Calculator Inputs
Formula Used
For a flat film membrane under steady-state conditions, the permeability coefficient is calculated from the measured permeant rate:
- P = (N × l) / (A × Δp)
Related outputs are derived as:
- Permeance = P / l = N / (A × Δp)
- Flux = N / A
How to Use This Calculator
- Pick a calculation mode: compute permeability from rate, or rate from permeability.
- Enter membrane geometry (thickness and area) using your recorded units.
- Enter feed and permeate partial pressures; the tool uses Δp = feed − permeate.
- Provide permeant rate (molar or STP volumetric) or a known permeability value.
- Press Submit to see results above the form, then export to CSV or PDF.
Example Data Table
| Material | Permeant | Thickness (µm) | Area (cm²) | Feed (bar) | Perm (bar) | Rate (cm³(STP)/s) | Estimated P (Barrer) |
|---|---|---|---|---|---|---|---|
| Polymer A | CO₂ | 100 | 10 | 1.0 | 0.0 | 0.0020 | ~27 |
| Polymer B | O₂ | 50 | 5 | 0.8 | 0.1 | 0.0008 | ~19 |
| Composite C | N₂ | 25 | 20 | 2.0 | 0.2 | 0.0015 | ~7 |
Material permeability benchmarks in labs
Gas separation membranes often report CO2 permeability between 20–200 Barrer for many glassy polymers, while O2 may sit near 5–50 Barrer under similar conditions. Dense barrier films for packaging can be below 1 Barrer for O2, emphasizing diffusion control and low free volume. Elastomeric materials may show higher permeability but lower selectivity, so reporting both permeability and selectivity is standard in screening tables.
Impact of thickness and area on reported values
Permeability is an intrinsic property when steady state is reached, but the measured rate scales with area and inversely with thickness. Doubling area doubles flow, while doubling thickness halves flow. Use consistent thickness metrology because a 10% thickness error produces a 10% permeability error. For very thin films, support layers and edge leakage can dominate; document the effective area and sealing method.
Pressure driving force and partial-pressure practice
The calculator uses Δp as feed minus permeate partial pressure, not total pressure. For mixtures, compute y·Ptotal on each side, because selectivity calculations depend on partial pressures. In common permeation rigs, Δp ranges from 0.1 to 3 bar; keep units consistent to avoid order-of-magnitude mistakes. When sweep gas is used, estimate permeate partial pressure from sweep composition and total pressure rather than assuming zero.
Unit conversion checkpoints for reporting
SI permeability is mol·m/(m²·s·Pa). Barrer is widely used for gases, where 1 Barrer equals 3.35×10⁻¹⁶ in SI units. Permeance is P/l and is often expressed in GPU; GPU relates to cm³(STP)/(cm²·s·cmHg). Report the STP basis (22,414 or 22,400 cm³/mol) to keep comparisons fair. Include temperature, upstream humidity, and whether pressures are absolute or gauge, since these change Δp and the derived P.
Quality controls for reliable permeability runs
Confirm steady state by monitoring constant flux over time and repeat at least three runs per sample. Minimize leaks, calibrate flow meters, and record temperature because permeability typically increases with temperature. If you see nonlinearity versus Δp, check for plasticization, defects, or concentration polarization before publishing. A quick mass-balance check—feed loss versus permeate gain—helps flag leaks and adsorption effects early.
FAQs
What does permeability represent in membrane testing?
Permeability quantifies how readily a species transports through a material, combining diffusion and solubility effects. It normalizes measured flow by thickness, area, and partial-pressure driving force, enabling fair comparison between different film geometries.
Permeability vs permeance: what is the difference?
Permeability is an intrinsic material coefficient. Permeance is permeability divided by thickness, so it depends on film thickness. Permeance is convenient for modules and thin-film composites where an exact selective-layer thickness is uncertain.
Why does the calculator ask for partial pressures?
Transport is driven by the permeant’s partial-pressure difference across the film. Using total pressure can overestimate Δp for mixtures and distort selectivity. Enter feed and permeate partial pressures or compute them from composition and total pressure.
When should I use Barrer or SI units?
Barrer is common in gas-separation literature and is easy for comparing polymers. SI units are preferred for rigorous modeling and cross-domain reporting. The calculator shows both so you can match journal conventions and internal lab standards.
How do I estimate permeate pressure when using a sweep gas?
Treat the permeate side as a mixture. Estimate permeate partial pressure from measured sweep composition and total permeate pressure. If composition is unknown, use a conservative upper bound rather than assuming zero, especially at high flux.
Why are my results changing with Δp?
Permeability should be constant at steady state, but real materials can plasticize, swell, or show concentration polarization. Leaks and inaccurate pressure readings also cause apparent Δp dependence. Validate sealing, reach steady state, and repeat runs to confirm trends.