Assessment of hydraulic flocculation processes ... - Wiley Online Library

The performance of flocculation tanks either in full- or pilot-scale systems cannot be fully quantified using average velocity gradient values (G values) alone. The computational fluid dynamics (CFD) process was used to investigate the turbulent flow characteristics of a three-stage hydraulic flocculation facility at the J.D. Kline Water Supply Plant in Halifax, Nova Scotia. Calculations of the local velocity gradient were achieved using predicted energy dissipation rates. CFD analysis showed unbalanced mixing conditions in the hydraulic flocculation tanks resulting from short-circuiting and from recirculation zones. Inconsistent mixing energy, interrupted with severe spikes in the localized G values at the weir columns, led to little or no mixing energy in most of the regions in the flocculation tanks. Practical outcomes of operating at such varying mixing gradients can be detrimental to the flocculation process and overall organic removal in the treatment plant. A case study of the three-stage tapered hydraulic flocculation tank at the J.D. Kline Water Supply Plant in Halifax, Nova Scotia was initiated using computational fluid dynamics to evaluate the mixing conditions in the tanks.

Assessment of hydraulic flocculation processes using CFD

C YAMUNA S. VADASARUKKAI, GRAHAM A. GAGNON, D. REID CAMPBELL, AND SARAH C. CLARK

66

oagulation and flocculation are key processes in optimizing natural organic matter removal and subsequent mitigation of disinfection by-products (DBPs) formation (Jarvis et al, 2008). Proper use of coagulant type and dosage, optimal pH and alkalinity conditions, and mixing arrangements are imperative for effective destabilization of particles through the coagulation process. Subsequent enhancement of contact between the coagulant, destabilized particles, and primary particles in water occurs predominantly in the flocculation process through gentle mixing for 20 to 45 min (Crittenden & MWH, 2005). The flocculation process promotes the agglomeration of particles—called flocs—to form irregularly shaped aggregates that can be filtered or settled. These aggregates are then removed in downstream separation processes (e.g., sedimentation, filtration, dissolved air flotation). Floc characteristics (i.e., size and structure) formed during coagulation–flocculation processes govern the performance of downstream processes for improved particle and microbial removal (Jarvis et al, 2008). The flow conditions in flocculation tanks are driven by localized fluid turbulence, and the resulting flocs are subjected to varying shear rates. The resulting nonuniform energy distribution (i.e., in the x, y, and z directions) within the tank relates

NOVEMBER 2011 | JOURNAL AWWA • 103:11 | PEER-REVIEWED | VADASARUKKAI ET AL

2011 © American Water Works Association

The J.D. Kline Water Supply Plant (bottom) at Pockwock Lake (top), Halifax, Nova Scotia, is located in a protected watershed. The lake water has a low pH, a low alkalinity of calcium carbonate, and a low turbidity. Source water is pumped into the treatment facility at a constant flow rate; thereafter, it flows into subsequent treatment processes by gravity.

to the rate of particle collision (Bridgeman et al, 2008; Crittenden & MWH, 2005; Haarhoff & Van der Walt, 2001). Preformed flocs may adhere or break up during the flocculation process depending on the prevailing local hydrodynamics and physicochemical conditions (Bouyer et al, 2005). Previous studies (Bridgeman et al, 2010, 2008; Bouyer et al, 2005; Gregory, 2004) have determined that for a given hydrodynamic flow condition, flocs reach a certain threshold size in their growth phase. Beyond this limit, the relative fluid velocity that caused smaller particles to aggregate into larger flocs can also result in their breakup. Bridgeman et al (2008) expressed floc breakage threshold value in terms of local velocity gradients prevailing in a jar test apparatus. The hydrodynamic flow condition depends on both the geometry of the flocculation tank and the impeller speed and type. These hydrodynamic phenomena are often characterized by the average energy dissipation in the tank (i.e., the global root mean square velocity gradient [G value]; Bouyer et al, 2005). Analogous to the highturbulence zones at the tip and edges of mechanical impellers and paddles, hydraulic flocculation designs suffer from zones of high turbulence at the edges of the baffles. These zones could induce floc breakup. Having invested time and energy in developing flocs however, it is clear that these operating (hydraulic) conditions subsequently should not cause floc breakup and thus need to be quantified (Bridgeman et al, 2010; 2008). The degree of variability in energy dissipation in hydraulic flocculators can be measured through analysis

of local G-value distribution (Bridgeman et al, 2010; Haarhoff & Van der Walt, 2001). Using computational fluid dynamics (CFD)—a numerical modeling ap proach—Haarhoff and Van der Walt (2001) quantified high-turbulence zones in terms of estimated local G value as approximately 5% of the total flocculator volume for an around-the-end hydraulic flocculator. Review of previous studies, however, reveals that the application of CFD is more confined to hydrodynamics related to bench-scale mixers (impellers), with fewer examples (Bridgeman et al, 2010; Samaras et al, 2010; Essemiani et al, 2002; Haarhoff & Van der Walt, 2001) available with regard to the pilot- and full-scale flocculation process. As a result of wide variation in flocculator designs used in water treatment plants (WTPs), a detailed understanding of the fluid mechanics in these flocculators is critical for enhancing floc growth and stability at optimal retention time. Table 1 shows examples of WTPs in Canada and the type of flocculator designs used in such conventional and direct filtration plants. As shown, several direct filtration utilities are equipped with hydraulic flocculation designs for treating high-quality surface water. In this study, a CFD modeling strategy was implemented in a direct filtration plant to investigate the performance of a hydraulic flocculation process. The case study in Halifax, Nova Scotia, uses four sets of three-stage tapered hydraulic flocculation, having an up-and-down flow arrangement for mixing purposes. The main objective of this study was to evaluate the mixing condition for each of the three-stage flocculation tanks in terms of the spatial distribution of the local G value (Glocal) using CFD. The effect of flow condition on the design parameters, i.e., the volume average G value and the residence time (t) of fluid flow, were investigated.

VADASARUKKAI ET AL | PEER-REVIEWED | 103:11 • JOURNAL AWWA | NOVEMBER 2011


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BACKGROUND DESIGN CONCEPTS G value and its calculation. The G value in Eq 1 is used to calculate the intensity of mixing energy input required in a flocculation process (Crittenden & MWH, 2005; AWWA/ASCE, 1997). G

P 冪莦冪莦 µV µ m

(1)

in which m is the mean value of the work input per unit of time per unit of volume (J/s), µ is the dynamic viscosity of water (kg/m s), P is the average power of mixing input to the entire mixing vessel (J/s), and V is the volume in the tank. The G value in Eq 1 can also be interpreted in terms of the root mean energy dissipation per unit of mass (Haarhoff et al, 2001; Cleasby, 1984), as given in Eq 2, –

G

冪莦v

(2)

in which – is the average energy dissipated per unit of mass (m2/s3) and v is the kinematic viscosity of water (m2/s). The G value for the hydraulic flocculation process is largely a function of flow and is measured in terms of the total head loss estimated across the tank (Bridgeman et al, 2010; Haarhoff & Van der Walt, 2001; Haarhoff, 1998; AWWA/ASCE, 1997) as shown by Eq 3. G

gH 冪莦 µ

Glocal

冪莦v

(4)

Equation 5 is then used to determine the overall power consumption by numerically integrating the local power consumption over the entire vessel contents (Bridgeman et al, 2008).

冕

(3)

in which is the density of water, g is acceleration from gravity, H is total headloss (m), and is the hydraulic retention time of the fluid (s).

TABLE 1

Precise hydraulic measurements are required to account for the actual energy loss at the tank entrance and during the passage of water from one tank to another. This additional energy loss could result in an increase of about 25% in the estimated G value (Hargrave & Loucks, 1990). Previous studies (e.g., Bridgeman et al, 2010, 2008; Ducoste & Clark, 1999; Clark, 1994; Cleasby, 1984) have evaluated the validity of the G value to represent the average velocity gradient in a complex turbulent field. The authors argued that the distribution of turbulent energy is more dependent on the tank geometry and impeller configuration than the average G value (i.e., calculated using Eqs 1 and 3). Consequently, these studies suggest the need for a detailed investigation of the hydrodynamic flow characteristics. The approach to evaluating the turbulent flow field presented in this study would provide adequate information to describe the distribution of local energy dissipation rates at various locations in the tank. With the use of CFD it is possible to compute the local G value (Glocal) at any location in the tank as given in Eq 4 (Bridgeman et al, 2010). The local turbulent dissipation rate () is calculated using an appropriate turbulence closure model.

P dV

(5)

in which dV is the numerical integration over the entire volume.

Examples of flocculator designs used in conventional and direct-filtration WTPs in Canada

Type of Flocculator WTP Type

Treatment Capacity ML/d

Mannheim WTP (Kitchener, Ontario)

72.6

Yes

No

Arnold, 2008

R.L. Clark WTP (Toronto, Ontario)

415

Yes

No

City of Toronto, 2010b

R.C. Harris WTP (Toronto, Ontario)

453

No

Yes

Hargrave et al, 1990

Mechanical

Hydraulic

Reference

Conventional

Direct filtration Island WTP (Toronto, Ontario)

410

No

Yes

City of Toronto, 2010a

Prescott WTP (East of Brockville, Ontario)

8.2

Yes

No

Doyle et al, 2002

Point Pleasant WTP (Kingston, Ontario)

NA

Yes

No

Kingston Utilities, 2009

Sydenham WTP (Kingston, Ontario)

NA

No

Yes

Kingston Utilities, 2009

F.J. Horgan WTP (Toronto, Ontario)

570

Yes

Yes

Doyle et al, 2002

J.D. Kline WTP (Halifax, Nova Scotia)

95

No

Yes

NA—not available, WTP—water treatment plant

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Residence time distribution and its measurement. Residence time distribution (RTD) curves are used to identify the imperfect hydraulic behavior of the treatment units. These curves are usually expressed in terms of stagnant (dead) spaces and bypassing flow. Applying material balance principles and Laplace transform solution techniques, Martin-Dominguez and colleagues (2005) developed an RTD function for reactors in series with stagnation spaces and bypassing over the whole series of reactors. The resultant three-parameter tank-in-series (TIS) model is given in Eq 6a. NN nN 1 E( ) M (N – 1)!

n M

N–1

冢冣

tm t苶N (6a)

Nn Nn exp – (1 – n) M M

冢

冣

冢

冣

in which E( ) is a normalized exit age distribution curve; n is a fraction of flow rate effectively used in the treatment process (with no global bypassing); N is the number of reactors in the series; M is the fraction of a unit’s volume effectively used in the treatment process (with no stagnation of space); is the normalized residence time, – – ⬅ t/t N (dimensionless); t N is the total mean residence – – – time in N tanks (s), t N = N t s = Vs/Q; t s is the mean hydraulic residence time (HRT) of a single tank, calculated as the ratio of volume of the flocculation tank (Vs) in m3 to the bulk flow rate (Q) in ML/d; and is the Dirac delta function, = 0.0069 (assumed). The TIS model represents the flow through a series of equal volume of N continuously mixed flow reactors (CMFRs), allowing for dead-spaces (1 – M) and global bypassing (1 – n) over the whole series of reactors. For n = 1 (no bypassing) and M = 1 (no dead-space), it can be seen that Eq 6a simplifies to a well-known singleparameter RTD function for a series of completely stirred reactors (Levenspiel, 1999), as given in Eq 6b. N E( ) (N )N–1 exp (– N ) (N – 1)!

(6b)

The parameter Θ in the E(Θ) curve represents the number of reactor volumes of fluid based on entrance conditions that have flowed through the reactor in time t (Fogler, 2006), given as t – ⬅ tN

(7) –

in the TIS model are statistically independent of one another because of a perfect mixing that exists at any boundary between two tanks (Teefy & Singer, 1990). Mean residence time and variance calculations. The mean residence time (tm) of a fluid element in the flocculation tank is calculated from the first moment of the E(Θ) curve, as given in Eq 8, whereas the magnitude of 2 the spread of the distribution ( Θ , in which 2 indicates variance, the second moment of the centroid of the RTD curve about the mean of the distribution [s2]) is determined from the second moment about the mean, as indicated in Eq 9.

–

in which the total reactor volume is t N = Nt s = Vs /Q. The function E(Θ) in Eqs 6a and 6b is a normalized RTD. It characterizes the probability distribution function of the residence time (Θ) of a fluid element in the total tank (Stamou, 2008). The RTD functions of the individual tanks

冕

2 2 t2m

0

冕

0

E( )d E( )d

(8)

(1 – )2 E( )d

(9)

2 These two important parameters, tm and Θ , are used to characterize RTD curves (Teefy & Singer, 1990). Comparison of the calculated tm with the theoretical mean – (HRT t N) yields an insight into the importance of preferential flow paths and stagnation zones in the tank (Kennedy et al, 2006). The dimensionless exit-age distribution function E(Θ) can be statistically related to the cumulative exit-age distribution, also known as F(Θ) curve, given in Eq 10.

F( )

冕

0

n

E( )d 冱

1

E

(10)

The function F(Θ) has an S-curve when plotted with respect to time t bounded between a minimum of 0 and a maximum of 1 (Templeton et al, 2006). The F(Θ) curve therefore represents the cumulative probability of x fraction of fluid element leaving the tank at a residence time of Θx, which is less than or equal to the normalized residence time (Θ). Certain flow-through curve characteristics 2, Θ , Θ (e.g., tm, Θ x max [normalized time at which E(Θ) is equal to maximum {dimensionless}]) of both the E(Θ) and F(Θ) are used as “indicators of flow.” These parameters were used in characterizing the flow behavior in the flocculation tanks, which is consistent with other studies (Stamou, 2008; Kennedy et al, 2006). The F(Θ) curves generated from the TIS model were used to compare the results of the CFD particle-tracking simulations. For each residence time (Θ), the difference (or error) between the F(Θ) predicted by the TIS model and the CFD analysis was calculated (Martin-Dominguez et al, 2005), given as

冑冱冤 imax

i=1

冥

F( i)CFDpredicted – F( i)TISpredicted

2

erf (M,n,N) (11) (imax – 1)



69

in which erf is error function, imax is the number of measured concentration, and i is the index representing current concentration, tank number or time value.

METHODOLOGY Description of the full-scale system. The direct filtration system of J.D. Kline Water Supply Plant (JDKWSP) treats water from Pockwock Lake, which is located in a protected watershed. The lake water is characterized by a low pH (5.0–5.2), a low alkalinity of ~ 0 mg/L (i.e., below detection limit) calcium carbonate, and a low turbidity of 0.3–0.5 ntu. The design capacity of JDKWSP is about 220 ML/d, with an average daily intake of 95 ML/d. The source water is pumped into the treatment facility at a constant flow rate through a 1.2-m (48-in.) inlet pipe; thereafter, it flows into subsequent treatment processes

FIGURE 1

by gravity. The treatment system consists of three rapidmixing tanks in series, four parallel units of a three-stage tapered hydraulic flocculation tank, eight direct dualmedia filtration units (filled with a 0.6-m-deep layer of anthracite over a 0.3-m layer of sand), followed by disinfection with free chlorine. A four-flat-bladed propeller is installed in the rapid-mixing tanks for mixing the chemicals added during preoxidation and coagulation processes (i.e., lime, potassium permanganate, carbon dioxide, aluminum sulfate). Flow from the third rapid-mixing tank spills over a weir into the premixed shaft and then into a 1.2-m (48in.) distribution header system (Figure 1). This header delivers the flow to four identical hydraulic flocculation tanks through four 0.6-m (24-in.) tees. Each 0.6-m tee is placed 10.7 m equidistant. Isolation butterfly valves are

Flow distribution arrangements of the three-stage hydraulic flocculation process of JDKWSP’s direct filtration* 4.0 m Rapid mix tank 1

Tank 2

1.2 m- (48 in.-) diameter conduit of length 19.5 m

Outflow of coagulated water from the third rapid mix tank through a weir 1.2 m- (48 in.-) diameter conduit of length 12.8 m

Rectangular tank

5.0 m

Tank 1

1. 2

Pipe size and distance between the pipe dimensions are same for other pipes exiting from 1.2 m (48 in.)

m

10.7 m

5.0 m

0.6 m- (24 in.-) diameter pipe

Tank 3 4.0 m

Raw water supply 1.2 m- (48 in.-) diameter pipe

Tapered hydraulic flocculation tank

1. 5

m

Tank 2

Tank 3

Floc water conduit of 45.4 m length

Dual media filtration unit

JDKWSP—J.D. Kline Water Supply Plant *Not to scale

70



provided on each of the flocculation tank inlets but are not used to control the flow split. Flow-splitting is based on hydraulics associated with piping and conduits. As shown in Figure 1, each flocculation tank consists of three rows of two parallel sets of cells (i.e., a total of six cells). The length, width, and depth of each flocculation cell are 5.0 m, 5.0 m, and 8.3 m, respectively. Two tapered vertical shafts, each with corresponding volumes of 11.95 m3 and 18.68 m3, are provided for flow transfer between the three rows of flocculation chambers. Water flows over a weir, through a vertical shaft, and enters the next cell at the bottom. The design of such an up-and-down flow arrangement provided in the subsequent second and third flocculation chamber facilitates in achieving the G value for mixing purposes. After flocculation, the flow exits the tanks through a port near the top of the last row of the chambers and is distributed to eight filters through a floc water conduit. Flow split to the filters is controlled by the effluent control values at the discharge of each filter. CFD modeling procedure. All numerical simulations of the present study were carried out using a finite volume– based software program.1 Using the program’s built-in features, the Navier-Stokes equations coupled with turbulence flow transport equations were approximated to a system of algebraic equations using discretization techniques (Essemiani & De Traversay, 2002; Versteeg & Malalasekera, 1995). These equations governing the fluid flow were solved iteratively on a computer. A three-dimensional, single-phase (i.e., water being the only fluid medium) simulation was performed to evaluate the flow distribution from the rapid mixing to the flocculation tanks (Baek et al, 2005). The resultant flow distributed to each flocculation tank inlet was then used to investigate the flow-field characteristics in each flocculation tank. Two separate computational domains were defined using a preprocessing tool2 for flow distribution and flocculation tank simulations. The full-scale drawing of JDKWSP was used to create an exact geometry of the two flow problems. Symmetrical geometries of the first, second, and third flocculation chambers of a hydraulic flocculation tank were modeled, as shown in Figure 1. In this study, a mesh-density analysis was conducted to obtain a mesh-independent flow solution. The effect of mesh density on the average G-value calculation (Eqs 1, 5) was investigated for the flow distribution and the flocculation tank analysis separately. For instance, a mesh-density analysis was conducted at three mesh conditions (i.e., coarse, medium, and finer grids) for the flocculation tank analysis. Medium and finer mesh densities of 524,584 and 638,575, respectively, were obtained by refining the highgradient regions in the coarse mesh (i.e., 100,130 tetrahedral elements). A maximum percentage difference in the predicted average G values between the coarse and medium meshes was determined to be 12.86% for the flow distribution and 21.92% for the flocculation tank analysis. To ensure the quality of mesh, finer mesh densities of 518,425

and 638,575, respectively for the flow distribution and flocculation tank analysis, were selected. The material properties (e.g., density and viscosity) of water were changed to simulate summer and winter trials. The temperature, density, and viscosity of water during the summer trial were set to 15°C, 998.23 kg/m3, and 0.001002 kg/m s, respectively; whereas the fluid properties of the winter trial were changed to 2.5°C, 999.9 kg/m3, and 0.001645 kg/m s, respectively. The total raw water flow into the plant was varied to four discharges of 69, 75, 90, and 120 ML/d for the flow distribution analysis. The Reynolds number for those discharges was estimated as 90,000–162,000 during the flow-distribution investigation, whereas it ranged from 95,000 to 169,000 in each flocculation tank. A fully turbulent flow regime developed in the tanks was modeled using the standard k- model, which is consistent with other studies (Bridgeman et al, 2010; Stamou, 2008; Templeton et al, 2006; Essemiani & De Traversay, 2002; Haarhoff & Van der Walt, 2001), and in which k = turbulent kinetic energy (m2/s2). Under steady-state conditions, the distribution of k and at various locations in the tank was predicted by solving the corresponding transport equations for k and of the standard k- model. Equation 4 was then used to calculate the Glocal values for each of the control volumes (cells) using the corresponding , whereas Eqs 1 and 5 were used to estimate the average velocity gradient in the flocculation tanks. Boundary conditions. Mass-flow inlet boundary conditions (BCs) were assigned to the 1.2-m (48-in.) inlet pipe for the flow distribution. Simulations were performed for the flow distribution analysis by varying the mass-flow rates from 796.6 to 1,386.4 kg/s at the 1.2-m (48-in.) raw water inlet. The total mass flux exiting the 0.6-m (24-in.) tee in the flow distribution analysis was used to set the mass-flow inlet BC for the flocculation tank analysis, satisfying continuity principles. The mass-flow rate in accordance with the results obtained from the flow distribution analysis varied from 76.2 to 194.84 kg/s. Pressure-outlet BCs assigned for the outlets were specified with a 0-Pa gauge pressure. A zero gradient was assumed for the flow variables (except pressure) at the outlet. The k and at the inlet and outlet BCs were estimated based on the turbulence intensity (I) that typically ranged between 5 and 10%. The normal velocity component and the normal gradient of all other flow variables were set to zero using rigidlid approximation at the symmetry plane of the flocculation tank. The free surface was also modeled using the symmetric BCs because of a zero flux condition across the symmetry, which was consistent with other studies (Goula et al, 2008; Stamou, 2008; Wang et al, 2008; Baek et al, 2005; Zhou & McCorquodale, 1992). No-slip BC was specified for the wall boundary, signifying a zerofluid velocity occurred at the solid–fluid interface relative to the wall boundary, whereas the standard wall function was used to model the viscosity-affected region between



71

FIGURE 2

Flow distribution pattern of the four flocculation tank inlets at a minimum discharge condition of 69 ML/d (summer simulation at 15°C) 1.2194 1.1585 1.0976 1.0367 0.9758

Velocity Magnitude—m/s

0.9149 0.8540 0.7930 0.6712 Inflow (Q total) = 69 ML/d

0.6103 0.5494 0.4885

Q4 (Qmax) = 19.3 ML /d

0.4276 0.3666 0.3057

Q 3 (Qmin) = 13.6 ML /d

0.2448 0.1839 Q 2 = 17.5 ML /d

0.1230 0.0621 0.0011

Y

Q 1 = 18.5 ML/d

Z X

Qmax—maximum discharge, Qmin—minimum discharge, Qtotal—total inflow into the treatment plant, Qx—discharge in flocculation tanks, X—depth of tank, Y—width of tank, Z—length of tank Red circle indicates the inlet location of the third flocculation tank, where minimum discharge occurs.

initial sets of values and BCs were solved iteratively under steady-state conditions until convergence was attained. Convergence of solution was distinct when the monitoring residuals of the continuity equation were below the tolerance limit of 1 × 10–5 and the momentum equation along the x, y, and z directions was < 0.001; the total mass flow rate imbalance between inlet and outlet was less than 0.2%; and the velocity profile of the outlet surface remained constant with the increment in the number of iterations (Vadasarukkai & Gagnon, 2010). All the computations were converged within ~ 2,000 iterations.

the wall and the fully turbulent region (Stamou, 2008; Wang et al, 2008; Baek et al, 2005). A pressure-based solver using a segregated algorithm was used for all the simulations because of an incompressible flow condition. The numerical algorithm (interpolation methods) used to solve the governing equations for each individual control volume was “simple” for pressure-velocity coupling, “standard” for pressure, and “second-order upwind” for momentum, turbulent kinetic energy, and turbulent dissipation energy. The flow-field problems that were thus generated using appropriate

TABLE 2

Effect of total discharge on flow distribution to flocculation tank inlets (summer simulation at 15oC) Flow Distribution to the Four Flocculation Tanks

Standard Deviation From the Average Flow Rate ( ) ML/d

Total Plant Flow ML/d

Q1

Q2

Q3

Q4

Q1

Q2

Q3

Q4

Average Flow Rate (Qavg) ML/d

69

18.5

17.5

13.6

19.3

26.9

25.4

19.7

28.0

17.2

2.54

75

20.1

19.0

14.8

21.0

26.9

25.4

19.7

28.0

18.8

2.76

90

24.2

22.8

17.8

25.2

26.9

25.4

19.7

28.0

22.5

3.31

120

32.2

30.5

23.7

33.6

26.9

25.4

19.7

28.0

30

4.41

ML/d

%

Qavg—average discharge across the four flocculation tanks, Qx—discharge to flocculation tanks

72



RESULTS AND DISCUSSION Analysis of flow distribution. Figure 2 shows the characterization of the flow distribution to each flocculation tank inlet (i.e., Q1, Q2, Q3, and Q4) at a total inflow of 69 ML/d. From the velocity profile, it was evident that there was an inequity in flow distribution among the flocculation tanks. The inlet pipe located at Q4, which delivered water to the outermost flocculation tank, had a maximum discharge of 19.3 ML/d. The inlet pipe connected to flocculation tank Q3 received a minimum discharge of 13.6 ML/d. The percentage of flow distribution across Q3 was 79% of the average flow across the four flocculation tanks (Qavg = 17.2 ML/d). The effect of variation in the actual plant’s intake rate on the flow distribution pattern was investigated. Three simulations were performed by increasing the total inflow to 75, 90, and 120 ML/d, respectively. As shown in Table 2, the discharge in the third flocculation tank inlet was significantly less compared with the Q1, Q2, and Q4 inlets. Increasing the total inflow significantly increased the deviation from the average flow. For instance, the standard deviation ( ) was calculated to be 2.54 and 4.41 ML/d at minimum and maximum inflow conditions of 69 and 120 ML/d, respectively. A comparison of summer and winter simulations revealed no significant variation in the percentage of flow distribution. The viscous effect of water was negligible in the flow field because of dominant inertial effects (Cleasby, 1984); however, there was a marginal increase of about 0.01% of flow into Q3. The volume-weighted

Local Velocity Gradient—s–1

FIGURE 3

average of turbulent viscosity (µt) was 1.5 kg/m s during summer and winter conditions. Changing the absolute value of viscosity (µ) and density of water for summer and winter trials did not alter the flow-field characteristics; however, the distribution of temperature was assumed to be spatially uniform throughout the tank. Future research, based on the work of Goula and colleagues (2008), will require investigating the influence of temperature gradient in the influent and bulk water on the mixing characteristics in the flocculation tank. Through the flow-distribution analysis, the design of the flow distribution header system was shown to impart unequal hydraulic losses and thus an unequal flow split to the flocculation tanks. In particular, the Q3 inlet was situated at a hydrostatic depth of 7.8 m immediately below the weir outflow. The pipe diameter of Q3 was half the size of other conduits (i.e., 0.6 m or 24 in. each) connected to the distribution header. A turbulence region was created at the entrance of the third inlet (Q3) resulting in an increased energy loss of nearly 0.22 m3/s3, which caused a minimum discharge condition at the Q3 inlet. However, the Q4 inlet, which experienced the maximum flow, had a relatively low average of about 0.0026 m3/s3. Analysis of flow-field pattern in the flocculation tank. Inequity in the flow distribution resulted in a range of minimum and maximum flow conditions at the flocculation tank inlets. Initial simulation was carried out in the third flocculation tank experiencing a minimum inflow of 13.6 ML/d at Q3, as predicted from the flow distribution analysis. Equal distribution of the jet flow

Spatial variation of the G local values for the three-stage tapered hydraulic flocculation tank*

50.0000 47.5111 45.0222 42.5332 40.0443 37.5554 35.0665 32.5776 30.0886 27.5997 25.1108 22.6219 20.1329 17.6440 15.1551 12.6662 10.1773 7.6883 5.1994 2.7105 0.2216

Qmin1 = 6.8 ML/d (assuming equal flow into the symmetric tanks) Large recirculation zone

G floc1 = 9.5 s–1

G floc2 = 3.0 s–1

G floc3 = 2.0 s–1

G local = 40–50 s–1

Y

Z

X

Glocal — local velocity gradient, Gt—shear work, a dimensionless quality, Gflocx — average velocity gradient in each flocculation chamber, Qmin1—minimum discharge condition at the third flocculation tank, X—depth of tank, Y—width of tank, Z—length of tank *Flocculation design criteria: typical Gt values for flocculation process of 40,000 to 75,000 at 20°C (AWWA/ASCE, 1997)



73

FIGURE 4

the first flocculation chamber had a range of Glocal values 9.5 s–1, the average G value, whereas the maximum limit increased to 104.1 s–1 when 95% of the tank volume was considered. The remaining 5% of the tank volume had a range of Glocal values between 104.1 and 1,230.5 s–1. Only 1% of those control volumes (cells) located near the influence of high turbulence zones (e.g., the tank inlet and exit) experienced a high set of Glocal values (i.e., 254.8 s–1 < Glocal < 1,230. 5 s–1). Similarly, the upper limit of the Glocal value for 95% of the tank volume was 24.87 and 14.4 s–1 in the subsequent second and third chambers, respectively. Table 3 outlines the 5th, 50th, and 95th percentile of the Glocal values in the third tapered hydraulic flocculation tank. The 50th percentile values in the first, second, and third chambers represented a highly skewed Glocal distribution; with 50% of the Glocal values concentrated toward the left of the average G value, which was calculated using Eqs 1 and 5. The median value was 2.11 s–1 only as compared with the average G value of 9.5 s–1 in the first flocculation tank. A short-circuiting path was formed near the inlet region because of a recirculation zone in the interior of the first flocculation chamber. In addition, a jet velocity of nearly 0.4–0.5 s–1 at the entrance caused some portion of the incoming flow to rapidly exit into the second flocculation chamber. The observed flow phenomenon was consistent with the interpretations made by other researchers (Goula et al, 2008; Zhou & McCorquodale, 1992) for the sedimentation tanks. Their studies showed an intense formation of recirculation zones and short-circuiting effects in those sedimentation tanks at a low turbulent kinetic energy–dissipation rate. In contrast, the design of the inlet openings at the bottom of the second and third flocculation chambers directed the flow more toward the sidewalls (i.e., in the y direction, as shown in Figure 3). Thus, the short-circuiting path was avoided. However, a relatively flat hydraulic gradient line (HGL) of about 0.23 m between the second and third flocculation chambers caused an overall reduction in the average G values to 3.0 and 2.0 s–1, respectively.

Frequency distribution function of the Glocal for the three-stage tapered hydraulic flocculation tank at a minimum flow of 13.2 ML/d Tank 1 Tank 2 Tank 3

100

Cumulative Occurrence—%

90 80 70 60 50 40 30 20 10 0 0.1

1

10

100

1,000

Glocal—s–1 Glocal—local velocity gradient

into the symmetrical chambers was assumed so that each chamber had a net inflow of 6.8 ML/d. Figure 3 shows the spatial distribution of the Glocal values in the third tapered hydraulic flocculation tank. Similar to other studies (e.g., Bridgeman et al, 2010; Haarhoff & Van der Walt, 2001), this study also found a nonuniform spatial variation in the Glocal values at different locations within the tank. A quantitative description of variation in the Glocal values in the first, second, and third symmetrical flocculation chambers was expressed in terms of a frequency distribution function. Figure 4 shows the cumulative frequency of occurrence of the total number of control volumes (cells) within a particular range of Glocal values. For instance, about 76.4% of the total tank volume in

TABLE 3

Percentiles of Glocal values for flocculation tanks 1, 2, and 3 at a minimum flow of 13.2 ML/d Glocal Values—s–1

Flocculation Tank

5th Percentile

50th Percentile (Median)

95th Percentile

1—Total number of cells = 216,475

1.07

2.11

104.1

9.5


0.41

1.08

24.87

3.0


0.33

0.8

14.4

2.0

Glocal—local velocity gradient *The average G value was calculated using Eqs 1 and 5 for each flocculation tank.

74

Average G Value*—s–1



FIGURE 5

309.3 293.9 278.4 262.9 247.5 232 216.5 201.1 185.6 170.1 154.7 139.2 123.7 108.3 92.8 77.33 61.86 46.4 30.93 15.47 0

Path Lines—min.

Particle-tracking and RTD curve analysis. To visualize the recirculation and short-circuiting effects, the trajectories of simulated particles were investigated as a function of space and time (Kukura et al, 2004). The particles were intended to represent a conservative tracer that was in equilibrium with the fluid motion (Kennedy et al, 2006). Using the flow modeling simulation software’s flow visualization feature, such neutrally buoyant particles were released at the inlet surface of the third hydraulic flocculation tank. The time required for those particles to reach the outlet was tracked. Initially, particles were released from the inlet surface. This number was generated automatically in the flow modeling simulation software depending on the two-dimensional facets (i.e., the number of two-dimensional triangular faces) in the inlet surface. Sensitivity analysis was conducted to study the effect of increasing the total number of particles released (Np = 77, 180, 383, 766, 1,665, and 3,363) on the particle residence time. (Np is the total

69 of 77 particles exit at a theoretical t of 308 min

Y

Z

X

Dead (stagnant/nonmixing) zones 77 path lines of particles injected at t = 0

t—detention time, X—depth of tank, Y—width of tank, Z—length of tank

FIGURE 6

Optimization of hydraulic flocculator designs are required to provide better mixing for particle–chemical interaction and growth of flocs. Contours of Velocity Magnitude—m/s

A

Dead (stagnant/nonmixing) zones represented through a velocity contour plot along the vertical plane at the mid-depth location in the second flocculation tank (A) and the third flocculation tank (B)

0.100 0.095 0.090 0.085 0.080 0.075 0.070 0.065 0.060 0.055 0.050 0.045 0.040 0.035 0.025 0.020 0.015 0.010 0.005 0.000

Y

Z X

B Contours of Velocity Magnitude—m/s

number of neutrally buoyant particles released using particle tracking analysis.) Figure 5 shows the trajectories of 77 particles, which were injected at the inlet surface of the first flocculation chamber and tracked for 308 min. At a total inflow of 6.6 ML/d, the theoretical HRT was calculated to be 154 min (i.e., HRT = volume/bulk flow rate). At that theoretical HRT, the path lines of less than half the number of particles (i.e., 41 of 77 total particles) were traced at the outlet of the third flocculation tank. With an increase in the time interval to twice the theoretical HRT of 308 min, the number of path lines that reached the outlet surface increased from 41 to 69 particles. However, about 10.4% (i.e., 8 of 77) particles were still residing in the tank. This phenomenon can be correlated to the recirculation flow, which was identified in the first flocculation chamber during the flow-field analysis. Most of the particles were entrained in the recirculation region, whereas the short-circuiting path carried the remaining particles to the second flocculation chamber. As shown in Figures 5 and 6, the path lines of particles never visited some portions of the second and third flocculation chambers. It was evident from the analysis of particle-tracking that each individual particle had a unique flow path. The path lines were analyzed to develop a probability distri-

Path lines of neutrally buoyant particles released at the inlet of the hydraulic flocculation tank at 308 min

0.100 0.095 0.090 0.085 0.080 0.075 0.070 0.065 0.060 0.055 0.050 0.045 0.040 0.035 0.025 0.020 0.015 0.010 0.005 0.000

Y

Z X

X—depth of tank, Y—width of tank, Z—length of tank



75

bution function of the particle residence time in the third tapered hydraulic flocculation tank (Figure 7). The probability distribution function also represented the dimensionless exit-age distribution [E(Θ)] curve as shown in Figure 8. The dimensionless exit-age distribution was computed as the ratio of the number of particles (Ni) that exited the flocculation tank in a discrete time increment of dΘ to the total number of particles initially released (NP). In the E(Θ) curve, the principal peak of the particles exiting the outlet occurred at about Θ = 0.45 (i.e., t = 69.3 min), before the theoretical HRT at Θ = 1 (i.e., t = 154 min). This reflected the stagnant backwater (dead) regions in the tank (Figure 6), which reduced the effective tank volume. As a result, a larger portion of flow reached the outlet at a shorter residence time. The residence time of those particles entrapped in the dead space and recirculation zone was represented by the tail elongated to the right of the theoretical HRT (i.e., Θ > 1). Using Eq 8 and 9, the mean residence time (tm) and the standard deviation (Θ) were calculated from the E(Θ) curve as 107.9 and 6.82 min, respectively. The E(Θ) curve indicated that about 68% of the fluid elements spent between 101.1 and 114.7 min in the tank (i.e., tm ± Θ),

FIGURE 7

which was significantly less than the theoretical HRT. As shown in Figure 8, the cumulative exit-age distribution [i.e., the F(Θ) curve] was developed from the E(Θ) curve. The Θ10, Θ50, and Θ90 values (i.e., the time taken by 10, 50, and 90% of the fluid particles to exit the outlet) were determined from the F(Θ) curve as 44.7, 95.48, and 138.6 min, respectively. Increasing the total number of particles from NP = 77 to 3,363 particles did not significantly improve the predictive accuracy of the E(Θ) curve. The tm calculated for NP = 3,363 particles was 111.3 min with a standard deviation of 7.3 min. As a result, it was concluded from a computational standpoint that 77 particles should be selected for particle-tracking analysis. Martin-Dominguez et al (2005) showed that the tall and asymmetric characteristics of the E(Θ) curve were prevalent in a small number of reactors in series (N < 11), and in reactors with a large amount of dead space (M < 1). Accordingly, different combinations of parameters of the TIS model (i.e., N, n, and M) were analyzed for the threestage tapered hydraulic flocculation tank. Using Eq 10, the F(t) curve was generated from the E(t) curve for the proposed TIS model. Figure 9 shows a comparison of the F(t) curve predicted using the particle-tracking analysis in

Probability distribution function of the residence time of particles in the hydraulic flocculation tank

Fitted lognormal distribution Density of observation 1.4

1.2

1.0

Ni/NP

0.8

0.6

0.4

0.2

0.0 0.00

0.45

0.90

1.35

1.80

2.25

2.70

t

Normalized Residence Time — = – tN Ni—number of particles that exited the flocculation tank in a discrete time increment of d , NP—number of neutrally buoyant – particles initially released, t—detention time, tN—total mean residence time in N tanks, —normalized residence time The bar represents the density of observations falling within each bin (i.e., residence time); the height of each bar represents the proportion of particles (ratio) having that range of . The area under the curve gives the probability distribution function of the particle residence time.

76



CFD and the TIS model. Initially, bypassing and dead space in the tank were neglected (i.e., n = M = 1) to generate an ideal or a single-parameter TIS model (Eq 6b). The predicted tx values from the CFD simulations were significantly lower than the ideal tx values. For instance, the predicted t50 value obtained from the CFD simulation was about 36 min below the ideal t50 value of ~ 132 min. With a decrease in the n value to 0.95 (i.e., 5% bypassing) and M value to 0.80 (i.e., 20% dead space), the F(t) curve shifted to the left of the ideal curve (i.e., the single-parameter TIS model). The three-parameter TIS model showed a reasonable agreement with the CFD-predicted tx values for M = 0.62 and n = 0.98, with an error function of 0.00823 (Eq 11). Allowing a high fraction of stagnant space (38%; i.e., M = 0.62) in the entire flocculation tank, the maximum cumulative fraction of tracer predicted using the TIS model was nearly 88%, with 12% of the tracer still residing in the tank. Implications on future operations. Table 4 shows the expected design parameter calculated from the CFD analyses and the typical range of G value and detention time recommended by AWWA/ASCE (1997) for a flocculation process. The average G values of the existing hydraulic flocculation process did not achieve the highenergy input required for a direct filtration system. High G values of 83 s–1 in the distribution header and 40 s–1 in the flocculation tank were achieved only at a maximum inflow of 120 ML/d. Otherwise, the plant oper-

FIGURE 8

Hydrodynamic flow condition depends on both the geometry of the flocculation tank and the impeller speed and type.

30 min) in the flocculation tanks created an offset in the product Gavgt. This situation may give rise to an inadequate number of effective particle collisions and consequently the formation of filterable flocs. The finding of Bernhardt and Schell (1993) agrees with the interpretation that an average G value of < 30 s–1 cannot be offset by a longer aggregation time ( 30 min) in order to attain the optimum turbidity removal ( 80%). The applicability of the Gt concept as an effective design parameter in classifying the performance of a particular flocculation system has been previously discussed. Argaman (1971) showed that the performance of a flocculation system is directly dependent on the product

E( ) and F( ) curves predicted using the results of particle tracking CFD analysis for the hydraulic flocculation tank Exiting particles older than the theoretical hydraulic time

E ( ) F ( )

1.4

ated at a low range of G values for most other inflow conditions, reflecting inadequate mixing in the flocculation tanks. In contrast to the observed insufficient G value in the tanks, the nondimensional product Gavgt was still maintained at an adequate flocculation range of 44,788 to 71,596. The prolonged residence time (

1.0

0.8

E( )

1.0

0.7 0.6

0.8

0.5 0.6

0.4 0.3

0.4

0.2 0.2

Cumulative Fraction of Particles Leaving Tank at

0.9

1.2

0.1 0.0

0.0 0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

2.2

–

Normalized Time— = t/ tN –

CFD—computational fluid dynamics, E( )—exit age distribution, F( )—cumulative exit age distribution, t—detention time, tN—total mean residence time in N tanks, —normalized residence time The hatched area indicates the fraction of those particles exiting the outlet—because of dead space and recirculation zones—that are older than the theoretical hydraulic retention time.



77

FIGURE 9

Comparison of cumulative exit age distribution curves predicted from the CFD simulation ideal or TIS models CFD simulation Ideal or single-parameter TIS model (n = 1, M = 1, N = 3, erf = 0.02355) Three-parameter TIS model (n = 0.95, M = 0.80, N = 3, erf = 0.0250) Three-parameter TIS model (n = 0.98, M = 0.62, N = 3, erf = 0.00823)

1.0

Cumulative Fraction of Particles Leaving Tank at t

0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0

0

40

80

120

160

200

240

280

320

Residence Time—min CFD—computational fluid dynamics, erf—error function, M—fraction of unit’s volume effectively used in the treatment process (with no stagnation space), n—fraction of flow rate effectively used in treatment process (with no global bypassing), N—number of reactors in series, t—detention time, TIS—tank-in-series model

Gt only for low values of G or for very strong flocs. However, the author also indicated that a fine structure of turbulence field is required, which has a significant effect on performance. There are certain limitations with the Gt concept because it fails to consider the flocbreakup phenomenon. This study shows that product Gt alone was not an adequate parameter for describing flocculation performance. A better estimation of the Gt value was obtained when the mean residence time (tm; e.g.,

TABLE 4

107.9 min at an inflow of 69 ML/d) was used instead of the theoretical HRT (i.e., 154 min). CFD analyses of the hydrodynamics of flow distribution and the flocculation process raised a number of concerns that may have an effect on overall treatment efficiency. Figure 10 illustrates the inference of the CFD outcomes on Halifax Water in terms of meeting the water quality standards and regulatory amendments. Previous work on floc formation and breakage (Bridgeman et al, 2008; Bouyer et al, 2005; Gregory, 2004) have shown significant evidence of floc breakage with an increase in the level of shear and a limit in their regrowth capacity when the shear rate was reduced. Although the JDKWSP has a relatively flat HGL during the plant’s average inflow of 95 ML/d, there is a major break in the HGL at the weir located immediately near the downstream of the third premix tank. The surface water elevation drops to ~ 0.94 m at that weir location during an average flow of 95 ML/d, imparting an increased level of shear as the flocs travel through the distribution header toward the flocculation stage. An unbalanced mixing condition in the flocculation tank offers a limited supply of active mixing for floc aggregation, apart from high spikes in the G values at the tank inlet and outlet locations. Thus the flocs are subjected to an uneven proportion of high and low G values, which can potentially cause damage to the flocs that have only been partially developed. The next step will be to account for the interaction of the local physicochemical flocculation processes in the complex flow field developed through a passive scalar description of the particle phase (Samaras et al, 2010). The present flocculation process of a relatively quiescent condition, interrupted with severe spikes in the mixing energy, can be remediated by promoting a more consistent G value in the design. Neutralizing spikes in the mixing gradient through a uniform tapered flocculation will improve floc formation, thereby optimizing the efficiency of the flocculation process. Haarhoff (1998) developed a design equation to determine the exact floor

G, t, and Gavgt values of hydraulic flocculators and the recommended design criteria for the flocculation process G—s–1 Treatment Process

Distribution channels mixer to flocculator High-energy flocculation for direct filtration

t—s* Design Criteria‡

Gavgt†

Design Criteria‡

Present Study

Present Study

Design Criteria‡

Present Study

100–150

36–83

Varies

173–300

NA

NA

20–75

2–40§

900–1,500

3,600–9,240

40,000–75,000

44,788–71,596

G—average velocity gradient value, Gavgt—shear work, a dimensionless quality, t—detention time *Detention time for the design is the overall mean residence time in N number of flocculation tank-in-series (AWWA/ASCE, 1997). †Gavgt is approximately calculated as the product of average of velocity gradients in the compartment, assuming equal size tanks, i.e., Gavg = (Gfloc1 + Gfloc2 + – Gfloc3)/N and t N (Hargrave et al, 1990). ‡Flocculation design criteria: typical G values and detention time for flocculation process at 20oC (AWWA/ASCE, 1997). §Average G value in each flocculation tank, calculated corresponding to the inflow condition (i.e., 69–120 ML/d).

78



slope and water depth that would satisfy a range of flocculation requirements for different flow rates. Another alternative for providing a controlled mixing gradient is to install mechanical mixers in each of the flocculation chambers.

FIGURE 10 Flow diagram of implication of CFD analyses on future operations

Research outcomes from CFD analysis

CONCLUSIONS This study reports on a computational analysis for hydraulic flocculation tanks. The CFD results indicated that the present design offered inadequate mixing in these tanks. The mixing intensity (i.e., the G value) calculated for the flocculation tank was dependent on the total inflow into the treatment plant and its distribution across the tanks. High spikes in the G values (~ 40–50 s–1) were observed at the bottom of the tank; the high spikes accounted for as much as 20% to as little as 5% of the total mixing in the flocculation tank. Most flocculation tanks have little to no mixing. From a tapered mixing perspective, the average G value significantly drops from the first to the second tank, with a minimum variation existing between the G values of the second and third flocculations. This work focused on a plant in Halifax; however, several plants across Canada have similar infrastructure. These designs are based on an older design approach; as a result, there is a potential need to evaluate the design in terms of local hydrodynamic parameters, which can be predicted effectively by CFD applications. Optimization of hydraulic flocculator designs are required to provide better mixing for particle–chemical interaction and growth of flocs. Practical outcome of operating at ineffective mixing conditions might lead to potential negative consequences such as poor floc formation, reliance on excess flocculant aid, decreased incorporation of dissolved organics in floc, and increased particle load to the filters.

ACKNOWLEDGMENT The authors thank Halifax Water and Natural Sciences and Engineering Resource Council of Canada (NSERC) for financial support to the NSERC/Halifax Water Industrial Research Chair. The authors also acknowledge Atlantic Computational Excellence Network for providing the high-performance computing facility.

• • • •

Uneven flow distribution Inadequate and unbalanced mixing conditions in flocculators Short-circuiting and large dead volumes with lower G values Inflexibility in adjusting the flow rates and therefore G value

Water quality

Effect on Halifax Water

• Poor (low-density) floc formation • Reliance on polymer in the winter required for minimizing floc breakups • Load on downstream filtration unit • Imbalance in ripening performance among filters

Future plan

• Mechanical flocculators • Premix modification • Coagulant change

Surface water treatment standards (e.g., DBP rules)

Regulatory

Regulatory

CFD—computational fluid dynamics, DBP—disinfection by-product, G value—average velocity gradient value

modeling of unit processes for drinking water treatment optimization. Graham A. Gagnon (to whom correspondence should be addressed) is a professor and NSERC/Halifax Water Industrial Research Chair, Dalhousie University, Sexton Campus, 1360 Barrington St., Halifax, Nova Scotia, Canada B3J 2X4; graham. [email protected]. D. Reid Campbell is director of water services at Halifax Regional Water Commission. Sarah C. Clark is a senior project manager at HDR Engineering, Denver, Colo. Date of submission: 12/16/2010 Date of acceptance: 09/12/2011

FOOTNOTES

ABOUT THE AUTHORS

Yamuna S. Vadasarukkai is a graduate research assistant at the Center for Water Resource Studies at Dalhousie University, Halifax, Nova Scotia, Canada. She is involved in the research activity of Natural Sciences and Engineering Research Council (NSERC)/Halifax Water Industrial Research Chair at the J.D. Kline Water Supply Plant. Vadasarukkai’s research work involves water quality

1ANSYS

FLUENT flow modeling simulation software, version 6.3.26, ANSYS, Lebanon, N.H. 2GAMBIT meshing software, ANSYS, Lebanon, N.H.

JOURNAL AWWA welcomes comments and feedback at [email protected].



79

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