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

• Published in: Mathematics
• Main Authors: Ahmed K. Abu-Nab, Alexander V. Koldoba, Elena V. Koldoba, Yury A. Poveshchenko, Viktoriia O. Podryga, Parvin I. Rahimly, Ahmed E. Bakeer
• Format: Article in Journal/Newspaper
• Language: English
• Published: MDPI AG 2023
• Subjects: methane hydrates; porous medium; phase transition; finite difference technique; hydrate decomposition; Mathematics; QA1-939; Methane hydrate
• Online Access: https://doi.org/10.3390/math11020341; https://doaj.org/article/253781ca03a24b7fad4502b9a13b3339

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 <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mrow><mo>(</mo><mrow><mi>P</mi><mo>−</mo><mi>T</mi></mrow><mo>)</mo></mrow></mrow></semantics></math> 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, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>t</mi><mo>=</mo><mn>1</mn><mo>,</mo><mo> </mo><mn>10</mn><mo>,</mo><mo> </mo><mn>50</mn><mo> </mo><mi mathvariant="normal">s</mi></mrow></semantics></math> , the pressure and temperature distributions during the decomposition of methane hydrates are introduced and investigated. The obtained results include more accurate ...