How to Calculate Membrane Flux and Permeability: Formulas and Examples

How to Calculate Membrane Flux and Permeability: Formulas and Examples

Membrane flux and permeability are the two most fundamental performance parameters in membrane science. Understanding how to calculate, measure, and interpret these values is essential for membrane researchers, process engineers, and system designers. This guide provides the formulas, calculation methods, and practical examples.

What Is Membrane Flux?

Flux (J) is the volume of permeate passing through a unit area of membrane per unit time. It is the primary measure of membrane productivity.

Formula: J = V / (A x t)

• J = flux (L/m2.h or LMH)

• V = volume of permeate collected (L)

• A = effective membrane area (m2)

• t = collection time (h)

Example: If 250 mL of permeate is collected from a membrane with 42 cm2 effective area in 30 minutes: J = 0.250 / (0.0042 x 0.5) = 119 LMH

What Is Membrane Permeability?

Permeability (A-value or Lp) normalizes flux by the net driving pressure, allowing comparison of intrinsic membrane performance independent of operating conditions.

Formula: Lp = J / DP_net

• Lp = permeability (LMH/bar)

• J = flux (LMH)

• DP_net = net driving pressure (bar) = DP_applied - Dpi

• DP_applied = transmembrane pressure (bar)

• Dpi = osmotic pressure difference across the membrane (bar)

For MF/UF (No Osmotic Pressure)

For MF and UF membranes treating low-salinity water, osmotic pressure is negligible: Lp = J / TMP, where TMP is the transmembrane pressure.

For RO/NF (Osmotic Pressure Significant)

For RO and NF, osmotic pressure must be subtracted: Lp = J / (TMP - Dpi). For NaCl solutions, osmotic pressure is approximately 0.7 bar per 1000 ppm.

Temperature Normalization

Flux increases approximately 3% per C due to decreased water viscosity. To normalize flux to the standard temperature of 25C:

J_25 = J_T x TCF, where TCF = exp[2640 x (1/T - 1/298.15)] and T is in Kelvin.

Tech Inc. membrane test systems include precision flow measurement and data acquisition for accurate flux and permeability calculations. Our software automatically normalizes results to standard temperature conditions.

Frequently Asked Questions

What is a typical flux for RO membranes?

Commercial RO systems operate at 15-25 LMH for seawater and 20-35 LMH for brackish water. Laboratory flux can be higher (30-60 LMH) due to lower recovery and concentration polarization.

Why does flux decline over time?

Flux decline is caused by membrane fouling (deposition of particles, organics, or biological material), concentration polarization (salt buildup at the membrane surface), membrane compaction (especially for new membranes under pressure), and scaling (precipitation of sparingly soluble salts).