Minimum turndown and H₂ in O₂

Method, assumptions and limits

Hydrogen crossover is modeled as steady-state Fickian diffusion through the membrane, driven by the H₂ partial-pressure differential between electrodes, competing against oxygen generation which scales directly with current:

The driving force is the H₂ partial-pressure differential across the membrane, not cathode pressure minus anode total pressure — the anode side is mostly O₂ and water vapor, and its H₂ partial pressure is approximated as ~0 (a standard simplification, valid in exactly the low-single-digit-vol% regime this tool screens for). Anode pressure is still shown for context but does not itself change this result — only the cathode/anode H₂ partial-pressure gap does. Permeability P(T) is Arrhenius-scaled from a value calibrated at 80°C. δ is membrane thickness. This is why crossover is worst at low current: N″_H2 doesn't depend on j at all in this model, while N″_O2 — the thing diluting it — scales linearly with j. Minimum turndown is a dilution problem, not a leak-rate problem.

Membrane calibration

Nafion N117 (178µm) and N212 (50µm) permeability directly calibrated from Bernt, Schröter, Möckl & Gasteiger, "Analysis of Gas Permeation Phenomena in a PEM Water Electrolyzer Operated at High Pressure and High Current Density," J. Electrochem. Soc. 167 (2020), TU München — reported crossover of 0.31 mA/cm²/bar (N117) and 1.10 mA/cm²/bar (N212) at 80°C. Converting both to intrinsic permeability agrees to within 1% (2.86×10⁻¹¹ vs 2.85×10⁻¹¹ mol/(cm·s·bar)) — a strong cross-check that simple 1/thickness scaling holds across this membrane family, which is how N115 and N211 (no direct literature point) are derived.

Zirfon PERL (462µm, AWE) calibrated from Schalenbach & Lueke, "Hydrogen Diffusivity and Electrolyte Permeability of the Zirfon PERL Separator for Alkaline Water Electrolysis," J. Electrochem. Soc. — ~1.5×10⁻⁹ mol/(cm·s·bar) at 80°C, 30 wt% KOH. Zirfon is a porous, liquid-electrolyte-wetted diaphragm, not a dense ion-exchange membrane — a genuinely different transport mechanism from Nafion, so it carries its own activation energy rather than sharing Nafion's.

The lower flammability limit (LFL) of hydrogen in oxygen is about 4 vol% at ambient conditions (Schröder et al., 2004). It changes with pressure and temperature. Alarm and trip thresholds are inputs to this tool, never built-in standards: set them from your own safety case.

What this tool deliberately does not do

• It does not model crossover's dependence on current density. Real permeation rises with j — Bernt et al. report up to ~20x from low to high current at 1 bar (much less, ~1.2x, at 30 bar) — while this tool holds N″_H2 constant and derives the whole j-dependence of x_H2inO2 from O₂ dilution alone. That still gets the safety-relevant direction right (x_H2inO2 falls as load rises), but will understate true crossover at low differential pressure and high current, where the source data shows permeation itself climbing fastest.
• It does not model hydrogen supersaturation in the anode water. Dissolved H₂ can exceed its equilibrium solubility at high current, so real crossover can exceed this Fickian estimate.
• It does not model transient crossover during startup/shutdown or load ramps — steady-state only.
• It does not account for membrane degradation, pinholes, or mechanical damage — permeability is treated as constant with stack age, which real membranes are not.
• It does not know your actual recombiner's real-world efficiency — the number you enter is taken as given, not derived or verified.
• It is current-density based, not flow-based — very small stacks and very large stacks at the same current density and pressure will show the same %, but absolute flow rates (relevant to ventilation/dilution system sizing) differ and are not computed here.