Probabilistic Assessment of Time to Reach the Lower Explosive Limit Following Accidental Methane Leaks

Accidental methane leaks in enclosed or semi-enclosed spaces may generate hazardous atmospheres within short time intervals, particularly when ventilation is weak or uncertain. Deterministic calculations are commonly used to estimate the time required to reach the lower explosive limit (LEL), but such approaches do not account for uncertainty in rupture geometry, discharge characteristics, gas pressure, or ventilation conditions. This paper develops a probabilistic framework for assessing methane accumulation based on a deterministic zero-dimensional mass-balance model extended through Monte Carlo uncertainty propagation using Latin Hypercube Sampling. Uncertainty is introduced in the effective area factor, discharge coefficient, pipe pressure, wind speed, and pressure coefficient difference, and the resulting distributions of time to reach the LEL, steady-state concentration, and critical ventilation thresholds are evaluated. Two representative residential scenarios are analysed: a kitchen of 18 m³ with a 3/4” hose and a kitchen of 18 m³ with a 1/2” hose, both at 25 mbar. For the 3/4” scenario, the predicted 90% interval for the time to reach the LEL is 50.3–102.3 s, compared with a deterministic estimate of 60.4 s. For the 1/2” scenario, the corresponding interval is 71.9–146.0 s, compared with a deterministic estimate of 86.4 s. Sensitivity analysis shows that the effective area factor dominates the airtight case, whereas wind speed and pressure coefficient difference dominate the ventilated case. The concept of a deterministic critical ventilation threshold is further generalized into probabilistic ventilation thresholds linked to specified confidence levels. For Scenario S1, achieving 95% confidence that the steady-state concentration remains below the LEL requires ACH=71.6 h⁻¹, compared with a deterministic threshold of 59.6 h⁻¹. The proposed framework provides a more realistic basis for forensic interpretation, detector placement, ventilation design, and risk-informed gas safety assessment than deterministic methods alone.