Advection of methane in the hydrate zone: model, analysis and examples
A two‐phase two‐component model is formulated for the advective–diffusive transport of methane in liquid phase through sediment with the accompanying formation and dissolution of methane hydrate. This free‐boundary problem has a unique generalized solution in L 1 the proof combines analysis of the s...
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crwiley:10.1002/mma.3401 2024-06-23T07:54:37+00:00 Advection of methane in the hydrate zone: model, analysis and examples Peszynska, Malgorzata Showalter, Ralph E. Webster, Justin T. 2015 http://dx.doi.org/10.1002/mma.3401 https://api.wiley.com/onlinelibrary/tdm/v1/articles/10.1002%2Fmma.3401 https://onlinelibrary.wiley.com/doi/pdf/10.1002/mma.3401 en eng Wiley http://onlinelibrary.wiley.com/termsAndConditions#vor Mathematical Methods in the Applied Sciences volume 38, issue 18, page 4613-4629 ISSN 0170-4214 1099-1476 journal-article 2015 crwiley https://doi.org/10.1002/mma.3401 2024-06-06T04:23:51Z A two‐phase two‐component model is formulated for the advective–diffusive transport of methane in liquid phase through sediment with the accompanying formation and dissolution of methane hydrate. This free‐boundary problem has a unique generalized solution in L 1 the proof combines analysis of the stationary semilinear elliptic Dirichlet problem with the nonlinear semigroup theory in Banach space for an m‐accretive multi‐valued operator. Additional estimates of maximum principle type are obtained, and these permit appropriate maximal extensions of the phase‐change relations. An example with pure advection indicates the limitations of these estimates and of the model developed here. We also consider and analyze the coupled pressure equation that determines the advective flux in the transport model. Copyright © 2015 John Wiley & Sons, Ltd. Article in Journal/Newspaper Methane hydrate Wiley Online Library Mathematical Methods in the Applied Sciences 38 18 4613 4629 |
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English |
description |
A two‐phase two‐component model is formulated for the advective–diffusive transport of methane in liquid phase through sediment with the accompanying formation and dissolution of methane hydrate. This free‐boundary problem has a unique generalized solution in L 1 the proof combines analysis of the stationary semilinear elliptic Dirichlet problem with the nonlinear semigroup theory in Banach space for an m‐accretive multi‐valued operator. Additional estimates of maximum principle type are obtained, and these permit appropriate maximal extensions of the phase‐change relations. An example with pure advection indicates the limitations of these estimates and of the model developed here. We also consider and analyze the coupled pressure equation that determines the advective flux in the transport model. Copyright © 2015 John Wiley & Sons, Ltd. |
format |
Article in Journal/Newspaper |
author |
Peszynska, Malgorzata Showalter, Ralph E. Webster, Justin T. |
spellingShingle |
Peszynska, Malgorzata Showalter, Ralph E. Webster, Justin T. Advection of methane in the hydrate zone: model, analysis and examples |
author_facet |
Peszynska, Malgorzata Showalter, Ralph E. Webster, Justin T. |
author_sort |
Peszynska, Malgorzata |
title |
Advection of methane in the hydrate zone: model, analysis and examples |
title_short |
Advection of methane in the hydrate zone: model, analysis and examples |
title_full |
Advection of methane in the hydrate zone: model, analysis and examples |
title_fullStr |
Advection of methane in the hydrate zone: model, analysis and examples |
title_full_unstemmed |
Advection of methane in the hydrate zone: model, analysis and examples |
title_sort |
advection of methane in the hydrate zone: model, analysis and examples |
publisher |
Wiley |
publishDate |
2015 |
url |
http://dx.doi.org/10.1002/mma.3401 https://api.wiley.com/onlinelibrary/tdm/v1/articles/10.1002%2Fmma.3401 https://onlinelibrary.wiley.com/doi/pdf/10.1002/mma.3401 |
genre |
Methane hydrate |
genre_facet |
Methane hydrate |
op_source |
Mathematical Methods in the Applied Sciences volume 38, issue 18, page 4613-4629 ISSN 0170-4214 1099-1476 |
op_rights |
http://onlinelibrary.wiley.com/termsAndConditions#vor |
op_doi |
https://doi.org/10.1002/mma.3401 |
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Mathematical Methods in the Applied Sciences |
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38 |
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18 |
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4613 |
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4629 |
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1802646824845049856 |