2.3 Flocculation Basin Design, Clarification & Sedimentation

2.3 Flocculation Basin Design, Clarification & Sedimentation

Quick Answer: After colloids are destabilized in rapid mixing, water flows into the flocculation basin, where gentle, controlled agitation promotes particle collisions to build large, dense macro-flocs. To prevent shear forces from breaking the fragile flocs, the velocity gradient is systematically tapered downward across successive compartments ($50\text{ s}^{-1} \to 30\text{ s}^{-1} \to 20\text{ s}^{-1}$) over a 20- to 45-minute detention time. Clarified water then enters the sedimentation basin, where gravity removes $80\%\text{ to }95\%$ of solids prior to filtration, governed by the Surface Overflow Rate ($\text{SOR} = Q / A$) and Weir Overflow Rate ($\text{WOR} = Q / L$).

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Flocculation Process Engineering

Flocculation is the physical process of slowly mixing destabilized water to induce contact between micro-floc particles, agglomerating them into larger, visible, settleable macro-flocs (often called "pin floc" transitioning to "snowball floc").

Collision Kinetics: Perikinetic vs. Orthokinetic

• Perikinetic Flocculation: Particle collisions driven by random thermal Brownian motion. Dominates in the initial seconds for sub-micron particles ($< 1\text{ }\mu\text{m}$).
• Orthokinetic Flocculation: Collisions induced by bulk fluid shear, velocity gradients, and physical agitation. Dominates particle collisions once particles exceed $1\text{ to }2\text{ }\mu\text{m}$.

Velocity Gradient Tapering ($G$ Value)

Flocculation requires balancing two competing hydrodynamic forces:

1. Agitation: Sufficient fluid motion to bring particles into contact.
2. Hydrodynamic Shear Stress: Excessive fluid turbulence that tears fragile chemical bridges and fractures floc particles.

To optimize this balance, modern flocculation basins are partitioned into three or more successive stages separated by baffle walls, with the velocity gradient ($G$) systematically tapered downward:

The Camp Number ($Gt$)

The product of the velocity gradient and detention time is the dimensionless Camp Number ($Gt$):

$Gt = G \times t$

• Target $Gt$ Range: $10,000\text{ to }100,000$ (typically $20,000\text{ to }60,000$).
• If $Gt < 10,000$: Insufficient collisions occur, yielding small, poorly settling "pin floc" that carries over to filters.
• If $Gt > 100,000$ or if $G > 75\text{ s}^{-1}$ in later stages: Fluid shear ruptures floc polymers, shearing flocs into fine particles that blind filter media.

Flocculation Equipment

• Paddle-Wheel Flocculators: Large, slowly rotating wooden or fiberglass paddle blades mounted on horizontal or vertical shafts. Horizontal-shaft units feature variable-speed drives (VSDs) to adjust reel speed ($0.5\text{ to }3.0\text{ rpm}$) as water temperature and turbidity fluctuate.
• Vertical Turbine Hydrofoils: Modern axial-flow hydrofoil impellers installed in square compartments. Provide uniform mixing with lower energy consumption and eliminate submerged drive packings.
• Baffled Hydraulic Channels: Water flows through a labyrinth of channels. Around-the-end (horizontal flow) and over-and-under (vertical flow) baffles generate velocity gradients through frictional head loss. They require no motors but lack flexibility: when plant flow drops, $G$ drops proportionally.

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Sedimentation Basin Theory & Functional Zones

Sedimentation (clarification) is the physical separation of suspended particles from water by gravitational settling. Under ideal conditions, a particle settles when its downward settling velocity ($v_s$) carries it into the sludge zone before the water exits the basin.

Stokes' Law for Settling Velocity

For discrete, spherical particles in laminar flow, terminal settling velocity is defined by Stokes' Law:

$v_s = \frac{g (\rho_p - \rho_w) d^2}{18 \mu}$

where $g$ is acceleration due to gravity, $\rho_p$ is particle density, $\rho_w$ is water density, $d$ is particle diameter, and $\mu$ is dynamic viscosity of water.

Practical Operational Takeaways from Stokes' Law:

1. Particle Diameter ($d^2$): Settling velocity increases with the square of the particle diameter. Doubling floc diameter via proper coagulation/flocculation quadruples settling velocity.
2. Density Difference ($(\rho_p - \rho_w)$): Mineral clays and silt ($\rho \approx 2.65\text{ g/cm}^3$) settle rapidly, whereas organic flocs ($\rho \approx 1.01\text{ to }1.05\text{ g/cm}^3$) have densities near that of water and settle slowly.
3. Water Viscosity ($\mu$): Viscosity increases substantially as water cools. Alum floc settles roughly $30\%\text{ to }40\%$ slower at $4^\circ\text{C}$ than at $20^\circ\text{C}$, requiring lower loading rates or coagulant aid polymers during winter.

The Four Functional Zones of a Clarifier

+---------------------------------------------------------------------------------+
|                           CONVENTIONAL RECTANGULAR BASIN                        |
|                                                                                 |
|  INLET ZONE         SETTLING ZONE                             OUTLET ZONE       |
|  +---------+  --------------------------------------------->  +-------------+   |
|  | Perfor- |           Water Flow Streamline                  | Effluent    |   |
|  | ated    |  . . . . . . . . . . . . . . . . . . . . . . .   | Launder &   |   |
|  | Baffle  |    \                                             | V-Notch     |   |
|  | Wall    |      \                                           | Weirs       |   |
|  +---------+        \ Particle Settling Trajectory            +-------------+   |
|                       \                                                         |
|  =======================\====================================================   |
|  SLUDGE ZONE: Floor Sludge Blanket & Collector Scraper Flights                  |
|  [ Sludge Hopper & Blow-Off Valve ]                                             |
+---------------------------------------------------------------------------------+

1. Inlet Zone: Transitions turbulent flow from the flocculator into uniform, non-turbulent, horizontal plug flow. Uses perforated diffuser walls or submerged target baffles to evenly distribute flow across the basin cross-section.
2. Settling Zone: The central, quiescent volume of the tank where settling occurs without hydraulic disturbance.
3. Outlet Zone: Collects clarified supernatant and channels it to filter influent conduits. Uses effluent launders equipped with adjustable V-notch weirs or submerged orifices to ensure uniform draw-off without generating localized upwelling currents.
4. Sludge Zone: The bottom section where settled solids consolidate. Features bottom scrapers (flight-and-chain or traveling bridge rakes) that push sludge toward hoppers for continuous or intermittent blow-off.

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High-Rate Clarification Technologies

Shallow-Depth Settling Theory (Hazen's Principle)

In 1904, Allen Hazen demonstrated that the clarification capacity of a sedimentation basin depends strictly on its surface area, completely independent of tank depth. A particle settling at $1.0\text{ ft/min}$ in a $12\text{-foot-deep}$ basin takes $12\text{ minutes}$ to reach the bottom. If horizontal false floors are inserted every $2\text{ inches}$, that same particle settles out in 10 seconds.

Tube Settlers & Lamella Plate Settlers

High-rate settlers exploit shallow-depth settling by placing inclined tubes or parallel plates within the settling zone:

• Configuration: Polyvinyl chloride (PVC) hexagonal tubes or stainless steel lamella plates inclined at an angle of $60^\circ$.
• Self-Cleaning Slope: An angle of $60^\circ$ exceeds the angle of repose of coagulated chemical sludge. Accumulated solids slide down the bottom surface of the tubes by gravity, dropping into the sludge hopper below while clarified water flows upward.
• Performance Benefit: Reduces vertical settling distance from $12\text{ feet}$ down to $2\text{ inches}$, increasing the hydraulic capacity of existing basins by $150\%\text{ to }300\%$ without increasing plant footprint.

Solids-Contact (Sludge Blanket) Clarifiers

Solids-contact units combine rapid mixing, flocculation, and sedimentation inside a single compact basin. Raw water and chemicals are introduced into a central draft tube where rotating impellers mix them with pre-formed, recirculated sludge.

The water then flows outward and upward through a suspended, fluidized sludge blanket. The blanket acts as a dynamic mechanical and chemical filter: upward-flowing micro-flocs collide with and stick to the vast surface area of pre-existing flocs.

• Operational Metric: Operators perform a 5-minute sludge settleability test using a $100\text{ mL}$ graduated cylinder. The target sludge volume is typically maintained at $10\%\text{ to }20\%$. If the blanket level rises too high, sludge blows over onto filters; if drawn down too low, clarification efficiency collapses.

Dissolved Air Flotation (DAF)

An alternative clarification process for raw waters carrying low-density particles that resist settling (algal blooms, low-turbidity high-color waters):

• A side-stream of clarified water is pressurized to roughly $60\text{ to }85\text{ psi}$ (about 400 to 600 kPa) and saturated with air in a pressure vessel.
• When injected into the flotation basin at atmospheric pressure, dissolved air precipitates as microscopic bubbles ($20\text{ to }80\text{ }\mu\text{m}$).
• Bubbles attach to floc particles, reducing their apparent density below that of water and floating them to the surface as a float layer (skum) carrying $2\%\text{ to }4\%$ dry solids, which is mechanically scraped off.

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Clarifier Hydraulic Calculations & Worked Examples

Plant operators must master three foundational hydraulic parameters governing clarifiers:

1. Detention Time ($DT$)

The theoretical time water resides inside the tank:

$DT\text{ (hours)} = \frac{\text{Basin Volume (gallons)}}{\text{Flow Rate (gpm)} \times 60\text{ min/hr}} = \frac{\text{Basin Volume (gallons)} \times 24\text{ hr/day}}{\text{Flow Rate (gpd)}}$

Standard Range: $2.0\text{ to }4.0\text{ hours}$ for conventional rectangular basins.

2. Surface Overflow Rate ($SOR$ / Surface Loading Rate)

The flow rate applied per square foot of basin surface area, representing the upward fluid velocity:

$SOR\text{ (gpd/ft}^2) = \frac{\text{Flow Rate (gpd)}}{\text{Surface Area (ft}^2)} = \frac{Q}{L \times W}$

Design Standards:

• Conventional Rectangular Basins: $500\text{ to }800\text{ gpd/ft}^2$ (up to $1,000\text{ gpd/ft}^2$ for iron flocs).
• Basins with Tube Settlers: $1,200\text{ to }2,500\text{ gpd/ft}^2$.

3. Weir Overflow Rate ($WOR$ / Weir Loading Rate)

The volume of water discharging per linear foot of active effluent weir:

$WOR\text{ (gpd/ft)} = \frac{\text{Flow Rate (gpd)}}{\text{Total Active Weir Length (ft)}}$

Standard Limit: Typically $< 10,000\text{ to }20,000\text{ gpd/ft}$. Exceeding design WOR creates high-velocity exit currents near launders that pull settled floc up off the floor and over the weirs.

Worked Engineering Problem: Clarifier Performance Check

Problem: A water treatment plant operates two identical parallel rectangular sedimentation basins. Each basin is $140\text{ feet}$ long, $35\text{ feet}$ wide, and has a water depth of $14\text{ feet}$. Each basin has $120\text{ linear feet}$ of effluent weir trough. The total plant flow is $8.4\text{ MGD}$. Calculate for a single basin:

1. The flow treated per basin ($Q$).
2. The detention time ($DT$) in hours.
3. The surface overflow rate ($SOR$) in $\text{gpd/ft}^2$.
4. The weir overflow rate ($WOR$) in $\text{gpd/ft}$.

Step 1: Determine Flow per Basin: $Q = \frac{8,400,000\text{ gpd}}{2} = 4,200,000\text{ gpd}$

Step 2: Calculate Basin Volume in Gallons: $\text{Volume (cu ft)} = 140\text{ ft} \times 35\text{ ft} \times 14\text{ ft} = 68,600\text{ ft}^3$ $\text{Volume (gal)} = 68,600\text{ ft}^3 \times 7.48\text{ gal/ft}^3 = 513,128\text{ gallons}$

Step 3: Calculate Detention Time ($DT$): $DT = \frac{\text{Volume (gal)} \times 24\text{ hr/day}}{Q\text{ (gpd)}} = \frac{513,128 \times 24}{4,200,000} = \frac{12,315,072}{4,200,000} = 2.93\text{ hours}$

Step 4: Calculate Surface Overflow Rate ($SOR$): $\text{Surface Area} = 140\text{ ft} \times 35\text{ ft} = 4,900\text{ ft}^2$ $SOR = \frac{4,200,000\text{ gpd}}{4,900\text{ ft}^2} = 857.14\text{ gpd/ft}^2$

Step 5: Calculate Weir Overflow Rate ($WOR$): $WOR = \frac{4,200,000\text{ gpd}}{120\text{ ft}} = 35,000\text{ gpd/ft}$

Evaluation: The calculated $WOR$ ($35,000\text{ gpd/ft}$) significantly exceeds the standard limit of $20,000\text{ gpd/ft}$, indicating that the effluent weir length is deficient, creating localized approach velocities that carry over floc.

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Clarifier Troubleshooting & Performance Control