Even considering the high standards of safety involved, the significant and continuous increase in offshore oil exploitation rise the risks of a pipeline rupture, leading to oil spills. If an oil leakage occur, it is necessary to accurately quantify the volume released to correctly foresee the potential environmental impacts and define actions to soften them and clean up the oil spill. The present article introduces a mathematical alternative approach, based on the theories of perturbation and unstable immiscible displacement, to evaluate the occurrence or not of oil leakages through the advective migration phenomenon and estimate the oil volume released. According to preliminary results, the model shows to be promising in accurate estimate the oil volume leaked from a submarine pipeline in case of accident.

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