Governing Formula & Flow Balance
In Reverse Osmosis (RO) systems, Recovery rate (Y) represents the percentage of feed water converted into treated product water (permeate). The remaining stream contains concentrated rejected solutes and is discharged as concentrate (brine or reject).
Recovery (Y) = (Qp / Qf) × 100 Where:
-
Y= System Recovery rate (percentage of feed converted to permeate) [%] -
Qf= Feed water flow rate delivered to RO high pressure pump [m³/day, L/min, GPD] -
Qp= Permeate (product water) flow rate passing through membrane barrier [m³/day, L/min, GPD] -
Qc= Concentrate (brine / reject) flow rate discharging mineral salts [m³/day, L/min, GPD]
Derived Equations:
Qp = Qf × (Y / 100) Qc = Qf - Qp CF = 1 / (1 - Y / 100) How the Calculation Works
Reverse osmosis systems operate under strict conservation of mass principles. For continuous, steady-state membrane operations where density differences between streams are negligible, the overall volumetric balance simplifies to:
Qfeed = Qpermeate + Qconcentrate
Given an incoming feed flow rate Qf and an engineered recovery target Y, the required product delivery and resulting wastewater stream are determined deterministically.
Worked Engineering Example
Design Scenario: Industrial Seawater RO (SWRO) Facility
An engineer is designing a single-pass seawater desalination train receiving a high-pressure raw feed flow of 100 m³/day with an operating recovery set at 40%.
- Calculate Permeate Flow (Qp):
Qp = 100 m³/day × (40 / 100) = 40.00 m³/day - Calculate Concentrate / Brine Flow (Qc):
Qc = 100 m³/day - 40.00 m³/day = 60.00 m³/day - Calculate Concentration Factor (CF):
CF = 1 / (1 - 0.40) = 1.667
The reject stream will concentrate non-permeating feed salts by approximately 1.67 times the feed concentration.
Engineering Notes & Design Benchmarks
System recovery targets are heavily constrained by feed water chemistry, osmotic pressure limits, and scaling hazards:
| Application Source | Typical Recovery Range | Primary Design Constraints |
|---|---|---|
| Seawater Desalination (SWRO) | 35% – 50% | High osmotic pressure (>65–70 bar discharge pressure limit) |
| Brackish Groundwater (BWRO) | 65% – 85% | Mineral scaling (calcium sulfate, silica, barium sulfate) |
| Wastewater Water Reuse (MBR-RO) | 70% – 80% | Organic fouling, biofouling, and chloramine/silica scaling |
| High Recovery / ZLD RO | 85% – 95% | Requires softening, pH adjustment, antiscalants, and interstage pumps |
Assumptions & Limitations
Engineering Assumptions:
- Conservation of Volume: Assumes fluid densities of feed, permeate, and concentrate are sufficiently close for volumetric mass balance (valid for standard municipal and industrial design calculations).
- Steady-State Condition: Operating pressures, temperatures, and membrane fluxes are assumed constant over time.
Design Limitations:
- This calculator determines volumetric mass flows. It does not replace membrane projection software (e.g., Dupont WAVE, Hydranautics IMSDesign, Toray DS2) which calculates osmotic pressures, temperature corrections, element flux profiles, and concentration polarization.
- Do not set recovery without verifying scaling saturation indices (LSI, SDI, Stiff-Davis) and antiscalant dosages.
Continue in the RO Engineering Workbench
Take your feed flow and recovery into the RO Engineering Workbench and complete the cascade in one saved project: feed TDS, rejection, and temperature combine with these values to resolve concentrate salinity, osmotic pressure, permeate quality, and scaling-risk screening.
Frequently Asked Questions
Why can't reverse osmosis systems operate at 100% recovery?
Operating at 100% recovery would mean zero concentrate discharge, causing salt concentration to approach infinity. This would cause instantaneous precipitation of minerals (scaling), severe membrane destruction, and require infinite osmotic pressure.
How does recovery relate to concentration factor?
The concentration factor (CF) equals 1 / (1 - Recovery). At 50% recovery, salts are concentrated 2.0× in the brine. At 80% recovery, salts are concentrated 5.0×. At 90% recovery, salts are concentrated 10.0×.
What is the difference between element recovery and system recovery?
An individual standard 8-inch membrane element typically operates at 8% to 15% recovery to prevent concentration polarization. Multi-element pressure vessels arranged in staged arrays (e.g., 2:1 staging) combine individual elements to achieve overall system recoveries of 75% to 85%.
Engineering Disclaimer
Engineering Note: This calculator provides simplified engineering estimates for preliminary analysis and educational use. Actual RO system performance depends on membrane type, feedwater chemistry, temperature, pressure, recovery, concentration polarization, pretreatment, and operating conditions. Final system design should be verified using manufacturer data, validated design software, applicable standards, and qualified engineering review.
Technical References
- DuPont FilmTec™ Reverse Osmosis and Nanofiltration Technical Manual (Form No. 45-D01504-en).
- AWWA Manual M46: Reverse Osmosis and Nanofiltration, American Water Works Association.