Secondary Clarifier

Gravity settling for separation of biological solids from treated effluent in activated sludge systems

Overview

Secondary clarifiers perform the critical dual function of clarification (producing low-TSS effluent) and thickening (concentrating return activated sludge, RAS). Unlike primary clarifiers that handle discrete particle settling, secondary clarifiers must handle flocculent biological solids with complex settling characteristics including hindered settling, compression, and potential for rising sludge due to denitrification.

The performance of secondary clarifiers directly impacts the entire activated sludge system. Inadequate clarifier capacity leads to solids carryover in the effluent, loss of biomass from the system, and reduced SRT. Conversely, poor thickening results in dilute RAS, requiring higher recycle ratios and potentially hydraulic overload of the aeration basin.

Secondary clarifiers are typically circular (15-60m diameter) with center-feed mechanisms or rectangular with end-feed configurations. Design is based on solids flux theory, which considers both gravity settling and hydraulic transport of solids. The limiting solids flux determines the maximum solids loading the clarifier can handle while maintaining both clarification and thickening functions.

Theory and Equations

Basic Mode

Simple effluent quality based on typical secondary clarifier performance:

$$\text{TSS}{effluent} = \text{TSS}$$

$$\text{BOD}{effluent} = \text{BOD}$$

$$\text{RAS concentration} = X_{RAS,typical}$$

Where:

• $\text{TSS}_{typical}$ = typical effluent TSS (5-30 mg/L)
• $\text{BOD}_{effluent,typical}$ = effluent BOD (5-20 mg/L)
• $X_{RAS,typical}$ = typical RAS concentration (8,000-12,000 mg/L)

RAS Flow Calculation:

To maintain target MLSS in aeration basin:

$$Q_{RAS} = Q \times \frac{X_{MLSS}}{X_{RAS} - X_{MLSS}}$$

Where:

• $Q$ = influent flow (m³/d)
• $X_{MLSS}$ = mixed liquor SS in aeration basin (mg/L)
• $X_{RAS}$ = return activated sludge concentration (mg/L)

Advanced Mode

Solids Flux Theory:

Total solids flux is the sum of gravity settling flux and bulk transport flux:

$$G_{total} = G_{gravity} + G_{bulk}$$

$$G_{gravity} = v_s(X) \times X$$

$$G_{bulk} = v_{bulk} \times X$$

Where:

• $G_{total}$ = total solids flux (kg/m²·h)
• $G_{gravity}$ = gravity settling flux (kg/m²·h)
• $G_{bulk}$ = bulk hydraulic flux (kg/m²·h)
• $v_s(X)$ = settling velocity as function of concentration (m/h)
• $v_{bulk}$ = bulk hydraulic velocity (m/h)
• $X$ = solids concentration (kg/m³)

Vesilind Settling Velocity:

$$v_s(X) = v_0 \times e^{-k \cdot X}$$

Where:

• $v_0$ = maximum settling velocity (m/h)
• $k$ = settling parameter (m³/kg)
• $X$ = solids concentration (kg/m³)

Takács Settling Model:

$$v_s(X) = \max\left(0, \min\left(v_0, \frac{v_0 \cdot (e^{-r_h(X-X_{min})} - e^{-r_p(X-X_{min})})}{e^{-r_h \cdot X_{min}} - e^{-r_p \cdot X_{min}}}\right)\right)$$

Where:

• $v_0$ = maximum settling velocity (m/h)
• $r_h$ = hindered settling parameter (m³/kg)
• $r_p$ = flocculent settling parameter (m³/kg)
• $X_{min}$ = minimum attainable concentration (kg/m³)

State Point Analysis:

The limiting solids flux is found at the intersection of underflow and overflow lines:

$$G_{limit} = \min(G_{overflow}, G_{underflow})$$

$$G_{overflow} = v_s(X_f) \times X_f + \frac{Q}{A} \times X_f$$

$$G_{underflow} = v_s(X_u) \times X_u - \frac{Q_u}{A} \times X_u$$

Where:

• $X_f$ = feed solids concentration (kg/m³)
• $X_u$ = underflow solids concentration (kg/m³)
• $Q$ = overflow rate (m³/h)
• $Q_u$ = underflow rate (m³/h)
• $A$ = surface area (m²)

Solids Loading Rate (SLR):

$$\text{SLR} = \frac{(Q + Q_{RAS}) \times X_{MLSS}}{A}$$

Where:

• $\text{SLR}$ = solids loading rate (kg/m²·h)
• $Q$ = influent flow (m³/h)
• $Q_{RAS}$ = RAS flow (m³/h)
• $X_{MLSS}$ = mixed liquor concentration (kg/m³)
• $A$ = surface area (m²)

Sludge Volume Index (SVI):

$$\text{SVI} = \frac{\text{Settled volume (mL/L)} \times 1000}{\text{MLSS (mg/L)}}$$

A key indicator of sludge settleability:

• SVI < 100: Excellent settling
• SVI 100-150: Good settling
• SVI 150-200: Fair settling, potential issues
• SVI > 200: Poor settling, bulking sludge

Model Parameters

Basic Mode Parameters

Parameter	Symbol	Unit	Default	Range	Description
Effluent TSS	TSS_eff	mg/L	15	5-30	Typical effluent suspended solids
RAS Concentration	X_RAS	mg/L	10,000	8,000-15,000	Return activated sludge concentration
MLSS Target	X_MLSS	mg/L	3,000	2,000-5,000	Mixed liquor suspended solids

Advanced Mode Parameters

Parameter	Symbol	Unit	Default	Range	Description
Surface Area	A	m²	-	-	Clarifier surface area
Side Water Depth	H	m	4.0	3.5-5.0	Depth from surface to bottom
Max Settling Velocity	v₀	m/h	8.0	4.0-15.0	Maximum settling velocity
Vesilind k Parameter	k	m³/kg	0.45	0.30-0.80	Vesilind settling parameter
Takács rₕ Parameter	rₕ	m³/kg	0.000576	0.0003-0.001	Hindered settling parameter
Takács rₚ Parameter	rₚ	m³/kg	0.00286	0.001-0.005	Flocculent settling parameter
Min Concentration	X_min	kg/m³	0.0001	0.00001-0.001	Minimum attainable concentration
MLSS	X_MLSS	mg/L	3,000	2,000-5,000	Mixed liquor suspended solids
RAS Ratio	r	-	0.50	0.25-1.50	RAS flow / influent flow

Design Criteria

Parameter	Typical Range	Peak Range	Notes
Surface Overflow Rate	16-32 m³/m²/d	40-50 m³/m²/d	Based on Q + Q_RAS
Solids Loading Rate	100-150 kg/m²/d	200-250 kg/m²/d	Critical parameter
Side Water Depth	3.5-5.0 m	-	Circular clarifiers
Weir Loading	125-250 m³/m/d	375 m³/m/d	Effluent weir
RAS Concentration	8,000-12,000 mg/L	-	Typical thickening
Detention Time	2-4 hours	-	At average flow
Surface Area per Tank	200-2,000 m²	-	Practical limits

Worked Examples

Example 1: Basic Mode - RAS Flow Calculation

Given:

• Influent flow (Q): 10,000 m³/d
• Target MLSS: 3,000 mg/L
• RAS concentration: 10,000 mg/L

Calculate: Required RAS flow rate

1. RAS flow rate:

   • $Q_{RAS} = Q \times \frac{X_{MLSS}}{X_{RAS} - X_{MLSS}}$
   • $Q_{RAS} = 10,000 \times \frac{3,000}{10,000 - 3,000}$
   • $Q_{RAS} = 10,000 \times \frac{3,000}{7,000} = 10,000 \times 0.429 = 4,290 \text{ m³/d}$

2. RAS ratio:

   • $r = \frac{Q_{RAS}}{Q} = \frac{4,290}{10,000} = 0.43 = 43%$

Solution:

• RAS flow rate: 4,290 m³/d
• RAS ratio: 43% or 0.43 Q

Example 2: Advanced Mode - Solids Loading Rate Check

Given:

• Flow (Q): 15,000 m³/d
• RAS flow: 7,500 m³/d (50% of Q)
• MLSS: 3,500 mg/L
• Clarifier diameter: 35 m
• Peak flow: 30,000 m³/d

Calculate: Average and peak solids loading rates

1. Surface area:

   • $A = \frac{\pi D^2}{4} = \frac{\pi \times 35^2}{4} = \frac{3.14159 \times 1,225}{4} = 962 \text{ m²}$

2. Average solids loading rate:

   • $\text{SLR}{avg} = \frac{(Q + Q) \times X_{MLSS}}{A \times 24}$
   • $\text{SLR}_{avg} = \frac{(15,000 + 7,500) \times 3.5}{962 \times 24}$
   • $\text{SLR}_{avg} = \frac{22,500 \times 3.5}{23,088} = \frac{78,750}{23,088} = 3.41 \text{ kg/m²·h}$
   • Or: $\text{SLR}_{avg} = 3.41 \times 24 = 82 \text{ kg/m²·d}$

3. Peak solids loading rate (assuming same RAS ratio):

   • $Q_{RAS,peak} = 30,000 \times 0.5 = 15,000 \text{ m³/d}$
   • $\text{SLR}_{peak} = \frac{(30,000 + 15,000) \times 3.5}{962 \times 24}$
   • $\text{SLR}_{peak} = \frac{157,500}{23,088} = 6.82 \text{ kg/m²·h} = 164 \text{ kg/m²·d}$

4. Surface overflow rate (average, based on Q + RAS):

   • $\text{SOR} = \frac{Q + Q_{RAS}}{A} = \frac{22,500}{962} = 23.4 \text{ m³/m²·d}$

Solution:

• Average SLR: 82 kg/m²·d (within typical range of 100-150, on lower side)
• Peak SLR: 164 kg/m²·d (within peak range of 200-250)
• Average SOR: 23.4 m³/m²·d (good, well below 32)

Example 3: State Point Analysis - Limiting Flux

Given:

• Flow: 10,000 m³/d = 417 m³/h
• Clarifier area: 500 m²
• MLSS: 4,000 mg/L = 4.0 kg/m³
• RAS concentration target: 12,000 mg/L = 12.0 kg/m³
• Vesilind parameters: v₀ = 8 m/h, k = 0.45 m³/kg
• RAS ratio: 50% (Q_RAS = 208 m³/h)

Calculate: Limiting solids flux and verify clarifier capacity

1. Settling velocity at feed concentration (X = 4.0 kg/m³):

   • $v_s(4.0) = 8 \times e^{-0.45 \times 4.0} = 8 \times e^{-1.8} = 8 \times 0.1653 = 1.32 \text{ m/h}$

2. Overflow hydraulic velocity:

   • $v_{overflow} = \frac{Q}{A} = \frac{417}{500} = 0.83 \text{ m/h}$

3. Overflow solids flux:

   • $G_{overflow} = v_s(X_f) \times X_f + v_{overflow} \times X_f$
   • $G_{overflow} = 1.32 \times 4.0 + 0.83 \times 4.0 = 5.28 + 3.32 = 8.60 \text{ kg/m²·h}$

4. Settling velocity at underflow concentration (X = 12.0 kg/m³):

   • $v_s(12.0) = 8 \times e^{-0.45 \times 12.0} = 8 \times e^{-5.4} = 8 \times 0.00450 = 0.036 \text{ m/h}$

5. Underflow hydraulic velocity:

   • $v_{underflow} = \frac{Q_{RAS}}{A} = \frac{208}{500} = 0.42 \text{ m/h}$

6. Underflow solids flux:

   • $G_{underflow} = v_s(X_u) \times X_u - v_{underflow} \times X_u$
   • $G_{underflow} = 0.036 \times 12.0 - 0.42 \times 12.0 = 0.43 - 5.04 = -4.61 \text{ kg/m²·h}$

Note: Negative underflow flux indicates the RAS pumping rate exceeds gravity settling capacity at this concentration.

7. Applied solids loading:
   • $\text{Applied load} = \frac{(Q + Q_{RAS}) \times X}{A} = \frac{(417 + 208) \times 4.0}{500} = \frac{2,500}{500} = 5.0 \text{ kg/m²·h}$

Solution:

• Applied solids load: 5.0 kg/m²·h (120 kg/m²·d)
• Limiting flux: Analysis shows the clarifier can handle the overflow flux of 8.60 kg/m²·h
• The underflow flux calculation indicates the target RAS concentration of 12,000 mg/L may not be achievable at this RAS ratio
• Recommendation: Reduce RAS ratio or accept lower RAS concentration (~8,000-10,000 mg/L)

Assumptions and Limitations

• Assumes ideal settling conditions without short-circuiting or density currents
• Does not account for denitrification causing rising sludge
• Vesilind and Takács models are empirical and require site-specific calibration
• Temperature effects on settling are not explicitly included
• Does not model time-varying or dynamic conditions
• Assumes uniform sludge characteristics (SVI, settling velocity)
• Neglects wind effects and surface disturbances
• Basic mode uses typical values that may not apply to all activated sludge systems
• Does not account for filamentous bulking or pin floc conditions
• RAS concentration depends on clarifier geometry, scraper design, and withdrawal location

Troubleshooting

Issue	Possible Cause	Solution
High effluent TSS	Hydraulic overload, poor settling	Reduce SOR/SLR, increase RAS, check SVI
Rising sludge	Denitrification in blanket	Increase RAS rate, reduce aeration basin DO
Thin RAS	Low sludge blanket, high RAS rate	Reduce RAS flow, increase blanket depth
Thick sludge blanket	Insufficient RAS pumping	Increase RAS rate, check scrapers
Septic conditions	Long detention, warm weather	Increase RAS, reduce sludge age in clarifier
Pin floc carryover	Young sludge, high F/M	Increase SRT, reduce F/M in aeration
Filamentous bulking	Low F/M, nutrient deficiency	Address in aeration basin, check SVI
Uneven flow distribution	Inlet baffle damage	Inspect and repair inlet structure
Poor sludge collection	Scraper malfunction	Check mechanical equipment

Related Process Units

• Activated Sludge - Upstream biological treatment
• Primary Clarifier - Similar settling principles
• Gravity Thickener - Similar thickening function
• MBR - Membrane alternative to secondary clarification
• DAF - Alternative clarification technology

References

1. Metcalf & Eddy (2014). Wastewater Engineering: Treatment and Resource Recovery, 5th Edition, McGraw-Hill.
2. Dick, R.I. and Ewing, B.B. (1967). "The Rheology of Activated Sludge," Journal WPCF, 39(4):543-560.
3. Vesilind, P.A. (1968). "Design of Prototype Thickeners from Batch Settling Tests," Water and Sewage Works, 115(7):302-307.
4. Takács, I., Patry, G.G., and Nolasco, D. (1991). "A Dynamic Model of the Clarification-Thickening Process," Water Research, 25(10):1263-1271.
5. Ekama, G.A., Barnard, J.L., Günthert, F.W., Krebs, P., McCorquodale, J.A., Parker, D.S., and Wahlberg, E.J. (1997). "Secondary Settling Tanks: Theory, Modelling, Design and Operation," IAWQ STR No. 6, IWA Publishing.
6. WEF (2005). Clarifier Design, 2nd Edition, Water Environment Federation.
7. Daigger, G.T. (1995). "Development of Refined Clarifier Operating Diagrams Using an Updated Settling Characteristics Database," Water Environment Research, 67(1):95-100.

Model Implementation

TypeScript Model Location: backend/models/processes/SecondaryClarifier.ts

Key Methods:

• calculateBasic() - Simple RAS flow calculation
• calculateAdvanced() - Solids flux analysis with Vesilind/Takács models
• calculateSLR() - Solids loading rate
• calculateStatePoint() - Limiting flux determination
• validate() - Parameter range validation

Change Log

Date	Version	Changes
2025-12-30	1.0	Initial documentation with solids flux theory and state point analysis