The significant growth in offshore operations increases the risk of a pipeline rupture, even considering the high standards of safety involved. Throughout a submarine leakage, four different amounts of oil may be accounted. The first one is the oil volume released until the leakage detection. The second one is the volume leaked throughout mitigation initiatives (e.g., pump shutdown and valve closure). The third parcel is the amount released by gravitational flow. Finally, the fourth and last amount of oil is released due to the water-oil entrainment, generally known as advective migration. Normally, a considerable amount of oil is released in this step. It begins just after the internal pipeline pressure becomes equal to the external one. The present work continues to introduce a mathematical alternative approach, based on the theories of perturbation and unstable immiscible displacement, to accurately estimate the leakage kinetics and the amount of oil released by the advective migration phenomenon. Situations considering different hole sizes and thicknesses were tested experimentally and through simulations. Additional experiments were accomplished using smooth and rough edge surfaces, besides different slopes (using the horizontal plane as reference). Those experiments permitted a preliminary evaluation of the importance of these factors. The results obtained with the model showed good agreement with the experimental data in many situations considered.