Appearance
Nanofiltration (NF)
Pressure-driven membrane separation between UF and RO using charged membranes (MWCO 200-1000 Da) for selective rejection of divalent ions, hardness, color, and organic micropollutants at 5-20 bar operating pressure.
Overview
Nanofiltration (NF) occupies the middle ground between ultrafiltration and reverse osmosis, offering selective removal of multivalent ions while allowing partial passage of monovalent salts. NF is characterized by both size exclusion (MWCO 200-1000 Da) and charge-based (Donnan) exclusion, making it ideal for water softening, color removal, and micropollutant removal at lower pressure than RO.
When to Use
- Water softening (Ca²⁺, Mg²⁺ removal: 85-98%)
- Micropollutant removal (pharmaceuticals, pesticides, endocrine disruptors)
- Color removal (humic and fulvic acids: 90-99%)
- Sulfate removal (mining, industrial wastewater)
- Partial desalination (brackish water, lower pressure than RO)
- TOC reduction for water reuse
- Pretreatment for RO (reduce scaling potential)
- Drinking water treatment (taste, odor, organics)
Key Characteristics
- MWCO: 200-1000 Da (typically 300-400 Da)
- Equivalent pore size: 0.5-2 nm (0.001-0.002 μm)
- Operating pressure: 5-20 bar (70-300 psi)
- Permeate flux: 15-50 LMH for wastewater
- Recovery: 70-85% (typical), up to 90% for low-scaling feeds
- Divalent ion rejection: 85-99% (Ca²⁺, Mg²⁺, SO₄²⁻)
- Monovalent ion rejection: 20-80% (Na⁺, Cl⁻)
- Organic molecule (>300 Da) rejection: 90-99%
- Color removal: 90-99%
- TDS rejection: 40-80% (partial desalination)
Operating Modes
Basic Mode
- Constant pressure operation
- Fixed flux (determined by feed TDS and fouling)
- Simple solution-diffusion model
- Default rejection coefficients
- Concentrate disposal to drain
Advanced Mode
- Solution-diffusion-electromigration model
- Donnan exclusion calculation (charge effects)
- Concentration polarization correction
- Scaling prediction (LSI, SDI for CaSO₄, CaCO₃, BaSO₄)
- Antiscalant dosing optimization
- Energy recovery device (ERD) simulation
- Concentrate minimization (high recovery operation)
Mathematical Model
Solution-Diffusion Model
Water flux:
$$J_w = A \times (\Delta P - \sigma \times \Delta \pi)$$
Where:
- $J_w$ = water flux (L/m²·h or m/s)
- $A$ = water permeability coefficient (L/m²·h·bar or m/s·Pa)
- $\Delta P$ = transmembrane pressure (bar)
- $\sigma$ = reflection coefficient (0.8-0.95 for NF, between UF and RO)
- $\Delta \pi$ = osmotic pressure difference (bar)
Solute flux:
$$J_s = B \times \Delta C$$
Where:
- $J_s$ = solute flux (mol/m²·s)
- $B$ = solute permeability coefficient (m/s)
- $\Delta C$ = concentration difference across membrane (mol/m³)
Osmotic Pressure
Van't Hoff equation:
$$\pi = i \times M \times R \times T$$
Where:
- $i$ = van't Hoff factor (dissociation factor)
- $M$ = molar concentration (mol/L)
- $R$ = gas constant (0.08314 L·bar/mol·K)
- $T$ = temperature (K)
Approximation for TDS:
$$\pi [bar] \approx 0.00075 \times TDS [mg/L]$$
Example:
TDS = 1,000 mg/L → π ≈ 0.75 bar
TDS = 5,000 mg/L → π ≈ 3.75 barNet driving pressure for NF:
$$\Delta P_{net} = \Delta P_{applied} - (\pi_{feed} - \pi_{permeate})$$
Rejection Coefficient
$$R = 1 - \frac{C_p}{C_f}$$
Where:
- $C_p$ = permeate concentration
- $C_f$ = feed concentration (bulk)
Observed rejection (accounting for concentration polarization):
$$R_{obs} = \frac{R_{real}}{R_{real} + (1 - R_{real}) \times \exp(-J_w / k)}$$
Where $k$ = mass transfer coefficient
Donnan Exclusion (Charge Effects)
NF membranes carry surface charge (typically negative):
For divalent cations (Ca²⁺, Mg²⁺):
- Strong electrostatic repulsion
- Rejection: 85-98%
For divalent anions (SO₄²⁻):
- Strong electrostatic repulsion (co-ion exclusion)
- Rejection: 95-99%
For monovalent ions (Na⁺, Cl⁻):
- Weak rejection (size only, minimal charge effect)
- Rejection: 20-70%
Rejection hierarchy:
$$R_{SO_4^{2-}} > R_{Ca^{2+}} > R_{Mg^{2+}} > R_{Cl^-} > R_{Na^+}$$
Concentration Polarization
Solute accumulation at membrane surface:
$$\frac{C_{wall}}{C_{bulk}} = \exp\left(\frac{J_w}{k}\right)$$
Where $k$ = mass transfer coefficient (1-5 × 10⁻⁵ m/s for NF)
Effect:
- Increases local osmotic pressure
- Reduces flux by 10-30%
- Promotes scaling
Mitigation:
- Crossflow velocity (reduce $C_{wall}$)
- Turbulence promoters (spacers)
- Lower flux operation
Scaling Prediction
Saturation index:
$$SI = \frac{IP}{K_{sp}}$$
Where:
- $IP$ = ion product (measured concentrations)
- $K_{sp}$ = solubility product
Common scalants in NF:
Calcium carbonate (CaCO₃):
- $K_{sp}$ = 3.3 × 10⁻⁹ (25°C)
- Langelier Saturation Index (LSI) for prediction
- Control: pH adjustment, antiscalant
Calcium sulfate (CaSO₄):
- $K_{sp}$ = 2.4 × 10⁻⁵ (25°C)
- Critical in concentrate stream
- Recovery limit often set by CaSO₄
Barium sulfate (BaSO₄):
- $K_{sp}$ = 1.1 × 10⁻¹⁰ (very low, highly insoluble)
- Forms even at low concentrations
- Difficult to remove once formed
Recovery limit:
$$Recovery_{max} = 1 - \frac{K_{sp}}{IP_{feed} \times SF}$$
Where $SF$ = safety factor (typically 0.8)
Design Parameters
Input Parameters
| Parameter | Symbol | Unit | Range | Default | Description |
|---|---|---|---|---|---|
| MWCO | - | Da | 200-1000 | 400 | Molecular weight cut-off |
| Operating pressure | $\Delta P$ | bar | 5-20 | 10 | Applied pressure |
| Temperature | $T$ | °C | 10-30 | 20 | Feed water temperature |
| Design flux | $J_w$ | LMH | 15-50 | 30 | Permeate flux |
| Recovery | $Y$ | % | 60-90 | 75 | Water recovery ratio |
| Feed TDS | - | mg/L | 200-5000 | 1000 | Total dissolved solids |
| Feed hardness (CaCO₃) | - | mg/L | 50-500 | 200 | Calcium + magnesium |
| Feed sulfate (SO₄²⁻) | - | mg/L | 10-300 | 100 | Sulfate concentration |
| Feed pH | - | - | 5-9 | 7.5 | Feed water pH |
| Feed TOC | - | mg/L | 2-20 | 5 | Total organic carbon |
| Antiscalant dose | - | mg/L | 2-10 | 5 | Scaling inhibitor |
Output Parameters
| Parameter | Unit | Description |
|---|---|---|
| Membrane area | m² | Required membrane surface area |
| Number of elements | - | 8"×40" spiral-wound elements |
| Permeate TDS | mg/L | Product water TDS |
| Permeate hardness | mg/L | Residual hardness (as CaCO₃) |
| Concentrate TDS | mg/L | Reject stream TDS |
| Osmotic pressure (feed) | bar | π of feed stream |
| Osmotic pressure (conc) | bar | π of concentrate |
| Net driving pressure | bar | ΔP - Δπ |
| Scaling potential | - | Saturation indices |
| Energy consumption | kWh/m³ | Specific energy (with ERD) |
| Antiscalant cost | $/year | Chemical cost |
Configuration Guide
Step-by-Step Setup
Water Quality Analysis
Determine if NF is appropriate:
NF suitable for: - Hardness removal: 100-400 mg/L as CaCO₃ - Moderate TDS: 500-3,000 mg/L - Color removal: Humic/fulvic acids present - Micropollutant removal: Pharmaceuticals, pesticides (MW >300 Da) NOT suitable for: - Low TDS (<300 mg/L): UF more economical - High TDS (>5,000 mg/L): RO required - Virus barrier only: UF sufficientSelect Operating Pressure
Based on feed TDS and target recovery:
TDS 500-1,000 mg/L, Recovery 75%: ΔP = 8-12 bar TDS 1,000-2,000 mg/L, Recovery 75%: ΔP = 10-15 bar TDS 2,000-5,000 mg/L, Recovery 75%: ΔP = 15-20 bar Higher recovery requires higher pressure (overcome concentrate π)Estimate Permeate Flux
Manufacturer's data, but typical:
J_w = A × (ΔP - σ × Δπ) For NF (MWCO 400 Da): A ≈ 3-5 LMH/bar σ ≈ 0.85 Example: ΔP = 12 bar π_feed = 0.75 bar (TDS 1,000 mg/L) π_permeate ≈ 0 bar (low TDS) J_w = 4 × (12 - 0.85 × 0.75) = 4 × 11.36 = 45.4 LMH Use conservative J = 30 LMH for design (fouling margin)Calculate Membrane Area
$$A = \frac{Q_{permeate}}{J}$$
Q = 2,000 m³/d = 83.3 m³/h J = 30 LMH A = 83.3 × 1000 / 30 = 2,777 m²Select Membrane Elements
Standard 8" × 40" spiral-wound elements:
- Area per element: 37 m² (typical NF)
- Elements in series: 6-7 per pressure vessel
- Pressure vessels in parallel: Based on total elements
Total elements = 2,777 / 37 = 75 elements Configuration: 12 pressure vessels × 6 elements = 72 elements (2,664 m²) Actual flux = 83.3 × 1000 / 2,664 = 31.3 LMH ✓Check Scaling Potential
Concentrate stream composition:
$$C_{concentrate} = \frac{C_{feed}}{1 - Recovery}$$
Recovery = 75% = 0.75 Feed hardness = 200 mg/L as CaCO₃ Feed SO₄²⁻ = 100 mg/L Concentrate hardness = 200 / (1 - 0.75) = 800 mg/L Concentrate SO₄²⁻ = 100 / (1 - 0.75) = 400 mg/LCaSO₄ saturation check:
Assume 50% of hardness is Ca²⁺:
- Concentrate Ca²⁺ ≈ 400 mg/L as CaCO₃ = 160 mg/L as Ca
- Concentrate SO₄²⁻ = 400 mg/L
$IP_{CaSO_4} = [Ca^{2+}] \times [SO_4^{2-}]$ (molar units)
IP ≈ 1.2 × 10⁻⁴ (rough estimate) K_sp = 2.4 × 10⁻⁵ SI = IP / K_sp = 5 > 1 (SCALING RISK!)Solution: Add antiscalant or reduce recovery to 70%
Antiscalant Dosing
Typical antiscalant allows SI up to 2-3× without scaling:
Dose: 3-5 mg/L (feed stream) Daily consumption = Q_feed × Dose Q_feed = Q_permeate / Recovery = 2,000 / 0.75 = 2,667 m³/d Antiscalant = 2,667 × 4 × 10⁻³ = 10.7 kg/d Annual = 3,906 kg/year Cost @ $5/kg = $19,530/yearCalculate Energy Consumption
Without energy recovery:
Q_feed = 2,667 m³/d = 111 m³/h ΔP = 12 bar Power = (Q × ΔP) / η = (111 × 12 × 10⁵) / (0.75 × 3600) = 49.3 kW Daily energy = 49.3 × 24 = 1,183 kWh/d Specific energy = 1,183 / 2,000 = 0.59 kWh/m³With energy recovery device (ERD, 90% efficiency):
Q_concentrate = Q_feed - Q_permeate = 2,667 - 2,000 = 667 m³/d = 27.8 m³/h Recovered pressure ≈ 11 bar (concentrate pressure) Recovered power = 27.8 × 11 × 10⁵ × 0.90 / 3600 = 7.6 kW Net power = 49.3 - 7.6 = 41.7 kW Daily energy = 41.7 × 24 = 1,001 kWh/d Specific energy = 0.50 kWh/m³ (15% savings)
Typical Design Values
| Application | TDS (mg/L) | Pressure (bar) | Flux (LMH) | Recovery (%) | Energy (kWh/m³) |
|---|---|---|---|---|---|
| Water softening | 300-800 | 8-12 | 25-40 | 75-85 | 0.4-0.6 |
| Color removal | 500-1500 | 10-15 | 20-35 | 70-80 | 0.5-0.7 |
| Micropollutant removal | 400-1200 | 8-14 | 25-40 | 75-85 | 0.4-0.6 |
| Brackish water (partial desal) | 2000-5000 | 15-20 | 15-30 | 65-75 | 0.8-1.2 |
| RO pretreatment | 1000-3000 | 10-16 | 20-35 | 70-80 | 0.5-0.8 |
Performance Criteria
Rejection Characteristics
| Species | Typical Rejection | Mechanism |
|---|---|---|
| Ca²⁺, Mg²⁺ (hardness) | 85-98% | Charge + size |
| SO₄²⁻ | 95-99% | Strong charge repulsion |
| Na⁺ | 20-50% | Size only (small) |
| Cl⁻ | 30-70% | Size + weak charge |
| NO₃⁻ | 40-80% | Size |
| Organic (MW >400 Da) | 90-99% | Size exclusion |
| Color (humic acids) | 90-99% | Size + charge |
| Pesticides (MW 200-600 Da) | 70-95% | Size-dependent |
| Pharmaceuticals (MW 200-500 Da) | 60-95% | Compound-specific |
Comparison to RO
| Parameter | NF (400 Da) | RO (Brackish) | RO (Seawater) |
|---|---|---|---|
| MWCO | 200-1000 Da | <100 Da | <100 Da |
| Divalent rejection | 85-98% | 99-99.5% | 99.5-99.8% |
| Monovalent rejection | 20-70% | 95-99% | 99-99.7% |
| TDS rejection | 40-80% | 95-99% | 99-99.5% |
| Operating pressure | 5-20 bar | 10-25 bar | 55-70 bar |
| Flux | 20-40 LMH | 15-25 LMH | 10-15 LMH |
| Energy (w/ ERD) | 0.4-0.8 kWh/m³ | 0.8-1.5 kWh/m³ | 3-5 kWh/m³ |
| Scaling sensitivity | Moderate | High | Very high |
When to use NF vs. RO:
- NF: Softening, partial desalination, micropollutants, color (lower energy)
- RO: High TDS removal, desalination, water reuse requiring low TDS
Troubleshooting
| Issue | Cause | Solution |
|---|---|---|
| Rapid flux decline | Scaling (CaSO₄, CaCO₃, BaSO₄) | Increase antiscalant dose, reduce recovery, acid cleaning |
| Organic fouling | Chlorination (if compatible), caustic cleaning | |
| Colloidal fouling | Improve pretreatment (UF/MF, coagulation) | |
| Biological fouling | Chlorination, increase cleaning frequency | |
| High permeate TDS | Membrane degradation (chlorine attack) | Dechlorination of feed, replace elements |
| Low operating pressure | Increase ΔP to design value | |
| Temperature too high (increased B) | Cool feed or accept higher TDS | |
| Low permeate hardness (>target) | Insufficient rejection | Use tighter membrane (lower MWCO) |
| Membrane aging | Performance test, replace if needed | |
| Scaling observed | Antiscalant underdose | Increase dose, check injection point |
| Recovery too high | Reduce recovery by 5-10% | |
| pH too high (CaCO₃) | Lower pH to 6.5-7.0 with acid | |
| High differential pressure | Fouling in lead elements | Clean membranes, improve pretreatment |
| Flow too high | Reduce flow rate per vessel | |
| Variable product quality | Feed quality variation | Equalization tank, continuous monitoring |
| Temperature swings | Normalize flux and rejection for temperature | |
| Membrane damage | Chlorine exposure (polyamide) | Ensure complete dechlorination, free Cl₂ <0.1 mg/L |
| High pressure transients | Pressure relief valves, smooth startup/shutdown | |
| Cleaning chemical incompatibility | Follow manufacturer's CIP protocols |
Operation & Maintenance
Continuous Monitoring (SCADA)
- Feed, concentrate, and permeate flow rates
- Feed and concentrate pressure (differential pressure)
- Permeate TDS (conductivity)
- Feed temperature (normalize performance)
- Antiscalant flow rate
- Normalized permeate flux (correct for T, ΔP)
Daily Checks
- Review normalized flux (flag if <10% decline)
- Check permeate TDS (flag if >10% increase)
- Verify antiscalant injection
- Measure differential pressure (scaling indicator)
- Inspect for leaks
- Review recovery ratio
Weekly Maintenance
- Lab analysis: Feed and permeate TDS, hardness, sulfate
- Calibrate conductivity meters
- Check pretreatment performance (SDI, turbidity)
- Inspect high-pressure pump
- Review chemical tank levels
- Scaling potential calculation (update water quality)
Monthly Tasks
- Detailed performance normalization (flux, salt passage, ΔP)
- Clean cartridge filters (5 μm prefilter)
- Inspect membrane elements (if possible)
- Antiscalant effectiveness review
- Energy consumption analysis
- Plan CIP if flux declined >10-15%
Quarterly/CIP Events
- Full CIP (acid for scaling, caustic for organics, biocide)
- Post-CIP performance test (flux recovery target: >95%)
- Replace damaged elements if needed
- Membrane autopsy (if chronic fouling)
- Calibrate all instruments
- Review operating conditions and optimize
Annual Tasks
- Comprehensive performance audit
- Scaling projection for coming year (water quality trends)
- Optimize recovery and antiscalant dose
- Cost analysis: Energy, chemicals, membrane replacement
- Evaluate membrane life (typically 3-5 years)
- Consider process improvements (pretreatment, ERD)
Advanced Features
Variable Recovery Operation
Adjust recovery based on feed quality:
- High hardness/sulfate: Reduce recovery to 65-70%
- Low scaling potential: Increase recovery to 85-90%
- Automated control based on online saturation index
Two-Stage NF
Stage 1: High recovery (80-85%), produce softened water Stage 2: Treat concentrate from Stage 1, additional recovery (50%)
Overall recovery: 80% + (20% × 50%) = 90%
Hybrid NF-RO
NF first: Remove hardness, reduce scaling in RO RO second: Final TDS removal
Benefits:
- RO operates at higher recovery (no CaSO₄ limit)
- Lower RO fouling
- Lower overall energy (NF is lower pressure)
pH Adjustment for Scaling Control
CaCO₃ control: Lower pH to 6.5-7.0 with H₂SO₄ or HCl:
- Converts CO₃²⁻ to HCO₃⁻ (more soluble)
- Reduces CaCO₃ precipitation
- May increase CaSO₄ risk (if using H₂SO₄)
Brine Management
Concentrate disposal options:
- Deep well injection (geological availability)
- Discharge to sewer (municipal approval, volume limits)
- Evaporation ponds (arid climates)
- Brine concentrator + crystallizer (ZLD, zero liquid discharge)
- Beneficial reuse (e.g., dust suppression)
Worked Example
Given
- Flow: 1,500 m³/d (water softening application)
- Feed: TDS = 800 mg/L, Hardness = 300 mg/L as CaCO₃, SO₄²⁻ = 120 mg/L, pH = 7.8, T = 18°C
- Target: Permeate hardness <30 mg/L (>90% removal)
- Minimize energy cost
Solution
Step 1: Select NF Membrane
For hardness removal: MWCO 300-400 Da
Use MWCO 400 Da (balance of flux and rejection)
Expected hardness rejection: 92-95%Step 2: Estimate Osmotic Pressure
π_feed = 0.00075 × 800 = 0.6 barStep 3: Select Operating Pressure
Target flux: J = 35 LMH (moderate for softening)
A = 4 LMH/bar (typical for NF)
σ = 0.85
J = A × (ΔP - σ × Δπ)
35 = 4 × (ΔP - 0.85 × 0.6)
ΔP = 35/4 + 0.51 = 9.26 bar
Use ΔP = 10 bar (standard)Step 4: Calculate Membrane Area
Q = 1,500 m³/d = 62.5 m³/h
J = 35 LMH
A = 62.5 × 1000 / 35 = 1,786 m²
Elements (37 m²/element): 1,786 / 37 = 48.3 elements
Use 48 elements = 1,776 m² (8 vessels × 6 elements)Step 5: Select Recovery
Check CaSO₄ scaling potential:
Assume 50% of hardness is Ca²⁺ = 150 mg/L as CaCO₃ = 60 mg/L as Ca
SO₄²⁻ = 120 mg/L
Try Recovery = 80%:
Concentrate Ca²⁺ = 60 / 0.2 = 300 mg/L
Concentrate SO₄²⁻ = 120 / 0.2 = 600 mg/L
IP/K_sp ≈ 6 (HIGH SCALING RISK)
Reduce to Recovery = 75%:
Concentrate Ca²⁺ = 60 / 0.25 = 240 mg/L
Concentrate SO₄²⁻ = 120 / 0.25 = 480 mg/L
IP/K_sp ≈ 4 (Still high, use antiscalant)
With antiscalant (allows IP/K_sp up to 3×), Recovery = 75% is acceptable.Step 6: Verify Permeate Hardness
Rejection = 93% (typical for 400 Da NF)
Permeate hardness = 300 × (1 - 0.93) = 21 mg/L ✓ (below 30 mg/L target)Step 7: Antiscalant Dosing
Dose: 4 mg/L
Q_feed = 1,500 / 0.75 = 2,000 m³/d
Daily consumption = 2,000 × 4 × 10⁻³ = 8 kg/d
Annual = 2,920 kg/year
Cost @ $5/kg = $14,600/yearStep 8: Energy Consumption
Without ERD:
Q_feed = 2,000 m³/d = 83.3 m³/h
Power = (83.3 × 10 × 10⁵) / (0.75 × 3600) = 30.9 kW
Daily energy = 30.9 × 24 = 742 kWh/d
Specific energy = 742 / 1,500 = 0.49 kWh/m³
With ERD (recommended for >10 bar):
Q_concentrate = 500 m³/d = 20.8 m³/h
Recovered power = 20.8 × 9 × 10⁵ × 0.88 / 3600 = 4.6 kW
Net power = 30.9 - 4.6 = 26.3 kW
Daily energy = 26.3 × 24 = 631 kWh/d
Specific energy = 0.42 kWh/m³
Annual energy cost (with ERD) @ $0.15/kWh = 631 × 365 × 0.15 = $34,550/yearStep 9: Total Operating Cost
Energy: $34,550/year
Antiscalant: $14,600/year
Cartridge filters (5 μm): $2,000/year (estimate)
Membrane replacement (5-year life): $100,000 / 5 = $20,000/year
CIP chemicals: $1,500/year
Total: $72,650/year = $0.13/m³Related Units
- Ultrafiltration - Pretreatment for NF
- Reverse-Osmosis - Higher TDS removal
- UV-Disinfection - Disinfection (NF doesn't disinfect)
- Chemical-Dosing - Antiscalant, acid dosing
- Ion-Exchange - Alternative softening method
References
- Crittenden, J.C. et al. (2012). MWH's Water Treatment, 3rd Ed., Ch. 12: Nanofiltration.
- AWWA (2011). Water Quality and Treatment, 6th Ed., Ch. 12: Nanofiltration and RO.
- Baker, R.W. (2012). Membrane Technology and Applications, 3rd Ed., Wiley, Ch. 4.
- WEF (2018). Design of Municipal Wastewater Treatment Plants, MOP 8, 6th Ed., Ch. 17.
- Schäfer, A.I. et al. (2005). Nanofiltration: Principles and Applications, Elsevier.
- Van der Bruggen, B. et al. (2008). "A Review of Pressure-Driven Membrane Processes in Wastewater Treatment and Drinking Water Production." Environ. Prog. 27(1): 46-56.
- US EPA (2005). Membrane Filtration Guidance Manual, EPA 815-R-06-009.