On the Theory of Methane Hydrate Decomposition in a One-Dimensional Model in Porous Sediments: Numerical Study

Ahmed K. Abu-Nab (), Alexander V. Koldoba, Elena V. Koldoba, Yury A. Poveshchenko, Viktoriia O. Podryga, Parvin I. Rahimly and Ahmed E. Bakeer
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Ahmed K. Abu-Nab: Phystech School of Applied Mathematics and Informatics, Moscow Institute of Physics and Technology, Dolgoprudny 141700, Russia
Alexander V. Koldoba: Phystech School of Applied Mathematics and Informatics, Moscow Institute of Physics and Technology, Dolgoprudny 141700, Russia
Elena V. Koldoba: Department of Computational Mechanics, Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow 119991, Russia
Yury A. Poveshchenko: Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Moscow 125047, Russia
Viktoriia O. Podryga: Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Moscow 125047, Russia
Parvin I. Rahimly: Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Moscow 125047, Russia
Ahmed E. Bakeer: Phystech School of Applied Mathematics and Informatics, Moscow Institute of Physics and Technology, Dolgoprudny 141700, Russia

Mathematics, 2023, vol. 11, issue 2, 1-22

Abstract: The purpose of this paper is to present a one-dimensional model that simulates the thermo-physical processes for methane hydrate decomposition in porous media. The mathematical model consists of equations for the conservation of energy, gas, and liquid as well as the thermodynamic equilibrium equation for temperature and pressure ( P − T ) in the hydrate stability region. The developed model is solved numerically by using the implicit finite difference technique on the grid system, which correctly describes the appearance of phase, latency, and boundary conditions. The Newton–Raphson method was employed to solve a system of nonlinear algebraic equations after defining and preparing the Jacobean matrix. Additionally, the proposed model describes the decomposition of methane hydrate by thermal catalysis of the components that make up the medium through multiple phases in porous media. In addition, the effect of thermodynamic processes during the hydrate decomposition on the pore saturation rate with hydrates a7nd water during different time periods was studied in a one-dimensional model. Finally, in a one-dimensional model over various time intervals, t = 1 , 10 , 50 s , the pressure and temperature distributions during the decomposition of methane hydrates are introduced and investigated. The obtained results include more accurate solutions and are consistent with previous models based on the analysis of simulations and system stability.

Keywords: methane hydrates; porous medium; phase transition; finite difference technique; hydrate decomposition (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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