Governing Balance & Energy Model
The required feed pressure of an RO train must overcome the osmotic gap between feed and permeate, the net driving pressure that actually transports water through the membrane, and the concentrate-side frictional drop across the vessel train.
Pf = (πf - πp) + NDP + ΔPc Where:
-
πf= Feed osmotic pressure (from feedwater TDS) [bar] -
πp= Permeate osmotic pressure (product water) [bar] -
NDP= Net driving pressure across the membrane [bar] -
ΔPc= Concentrate-side frictional pressure drop [bar] -
Pf= Required feed pressure at the high-pressure pump outlet [bar] -
SEC= Specific energy consumption per m³ of permeate [kWh/m³]
Derived Equations:
Pf = (πf - πp) + NDP + ΔPc SEC = (Pf × Qf) / (η pump × Qp) SEC_ERD = SEC × (1 - ηERD × (1 - Y)) Specific energy is the hydraulic power delivered per m³ of permeate, penalized by pump efficiency. When an energy recovery device (Pelton wheel, turbocharger, or pressure exchanger) is fitted, its recovered fraction depends on recovery: SEC_ERD = SEC × (1 − η_ERD × (1 − Y)).
How to Use This Calculator
- Enter the feed and permeate osmotic pressures (use the osmotic pressure calculator for πf).
- Enter the net driving pressure (typically 5–10 bar for BWRO, 2–3 bar for SWRO).
- Enter the concentrate ΔP (about 1–2 bar per 7-element vessel train).
- Set pump efficiency and recovery; optionally enter an ERD efficiency to quantify energy savings.
Interpreting Results
A BWRO at 50% recovery typically consumes 2–3 kWh/m³ of permeate; modern SWRO with a pressure exchanger drops from about 4 to below 2.5 kWh/m³. The ERD credit scales with (1 − Y), which is why high-recovery systems capture less from an ERD.
Accuracy Limits & Design Notes
- This is a lumped pressure balance — it does not model per-element flux or concentration polarization.
- SEC is theoretical hydraulic/electrical conversion; motor and VFD losses are captured in pump efficiency.
- Osmotic pressure rises along the vessel; using feed π alone understates the true trailing-π requirement.
Frequently Asked Questions
How do I get the feed osmotic pressure?
Use the osmotic pressure calculator with the membrane feed TDS (post-pretreatment). As a rule of thumb, each 1,000 mg/L of NaCl contributes about 0.25 bar of osmotic pressure at 25°C.
What is a typical SWRO feed pressure?
Seawater RO trains commonly run at 55–70 bar feed pressure, of which roughly 25–27 bar is the osmotic pressure of standard seawater and the rest is NDP plus frictional and hardware losses.
How much energy does an energy recovery device save?
A pressure exchanger at 95% efficiency on a 45% recovery SWRO plant cuts SEC by roughly 55–60% compared with the same train without ERD. The saving is larger at lower recovery.
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.