Optimizing dual-fuel ship operations considering methane slip

Liquefied natural gas (LNG) is increasingly viewed as a promising fuel for dual-fuel ships due to its cost-effectiveness, low emissions, and alignment with regulatory requirements. However, the high methane content of LNG, ranging from 85% to 95%, presents a significant challenge because of the phenomenon of methane slip whereby unburned methane escapes from the engine's combustion chamber and other parts of the storage and transportation systems. Methane slip, which peaks at low ship speeds and decreases at higher speeds, can lead to substantial environmental pollution if it is not properly managed. This study rigorously examines the impact of sailing speed on methane slip rates and recognizes the complexities of fuel usage in dual-fuel ships. We develop a nonlinear mixed-integer programming model designed for container shipping companies that aims to optimize fleet composition, sailing speed, and fuel usage strategies. The objective of the model is to minimize total operational costs, including fuel expenses and taxes related to carbon emissions and methane slip. To address the computational challenges posed by the model's nonlinearity, we propose a tailored solution method that uses sailing time as a proxy for speed, discretizing these times for effective implementation. The validity of this method is supported by theoretical guarantees and demonstrated through numerical experiments. Our computational results indicate that accounting for methane slip in the operational management of dual-fuel ships can help mitigate financial losses under certain conditions.