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Reverse Osmosis (RO) ​

High-pressure membrane separation achieving 95-99.5% salt rejection through solution-diffusion mechanism, producing high-purity permeate for water reuse, desalination, and industrial applications at 10-70 bar depending on feed salinity.

Overview ​

Reverse osmosis (RO) is the tightest membrane process, capable of removing dissolved salts, organics, and essentially all suspended and colloidal matter. RO operates by applying pressure greater than the osmotic pressure of the feed solution, forcing water through a semi-permeable membrane while retaining >95% of dissolved solids. This technology enables drinking water production from seawater, brackish water, and wastewater reuse for potable and industrial applications.

When to Use ​

  • Seawater desalination (TDS 35,000-45,000 mg/L → <500 mg/L)
  • Brackish water desalination (TDS 1,500-10,000 mg/L → <250 mg/L)
  • Direct and indirect potable reuse (wastewater → drinking water)
  • Ultrapure water production (pharmaceutical, electronics, power generation)
  • Industrial process water (boiler feed, semiconductor manufacturing)
  • Zero liquid discharge (ZLD) concentration step
  • Heavy metal removal (>99% for most metals)
  • Nitrate removal (>95%)
  • Organic micropollutant removal (>95% for most compounds)

Key Characteristics ​

  • Salt rejection: 95-99.5% (brackish water), 99-99.7% (seawater)
  • Operating pressure: 10-25 bar (brackish), 55-70 bar (seawater)
  • Permeate flux: 15-25 LMH (brackish), 10-15 LMH (seawater)
  • Recovery: 75-85% (brackish), 40-50% (seawater)
  • Permeate TDS: <250 mg/L (brackish), <500 mg/L (seawater)
  • Boron rejection: 70-90% (standard), >95% (high rejection membranes)
  • TOC rejection: 95-99%
  • Silica rejection: 95-98%
  • Energy: 0.8-1.5 kWh/m³ (brackish with ERD), 3-5 kWh/m³ (seawater with ERD)

Operating Modes ​

Basic Mode ​

  • Constant pressure operation
  • Fixed recovery ratio
  • Simple solution-diffusion model (default rejection coefficients)
  • Concentrate to drain
  • Basic scaling prediction (Langelier Saturation Index)

Advanced Mode ​

  • Solution-diffusion model with concentration polarization correction
  • Multi-stage configuration (two-pass for ultrapure water)
  • Detailed scaling prediction (Stiff-Davis, ROSA/WAVE software)
  • Antiscalant optimization
  • Energy recovery device (ERD) simulation: pressure exchanger or turbocharger
  • Brine management: ZLD, deep well injection, evaporation
  • Membrane aging simulation (salt passage increase over time)
  • Cleaning frequency prediction

Mathematical Model ​

Solution-Diffusion Model ​

Water flux:

$$J_w = A \times (\Delta P - \Delta \pi)$$

Where:

  • $J_w$ = water flux (L/m²·h or m/s)
  • $A$ = water permeability coefficient (L/m²·h·bar)
  • $\Delta P$ = transmembrane pressure (bar)
  • $\Delta \pi$ = osmotic pressure difference (bar)

For RO, reflection coefficient $\sigma \approx 1.0$ (near-perfect semi-permeable membrane).

Solute flux:

$$J_s = B \times \Delta C$$

Where:

  • $J_s$ = solute flux (g/m²·s)
  • $B$ = solute permeability coefficient (m/s)
  • $\Delta C$ = concentration difference (g/m³)

Observed rejection:

$$R = 1 - \frac{C_p}{C_f} = \frac{A \times (\Delta P - \Delta \pi)}{A \times (\Delta P - \Delta \pi) + B}$$

Osmotic Pressure ​

Van't Hoff equation for multi-component solutions:

$$\pi = \sum_i i \times M_i \times R \times T$$

Simplified for TDS:

$$\pi [bar] \approx 0.00075 \times TDS [mg/L]$$

Examples:

  • Brackish water (TDS 2,000 mg/L): π ≈ 1.5 bar
  • Brackish water (TDS 5,000 mg/L): π ≈ 3.75 bar
  • Seawater (TDS 35,000 mg/L): π ≈ 26 bar
  • Brine (TDS 70,000 mg/L): π ≈ 53 bar

Net driving pressure:

$$\Delta P_{net} = \Delta P_{applied} - (\pi_{concentrate} - \pi_{permeate})$$

Key insight: As recovery increases, concentrate TDS and π increase, requiring higher applied pressure.

Recovery and Concentration Factor ​

Recovery:

$$Y = \frac{Q_p}{Q_f} \times 100%$$

Concentration factor:

$$CF = \frac{1}{1 - Y} = \frac{C_{concentrate}}{C_{feed}}$$

Examples:

  • Y = 75% → CF = 4× (concentrate is 4× more concentrated than feed)
  • Y = 80% → CF = 5×
  • Y = 50% (seawater) → CF = 2×

Concentrate TDS:

$$TDS_{concentrate} = \frac{TDS_{feed} - Y \times TDS_{permeate}}{1 - Y}$$

For high rejection (R > 0.98):

$$TDS_{concentrate} \approx \frac{TDS_{feed}}{1 - Y}$$

Concentration Polarization ​

Solute accumulation at membrane surface:

$$\frac{C_{wall}}{C_{bulk}} = \exp\left(\frac{J_w}{k}\right)$$

Where $k$ = mass transfer coefficient (2-6 × 10⁻⁵ m/s for RO)

Effect of concentration polarization:

  • Increases local osmotic pressure by 10-30%
  • Reduces flux
  • Promotes scaling

Mitigation:

  • High crossflow velocity (turbulence)
  • Feed spacers (channel height 0.7-1.0 mm)
  • Lower flux operation

Scaling Prediction ​

Common scalants:

  1. Calcium carbonate (CaCO₃):

    • Langelier Saturation Index (LSI): $$LSI = pH - pH_s$$
    • Scale risk if LSI > 0
    • Control: Acid dosing (lower pH to 6.5-7.0), antiscalant

  2. Calcium sulfate (CaSO₄·2H₂O, gypsum):

    • Saturation level (% of solubility): $$SL_{CaSO_4} = \frac{[Ca^{2+}] \times [SO_4^{2-}]}{K_{sp}}$$
    • Scale risk if SL > 100% (with antiscalant, allow up to 200-250%)
    • Often limits recovery in brackish water RO

  3. Barium sulfate (BaSO₄):

    • $K_{sp}$ = 1.1 × 10⁻¹⁰ (extremely low)
    • Even trace Ba²⁺ can cause scaling
    • Must remove Ba²⁺ upstream (ion exchange, NF)

  4. Silica (SiO₂):

    • Colloidal and reactive silica
    • Solubility: 120-150 mg/L (amorphous, pH 7-8)
    • Forms metal silicates (difficult to clean)
    • Limit concentrate silica to <120 mg/L or use specialized antiscalant

  5. Strontium sulfate (SrSO₄):

    • Similar to CaSO₄, but less common

Membrane Fouling ​

Types of fouling:

  1. Scaling (inorganic): CaCO₃, CaSO₄, silica, BaSO₄
  2. Colloidal: Clays, metal hydroxides (Fe, Al, Mn)
  3. Organic: Humic acids, oils, surfactants
  4. Biological: Bacteria, biofilms (polysaccharides)

Silt Density Index (SDI):

Measure of colloidal fouling potential:

$$SDI = \frac{100 \times (1 - t_i / t_f)}{T}$$

Where:

  • $t_i$ = initial time to collect 500 mL
  • $t_f$ = final time to collect 500 mL (after T minutes)
  • $T$ = test duration (typically 15 min)

Requirement: SDI₁₅ < 3 for RO feed (preferably <2)

Temperature Correction ​

Viscosity and permeability change with temperature:

$$J_T = J_{25°C} \times TCF$$

Where $TCF$ = temperature correction factor:

$$TCF = \exp\left[2640 \times \left(\frac{1}{298} - \frac{1}{T_K}\right)\right]$$

Simplified:

$$J_T \approx J_{25} \times 1.03^{(T-25)}$$

Example:

J₂₅ = 20 LMH @ 25°C
J₁₅ = 20 × 1.03⁻¹⁰ = 14.8 LMH @ 15°C (26% reduction!)
J₃₅ = 20 × 1.03¹⁰ = 26.9 LMH @ 35°C (35% increase)

Critical for design: Always normalize flux to 25°C for performance evaluation.

Design Parameters ​

Brackish Water RO (BWRO) ​

ParameterSymbolUnitRangeDefaultDescription
Feed TDS-mg/L1,500-10,0003,000Total dissolved solids
Operating pressure$\Delta P$bar10-2515Applied pressure
Temperature$T$°C10-3025Feed water temperature
Design flux$J_w$LMH15-2520Permeate flux @ 25°C
Recovery$Y$%70-8575Water recovery ratio
Salt rejection$R$%97-99.598.5TDS rejection
Permeate TDS-mg/L50-300150Product water TDS

Seawater RO (SWRO) ​

ParameterSymbolUnitRangeDefaultDescription
Feed TDS-mg/L30,000-45,00035,000Seawater TDS
Operating pressure$\Delta P$bar55-7060High pressure
Temperature$T$°C15-3020Seawater temperature
Design flux$J_w$LMH10-1512Permeate flux @ 25°C
Recovery$Y$%35-5045Lower recovery (high π)
Salt rejection$R$%99.2-99.799.5High rejection
Permeate TDS-mg/L200-500400Potable water limit: 500 mg/L

Configuration Guide ​

Step-by-Step Setup (Brackish Water RO) ​

  1. Feed Water Analysis

    Minimum required parameters:

    • TDS, pH, temperature, alkalinity
    • Hardness (Ca²⁺, Mg²⁺), sulfate, chloride, silica
    • Barium (critical, even at trace levels)
    • Iron, manganese (oxidation/fouling risk)
    • TOC (organic fouling potential)
    • SDI₁₅ (colloidal fouling)
    Example feed water:
TDS = 2,500 mg/L, pH = 7.6, T = 20°C
Ca²⁺ = 120 mg/L, SO₄²⁻ = 350 mg/L
Silica = 35 mg/L, Ba²⁺ = 0.05 mg/L (trace)
SDI₁₅ = 2.5

  2. Select Recovery

    Limited by scaling:

    Calculate concentrate composition at various recoveries:

Y = 75%:
Concentrate Ca²⁺ = 120 / 0.25 = 480 mg/L
Concentrate SO₄²⁻ = 350 / 0.25 = 1,400 mg/L
Concentrate silica = 35 / 0.25 = 140 mg/L (above 120 mg/L limit)

Y = 70%:
Concentrate silica = 35 / 0.30 = 117 mg/L ✓ (below limit)

Check CaSO₄: Use scaling software (ROSA, WAVE)
With antiscalant, Y = 75-80% may be achievable

Use Y = 75% with silica antiscalant

  3. Estimate Osmotic Pressure

    Feed: π_f = 0.00075 × 2,500 = 1.875 bar
Permeate (98.5% rejection): TDS_p = 2,500 × 0.015 = 37.5 mg/L
           π_p = 0.00075 × 37.5 = 0.03 bar ≈ 0 (negligible)
Concentrate (Y=75%): TDS_c = 2,500 / 0.25 = 10,000 mg/L
           π_c = 0.00075 × 10,000 = 7.5 bar

Average π (concentrate avg ≈ feed + concentrate / 2):
π_avg ≈ (1.875 + 7.5) / 2 = 4.7 bar

  4. Select Operating Pressure

    $$\Delta P = \pi_{avg} + \Delta P_{margin}$$

    ΔP = 4.7 + 5 = 9.7 bar (margin for flux and pressure drop)

Use ΔP = 15 bar (standard BWRO, provides good margin)
Net driving pressure = 15 - 4.7 = 10.3 bar

  5. Estimate Flux

    Manufacturer's data, but typical:

    A = 1.5 LMH/bar (typical BWRO membrane @ 25°C)
J_w = A × ΔP_net = 1.5 × 10.3 = 15.5 LMH

Temperature correction (20°C):
J_20 = 15.5 × 1.03⁻⁵ = 13.3 LMH

Use J = 20 LMH for design (assumes 25°C normalized, or increase ΔP)

  6. Calculate Membrane Area

    Q_permeate = 5,000 m³/d = 208 m³/h
J = 20 LMH

A = 208 × 1000 / 20 = 10,400 m²

Standard 8"×40" BWRO elements: 37 m² each
Total elements = 10,400 / 37 = 281 elements

Configuration: 47 pressure vessels × 6 elements = 282 elements (10,434 m²)

  7. Pretreatment Requirements

    Essential for RO feed:

    • Cartridge filter: 5 μm absolute, protect from particles
    • SDI reduction: ❤️ required, <2 preferred
      • Options: UF/MF (best), multimedia filter, coagulation + sedimentation
    • Dechlorination: Free Cl₂ <0.05 mg/L (polyamide membrane damage)
      • Sodium metabisulfite: 3× stoichiometric dose
    • Antiscalant: 3-5 mg/L, inhibit CaSO₄, CaCO₃, silica scaling
    • Acid dosing (optional): Lower pH to 6.5-7.0 for CaCO₃ control

  8. Energy Recovery Device (ERD)

    For BWRO >10 bar, ERD recommended:

    Pressure exchanger (isobaric):

    • Efficiency: 94-97%
    • No rotating seals, low maintenance
    • Most common for large SWRO and BWRO >15 bar

    Turbocharger (Pelton wheel):

    • Efficiency: 80-88%
    • Simpler, lower cost
    • Suitable for BWRO 10-20 bar
    Example (pressure exchanger, 95% efficiency):
Q_concentrate = 5,000 / 0.75 - 5,000 = 1,667 m³/d = 69.4 m³/h
Pressure recovered ≈ 14 bar (near feed pressure)

Power recovered = 69.4 × 14 × 10⁵ × 0.95 / 3600 = 25.5 kW

  9. Calculate Energy Consumption

    High-pressure pump (without ERD):

    Q_feed = 5,000 / 0.75 = 6,667 m³/d = 278 m³/h
ΔP = 15 bar
η_pump = 0.80

Power = (278 × 15 × 10⁵) / (0.80 × 3600) = 145 kW
Daily energy = 145 × 24 = 3,480 kWh/d
Specific energy = 3,480 / 5,000 = 0.70 kWh/m³

    With ERD (95% efficiency):

    Net power = 145 - 25.5 = 119.5 kW
Daily energy = 119.5 × 24 = 2,868 kWh/d
Specific energy = 0.57 kWh/m³ (18% savings)

  10. Chemical Dosing

    Antiscalant:

    Dose = 4 mg/L (feed)
Daily = 6,667 × 4 × 10⁻³ = 26.7 kg/d
Annual = 9,746 kg/year
Cost @ $5/kg = $48,730/year

    Dechlorination (sodium metabisulfite):

    Feed Cl₂ = 0.5 mg/L (from upstream chlorination)
Na₂S₂O₅ dose = 3 × 0.5 / 0.35 = 4.3 mg/L (35% purity)
Daily = 6,667 × 4.3 × 10⁻³ = 28.7 kg/d
Annual = 10,475 kg/year
Cost @ $2/kg = $20,950/year

Typical Design Values ​

ApplicationFeed TDS (mg/L)Pressure (bar)Flux (LMH)Recovery (%)Permeate TDS (mg/L)Energy (kWh/m³)
Low brackish1,500-3,00010-1518-2575-8530-1000.5-0.8 (w/ ERD)
High brackish5,000-10,00018-2515-2270-80100-2501.0-1.5 (w/ ERD)
Seawater35,000-38,00055-6510-1540-50300-5003.0-4.5 (w/ ERD)
High-salinity seawater40,000-45,00065-708-1235-45400-5004.5-6.0 (w/ ERD)
Wastewater reuse800-2,00010-1515-2075-8520-800.5-0.8 (w/ ERD)

Performance Criteria ​

Salt Rejection ​

IonBrackish ROSeawater RO
Na⁺, Cl⁻95-99%99-99.7%
Ca²⁺, Mg²⁺97-99.5%99.5-99.8%
SO₄²⁻99-99.9%99.8-99.9%
NO₃⁻93-97%97-99%
F⁻94-97%97-99%
Boron (B(OH)₃)70-90%70-90% (pH-dependent)
Silica95-98%97-99%
TOC95-99%97-99.5%

Boron removal:

  • At pH 7-8: 70-85% rejection (uncharged boric acid)
  • At pH >9: >95% rejection (charged borate ion)
  • For drinking water (<1 mg/L B): Use high-boron-rejection membranes or two-pass RO

Comparison: BWRO vs. SWRO ​

ParameterBrackish Water ROSeawater RO
Feed TDS1,500-10,000 mg/L30,000-45,000 mg/L
Osmotic pressure1-8 bar25-35 bar
Operating pressure10-25 bar55-70 bar
Salt rejection97-99.5%99.2-99.7%
Recovery70-85%35-50%
Flux15-25 LMH10-15 LMH
Energy (w/ ERD)0.5-1.5 kWh/m³3.0-5.0 kWh/m³
Membrane elementsStandard pressureHigh pressure (thicker)
PretreatmentStandard (SDI<3)More rigorous (SDI<2)
Scaling riskModerate (CaSO₄)Lower (dilution by water)
Brine disposalEasier (lower volume)Challenging (high volume, salinity)

Troubleshooting ​

IssueCauseSolution
Flux decline (normalized)Membrane fouling (organic, colloidal)CIP with caustic + surfactant
Scaling (CaCO₃, CaSO₄, silica)CIP with acid, increase antiscalant dose
Biological foulingCIP with biocide, improve pretreatment
Membrane compaction (aging)Accept gradual decline, plan replacement
Salt passage increaseMembrane degradation (chlorine, oxidation)Improve dechlorination, replace elements
High temperatureCool feed, check permeate TDS trend
Seal leak (O-ring)Inspect and replace O-rings
Membrane aging (end of life)Replace membranes (typically 3-7 years)
High differential pressureParticulate fouling (lead elements)CIP, improve pretreatment, check SDI
Biological foulingBiocide treatment, chlorination of pretreatment
Scale buildupAcid cleaning, optimize antiscalant
Low recoveryConcentrate pressure too lowCheck ERD operation, increase feed flow
Scaling concern (over-conservative)Scaling analysis, optimize recovery
High permeate TDSLow feed pressureIncrease pressure to design value
Temperature spikeNormal, verify normalized salt passage
Membrane damageIntegrity test, replace faulty elements
Excessive CIP frequency (❤️ months)Poor pretreatment (high SDI)Improve UF/MF, multimedia filter
Organic foulingUpstream TOC removal (GAC, ozone)
Flux too highReduce flux by 10-20%
Permeate hardness (bypass)O-ring leakInspect seals, pressure test
Membrane glue line failureReplace element
Pressure drop in ERDFouling in ERDClean ERD, improve feed filtration
Mechanical wearInspect and repair/replace

Operation & Maintenance ​

Continuous Monitoring (SCADA) ​

  • Feed, concentrate, permeate flow rates
  • Feed, interstage, and permeate pressure
  • Permeate conductivity (TDS)
  • Temperature (normalize performance)
  • Differential pressure (fouling indicator)
  • Normalized flux and salt passage (correct for T, ΔP)

Daily Checks ​

  • Review normalized flux (flag if <10% decline from baseline)
  • Check normalized salt passage (flag if >10% increase)
  • Verify antiscalant injection rate
  • Check dechlorination (free Cl₂ <0.05 mg/L in RO feed)
  • Measure differential pressure (scaling/fouling trend)
  • Inspect for leaks
  • Review ERD operation (if equipped)

Weekly Maintenance ​

  • Lab analysis: Feed, permeate, concentrate TDS and major ions
  • SDI test on RO feed (target: ❤️, preferably <2)
  • Calibrate conductivity probes
  • Check cartridge filter differential pressure (replace if >1 bar)
  • Review chemical tank levels
  • Scaling potential calculation (update water quality)

Monthly Tasks ​

  • Detailed performance normalization (flux, salt passage, ΔP, T correction)
  • Fouling/scaling analysis (compare to baseline)
  • Pretreatment performance review (UF/MF integrity)
  • Inspect high-pressure pump
  • Antiscalant effectiveness (check scaling indices)
  • Energy consumption analysis
  • Plan CIP if normalized flux declined >10-15%

Quarterly/CIP Events ​

  • Full CIP protocol:
    • Low pH (acid): Remove CaCO₃, CaSO₄, metal hydroxides
    • High pH (caustic + surfactant): Remove organics, biofilm, silica
    • Biocide (if biofouling): Sodium hypochlorite (check compatibility)
  • Post-CIP performance test (flux recovery target: >95%)
  • Replace fouled/damaged elements
  • Membrane autopsy (if chronic fouling, send to manufacturer)
  • Calibrate all instruments
  • Review operating conditions and optimize

Annual Tasks ​

  • Comprehensive performance audit (compare to design)
  • Membrane element inspection (open pressure vessels)
  • Replace cartridge filters (preventive, all housings)
  • ERD overhaul (if equipped): Inspect, replace wear parts
  • High-pressure pump seal replacement (preventive)
  • Scaling/fouling trend analysis (multi-year)
  • Membrane life assessment (plan replacement, typically 3-7 years)
  • Brine disposal compliance (environmental permits)
  • Cost-benefit analysis: Energy, chemicals, membranes
  • Consider process improvements (staged RO, two-pass, etc.)

Advanced Features ​

Two-Pass RO (Ultrapure Water) ​

First pass: Standard BWRO (TDS reduction to 50-200 mg/L) Second pass: Polish to <1 mg/L TDS (ultrapure water)

Applications:

  • Pharmaceutical manufacturing
  • Semiconductor fabrication
  • Power plant boiler feed
  • Laboratory-grade water

Benefits:

  • Permeate TDS <1 mg/L (resistivity >15 MΩ·cm)
  • TOC <10 ppb
  • Silica <10 ppb
  • Bacteria <1 cfu/mL

Staged RO (Maximize Recovery) ​

Two-stage configuration:

  • Stage 1: 6 pressure vessels × 6 elements (primary production)
  • Stage 2: 2 pressure vessels × 6 elements (treat Stage 1 concentrate)

Recovery boost:

  • Single-stage: 75%
  • Two-stage: 75% + (25% × 50%) = 87.5% overall

Interstage booster pump: Required to overcome Stage 2 osmotic pressure

Seawater RO with ERD ​

Energy recovery device essential:

  • Concentrate pressure: 55-60 bar
  • Concentrate flow: 50-60% of feed (50-65% recovery)
  • Energy recovery: 94-97% (pressure exchanger)

Specific energy breakdown (SWRO, 45% recovery):

Theoretical minimum = π × ln(1/(1-Y)) = 26 × ln(1/0.55) = 15.6 bar·m³/m³ = 0.43 kWh/m³

Actual with ERD:
- High-pressure pump: 55 bar
- ERD recovers: 95% of 55 bar × 55% flow = 28.7 bar·m³/m³
- Net energy: 55 - 28.7 = 26.3 bar·m³/m³ = 0.73 kWh/m³
- Inefficiencies (pumps, motors, piping): ×1.3
- Total: 0.95 kWh/m³

Add pretreatment (intake, UF): +0.5 kWh/m³
Add post-treatment (remineralization, disinfection): +0.2 kWh/m³

Total SWRO plant: 1.65 kWh/m³ (state-of-the-art)
Older plants without ERD: 6-10 kWh/m³

Brine Concentrate Management ​

Disposal options:

  1. Surface water discharge:

    • Requires mixing zone analysis (dilution modeling)
    • Salinity impact on aquatic life
    • Thermal discharge consideration (SWRO)

  2. Deep well injection:

    • Geological suitability (confined aquifer)
    • Regulatory approval (UIC permit)
    • Monitor groundwater quality

  3. Sewer discharge:

    • Municipal approval required
    • Volume and TDS limits
    • Discharge fees

  4. Evaporation ponds:

    • Arid climates only (high evaporation rate)
    • Large land area required
    • Crystallized salts disposal

  5. Zero Liquid Discharge (ZLD):

    • Brine concentrator (additional RO, thermal, MVC)
    • Crystallizer (evaporate final brine to solid salts)
    • High cost: $5-20/m³ concentrate
    • Solid salt disposal or beneficial use

  6. Beneficial reuse:

    • Dust suppression (roads, mining)
    • Industrial processes (cooling towers, process water)
    • Salt production (selective crystallization)

Hybrid Processes ​

RO + Thermal (MSF/MED):

  • RO produces 60-70% of freshwater (low energy)
  • Thermal desalination treats RO concentrate (high recovery)
  • Common in Middle East (energy-rich regions)

RO + Ion Exchange:

  • RO bulk TDS removal
  • IX polish final product (ultrapure water)

NF + RO:

  • NF softening (remove hardness)
  • RO operates at higher recovery (no CaSO₄ scaling)

Worked Example: Brackish Water RO Plant ​

Given ​

  • Flow: 10,000 m³/d permeate (average)
  • Feed water: TDS = 3,500 mg/L, Ca²⁺ = 150 mg/L, SO₄²⁻ = 450 mg/L, Silica = 40 mg/L, pH = 7.8, T = 22°C, SDI₁₅ = 3.5
  • Target: Permeate TDS <200 mg/L, potable water reuse
  • Include pretreatment, antiscalant, ERD

Solution ​

Step 1: Pretreatment Design

SDI = 3.5 > 3.0 (too high for RO)

Pretreatment: UF (0.04 μm) to reduce SDI to <2
- UF flux: 60 LMH, Recovery: 93%
- UF area = 10,000 / 0.93 / 60 / 24 = 7,491 m² (125 modules × 60 m²)
- UF energy: 0.06 kWh/m³ × 10,753 m³/d = 645 kWh/d

Dechlorination: Sodium metabisulfite (assume 0.8 mg/L Cl₂ in UF feed)
- Dose: 3 × 0.8 / 0.35 = 6.9 mg/L
- Daily: 10,753 × 6.9 × 10⁻³ = 74.2 kg/d

Step 2: Select RO Recovery

Check silica limit (120 mg/L in concentrate):
Y_max = 1 - (40 / 120) = 66.7%

Check CaSO₄ scaling (use software, simplified here):
Y = 75% → Concentrate SO₄²⁻ = 450 / 0.25 = 1,800 mg/L (likely to scale)
Y = 70% → Concentrate SO₄²⁻ = 450 / 0.30 = 1,500 mg/L (with antiscalant, acceptable)

Use Y = 75% with silica-compatible antiscalant (assume effective)

Step 3: Calculate Osmotic Pressures

Feed: π_f = 0.00075 × 3,500 = 2.625 bar
Permeate (98.5% rejection): π_p ≈ 0 bar
Concentrate: TDS_c = 3,500 / 0.25 = 14,000 mg/L
            π_c = 0.00075 × 14,000 = 10.5 bar

Average: π_avg ≈ (2.625 + 10.5) / 2 = 6.6 bar

Step 4: Operating Pressure and Flux

ΔP = 18 bar (standard BWRO, provides 18 - 6.6 = 11.4 bar net driving pressure)

Temperature correction factor (22°C):
TCF = 1.03^(22-25) = 0.913

Flux @ 25°C: J₂₅ = 1.5 × 11.4 = 17.1 LMH
Flux @ 22°C: J₂₂ = 17.1 × 0.913 = 15.6 LMH

Use J = 20 LMH for design (conservative, allows fouling margin)

Step 5: Membrane Area

Q_permeate = 10,000 m³/d = 417 m³/h
A = 417 × 1000 / 20 = 20,850 m²

Elements (37 m²/element): 20,850 / 37 = 563 elements

Configuration: 94 pressure vessels × 6 elements = 564 elements (20,868 m²)
Organize in 2 trains for redundancy: 47 vessels per train

Step 6: Antiscalant Dosing

Dose: 5 mg/L (feed, silica-compatible formulation)
Q_feed = 10,000 / 0.75 = 13,333 m³/d
Daily: 13,333 × 5 × 10⁻³ = 66.7 kg/d
Annual: 24,346 kg/year
Cost @ $5/kg = $121,730/year

Step 7: Energy Consumption

High-pressure pump:
Q_feed = 13,333 m³/d = 556 m³/h
Power = (556 × 18 × 10⁵) / (0.80 × 3600) = 348 kW

ERD (pressure exchanger, 95% efficiency):
Q_concentrate = 3,333 m³/d = 139 m³/h
Pressure recovered = 17 bar
Power recovered = 139 × 17 × 10⁵ × 0.95 / 3600 = 62.2 kW

Net RO power = 348 - 62.2 = 285.8 kW
Daily RO energy = 285.8 × 24 = 6,859 kWh/d
RO specific energy = 0.69 kWh/m³

Total plant (RO + UF + misc):
Total = 6,859 + 645 + 200 = 7,704 kWh/d
Specific energy = 0.77 kWh/m³
Annual energy cost @ $0.12/kWh = 7,704 × 365 × 0.12 = $337,686/year

Step 8: Operating Cost Summary

Energy: $337,686/year
Antiscalant: $121,730/year
Dechlorination: $54,200/year (74.2 kg/d × $2/kg)
UF membranes (7-year life): $300,000 / 7 = $42,857/year
RO membranes (5-year life): $700,000 / 5 = $140,000/year
UF + RO CIP chemicals: $10,000/year
Cartridge filters: $20,000/year
Maintenance: $50,000/year

Total: $776,473/year = $0.21/m³ produced
  • Nanofiltration - Lower pressure, partial desalination
  • Ultrafiltration - RO pretreatment
  • UV-Disinfection - Post-treatment disinfection
  • Chemical-Dosing - Antiscalant, dechlorination, acid
  • Remineralization - Post-RO stabilization

References ​

  1. Crittenden, J.C. et al. (2012). MWH's Water Treatment, 3rd Ed., Ch. 12: Reverse Osmosis.
  2. AWWA (2011). Water Quality and Treatment, 6th Ed., Ch. 12: RO and Nanofiltration.
  3. Baker, R.W. (2012). Membrane Technology and Applications, 3rd Ed., Wiley, Ch. 4.
  4. WEF (2018). Design of Municipal Wastewater Treatment Plants, MOP 8, 6th Ed., Ch. 17.
  5. Voutchkov, N. (2013). Desalination Engineering: Planning and Design, McGraw-Hill.
  6. US EPA (2012). Guidelines for Water Reuse, EPA/600/R-12/618.
  7. IDA (2023). Desalination Yearbook 2022-2023, International Desalination Association.