Filtration

Removal of suspended solids through granular media or membrane filters

Overview

Tertiary filtration removes residual TSS after secondary treatment, achieving <5 mg/L TSS and <2 NTU turbidity. Types include rapid sand filters, dual-media filters, continuous backwash filters, and disk/cloth filters. Essential for disinfection effectiveness and water reuse applications.

Theory - Basic Mode

$$\text{TSS}{out} = \text{TSS}$$ $$\text{Turbidity}{out} = \text{Turbidity}$$

Typical performance:

• Rapid sand: TSS <5 mg/L, Turb <2 NTU
• Dual-media: TSS ❤️ mg/L, Turb <1 NTU
• Cloth disk: TSS <5 mg/L
• Membrane: TSS <0.1 mg/L

Theory - Advanced Mode

Carmen-Kozeny Headloss:

$$h = \frac{k \times \mu \times v \times L}{g \times d^2 \times \epsilon^3} \times (1-\epsilon)^2$$

Where:

• h = headloss (m)
• k = shape factor (~5)
• μ = viscosity
• v = filtration rate (m/h)
• L = bed depth (m)
• d = media diameter (m)
• ε = porosity (0.40-0.45)

Filtration Rate:

$$q = \frac{Q}{A}$$

Typical rates: 5-15 m/h (gravity), 10-30 m/h (pressure)

Parameters

Filter Type	Rate	Depth	Media	TSS Out
Rapid Sand	5-10	0.6-1.0	0.5-1.0 mm sand	<5 mg/L
Dual Media	10-20	0.6-0.9	Sand + anthracite	❤️ mg/L
Continuous	5-10	0.6-1.2	Sand	<5 mg/L
Cloth Disk	-	-	10-20 μm	<5 mg/L

Worked Example

Given: Dual-media filter for 15,000 m³/d Calculate: Filter area

1. Design rate: 12 m/h
2. Area required: 15,000 / 24 / 12 = 52 m²
3. Use 4 filters × 15 m² = 60 m² (allows 1 out for backwash)

References

1. Metcalf & Eddy (2014)
2. AWWA (2011). Water Treatment Plant Design