The Conditions for the Existence of an Extended Region of Gas Hydrate Formation in a Porous Medium
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The Conditions for the Existence of an Extended Region of Gas Hydrate Formation in a Porous Medium M. K. Khasanov1* and N. G. Musakaev2** (Submitted by A. M. Elizarov) 1
2
Sterlitamak Branch of the Bashkir State University, Sterlitamak, 453103 Russia
Tyumen Branch of the Khristianovich Institute of Theoretical and Applied Mechanics, Siberian Branch, Russian Academy of Sciences, Tyumen, 625026 Russia Received March 11, 2020; revised March 20, 2020; accepted March 22, 2020
Abstract—Mathematical model of the formation of methane hydrate during gas injection into a porous medium saturated with gas and water is presented. Self-similar solutions, which describe the distributions of parameters in the porous medium, are constructed. The necessary conditions for the existence of a solution with an extended region of gas hydrate formation in the porous medium are proved. DOI: 10.1134/S1995080220070203 Keywords and phrases: self-similar solution, porous medium, gas hydrate, extended region of gas hydrate formation.
1. INTRODUCTION Currently, there is an interest in the use of gas hydrate technologies in the industry. Among them, one can single out the possibility of organizing storages of gas in gas hydrate state in porous media near large gas consumers [1, 2]. A number of works are devoted to the researches of the formation of gas hydrates in a porous reservoir, for example [3–10]. In these works the process of pumping cold gas into a reservoir is studied, the reservoir pores are initially filled with gas and water [3–6, 10] or gas and ice [7–9]. In particular, it was shown that the formation of gas hydrate in a porous medium is possible either on a frontal surface or in an extended region. In [10], for the case of a temperature jump at the gas hydrate formation front, using the method of successive changes of stationary states, an approximate analytical solution was constructed that allows one to determine the position of the boundary of methane hydrate formation depending on various parameters. This study differs from the above works in that based on the self-similar solutions of considered problem the conditions for the existence of a solution with an extended region of phase transitions are formulated and proved. * **
E-mail: [email protected] E-mail: [email protected]
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THE CONDITIONS FOR THE EXISTENCE OF AN EXTENDED REGION
pe Te
1
2
3
Methane + hydrate CH4
Methane + water Water + hydrate CH4
Methane + water Water (p0, T0, Sl0)
0
x(n)
x(d)
1223
x
Fig. 1. Schematic representation of studied processes. At the boundary between the second and third zones x = x(d) , the methane hydrate formation begins, and at the boundary between the first and second zones x = x(n) it ends.
2. SELF-SIMILAR SOLUTIONS OF THE PROBLEM Similarly to [3, 5, 11], we consider the following problem statement. Let methane is injected into a semi-infinite horizontal reservoir the pores of which initially filled with gas (methane) and water. The injected methane temperature is constant and lower than the initial reservoir temperature. G
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