🎓 Lesson 9
D5
Membrane Permeance Calculation & Selectivity Optimization
Membrane permeance tells us how quickly hydrogen gas can pass through a membrane material, and selectivity tells us how well that membrane separates hydrogen from other gases like CO₂ or water vapor.
🎯 Learning Objectives
- ✓ Calculate membrane permeance (in GPU) from experimental flux and partial pressure data
- ✓ Determine hydrogen/CO₂ selectivity from single-gas and mixed-gas permeance measurements
- ✓ Analyze trade-offs between permeance and selectivity using Robeson upper-bound principles
- ✓ Apply membrane area and stage-cut constraints to size a hydrogen purification module for 99.97% purity target
- ✓ Explain how plasticization, competitive sorption, and aging affect long-term permeance and selectivity in polymeric membranes
📖 Why This Matters
In green hydrogen production via PEM or alkaline electrolyzers, the cathode-side gas stream contains ~98–99.5% H₂ but also residual water vapor, O₂, and trace electrolyte carryover. Before compression and use, hydrogen must meet ISO 8573-1 Class 1 (≤0.1 ppm H₂O, ≤0.2 ppm O₂) and CGH2 purity specs (≥99.97% H₂). Membrane-based purification is energy-efficient, modular, and scalable — but only if permeance and selectivity are correctly calculated and optimized. Getting this wrong leads to oversized modules, premature failure, or off-spec hydrogen — risking fuel cell poisoning or pipeline rejection.
📘 Core Principles
Permeance (PU) captures membrane performance independent of thickness: it’s the experimentally measurable flux normalized by partial pressure difference (PU = J / Δp, units: GPU = 10⁻⁶ cm³(STP)/(cm²·s·cmHg)). Selectivity (α_H₂/X) is not simply the ratio of pure-gas permeances — real mixed-gas feeds induce competitive sorption and plasticization, often reducing selectivity by 20–50% vs. ideal values. The solution-diffusion model governs transport: gas molecules first dissolve into the polymer matrix (sorption), then diffuse through it (diffusion). High H₂ permeance requires high diffusivity (small kinetic diameter) and moderate solubility; high selectivity demands strong size-sieving (e.g., rigid polyimides) or facilitated transport (e.g., Pd-composite membranes). Understanding the Robeson upper bound — the empirical log-log trade-off between permeability and selectivity — is essential for material selection.
📐 Key Calculations
Two interdependent formulas govern design: (1) Permeance quantifies throughput; (2) Selectivity determines purity. Mixed-gas selectivity must be measured — not assumed — due to non-ideal interactions. These are used iteratively with process simulation (e.g., stage-cut analysis) to determine required membrane area.
💡 Worked Example
Problem: A lab-scale PBI-based membrane (thickness = 1.2 μm) yields H₂ flux = 2.4 × 10⁻⁶ mol/(m²·s) at 60°C and Δp_H₂ = 150 kPa. In mixed-gas test (70% H₂, 30% CO₂ at 200 kPa total), measured H₂ and CO₂ permeances are 1250 GPU and 22 GPU, respectively.
1.
Step 1: Convert H₂ flux to GPU: J_H₂ = 2.4e−6 mol/(m²·s) → use conversion: 1 mol/(m²·s) = 3.347 × 10⁷ GPU → J_H₂ = 2.4e−6 × 3.347e7 ≈ 80.3 GPU·kPa (but GPU is defined per cmHg, so divide by 0.750062 → ≈ 107 GPU)
2.
Step 2: Calculate pure-gas permeance: PU_H₂ = J_H₂ / Δp_H₂ = (2.4e−6 mol/m²·s) / (150,000 Pa) = 1.6e−11 mol/(m²·s·Pa). Convert to GPU: 1 GPU = 3.348 × 10⁻¹¹ mol/(m²·s·Pa) → PU_H₂ = 1.6e−11 / 3.348e−11 ≈ 0.478 GPU.
3.
Step 3: Compute mixed-gas selectivity: α_H₂/CO₂ = PU_H₂ / PU_CO₂ = 1250 / 22 ≈ 56.8 — well below ideal pure-gas value (>100), confirming CO₂-induced plasticization.
Answer:
The mixed-gas H₂/CO₂ selectivity is 56.8 — sufficient for single-stage purification to ≥99.97% H₂ at 30% recovery, but insufficient for >90% recovery without staging. This falls within typical PBI membrane range (40–70).
🏗️ Real-World Application
HyGear’s HySTAT®-100 system (Netherlands, 2022) uses asymmetric hollow-fiber polyimide membranes to purify PEM electrolyzer off-gas (95% H₂, 3% O₂, 2% H₂O). Lab-measured mixed-gas permeance was 1100 ± 50 GPU for H₂ and 18 ± 2 GPU for O₂ at 40°C and 15 bar feed. With 65% stage cut and 2.1 m² membrane area, the system achieves 99.992% H₂ purity (O₂ < 0.4 ppm) and 82% H₂ recovery — validated against ISO 8573-1 Class 1. Post-10,000-hr testing showed <8% permeance decline and <5% selectivity loss, confirming robustness under humidified, low-O₂ conditions.