How to Measure Gas Permeance and Selectivity of Separation Membranes

2 days ago

6 min read

At a glance. Gas permeance is the flux of a gas divided by its partial pressure difference across the membrane, usually reported in GPU for asymmetric and composite membranes. Permeability is permeance multiplied by the thickness of a homogeneous dense layer, reported in Barrer. Measure dense films by the constant-volume, variable-pressure (time-lag) method, measure high-flux membranes and hollow fibre modules by the constant-pressure, variable-volume method, and confirm selectivity with mixed-gas tests before drawing conclusions.

What is the difference between permeance, permeability and selectivity?

Permeance is the steady-state flux of gas i divided by its partial pressure difference: N_i / Δp_i. ASTM D1434 gives its SI unit as mol m⁻² s⁻¹ Pa⁻¹. Membrane scientists more often use the gas permeation unit: 1 GPU = 10⁻⁶ cm³(STP) cm⁻² s⁻¹ cmHg⁻¹ ≈ 3.35 × 10⁻¹⁰ mol m⁻² s⁻¹ Pa⁻¹.

Permeability is permeance multiplied by the thickness of the selective layer, and is a material property: 1 Barrer = 10⁻¹⁰ cm³(STP) cm cm⁻² s⁻¹ cmHg⁻¹ ≈ 3.35 × 10⁻¹⁶ mol m m⁻² s⁻¹ Pa⁻¹. A 1 µm dense layer of a 1 Barrer polymer therefore has a permeance of 1 GPU. ASTM D1434 notes that permeability is meaningful only for homogeneous materials, so for an asymmetric or thin-film composite membrane, report permeance.

Selectivity comes in two forms. Ideal selectivity is the ratio of single-gas permeabilities or permeances, α = P_A / P_B. The separation factor from a mixed-gas test is (y_A / y_B) / (x_A / x_B), where y and x are permeate and feed mole fractions. In the solution–diffusion model, permeability is the product of diffusivity and solubility, P = D × S, which is why a time-lag test that separates the two is so useful. The Koros and Fleming review remains a sound reference on these fundamentals.

Accuracy matters because candidate materials are judged against Robeson's upper bound, the empirical trade-off between permeability and selectivity. A modest error on either axis can move a result across the line. For the liquid-phase equivalents of these calculations, see our membrane flux and permeability guide.

Which test method should I use?

Feature	Constant-volume, variable-pressure	Constant-pressure, variable-volume	Mixed-gas test
Best for	Dense films and low-permeability materials	Asymmetric and composite membranes, hollow fibre modules	Real separation performance
What is measured	Pressure rise in a calibrated, evacuated downstream volume	Permeate flow at about atmospheric pressure	Feed, retentate and permeate flows and compositions
Main results	Permeability, time lag, diffusivity and solubility	Permeance	Separation factor and mixed-gas permeances
Standard reference	ASTM D1434 Procedure M (manometric)	ASTM D1434 Procedure V (volumetric)	Laboratory practice, with GC analysis
Main error sources	Leaks, outgassing, volume calibration	Flow-meter range, permeate back-pressure	Stage cut, concentration polarisation, GC calibration

Constant-volume, variable-pressure (time-lag) method

The membrane is degassed under vacuum, the downstream volume is isolated and the feed gas is admitted. A sensitive absolute pressure transducer records the downstream pressure rise. Once the rise is linear, permeability follows from P = (V l / (A R T p_feed)) × (dp/dt), where V is the downstream volume, l the thickness, A the area and T the temperature, provided the downstream pressure stays far below the feed. Extrapolating the linear portion back to the time axis gives the time lag θ, and diffusivity follows from the classical Daynes–Barrer relation D = l² / 6θ (see an applied example of the method). Solubility is then S = P / D.

Before each test, measure the leak and outgassing rate with the feed isolated and subtract it. Calibrate the downstream volume, typically by gas expansion from a known reference volume, because every result scales with it.

Constant-pressure, variable-volume method

The permeate leaves at about atmospheric pressure and its flow is measured with a bubble flowmeter or a calibrated mass flow meter. This is the practical route for high-flux asymmetric membranes and hollow fibre modules, where a closed downstream volume would fill in seconds. Keep permeate back-pressure low and known, and check that the flow meter is calibrated for each gas.

Mixed-gas testing

Single-gas tests can misstate selectivity when gases compete for sorption sites or when one gas, typically CO₂, swells the polymer. In a mixed-gas test the feed composition is fixed, a retentate valve sets the flow, and a gas chromatograph analyses the permeate, swept or under vacuum. Keep the stage cut, the ratio of permeate to feed flow, low (1% or less is common in laboratory tests) so the feed composition stays effectively constant along the membrane, and calculate driving forces from partial pressures, or fugacities at high pressure.

How do I test hollow fibre membranes?

Pot a small module of a few fibres, count them, and measure their effective length and diameters. State whether the area is based on the outer or inner diameter, because the two differ substantially for thick-walled fibres. Shell-side feed suits most gas separation fibres; bore-side feed is limited by the fibre's burst pressure and by pressure drop along the lumen.

If the ideal selectivity of a fibre falls well below that of a dense film of the same polymer, the skin has defects. Henis and Tripodi's resistance model explains why a thin silicone coating plugs those defects and restores selectivity with little loss of permeance.

What affects the accuracy of a permeation result?

Temperature. Permeability changes with temperature, so control the cell and the feed gas and report the test temperature.
Pressure. In glassy polymers, CO₂ above a threshold pressure plasticises the membrane, raising permeability and lowering selectivity. Run a pressure sweep rather than a single point.
Physical ageing. Thin glassy films and hollow fibre skins lose permeance over time, so record sample age at each test.
Gas order. Test non-condensable gases such as He, H₂, N₂, O₂ and CH₄ before CO₂ to avoid conditioning effects.
Thickness. Measure dense films at several points; a thickness error passes straight into permeability.
Leaks. Leak-test the cell and lines with the membrane replaced by an impermeable disc.

Step-by-step checklist for a gas permeation test

Decide whether you need an intrinsic material property (dense film, Barrer) or product performance (permeance, GPU).
Choose the method from the expected flux: constant volume for low flux, constant pressure for high flux.
Define the gases, feed pressures, temperature and test order.
Prepare and measure the sample: thickness, effective area and sealing method, or fibre count, length and diameter basis.
Leak-test the cell and downstream system and record the baseline rate.
Degas the sample under vacuum before each gas.
Run to steady state, for several multiples of the time lag, before taking the slope.
Calculate in consistent units and convert between SI, GPU and Barrer.
Repeat on at least three samples and report the mean and spread.
For mixed gases, set a low stage cut, calibrate the GC with certified standards and report partial pressures.

Frequently asked questions

What is a GPU?

The gas permeation unit is a permeance: 10⁻⁶ cm³(STP) of gas per cm² of membrane per second per cmHg of partial pressure difference, or about 3.35 × 10⁻¹⁰ mol m⁻² s⁻¹ Pa⁻¹. It is used for asymmetric and composite membranes, where the selective layer thickness is not known precisely.

What is the difference between ideal selectivity and separation factor?

Ideal selectivity is the ratio of two single-gas permeabilities or permeances measured separately. The separation factor is calculated from permeate and feed compositions in a mixed-gas test. The two often differ, because competitive sorption, plasticisation and concentration polarisation only appear when gases permeate together. For CO₂ separations at high pressure, the mixed-gas value is often the lower one.

Can I report permeability for a composite membrane?

Report permeance instead. Permeability assumes a homogeneous layer of known thickness, which a composite or asymmetric membrane does not have, and ASTM D1434 restricts permeability to homogeneous materials.

How long does a time-lag test take?

The time lag is l² / 6D, so it grows with the square of thickness: doubling the film thickness quadruples the time lag. Allow several time lags for the pressure rise to become linear before measuring the slope. Thin, fast films take minutes; thick films of slow gases can take hours.

Why do my hollow fibres show low selectivity?

The usual cause is defects in the skin, which let gas bypass the selective layer by Knudsen or viscous flow. Check the potting for leaks first, then compare with a dense film of the same polymer. A thin silicone coating can seal skin defects and confirm the diagnosis.

Why does CO₂ permeability rise with feed pressure?

Above a polymer-specific pressure, dissolved CO₂ swells glassy polymers and increases chain mobility, a process called plasticisation. Permeability of all gases rises and selectivity falls. Measuring a pressure sweep shows where it starts.

How Tech Inc. builds gas permeation test systems

We build gas permeation rigs to the client's duty: flat-sheet cells and hollow fibre module holders, upstream gas panels with regulation and stream switching, evacuated downstream volumes with absolute pressure transducers for time-lag work, mass flow measurement for constant-pressure tests, temperature-controlled enclosures and GC connections for mixed gases. Our permeameter range includes a gas permeameter for membranes, films and porous media, a gas diffusion analyser for diffusion coefficients and a gas adsorption and permeation analyser that adds sorption isotherms, so solubility and diffusivity can be measured on the same material.

For fibre development, our laboratory hollow fibre spinning machine and potting machine produce the modules these rigs test. Every system is designed, built and factory-tested in our own facilities. Tech Inc. is part of an engineering group founded in 1990, with offices in Canada, India, Estonia and Saudi Arabia, and our test equipment is trusted by universities and R&D laboratories worldwide. For how consistent permeation data supports model-guided materials discovery, see AI in membrane research.

Send your gases, pressures, temperatures and membrane formats to mail@techincresearch.com or call +1 (289) 622-1032, and we will propose a permeation system configured for your work.