Appearance
Rapid Sand Filter
Granular media filtration using sand (0.5-1.0 mm) to remove suspended solids from secondary effluent, achieving <5 mg/L TSS with Iwasaki depth filtration model.
Overview
Rapid sand filters are the workhorse of tertiary filtration, providing reliable TSS removal for effluent polishing, water reuse, and upstream of disinfection systems. They combine physical straining, sedimentation within pores, and biological activity to produce high-quality effluent.
When to Use
- Tertiary polishing after secondary treatment
- Upstream of UV or chlorine disinfection (turbidity reduction)
- Water reuse applications (non-potable to potable)
- Phosphorus removal (with chemical coagulation)
- Nitrification polishing (biological filtration mode)
- Giardia/Cryptosporidium removal (2-3 log with proper operation)
Key Characteristics
- TSS removal: Secondary effluent 10-20 mg/L → <5 mg/L
- Filtration rate: 5-15 m/h (120-360 m³/m²·d)
- Backwash frequency: Every 24-72 hours
- Headloss buildup: 0.5-2.5 m during filter run
- Media depth: 0.6-1.2 m
- Low chemical consumption (except if coagulant used)
Operating Modes
Basic Mode
- Fixed filtration rate
- Simple headloss calculation
- Time-based backwash trigger
- Default removal efficiency curve
Advanced Mode
- Iwasaki depth filtration model
- Dynamic filter coefficient λ(t)
- Headloss prediction (Carmen-Kozeny)
- Backwash optimization (minimize water use)
- Biological filtration kinetics (if nitrifying)
Mathematical Model
Governing Equation - Iwasaki Filtration
Solids removal through filter depth follows exponential decay:
$$\frac{\partial C}{\partial z} = -\lambda \times C$$
Solution:
$$C(z) = C_0 \times e^{-\lambda \times z}$$
Where:
- $C(z)$ = particle concentration at depth z (mg/L)
- $C_0$ = influent concentration (mg/L)
- $\lambda$ = filter coefficient (m⁻¹), typically 3-8 m⁻¹
- $z$ = depth through filter bed (m)
Overall removal efficiency:
$$\eta = 1 - \frac{C_effluent}{C_influent} = 1 - e^{-\lambda \times L}$$
Where $L$ = total media depth (m)
Filter Coefficient (Yao Model)
$$\lambda = \frac{3(1-\epsilon)}{2 d_c} \times \eta_0$$
Where:
- $\epsilon$ = porosity (0.4-0.45 for sand)
- $d_c$ = collector (media grain) diameter (m)
- $\eta_0$ = single collector efficiency
Single collector efficiency:
$$\eta_0 = \eta_{diffusion} + \eta_{interception} + \eta_{sedimentation}$$
Simplified for rapid sand filters:
$$\eta_0 \approx 0.9 \times \left(\frac{d_p}{d_c}\right)^{1.5} \times Re^{-0.4}$$
Where:
- $d_p$ = particle diameter (m)
- $Re$ = Reynolds number = $\frac{v \times d_c}{\nu}$
- $v$ = filtration velocity (m/s)
- $\nu$ = kinematic viscosity (m²/s)
Headloss Development - Carmen-Kozeny
Clean bed headloss:
$$h_0 = f \times \frac{L}{d_c} \times \frac{(1-\epsilon)^2}{\epsilon^3} \times \frac{v^2}{2g}$$
Where $f$ = friction factor ≈ 150/Re
Headloss increase with loading:
$$h(t) = h_0 + k_{buildup} \times \sigma(t)$$
Where:
- $\sigma(t)$ = specific deposit (volume solids per volume media)
- $k_{buildup}$ = empirical coefficient (typically 1000-5000)
Specific deposit:
$$\frac{d\sigma}{dt} = \frac{C_{in} \times v \times \eta}{L \times \rho_s}$$
Backwash Requirements
Minimum fluidization velocity:
$$v_{mf} = \frac{g \times d_c^2 \times (\rho_s - \rho_w)}{1650 \times \mu}$$
For sand ($\rho_s$ = 2650 kg/m³, $d_c$ = 0.7 mm) @ 15°C:
$$v_{mf} \approx 0.6-0.8 \text{ m/min} = 36-48 \text{ m/h}$$
Design backwash rate: 1.2-1.5 × $v_{mf}$ = 50-70 m/h
Backwash water volume:
$$V_{BW} = A \times v_{BW} \times t_{BW}$$
Typical: 3-5% of filtered water
Design Parameters
Input Parameters
| Parameter | Symbol | Unit | Range | Default | Description |
|---|---|---|---|---|---|
| Filtration rate | $v$ | m/h | 5-15 | 10 | Design filtration velocity |
| Media depth | $L$ | m | 0.6-1.2 | 0.9 | Sand bed depth |
| Media size (d10) | $d_c$ | mm | 0.4-1.0 | 0.5 | Effective size |
| Uniformity coefficient | UC | - | 1.3-1.7 | 1.5 | d60/d10 |
| Bed porosity | $\epsilon$ | - | 0.38-0.45 | 0.42 | Void fraction |
| Influent TSS | $C_0$ | mg/L | 5-30 | 15 | Secondary effluent quality |
| Target effluent TSS | $C_e$ | mg/L | 2-5 | 3 | Design goal |
| Filter run time | $t_{run}$ | h | 24-72 | 48 | Time between backwashes |
| Terminal headloss | $h_{max}$ | m | 2.0-3.0 | 2.5 | Backwash trigger |
| Backwash rate | $v_{BW}$ | m/h | 40-70 | 55 | Fluidization velocity |
| Backwash duration | $t_{BW}$ | min | 8-15 | 10 | Cleaning time |
Output Parameters
| Parameter | Unit | Description |
|---|---|---|
| Filter area | m² | Required filtration area |
| Number of cells | - | Parallel filter cells |
| Filter coefficient λ | m⁻¹ | Iwasaki removal parameter |
| Clean bed headloss | m | Initial pressure drop |
| Headloss @ 24h | m | Predicted headloss buildup |
| Backwash frequency | h | Time between backwashes |
| Backwash water % | % | Percentage of production |
| Annual backwash vol | m³/year | Total wash water required |
Configuration Guide
Step-by-Step Setup
Determine Filtration Rate
Selection depends on application:
Tertiary TSS removal only: 10-15 m/h (aggressive) With chemical coagulation: 8-12 m/h (moderate) Biological nitrification: 5-8 m/h (conservative, long contact time) Cryptosporidium removal: 5-7 m/h (conservative, deep bed)Calculate Required Area
$$A = \frac{Q_{avg}}{v \times n_{operating}}$$
Where $n_{operating}$ = fraction of cells online (account for backwash)
Example: Q = 10,000 m³/d = 417 m³/h v = 10 m/h n_operating = 0.90 (10% offline for backwash at any time) A = 417 / (10 × 0.90) = 46.3 m²Select Number and Size of Cells
Minimize cells for capital cost, but ensure:
- Minimum 4 cells (allow one offline for backwash)
- Maximum cell size: 50-100 m² (manageable backwash)
A_total = 46.3 m² → Use 4 cells × 12.5 m² each = 50 m² Cell dimensions: 3.5m × 3.5m eachDesign Media Specification
Sand specification:
- Effective size (d10): 0.5-0.7 mm
- Uniformity coefficient: <1.6 (well-graded)
- Depth: 0.9-1.2 m
- Silica content: >95%
- Acid solubility: <5%
Gravel support layers (if using):
- Layer 1 (bottom): 25-50 mm, 100 mm deep
- Layer 2: 12-25 mm, 75 mm deep
- Layer 3: 6-12 mm, 75 mm deep
- Layer 4 (top): 3-6 mm, 50 mm deep
- Total gravel: 300 mm
Design Underdrain System
Options:
- Nozzle type (plastic filter nozzles)
- Pipe lateral type (perforated pipes in gravel)
- Block type (proprietary plastic blocks)
Criteria:
- Backwash distribution uniformity: ±10%
- No media passage through nozzles
- Minimal headloss (<0.2 m)
Calculate Backwash Requirements
Backwash rate: v_BW = 55 m/h = 0.917 m/min Duration: t_BW = 10 minutes Cell area: A_cell = 12.5 m² Backwash volume per cycle = 0.917 × 10 × 12.5 = 114.6 m³ Filter run time = 48 hours Backwashes per day = 4 cells / 48 h × 24 h = 2 backwashes/day Daily backwash volume = 2 × 114.6 = 229.2 m³/day Backwash as % of production = 229.2 / 10,000 = 2.3% ✓Air Scour (Optional but Recommended)
Air scour before water backwash improves cleaning:
- Air rate: 0.6-1.0 m/min (36-60 m/h)
- Duration: 2-5 minutes
- Then water backwash (possibly concurrent for 1-2 min)
Surface Wash (Optional)
Rotating arms with high-pressure jets:
- Pressure: 200-400 kPa
- Flow: 10-20 m³/h per unit
- Concurrent with backwash
Typical Design Values
| Application | Filtration Rate (m/h) | Media Depth (m) | Effluent TSS (mg/L) | Run Time (h) | Backwash % |
|---|---|---|---|---|---|
| Tertiary polishing | 10-12 | 0.9 | 3-5 | 48-72 | 2-3% |
| With coagulant | 8-10 | 1.0 | 2-3 | 24-48 | 3-4% |
| Biological nitrification | 5-7 | 1.2 | 3-5 | 72+ | 1-2% |
| Giardia/Crypto removal | 5-7 | 1.0-1.2 | <2 | 48-72 | 2-3% |
| Water reuse (potable) | 5-8 | 1.2 | <2 | 48-72 | 2-4% |
Performance Criteria
TSS Removal Efficiency
| Influent TSS (mg/L) | Filtration Rate (m/h) | Media Depth (m) | Expected Effluent TSS (mg/L) |
|---|---|---|---|
| 10-15 | 10 | 0.9 | 2-4 |
| 15-20 | 10 | 0.9 | 3-5 |
| 20-30 | 8 | 1.0 | 4-6 |
| 10-15 (with coag) | 10 | 1.0 | 1-2 |
| 15-20 (with coag) | 10 | 1.0 | 2-3 |
Pathogen Removal
Without chemical coagulation:
- Giardia: 1.5-2.0 log removal
- Cryptosporidium: 1.0-1.5 log removal
- Viruses: 0.5-1.0 log removal
With coagulation (ferric or alum):
- Giardia: 2.5-3.5 log removal
- Cryptosporidium: 2.0-3.0 log removal
- Viruses: 1.5-2.5 log removal
Turbidity Reduction
Critical for downstream UV disinfection:
- Influent: 2-5 NTU (secondary effluent)
- Effluent: 0.5-1.0 NTU (without coagulant)
- Effluent: 0.1-0.3 NTU (with coagulant)
Troubleshooting
| Issue | Cause | Solution |
|---|---|---|
| High effluent TSS (breakthrough) | Filtration rate too high | Reduce rate, add cells |
| Media too coarse | Replace with finer sand | |
| Filter run too long | Reduce run time, backwash sooner | |
| Insufficient media depth | Add media to 1.0-1.2m | |
| Rapid headloss buildup | High influent TSS | Improve secondary treatment |
| Mudballing (consolidated solids) | Increase backwash intensity, air scour | |
| Biological growth | Chlorinate filter, increase backwash | |
| Coagulant overdose | Reduce chemical dose | |
| Poor backwash (media not clean) | Insufficient fluidization | Increase backwash rate |
| No air scour | Install air scour system | |
| Water temperature low (high viscosity) | Adjust for temperature, longer backwash | |
| Media graded (fine on top) | Fluidize more vigorously to remix | |
| Media loss during backwash | Backwash rate too high | Reduce to proper v_mf |
| Inadequate freeboard | Increase freeboard or add wash troughs | |
| Channeling/short-circuiting | Uneven backwash distribution | Repair underdrain, check nozzles |
| Media consolidated | Break up mudball, air scour | |
| Low filter run time (<24h) | Very high influent TSS | Pre-treatment or coagulation |
| Biological fouling | Chlorinate periodically | |
| Negative head in filter | Terminal headloss too high | Backwash before negative head develops |
| Filter rate too high | Reduce rate |
Operation & Maintenance
Daily Checks
- Monitor effluent turbidity/TSS online
- Record headloss for each filter cell
- Observe backwash cycles (visual inspection)
- Verify influent TSS quality
- Check filter run time since last backwash
- Inspect for media loss or uneven bed surface
Weekly Maintenance
- Measure effluent TSS (lab confirmation)
- Inspect underdrains during backwash
- Check backwash rate (flow meter)
- Verify air scour operation (if equipped)
- Clean filter galleries and channels
- Review headloss development curves
Monthly Tasks
- Measure media depth in each cell
- Check for mudballing (core sample if suspected)
- Inspect valves and actuators
- Calibrate online turbidity meters
- Review backwash water usage trends
- Verify chemical dosing (if coagulant used)
Annual Tasks
- Drain filter and inspect media condition
- Replace media if degraded or lost
- Inspect and repair underdrain system
- Check for structural cracks
- Full media analysis (effective size, UC, acid solubility)
- Review performance vs. design
- Optimize backwash strategy
Advanced Features
Variable Declining Rate Filtration
Filters operate at variable rate based on headloss:
- No rate control valves (gravity flow)
- Clean filters accept higher flow
- Dirty filters slow down naturally
- Equalizes run time across cells
- Reduces operational complexity
Biological Filtration (Nitrifying Filters)
Filters can nitrify if operated at low rate with long contact time:
$$r_{nitrification} = k_{nitr} \times X_{biofilm} \times \frac{NH_4}{K_{NH4} + NH_4} \times \frac{DO}{K_O + DO}$$
- Requires DO >2 mg/L in influent
- Filtration rate: 2-5 m/h (long HRT)
- Periodic backwash removes excess biofilm
- Achieves NH₄-N <1 mg/L from 3-5 mg/L
Filter-to-Waste
Initial filtrate after backwash contains:
- Fines from media degradation
- Residual backwash water
- Higher turbidity than steady-state
Solution: Waste first 5-10 minutes of filtrate to drain
Online Monitoring and Automation
- Turbidity meters (influent and effluent per cell)
- Headloss transmitters (trigger backwash at setpoint)
- Automated backwash sequence (PLC-controlled)
- Filter run time optimization (machine learning)
Worked Example
Given
- Flow: 12,000 m³/d (average), 18,000 m³/d (peak)
- Influent TSS: 12 mg/L (secondary effluent)
- Target effluent: ❤️ mg/L TSS, <0.5 NTU
- Application: Tertiary polishing before UV disinfection
Solution
Step 1: Select Filtration Rate
For TSS polishing without coagulant: v = 10 m/hStep 2: Calculate Area
Account for 10% offline for backwash:
A = Q_avg / (v × 0.90) = (12,000/24) / (10 × 0.90) = 500 / 9 = 55.6 m²Step 3: Select Configuration
Use 6 cells × 10 m² each = 60 m²
Cell size: 3.16m × 3.16m (use 3.2m × 3.2m = 10.24 m²)
Total area: 61.4 m²Step 4: Verify Peak Conditions
At peak flow, maximum 1 cell offline:
Q_peak = 18,000 m³/d = 750 m³/h
Cells operating = 5
Area per cell = 10.24 m²
v_peak = 750 / (5 × 10.24) = 14.6 m/h
(Acceptable for short-duration peak)Step 5: Design Media
Sand specification:
- Effective size: 0.6 mm
- Uniformity coefficient: 1.5
- Depth: 1.0 m
- Gravel support: 300 mm (nozzle floor, skip gravel)Step 6: Predict Performance (Iwasaki)
Assume λ = 4 m⁻¹ (typical for 0.6mm sand @ v=10 m/h)
L = 1.0 m
η = 1 - exp(-4 × 1.0) = 1 - 0.0183 = 0.982 = 98.2%
C_effluent = C_influent × (1 - η) = 12 × 0.018 = 0.22 mg/L ✓
(Excellent, target was <3 mg/L)Step 7: Backwash Design
Backwash rate: 55 m/h (1.2 × v_mf for 0.6mm sand)
Duration: 10 minutes
Air scour: 1.0 m/min for 3 minutes before water
Backwash volume per cell = (55/60) × 10 × 10.24 = 94.0 m³
Filter run time (assume): 48 hours
Backwashes per day = 6 cells / 48 h × 24 h = 3 backwashes/day
Daily backwash = 3 × 94.0 = 282 m³/day
Backwash % = 282 / 12,000 = 2.35% ✓Step 8: Headloss Prediction
Clean bed headloss (Carmen-Kozeny):
h_0 ≈ 0.15 m (typical for v=10 m/h, L=1.0m, d=0.6mm)
Headloss after 24h (empirical):
h_24 ≈ 0.15 + 0.8 = 0.95 m
Headloss after 48h:
h_48 ≈ 0.15 + 1.5 = 1.65 m ✓ (well below 2.5m terminal limit)Related Units
- Disk-Filter - Alternative cloth media
- GAC-Filter - Activated carbon for organics
- Dual-Media-Filter - Anthracite + sand
- UV-Disinfection - Downstream disinfection
- Chemical-Dosing - Coagulation upstream
References
- Iwasaki, T. (1937). "Some Notes on Sand Filtration." J. AWWA 29(10): 1591-1602.
- Yao, K.M., Habibian, M.T., and O'Melia, C.R. (1971). "Water and Waste Water Filtration: Concepts and Applications." Environ. Sci. Technol. 5(11): 1105-1112.
- WEF (2018). Design of Municipal Wastewater Treatment Plants, MOP 8, 6th Ed., Ch. 16.
- Metcalf & Eddy (2014). Wastewater Engineering, 5th Ed., pp. 1242-1290.
- Crittenden, J.C. et al. (2012). MWH's Water Treatment: Principles and Design, 3rd Ed., Wiley.
- Kawamura, S. (2000). Integrated Design and Operation of Water Treatment Facilities, 2nd Ed., Wiley.
- AWWA (2011). Water Quality and Treatment: A Handbook on Drinking Water, 6th Ed., McGraw-Hill.