Reverse Osmosis (RO) Membrane Sizing & Flux Calculator

Pushing system recovery ($Y$) beyond saturation limits causes reactive silica ($SiO_2 > 120-150$ mg/L in reject) or gypsum ($CaSO_4$) to precipitate instantaneously on tail elements. Unlike carbonate scale which dissolves with acid cleaning, polymerized silica scale forms a glass-like vitrified glaze requiring harsh hazardous ammonium bifluoride or full membrane bundle replacement.

Polyamide membrane permeability drops by approximately 3% per °C reduction due to water viscosity increase. Sizing an RO system at 25°C design conditions results in severe feed pressure starvation in winter (e.g. 10°C water requires ~45% higher NDP for identical permeate output). If the high-pressure pump variable frequency drive lacks head margin, permeate volume collapses.

Solutes rejected by the active skin accumulate in the stagnant boundary layer, creating a wall concentration ($C_m$) significantly higher than bulk stream ($C_b$). At low crossflow velocity ($N_{Re} < 100$ in spacer channels), the polarization modulus $eta = C_m / C_b$ exceeds 1.20, driving local osmotic pressure up and slashing effective NDP while tripling salt passage.

In a 6-element or 7-element pressure vessel, the lead element faces fresh feed water with minimum osmotic pressure, operating at fluxes exceeding 25-30 LMH and experiencing accelerated colloidal/biofouling. Meanwhile, the 7th element faces concentrated reject with elevated osmotic pressure, generating barely 5 LMH. Unbalanced multi-stage arrays without interstage booster pumps suffer premature lead fouling and tail scaling.

Aromatic polyamide membranes tolerate less than 1,000 ppm-hours of free chlorine before the nitrogen-hydrogen amide bonds undergo irreversible $N$-chlorination followed by Orton rearrangement and ring cleavage. This destroys salt rejection irreversibly. Continuous bisulfite ($SBS$) dosing with dual online ORP sensors ($< 250$ mV) upstream of membranes is mandatory.