An All-At-Once Newton Strategy for Marine Methane Hydrate Reservoir Models
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 mar...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-01-01
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| Series: | Energies |
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| Online Access: | https://www.mdpi.com/1996-1073/13/2/503 |
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| author | Shubhangi Gupta Barbara Wohlmuth Matthias Haeckel |
| author_facet | Shubhangi Gupta Barbara Wohlmuth Matthias Haeckel |
| author_sort | Shubhangi Gupta |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-10T07:17:43Z |
| format | Article |
| id | doaj.art-1cc7a08cd64944ab97027b0daa49714b |
| institution | Directory Open Access Journal |
| issn | 1996-1073 |
| language | English |
| last_indexed | 2024-12-10T07:17:43Z |
| publishDate | 2020-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Energies |
| spelling | doaj.art-1cc7a08cd64944ab97027b0daa49714b2022-12-22T01:57:54ZengMDPI AGEnergies1996-10732020-01-0113250310.3390/en13020503en13020503An All-At-Once Newton Strategy for Marine Methane Hydrate Reservoir ModelsShubhangi Gupta0Barbara Wohlmuth1Matthias Haeckel2GEOMAR Helmholtz Center for Ocean Research Kiel, Wischhofstraße 1-3, 24148 Kiel, GermanyDepartment of Mathematics, Technical University of Munich, Boltzmannstraße 3, 85748 Garching bei München, GermanyGEOMAR Helmholtz Center for Ocean Research Kiel, Wischhofstraße 1-3, 24148 Kiel, GermanyThe 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.https://www.mdpi.com/1996-1073/13/2/503methane hydratephase transitionsncpnonlinear complementary constraintssemi-smooth newton methodactive-sets strategy |
| spellingShingle | Shubhangi Gupta Barbara Wohlmuth Matthias Haeckel An All-At-Once Newton Strategy for Marine Methane Hydrate Reservoir Models Energies methane hydrate phase transitions ncp nonlinear complementary constraints semi-smooth newton method active-sets strategy |
| title | An All-At-Once Newton Strategy for Marine Methane Hydrate Reservoir Models |
| title_full | An All-At-Once Newton Strategy for Marine Methane Hydrate Reservoir Models |
| title_fullStr | An All-At-Once Newton Strategy for Marine Methane Hydrate Reservoir Models |
| title_full_unstemmed | An All-At-Once Newton Strategy for Marine Methane Hydrate Reservoir Models |
| title_short | An All-At-Once Newton Strategy for Marine Methane Hydrate Reservoir Models |
| title_sort | all at once newton strategy for marine methane hydrate reservoir models |
| topic | methane hydrate phase transitions ncp nonlinear complementary constraints semi-smooth newton method active-sets strategy |
| url | https://www.mdpi.com/1996-1073/13/2/503 |
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