Circular Primary Clarifier

Conventional center-feed primary sedimentation tank for removal of settleable solids and BOD through gravity settling.

Overview

The circular primary clarifier is the most common configuration for primary sedimentation in wastewater treatment. It features a center-feed inlet with peripheral overflow weirs and a rotating sludge collection mechanism.

When to Use

• Municipal wastewater treatment plants (>1,000 PE)
• Industrial pretreatment facilities
• Sites with space for circular footprint
• Applications requiring robust, proven technology

Settling Theory

Type I - Discrete Settling (Stokes' Law)

Large, discrete particles settle independently according to Stokes' Law:

$$V_s = \frac{g \times d^2 \times (\rho_s - \rho_w)}{18 \times \mu}$$

Where:

• $V_s$ = settling velocity (m/s)
• $g$ = gravitational acceleration (9.81 m/s²)
• $d$ = particle diameter (m)
• $\rho_s$ = particle density (kg/m³)
• $\rho_w$ = water density (998 kg/m³ at 20°C)
• $\mu$ = dynamic viscosity (Pa·s)

Type II - Flocculent Settling (Camp Formula)

For flocculating particles that aggregate during settling:

$$\eta = 1 - \left(1 + \frac{n \times V_s \times t}{H}\right)^{-1/n}$$

Where:

• $\eta$ = removal efficiency (fraction)
• $n$ = flocculation parameter (0.2-0.5, typically 0.35)
• $t$ = detention time (s)
• $H$ = settling depth (m)

Temperature Effects on Viscosity

Viscosity varies significantly with temperature, affecting settling:

$$\mu(T) = \mu(20°C) \times 1.002^{(20-T)}$$

Temperature (°C)	Relative Viscosity	Effect on Settling
5	1.52	-34% efficiency
10	1.31	-23% efficiency
15	1.14	-12% efficiency
20	1.00	Baseline
25	0.89	+12% efficiency
30	0.80	+25% efficiency

Design Equations

Surface Overflow Rate (SOR)

$$SOR = \frac{Q}{A} = \frac{Q}{\pi \times (D/2)^2}$$

Where:

• $Q$ = flow rate (m³/d)
• $A$ = surface area (m²)
• $D$ = tank diameter (m)

Hydraulic Retention Time (HRT)

$$HRT = \frac{V}{Q} = \frac{A \times SWD}{Q}$$

Where:

• $V$ = tank volume (m³)
• $SWD$ = sidewater depth (m)

Weir Loading Rate

$$WLR = \frac{Q}{\pi \times D}$$

Where:

• $WLR$ = weir loading rate (m³/m/d)

Upflow Velocity

$$v_{up} = \frac{Q}{A \times 24}$$

Converting to m/h for comparison with design criteria.

Particle Size Distribution Model

ErgoPlanner uses a 5-class velocity distribution for realistic modeling:

Class	Settling Velocity (m/h)	TSS Fraction	Typical Particles
1	0.1	5%	Colloidal, fine organics
2	0.5	15%	Fine suspended solids
3	2.0	40%	Medium organic flocs
4	5.0	30%	Coarse settleable solids
5	10.0	10%	Very coarse, grit

Per-Class Removal Efficiency

For each particle class:

$$\eta_i = \begin{cases} 1 & \text{if } V_{s,i} > SOR \ V_{s,i} / SOR & \text{if } V_{s,i} \leq SOR \end{cases}$$

Total TSS removal:

$$\eta_{TSS} = \sum_{i=1}^{5} f_i \times \eta_i$$

Short-Circuiting Model

Real tanks experience short-circuiting, reducing effective detention time:

Tanks-in-Series (TIS) Model

$$N_{tanks} = \frac{t_{actual}}{t_{ideal}}$$

For circular clarifiers: $N = 3-5$ typically

The effective removal with short-circuiting:

$$\eta_{eff} = \eta_{ideal} \times \left(\frac{N}{N+1}\right)$$

Particulate Nutrient Removal

Nutrients bound to settleable solids are removed proportionally:

$$TP_{removed} = TSS_{removed} \times \frac{f_{pP}}{TSS_{inlet}}$$

$$TKN_{removed} = TSS_{removed} \times \frac{f_{pN}}{TSS_{inlet}}$$

$$COD_{removed} = TSS_{removed} \times \frac{f_{pCOD}}{TSS_{inlet}}$$

Where:

• $f_{pP}$ = particulate P fraction (20-60%, typically 40%)
• $f_{pN}$ = particulate N fraction (15-45%, typically 30%)
• $f_{pCOD}$ = particulate COD fraction

Parameters

Design Parameters

Parameter	Symbol	Unit	Range	Default	Description
Diameter	D	m	10-60	25	Tank diameter
Sidewater Depth	SWD	m	2.5-5.0	3.0	Minimum PS208: 2.5m
Floor Slope	-	°	8-15	10	Toward center hopper
Number of Tanks	N	-	2-6	2	Minimum 2 for N-1

Hydraulic Criteria (UK PS208)

Parameter	Unit	DWF Limit	FFT Limit
Surface Overflow Rate	m³/m²/d	28.8	48.0
Upflow Velocity	m/h	1.2	2.0
HRT	hours	>2.0	>2.0
Weir Loading	m³/m/d	<300	<500

Advanced Parameters (Mechanistic Mode)

Parameter	Unit	Default	Range	Description
settlingVelocityDistribution	-	default	5-class	Particle velocity classes
flocculationParameter	-	0.35	0.2-0.5	Camp formula n value
shortCircuitFactor	-	4	2-10	Tanks-in-series N
temperature	°C	15	5-30	Affects viscosity
particulatePFraction	%	40	20-60	P in particulate form
particulateNFraction	%	30	15-45	N in particulate form
sludgeDensity	kg/m³	1020	1010-1050	Settled sludge density
compressionTime	h	4	2-8	Sludge compression time

Removal Efficiencies

Without Chemical Dosing

Parameter	Removal (%)	Notes
BOD	25-35	Primarily particulate
TSS	50-65	Design dependent
COD	25-40	Particulate fraction
NH₃-N	0	Dissolved, not removed
Total P	10-20	Particulate only

With Chemical Dosing (Fe/Al)

Parameter	Removal (%)	Notes
BOD	35-45	Enhanced flocculation
TSS	60-75	Chemical precipitation
COD	35-50	Enhanced
NH₃-N	0	Not affected
Total P	60-85	Primary removal mechanism

Sludge Production

Primary Sludge Characteristics

Parameter	Value	Unit
Dry Solids	2-5	% DS
Typical	3	% DS
VS/TS Ratio	0.65-0.80	-
Density	1020-1030	kg/m³

Sludge Mass Calculation

$$M_{sludge} = Q \times TSS_{inf} \times \eta_{TSS}$$

$$Q_{sludge} = \frac{M_{sludge}}{DS% \times 10}$$

Configuration

Step-by-Step Setup

1. Define Geometry

   • Select tank type: Circular (radial)
   • Enter diameter based on site constraints
   • Set sidewater depth (min 2.5m per PS208)
   • Define floor slope (8-15°)

2. Set Tank Count

   • Minimum 2 tanks for N-1 redundancy
   • Consider maintenance scheduling

3. Chemical Dosing

   • Enable if P removal required
   • Typical: Ferric chloride or PAC

4. Verify Design

   • Check upflow velocity < 1.2 m/h at DWF
   • Check upflow velocity < 2.0 m/h at FFT
   • Verify HRT > 2 hours
   • Confirm N-1 compliance

Example Configuration

{
  "type": "primaryClarifier",
  "subtype": "circular",
  "parameters": {
    "diameter": 25,
    "sidewaterDepth": 3.0,
    "floorSlope": 10,
    "numberOfTanks": 2,
    "chemicalDosing": false,
    "calculationMode": "advanced",
    "advancedParams": {
      "flocculationParameter": 0.35,
      "shortCircuitFactor": 4,
      "temperature": 15
    }
  }
}

N-1 Compliance

UK PS208 requires facilities to operate within limits with one tank out of service:

Verification Steps

1. Calculate area/volume with (N-1) tanks
2. Check upflow velocity at DWF < 1.2 m/h
3. Check upflow velocity at FFT < 2.0 m/h
4. Verify HRT > 2 hours at FFT

N-1 Calculations

$$A_{N-1} = A_{total} \times \frac{N-1}{N}$$

$$V_{N-1} = V_{total} \times \frac{N-1}{N}$$

Worked Example

Given

• Population: 50,000 PE
• DWF: 12,500 m³/d (250 L/PE/d)
• FFT: 37,500 m³/d (3× DWF)
• Influent TSS: 350 mg/L
• Influent BOD: 300 mg/L

Design

Step 1: Calculate Required Area

Target SOR at FFT = 40 m³/m²/d (below 48 limit)

$$A_{required} = \frac{37,500}{40} = 938 \text{ m}^2$$

Step 2: Select Configuration

Two tanks, diameter = 25m each

$$A_{actual} = 2 \times \pi \times (12.5)^2 = 982 \text{ m}^2$$

Step 3: Check Upflow Velocities

At DWF: $$v_{up} = \frac{12,500}{982 \times 24} = 0.53 \text{ m/h}$$ ✓ (<1.2)

At FFT: $$v_{up} = \frac{37,500}{982 \times 24} = 1.59 \text{ m/h}$$ ✓ (<2.0)

Step 4: Check HRT

Volume (SWD=3.0m): $V = 982 \times 3.0 = 2,946$ m³

At DWF: $HRT = \frac{2,946}{12,500} \times 24 = 5.66$ hours ✓

At FFT: $HRT = \frac{2,946}{37,500} \times 24 = 1.89$ hours ⚠ (near limit)

Step 5: N-1 Check

With one tank: $A_{N-1} = 491$ m²

At FFT: $v_{up} = \frac{37,500}{491 \times 24} = 3.18$ m/h ✗ (exceeds 2.0)

Recommendation: Add third tank or increase diameter.

Troubleshooting

Issue	Cause	Solution
High effluent TSS	Hydraulic overload	Reduce flow, add tanks
	Poor flocculation	Optimize chemical dose
	Short-circuiting	Install baffles
Poor P removal	Insufficient chemical	Increase Fe/Al dose
	pH too high	Adjust to 6.5-7.0
Sludge rising	Septicity/gas	Increase withdrawal
	Too long HRT	Reduce detention
Scum accumulation	Insufficient skimming	Adjust skimmer speed

Best Practices

1. Design Margin: Target 80% of maximum allowable SOR
2. Redundancy: Always provide N-1 capability
3. Sludge Withdrawal: Regular, frequent removal prevents septicity
4. Inlet Design: Use center well for energy dissipation
5. Weir Level: Maintain level weirs for even flow distribution
6. Temperature Monitoring: Adjust expectations for cold water

Related Topics

• Rectangular-Primary-Clarifier
• Lamella-Primary-Clarifier
• Secondary-Clarifier
• Chemical-Dosing

References

1. Metcalf & Eddy (2014). Wastewater Engineering: Treatment and Resource Recovery, 5th Ed.
2. UK Water Industry (2020). Sewers for Adoption, 8th Ed. (PS208)
3. WEF (2018). Design of Municipal Wastewater Treatment Plants, MOP 8
4. Camp, T.R. (1946). "Sedimentation and the Design of Settling Tanks"