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Kildibaeva S.R., Dalinskij E.T., Kildibaeva G.R. Mathematical model of multiphase flow propagation for the case of underwater pipeline damage. Multiphase Systems. 14 (2019) 2. 142–147 (in Russian).
2019. Vol. 14. Issue 2, Pp. 142–147
URL: http://mfs.uimech.org/mfs2019.2.020
DOI: 10.21662/mfs2019.2.020
Mathematical model of multiphase flow propagation for the case of underwater pipeline damage
Kildibaeva S.R., Dalinskij E.T., Kildibaeva G.R.
Sterlitamak Branch of Bashkir State University, Sterlitamak

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.

Keywords

hydrocarbons,
oil spill,
pipeline rupture,
oil,
methane,
hydrate formation,
hydrate

Article outline

The purpose of this work is to study the flow of hydrocarbons coming from a damaged pipeline in the form of a jet. The paper considers the flow of a multiphase submerged jet at different depths, including flows with phase transitions.

Due to the increase oil production in deep-water fields of the World ocean, the probability of oil spills into the ocean increases. Often such spills are man-made: damage to wells, oil pipelines and drilling rigs. The cause of the spill may be corrosion of the pipeline, mechanical damage to the oil production structure, fire, etc. Oil spills in the Gulf of Mexico on platforms Deepwater Horizon, Ixtoc-1; in the Gulf of Alaska Exxon Valdez indicate the need to study methods to eliminate leaks. Over the past decade, more than 1 billion gallons of oil have spilled into the world's oceans as a result of accidents around the world. This shows the serious scale of the problem.

In connection with the possible leakage of hydrocarbons into the waters of the World ocean, there is a need to study the characteristics of the distribution of petroleum products. Forecast migration of petroleum products will reduce the time of elimination of leakage. To do this, it is important to study the characteristics of the distribution of oil and associated gas, their interaction with the surrounding water; as well as the study of the influence of undercurrents on the distribution of oil in the environment.

The Integral Lagrangian control volume method is considered as the method used to describe hydrocarbon migration. According to this method, the jet is considered as a sequence of elementary volumes, each of which is characterized by temperature, velocity, density, coordinates in space, volume contents of each component in the jet. Knowing the changes of these parameters from the vertical coordinate, we get information about the propagation of the jet. The method is supplemented with ratios that correspond to the process of hydrate formation. The process of hydrate formation has a significant impact on the parameters of the jet propagation: since hydrate formation is an exothermic process, the temperature of the jet in the case of hydrate formation and its absence may vary. The intensity of heat release directly depends on the intensity of hydrate formation. 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.

As a result, two cases of flow of a multiphase jet from a damaged pipeline are considered/ the First case when the depth of the pipeline corresponds to the conditions of stable existence of the hydrate (deep-water case). The second case, when the depth of the pipeline does not meet the conditions of hydrate formation (shallow case). The first case corresponds to the conditions of production and transportation of hydrocarbons in the Gulf of Mexico, the second case corresponds to the transportation of hydrocarbons through pipelines in the Baltic sea.

The peculiarities of hydrocarbon propagation for each of the cases are studied, jet trajectories, dependences of the thermophysical parameters of the jet on the vertical coordinate from the initial conditions of the pipeline are obtained.

Originality. Studying the flow of multiphase submerged jets will expand knowledge about the behavior of hydrocarbons flowing from a damaged pipeline or well. Information about the process of distribution of submerged jets will reduce the time of elimination of leaks.

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