., 2007, 2011). For calibration, the adaptive Markov Chain Monte Carlo (MCMC) Bayesian global optimization method DREAM(ZS) (Laloy and Vrugt, 2012) was used. The 1-D model calculates the total solids flux for a finite number of equally thick horizontal layers. 60 layers were found to be optimal in order for model predictions to be independent of the number of layers, and enabling efficient calibration using the DREAM(ZS) algorithm which required a high number of simulations (over 5000). The minimization function in the DREAM(ZS) algorithm was defined as an averaged nondimensional sum of squared errors (Marler and Arora, 2004). ! n X m bi;j q 2 yi;j y 1 X SSEN ¼ n m i¼1 j¼1 yi;j
(1)
where n is the number of measured time-series (including SBH alone or both SBH and Xb); m is the number of data points in bðqÞ is the model each time-series; y is the measured values; y prediction with the parameter set q. Prediction uncertainty for the estimated parameters is provided by the posterior parameter distributions.
2.4.
Numerical modelling of the SST
2.4.1.
Hydrodynamics and solids transport
The CFD modelling was performed in the open source CFD toolbox OpenFOAM® (OpenCFD, 2012) and with the settlingFoam solver (Brennan, 2001). The hydrodynamics solver employs the averaged form of the Eulerian two-phase flow, where the mixture is considered as a whole rather than two separate phases. The turbulence was modelled using the
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buoyancy modified k-ε model (with k as the turbulent kinetic energy, and ε as the dissipation rate of k), accounting for density stratification (Dahl, 1993; Rodi, 1993). The CFD simulation model solves the convection-diffusion equation derived from the continuity equation for the solid phase to predict the distribution of solids (drift flux model). The hydrodynamics and transport equations are provided in the Supporting Information.
2.4.2.
facilitating sludge flow to the hopper for removal, as proposed by Deininger et al. (1998). The free water surface was considered to be a symmetrical plane. The remaining walls were considered to be non-slip boundaries with standard wallfunctions to estimate the mean fluid velocity near the wall (Brennan, 2001).
3.
Results and discussion
3.1.
Settling velocity model
Computational domain and boundary conditions
The flow in the circular SST was assumed to be axisymmetric, thus only a segment of the tank was modelled and discretized in radial and depth directions using the polyhedral mesh type. Mesh-independence was investigated for the CFD model by comparing the velocity and sludge concentrations profiles simulated with 5816 (coarse), 15292 (medium) and 22906 (fine) grids. The simulation results of the CFD model with the coarse mesh did not diverge significantly from the cases with medium and fine mesh (data not shown), and thus we used the coarse meshing in our simulations. The geometry and mesh of the SST model is illustrated later in the results section along with the CFD simulation results (Fig. 7a). Regarding the boundary conditions, we assumed a frictionless boundary at the tank bottom to simulate the influence of an ideal “scraper” in overcoming the wall stress,
In this section, experimental observations are presented (Fig. 2a,b) and are used to evaluate currently available settling velocity models, which then motivated the development of a new settling velocity model (Fig. 2c,d). The estimated parameter values of the settling velocity models are provided in the Supporting Information (Tables S1eS3).
3.1.1.
Experimental observations
The SBH measurements in the settling column (Fig. 2a) allowed identification of the four different settling regimes typically observed during batch activated sludge settling column tests: lag, hindered, transient, and compression (Ekama et al., 1997). The lag period observed at the beginning of the
Fig. 2 e Settling phases observed from the batch measurements of sludge blanket height SBH (a), and sludge concentration at the bottom Xb (b), for X0 ¼ 2.7 kg/m3 (Lundtofte WWTP sludge). Calibrating different settling velocity models to the SBH measurements (c), and evaluating their prediction of Xb (d).
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experiment resulted from the dissipation of kinetic energy introduced with coarse air bubbles used to homogenize sludge in the column before measurements start. The subsequent period of constant descent of the liquid/solid interface corresponds to the hindered settling regime, where the mixture settles as a whole with a concentration equal to the initial value of sludge (X0). The particles entering the bottom of the column encounter compressive solids stress and settle slower than in the hindered regime. Based only on SBH measurements in conventional settling experiments, the observation of the transition of settling regime from hindered to compression is limited, and can only be observed when the accumulation of sludge at the bottom propagates upwards and meets the liquid/solid interface. By additionally measuring Xb using the novel setup presented in this paper, the onset of the transient and the compression regimes can be observed more clearly (Fig. 2b). The hindered regime is absent in the Xb time series as a result of the immediate accumulation of sludge at the bottom of the column. Possibly, as a result of the faster dissipation of kinetic energy at the bottom of the column, no lag period can be detected in the Xb measurements.
3.1.2.
Evaluation of state-of-the-art settling velocity models
Fig. 2c,d shows a comparison of the state-of-the-art settling velocity functions to predict SBH and Xb measurements. The lag period was excluded from the SBH measurements (Fig. 2c) since it does not occur in continuous settlers (De Clercq, 2006). We first employed the hindered settling velocity model (vh) of cs et al. (1991). Taka vh ¼ v0 erH X erP X
(2)
where v0 is the maximum settling velocity; rH and rP are the hindered and low concentration indices, respectively; X is the sludge concentration. This settling velocity model could very well describe the hindered settling regime; however, as expected, SBH and Xb predictions diverged from the measurements during the transient and compression settling regime (dotted line in Fig. 2c,d). To address this problem, we tested a settling velocity model that includes a mechanistic compression settling velocity, vc (Bu¨rger, 2000; Kinnear, 2002; De Clercq et al., 2008). 1 rS ds dXA @ vc ¼ vh 1 rS rf gX dX dz 0
(3)
with the effective solids stress (s) gradient formulation developed by De Clercq et al. (2008). 8 <
0 X < XC ds ¼ a dX : X XC X XC þ b
(4)
where vh is the hindered settling velocity (Eq. (2)), rs and rf are the sludge and water density, respectively; g denotes the gravity constant; z is depth in the settling column; a and b are compression parameters; XC is the threshold compression concentration. Unfortunately, this model over-predicted the Xb data (dash-dotted line in Fig. 2d) when it was calibrated to the SBH data (dash-dotted line in Fig. 2c). This outcome
indicates that calibrating the settling velocity model to only the SBH measurements does not correctly predict all the settling regimes. Furthermore, the discontinuity in the mathematical formulation of s gradient (Eq. (4)) makes the computation time of parameter estimation with DREAM(ZS) inefficient.
3.1.3.
Settling velocity model development
To improve the prediction of the settling velocity model (Eqs. (2)e(4)), we investigated alternative formulations for the effective solids stress gradient (data not shown). By replacing the power formulation (Eq. (5)) with the formulation of De Clercq et al. (2008) in Eq. (4), we can achieve more accurate predictions of Xb (dashed line in Fig. 2d). 8 > <
0 ds ¼ X XC C2 dX > : C1
X < XC (5)
X XC
where C1 and C2 are the parameters in the new compression settling model. This formulation is a modified form of similar power formulations for effective solids stress proposed in literature (Holdich and Butt, 1997; Bu¨rger, 2000). With the new formulation for the effective solids stress (Eq. (5)), the discontinuity in the mathematical formulation of settling velocity is avoided, which significantly increased the speed of the simulation and optimization process (data not shown). We could further improve the prediction of Xb in the compression settling regime (solid line in Fig. 2d) by applying the following transient velocity formulation accounting immediately after hindered settling, i.e. X > X0. vt ¼ v0;t ert X
(6)
where v0,t and rt are the transient settling parameters. This new exponential transient formulation was chosen analogous to the hindered settling velocity formulation (Eq. (2)). To avoid discontinuity in the transition from the hindered to the transient regime, the settling velocities were set to be equal at the transition point, i.e. vh ¼ vt at X ¼ X0. We could then calculate one of the transient settling parameters as v0;t ¼
v0 erH X0 ert X0
(7)
and reduce the number of calibration parameters to rt, XC, C1, and C2. The complete formulation of the new settling velocity model is as follows 8 v erH $X v0 erP $X > > > 0 > < v0;t ert X vS ¼ > > > > : v0;t ert X 1 fC dX dz
X X0 X0 < X < XC
(8)
X XC
where the compression factor fC is defined as fC ¼
C X XC 2 C1 rS rf gX rS
(9)
In this paper, Eq. (8), which includes Hindered, Transient and Compression settling velocity formulations, is referred to as the HTC settling velocity model.
452
3.1.4. model
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Calibration and evaluation of the HTC settling velocity
The form of the HTC settling velocity model is shown in Fig. 3a with the parameters rt, XC, C1, and C2 estimated based on simultaneous calibration to SBH and Xb measurements (Fig. 3b). To reduce the complexity of the HTC model and thus the number of calibration parameters, XC was set to be equal to 1.1 X0 since parameter estimation showed that it was estimated very close to X0 (Fig. 3a). Therefore, the calibration parameters are reduced to (rt, C1, C2). Fig. 4 shows the predictive accuracy and uncertainty of the calibrated HTC settling velocity model to SBH and Xb measurements for X0 ¼ 2.7 kg/m3 (Lundtofte WWTP sludge). The HTC model can be seen to have very good predictive accuracy with an acceptably low predictive uncertainty (Fig. 4a,b). The low uncertainty of two of the three estimated
parameters (Fig. 4 c, d, and e), and no strong correlations between all the three parameters (not shown) indicate that the model is well defined. Results of the HTC model calibration to all of the measurement sets (with sludge samples from the two WWTPs) are reported in Fig. 5. The measurements with X0 ¼ 5.1 kg/m3 (Lundtofte WWTP sludge) were not considered because of the very long lag period in the SBH measurements (see Fig. 1c).
3.1.5. Implementation of the HTC settling velocity model in the CFD model of SST The HTC settling velocity model (Eq. (8)) was implemented in the CFD model of the Lundtofte SST with the estimated settling parameter values set as follows based on the values reported in Table S3 in the Supporting Information using Lundtofte WWTP sludge. X0 was assumed to be equal to the SST feed flow concentration. The estimated values of rt for different Xo were in a comparably narrow range (0.71e0.82), therefore a constant value of 0.77 was used. The model was insensitive to C1 (Fig. 4d), and a constant averaged value of 15.6 was used. C2 values showed a clear dependency to X0 (Table S3, Lundtofte sludge), which was summarized by the function (R2 ¼ 0.99): C2 ¼ 1:6e0:4X0
(10)
For the CFD model, C2 was calculated with Eq. (10) for X0 equal to the SST feed concentration.
3.2.
Rheological model
3.2.1.
Experimental results
The rheological measurements from the batch experiments with different sludge concentrations were analysed by plotting the applied external force (shear stress, t) versus the measured internal velocity gradients (shear rates, g). A pseudo-plastic behaviour of sludge with yield stress was identified (Fig. 6a).
3.2.2.
Rheological model selection and calibration
Among the proposed empirical formulations in literature (Eshtiaghi et al., 2013; Ratkovich et al., 2013), the HerscheleBulkley model could describe the observed rheological behaviour of activated sludge more accurately (fitted curves in Fig. 6a,b): t ¼ t0 þ Kgn h¼
Fig. 3 e The graphical form of HTC settling velocity model (Eq. (8)), including hindered (vh), transient (vt) and compression (fC) components (a), calibrated to SBH and Xb measurements with Lundtofte WWTP sludge at X0 ¼ 2.7 kg/m3 by implementing the settling velocity model in a 1-D model of the settling column with 60-layer discretization (b); the lines in b correspond to the simulated evolution of sludge concentration in each layer.
t g
(12) (13)
where t0 is the yield stress; K is the consistency index; n is the flow behaviour index; h is the apparent viscosity of sludge. The three parameters (t0, K, n) were estimated by fitting the Herschel-Bulkley model to the rheological measurements at the shear rates between 0.01 and 250 s1. As shown in Fig. 6b, a maximum viscosity (mmax) constraint - set at the critical shear rate of 0.01 s1 e is imposed to avoid predicting unrealistic viscosity values under very low shear conditions (Craig et al., 2013). The estimated parameter values for the experiments e run at T ¼ 15 C e are plotted in Fig. 6c, d, e. Notably, less accurate estimation of yield stress at high sludge
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Fig. 4 e Predictive accuracy and uncertainty (95% confidence intervals of the model prediction due to parameter uncertainty) of the HTC settling velocity model with the estimated parameters (rt, C1, C2) for X0 ¼ 2.7 kg/m3 (Lundtofte WWTP sludge) (a, b). The histograms (c, d, and e) show the posterior distribution of the three parameters estimated using DREAM(ZS), with a fitted Gaussian distribution (red curves). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
concentrations (Fig. 6a) resulted in a comparably large variance in the estimated yield stress values (error lines in Fig. 6c). The estimated rheology parameter values are comparable for the three different temperature conditions (Table 2), which suggests that the typical seasonal temperature variation in the bioreactors in WWTPs may not have significant “direct” impact on the rheological behaviour of activated sludge. We note that this result does not take into account the fact that the seasonal temperature variations can impact the microbial composition of activated sludge, which may influence the rheological behaviour of activated sludge in the SST. Nevertheless, the parameter values obtained at T ¼ 15 C were used in the CFD model, which was the average temperature degree detected by the Vectrino® sensor during the full-scale profile measurements.
3.2.3. Implementation of the rheological model in the CFD model of SST The three estimated HerscheleBulkley model parameters (t0, K, n) were found to be dependent on the sludge concentration of the samples, X (Fig. 6c, d, and e). To implement this dependency in the CFD model, three relations were established (fitted curves in Fig. 6c, d, and e). Other alternative correlation formulations for the yield stress (t0) and the consistency index (K) have been previously reported (De Clercq, 2003; Eshtiaghi et al., 2012). Based on the correlations in Fig. 6c, d, e, the apparent viscosity of the sludge mixture correctly converges to water viscosity at very low sludge concentrations; i.e. if X / 0, then t0 / 0, K / mw (viscosity of water), and n / 1.
3.3.
CFD simulations of the SST
Fig. 7 shows the steady-state simulation results of two CFD models using the calibrated HerscheleBulkley rheological model in combination with: (i) the HTC settling velocity model cs settling velocity model (Eq. (2)). The (Eq. (8)), and (ii) Taka simulation results are compared with the full-scale measured vertical velocity and sludge concentration profiles, at four different radial distances from the centre of the tank.
3.3.1.
Validation of the developed CFD model
In Fig. 7a, the predictions of the CFD model developed using the new HTC settling velocity model and the identified rheological correlations show an overall close agreement with the measured profiles, particularly in terms of sludge distribution in the tank. The sludge blanket height is predicted with high accuracy. Prediction of the sludge concentration at the bottom cannot be validated since the TSS sensor was constrained by the velocimeter to reach the bottom of the tank. The CFD-predicted velocity field show a strong density current also captured by the velocity measurements just over the sludge blanket, which result in a counter current in the upper part of the tank (Fig. 7b). Moreover, the peak velocity magnitudes predicted at the 3, 7, and 10 m radial distances from the center (Fig. 7b) are in close agreement with the measured data. However, according to Fig. 7b (lower part), the developed CFD model over predicts the velocity of the dense mixture flowing to the hopper over the inclined bottom. This can be due to the underestimation of yield stress at high
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Fig. 5 e Predictive uncertainty (95% confidence intervals of the model prediction due to parameter uncertainty) of the HTC settling velocity model calibrated to the measurements with the Lundtofte (a, b) and Lynetten (c, d) WWTP sludge using DREAM(ZS) optimization algorithm. The total predictive accuracy of the two measured time series (SBH and Xb) are shown in b and d based on SSEN (Eq. (1)). sludge concentrations (see Fig. 7c), which can effectively increase the flowability of viscous sludge to the hopper. Fig. 8 illustrates the geometry and mesh of the CFD model of the Lundtofte SST (Fig. 8a), as well as the distributions of the sludge concentration (Fig. 8b), the magnitude of the convective velocity and the settling velocity (Fig. 8c and d, respectively), and the turbulence and molecular viscosities (Fig. 8e and f, respectively) computed in the numerical domain for average operating boundary conditions (Qoverflow ¼ 100 m3/h, R ¼ 1.42, XFeed ¼ 5.64 kg/m3) during the measurement campaign. These figures show the complexity of the predicted flow field in the SST and the high gradients particularly in case of sludge concentration and molecular viscosity. The velocity magnitude (Fig. 8c) shows the strong horizontal density current and several recirculation zones in the tank. The significance of the estimated apparent molecular viscosity with the rheological model on the dampening of turbulence viscosity can be clearly observed in Fig. 8e and f, in the vicinity of the sludge blanket, where the molecular viscosity is estimated orders of magnitude higher than the turbulent viscosity.
3.3.2. Relative impact of settling velocity model on CFD predictions In Fig. 7a, comparing the simulation results of the two CFD models to the measurements indicates that the error in
underestimating SBH is significantly higher when using the cs settling velocity model (see errors reported in Fig. 7a). Taka The CFD-predicted flow-field is also influenced by the performance of the settling velocity model (Fig. 7b). These results indicate the benefit of including transient and compression settling by employing the new HTC settling velocity model for the simulation of sludge distribution in SSTs using CFD modelling. We further assessed the influence of the settling velocity model on the CFD predictions under wet-weather flow conditions, i.e. where there is increased hydraulic load to the WWTP and thus to the SST. We performed simulations using cs settling velocity the CFD model with the HTC and Taka models, under a constant wet-weather flow rate, for three hours real time. The wet-weather condition was simulated based on the ATV design standards for peak wet-weather flow rate (Ekama et al., 1997), where the actual overflow rate was increased by a factor of 2.39 and the recycle ratio was decreased to 0.75. The initial conditions were set to the steady-state simulation results under the average operational condition (Fig. 7). Fig. 9 shows the results, and demonstrates that the omission of transient and compression settling velocity in the CFD domain can significantly influence the predicted SST behaviour, in terms of thickening and storage capacity, under wet-weather conditions. Predictions made by explicitly accounting for hindered, transient and compression
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455
Fig. 6 e Prediction of rheological measurements at T ¼ 15 C with the HerscheleBulkley model (a). A maximum viscosity (mmax) constraint was set for g < 0.01 s¡1 to avoid unrealistic viscosity values predicted by the model under very low shear conditions (b). Mean and standard deviation of the estimated Herschel-Bulkley model parameters and their dependency on the concentration of sludge samples X (c, d, and e); A ¼ 0.00066 [kg1¡B m3£B¡1s¡2], B ¼ 2.18 [e], C ¼ 0.28 [m3/kg], D ¼ 0.00083 [m3£E kg¡E], E ¼ 2.57 [e].
settling in the CFD model (i.e. employing the HTC settling function, Fig. 9a), are 92% higher SBH and 20% lower TSSrecycled values than that obtained with the domain, only representing cs settling hindered (and flocculant) settling using the Taka velocity model. This model structural uncertainty can significantly hinder decision makings when assessing SST storage capacity under wet weather flow conditions.
measurements such as rheological laboratory experiments (sampling, storage, and instrument) and full-scale profiling in SST with the Vectrino® sensor (may require different calibration when used for measurements in the clarification zone and in the sludge blanket due to sound speed difference in different media).
3.4.
4.
Outlook and perspectives
Besides CFD modelling, the new settling velocity model can be used explicitly in simpler 1-D SST models for integrated WWTP modelling. Moreover, the efficiency in its calibration using the new experimental set-up combined with the Bayesian optimization method makes it useful in engineering practice e.g., for on-line control purposes. Our results indicate that the CFD model developed using the new settling and rheology functions, can predict the sludge distribution in the SST with fairly good accuracy. This is achieved without any arbitrary adjustment of the parameters and boundary conditions. Therefore, the relative impact of improving the settling velocity model on the CFD predictions could be assessed. The accuracy of CFD predictions could be further increased by assessing the uncertainties associated with the simplifications in the boundary condition (e.g. 2D axisymmetric, slip bottom) or
Conclusion
In this study, we presented a straightforward experimentalmodelling methodology using a simple, novel batch settling column experimental set-up combined with a Bayesian optimization method to identify a new settling velocity model for activated sludge. Additionally, rheological correlations for activated sludge were identified using data from batch laboratory experiments. Based on the evaluation of the state-of-the-art settling velocity models, a new settling velocity model was developed, which accounts for hindered, transient and compression settling regimes of activated sludge. We showed that this model can be calibrated to data from the novel settling column experimental set-up presented in this study using a Bayesian optimization algorithm. The proposed settling velocity model was validated with
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Fig. 7 e Vertical profiles (normalized height) of sludge concentration X (a), and radial velocity (b). Measurements (thin marked lines) at four different radial distances from the centre of the tank. CFD model predictions with the HTC settling cs settling velocity model (dashed line). velocity model (solid line), and CFD model predictions using Taka
measurements using activated sludge samples from two different WWTPs and at different dilutions. A pseudo-plastic behaviour of activated sludge with yield stress was identified based on measurements from rheological batch experiments. The HerscheleBulkley rheological model could effectively describe the measurements. We identified correlations to describe the strong dependency of rheological model parameters to sludge concentration. The direct effect of temperature change (10, 15, and 20 C, as typical seasonal temperature variations in SSTs) on the rheology of activated sludge was found insignificant. A 2-D axisymmetric CFD model of the circular conical SST (Lundtofte WWTP) was developed, including the new
settling velocity model and the calibrated rheological correlations. The CFD model could describe the full-scale measurements with fairly good accuracy and was further used to assess the relative impact of the new settling velocity model on the prediction of sludge distribution in SSTs. In this regards, we compared the simulation results of the CFD model using the new settling velocity model, which includes hindered, transient, and compression cs settling velocity settling, and the widely used Taka model, which only accounts for hindered (and flocculent) settling. The results showed that the representation of transient and compression settling in the CFD model can significantly improve the prediction of sludge distribution in the SSTs. Moreover, by performing CFD simulations of
Table 2 e The estimated parameters of the Herschel-Bulkley rheological model from measurements with five different sludge concentrations (X) at three different temperature conditions. X [kg/m3]
12.79 9.95 8.53 7.10 4.97
K [Pa sn]
t0 [Pa]
n [e]
10 C
15 C
20 C
10 C
15 C
20 C
10 C
15 C
20 C
0.20 0.10 0.07 0.05 0.03
0.17 0.10 0.07 0.05 0.02
0.19 0.10 0.06 0.04 0.02
0.047 0.024 0.012 0.006 0.002
0.044 0.019 0.010 0.006 0.003
0.035 0.018 0.010 0.005 0.002
0.67 0.72 0.81 0.90 1.02
0.65 0.74 0.82 0.88 1.00
0.68 0.74 0.82 0.89 1.00
w a t e r r e s e a r c h 6 6 ( 2 0 1 4 ) 4 4 7 e4 5 8
457
Fig. 8 e The CFD simulation results of the SST for the averaged operating conditions (Qoverflow ¼ 100 m3/h, R ¼ 1.42, XFeed ¼ 5.64 kg/m3) during the measurement campaign. For clear illustration, the values are shown in logarithmic scale. cs the SST under wet-weather flow condition, using Taka settling velocity model resulted in 92% underestimation of SBH and 20% overestimation of TSSrecycled as compared to when the proposed settling velocity model was used. This
model structural uncertainty can significantly affect the accurate assessment of SST storage capacity under wetweather flow conditions.
Acknowledgments The research was financially supported by the Danish Council for Strategic Research, Programme Commission on Sustainable Energy and Environment, as part of the Storm and Wastewater Informatics (SWI) project (http://www.swi.env. dtu.dk). The authors would like to thank Associate Professor Thomas Ruby Bentzen from Aalborg University for his valuable comments on the manuscript.
Appendix A. Supplementary data Supplementary data related to this article can be found at http://dx.doi.org/10.1016/j.watres.2014.08.034.
references Fig. 9 e Predicted sludge distributions with CFD simulations under constant wet-weather flow conditions (Qin ¼ 414 m3/h, R ¼ 0.75, XFeed ¼ 5.64 kg/m3) for three hours real time using the HTC settling velocity model (a), cs settling velocity model (b). and Taka
Adams, E.W., Rodi, W., 1990. Modeling flow and mixing in sedimentation tanks. J. Hyd. Eng. 116 (7), 895e913. Brennan, D., 2001. The Numerical Simulation of Two-phase Flows in Settling Tanks. Ph.D. Dissertation. Imperial College, London.
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Bretscher, U., Krebs, P., Hager, W.H., 1992. Improvement of flow in final settling tanks. J. Environ. Eng. 118 (3), 307e321. Bu¨rger, R., 2000. Phenomenological foundation and mathematical theory of sedimentationeconsolidation processes. Chem. Eng. J. 80, 177e188. Bu¨rger, R., Diehl, S., Nopens, I., 2011. A consistent modelling methodology for secondary settling tanks in wastewater treatment. Water Res. 45 (6), 2247e2260. Craig, K.J., Nieuwoudt, M.N., Niemand, L.J., 2013. CFD simulation of anaerobic digester with variable sewage sludge rheology. Water Res. 47 (13), 4485e4497. De Clercq, B., 2003. Computational Fluid Dynamics of Settling Tanks: Development of Experiments and Rheological, Settling, and Scraper Submodels. Ph.D. Dissertation. University of Gent, Belgium. De Clercq, J., Jacobs, F., Kinnear, D.J., Nopens, I., Dierckx, R.A., Defrancq, J., Vanrolleghem, P.A., 2005. Detailed spatiotemporal solids concentration profiling during batch settling of activated sludge using a radiotracer. Water Res. 39 (10), 2125e2135. De Clercq, J., 2006. Batch and Continuous Settling of Activated Sludge: In-depth Monitoring and 1D Compression Modelling. Ph.D. Dissertation. University of Gent, Belgium. De Clercq, J., Nopens, I., Defrancq, J., Vanrolleghem, P.A., 2008. Extending and calibrating a mechanistic hindered and compression settling model for activated sludge using indepth batch experiments. Water Res. 42 (3), 781e791. Dahl, C.P., 1993. Modelling of Flow Field and Settling in Secondary Settling Tanks. Ph.D. Dissertation. University of Aalborg, Denmark. Deininger, A., Holthausen, E., Wilderer, P.A., 1998. Velocity and solids distribution in circular secondary clarifiers: full scale measurements and numerical modelling. Water Res. 32 (10), 2951e2958. Ekama, G.A., Barnard, G.L., Gunthert, F.W., Krebs, P., McCorquodale, J.A., Parker, D.S., Wahlberg, E.J., 1997. Secondary Settling Tanks: Theory, Modelling, Design and Operation. International Association on Water Quality, London, UK. Eshtiaghi, N., Markis, F., Slatter, P., 2012. The laminar/turbulent transition in a sludge pipeline. Water Sci. Technol. 65 (4), 697e702. Eshtiaghi, N., Markis, F., Yap, S.D., Baudez, J.-C., Slatter, P., 2013. Rheological characterisation of municipal sludge: a review. Water Res. 47 (15), 5493e5510. Holdich, R.G., Butt, G., 1997. Experimental and numerical analysis of a sedimentation forming compressible compacts. Sep. Sci. Technol. 32 (13), 2149e2171.
Imam, E., McCorquodale, J., Bewtra, J., 1983. Numerical modeling of sedimentation tanks. J. Hyd. Eng. 109 (12), 1740e1754. Kinnear, D.J., 2002. Biological Solids Sedimentation: a Model Incorporating Fundamental Settling Parameters. PhD dissertation. University of Utah, Salt Lake City, UT. Lakehal, D., Krebs, P., Krijgsman, J., Rodi, W., 1999. Computing shear flow and sludge blanket in secondary clarifiers. J. Hyd. Eng. 125 (3), 253e262. Laloy, E., Vrugt, J.A., 2012. High-dimensional posterior exploration of hydrologic models using multiple-try DREAM (ZS) and highperformance computing. Water Resour. Res. 48 (1), W01526. Larsen, A.N., Gregersen, I.B., Christensen, O.B., Linde, J.J., Mikkelsen, P.S., 2009. Potential future increase in extreme one-hour precipitation events over Europe due to climate change. Water Sci. Technol. 60 (9), 2205e2216. Larsen, P., 1977. On the Hydraulics of Rectangular Settling Basins, Experimental and Theoretical Studies. Report No. 1001. Water Research Engineering, Lund Institute of Technology, Lund. Li, D., Ganczarczyk, J., 1991. Size distribution of activated sludge flocs. Res. J. Water Pollut. Control Fed. 63 (5), 806e814. Marler, R.T., Arora, J.S., 2004. Survey of multi-objective optimization methods for engineering. Struct. Multidiscip. Optim. 26 (6), 369e395. sz, B.G., Weiss, M., Printemps, C., Essemiani, K., Meinhold, J., Plo 2007. One-dimensional modelling of the secondary clarifierfactors affecting simulation in the clarification zone and the assessment of the thickening flow dependence. Water Res. 41 (15), 3359e3371. sz, B.G., Liltved, H., Ratnaweera, H., 2009. Climate change Plo impacts on activated sludge wastewater treatment: a case study from Norway. Water Sci. Technol. 60 (2), 533e541. sz, B.G., De Clercq, J., Nopens, I., Benedetti, L., Plo Vanrolleghem, P.A., 2011. Shall we upgrade one-dimensional secondary settler models used in WWTP simulators?eAn assessment of model structure uncertainty and its propagation. Water Sci. Technol. 63 (8), 1726e1738. Ratkovich, N., Horn, W., Helmus, F.P., Rosenberger, S., Naessens, W., Nopens, I., Bentzen, T.R., 2013. Activated sludge rheology: a critical review on data collection and modelling. Water Res. 47 (2), 463e482. Rodi, W., 1993. Turbulence Models and Their Application in Hydraulics, third ed. Balkema, Rotterdam, The Netherlands. cs, I., Patry, G., Nolasco, D., 1991. A dynamic model of the Taka clarification-thickening process. Water Res. 25 (10), 1263e1271. sz, B.G., Essemiani, K., Meinhold, J., 2007. SuctionWeiss, M., Plo lift sludge removal and non-Newtonian flow behaviour in circular secondary clarifiers: numerical modelling and measurements. Chem. Eng. J. 132 (1e3), 241e255.
Available online at www.sciencedirect.com
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A new settling velocity model to describe secondary sedimentation gner a, Lars Yde b, Philip J. Binning a, Elham Ramin a,*, Dorottya S. Wa sz a,* Michael R. Rasmussen c, Peter Steen Mikkelsen a, Benedek Gy. Plo a
Department of Environmental Engineering, Technical University of Denmark, Miljøvej, Building 113, 2800 Kgs. Lyngby, Denmark b DHI Water & Environment (S) Pte Ltd, Singapore 63714, Singapore c Department of Civil Engineering, Aalborg University, Sohngaardsholmsvej 57, 9000 Aalborg, Denmark
article info
abstract
Article history:
Secondary settling tanks (SSTs) are the most hydraulically sensitive unit operations in
Received 31 March 2014
biological wastewater treatment plants. The maximum permissible inflow to the plant
Received in revised form
depends on the efficiency of SSTs in separating and thickening the activated sludge. The
25 July 2014
flow conditions and solids distribution in SSTs can be predicted using computational fluid
Accepted 23 August 2014
dynamics (CFD) tools. Despite extensive studies on the compression settling behaviour of
Available online 3 September 2014
activated sludge and the development of advanced settling velocity models for use in SST simulations, these models are not often used, due to the challenges associated with their
Keywords:
calibration. In this study, we developed a new settling velocity model, including hindered,
Activated sludge
transient and compression settling, and showed that it can be calibrated to data from a
Compression
simple, novel settling column experimental set-up using the Bayesian optimization
Calibration
method DREAM(ZS). In addition, correlations between the Herschel-Bulkley rheological
Computational fluid dynamics
model parameters and sludge concentration were identified with data from batch rheo-
Rheology
logical experiments. A 2-D axisymmetric CFD model of a circular SST containing the new
Monte Carlo Markov Chain
settling velocity and rheological model was validated with full-scale measurements. Finally, it was shown that the representation of compression settling in the CFD model can significantly influence the prediction of sludge distribution in the SSTs under dry- and wetweather flow conditions. © 2014 Elsevier Ltd. All rights reserved.
1.
Introduction
In conventional wastewater treatment plants (WWTPs), bioreactors are connected to secondary settling tanks (SSTs) to separate the suspended biomass from treated water by means
of gravity sedimentation. The thickening and clarification efficiency of SSTs is significantly influenced by hydraulic disturbances during wet-weather flow conditions. This is of particular concern due to the increasing frequency of hydraulic shock-loads from urban run-offs to WWTPs associated with the effect of climate change on peak rainfall intensities
* Corresponding authors. Tel.: þ45 45 25 16 94. gner), [email protected] (L. Yde), [email protected] (P.J. E-mail addresses: [email protected] (E. Ramin), [email protected] (D.S. Wa sz). Binning), [email protected] (M.R. Rasmussen), [email protected] (P.S. Mikkelsen), [email protected] (B.Gy. Plo http://dx.doi.org/10.1016/j.watres.2014.08.034 0043-1354/© 2014 Elsevier Ltd. All rights reserved.
448
w a t e r r e s e a r c h 6 6 ( 2 0 1 4 ) 4 4 7 e4 5 8
sz et al., 2009). When examining SSTs (Larsen et al., 2009; Plo performance, it is important to consider the non-Newtonian (rheological) and settling behaviour of activated sludge because they have significant impacts on the overall transport and removal of solids (Ekama et al., 1997; Lakehal et al., 1999; De Clercq, 2003). To predict the internal flow field and solids distribution, complex computational fluid dynamics (CFD) models of SSTs have been developed (Larsen, 1977; Imam et al., 1983; Dahl, 1993). CFD models are based on the NaviereStokes equations and are computationally demanding. Nevertheless, they are cost effective because validated CFD models can be employed instead of field experiments to generate data for the calibration and validation of simpler one-dimensional (1-D) SST models for WWTP simulations under a range of boundary conditions (De Clercq, sz et al., 2007). 2003; Plo Since the first CFD model of an SST was developed by Larsen (1977), research has mostly aimed to improve the prediction accuracy of the CFD models by optimizing the mathematical structure of the turbulence and buoyant flow modelling components (Adams and Rodi, 1990; Bretscher et al., 1992; Lakehal et al., 1999; De Clercq, 2003; Weiss et al., 2007). Currently, despite significant advancements in the research on the settling and rheological characteristics of activated sludge, their representation in CFD models of SSTs is not well-established. Concerning the settling velocity models, the recent development of phenomenological sedimentation-consolidation theory has led to extensive studies on the compression settling behaviour of activated sludge, and has subsequently been expressed in settling velocity models (Bu¨rger, 2000; Kinnear, 2002; De Clercq et al., 2008). The proposed calibration methods for these models, however, require non-destructive monitoring of dynamic settling profiles during batch experiments such as radiotracer tests (De Clercq et al., 2005) and are not simple to do in practice. Therefore, the application of compression settling models is limited to a few cases of 1-D SST modelling (De Clercq et al., 2008; Bu¨rger et al., 2011). Most of the CFD studies consider only the hindered (and flocculent) settling cs et al. (1991). regimes using the empirical formulation of Taka To encourage a broader application of compression settling models for numerical modelling of SSTs, there is a need for a simple but robust experimental methodology. Regarding the rheological models for activated sludge, Ratkovich et al. (2013) were critical about the procedures currently used to select and calibrate them. They demonstrated the need for high quality measurements and stressed the importance of good modelling practice in rheological modelling. These factors need to be considered in CFD modelling of SSTs, where the rheological model of activated sludge plays an important role in accurate prediction of hydrodynamics in SSTs. This paper aims to (i) l set-up and use the obtained data to evaluate the accuracy of current settling velocity models and propose a new settling velocity model that describes the experimental observations more accurately; (ii) perform rheological measurements to obtain high quality data for selection and calibration of a rheological model for activated sludge, and establish correlations between rheological model parameters and sludge concentration; and finally, (iii)
perform simulations with a 2-D axisymmetric CFD model with the new settling and rheological models and validate the CFD model with full-scale measurements. In addition, an assessment is conducted of the influence of omitting the transient and compression settling from the CFD model cs hindered (and flocculent) settling velocity when using Taka model.
2.
Materials and methods
2.1.
Case study
The SST studied is located in Lundtofte WWTP (Lyngby, Denmark). It is a circular centre-feed conical tank. During the measurement campaign, the SST was operated with 100 m3/h average overflow rate, 1.45 recycle ratio, and 5.64 kg/ m3average feed sludge concentration. An activated sludge sample was collected from the combined recycle flow channel of Lundtofte WWTP on the day of the settling experiments. Sludge samples taken were aerated overnight with coarse air bubbles and the sampled effluent SST was stored at 4 C for the rheological experiments conducted on the following day. To validate the settling velocity model, another sludge sample was collected from a different WWTP (Lynetten). The description of the two WWTPs, the detailed design of the Lundtofte SST, and the list of corresponding experiments are given in Table 1.
2.2.
Experiments
2.2.1.
Settling column tests
We developed a simple laboratory set-up, consisting of a glass column (Fig. 1a) with a Solitax® total suspended solids (TSS)
Table 1 e The description of WWTPs and the list of corresponding experiments. Parameters a
PE SRT [d] SST type c DSVI [ml/g] SST design Clarifier diameter [m] Depth of outer wall [m] Bottom slope [%] Centre wall diameter [m] Centre wall depth [m] Inlet surface area [m2] Recycle surface area [m2] Tank surface area [m2] Sludge removal mechanism Experiments Settling Rheology Full-scale measurements b
a b c
Lundtofte WWTP
Lynetten WWTP
135,000 31 circular 125
750,000 29 rectangular 90
24.5 3.48 7.66 3 6.2 4.24 3.96 470 scraper
Not investigated
x x x
x e e
Population equivalent (design). Sludge retention time (design). Diluted sludge volume index of the sampled sludge.
w a t e r r e s e a r c h 6 6 ( 2 0 1 4 ) 4 4 7 e4 5 8
a
c
d
bubbles, no pre-shearing was applied to the sludge sample. The diluted sludge sample was replaced with a new aliquot for each experiment to minimize the uncertainty associated with the changes in sludge characteristics. By applying the decreasing shear stress mode in through consecutive experiments (starting from the maximum value corresponding to shear rate of around 250 s1 with the frequency of 10 points per decade on a logarithmic scale), we could minimize sludge settling. The flow in the gap was assumed laminar during the measurements. The conversion equations of torque and angular velocity to shear stress and shear rate, respectively, are described in the Supporting Information.
2.2.3.
b
Fig. 1 e Settling column (a), with a Solitax TSS sensor installed at the bottom of the column (b). Evolution of the sludge blanket height SBH (c), and the sludge concentration measured in the bottom of the column Xb (d), for different initial sludge concentrations (Lundtofte WWTP sludge).
sensor (Hach Lange, Germany) installed at the bottom (Fig. 1b). A series of batch settling tests were performed using the sludge samples diluted with SST effluent over a concentration range of 1.7e5.1 kg/m3, which is typical for feed concentration into SSTs. Before each settling test, the sludge sample was homogenized in the column with coarse air bubbles. The TSS sensor was validated in-situ by comparing the measured initial sludge concentration at the start of each test to the values obtained from gravimetric analysis. The evolution of sludge blanket height, SBH (Fig. 1c), and sludge concentration at the bottom, Xb (Fig. 1d) were recorded over the 60 min duration of each test.
2.2.2.
Rheological experiments
The non-Newtonian behaviour of the sampled sludge from the Lundtofte WWTP was studied using laboratory shear stress-controlled measurements in a rotational rheometer (AR 2000, TA Instruments, USA), with concentric conicalcylindrical geometry. To avoid breakage of flocs, the annular gap size was set to 5.92 mm, which is larger than the maximum floc size reported in literature (Li and Ganczarczyk, 1991). A Smart Swap™-based Peltier Plate temperature system was used to perform measurements under different isothermal conditions (10, 15, 20 C) typically observed at WWTPs under seasonal temperature variations. The sludge sample was diluted with SST effluent to 5e13 kg/m3 concentration range, which is typically found in the vicinity of the sludge blanket in SSTs where the rheological behaviour of sludge significantly impacts the flow field (Ratkovich et al., 2013). Besides the overnight aeration with the coarse air
449
Full-scale measurements
Full-scale measurements were performed at Lundtofte SST to validate the CFD model. The sludge concentration and velocity profiles were measured at four different radial distances from the centre of the tank using a Solitax® TSS sensor and a Vectrino® 3-D acoustic Doppler velocimeter (Nortek BV, the Netherlands) simultaneously (see Fig. S2 in the Supporting Information). The Vectrino® receivers were located 20 cm below the Solitax® sensor to avoid flow disturbance during velocity measurements.
2.3.
Calibration of the settling velocity models
To calibrate the selected settling velocity models (presented in section 3.1) to the settling measurements, they were imple sz mented in a dynamic 1-D model of the settling column (Plo et al., 2007, 2011). For calibration, the adaptive Markov Chain Monte Carlo (MCMC) Bayesian global optimization method DREAM(ZS) (Laloy and Vrugt, 2012) was used. The 1-D model calculates the total solids flux for a finite number of equally thick horizontal layers. 60 layers were found to be optimal in order for model predictions to be independent of the number of layers, and enabling efficient calibration using the DREAM(ZS) algorithm which required a high number of simulations (over 5000). The minimization function in the DREAM(ZS) algorithm was defined as an averaged nondimensional sum of squared errors (Marler and Arora, 2004). ! n X m bi;j q 2 yi;j y 1 X SSEN ¼ n m i¼1 j¼1 yi;j
(1)
where n is the number of measured time-series (including SBH alone or both SBH and Xb); m is the number of data points in bðqÞ is the model each time-series; y is the measured values; y prediction with the parameter set q. Prediction uncertainty for the estimated parameters is provided by the posterior parameter distributions.
2.4.
Numerical modelling of the SST
2.4.1.
Hydrodynamics and solids transport
The CFD modelling was performed in the open source CFD toolbox OpenFOAM® (OpenCFD, 2012) and with the settlingFoam solver (Brennan, 2001). The hydrodynamics solver employs the averaged form of the Eulerian two-phase flow, where the mixture is considered as a whole rather than two separate phases. The turbulence was modelled using the
450
w a t e r r e s e a r c h 6 6 ( 2 0 1 4 ) 4 4 7 e4 5 8
buoyancy modified k-ε model (with k as the turbulent kinetic energy, and ε as the dissipation rate of k), accounting for density stratification (Dahl, 1993; Rodi, 1993). The CFD simulation model solves the convection-diffusion equation derived from the continuity equation for the solid phase to predict the distribution of solids (drift flux model). The hydrodynamics and transport equations are provided in the Supporting Information.
2.4.2.
facilitating sludge flow to the hopper for removal, as proposed by Deininger et al. (1998). The free water surface was considered to be a symmetrical plane. The remaining walls were considered to be non-slip boundaries with standard wallfunctions to estimate the mean fluid velocity near the wall (Brennan, 2001).
3.
Results and discussion
3.1.
Settling velocity model
Computational domain and boundary conditions
The flow in the circular SST was assumed to be axisymmetric, thus only a segment of the tank was modelled and discretized in radial and depth directions using the polyhedral mesh type. Mesh-independence was investigated for the CFD model by comparing the velocity and sludge concentrations profiles simulated with 5816 (coarse), 15292 (medium) and 22906 (fine) grids. The simulation results of the CFD model with the coarse mesh did not diverge significantly from the cases with medium and fine mesh (data not shown), and thus we used the coarse meshing in our simulations. The geometry and mesh of the SST model is illustrated later in the results section along with the CFD simulation results (Fig. 7a). Regarding the boundary conditions, we assumed a frictionless boundary at the tank bottom to simulate the influence of an ideal “scraper” in overcoming the wall stress,
In this section, experimental observations are presented (Fig. 2a,b) and are used to evaluate currently available settling velocity models, which then motivated the development of a new settling velocity model (Fig. 2c,d). The estimated parameter values of the settling velocity models are provided in the Supporting Information (Tables S1eS3).
3.1.1.
Experimental observations
The SBH measurements in the settling column (Fig. 2a) allowed identification of the four different settling regimes typically observed during batch activated sludge settling column tests: lag, hindered, transient, and compression (Ekama et al., 1997). The lag period observed at the beginning of the
Fig. 2 e Settling phases observed from the batch measurements of sludge blanket height SBH (a), and sludge concentration at the bottom Xb (b), for X0 ¼ 2.7 kg/m3 (Lundtofte WWTP sludge). Calibrating different settling velocity models to the SBH measurements (c), and evaluating their prediction of Xb (d).
451
w a t e r r e s e a r c h 6 6 ( 2 0 1 4 ) 4 4 7 e4 5 8
experiment resulted from the dissipation of kinetic energy introduced with coarse air bubbles used to homogenize sludge in the column before measurements start. The subsequent period of constant descent of the liquid/solid interface corresponds to the hindered settling regime, where the mixture settles as a whole with a concentration equal to the initial value of sludge (X0). The particles entering the bottom of the column encounter compressive solids stress and settle slower than in the hindered regime. Based only on SBH measurements in conventional settling experiments, the observation of the transition of settling regime from hindered to compression is limited, and can only be observed when the accumulation of sludge at the bottom propagates upwards and meets the liquid/solid interface. By additionally measuring Xb using the novel setup presented in this paper, the onset of the transient and the compression regimes can be observed more clearly (Fig. 2b). The hindered regime is absent in the Xb time series as a result of the immediate accumulation of sludge at the bottom of the column. Possibly, as a result of the faster dissipation of kinetic energy at the bottom of the column, no lag period can be detected in the Xb measurements.
3.1.2.
Evaluation of state-of-the-art settling velocity models
Fig. 2c,d shows a comparison of the state-of-the-art settling velocity functions to predict SBH and Xb measurements. The lag period was excluded from the SBH measurements (Fig. 2c) since it does not occur in continuous settlers (De Clercq, 2006). We first employed the hindered settling velocity model (vh) of cs et al. (1991). Taka vh ¼ v0 erH X erP X
(2)
where v0 is the maximum settling velocity; rH and rP are the hindered and low concentration indices, respectively; X is the sludge concentration. This settling velocity model could very well describe the hindered settling regime; however, as expected, SBH and Xb predictions diverged from the measurements during the transient and compression settling regime (dotted line in Fig. 2c,d). To address this problem, we tested a settling velocity model that includes a mechanistic compression settling velocity, vc (Bu¨rger, 2000; Kinnear, 2002; De Clercq et al., 2008). 1 rS ds dXA @ vc ¼ vh 1 rS rf gX dX dz 0
(3)
with the effective solids stress (s) gradient formulation developed by De Clercq et al. (2008). 8 <
0 X < XC ds ¼ a dX : X XC X XC þ b
(4)
where vh is the hindered settling velocity (Eq. (2)), rs and rf are the sludge and water density, respectively; g denotes the gravity constant; z is depth in the settling column; a and b are compression parameters; XC is the threshold compression concentration. Unfortunately, this model over-predicted the Xb data (dash-dotted line in Fig. 2d) when it was calibrated to the SBH data (dash-dotted line in Fig. 2c). This outcome
indicates that calibrating the settling velocity model to only the SBH measurements does not correctly predict all the settling regimes. Furthermore, the discontinuity in the mathematical formulation of s gradient (Eq. (4)) makes the computation time of parameter estimation with DREAM(ZS) inefficient.
3.1.3.
Settling velocity model development
To improve the prediction of the settling velocity model (Eqs. (2)e(4)), we investigated alternative formulations for the effective solids stress gradient (data not shown). By replacing the power formulation (Eq. (5)) with the formulation of De Clercq et al. (2008) in Eq. (4), we can achieve more accurate predictions of Xb (dashed line in Fig. 2d). 8 > <
0 ds ¼ X XC C2 dX > : C1
X < XC (5)
X XC
where C1 and C2 are the parameters in the new compression settling model. This formulation is a modified form of similar power formulations for effective solids stress proposed in literature (Holdich and Butt, 1997; Bu¨rger, 2000). With the new formulation for the effective solids stress (Eq. (5)), the discontinuity in the mathematical formulation of settling velocity is avoided, which significantly increased the speed of the simulation and optimization process (data not shown). We could further improve the prediction of Xb in the compression settling regime (solid line in Fig. 2d) by applying the following transient velocity formulation accounting immediately after hindered settling, i.e. X > X0. vt ¼ v0;t ert X
(6)
where v0,t and rt are the transient settling parameters. This new exponential transient formulation was chosen analogous to the hindered settling velocity formulation (Eq. (2)). To avoid discontinuity in the transition from the hindered to the transient regime, the settling velocities were set to be equal at the transition point, i.e. vh ¼ vt at X ¼ X0. We could then calculate one of the transient settling parameters as v0;t ¼
v0 erH X0 ert X0
(7)
and reduce the number of calibration parameters to rt, XC, C1, and C2. The complete formulation of the new settling velocity model is as follows 8 v erH $X v0 erP $X > > > 0 > < v0;t ert X vS ¼ > > > > : v0;t ert X 1 fC dX dz
X X0 X0 < X < XC
(8)
X XC
where the compression factor fC is defined as fC ¼
C X XC 2 C1 rS rf gX rS
(9)
In this paper, Eq. (8), which includes Hindered, Transient and Compression settling velocity formulations, is referred to as the HTC settling velocity model.
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3.1.4. model
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Calibration and evaluation of the HTC settling velocity
The form of the HTC settling velocity model is shown in Fig. 3a with the parameters rt, XC, C1, and C2 estimated based on simultaneous calibration to SBH and Xb measurements (Fig. 3b). To reduce the complexity of the HTC model and thus the number of calibration parameters, XC was set to be equal to 1.1 X0 since parameter estimation showed that it was estimated very close to X0 (Fig. 3a). Therefore, the calibration parameters are reduced to (rt, C1, C2). Fig. 4 shows the predictive accuracy and uncertainty of the calibrated HTC settling velocity model to SBH and Xb measurements for X0 ¼ 2.7 kg/m3 (Lundtofte WWTP sludge). The HTC model can be seen to have very good predictive accuracy with an acceptably low predictive uncertainty (Fig. 4a,b). The low uncertainty of two of the three estimated
parameters (Fig. 4 c, d, and e), and no strong correlations between all the three parameters (not shown) indicate that the model is well defined. Results of the HTC model calibration to all of the measurement sets (with sludge samples from the two WWTPs) are reported in Fig. 5. The measurements with X0 ¼ 5.1 kg/m3 (Lundtofte WWTP sludge) were not considered because of the very long lag period in the SBH measurements (see Fig. 1c).
3.1.5. Implementation of the HTC settling velocity model in the CFD model of SST The HTC settling velocity model (Eq. (8)) was implemented in the CFD model of the Lundtofte SST with the estimated settling parameter values set as follows based on the values reported in Table S3 in the Supporting Information using Lundtofte WWTP sludge. X0 was assumed to be equal to the SST feed flow concentration. The estimated values of rt for different Xo were in a comparably narrow range (0.71e0.82), therefore a constant value of 0.77 was used. The model was insensitive to C1 (Fig. 4d), and a constant averaged value of 15.6 was used. C2 values showed a clear dependency to X0 (Table S3, Lundtofte sludge), which was summarized by the function (R2 ¼ 0.99): C2 ¼ 1:6e0:4X0
(10)
For the CFD model, C2 was calculated with Eq. (10) for X0 equal to the SST feed concentration.
3.2.
Rheological model
3.2.1.
Experimental results
The rheological measurements from the batch experiments with different sludge concentrations were analysed by plotting the applied external force (shear stress, t) versus the measured internal velocity gradients (shear rates, g). A pseudo-plastic behaviour of sludge with yield stress was identified (Fig. 6a).
3.2.2.
Rheological model selection and calibration
Among the proposed empirical formulations in literature (Eshtiaghi et al., 2013; Ratkovich et al., 2013), the HerscheleBulkley model could describe the observed rheological behaviour of activated sludge more accurately (fitted curves in Fig. 6a,b): t ¼ t0 þ Kgn h¼
Fig. 3 e The graphical form of HTC settling velocity model (Eq. (8)), including hindered (vh), transient (vt) and compression (fC) components (a), calibrated to SBH and Xb measurements with Lundtofte WWTP sludge at X0 ¼ 2.7 kg/m3 by implementing the settling velocity model in a 1-D model of the settling column with 60-layer discretization (b); the lines in b correspond to the simulated evolution of sludge concentration in each layer.
t g
(12) (13)
where t0 is the yield stress; K is the consistency index; n is the flow behaviour index; h is the apparent viscosity of sludge. The three parameters (t0, K, n) were estimated by fitting the Herschel-Bulkley model to the rheological measurements at the shear rates between 0.01 and 250 s1. As shown in Fig. 6b, a maximum viscosity (mmax) constraint - set at the critical shear rate of 0.01 s1 e is imposed to avoid predicting unrealistic viscosity values under very low shear conditions (Craig et al., 2013). The estimated parameter values for the experiments e run at T ¼ 15 C e are plotted in Fig. 6c, d, e. Notably, less accurate estimation of yield stress at high sludge
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Fig. 4 e Predictive accuracy and uncertainty (95% confidence intervals of the model prediction due to parameter uncertainty) of the HTC settling velocity model with the estimated parameters (rt, C1, C2) for X0 ¼ 2.7 kg/m3 (Lundtofte WWTP sludge) (a, b). The histograms (c, d, and e) show the posterior distribution of the three parameters estimated using DREAM(ZS), with a fitted Gaussian distribution (red curves). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
concentrations (Fig. 6a) resulted in a comparably large variance in the estimated yield stress values (error lines in Fig. 6c). The estimated rheology parameter values are comparable for the three different temperature conditions (Table 2), which suggests that the typical seasonal temperature variation in the bioreactors in WWTPs may not have significant “direct” impact on the rheological behaviour of activated sludge. We note that this result does not take into account the fact that the seasonal temperature variations can impact the microbial composition of activated sludge, which may influence the rheological behaviour of activated sludge in the SST. Nevertheless, the parameter values obtained at T ¼ 15 C were used in the CFD model, which was the average temperature degree detected by the Vectrino® sensor during the full-scale profile measurements.
3.2.3. Implementation of the rheological model in the CFD model of SST The three estimated HerscheleBulkley model parameters (t0, K, n) were found to be dependent on the sludge concentration of the samples, X (Fig. 6c, d, and e). To implement this dependency in the CFD model, three relations were established (fitted curves in Fig. 6c, d, and e). Other alternative correlation formulations for the yield stress (t0) and the consistency index (K) have been previously reported (De Clercq, 2003; Eshtiaghi et al., 2012). Based on the correlations in Fig. 6c, d, e, the apparent viscosity of the sludge mixture correctly converges to water viscosity at very low sludge concentrations; i.e. if X / 0, then t0 / 0, K / mw (viscosity of water), and n / 1.
3.3.
CFD simulations of the SST
Fig. 7 shows the steady-state simulation results of two CFD models using the calibrated HerscheleBulkley rheological model in combination with: (i) the HTC settling velocity model cs settling velocity model (Eq. (2)). The (Eq. (8)), and (ii) Taka simulation results are compared with the full-scale measured vertical velocity and sludge concentration profiles, at four different radial distances from the centre of the tank.
3.3.1.
Validation of the developed CFD model
In Fig. 7a, the predictions of the CFD model developed using the new HTC settling velocity model and the identified rheological correlations show an overall close agreement with the measured profiles, particularly in terms of sludge distribution in the tank. The sludge blanket height is predicted with high accuracy. Prediction of the sludge concentration at the bottom cannot be validated since the TSS sensor was constrained by the velocimeter to reach the bottom of the tank. The CFD-predicted velocity field show a strong density current also captured by the velocity measurements just over the sludge blanket, which result in a counter current in the upper part of the tank (Fig. 7b). Moreover, the peak velocity magnitudes predicted at the 3, 7, and 10 m radial distances from the center (Fig. 7b) are in close agreement with the measured data. However, according to Fig. 7b (lower part), the developed CFD model over predicts the velocity of the dense mixture flowing to the hopper over the inclined bottom. This can be due to the underestimation of yield stress at high
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Fig. 5 e Predictive uncertainty (95% confidence intervals of the model prediction due to parameter uncertainty) of the HTC settling velocity model calibrated to the measurements with the Lundtofte (a, b) and Lynetten (c, d) WWTP sludge using DREAM(ZS) optimization algorithm. The total predictive accuracy of the two measured time series (SBH and Xb) are shown in b and d based on SSEN (Eq. (1)). sludge concentrations (see Fig. 7c), which can effectively increase the flowability of viscous sludge to the hopper. Fig. 8 illustrates the geometry and mesh of the CFD model of the Lundtofte SST (Fig. 8a), as well as the distributions of the sludge concentration (Fig. 8b), the magnitude of the convective velocity and the settling velocity (Fig. 8c and d, respectively), and the turbulence and molecular viscosities (Fig. 8e and f, respectively) computed in the numerical domain for average operating boundary conditions (Qoverflow ¼ 100 m3/h, R ¼ 1.42, XFeed ¼ 5.64 kg/m3) during the measurement campaign. These figures show the complexity of the predicted flow field in the SST and the high gradients particularly in case of sludge concentration and molecular viscosity. The velocity magnitude (Fig. 8c) shows the strong horizontal density current and several recirculation zones in the tank. The significance of the estimated apparent molecular viscosity with the rheological model on the dampening of turbulence viscosity can be clearly observed in Fig. 8e and f, in the vicinity of the sludge blanket, where the molecular viscosity is estimated orders of magnitude higher than the turbulent viscosity.
3.3.2. Relative impact of settling velocity model on CFD predictions In Fig. 7a, comparing the simulation results of the two CFD models to the measurements indicates that the error in
underestimating SBH is significantly higher when using the cs settling velocity model (see errors reported in Fig. 7a). Taka The CFD-predicted flow-field is also influenced by the performance of the settling velocity model (Fig. 7b). These results indicate the benefit of including transient and compression settling by employing the new HTC settling velocity model for the simulation of sludge distribution in SSTs using CFD modelling. We further assessed the influence of the settling velocity model on the CFD predictions under wet-weather flow conditions, i.e. where there is increased hydraulic load to the WWTP and thus to the SST. We performed simulations using cs settling velocity the CFD model with the HTC and Taka models, under a constant wet-weather flow rate, for three hours real time. The wet-weather condition was simulated based on the ATV design standards for peak wet-weather flow rate (Ekama et al., 1997), where the actual overflow rate was increased by a factor of 2.39 and the recycle ratio was decreased to 0.75. The initial conditions were set to the steady-state simulation results under the average operational condition (Fig. 7). Fig. 9 shows the results, and demonstrates that the omission of transient and compression settling velocity in the CFD domain can significantly influence the predicted SST behaviour, in terms of thickening and storage capacity, under wet-weather conditions. Predictions made by explicitly accounting for hindered, transient and compression
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455
Fig. 6 e Prediction of rheological measurements at T ¼ 15 C with the HerscheleBulkley model (a). A maximum viscosity (mmax) constraint was set for g < 0.01 s¡1 to avoid unrealistic viscosity values predicted by the model under very low shear conditions (b). Mean and standard deviation of the estimated Herschel-Bulkley model parameters and their dependency on the concentration of sludge samples X (c, d, and e); A ¼ 0.00066 [kg1¡B m3£B¡1s¡2], B ¼ 2.18 [e], C ¼ 0.28 [m3/kg], D ¼ 0.00083 [m3£E kg¡E], E ¼ 2.57 [e].
settling in the CFD model (i.e. employing the HTC settling function, Fig. 9a), are 92% higher SBH and 20% lower TSSrecycled values than that obtained with the domain, only representing cs settling hindered (and flocculant) settling using the Taka velocity model. This model structural uncertainty can significantly hinder decision makings when assessing SST storage capacity under wet weather flow conditions.
measurements such as rheological laboratory experiments (sampling, storage, and instrument) and full-scale profiling in SST with the Vectrino® sensor (may require different calibration when used for measurements in the clarification zone and in the sludge blanket due to sound speed difference in different media).
3.4.
4.
Outlook and perspectives
Besides CFD modelling, the new settling velocity model can be used explicitly in simpler 1-D SST models for integrated WWTP modelling. Moreover, the efficiency in its calibration using the new experimental set-up combined with the Bayesian optimization method makes it useful in engineering practice e.g., for on-line control purposes. Our results indicate that the CFD model developed using the new settling and rheology functions, can predict the sludge distribution in the SST with fairly good accuracy. This is achieved without any arbitrary adjustment of the parameters and boundary conditions. Therefore, the relative impact of improving the settling velocity model on the CFD predictions could be assessed. The accuracy of CFD predictions could be further increased by assessing the uncertainties associated with the simplifications in the boundary condition (e.g. 2D axisymmetric, slip bottom) or
Conclusion
In this study, we presented a straightforward experimentalmodelling methodology using a simple, novel batch settling column experimental set-up combined with a Bayesian optimization method to identify a new settling velocity model for activated sludge. Additionally, rheological correlations for activated sludge were identified using data from batch laboratory experiments. Based on the evaluation of the state-of-the-art settling velocity models, a new settling velocity model was developed, which accounts for hindered, transient and compression settling regimes of activated sludge. We showed that this model can be calibrated to data from the novel settling column experimental set-up presented in this study using a Bayesian optimization algorithm. The proposed settling velocity model was validated with
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Fig. 7 e Vertical profiles (normalized height) of sludge concentration X (a), and radial velocity (b). Measurements (thin marked lines) at four different radial distances from the centre of the tank. CFD model predictions with the HTC settling cs settling velocity model (dashed line). velocity model (solid line), and CFD model predictions using Taka
measurements using activated sludge samples from two different WWTPs and at different dilutions. A pseudo-plastic behaviour of activated sludge with yield stress was identified based on measurements from rheological batch experiments. The HerscheleBulkley rheological model could effectively describe the measurements. We identified correlations to describe the strong dependency of rheological model parameters to sludge concentration. The direct effect of temperature change (10, 15, and 20 C, as typical seasonal temperature variations in SSTs) on the rheology of activated sludge was found insignificant. A 2-D axisymmetric CFD model of the circular conical SST (Lundtofte WWTP) was developed, including the new
settling velocity model and the calibrated rheological correlations. The CFD model could describe the full-scale measurements with fairly good accuracy and was further used to assess the relative impact of the new settling velocity model on the prediction of sludge distribution in SSTs. In this regards, we compared the simulation results of the CFD model using the new settling velocity model, which includes hindered, transient, and compression cs settling velocity settling, and the widely used Taka model, which only accounts for hindered (and flocculent) settling. The results showed that the representation of transient and compression settling in the CFD model can significantly improve the prediction of sludge distribution in the SSTs. Moreover, by performing CFD simulations of
Table 2 e The estimated parameters of the Herschel-Bulkley rheological model from measurements with five different sludge concentrations (X) at three different temperature conditions. X [kg/m3]
12.79 9.95 8.53 7.10 4.97
K [Pa sn]
t0 [Pa]
n [e]
10 C
15 C
20 C
10 C
15 C
20 C
10 C
15 C
20 C
0.20 0.10 0.07 0.05 0.03
0.17 0.10 0.07 0.05 0.02
0.19 0.10 0.06 0.04 0.02
0.047 0.024 0.012 0.006 0.002
0.044 0.019 0.010 0.006 0.003
0.035 0.018 0.010 0.005 0.002
0.67 0.72 0.81 0.90 1.02
0.65 0.74 0.82 0.88 1.00
0.68 0.74 0.82 0.89 1.00
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Fig. 8 e The CFD simulation results of the SST for the averaged operating conditions (Qoverflow ¼ 100 m3/h, R ¼ 1.42, XFeed ¼ 5.64 kg/m3) during the measurement campaign. For clear illustration, the values are shown in logarithmic scale. cs the SST under wet-weather flow condition, using Taka settling velocity model resulted in 92% underestimation of SBH and 20% overestimation of TSSrecycled as compared to when the proposed settling velocity model was used. This
model structural uncertainty can significantly affect the accurate assessment of SST storage capacity under wetweather flow conditions.
Acknowledgments The research was financially supported by the Danish Council for Strategic Research, Programme Commission on Sustainable Energy and Environment, as part of the Storm and Wastewater Informatics (SWI) project (http://www.swi.env. dtu.dk). The authors would like to thank Associate Professor Thomas Ruby Bentzen from Aalborg University for his valuable comments on the manuscript.
Appendix A. Supplementary data Supplementary data related to this article can be found at http://dx.doi.org/10.1016/j.watres.2014.08.034.
references Fig. 9 e Predicted sludge distributions with CFD simulations under constant wet-weather flow conditions (Qin ¼ 414 m3/h, R ¼ 0.75, XFeed ¼ 5.64 kg/m3) for three hours real time using the HTC settling velocity model (a), cs settling velocity model (b). and Taka
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