Reference ID: MET-077B | Process Engineering Reference Sheets Calculation Guide
Introduction & Context
Membrane processes (RO, NF, UF, MF) are strongly temperature-dependent because the permeate flux is inversely proportional to the dynamic viscosity of the feed water. A 1 °C rise typically increases flux by ≈ 1.5–3 % because viscosity drops exponentially with temperature. Engineers use this correlation to:
normalise pilot data collected at different seasons,
predict summer/winter capacity for system design,
check whether higher temperature will exceed membrane or sanitisation limits.
Methodology & Formulas
Assume pure-water viscosity ratio governs flux ratio; membrane structure, pressure and recovery remain unchanged.
Measure or look up dynamic viscosities at the two temperatures:
\[ \mu(T) \quad [\text{cP}] \]
Compute the flux correction factor
\[ \frac{J_{T_2}}{J_{T_1}} = \frac{\mu(T_1)}{\mu(T_2)} \]
Apply the factor to the measured flux
\[ J_{T_2} = J_{T_1} \cdot \frac{\mu(T_1)}{\mu(T_2)} \]
Operating Regimes & Limits
Parameter
Range / Threshold
Comment
Correlation validity
15 °C ≤ T ≤ 55 °C
Linear viscosity ratio assumption holds
Membrane rating
T ≤ 55 °C
Manufacturer’s maximum continuous temperature
Sanitisation trigger
T > 45 °C
Consider loop sanitisation if idle > 2 h
For most thin-film composite RO membranes, water viscosity drops about 2.5 % per °C, so a 10 °C increase typically raises pure-water flux by 25–30 %. Real seawater systems see slightly less gain (≈20 %) because osmotic pressure also rises with temperature. Expect roughly 3 % flux increase per °C as a quick rule of thumb.
The apparent salt permeability coefficient (B) follows an Arrhenius relationship with a higher activation energy than the water permeability coefficient (A). Typical values:
EA for A ≈ 15 kJ mol⁻¹
EA for B ≈ 25 kJ mol⁻¹
Consequently, every 10 °C rise can boost salt passage 30–40 % while water flux increases only 20–30 %, causing permeate conductivity to climb.
Check these membrane-specific limits:
Maximum continuous temperature (usually 45 °C for RO, 70 °C for some NF)
Feed pressure derating—above 35 °C many polyamide backings soften, so reduce ΔP by 0.1 bar per °C above 35 °C
Element shrinkage—thermal expansion mismatch between glue lines and permeate spacer can cause telescoping if ΔT > 5 °C across the vessel
Use the membrane supplier’s temperature correction factor (TCF) table to normalize flux at 25 °C. Steps:
Keep NF within ±10 % of baseline to avoid excessive fouling
If temperature rises >8 °C, lower feed pressure or increase recovery to hold NF constant; record the new operating point in the O&M log to maintain warranty coverage
Worked Example: Estimating Permeate Flux at 50 °C
A small dairy plant uses a spiral-wound RO unit to concentrate whey. During night-shift operation the feed temperature drops to 20 °C, giving a measured permeate flux of 30 L m-2 h-1. The process engineer wants to know the new steady-state flux when the feed is pre-heated to 50 °C, assuming pressure and concentration remain unchanged and the membrane is rated for 55 °C.
Knowns
Reference temperature, \(T_1\) = 20 °C
Target temperature, \(T_2\) = 50 °C
Flux at 20 °C, \(J_{T_1}\) = 30 L m-2 h-1
Dynamic viscosity at 20 °C, \(\mu_{20\,^\circ\text{C}}\) = 1.002 mPa·s
Dynamic viscosity at 50 °C, \(\mu_{50\,^\circ\text{C}}\) = 0.547 mPa·s
