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A new settling velocity model to describesecondary sedimentation

Elham Ramin a,*, Dorottya S. W�agner a, Lars Yde b, Philip J. Binning a,Michael R. Rasmussen c, Peter Steen Mikkelsen a, Benedek Gy. Pl�osz a,*

a Department of Environmental Engineering, Technical University of Denmark, Miljøvej, Building 113, 2800 Kgs.

Lyngby, Denmarkb DHI Water & Environment (S) Pte Ltd, Singapore 63714, Singaporec Department of Civil Engineering, Aalborg University, Sohngaardsholmsvej 57, 9000 Aalborg, Denmark

a r t i c l e i n f o

Article history:

Received 31 March 2014

Received in revised form

25 July 2014

Accepted 23 August 2014

Available online 3 September 2014

Keywords:

Activated sludge

Compression

Calibration

Computational fluid dynamics

Rheology

Monte Carlo Markov Chain

* Corresponding authors. Tel.: þ45 45 25 16 9E-mail addresses: elhr@env.dtu.dk (E. Ra

Binning), mr@civil.aau.dk (M.R. Rasmussen)http://dx.doi.org/10.1016/j.watres.2014.08.0340043-1354/© 2014 Elsevier Ltd. All rights rese

a b s t r a c t

Secondary settling tanks (SSTs) are the most hydraulically sensitive unit operations in

biological wastewater treatment plants. The maximum permissible inflow to the plant

depends on the efficiency of SSTs in separating and thickening the activated sludge. The

flow conditions and solids distribution in SSTs can be predicted using computational fluid

dynamics (CFD) tools. Despite extensive studies on the compression settling behaviour of

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

calibration. In this study, we developed a new settling velocity model, including hindered,

transient and compression settling, and showed that it can be calibrated to data from a

simple, novel settling column experimental set-up using the Bayesian optimization

method DREAM(ZS). In addition, correlations between the Herschel-Bulkley rheological

model parameters and sludge concentration were identified with data from batch rheo-

logical experiments. A 2-D axisymmetric CFD model of a circular SST containing the new

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 wet-

weather flow conditions.

© 2014 Elsevier Ltd. All rights reserved.

1. Introduction

In conventional wastewater treatment plants (WWTPs), bio-

reactors are connected to secondary settling tanks (SSTs) to

separate the suspended biomass from treatedwater bymeans

4.min), dosaw@env.dtu.dk, psmi@env.dtu.dk (P.S. M

rved.

of gravity sedimentation. The thickening and clarification ef-

ficiency of SSTs is significantly influenced by hydraulic dis-

turbances during wet-weather flow conditions. This is of

particular concern due to the increasing frequency of hy-

draulic shock-loads fromurban run-offs toWWTPs associated

with the effect of climate change on peak rainfall intensities

(D.S. W�agner), lay@dhigroup.com (L. Yde), pjbi@env.dtu.dk (P.J.ikkelsen), beep@env.dtu.dk (B.Gy. Pl�osz).

Table 1 e The description of WWTPs and the list ofcorresponding experiments.

Parameters LundtofteWWTP

Lynetten WWTP

aPE 135,000 750,000bSRT [d] 31 29

SST type circular rectangularcDSVI [ml/g] 125 90

SST design

Clarifier diameter [m] 24.5 Not investigated

Depth of outer wall [m] 3.48

Bottom slope [%] 7.66

Centre wall diameter [m] 3

Centre wall depth [m] 6.2

Inlet surface area [m2] 4.24

Recycle surface area [m2] 3.96

Tank surface area [m2] 470

Sludge removal mechanism scraper

Experiments

Settling x x

Rheology x e

Full-scale measurements x e

a Population equivalent (design).b Sludge retention time (design).c Diluted sludge volume index of the sampled sludge.

wat e r r e s e a r c h 6 6 ( 2 0 1 4 ) 4 4 7e4 5 8448

(Larsen et al., 2009; Pl�osz et al., 2009). When examining SSTs

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 ex-

periments 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,

2003; Pl�osz et al., 2007).

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 CFDmodels of SSTs is

not well-established.

Concerning the settling velocity models, the recent devel-

opment 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 (Burger, 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 experi-

ments such as radiotracer tests (De Clercq et al., 2005) and are

not simple to do in practice. Therefore, the application of

compression settlingmodels is limited to a few cases of 1-D SST

modelling (De Clercq et al., 2008; Burger et al., 2011). Most of the

CFD studies consider only the hindered (and flocculent) settling

regimes using the empirical formulation of Tak�acs et al. (1991).

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 demon-

strated 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 hy-

drodynamics 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

when using Tak�acs hindered (and flocculent) settling velocity

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 velocitymodel, 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 testsWe developed a simple laboratory set-up, consisting of a glass

column (Fig. 1a) with a Solitax® total suspended solids (TSS)

a

b

c

d

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).

wat e r r e s e a r c h 6 6 ( 2 0 1 4 ) 4 4 7e4 5 8 449

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

sensorwas validated in-situ by comparing themeasured 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 experimentsThe non-Newtonian behaviour of the sampled sludge from

the Lundtofte WWTP was studied using laboratory shear

stress-controlledmeasurements in a rotational rheometer (AR

2000, TA Instruments, USA), with concentric conical-

cylindrical 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 concen-

tration 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

bubbles, no pre-shearing was applied to the sludge sample.

The diluted sludge samplewas replacedwith 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 experi-

ments (starting from the maximum value corresponding to

shear rate of around 250 s�1 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. Full-scale measurementsFull-scale measurements were performed at Lundtofte SST to

validate the CFD model. The sludge concentration and veloc-

ity 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 velocitymodels (presented in

section 3.1) to the settling measurements, they were imple-

mented in a dynamic 1-D model of the settling column (Pl�osz

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 simu-

lations (over 5000). The minimization function in the

DREAM(ZS) algorithm was defined as an averaged non-

dimensional sum of squared errors (Marler and Arora, 2004).

SSEN ¼ 1n�m

Xni¼1

Xmj¼1

yi;j � byi;j

�q�

yi;j

!2

(1)

where n is the number ofmeasured time-series (including SBH

alone or both SBH and Xb); m is the number of data points in

each time-series; y is the measured values; byðqÞ is the model

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 transportThe CFD modelling was performed in the open source CFD

toolbox OpenFOAM® (OpenCFD, 2012) and with the set-

tlingFoam 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

wat e r r e s e a r c h 6 6 ( 2 0 1 4 ) 4 4 7e4 5 8450

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 simu-

lationmodel 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. Computational domain and boundary conditionsThe 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 CFDmodel with the coarse

mesh did not diverge significantly from the cases with me-

dium and fine mesh (data not shown), and thus we used the

coarsemeshing in our simulations. The geometry andmesh 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 fric-

tionless boundary at the tank bottom to simulate the influ-

ence of an ideal “scraper” in overcoming the wall stress,

Fig. 2 e Settling phases observed from the batch measurements

at the bottom Xb (b), for X0 ¼ 2.7 kg/m3 (Lundtofte WWTP sludg

measurements (c), and evaluating their prediction of Xb (d).

facilitating sludge flow to the hopper for removal, as proposed

by Deininger et al. (1998). The free water surface was consid-

ered to be a symmetrical plane. The remaining walls were

considered to be non-slip boundaries with standard wall-

functions to estimate the mean fluid velocity near the wall

(Brennan, 2001).

3. Results and discussion

3.1. Settling velocity model

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 param-

eter values of the settling velocity models are provided in the

Supporting Information (Tables S1eS3).

3.1.1. Experimental observationsThe SBH measurements in the settling column (Fig. 2a)

allowed identification of the four different settling regimes

typically observed during batch activated sludge settling col-

umn tests: lag, hindered, transient, and compression (Ekama

et al., 1997). The lag period observed at the beginning of the

of sludge blanket height SBH (a), and sludge concentration

e). Calibrating different settling velocity models to the SBH

wat e r r e s e a r c h 6 6 ( 2 0 1 4 ) 4 4 7e4 5 8 451

experiment resulted from the dissipation of kinetic energy

introducedwith coarse air bubbles used to homogenize sludge

in the column before measurements start. The subsequent

period of constant descent of the liquid/solid interface corre-

sponds 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 im-

mediate 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 modelsFig. 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

Tak�acs et al. (1991).

vh ¼ v0

�e�rHX � e�rPX

�(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 ex-

pected, SBH and Xb predictions diverged from the measure-

ments 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 compres-

sion settling velocity, vc (Burger, 2000; Kinnear, 2002; De Clercq

et al., 2008).

vc ¼ vh

0@1� rS�rS � rf

�gX

dsdX

dXdz

1A (3)

with the effective solids stress (s) gradient formulation

developed by De Clercq et al. (2008).

dsdX

¼8<:

0 X<XC

a

X� XC þ bX � XC

(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 developmentTo 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).

dsdX

¼

8><>:0 X<XC�

X� XC

C1

�C2

X � XC

(5)

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; Burger, 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;te�rtX (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 tran-

sient 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 v0e�rHX0

e�rtX0(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

vS ¼

8>>>><>>>>:v0e

�rH$X � v0e�rP$X X � X0

v0;te�rtX X0 <X<XC

v0;te�rtX

�1� fC

dXdz

�X � XC

(8)

where the compression factor fC is defined as

fC ¼ rS�rS � rf

�gX

�X� XC

C1

�C2

(9)

In this paper, Eq. (8), which includes Hindered, Transient

and Compression settling velocity formulations, is referred to

as the HTC settling velocity model.

wat e r r e s e a r c h 6 6 ( 2 0 1 4 ) 4 4 7e4 5 8452

3.1.4. Calibration and evaluation of the HTC settling velocitymodelThe form of the HTC settling velocitymodel 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 esti-

mated very close to X0 (Fig. 3a). Therefore, the calibration

parameters are reduced to (rt, C1, C2). Fig. 4 shows the pre-

dictive accuracy and uncertainty of the calibratedHTC settling

velocitymodel to SBH andXbmeasurements for X0¼ 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

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 velocitymodel

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.

parameters (Fig. 4 c, d, and e), and no strong correlations be-

tween 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 inthe CFD model of SSTThe 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 1:6e�0:4X0 (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 resultsThe rheological measurements from the batch experiments

with different sludge concentrations were analysed by plot-

ting 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 calibrationAmong the proposed empirical formulations in literature

(Eshtiaghi et al., 2013; Ratkovich et al., 2013), the Her-

scheleBulkley model could describe the observed rheological

behaviour of activated sludgemore accurately (fitted curves in

Fig. 6a,b):

t ¼ t0 þ Kgn (12)

h ¼ t

g(13)

where t0 is the yield stress; K is the consistency index; n is the

flowbehaviour 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 s�1. As shown in Fig. 6b, a

maximum viscosity (mmax) constraint - set at the critical shear

rate of 0.01 s�1 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

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.)

wat e r r e s e a r c h 6 6 ( 2 0 1 4 ) 4 4 7e4 5 8 453

concentrations (Fig. 6a) resulted in a comparably large vari-

ance 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. Never-

theless, 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 CFDmodel of SSTThe 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 de-

pendency 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 velocitymodel

(Eq. (8)), and (ii) Tak�acs settling velocity model (Eq. (2)). The

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 modelIn Fig. 7a, the predictions of the CFD model developed using

the new HTC settling velocity model and the identified rheo-

logical 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

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)).

wat e r r e s e a r c h 6 6 ( 2 0 1 4 ) 4 4 7e4 5 8454

sludge concentrations (see Fig. 7c), which can effectively in-

crease 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 molec-

ular 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 CFDpredictionsIn 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

Tak�acs settling velocity model (see errors reported in Fig. 7a).

The CFD-predicted flow-field is also influenced by the per-

formance 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 con-

ditions, i.e. where there is increased hydraulic load to the

WWTP and thus to the SST. We performed simulations using

the CFD model with the HTC and Tak�acs settling velocity

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 ve-

locity in the CFD domain can significantly influence the pre-

dicted SST behaviour, in terms of thickening and storage

capacity, under wet-weather conditions. Predictions made by

explicitly accounting for hindered, transient and compression

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); A¼ 0.00066 [kg1¡B m3£B¡1s¡2], B¼ 2.18 [e], C¼ 0.28 [m3/kg], D¼ 0.00083

[m3£E kg¡E], E ¼ 2.57 [e].

wat e r r e s e a r c h 6 6 ( 2 0 1 4 ) 4 4 7e4 5 8 455

settling in the CFD model (i.e. employing the HTC settling

function, Fig. 9a), are 92% higher SBH and 20% lower TSSrecycledvalues than that obtained with the domain, only representing

hindered (and flocculant) settling using the Tak�acs settling

velocity model. This model structural uncertainty can signif-

icantly hinder decision makings when assessing SST storage

capacity under wet weather flow conditions.

3.4. Outlook and perspectives

Besides CFDmodelling, the new settling velocitymodel 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 param-

eters and boundary conditions. Therefore, the relative

impact of improving the settling velocity model on the CFD

predictions could be assessed. The accuracy of CFD pre-

dictions could be further increased by assessing the un-

certainties associated with the simplifications in the

boundary condition (e.g. 2D axisymmetric, slip bottom) or

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).

4. Conclusion

In this study, we presented a straightforward experimental-

modelling methodology using a simple, novel batch settling

column experimental set-up combined with a Bayesian opti-

mization method to identify a new settling velocity model for

activated sludge. Additionally, rheological correlations for

activated sludge were identified using data from batch labo-

ratory experiments.

� Based on the evaluation of the state-of-the-art settling

velocity models, a new settling velocity model was devel-

oped, 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

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

velocity model (solid line), and CFD model predictions using Tak�acs settling velocity model (dashed line).

wat e r r e s e a r c h 6 6 ( 2 0 1 4 ) 4 4 7e4 5 8456

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 rheo-

logical batch experiments. The HerscheleBulkley rheolog-

ical model could effectively describe the measurements.

We identified correlations to describe the strong de-

pendency of rheological model parameters to sludge con-

centration. 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

Table 2 e The estimated parameters of the Herschel-Bulkley rsludge concentrations (X) at three different temperature condi

X [kg/m3] t0 [Pa]

10 �C 15 �C 20 �C 10 �C

12.79 0.20 0.17 0.19 0.047

9.95 0.10 0.10 0.10 0.024

8.53 0.07 0.07 0.06 0.012

7.10 0.05 0.05 0.04 0.006

4.97 0.03 0.02 0.02 0.002

settling velocity model and the calibrated rheological cor-

relations. 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 ve-

locity 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

settling, and the widely used Tak�acs settling velocity

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

heological model from measurements with five differenttions.

K [Pa sn] n [e]

15 �C 20 �C 10 �C 15 �C 20 �C

0.044 0.035 0.67 0.65 0.68

0.019 0.018 0.72 0.74 0.74

0.010 0.010 0.81 0.82 0.82

0.006 0.005 0.90 0.88 0.89

0.003 0.002 1.02 1.00 1.00

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.

wat e r r e s e a r c h 6 6 ( 2 0 1 4 ) 4 4 7e4 5 8 457

the SST under wet-weather flow condition, using Tak�acs

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

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),

and Tak�acs settling velocity model (b).

model structural uncertainty can significantly affect the

accurate assessment of SST storage capacity under wet-

weather flow conditions.

Acknowledgments

The research was financially supported by the Danish Council

for Strategic Research, Programme Commission on Sustain-

able 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 valu-

able 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.

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