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An All-At-Once Newton Strategy for Marine Methane Hydrate Reservoir Models

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  • Shubhangi Gupta

    (GEOMAR Helmholtz Center for Ocean Research Kiel, Wischhofstraße 1-3, 24148 Kiel, Germany
    Department of Mathematics, Technical University of Munich, Boltzmannstraße 3, 85748 Garching bei München, Germany)

  • Barbara Wohlmuth

    (Department of Mathematics, Technical University of Munich, Boltzmannstraße 3, 85748 Garching bei München, Germany)

  • Matthias Haeckel

    (GEOMAR Helmholtz Center for Ocean Research Kiel, Wischhofstraße 1-3, 24148 Kiel, Germany)

Abstract

The migration of methane through the gas hydrate stability zone (GHSZ) in the marine subsurface is characterized by highly dynamic reactive transport processes coupled to thermodynamic phase transitions between solid gas hydrates, free methane gas, and dissolved methane in the aqueous phase. The marine subsurface is essentially a water-saturated porous medium where the thermodynamic instability of the hydrate phase can cause free gas pockets to appear and disappear locally, causing the model to degenerate. This poses serious convergence issues for the general-purpose nonlinear solvers (e.g., standard Newton), and often leads to extremely small time-step sizes. The convergence problem is particularly severe when the rate of hydrate phase change is much lower than the rate of gas dissolution. In order to overcome this numerical challenge, we have developed an all-at-once Newton scheme tailored to our gas hydrate model, which can handle rate-based hydrate phase change coupled with equilibrium gas dissolution in a mathematically consistent and robust manner.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jeners:v:13:y:2020:i:2:p:503-:d:311033
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    References listed on IDEAS

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    1. Fangtian Wang & Bin Zhao & Gang Li, 2018. "Prevention of Potential Hazards Associated with Marine Gas Hydrate Exploitation: A Review," Energies, MDPI, vol. 11(9), pages 1-19, September.
    2. Maria De La Fuente & Jean Vaunat & Héctor Marín-Moreno, 2019. "Thermo-Hydro-Mechanical Coupled Modeling of Methane Hydrate-Bearing Sediments: Formulation and Application," Energies, MDPI, vol. 12(11), pages 1-23, June.
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    Cited by:

    1. 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.
    2. Maria De La Fuente & Sandra Arndt & Héctor Marín-Moreno & Tim A. Minshull, 2022. "Assessing the Benthic Response to Climate-Driven Methane Hydrate Destabilisation: State of the Art and Future Modelling Perspectives," Energies, MDPI, vol. 15(9), pages 1-32, May.
    3. Mahboubeh Rahmati-Abkenar & Milad Alizadeh & Marcelo Ketzer, 2021. "A New Dynamic Modeling Approach to Predict Microbial Methane Generation and Consumption in Marine Sediments," Energies, MDPI, vol. 14(18), pages 1-17, September.

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