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Mathematical Modeling of Gas Hydrates Dissociation in Porous Media with Water-Ice Phase Transformations Using Differential Constrains

Author

Listed:
  • Natalia Alekseeva

    (Department of Physical and Environmental Science, Texas A&M University—Corpus Christi, Corpus Christi, TX 78412, USA)

  • Viktoriia Podryga

    (Keldysh Institute of Applied Mathematics of Russian Academy of Sciences, 125047 Moscow, Russia)

  • Parvin Rahimly

    (Keldysh Institute of Applied Mathematics of Russian Academy of Sciences, 125047 Moscow, Russia)

  • Richard Coffin

    (Department of Physical and Environmental Science, Texas A&M University—Corpus Christi, Corpus Christi, TX 78412, USA)

  • Ingo Pecher

    (Department of Physical and Environmental Science, Texas A&M University—Corpus Christi, Corpus Christi, TX 78412, USA)

Abstract

2D numerical modeling algorithms of multi-component, multi-phase filtration processes of mass transfer in frost-susceptible rocks using nonlinear partial differential equations are a valuable tool for problems of subsurface hydrodynamics considering the presence of free gas, free water, gas hydrates, ice formation and phase transitions. In this work, a previously developed one-dimensional numerical modeling approach is modified and 2D algorithms are formulated through means of the support-operators method (SOM) and presented for the entire area of the process extension. The SOM is used to generalize the method of finite difference for spatially irregular grids case. The approach is useful for objects where a lithological heterogeneity of rocks has a big influence on formation and accumulation of gas hydrates and therefore it allows to achieve a sufficiently good spatial approximation for numerical modeling of objects related to gas hydrates dissociation in porous media. The modeling approach presented here consistently applies the method of physical process splitting which allows to split the system into dissipative equation and hyperbolic unit. The governing variables were determined in flow areas of the hydrate equilibrium zone by applying the Gibbs phase rule. The problem of interaction of a vertical fault and horizontal formation containing gas hydrates was investigated and test calculations were done for understanding of influence of thermal effect of the fault on the formation fluid dynamic.

Suggested Citation

  • Natalia Alekseeva & Viktoriia Podryga & Parvin Rahimly & Richard Coffin & Ingo Pecher, 2022. "Mathematical Modeling of Gas Hydrates Dissociation in Porous Media with Water-Ice Phase Transformations Using Differential Constrains," Mathematics, MDPI, vol. 10(19), pages 1-19, September.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:19:p:3470-:d:923119
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    References listed on IDEAS

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    1. Shubhangi Gupta & Barbara Wohlmuth & Matthias Haeckel, 2020. "An All-At-Once Newton Strategy for Marine Methane Hydrate Reservoir Models," Energies, MDPI, vol. 13(2), pages 1-29, January.
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    Cited by:

    1. Yuliya O. Bobreneva & Yury Poveshchenko & Viktoriia O. Podryga & Sergey V. Polyakov & Ravil M. Uzyanbaev & Parvin I. Rahimly & Ainur A. Mazitov & Irek M. Gubaydullin, 2023. "One Approach to Numerical Modeling of the Heat and Mass Transfers of Two-Phase Fluids in Fractured-Porous Reservoirs," Mathematics, MDPI, vol. 11(18), pages 1-16, September.

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