Apr 13, 2005 - Abstract. We describe on-site measurements and numerical modelling work on the sedimentation of activated sludge in full-scale secondary ...
Sedimentation of Activated Sludge in Secondary Clarifiers Michael Weiss, Benedek Gy. Plosz, Karim Essemiani, Jens Meinhold Anjou Recherche Veolia Water Chemin de la Digue BP 76 78603 Maisons-Laffitte Cedex, France
Abstract We describe on-site measurements and numerical modelling work on the sedimentation of activated sludge in full-scale secondary clarifiers. These solid/liquid separation units represent the final stage in the activated sludge wastewater treatment process. The rheological flow behaviour of the activated sludge was studied experimentally for varying concentrations and temperatures. These measurements show that the relationship between the shear stress and the shear rate follows the Casson law at low shear rates that correspond more closely to the shear rates encountered in secondary clarifiers. At higher shear rates, the Bingham law is more appropriate to describe the non-Newtonian flow behaviour of the activated sludge. The parameters of the double-exponential settling velocity function, which describes the dependence of the settling velocity of the activated sludge flocs on the concentration, were obtained from batch sedimentation experiments. Light scattering was applied to measure concentration profiles in the clarifier. A computational fluid dynamics (CFD) model was developed using the CFD software Fluent. The convection-dispersion equation for turbulent flow, which governs the sludge transport in the clarifier, is extended to incorporate the sedimentation of sludge flocs in the field of gravity. The hydrodynamic model accounts for buoyancy flow and non-Newtonian flow behaviour of the mixed liquor. A one-dimensional sedimentation model, which is based on the convection-dispersion transport equation, was developed within the biological process modelling tool West. Both numerical models are validated using the sludge concentration profiles measured in the clarifier. Keywords: Secondary Clarifiers; Suction-Lift Sludge Removal; Activated Sludge; Rheology; Settling Velocity; Computational Fluid Dynamics; Modelling
1.
Introduction
Secondary clarifiers represent the final stage in the activated sludge wastewater treatment process (Fig. 1). They are preceded by the aeration basin, where previously developed biological flocs are brought into contact with the organic material of the wastewater. Within the activated sludge process, secondary clarifiers fulfil a triple role, serving as clarifier, thickener and sludge storage zone. Its clarifying function produces the clear supernatant, whereas its thickening function provides a continuous underflow of thickened sludge that is recycled to the aeration basin. The storage function ensures that sludge may be kept within the clarifier during peak flows. Failure with respect to either of these functions can result in increased suspended solids concentration in the effluent or in the deterioration of the activated sludge process. Practical experience has shown that the secondary clarifier is often the main bottleneck in the activated sludge process [1-3].
1
Numerical modelling tools are often used for designing and optimising new and existing secondary clarifiers, and to detect the causes of malfunction of these process separation units. Computational fluid dynamics (CFD) may be used to resolve the fluid mechanics and the sludge transport locally in the clarifier. Biological process modelling tools, which contain one-dimensional sedimentation models, are often employed to analyse the impact of the solid/liquid separation process on the performance of the biological conversion process in the aeration basin. For example, short circuits in the clarifier, a local hydraulic phenomenon, can result in the dilution of the sludge in the recirculation stream to the aeration basin, so that the concentration in the aeration basin falls below the value necessary for the efficient conversion of the organic matter in the wastewater. A local hydraulic problem can thus lead to the deterioration of the entire activated sludge process. Aeration Basin
Excess Sludge
Secondary Clarifier
Influent
Effluent
Sludge Recirculation Fig. 1. Schematic representation of the activated sludge wastewater treatment process. Off-the-shelf modelling solutions to tackle these problems rarely exist. This is particularly true in the case of CFD models, which, in addition to the settling characteristics of the activated sludge flocs, aim to account for the rheological flow behaviour and density of the activated sludge, and for the coupling between fluid mechanics and sludge transport. Physical models are needed to describe the underlying mechanisms correctly. In this paper, we describe on-site experiments and measurements that serve to parameterise and to validate our one-dimensional sedimentation model, developed within the biological process simulation tool West, and our CFD model of the secondary clarifier, which we have developed using the general-purpose CFD solver Fluent. A detailed account of both models is given elsewhere [4,5]. The present study concerns circular clarifiers that are equipped with suction-lift sludge removal systems. In these clarifier systems, which usually have a flat bottom, the sludge is withdrawn through an array of vertical suction (or aspiration) pipes from the near-bottom region (Fig. 2). This design form may be contrasted with clarifiers that have conical bottoms and bottom scraper systems, and where the sludge is removed centrally at the bottom through the sludge hopper [1]. The clarifiers at the wastewater treatment plant of Saint Malo in north-western France, where we have carried out on-site measurement campaigns in March/April and July 2005, have a depth of 3 m everywhere and a diameter of about 33 m. Settled sludge is removed from the bottom region of the clarifier by means of suction-lift through an array of six suction pipes. These pipes are situated underneath the slowly rotating clarifier bridge and remove sludge locally in the near-bottom region underneath the bridge.
2
Effluent
Sludge accumulation in the clarifier bottom region
Inlet
Fig. 2. Schematic drawing of the Saint Malo clarifier showing the inlet annulus and the effluent outlet. The dash-dotted line marks the vertical centre line of the axisymmetric clarifier, and the arrows indicate the direction of the flow in the clarifier. An array of vertical suction pipes (omitted in the drawing) removes settled sludge from the near-bottom region of the clarifier.
2.
Experimental Studies and Measurements
We have carried out rheology and settling experiments to study the non-Newtonian flow behaviour and the settling characteristics of the activated sludge mixture. Another important physical parameter, the sludge density, has not been measured. Instead, we have made use of data published in the literature to account for local sludge density variations in the clarifier. We have measured the flow rates in the recycle stream and at the effluent outlet of the clarifier, which serve as boundary conditions in the models. Our measurements of the local sludge distribution in the clarifier are used to validate the predictions of the numerical models. Whilst the sedimentation experiments serve to characterise the settling characteristics in both the one-dimensional sedimentation model and the CFD model, the density and the rheology of the sludge are only considered in the CFD model. 2.1
Rheology of Activated Sludge Mixtures
We have measured the rheological flow behaviour of the activated sludge in the clarifier using Brookfield’s LV II+ rotational viscometer in combination with Brookfield’s UL adapter. The measurement annulus in the UL adapter is formed by two coaxial cylinders of radii Ri = 12.58 mm and Ro = 13.81 mm for the inner and the outer cylinder, respectively. The effective length of the cylinders is L = 92.37 mm, giving a sample volume of V = 16 ml. This arrangement of coaxial cylinders allows for measuring the rheological flow behaviour of lowviscosity liquids. Its well-defined geometry facilitates the mathematical analysis of the experimental data. The outer cylinder of the UL adapter is fixed. The inner cylinder rotates at a defined speed, which may be set to values of 0 to 200 min-1. The resulting torque, in units of [Nm], is measured as a function of the rotational speed, in units of [min-1]. Both the rotational speed and the torque are converted to shear rate, in units of [s-1], and shear stress, in units of [kg m-1 s-2], respectively. A Lauda ProLine RP 845 refrigerated water bath was connected to the UL adapter to control the temperature during the measurements, which were performed at 10, 15, and 20°C. The viscometer was operated using Brookfield’s Rheocalc software, which was also used to record the data during the measurements.
3
The sludge samples were taken at the outlet of the aeration basin, and the sludge concentration was adjusted by decantation and dilution, covering a concentration range of about 2.5 to 8.5 g l-1. The rheology experiments were carried out parallel to the sludge settling experiments using the same sludge samples. 0.8
0.8
b)
a) 0.6
τ
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τ
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0
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c) 0.6
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e) 0.6
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γ& Fig. 3. Rheograms of activated sludge mixtures at varying total suspended solids concentrations, X = 2.82 g l-1 (a), 3.71 g l-1 (b), 4.56 g l-1 (c), 5.48 g l-1 (d), and 7.04 g l-1 (e). The data were measured on 13th April 2005 and are for T = 10°C (♦), 15°C (□), and 20°C (▲). The shear stress, τ, has the units [kg m-1 s-2], and the shear rate, γ& , is in units of [s-1]. During our measurements, the dependence of the shear stress, τ, on the shear rate, γ& , the total suspended solids concentration, X, and the temperature, T, was studied. Using increments of 5 min-1, the rotational speed of the inner cylinder of the UL adapter was varied between 0
4
and 200 min-1 (1 ≤ γ& ≤ 250 s-1). In the case of higher activated sludge concentrations, which exhibit higher viscosities, and to ensure a sufficient number of torque-speed value pairs for the mathematical analysis, the speed increment was lowered to 2.5 min-1, since the maximum torque of the viscometer was attained at lower rotational speeds of around 100 min-1. A time interval of 10 s between each measurement was necessary for the torque readings to become stable, which stands in contrast to the measurement procedure employed by Guibaud and coworkers, who took one reading every two seconds [6-8]. The rheograms shown in Fig. 3, which were measured on 13th April 2005, are representative for all our measurements. They show that at sufficiently large shear rates, typically at γ& > 50 s-1 for X < 5.0 g l-1 and at γ& > 100 s-1 for X > 5.0 g l-1, the curves exhibit Bingham-type flow behaviour. At low to moderate shear rates, where γ& < 50 s-1 for X < 5.0 g l-1 and γ& < 100 s-1 for X > 5.0 g l-1 and which correspond more closely to the shear rates encountered in a secondary clarifier, the activated sludge mixture displays Casson-type flow characteristics. Both types of flow behaviour are analysed below. At sludge concentrations of less than 5 g l-1 and at a temperature of 20°C, the rheograms in Fig. 3 show an increase in shear stress with increasing shear rate at shear rates > 200 s-1. This phenomenon, which is known as the Taylor-Couette effect, is caused by the onset of turbulent flow conditions in the measurement annulus [9]. We have disregarded these parts of the rheograms at the two lowest concentrations at 20°C in our Bingham rheology analysis of the rheological flow behaviour. In this paper, we present rheology analyses using experimental data that were measured in April 2005. The rheology experiments were repeated in July 2005, and the results have demonstrated that the rheological flow behaviour of the activated sludge had not changed. 2.1.1 Casson Rheology Analysis The Casson model is given by 12 τ = K 1 + K 2 γ& 1 2 , (1) where K1 is the Casson yield stress parameter, and K2 is the Casson viscosity parameter. Using the definition of the shear stress, τ = µγ& , (2) we arrive at 2
⎛K ⎞ (3) µ = νρ w = ⎜⎜ 1 12 + K 2 ⎟⎟ ⎝ γ& ⎠ for the dynamic viscosity of the sludge mixture, µ. In Eq. (3), ν is the kinematic viscosity of the activated sludge mixture, and ρw is the density of water. We determine the values for K1 and K2 from a fit of Eq. (1) to the experimental data at low shear rates. This fit is shown for the set of experimental data obtained on 13th April 2005 in Fig. 4. We have applied this procedure to our entire rheology data set, which was measured on 12th to 14th April 2005 for three different temperatures, and the values obtained for K1 and K2 are summarised in Table 1. The parameters K1 and K2 depend on the sludge concentration, X, and on the temperature, T, as shown in Fig. 5. We approximate the dependence of K1 on X using a parabolic function, K1 = C1 X 2 + C 2 X . (4) For X → 0, the yield stress parameter vanishes correctly, and we have that K1 → 0. The values for C1 and C2 are summarised in Table 2 for the temperatures applied during the measurements. The data in Table 2 show that C2 decreases with increasing temperature. C1, on the other hand, does not exhibit a clear functional dependence on the temperature. 5
Additional measurements at 5°C and 25°C may help to establish a clearer functional dependence and to reduce errors. Table 1. Parameters K1 and K2 of the Casson viscosity law, Eq. (1). The values for K2 at X = 0 correspond to µ 1w 2 , which we have taken from the 74th edition of the Handbook of Chemistry and Physics [10]. Note that some of the measurements were repeated. 10°C 15°C 20°C K2 K2 K2 K1 K1 K1 X γ& Date/ 1/2 1/2 1/2 1/2 1/2 1/2 ⎤ ⎡ kg ⎤ ⎡ kg ⎤ ⎡ kg ⎤ ⎡ kg ⎤ ⎡1 ⎤ ⎡ g ⎤ ⎡ kg ⎤ ⎡ kg Source ⎢ l ⎥ ⎢ m1/2 s ⎥ ⎢ m1/2 s1/2 ⎥ ⎢ m1/2 s ⎥ ⎢ m1/2 s1/2 ⎥ ⎢ m1/2 s ⎥ ⎢ m1/2 s1/2 ⎥ ⎢ s ⎥ ⎣ ⎦ ⎣ ⎦ ⎣ ⎦ ⎣ ⎦ ⎣ ⎦ ⎣ ⎦ ⎣ ⎦ ⎣ ⎦ 0 0 0.0362 0 0.0341 0 0.0316 [10] 2.82 0.0722 0.0470 0.0846 0.0432 0.0652 0.0441 0 - 50 13/04/05 2.99 0.0978 0.0439 0.0804 0.0446 0.0723 0.0432 0 - 50 12/04/05 3.56 0.1014 0.0493 0.0962 0.0459 0.0848 0.0455 0 - 50 14/04/05 3.71 0.1249 0.0467 0.0985 0.0472 0.0960 0.0459 0 - 50 13/04/05 4.00 0.1062 0.0455 0.1191 0.0445 0.1172 0.0432 0 - 50 12/04/05 4.00 0.1024 0.0470 0 - 50 12/04/05 4.56 0.1528 0.0467 0.1497 0.0469 0.1473 0.0477 0 - 50 13/04/05 5.36 0.1701 0.0497 0.1583 0.0447 0.1661 0.0447 0 - 100 14/04/05 5.48 0.2145 0.0485 0.2056 0.0453 0.1820 0.0463 0 - 100 13/04/05 5.80 0.2134 0.0458 0.1702 0.0433 0.1653 0.0412 0 - 100 12/04/05 5.80 0.1950 0.0479 0 - 100 12/04/05 7.04 0.2969 0.0479 0.2864 0.0444 0.2737 0.0458 0 - 100 13/04/05 8.37 0.3673 0.0470 0.3389 0.0473 0.3423 0.0445 0 - 100 14/04/05
Table 2. Parameters C1 and C2 in Eq. (4), and K 2 and µ 1w 2 in Eqs. (5) and (6) for varying temperatures, T. K2 C1 C2 µ 1w/ 2 T [°C]
10 15 20
⎡ m11/2 ⎤ ⎢ 3/2 ⎥ ⎣ kg s ⎦ 0.00307 0.00281 0.00319
⎡ m 5/2 ⎤ ⎢ 1/2 ⎥ ⎣ kg s ⎦ 0.0187 0.0176 0.0146
⎡ kg 1/2 ⎤ ⎢ 1/2 1/2 ⎥ ⎣m s ⎦ 0.0463 0.0445 0.0436
⎡ kg 1/2 ⎤ ⎢ 1/2 1/2 ⎥ ⎣m s ⎦ 0.0362 0.0341 0.0361
The viscosity parameter, K2, appears to be independent of the concentration over the range of concentrations measured (see Fig. 5). However, the scatter in the experimental data at low shear rates is considerable, in particular at the higher concentrations (see Figs. 3 and 4), and we are lacking measured data at concentrations below 2 g l-1.
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0.5
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b)
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5
γ& 1/2
10
γ& 1/2 0.8
e) 0.6
τ1/2
0.4 0.2 0 0
5
10
γ& 1/2 Fig. 4. Square root of the shear stress, τ1/2, in units of [kg1/2 m-1/2 s-1], as a function of the square root of the shear rate, γ& 1/2, in units of [s-1/2], for T = 10°C (♦), 15°C (□), and 20°C (▲). The experimental data were measured on 13th April 2005 and are for X = 2.82 g l-1 (a), 3.71 g l-1 (b), 4.56 g l-1 (c), 5.48 g l-1 (d), and 7.04 g l-1 (e). For the pure water case to emerge correctly, we must have that K 2 → µ 1w 2 as X → 0. For X > 0, K2 is assumed to increase linearly up to X = X* = 2 g l-1, where it reaches the mean value K 2 . For X > 2 g l-1, the viscosity parameter is assumed to be independent of X. Thus, for X ≤ X*, we have ( K 2 − µ 1w 2 ) X, X∗ and for X > X*, we have K 2 = µ 1w 2 +
(5)
7
K2 = K2 .
(6)
0.4
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20°C
20°C 0.03
0 0
5
10 -1
X [g l ]
0
5
10 -1
X [g l ]
Fig. 5. Casson viscosity model parameters, K1 and K2, as a function of the sludge concentration, X, and for varying temperatures. The curve fits (solid lines) were carried out using the experimental data (symbols) measured on 12th to 14th April 2005. K1 is given in units of [kg1/2 m-1/2 s-1], and K2 is given in units of [kg1/2 m-1/2 s-1/2]. The values for K 2 and µ 1w 2 are given in Table 2 for the temperatures under consideration in our study. Since both K 2 and µ 1w 2 decrease with increasing temperature, the Casson viscosity also decreases with increasing temperature. We have shown that at low to moderate shear rates, the Casson viscosity model is more appropriate to describe the rheological flow behaviour of the activated sludge mixture. This is an important result since the shear rates in secondary clarifiers are typically very low. We 8
have thus used Eqs. (3) to (6) in our CFD model to account for the non-Newtonian flow behaviour of the activated sludge in the secondary clarifier. However, in the aeration basin, where the shear rates are larger due to the aeration with air and the mixers that are present in the basin, the Bingham viscosity model (described below) is more likely to be appropriate. 2.1.2 Bingham Rheology Analysis The Bingham model contains two parameters; the initial (Bingham) yield stress, τB, and the Bingham viscosity, µB. The initial yield stress must be overcome to initiate flow. The shear stress increases proportionally with the shear rate once flow is initiated, the Bingham viscosity being the constant of proportionality. The Bingham law is given by τ = τ B + µ Bγ& . (7) Using the definition of the shear stress, Eq. (2), we arrive at
µ=
τB + µB γ&
(8)
for the dynamic viscosity of the activated sludge mixture. The fit of Eq. (7) to our experimental data at higher shear rates yields values for τB and µB (see Fig. 6). We have carried out this fit using our entire data set, and the values thus found are summarised in Table 3. Fig. 7 shows the dependence of both τB and µB on X for varying temperatures. Table 3. Bingham viscosity, µB, and yield stress, τB, as a function of temperature and concentration. The parameter valueswere obtained from a fit of Eq. (7) to the experimental data. µB [kg m-1 s-1] τB [kg m-1 s-2] -1 X [g l ] 10 °C 15 °C 20 °C 10 °C 15 °C 20 °C Date/Source 0 0.0013 0.0012 0.0010 0 0 0 [8] 2.82 0.0022 0.0020 0.0019 0.0502 0.0452 0.0391 13/04/2005 2.99 0.0021 0.0021 0.0019 0.0530 0.0465 0.0394 12/04/2005 3.56 0.0023 0.0021 0.0019 0.0842 0.0718 0.0669 14/04/2005 3.71 0.0024 0.0022 0.0020 0.0922 0.0769 0.0749 13/04/2005 4.00 0.0023 0.0022 0.0020 0.0728 0.0775 0.0749 12/04/2005 4.56 0.0026 0.0024 0.0021 0.1187 0.1243 0.1288 13/04/2005 5.36 0.0026 0.0024 0.0022 0.1797 0.1131 0.1536 14/04/2005 5.48 0.0027 0.0025 0.0023 0.2049 0.1739 0.1741 13/04/2005 5.80 0.0030 0.0023 0.0022 0.1503 0.1233 0.1009 12/04/2005 6.75 0.0041 0.0031 0.0030 0.1878 0.2426 0.2121 12/04/2005 7.04 0.0032 0.0031 0.0027 0.2410 0.2123 0.2551 13/04/2005 8.37 0.0030 0.0029 0.0029 0.3698 0.3287 0.2795 14/04/2005 An exponential law according to µ B = a exp(bX ) (9) is employed to describe the dependence of µB on the activated sludge concentration, X. In Eq. (9), a = µw is the viscosity of water, and b describes the increase in viscosity with increasing concentration. For X = 0, we have that µB = a = µw, and the viscosity takes the water value. The values of the parameters in Eq. (9), which are found from a fit of the exponential law to the experimental data in Fig. 7, are given in Table 4. Our values for a and b are somewhat higher than those found by Guibaud and co-workers [8].
9
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a) 0.4
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e) 0.7
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0.6 0.5 0.4 50
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γ& Fig. 6. Shear stress, τ, as a function of the shear rate, γ& , for T = 10°C (♦), 15°C (□), and 20°C (▲). The data were measured on 13th April 2005 and are for X = 2.82 g l-1 (a), 3.71 g l-1 (b), 4.56 g l-1 (c), 5.48 g l-1 (d), and 7.04 g l-1 (e). τ is given in units of [kg m-1 s-2], and γ& is given in units of [s-1].
10
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0.01
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10°C
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20°C 0.001
0 0
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Fig. 7. Bingham viscosity, µB, and yield stress, τB, for three temperatures and as a function of the concentration, Eqs. (9) and (10), and for the experimental data measured on 12th to 14th April 2005. τB is given in units of [kg m-1 s-2], and µB has the units [kg m-1 s-1]. The dependence of τB on X is well described by
τ B = cX 2 + dX .
(10)
For X = 0, we have that τB = 0. The values for c and d are obtained from a fit of Eq. (10) to the experimental data in Fig. 7. The parameter values thus found are given in Table 5.
11
Table 4. Parameters a and b of the exponential fit, Eq. (9), which are used to determine the Bingham viscosity, µB, at a given temperature. Our values are compared with those found by Guibaud et al. [8]. T [°C] a [kg m-1 s-1] b [l g-1] X [g l-1] Date/Source 10 0.00131 0.1364 2.82 - 8.37 12/04/05 - 14/04/05 15 0.00116 0.1400 2.82 - 8.37 12/04/05 - 14/04/05 20 0.00100 0.1524 2.82 - 8.37 12/04/05 - 14/04/05 20 0.00109 0.1120 2.8 - 9.8 [8] 20 0.00115 0.0970 2.9 - 9.8 [8] 20 0.00115 0.0730 1.9 - 17.7 [8] 20 0.00117 0.1010 3.3 - 11.3 [8] 20 0.00103 0.1030 3.3 - 11.3 [8] Table 5. Parameters c and d of Eq. (10), which are used to determine the Bingham yield stress, τB, at a given temperature. T [°C] c [m5 kg-1 s-2] d [m2 s-2] X [g/l] date 10 0.0042 0.0066 2.82 - 8.37 12/04/05 - 14/04/05 15 0.0041 0.0040 2.82 - 8.37 12/04/05 - 14/04/05 20 0.0033 0.0081 2.82 - 8.37 12/04/05 - 14/04/05 2.2
Sludge Density
The density of the sludge mixture, ρ, depends on the sludge concentration, X. This dependence is usually taken to be a linear function, given by ⎛ ρp ⎞ ρ = ρ w + ⎜⎜ − 1⎟⎟ X , (11) ⎝ ρw ⎠ where ρw = 998.2 kg m-3 is the density of water, and ρp is the density of the dry sludge. Dahl [11] and Nopens [12] have measured the sludge density as a function of the sludge concentration using pycnometry. Their measurements have confirmed the linear dependence of ρ on X, and they have found values for the dry sludge density from a fit of Eq. (11) to their measured data. In the CFD model, we rely on their measurements and use a value of ρp = 1600 kg m-3. Eq. (11) is used in the CFD model to account for buoyancy flow in the secondary clarifier. 2.3
Sludge Sedimentation
We have conducted batch settling experiments using Applitek’s Settlometer [13-15]. This automated device uses a scanner system to detect the height of the sludge blanket during the batch settling experiments, which take place in a column that has a height of 70 cm and a diameter of 14 cm, and that is equipped with a slowly rotating stirrer. We have carried out daily settling experiments at varying initial sludge concentrations of about 2 to 8 g l-1. We have used sludge taken at the outlet of the aeration basin, and the initial sludge concentration during the experiments was varied using decantation and dilution. The settling experiments were carried out parallel to the rheology experiments, and we have used sludge taken from the same sampling for both experiments. A typical set of smoothed batch settling curves is shown in Fig. 8.
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8
X [g/l]
Fig. 8. Batch settling curves (left) showing the height of the sludge blanket in the settling column, H, as a function of the settling time, t. The curves were measured on 13th April 2005 and are for sludge concentrations of 2.82 (□), 3.71 (♦), 4.56 (×), 5.48 (∆), and 7.04 (+) g l-1. The settling velocity, us = (dH/dt)max = us(X), is deduced from the batch settling curves (right). From the set of batch settling curves, we can deduce the parameters us0 and rh of the exponential settling velocity function of Vesilind [16], ⎛ dH ⎞ = u s 0 exp(− rh X ) . us = ⎜ ⎟ (12) ⎝ dt ⎠ max Table 6 summarises the values for us0 and rh that were obtained from our batch settling experiments in March/April and in July 2005. The results in Table 6 show that the settling behaviour was relatively constant. Table 6. Parameters of the Vesilind function, Eq. (12). Date us0 [m h-1] rh [m3 kg-1] 21/03/2005 5.0175 0.3485 23/03/2005 3.9326 0.3436 29/03/2005 5.0581 0.2723 30/03/2005 4.6398 0.2424 31/03/2005 4.3748 0.2501 01/04/2005 4.1813 0.2495 11/04/2005 5.4402 0.3350 12/04/2005 4.0096 0.2679 13/04/2005 4.1866 0.2844 14/04/2005 4.3210 0.2872 04/07/2005 3.0609 0.2436 11/07/2005 3.2100 0.2247 19/07/2005 4.1338 0.3059 20/07/2005 3.5063 0.2578 In our modelling work under West and Fluent, we have used the double-exponential settling velocity function of Takács et al. [17], an extension of the Vesilind function that has two additional parameters and that is given by u s = u s 0 exp[−rh ( X − X ns )] − u s 0 exp[− r p ( X − X ns )] . (13)
13
The parameter rp characterises the settling behaviour at low concentrations, and Xns is the concentration of non-settleable solids in the effluent of the clarifier. The value for rp is generally one order of magnitude larger than that of rh [18]. We have measured the concentration of non-settleable solids in the effluent by means of decantation, which gave a value of Xns = 5.2 × 10-3 kg m-3. Fig. 9 shows a fit of Eq. (13) to the data measured on 13th April 2005. 3
2 us [m/h] 1
0 0.001
0.01
0.1
1
10
X [g/l]
Fig. 9. Fit of the double-exponential settling velocity function, Eq. (13), to the experimental settling velocity data (symbols) that were measured on 13th April 2005. The parameter values are us0 = 4.1866 m h-1, rh = 0.2844 m3 kg-1, rp = 10 × rh, and Xns = 5.2 × 10-3 kg m-3. 2.4
Sludge Concentration Profile Measurements in the Clarifier
The local sludge distribution in the Clarifier was measured using a Solitax-ts light scattering sonde. The sonde was connected to a long aluminium tube (4.5 m in length) that allowed for measuring the sludge concentration at the bottom of the clarifier. A custom-built sonde support was used that enabled us to attach the aluminium tube to the clarifier bridge and to easily change both the vertical and horizontal position of the sonde. We have usually measured several vertical concentration profiles at varying radial distances from the centre of the clarifier along the slowly rotating bridge. The concentration profile measurements serve to validate our numerical sedimentation models under West and Fluent (see Figs. 11 and 12). 2.5
Flow Measurements
We have installed a Miltronics XPS10 ultrasonic flow metering sonde above the open effluent outlet channel of the clarifier to measure the height of water in the channel. These height measurements, together with the known geometry of the channel, were then used to calculate the effluent flow rate. In addition to the effluent flow rate data, we have used the data of the flow rate in the recirculation stream, which is continuously measured by the plant operator. Balancing the flow rates around the clarifier gave the flow rate at the inlet of the clarifier. We note that when balancing the flow rates around the clarifier, we have made the supposition that any change in flow rate at the inlet of the clarifier is instantaneously measurable at the effluent outlet, so that damping effects of the (large) clarifier volume are not considered. This assumption implies that the moving surface of the clarifier is not accounted for. 14
Under Fluent, both the flow rates at the inlet of the clarifier and in the recycle stream serve as boundary conditions. The one-dimensional sedimentation model under West considers the link between aeration basin and clarifier, and it requires the flow rate at the inflow of the plant as a boundary condition instead of the flow rate at the clarifier inlet. 1200 1000 800 Q 3
[m /h]
600 400 200 0 06:00
07:12
08:24
09:36
10:48
Time
Fig. 10. Flow rates, Q, measured at the effluent outlet (×) and in the recycle stream (∆). The flow rate at the clarifier inlet (■) was obtained from a flow balance around the clarifier. The data were measured in the morning of 7th July 2005. The flow rates that were recorded in the morning of 7th July 2005 are shown in Fig. 10. Clearly, the flow data vary considerably over time. The concentration profile measurements on 7th July (see Fig. 11) were carried out from about 9:30 to 10:30 in the morning. The flow data in Fig. 10 suggest that the sludge distribution in the clarifier is affected by the varying flow rates, not only during the time of measurements, but also by the history of the flow before the measurements. However, our concentration profile measurements, which were measured over time and at varying locations in the clarifier, have shown that the impact on the sludge distribution in the clarifier is rather moderate. We have thus calculated mean values for the flow rates, and the numerical computations were carried out at steady state.
3.
Numerical Modelling
Two numerical modelling approaches have been pursued; (i) a two-dimensional computational fluid dynamics (CFD) model that considers the clarifier geometry and the local hydrodynamics in the clarifier, and (ii) a one-dimensional settling model that is integrated in a biological process simulation tool. 3.1
Computational Fluid Mechanics
Our axisymmetric single-phase CFD model, which has been developed using the generalpurpose CFD solver Fluent 6, is based on the modelling efforts of Lakehal and co-workers [19]. The CFD model predicts the sedimentation of activated sludge in a full-scale circular secondary clarifier that is equipped with a suction-lift sludge removal system. We have
15
employed negative source terms on the governing partial differential equations to simulate the sludge removal mechanism in the near-bottom region of the clarifier. A convection-dispersion equation, which we have extended to incorporate the sedimentation of sludge flocs in the field of gravity, governs the sludge transport in the clarifier. The standard k-ε turbulence model is used to compute the turbulent motion, and our CFD model accounts for buoyancy flow in the clarifier. The Casson viscosity model is used to take the non-Newtonian flow behaviour of the sludge mixture into account. A detailed description of the mathematical model may be found elsewhere [5]. The comparison of measured and computed concentration profiles in Fig. 11 shows that the model predicts the sludge distribution in the inlet region well. At longer radial distances from the centre of the clarifier, the model overpredicts the height of the sludge blanket somewhat. Unequal sludge withdrawal through the suction pipes or dynamic flow conditions during the measurements may be the cause of this discrepancy. The concentration values that were measured near the clarifier bottom are not reproduced by the CFD model. However, the average concentration value in the sludge removal zone computed by the CFD model (9.04 kg m-3) compares very well to the value that was measured in the recycle stream (9.71 kg m-3). The computed effluent concentration value of 12.9 g m-3 agrees well with the average measured effluent concentration value of 11.0 g m-3. 3.2
One-Dimensional Sedimentation Model
The one-dimensional sludge sedimentation model has been developed within West, a biological process simulation tool that considers the link between secondary clarifier and aeration basin [4]. In this model, the transport of solids is assumed to be governed by the vertical bulk movement of the water and the gravity settling of the sludge. The convective flow in the underflow region of the model, below the inlet, is reduced to reflect the flat bottom geometry and the sludge removal mechanism of the clarifier. In addition, we have added a second-order dispersion term to the transport equation. This dispersion term contains a dispersion coefficient that may depend on the concentration and on the feed velocity [20,21]. We compare the concentration profile computed by the one-dimensional model under West with measured values in Fig. 12. The measured values were obtained by averaging measured concentration values at radial distances of 4.1 m, 7.1 m, 11 m, and 13.4 m from the centre of the clarifier. Concentration profiles that were measured in the inlet region of the clarifier and in the region close to the effluent outlet were not considered. In these regions of the clarifier, the sludge distribution is affected by the geometry of the clarifier, and these effects are not included in the one-dimensional model. As shown in Fig. 12, the height of the sludge blanket and the sludge distribution within the sludge blanket are well predicted by the onedimensional model. We have thus developed a validated one-dimensional sedimentation model within the biological process simulation software West that correctly predicts the sludge distribution in a flat-bottom clarifier equipped with suction-lift sludge removal. The “standard” onedimensional sedimentation model under West, which does not consider dispersion and in which the convective motion in the underflow region of the clarifier is not controlled, fails when applied to this type of secondary clarifier [4].
16
16
10 8 X 6 [g/l] 4 2 0
3.0 m
7.0 m
12 X 8 [g/l] 4 0
0
1
2
0
3
1
2
3
Distance from bottom [m]
Distance from bottom [m] 16
16 10.5 m
12 X 8 [g/l] 4
X 8 [g/l] 4
0
0
0
1
13.5 m
12
2
0
3
1
2
3
Distance from bottom [m]
Distance from bottom [m]
Fig. 11. Computed concentration profiles obtained from the CFD model (lines) and measured concentration profiles (symbols) in the clarifier at varying radial distances from the clarifier centre for 7th July 2005 (Xin = 4.93 kg m-3, Qrec = 362 m3 h-1, Qin = 662 m3 h-1). 10 8 6 X [g/l] 4 2 0 0
1
2
3
Distance from bottom [m]
Fig. 12. Computed concentration profile obtained from the one-dimensional model (line) and measured concentration values (symbols). The data are for 14th April 2005 (Xin = 3.67 kg m-3, Qrec = 449 m3 h-1, Qin = 823 m3 h-1).
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4.
Conclusions
We have described on-site measurements and experiments on the sedimentation of activated sludge in secondary clarifiers. The results of these measurements were used to parameterise and validate a two-dimensional fluid mechanics model, developed within the CFD code Fluent, and a one-dimensional sedimentation model, developed within the process simulation tool West. The sludge rheology measurements have shown that the rheological flow behaviour changes qualitatively depending on the shear rate. At shear rates of about 1 to 50 s-1 (1 to 100 s-1 at higher concentrations), which correspond more closely to the shear rates encountered in a secondary clarifier, the non-Newtonian flow behaviour of the activated sludge can be described using the Casson law. At shear rates > 50 s-1 (> 100 s-1 at higher concentrations), the Bingham law is more appropriate to describe the dependence of the shear stress on the shear rate. Based on our sludge settling experiments, the dependence of the settling velocity on the sludge concentration has been described using the double-exponential settling function. The flow rates at the effluent outlet and in the recycle sludge stream were measured, and we have calculated the flow rate at the clarifier inlet using these measurements. The flow rates serve as boundary conditions in the models. The local sludge distribution in the clarifier has been measured, and these measurements have been compared with the model predictions. Both models are well capable of predicting both the height of the sludge blanket and the sludge distribution within the sludge blanket correctly. The next step in the development of the models is to include a second class of finer sludge particles, and to account for flocculation and deflocculation mechanisms.
Acknowledgments
M. Weiss and B. Gy. Plosz gratefully acknowledge financial support from the European Commission for two industry-host Marie Curie post-doctoral research fellowships.
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