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

Author

Listed:
  • Ahmed K. Abu-Nab

    (Phystech School of Applied Mathematics and Informatics, Moscow Institute of Physics and Technology, Dolgoprudny 141700, Russia
    Department of Mathematics and Computer Science, Faculty of Science, Menoufia University, Shebin El-Koom 32511, Egypt)

  • 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
    Department of Mathematics, Faculty of Science, Damanhur University, Damanhur 22516, Egypt)

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.

Suggested Citation

  • Ahmed K. Abu-Nab & Alexander V. Koldoba & Elena V. Koldoba & Yury A. Poveshchenko & Viktoriia O. Podryga & Parvin I. Rahimly & Ahmed E. Bakeer, 2023. "On the Theory of Methane Hydrate Decomposition in a One-Dimensional Model in Porous Sediments: Numerical Study," Mathematics, MDPI, vol. 11(2), pages 1-22, January.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:2:p:341-:d:1029694
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    References listed on IDEAS

    as
    1. Marat K. Khasanov & Nail G. Musakaev & Maxim V. Stolpovsky & Svetlana R. Kildibaeva, 2020. "Mathematical Model of Decomposition of Methane Hydrate during the Injection of Liquid Carbon Dioxide into a Reservoir Saturated with Methane and Its Hydrate," Mathematics, MDPI, vol. 8(9), pages 1-15, September.
    2. Xuke Ruan & Yongchen Song & Jiafei Zhao & Haifeng Liang & Mingjun Yang & Yanghui Li, 2012. "Numerical Simulation of Methane Production from Hydrates Induced by Different Depressurizing Approaches," Energies, MDPI, vol. 5(2), pages 1-21, February.
    3. Christian Deusner & Nikolaus Bigalke & Elke Kossel & Matthias Haeckel, 2012. "Methane Production from Gas Hydrate Deposits through Injection of Supercritical CO 2," Energies, MDPI, vol. 5(7), pages 1-29, June.
    4. Hongyu Ye & Xuezhen Wu & Dayong Li, 2021. "Numerical Simulation of Natural Gas Hydrate Exploitation in Complex Structure Wells: Productivity Improvement Analysis," Mathematics, MDPI, vol. 9(18), pages 1-17, September.
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