Abstract
The study presents results of the development of a mathematical model of an oscillating gas bubble. It takes into account inertial and thermodynamic components of oscillation of gas bubbles in a liquid, mass transfer processes near a surface of a bubble and phase transition processes in a liquid. Considering mentioned features in the mathematical model, it is possible to get values of temperatures of gas, liquid and solid phases, pressure of a gas medium and a size of a bubble, a rate of a side movement, localization and a rate of phase transitions in a liquid, intensity of heat and mass transfer processes at a bubble boundary and many other data at any time. We performed a series of estimating calculations of the hydrate formation of the propane-butane mixture with the help of the proposed mathematical model. We investigated the influence of initial temperature and pressure of the gas mixture on the hydrate formation process. We obtained graphs of the hydration formation and temperature regime of a gas bubble, distribution of temperature fields in a liquid under conditions of phase transition processes and accumulation of hydrate in separate layers of a liquid. The performed studies show that the whole period of hydrate formation consists of three parts: the initial heating of gas in a bubble, the period of oscillations and the period of stationary heat transfer. The maximum rate of hydrate formation is observed during the period of heating of a gas in a bubble. It has a short duration of 2÷40 μs, but it is the most productive. The duration of the oscillation period depends on thermobaric conditions and may exceed 200 μs. We established that there exists a region of gas temperatures where the rate of the hydrate formation is maximal. We can use the proposed mathematical model to determine thermophysical characteristics of gas bubbles, liquid and steam in various technological processes associated with the formation of gas hydrates, dissolution of gases in liquid, hardening of foam, and others. The conducted study can be useful for optimization of technological processes connected with formation of gas hydrates.
Highlights
Thermodynamic processes, which occur on a surface of steam-and-gas bubbles, play a key role in many advanced industrial technologies
Under natural conditions and technological processes, formation of gas hydrates often occurs on a surface of gas bubbles in water under certain thermobaric conditions [6, 7]
We supplemented a mathematical model of transition thermodynamic processes of an oscillating gas bubble with a description of diffusion processes on the interphase gas-water surface
Summary
Thermodynamic processes, which occur on a surface of steam-and-gas bubbles, play a key role in many advanced industrial technologies These are obtaining of hydrate of natural gas [1, 2] for transportation and storage, desalination of seawater with a help of isobutane hydrate [3, 4], production of heat-insulating materials [5] by method of swelling, mixing of colloidal solutions, and many others. Direct observation of processes inside a bubble during formation of gas hydrates is a complex engineering and technological problem. Such bubbles are small in size (10-3÷10-4 m), they have high pressure (up to 20 MPa) and high oscillation rate (approximately 10-5 s). Such a mathematical model should take into account all thermodynamic peculiarities of this complex process
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