Appearance
Secondary Clarifier (Circular)
Circular settling tank using Takács double-exponential settling model to separate mixed liquor into clarified effluent and thickened return activated sludge.
Overview
Secondary clarifiers (final settling tanks) perform two critical functions: clarification of the mixed liquor to produce low-TSS effluent, and thickening of biological sludge for return to the aeration basin or waste. They are the most critical unit operation in activated sludge treatment - poor clarifier performance can cause complete process failure regardless of biological treatment effectiveness.
When to Use
- All activated sludge processes (conventional, extended aeration, MBR without membranes)
- Following trickling filters or RBCs for biofilm separation
- Nutrient removal systems (require proper RAS/WAS control)
- Small to large plants (0.1-100+ MLD)
Key Characteristics
- Dual function: clarification + thickening
- Sensitive to sludge settling characteristics (SVI)
- Requires continuous monitoring and control
- Critical for process stability
- Sludge blanket management essential
- Denitrification can occur in blanket (nutrient removal systems)
Operating Modes
Basic Mode
- Fixed overflow rate based on SVI
- Simplified effluent TSS calculation
- Default RAS/WAS split
- Basic solids balance
Advanced Mode
- 1D layer model (10 layers) with dynamic mass balance
- Takács double-exponential settling velocity model
- State point analysis for flux theory
- Sludge blanket tracking
- Denitrification in blanket (anoxic conditions)
- Effluent quality prediction based on loading
Mathematical Model
Governing Equation - Takács Settling Velocity
The Takács model describes activated sludge settling as a function of concentration:
$$V_s = V_0 \times (e^{-r_h \times (X - X_{min})} - e^{-r_p \times (X - X_{min})})$$
Where:
- $V_s$ = settling velocity (m/d)
- $V_0$ = maximum theoretical settling velocity (m/d), typically 474 m/d
- $r_h$ = hindered settling parameter (m³/g), typically 0.000576 m³/g
- $r_p$ = flocculant settling parameter (m³/g), typically 0.00286 m³/g
- $X$ = MLSS concentration (g/m³)
- $X_{min}$ = non-settleable fraction (g/m³), typically 0
Model Behavior:
- At low concentrations (X → 0): Dominated by first exponential (discrete settling)
- At high concentrations (X → Xmax): Dominated by second exponential (hindered settling)
- Produces characteristic parabolic settling velocity curve
Solids Flux Theory
Total solids flux is the sum of gravity flux and underflow flux:
$$G_{total} = G_{gravity} + G_{underflow}$$
$$G_{gravity} = V_s(X) \times X$$
$$G_{underflow} = \frac{Q_u}{A} \times X$$
Where:
- $G$ = solids flux (kg/m²·d)
- $Q_u$ = underflow rate (m³/d)
- $A$ = clarifier surface area (m²)
State Point Analysis
The state point defines the operating condition:
$$G_{applied} = \frac{Q_{in} \times X_{in}}{A}$$
The limiting flux $G_L$ is found from the flux curve:
$$G_L = \min(G_{total}) \text{ for } X \in [0, X_{underflow}]$$
Design Criterion: $$G_{applied} < G_L$$
Otherwise, sludge blanket will rise and overflow.
1D Layer Model
The clarifier is divided into N layers (typically 10):
Mass Balance per Layer i: $$\frac{dX_i}{dt} = \frac{1}{A \times h_i} \times (Q_{i-1} \times X_{i-1} - Q_i \times X_i + V_s(X_{i+1}) \times A \times X_{i+1} - V_s(X_i) \times A \times X_i)$$
Where:
- $h_i$ = layer height (m)
- $Q_i$ = flow from layer i (m³/d)
- Layer 0 = effluent (top)
- Layer 9 = underflow (bottom)
Effluent TSS Prediction
Empirical correlation based on overflow rate and sludge properties:
$$TSS_{eff} = TSS_{min} + k_{esc} \times \left(\frac{SOR}{SOR_{design}}\right)^{1.5} \times \left(\frac{SVI}{SVI_{design}}\right)^{0.8}$$
Where:
- $TSS_{min}$ = minimum achievable TSS (5-10 mg/L)
- $k_{esc}$ = solids escape coefficient (empirical)
- $SOR$ = surface overflow rate (m³/m²·d)
- $SVI$ = sludge volume index (mL/g)
Denitrification in Sludge Blanket
In nutrient removal systems, anoxic conditions develop in the sludge blanket:
$$r_{denit} = k_{denit} \times X \times \frac{NO_3}{K_{NO3} + NO_3} \times \frac{K_{O2}}{K_{O2} + DO}$$
Where:
- $r_{denit}$ = denitrification rate (mg N/L·h)
- $k_{denit}$ = rate constant (0.1-0.3 mg N/g MLSS·h)
- $K_{NO3}$ = half-saturation constant (0.5 mg/L)
- $K_{O2}$ = oxygen inhibition constant (0.2 mg/L)
Rising Sludge:
Excessive denitrification produces N₂ bubbles that attach to flocs, causing rising sludge:
$$\text{Rising sludge risk if: } NO_3 > 5 \text{ mg/L and blanket depth} > 1.5 \text{m}$$
Design Parameters
Input Parameters
| Parameter | Symbol | Unit | Range | Default | Description |
|---|---|---|---|---|---|
| Tank diameter | $D$ | m | 10-70 | 30 | Circular tank diameter |
| Sidewater depth | $H$ | m | 3-5 | 4.0 | Effective settling depth |
| Influent MLSS | $X_{in}$ | mg/L | 2000-5000 | 3500 | Mixed liquor concentration |
| Influent flow | $Q_{in}$ | m³/d | - | - | Flow from aeration basin |
| RAS flow | $Q_{RAS}$ | m³/d | - | - | Return activated sludge flow |
| Target RAS conc | $X_{RAS}$ | mg/L | 8000-12000 | 10000 | Underflow concentration |
| SVI | - | mL/g | 80-200 | 120 | Sludge volume index |
| V0 (Takács) | - | m/d | 200-800 | 474 | Max settling velocity |
| rh (Takács) | - | m³/g | 0.0003-0.001 | 0.000576 | Hindered parameter |
| rp (Takács) | - | m³/g | 0.001-0.005 | 0.00286 | Flocculant parameter |
Output Parameters
| Parameter | Unit | Description |
|---|---|---|
| Surface area | m² | Required clarifier area |
| SOR | m³/m²·d | Surface overflow rate |
| Solids loading | kg/m²·d | Solids loading rate |
| Effluent TSS | mg/L | Predicted effluent TSS |
| RAS flow required | m³/d | Required RAS pumping |
| Blanket depth | m | Sludge blanket level |
| State point flux | kg/m²·d | Applied solids flux |
| Limiting flux | kg/m²·d | Maximum sustainable flux |
Configuration Guide
Step-by-Step Setup
Determine Design Flows
- Peak wet weather flow (PWWF)
- Average flow
- Return activated sludge (RAS) ratio
- Typical RAS ratio: 0.5-1.5 × influent flow
Characterize Sludge
- Measure SVI (30-minute settling test)
- Typical values:
- Good settling: 80-120 mL/g
- Moderate: 120-150 mL/g
- Poor (bulking): >150 mL/g
- Determine operating MLSS (design parameter from aeration basin)
Select Surface Overflow Rate (SOR)
Conservative design:
SVI < 100: SOR = 20-25 m³/m²·d (average), 40-50 m³/m²·d (peak) SVI 100-150: SOR = 15-20 m³/m²·d (average), 30-40 m³/m²·d (peak) SVI > 150: SOR = 10-15 m³/m²·d (average), 20-30 m³/m²·d (peak)Calculate Required Area
$$A = \frac{Q_{peak}}{SOR_{peak}}$$
Example:
Qavg = 10,000 m³/d Qpeak = 15,000 m³/d SVI = 120 mL/g SOR_peak = 35 m³/m²·d A = 15,000 / 35 = 428.6 m² D = √(4×A/π) = 23.4 m → Use 24m diameter (452 m²)Verify Solids Loading Rate
$$SLR = \frac{Q \times X}{A}$$
Typical limits:
- Average: 100-150 kg/m²·d
- Peak: 200-250 kg/m²·d
SLR_avg = (10,000 × 3.5) / 452 = 77.4 kg/m²·d ✓ SLR_peak = (15,000 × 3.5) / 452 = 116.2 kg/m²·d ✓State Point Analysis (Advanced)
Calculate Takács settling velocity for range of concentrations:
At X = 3,500 mg/L: Vs = 474 × (exp(-0.000576×3500) - exp(-0.00286×3500)) = 8.6 m/d G_gravity = 8.6 × 3.5 = 30.1 kg/m²·d For RAS rate Qu = 10,000 m³/d (R=1.0): G_underflow = (10,000/452) × 3.5 = 77.4 kg/m²·d G_total = 30.1 + 77.4 = 107.5 kg/m²·d G_applied = (10,000 × 3.5) / 452 = 77.4 kg/m²·d Safety factor = G_limiting / G_applied > 1.2 ✓Configure RAS/WAS Control
- RAS pumping: Variable speed with blanket level control
- Target blanket depth: 1.0-1.5 m (1/3 of sidewater depth)
- WAS: Timer-based or flow-paced
- Sludge age control: Adjust WAS to maintain target SRT
Typical Design Values
| Application | SOR (avg) | SOR (peak) | SLR (avg) | SLR (peak) | Depth | Comments |
|---|---|---|---|---|---|---|
| Conventional AS (SVI 100) | 20-25 | 40-50 | 100-120 | 180-220 | 3.5-4.5 | Good settling |
| Extended aeration (SVI 120) | 16-20 | 30-40 | 80-100 | 140-180 | 4.0-4.5 | Moderate settling |
| Nitrification (SVI 100-120) | 16-20 | 30-35 | 80-100 | 150-180 | 4.0-5.0 | Avoid denitrification |
| BNR process (SVI 100-150) | 12-16 | 24-32 | 60-80 | 120-150 | 4.0-5.0 | Denitrification risk |
| Bulking sludge (SVI >150) | 10-12 | 20-24 | 50-70 | 100-120 | 4.5-5.0 | Poor settling |
Performance Criteria
Achievable Effluent TSS
| SVI (mL/g) | MLSS (mg/L) | SOR (m³/m²·d) | Effluent TSS (mg/L) | Performance |
|---|---|---|---|---|
| 80-100 | 2000-4000 | 15-20 | 5-10 | Excellent |
| 100-120 | 2500-4000 | 15-20 | 10-15 | Good |
| 120-150 | 3000-4500 | 12-16 | 15-25 | Moderate |
| 150-180 | 3000-5000 | 10-12 | 25-40 | Poor (borderline bulking) |
| >180 | - | <10 | >40 | Failing (bulking sludge) |
RAS Concentration
Target RAS concentration depends on MLSS and RAS ratio:
$$X_{RAS} = X_{MLSS} \times (1 + \frac{1}{R})$$
| MLSS (mg/L) | RAS Ratio (R) | Target RAS (mg/L) | Achievable with SVI |
|---|---|---|---|
| 2000 | 1.0 | 4000 | 80-150 |
| 3000 | 0.75 | 5250 | 80-130 |
| 3500 | 1.0 | 7000 | 80-120 |
| 4000 | 1.0 | 8000 | 80-110 |
| 5000 | 0.5 | 7500 | 80-100 |
Denitrification in Clarifier
Conditions favoring denitrification:
- High nitrate in MLSS (>5 mg/L)
- Deep sludge blanket (>1.5 m)
- High temperature (>15°C)
- Long blanket retention time
Consequences:
- Rising sludge (nitrogen gas bubbles)
- Poor effluent quality
- Loss of nitrate removal credit
- Phosphorus release (if anaerobic)
Mitigation:
- Increase RAS pumping rate (reduce blanket depth)
- Reduce nitrate recycling to anoxic zone
- Pre-anoxic zone to consume nitrate
- Shorter clarifier detention time
Troubleshooting
| Issue | Cause | Solution |
|---|---|---|
| High effluent TSS | Hydraulic overload (high SOR) | Reduce flow, add clarifiers, increase area |
| Solids overload (high SLR) | Reduce MLSS, waste more sludge | |
| Bulking sludge (high SVI) | Address bulking cause (see below) | |
| Rising sludge blanket | Increase RAS rate, reduce blanket depth | |
| Density currents | Check for temperature stratification, add baffles | |
| Rising sludge (denitrification) | High nitrate + deep blanket | Increase RAS rate, reduce nitrate to clarifier |
| Septicity in blanket | Increase WAS, reduce blanket retention | |
| Low RAS concentration | Poor settling (high SVI) | Address bulking, reduce SRT |
| High RAS rate | Reduce RAS pumping if possible | |
| Short-circuiting | Check feed distribution, improve mixing | |
| Blanket loss to effluent | RAS pump failure | Repair pump immediately, emergency shutdown |
| Sudden flow surge | Install flow equalization | |
| Scum/foam carryover | Install scum baffles, check for surfactants | |
| Filamentous bulking (SVI >150) | Low F/M ratio | Increase F/M, reduce SRT or aeration basin volume |
| Nutrient deficiency | Add nitrogen or phosphorus | |
| Low DO | Increase aeration | |
| Septic conditions | Eliminate dead zones, septage in primary | |
| Viscous bulking | High EPS production | Reduce SRT, check for shock loads |
| Pin floc | Very low F/M | Increase F/M, reduce aeration volume |
| Over-aeration | Reduce DO setpoint |
Operation & Maintenance
Daily Checks
- Visual inspection of effluent clarity
- Monitor blanket level (sludge judge or ultrasonic)
- Verify RAS/WAS pumping rates
- Check scum accumulation on surface
- Observe density currents or short-circuiting
- Record SVI (if daily sampling protocol)
Weekly Maintenance
- 30-minute settleability test (SVI measurement)
- Microscopic examination of sludge
- Clean scum baffles and overflow weirs
- Verify RAS/WAS flow meters
- Check blanket level sensors
- Inspect rotating mechanisms (scraper arms)
Monthly Tasks
- Complete sludge profile (blanket mapping)
- Calibrate level sensors
- Measure RAS concentration
- Review SVI trends
- Check for signs of structural damage
- Verify torque on rotating mechanisms
- Review effluent TSS vs. design
Annual Tasks
- Drain and inspect clarifier interior
- Inspect and repair scraper mechanisms
- Clean weirs and launders thoroughly
- Repaint exposed surfaces
- Structural inspection (concrete, welds)
- Review performance vs. design (consider uprate if needed)
- Update O&M procedures
Advanced Features
Dynamic Blanket Control
Modern clarifiers use ultrasonic or pressure sensors for real-time blanket level control:
$$Q_{RAS} = Q_{RAS,base} + K_p \times (h_{blanket} - h_{setpoint})$$
Where:
- $Q_{RAS,base}$ = baseline RAS flow (flow-paced)
- $K_p$ = proportional gain
- $h_{blanket}$ = measured blanket level (m)
- $h_{setpoint}$ = target blanket depth (typically 1.0-1.5 m)
Control Objectives:
- Maintain stable blanket depth
- Prevent blanket loss
- Maximize RAS concentration
- Minimize denitrification in blanket
Solids Flux Analysis
Plotting gravity flux vs. underflow flux identifies operating constraints:
For X from 0 to X_max:
Vs = Takács_model(X)
G_gravity = Vs × X
G_underflow = Qu/A × X
G_total = G_gravity + G_underflow
Plot G_total vs X:
Minimum = Limiting flux (design constraint)
At X_min = Critical concentrationDesign margin:
- Applied flux should be <80% of limiting flux for safety
Temperature Effects
Temperature affects settling primarily through viscosity:
$$V_s(T) = V_s(20°C) \times \frac{\mu(20°C)}{\mu(T)}$$
$$\mu(T) = \mu(20°C) \times 1.002^{(20-T)}$$
Impact:
- Cold weather (5°C): ~40% reduction in settling velocity
- Warm weather (25°C): ~10% improvement
- Design for worst-case (winter) conditions
Storm Flow Management
During wet weather:
- SOR increases dramatically
- Dilution of MLSS (if combined system)
- Risk of blanket loss
Strategies:
- Flow equalization upstream
- Storm tanks to dampen peaks
- Temporary acceptance of higher effluent TSS
- Emergency return of storm flow to head of plant
Worked Example
Given
- WWTP design: 15,000 m³/d (average), 22,500 m³/d (peak wet weather)
- Aeration basin MLSS: 3,500 mg/L
- SVI: 120 mL/g (design), measured: 110 mL/g
- Desired SRT: 10 days
- Aeration basin volume: 5,000 m³
Solution
Step 1: Select Design SOR
For SVI = 120 mL/g:
SOR_avg = 18 m³/m²·d
SOR_peak = 32 m³/m²·d (conservative)Step 2: Calculate Required Area
A = Q_peak / SOR_peak = 22,500 / 32 = 703.1 m²
D = √(4×703.1/π) = 29.9 m → Use two 24m diameter clarifiers
A_actual = 2 × π × 12² = 904.8 m²Step 3: Verify Average Conditions
SOR_avg = 15,000 / 904.8 = 16.6 m³/m²·d ✓ (within 18 limit)Step 4: Calculate Solids Loading
SLR_avg = (15,000 × 3.5) / 904.8 = 58.1 kg/m²·d ✓ (target <100)
SLR_peak = (22,500 × 3.5) / 904.8 = 87.0 kg/m²·d ✓ (target <150)Step 5: Determine RAS Flow
For MLSS balance and RAS concentration of 10,000 mg/L:
R = X_MLSS / (X_RAS - X_MLSS) = 3,500 / (10,000 - 3,500) = 0.538
Q_RAS = 0.538 × 15,000 = 8,070 m³/d (average)
Check if achievable with SVI=120:
Stirred SVI test: 1000 mL @ 3500 mg/L settles to 420 mL in 30 min
SVI = 420/3.5 = 120 mL/g ✓
Expected RAS concentration ≈ 1000/100 mL × 1000 = 10,000 mg/L ✓Step 6: Takács State Point Analysis
Takács parameters (default):
V0 = 474 m/d
rh = 0.000576 m³/g
rp = 0.00286 m³/g
At X = 3,500 mg/L:
Vs = 474 × (exp(-0.000576×3500) - exp(-0.00286×3500))
= 474 × (0.1184 - 0.0001)
= 56.1 m/d = 2.34 m/h
G_gravity = 56.1 × 3.5 = 196.4 kg/m²·d
G_underflow (avg) = (8,070/904.8) × 3.5 = 31.2 kg/m²·d
G_applied = 58.1 kg/m²·d
Limiting flux analysis shows G_L ≈ 150 kg/m²·d (occurs at X ≈ 6500 mg/L)
Safety factor = 150 / 58.1 = 2.58 ✓ (good margin)Step 7: WAS for SRT Control
SRT = (V × X) / (Qw × Xw + Qe × Xe)
Assuming Qw × Xw >> Qe × Xe:
Qw = (V × X) / (SRT × X_RAS)
= (5,000 × 3.5) / (10 × 10)
= 175 m³/d
Sludge production check:
Px ≈ 0.4 kg TSS/kg BOD removed (typical for AS)
BOD removal = 15,000 × 0.250 = 3,750 kg/d (assuming 250 mg/L)
Px = 0.4 × 3,750 = 1,500 kg/d
WAS mass = 175 × 10 = 1,750 kg/d (reasonable match)Step 8: Effluent TSS Prediction
At SVI = 110, SOR = 16.6 m³/m²·d, MLSS = 3500 mg/L:
TSS_eff ≈ 8 + 0.05 × (SOR - 15) = 8 + 0.08 = 8.1 mg/L (excellent)
At peak: SOR = 24.9 m³/m²·d:
TSS_eff ≈ 8 + 0.05 × (24.9 - 15) = 8 + 0.5 = 8.5 mg/L (still good)Summary
- Two 24m diameter clarifiers (904.8 m² total)
- Depth: 4.5 m (sidewater depth)
- RAS pumping: 8,070 m³/d (average) with VFD control
- WAS: 175 m³/d for SRT = 10 days
- Expected performance: <10 mg/L TSS effluent
Related Units
- Activated-Sludge-Basin - Upstream biological treatment
- RAS-Pumping - RAS/WAS pumping configuration
- Rectangular-Clarifier - Alternative geometry
- Lamella-Clarifier - High-rate alternative
- Membrane-Bioreactor - Membrane alternative to clarification
References
- Takács, I., Patry, G.G., and Nolasco, D. (1991). "A Dynamic Model of the Clarification-Thickening Process." Water Research 25(10): 1263-1271.
- WEF (2018). Design of Municipal Wastewater Treatment Plants, MOP 8, 6th Ed., Ch. 13.
- Metcalf & Eddy (2014). Wastewater Engineering: Treatment and Resource Recovery, 5th Ed., pp. 988-1045.
- Ekama, G.A., Barnard, J.L., Günthert, F.W., et al. (1997). Secondary Settling Tanks: Theory, Modelling, Design and Operation. IAWQ Scientific and Technical Report No. 6.
- ATV-DVWK (2000). Dimensioning of Single-Stage Activated Sludge Plants, ATV-A 131E.
- Parker, D.S., Kaufman, W.J., and Jenkins, D. (1972). "Floc Breakup in Turbulent Flocculation Processes." J. San. Eng. Div., ASCE 98(SA1): 79-99.
- UK Water Industry Research (2013). Activated Sludge Modelling for Design and Operation.