Appearance
Anthracite Filter
Single-media depth filtration using crushed anthracite coal (0.9-1.1 mm effective size) with higher void ratio and coarser grains than sand, enabling deeper solids penetration and longer filter runs.
Overview
Anthracite filters use crushed and graded anthracite coal as the filter media instead of silica sand. The key advantage is anthracite's lower density (1400-1700 kg/m³ vs. 2650 kg/m³ for sand) and coarser particle size, resulting in higher porosity (45% vs. 38-40% for sand) and deeper bed penetration of solids. This translates to longer filter runs and higher dirt-holding capacity.
When to Use
- High TSS loading requiring long filter runs
- Deeper bed filtration (1.2-2.0 m typical)
- Applications where backwash frequency must be minimized
- Retrofit of existing sand filters (deeper penetration, less headloss)
- Pre-filtration before dual-media or GAC filters
- High-rate tertiary treatment (12-20 m/h)
Key Characteristics
- TSS removal: 15-25 mg/L → 3-5 mg/L
- Filtration rate: 10-20 m/h (higher than sand)
- Filter run time: 48-120 hours (longer than sand)
- Media depth: 1.0-2.0 m (deeper than sand)
- Porosity: 0.45-0.50 (vs. 0.38-0.42 for sand)
- Effective size: 0.9-1.5 mm (coarser than sand)
- Lower headloss buildup rate
Operating Modes
Basic Mode
- Fixed filtration rate
- Constant removal efficiency
- Time-based backwash trigger
- Simple headloss calculation
Advanced Mode
- Iwasaki depth filtration model (same as sand)
- Dynamic filter coefficient λ(z,t) varying with depth
- Headloss prediction with larger particle correlation
- Backwash optimization
- Comparison with sand filter performance
Mathematical Model
Governing Equations
Anthracite filtration follows the same Iwasaki model as sand filters, but with different parameters due to larger grain size and higher porosity.
1. Iwasaki Filtration Equation
$$\frac{\partial C}{\partial z} = -\lambda \times C$$
Solution:
$$C(z) = C_0 \times e^{-\lambda \times z}$$
Overall removal:
$$\eta = 1 - e^{-\lambda \times L}$$
Key difference: Anthracite has lower λ (due to coarser grains), requiring deeper beds for equivalent removal:
- Sand (0.5 mm): λ ≈ 4-6 m⁻¹
- Anthracite (1.0 mm): λ ≈ 2-4 m⁻¹
2. Filter Coefficient (Yao Model)
$$\lambda = \frac{3(1-\epsilon)}{2 d_c} \times \eta_0$$
Where:
- $\epsilon$ = 0.45-0.50 for anthracite (higher than sand)
- $d_c$ = 0.9-1.5 mm for anthracite (larger than sand)
Result: Lower λ, requiring greater depth $L$ for same removal $\eta$.
3. Headloss - Carmen-Kozeny
Clean bed headloss:
$$h_0 = f \times \frac{L}{d_c} \times \frac{(1-\epsilon)^2}{\epsilon^3} \times \frac{v^2}{2g}$$
Comparison for same depth and velocity:
For sand: $d_c$ = 0.6 mm, $\epsilon$ = 0.40 $$\frac{(1-0.40)^2}{0.40^3} = \frac{0.36}{0.064} = 5.625$$
For anthracite: $d_c$ = 1.0 mm, $\epsilon$ = 0.47 $$\frac{(1-0.47)^2}{0.47^3} = \frac{0.281}{0.104} = 2.701$$
Anthracite has ~50% lower clean bed headloss than sand (for same depth/velocity).
Headloss buildup:
$$h(t) = h_0 + k_{buildup} \times \sigma(t)$$
Anthracite's higher porosity and coarser grains allow deeper penetration, so headloss builds up more slowly.
4. Backwash - Minimum Fluidization Velocity
$$v_{mf} = \frac{g \times d_c^2 \times (\rho_s - \rho_w)}{1650 \times \mu}$$
For anthracite ($\rho_s$ = 1500 kg/m³, $d_c$ = 1.0 mm) @ 15°C:
$$v_{mf} \approx 0.3-0.4 \text{ m/min} = 18-24 \text{ m/h}$$
Much lower than sand (36-48 m/h) due to lower density.
Design backwash rate: 1.3-1.5 × $v_{mf}$ = 25-35 m/h
Advantage: Lower backwash water consumption than sand.
Design Parameters
Input Parameters
| Parameter | Symbol | Unit | Range | Default | Description |
|---|---|---|---|---|---|
| Filtration rate | $v$ | m/h | 10-20 | 15 | Higher than sand |
| Media depth | $L$ | m | 1.0-2.0 | 1.5 | Deeper than sand |
| Media size (d10) | $d_c$ | mm | 0.9-1.5 | 1.0 | Effective size |
| Uniformity coefficient | UC | - | 1.3-1.6 | 1.4 | d60/d10 |
| Bed porosity | $\epsilon$ | - | 0.45-0.50 | 0.47 | Higher than sand |
| Influent TSS | $C_0$ | mg/L | 10-35 | 20 | Secondary effluent |
| Target effluent TSS | $C_e$ | mg/L | 3-6 | 4 | Design goal |
| Filter run time | $t_{run}$ | h | 48-120 | 72 | Longer than sand |
| Terminal headloss | $h_{max}$ | m | 2.0-3.0 | 2.5 | Backwash trigger |
| Backwash rate | $v_{BW}$ | m/h | 25-40 | 30 | Lower than sand |
| Backwash duration | $t_{BW}$ | min | 8-12 | 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 (lower than sand) |
| Clean bed headloss | m | Initial pressure drop (lower than sand) |
| Headloss @ 72h | m | Predicted headloss buildup |
| Backwash frequency | h | Time between backwashes (longer than sand) |
| Backwash water % | % | Percentage of production (lower than sand) |
| Annual anthracite cost | £/year | Replacement due to loss/degradation |
Configuration Guide
Step-by-Step Setup
Determine Filtration Rate
Anthracite can handle higher rates than sand:
Standard tertiary polishing: 12-18 m/h (vs. 10-12 for sand) High-rate operation: 15-20 m/h Conservative (long runs): 10-12 m/h With chemical coagulation: 10-15 m/hSelect Media Depth
Deeper than sand to compensate for lower λ:
For equivalent removal to 0.9m sand: Use 1.2-1.5m anthracite Standard depth: 1.5m High-rate, high-loading: 1.8-2.0mCalculate Required Area
$$A = \frac{Q_{avg}}{v \times n_{operating}}$$
Example: Q = 12,000 m³/d = 500 m³/h v = 15 m/h (high-rate) n_operating = 0.92 (8% offline, less frequent backwash) A = 500 / (15 × 0.92) = 36.2 m² Use 4 cells × 10 m² each = 40 m² (3.2m × 3.2m)Specify Anthracite Media
Specification:
- Source: Crushed anthracite coal
- Effective size (d10): 0.9-1.2 mm
- Uniformity coefficient: <1.5 (well-graded)
- Depth: 1.5 m
- Hardness: Moh's 2.0-2.8 (softer than sand, some attrition)
- Acid solubility: <5%
- Bulk density: 800-900 kg/m³ (dry)
Gravel support (if not using nozzle floor):
- Same as sand filter (300 mm total)
Design Backwash System
Lower backwash rates than sand:
Backwash rate: v_BW = 30 m/h = 0.5 m/min Duration: t_BW = 10 minutes Cell area: A_cell = 10 m² Backwash volume per cycle = 0.5 × 10 × 10 = 50 m³ Filter run time = 72 hours Backwashes per day = 4 cells / 72 h × 24 h = 1.33 backwashes/day Daily backwash volume = 1.33 × 50 = 66.5 m³/day Backwash % = 66.5 / 12,000 = 0.55% ✓ (very low!)Air Scour
Highly recommended for anthracite:
- Air rate: 0.6-1.0 m/min (same as sand)
- Duration: 3-5 minutes before water backwash
- Prevents media compaction
- Reduces attrition losses
Typical Design Values
| Application | Filtration Rate (m/h) | Media Depth (m) | Effluent TSS (mg/L) | Run Time (h) | Backwash % |
|---|---|---|---|---|---|
| Standard tertiary | 15 | 1.5 | 3-5 | 72 | 0.5-1.0% |
| High-rate polishing | 18 | 1.8 | 4-6 | 48 | 0.8-1.2% |
| With coagulant | 12 | 1.5 | 2-4 | 72 | 0.6-1.0% |
| Low-rate (long runs) | 10 | 2.0 | 3-5 | 96+ | 0.3-0.6% |
Performance Criteria
TSS Removal Efficiency
| Influent TSS (mg/L) | Filtration Rate (m/h) | Media Depth (m) | Expected Effluent TSS (mg/L) |
|---|---|---|---|
| 15-20 | 15 | 1.5 | 3-5 |
| 20-25 | 15 | 1.5 | 4-6 |
| 25-35 | 12 | 1.8 | 5-7 |
| 15-20 (with coag) | 12 | 1.5 | 2-3 |
Note: Slightly lower removal efficiency than sand at same depth, but compensated by using deeper beds and handling higher loading.
Headloss Development
Anthracite advantage: Slower headloss buildup
| Time (h) | Sand (0.9m @ 10 m/h) | Anthracite (1.5m @ 15 m/h) |
|---|---|---|
| 0 (clean) | 0.15 m | 0.15 m |
| 24 | 0.95 m | 0.50 m |
| 48 | 1.65 m | 0.90 m |
| 72 | 2.35 m (backwash!) | 1.40 m |
| 96 | - | 1.95 m |
Filter Run Comparison
For same TSS loading:
- Sand filter: 24-48 hour runs
- Anthracite filter: 48-120 hour runs (2-3× longer)
Troubleshooting
| Issue | Cause | Solution |
|---|---|---|
| High effluent TSS | Insufficient media depth | Increase to 1.8-2.0m |
| Filtration rate too high | Reduce to 12-15 m/h | |
| Media too coarse | Replace with finer anthracite (0.9mm) | |
| Short-circuiting | Check flow distribution | |
| Rapid headloss buildup | High influent TSS | Pre-treatment or reduce rate |
| Media grading (fine on top) | Vigorous backwash to remix | |
| Biological growth | Chlorinate periodically | |
| Media loss during backwash | Backwash rate too high | Reduce to 25-30 m/h |
| Attrition (media breakdown) | Replace with harder anthracite | |
| Inadequate freeboard | Increase or add wash troughs | |
| Poor backwash efficiency | Insufficient fluidization | Increase backwash rate to 35-40 m/h |
| No air scour | Install air scour system | |
| Media compacted | Break up with vigorous air scour | |
| Media compaction | Insufficient backwash | Increase rate or add air scour |
| Low-density fines on top | Surface wash or air scour | |
| Channeling | Uneven backwash | Repair underdrain distribution |
| Consolidated media | Air scour to break up |
Operation & Maintenance
Daily Checks
- Monitor effluent turbidity/TSS
- Record headloss for each cell
- Observe filter run time (should be longer than sand)
- Verify filtration rate
- Inspect for media loss
Weekly Maintenance
- Lab TSS measurement
- Inspect backwash operation
- Check for media compaction
- Measure media depth
- Review headloss development (compare to sand baseline)
Monthly Tasks
- Check for media loss or attrition
- Inspect underdrain
- Verify air scour operation
- Calibrate online instruments
- Assess media grading (core sample)
Annual Tasks
- Drain and inspect media condition
- Measure effective size and UC (sieve analysis)
- Replace lost or degraded media
- Inspect underdrain and repair
- Performance review vs. design
- Consider switch to dual-media if upgrading
Media Replacement
Anthracite degradation:
- Attrition: 3-5% loss per year (softer than sand)
- Top-up required annually
- Complete replacement: 8-12 years (vs. 10-15 for sand)
Cost: £300-600/tonne (vs. £50-150/tonne for sand)
Advanced Features
Biological Filtration
Anthracite's high porosity supports biofilm growth:
- Nitrification at low rates (5-8 m/h)
- Longer contact time than sand for same depth
- Higher biofilm attachment surface area
- Requires DO >2 mg/L, no residual chlorine
Variable Declining Rate (VDR)
Ideal for anthracite due to long runs:
- Filters self-adjust flow based on headloss
- Clean filters accept higher rates
- Dirty filters slow down
- Equalizes run time across cells
- Simplifies operation (no rate control valves)
Comparison to Sand
| Parameter | Sand Filter | Anthracite Filter |
|---|---|---|
| Effective size | 0.5-0.7 mm | 0.9-1.2 mm |
| Porosity | 38-42% | 45-50% |
| Density | 2650 kg/m³ | 1500 kg/m³ |
| Typical depth | 0.9-1.2 m | 1.5-2.0 m |
| Filtration rate | 8-12 m/h | 12-18 m/h |
| Clean bed headloss | Higher | Lower (50% less) |
| Filter run time | 24-48 h | 48-120 h |
| Backwash rate | 50-70 m/h | 25-40 m/h |
| Backwash water | 2-3% | 0.5-1.5% |
| Media cost | £50-150/tonne | £300-600/tonne |
| Media life | 10-15 years | 8-12 years |
When to choose anthracite over sand:
- Minimize backwash frequency and water use
- High TSS loading
- Space for deeper beds available
- Willing to pay higher media cost for lower operating cost
Pre-Treatment for Dual-Media
Anthracite layer on top of sand creates dual-media filter:
- Anthracite (coarse): Pre-filtration, remove bulk TSS
- Sand (fine): Polishing, final removal
- Combined benefits (see Dual-Media-Filter)
Worked Example
Given
- Flow: 18,000 m³/d (average), 27,000 m³/d (peak)
- Influent TSS: 22 mg/L (secondary effluent, higher loading)
- Target effluent: <5 mg/L TSS
- Application: High-rate tertiary treatment with infrequent backwash
Solution
Step 1: Select Filtration Rate
High-rate anthracite application: v = 15 m/hStep 2: Calculate Area
Q_avg = 18,000 m³/d = 750 m³/h
Account for 8% offline (long runs): n_operating = 0.92
A = Q_avg / (v × n_operating) = 750 / (15 × 0.92) = 54.3 m²
Use 6 cells × 10 m² each = 60 m² (3.2m × 3.2m cells)Step 3: Select Media Depth
For high loading and good removal: L = 1.8 mStep 4: Verify Peak Conditions
Q_peak = 27,000 m³/d = 1,125 m³/h
With 1 cell offline: 5 cells operating
v_peak = 1,125 / (5 × 10) = 22.5 m/h
(High but acceptable for short peak with anthracite)Step 5: Predict Performance
Anthracite λ ≈ 3 m⁻¹ (for 1.0mm @ 15 m/h)
L = 1.8 m
η = 1 - exp(-3 × 1.8) = 1 - exp(-5.4) = 1 - 0.0045 = 0.9955 = 99.55%
(This is too optimistic; real-world η ≈ 75-80% for anthracite)
Using empirical: C_effluent ≈ 22 × 0.22 = 4.8 mg/L ✓Step 6: Backwash Design
Backwash rate: 30 m/h = 0.5 m/min
Duration: 10 minutes
Air scour: 1.0 m/min for 3 minutes
Backwash volume per cell = 0.5 × 10 × 10 = 50 m³
Filter run time: 72 hours
Backwashes per day = 6 cells / 72 h × 24 h = 2 backwashes/day
Daily backwash = 2 × 50 = 100 m³/day
Backwash % = 100 / 18,000 = 0.56% ✓ (excellent!)Step 7: Media Quantity and Cost
Media volume per cell = 10 m² × 1.8 m = 18 m³
Total volume = 6 × 18 = 108 m³
Bulk density (dry): 850 kg/m³
Media mass = 108 m³ × 850 kg/m³ = 91,800 kg = 91.8 tonnes
Media cost (virgin): £450/tonne
Initial cost = 91.8 × £450 = £41,310
Annual replacement (5% attrition):
Annual cost = 91.8 × 0.05 × £450 = £2,066/year
Specific cost = £2,066 / (18,000 × 365) = £0.00031/m³ (negligible)Step 8: Headloss Prediction
Clean bed (empirical for anthracite): h_0 ≈ 0.20 m @ 15 m/h, 1.8m depth
After 72h with 22 mg/L TSS:
h_72 ≈ 0.20 + 1.4 = 1.6 m ✓ (well below 2.5m limit)
Sand equivalent would be ~2.3m after 72h (closer to backwash trigger)Related Units
- Rapid-Sand-Filter - Alternative single media
- Dual-Media-Filter - Anthracite + sand combination
- GAC-Filter - Activated carbon (similar coarse grains)
- Pile-Cloth-Filter - Cloth media alternative
- UV-Disinfection - Downstream disinfection
References
- Cleasby, J.L. and Logsdon, G.S. (1999). "Granular Bed and Precoat Filtration." Water Quality and Treatment, AWWA, 5th Ed., McGraw-Hill, Ch. 8.
- Kawamura, S. (2000). Integrated Design and Operation of Water Treatment Facilities, 2nd Ed., Wiley, pp. 251-298.
- WEF (2018). Design of Municipal Wastewater Treatment Plants, MOP 8, 6th Ed., Ch. 16.
- Metcalf & Eddy (2014). Wastewater Engineering, 5th Ed., pp. 1242-1290.
- Adin, A. and Rajagopalan, R. (1989). "Breakthrough Curves for Removal of Suspended Solids in Deep Bed Filters." Water Research 23(1): 73-79.