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Primary Clarifier
Gravity settling for removal of settleable solids from raw wastewater
Overview
Primary clarifiers are sedimentation tanks that remove suspended solids and associated organic matter from raw wastewater through gravity settling. They typically achieve 50-70% removal of total suspended solids (TSS) and 25-40% removal of biochemical oxygen demand (BOD5). Primary clarifiers are an essential component of conventional wastewater treatment, reducing the organic and solids loading to downstream biological treatment processes.
The process relies on the principle that particles denser than water will settle under quiescent conditions. Primary clarifiers are designed to provide sufficient detention time (typically 1.5-2.5 hours) and low surface overflow rates (30-50 m³/m²/day) to allow settleable solids to accumulate at the tank bottom. The clarified effluent overflows weirs at the tank perimeter, while settled sludge is collected by mechanical scrapers and pumped to sludge processing facilities.
Primary clarifiers can be circular (10-60m diameter) or rectangular (15-90m long) in configuration. Circular tanks use rotating sludge collectors, while rectangular tanks employ chain-and-flight scrapers. The concentrated primary sludge typically contains 2-6% solids and includes both organic and inorganic materials.
Theory and Equations
Basic Mode
Simple efficiency-based removal using empirical removal percentages:
$$\text{TSS}{out} = \text{TSS} \times (1 - \eta_{TSS})$$
$$\text{BOD}{out} = \text{BOD} \times (1 - \eta_{BOD})$$
$$\text{COD}{out} = \text{COD} \times (1 - \eta_{COD})$$
$$\text{TP}{out} = \text{TP} \times (1 - \eta_{TP})$$
$$\text{TKN}{out} = \text{TKN} \times (1 - \eta_{TKN})$$
Where:
- $\eta_{TSS}$ = TSS removal efficiency (typically 0.50-0.70)
- $\eta_{BOD}$ = BOD removal efficiency (typically 0.25-0.40)
- $\eta_{COD}$ = COD removal efficiency (typically 0.25-0.40)
- $\eta_{TP}$ = Total phosphorus removal efficiency (typically 0.05-0.15)
- $\eta_{TKN}$ = Total Kjeldahl nitrogen removal efficiency (typically 0.10-0.20)
Sludge Production:
$$\text{Sludge mass} = Q \times (\text{TSS}{in} - \text{TSS})$$
$$\text{Sludge volume} = \frac{\text{Sludge mass}}{\rho \times C_{sludge}}$$
Where:
- $Q$ = flow rate (m³/d)
- $\rho$ = sludge density (≈ 1000 kg/m³)
- $C_{sludge}$ = sludge concentration (typically 0.02-0.06, or 2-6%)
Advanced Mode
Overflow Rate Method (Ideal Settling):
The removal efficiency based on Stokes' Law settling velocity:
$$\eta = 1 - \exp\left(-\frac{v_s \cdot A}{Q}\right)$$
Where:
- $v_s$ = particle settling velocity (m/h)
- $A$ = surface area (m²)
- $Q$ = flow rate (m³/h)
Stokes' Law Settling Velocity:
$$v_s = \frac{g \cdot d_p^2 \cdot (\rho_p - \rho_w)}{18 \cdot \mu}$$
Where:
- $g$ = gravitational acceleration (9.81 m/s²)
- $d_p$ = particle diameter (m)
- $\rho_p$ = particle density (kg/m³)
- $\rho_w$ = water density (kg/m³)
- $\mu$ = dynamic viscosity (Pa·s)
Camp-Hazen Fraction Removed:
For a distribution of particle sizes:
$$\eta = \frac{1}{v_{s0}} \int_0^{v_{s0}} f(v_s) , dv_s + \int_{v_{s0}}^{\infty} \frac{v_{s0}}{v_s} f(v_s) , dv_s$$
Where:
- $v_{s0}$ = overflow rate = $Q/A$ (m/h)
- $f(v_s)$ = probability density function of settling velocities
Takács Settling Model (for hindered settling):
$$v_s(X) = v_0 \cdot \exp(-r_h \cdot X) - v_0' \cdot \exp(-r_p \cdot X)$$
Where:
- $v_0$ = maximum settling velocity (m/h)
- $v_0'$ = maximum rising velocity (m/h)
- $r_h$ = hindered settling parameter (L/g)
- $r_p$ = flocculent settling parameter (L/g)
- $X$ = solids concentration (g/L)
Model Parameters
Basic Mode Parameters
| Parameter | Symbol | Unit | Default | Range | Description |
|---|---|---|---|---|---|
| TSS Removal | η_TSS | - | 0.60 | 0.50-0.70 | TSS removal efficiency |
| BOD Removal | η_BOD | - | 0.30 | 0.25-0.40 | BOD removal efficiency |
| COD Removal | η_COD | - | 0.30 | 0.25-0.40 | COD removal efficiency |
| TP Removal | η_TP | - | 0.10 | 0.05-0.15 | Total phosphorus removal efficiency |
| TKN Removal | η_TKN | - | 0.15 | 0.10-0.20 | Total Kjeldahl nitrogen removal |
| Sludge Concentration | C_s | % | 4.0 | 2.0-6.0 | Primary sludge solids concentration |
Advanced Mode Parameters
| Parameter | Symbol | Unit | Default | Range | Description |
|---|---|---|---|---|---|
| Surface Area | A | m² | - | - | Tank surface area |
| Depth | H | m | 3.5 | 2.5-4.5 | Side water depth |
| Max Settling Velocity | v₀ | m/h | 10.0 | 5.0-20.0 | Maximum settling velocity |
| Max Rising Velocity | v₀' | m/h | 0.5 | 0.0-2.0 | Maximum rising velocity (density currents) |
| Hindered Parameter | rₕ | L/g | 0.5 | 0.3-0.8 | Hindered zone parameter |
| Flocculent Parameter | rₚ | L/g | 2.0 | 1.0-3.0 | Flocculent zone parameter |
| Particle Diameter | d_p | mm | 0.1 | 0.01-1.0 | Representative particle diameter |
| Particle Density | ρ_p | kg/m³ | 1050 | 1020-1200 | Particle density |
| Temperature | T | °C | 15 | 5-30 | Wastewater temperature |
Design Criteria
| Parameter | Typical Range | Notes |
|---|---|---|
| Surface Overflow Rate (Avg) | 30-50 m³/m²/d | Average dry weather flow |
| Surface Overflow Rate (Peak) | 80-120 m³/m²/d | Peak wet weather flow |
| Detention Time | 1.5-2.5 h | At average flow |
| Weir Loading Rate | 120-250 m³/m/d | Effluent weir overflow |
| Side Water Depth | 3.0-4.5 m | Circular or rectangular |
| Length to Width Ratio | 3:1 to 5:1 | Rectangular tanks only |
| Bottom Slope | 1% (circ), 2% (rect) | For sludge collection |
| Sludge Withdrawal Rate | 0.5-1.5 m³/m²/h | Prevents septicity |
| Scum Removal | Manual or mechanical | Beach or flights |
Worked Examples
Example 1: Basic Mode Calculation - Municipal WWTP
Given:
- Influent flow: 10,000 m³/d
- Influent TSS: 250 mg/L
- Influent BOD₅: 200 mg/L
- Influent COD: 450 mg/L
- TSS removal efficiency: 60%
- BOD removal efficiency: 30%
- COD removal efficiency: 30%
- Primary sludge concentration: 4%
Calculate: Effluent characteristics and sludge production
Effluent TSS:
- $\text{TSS}_{out} = 250 \times (1 - 0.60) = 250 \times 0.40 = 100 \text{ mg/L}$
Effluent BOD:
- $\text{BOD}_{out} = 200 \times (1 - 0.30) = 200 \times 0.70 = 140 \text{ mg/L}$
Effluent COD:
- $\text{COD}_{out} = 450 \times (1 - 0.30) = 450 \times 0.70 = 315 \text{ mg/L}$
TSS removed (mass):
- $\text{TSS removed} = 10,000 \times (250 - 100) / 1000 = 10,000 \times 150 / 1000 = 1,500 \text{ kg/d}$
Primary sludge volume:
- $V_{sludge} = \frac{1,500}{1000 \times 0.04} = \frac{1,500}{40} = 37.5 \text{ m³/d}$
Solution:
- Effluent TSS: 100 mg/L
- Effluent BOD₅: 140 mg/L
- Effluent COD: 315 mg/L
- Primary sludge production: 37.5 m³/d at 4% solids (1,500 kg dry solids/d)
Example 2: Advanced Mode - Overflow Rate Sizing
Given:
- Average flow: 15,000 m³/d
- Peak flow: 45,000 m³/d
- Target average overflow rate: 40 m³/m²/d
- Maximum peak overflow rate: 100 m³/m²/d
Calculate: Required surface area and tank dimensions
Surface area for average flow:
- $A_{avg} = \frac{Q_{avg}}{\text{SOR}_{avg}} = \frac{15,000}{40} = 375 \text{ m²}$
Surface area for peak flow:
- $A_{peak} = \frac{Q_{peak}}{\text{SOR}_{peak}} = \frac{45,000}{100} = 450 \text{ m²}$
Required surface area (governing):
- $A_{required} = \max(375, 450) = 450 \text{ m²}$
Circular tank diameter:
- $A = \frac{\pi D^2}{4}$
- $D = \sqrt{\frac{4A}{\pi}} = \sqrt{\frac{4 \times 450}{\pi}} = \sqrt{573} = 23.9 \text{ m}$
- Use $D = 24 \text{ m}$ (actual area = 452 m²)
Detention time at average flow (H = 3.5m):
- $V = A \times H = 452 \times 3.5 = 1,582 \text{ m³}$
- $\theta = \frac{V}{Q_{avg}} = \frac{1,582}{15,000/24} = \frac{1,582}{625} = 2.53 \text{ hours}$
Solution:
- Required surface area: 450 m²
- Tank diameter: 24 m (circular)
- Detention time: 2.53 hours (at average flow)
- Actual average SOR: 33.2 m³/m²/d
- Actual peak SOR: 99.6 m³/m²/d
Example 3: Advanced Mode - Settling Velocity Removal
Given:
- Flow rate: 20,000 m³/d
- Surface area: 500 m²
- Particle settling velocity: 0.5 m/h (from settling column tests)
Calculate: Theoretical removal efficiency
Overflow rate:
- $v_{s0} = \frac{Q}{A} = \frac{20,000/24}{500} = \frac{833.3}{500} = 1.67 \text{ m/h}$
Removal efficiency (particles with v_s = 0.5 m/h):
- For $v_s < v_{s0}$: Partial removal = $\frac{v_s}{v_{s0}}$
- $\eta = \frac{0.5}{1.67} = 0.30 = 30%$
For complete removal of these particles, required area:
- $A_{req} = \frac{Q}{v_s} = \frac{833.3}{0.5} = 1,667 \text{ m²}$
Solution:
- Overflow rate: 1.67 m/h
- Theoretical removal: 30% of particles with v_s = 0.5 m/h
- To achieve 100% removal of these particles: 1,667 m² required
Assumptions and Limitations
- Assumes ideal settling conditions (quiescent, uniform flow distribution)
- Does not account for short-circuiting, wind effects, or density currents
- Neglects temperature effects on settling velocity and viscosity
- Basic mode uses empirical efficiencies that vary with wastewater characteristics
- Advanced mode requires settling velocity data from jar or column tests
- Does not model biological activity or septic conditions in sludge blanket
- Assumes steady-state operation (not applicable to storm events)
- Particle size distribution must be known for accurate advanced calculations
- Does not account for effluent weir hydraulics affecting flow distribution
Troubleshooting
| Issue | Possible Cause | Solution |
|---|---|---|
| Low TSS removal (<50%) | Hydraulic overload | Reduce flow, add tankage, or check flow distribution |
| Rising sludge, septic odors | Sludge blanket too thick, septicity | Increase sludge withdrawal frequency |
| Effluent turbidity | High overflow rate at weirs | Reduce weir loading, add weir length |
| Excessive scum buildup | Insufficient skimming | Increase skimmer frequency or add mechanisms |
| High sludge volume | Low sludge concentration | Increase withdrawal rate, check scraper operation |
| Poor flow distribution | Inlet baffle issues | Inspect and repair inlet baffles/energy dissipators |
| Carry-over of solids | Wind effects | Add baffles or wind screens |
| Short-circuiting | Dead zones in tank | Modify baffling, check mixer operation |
Related Process Units
- Screens - Upstream removal of large objects
- Grit Removal - Upstream removal of heavy inorganic particles
- Activated Sludge - Downstream biological treatment
- Gravity Thickener - Similar settling principles for sludge concentration
- Secondary Clarifier - Similar design but different settling characteristics
References
- Metcalf & Eddy (2014). Wastewater Engineering: Treatment and Resource Recovery, 5th Edition, McGraw-Hill.
- Water Environment Federation (2018). Design of Water Resource Recovery Facilities, Manual of Practice No. 8, 6th Edition.
- Tchobanoglous, G., Stensel, H.D., Tsuchihashi, R., and Burton, F. (2014). Wastewater Engineering: Treatment and Resource Recovery, 5th Edition.
- Camp, T.R. (1946). "Sedimentation and the Design of Settling Tanks," Transactions ASCE, 111:895-958.
- Hazen, A. (1904). "On Sedimentation," Transactions ASCE, 53:45-71.
- Takács, I., Patry, G.G., and Nolasco, D. (1991). "A Dynamic Model of the Clarification-Thickening Process," Water Research, 25(10):1263-1271.
- Fair, G.M., Geyer, J.C., and Okun, D.A. (1968). Water and Wastewater Engineering, Volume 2, Wiley.
Model Implementation
TypeScript Model Location: backend/models/processes/PrimaryClarifier.ts
Key Methods:
calculateBasic()- Efficiency-based removal calculationscalculateAdvanced()- Overflow rate and settling velocity calculationsvalidate()- Parameter range validationestimateSludgeProduction()- Sludge mass and volume calculations
Change Log
| Date | Version | Changes |
|---|---|---|
| 2025-12-30 | 1.0 | Initial documentation with basic and advanced modes |