Governing Formula & Brine Balance
The concentration factor (CF) of a reverse osmosis system describes how the dissolved salts in the feed stream are concentrated in the brine. For a system operating at recovery Y, all the salt entering with the feed leaves with a reduced concentrate flow, so its concentration multiplies by CF = 1/(1 − Y/100).
CF = 1 / (1 - Y/100) Where:
-
Y= System Recovery rate (percentage of feed converted to permeate) [%] -
Cf= Feed water TDS entering the RO train (membrane feed after pretreatment) [mg/L] -
Qf= Feed water flow rate delivered to the RO high pressure pump [m³/h] -
CF= Concentration factor multiplying the feed TDS at the concentrate exit [—]
Derived Equations:
CF = 1 / (1 - Y/100) Cc = Cf × CF Ms = Qf × Cf / 1000 The concentrate TDS is approximated as the feed TDS multiplied by the concentration factor. This is the worst-case trailing-element concentration used to check scaling risk at the tail of a train.
How to Use This Calculator
- Enter the system recovery Y in percent (the permeate recovery of the entire train).
- Enter the membrane feed TDS (post-pretreatment) and the feed flow into the high pressure pump.
- The calculator returns the concentration factor, concentrate TDS, salt load, and the permeate/concentrate flows.
Interpreting Results
At 50% recovery the factor is 2.00; at 75% it is 4.00. High factors raise the solubility ratio in the last elements — pair this result with the scaling risk calculator to confirm the stage configuration.
Accuracy Limits & Design Notes
- Ignores membrane salt passage, so concentrate TDS is a mild overestimate of the true value.
- Recovery above 90% triggers a single-pass feasibility warning — verify with a staged design.
- Feed flow is the membrane feed to the high-pressure pump, not the raw intake flow.
Frequently Asked Questions
What is a typical RO concentration factor?
For a single-pass brackish water RO at 50–80% recovery, the factor is 2–5. Seawater systems typically run at 40–50% recovery with a factor of about 1.7–2.0.
Why does the concentrate flow matter?
Brine flow must stay above the minimum concentrate flow recommended by the membrane manufacturer to avoid heavy scaling and to keep the last elements well flushed.
Does salt passage change the concentration factor?
Slightly. A small fraction of salt passes into the permeate, so the true concentrate TDS is a touch lower than the feed TDS × CF approximation used here — a deliberately conservative estimate.
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.