Beyond the mean: A probabilistic approach using the probability density function for assessing ammonia leak consequences in ship-to-ship bunkering

Driven by net-zero emissions goals, ammonia has emerged as a promising alternative marine fuel. However, accidental leaks of ammonia pose risks of fatalities, injuries, financial losses, and environmental harm, highlighting the critical importance of safety regulations for its use. Traditional consequence assessments for hazardous material releases generally focus on the mean concentration to determine exposure or lethal zones. Dispersion models and Computational Fluid Dynamics (CFD) simulations are common tools for estimating this mean concentration. However, these assessments, which rely solely on the mean value of ammonia, neglect concentration fluctuations, potentially exposing personnel to unsafe levels even within seemingly safe zones. This study goes beyond the mean by using a probabilistic approach based on the presumed probability density function (PDF) to analyse the instantaneous concentration of ammonia leaked during ship-to-ship bunkering, a vital maritime activity. In this study, instantaneous concentration refers to statistically reconstructed local concentration values accounting for turbulent fluctuations around the mean, rather than time-resolved concentrations obtained from unsteady simulations. Reynolds-averaged Navier-Stokes (RANS) simulations are used to calculate the mean concentration, along with an additional transport equation to quantify the variance of concentration fluctuations. Unlike traditional methods that rely solely on the mean concentration, this probabilistic approach evaluates the likelihood of ammonia concentrations exceeding established threshold limits. Results reveal substantially larger areas with a 1% or 10% probability of surpassing these thresholds, compared to assessments based solely on the mean concentration. This indicates personnel could still encounter hazardous levels in areas considered safe. Therefore, incorporating concentration fluctuations into consequence assessments and safety regulations is essential for ensuring safer ammonia bunkering operations. The proposed PDF-based probabilistic approach provides a more informative framework for quantitative risk assessment.