Calculations

How to Calculate Membrane Flux, RO Recovery, and Pump Energy for Desalination Systems

The five formulas every membrane plant runs on, flux, recovery, pump power, normalization, and mass balance, worked with real units and numbers on one consistent RO train.

Every membrane plant decision traces back to five numbers: flux, recovery, feed pressure, specific energy, and normalized permeate flow. Get these right and sizing, troubleshooting, and performance guarantees all follow. This guide works each formula with real units and worked examples from a brackish water RO train producing 150 m3/h of permeate from 200 m3/h of feed, so you can follow one consistent system from feed water to brine. Inputs come from three places: the membrane datasheet, the plant SCADA historian, and lab water analyses. Where a calculator on this site does the arithmetic for you, it is named inline.

Membrane flux is permeate flow divided by active membrane area: J = Qp / A. Express it in liters per square meter per hour, LMH, or gallons per square foot per day, GFD, where 1 GFD equals 1.70 LMH. Our example train holds 29 pressure vessels with 7 elements each, and a standard 8 inch element carries 37.2 m2 (400 ft2) of area, so A = 29 x 7 x 37.2 = 7,552 m2. Flux is 150,000 L/h divided by 7,552 m2, or 19.9 LMH (11.7 GFD). The Membrane Flux Rate calculator runs this in both unit systems. Element area comes straight from the manufacturer datasheet, never from memory.

Recovery is the fraction of feed converted to permeate: R = Qp / Qf x 100. With 150 m3/h of permeate from 200 m3/h of feed, R = 75 percent, typical for brackish water and far above the 40 to 50 percent seawater plants can sustain. Recovery sets the concentration factor, CF = 1 / (1 minus R), so 75 percent recovery concentrates the reject stream 4 times. That single number governs scaling risk: if feed calcium and sulfate would exceed saturation at CF 4, you must drop recovery or add antiscalant. The RO Recovery Rate calculator handles the flow balance and flags the concentration factor automatically.

Hydraulic pump power in kW is flow times pressure divided by efficiency: P = Qf x dP / (36 x eta), with Qf in m3/h and dP in bar. Feeding 200 m3/h at 16 bar through a pump at 78 percent efficiency draws 200 x 16 / (36 x 0.78) = 114 kW. Divide by permeate output to get specific energy: 114 kW / 150 m3/h = 0.76 kWh/m3, squarely in the brackish RO range. At 8,000 operating hours and $0.09 per kWh that motor consumes about $82,000 per year, which the Pump Energy Cost calculator computes from the same four inputs. Pull pressure from the transmitter downstream of the cartridge filters, not the pump nameplate.

Raw permeate flow is meaningless without temperature correction because flux rises roughly 3 percent per degree C. Normalize with a temperature correction factor, TCF = exp(2640 x (1/298 minus 1/(273 + T))), then compare normalized flow against the day 1 baseline. A 10 to 15 percent decline in normalized permeate flow is the standard trigger for cleaning. To translate decline into production, the Membrane Fouling Loss calculator multiplies percent flux loss by rated output: a 10 percent loss on our 150 m3/h train forfeits 15 m3/h, or 360 m3 per day. Log normalized flow at the same recovery and pressure each time or the trend is noise.

Close the mass balance to size the reject line. Brine flow is feed minus permeate: 200 minus 150 = 50 m3/h. Brine concentration is roughly feed TDS times the concentration factor, so 2,000 mg/L feed at CF 4 leaves about 8,000 mg/L, less the small fraction passing into permeate. Check osmotic pressure too: NaCl solutions exert about 0.77 bar per 1,000 mg/L, so the brine end of the array sees roughly 6 bar of osmotic backpressure that your 16 bar feed must overcome with margin. These two outputs, flow and TDS, are exactly what the Brine Disposal Cost calculator takes as inputs.

Run the calculations in a fixed order: set recovery from the water chemistry, pick flux from the membrane supplier's guideline for your feed type, compute area and element count, estimate feed pressure from osmotic pressure plus differential losses, then compute pump power and specific energy. Two unit traps cause most errors. First, mixing LMH and GFD misstates area by 41 percent if you convert in the wrong direction. Second, 1 bar equals 14.5 psi, and confusing them on a 16 bar system wrecks the power estimate in one spreadsheet cell. Rerun the numbers quarterly against SCADA data, not just at design.

Published 2026-07-02.