Due to possible hydrocarbon leaks that can occur when a well is damaged during deep-sea offshore oil production, it is important to study methods for eliminating leaks. The article deals with the mathematical model of the device "dome-separator", which is used to eliminate deep-water leaks. The article also discusses the possibility of using and advantages of such a device. The paper presents a scheme of the device, a mathematical model that contains the basic equations. In the process of the computational experiments, the thermophysical characteristics of hydrocarbons accumulated inside the dome were determined, and the process of accumulation of hydrocarbons inside the dome was modeled.

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