Mathematical model of multiphase flow propagation for the case of underwater pipeline damage

Abstract

The paper deals with the case of damage to the underwater pipeline through which oil and associated gas are transported. The process of oil and gas migration is described by the flow of a multiphase submerged jet. At the initial moment, the temperature of the incoming hydrocarbons, their initial velocity, the temperature of the surrounding water, the depth of the pipeline is known. The paper considers two cases of different initial parameters of hydrocarbon outflow from the pipeline. In the first case, the thermobaric environmental conditions correspond to the conditions of hydrate formation and stable existence. Such a case corresponds to the conditions of the hydrocarbons flow in the Gulf of Mexico. In the second case, hydrate is not formed. Such flows correspond to the cases of oil transportation through pipelines in the Baltic sea (for example, Nord stream–2). The process of hydrate formation will be characterized by the following dynamics of the bubble: first, it will be completely gas, then a hydrate shell (composite bubble) will begin to form on its surface, then the bubble will become completely hydrate, which will be the final stage. The integral Lagrangian control volume method will be considered for modeling the dynamics of hydrocarbon jet propagation. According to this method, the jet is considered as a sequence of elementary volumes. When modeling the jet flow, the laws of conservation of mass, momentum and energy for the components included in the control volume are taken into account. The equations are used taking into account the possible formation of hydrate. Thermophysical characteristics of hydrocarbons coming from the damaged pipeline for cases of deep-water and shallow-water pipeline laying are obtained. The trajectories of hydrocarbon migration, the dependence of the jet temperature and density on the vertical coordinate are analyzed.