Application of fractional derivatives for simulating diffusion into porous matrix in mathematical modeling of the contaminant transport in a confined fractured porous aquifer

Sergei Fomin; Vladimir Chugunov; Toshiyuki Hashida

doi:10.1115/IMECE2006-16138

Application of fractional derivatives for simulating diffusion into porous matrix in mathematical modeling of the contaminant transport in a confined fractured porous aquifer

Sergei Fomin, Vladimir Chugunov, Toshiyuki Hashida

未来科学技術共同研究センター

研究成果: 書籍の章/レポート/Proceedings › 会議への寄与 › 査読

抄録

Solute transport in the fractured porous confined aquifer is modeled by the advection-dispersion equation with fractional time derivative of order γ, which may vary from 0 to 1. Accounting for diffusion in the surrounding rock mass leads to the introduction of an additional fractional time derivative of order 1/2 in the equation for solute transport. The closed-form solutions for concentrations in the aquifer and surrounding rocks are obtained for the arbitrary time-dependent source of contamination located in the inlet of the aquifer. Based on these solutions, different regimes of contamination of the aquifers with different physical properties are modeled and analyzed.

本文言語	英語
ホスト出版物のタイトル	Proceedings of 2006 ASME International Mechanical Engineering Congress and Exposition, IMECE2006 - Fluids Engineering Division
出版社	American Society of Mechanical Engineers (ASME)
ISBN（印刷版）	0791837904, 9780791837900
DOI	https://doi.org/10.1115/IMECE2006-16138
出版ステータス	出版済み - 2006
イベント	2006 ASME International Mechanical Engineering Congress and Exposition, IMECE2006 - Chicago, IL, 米国継続期間: 2006 11月 5 → 2006 11月 10

出版物シリーズ

名前	American Society of Mechanical Engineers, Fluids Engineering Division (Publication) FED
ISSN（印刷版）	0888-8116

会議

会議	2006 ASME International Mechanical Engineering Congress and Exposition, IMECE2006
国/地域	米国
City	Chicago, IL
Period	06/11/5 → 06/11/10

文献へのアクセス

10.1115/IMECE2006-16138

他のファイルとリンク

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引用スタイル

Fomin, S., Chugunov, V., & Hashida, T. (2006). Application of fractional derivatives for simulating diffusion into porous matrix in mathematical modeling of the contaminant transport in a confined fractured porous aquifer. In Proceedings of 2006 ASME International Mechanical Engineering Congress and Exposition, IMECE2006 - Fluids Engineering Division (American Society of Mechanical Engineers, Fluids Engineering Division (Publication) FED). American Society of Mechanical Engineers (ASME). https://doi.org/10.1115/IMECE2006-16138

Fomin, Sergei ; Chugunov, Vladimir ; Hashida, Toshiyuki. / Application of fractional derivatives for simulating diffusion into porous matrix in mathematical modeling of the contaminant transport in a confined fractured porous aquifer. Proceedings of 2006 ASME International Mechanical Engineering Congress and Exposition, IMECE2006 - Fluids Engineering Division. American Society of Mechanical Engineers (ASME), 2006. (American Society of Mechanical Engineers, Fluids Engineering Division (Publication) FED).

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title = "Application of fractional derivatives for simulating diffusion into porous matrix in mathematical modeling of the contaminant transport in a confined fractured porous aquifer",

abstract = "Solute transport in the fractured porous confined aquifer is modeled by the advection-dispersion equation with fractional time derivative of order γ, which may vary from 0 to 1. Accounting for diffusion in the surrounding rock mass leads to the introduction of an additional fractional time derivative of order 1/2 in the equation for solute transport. The closed-form solutions for concentrations in the aquifer and surrounding rocks are obtained for the arbitrary time-dependent source of contamination located in the inlet of the aquifer. Based on these solutions, different regimes of contamination of the aquifers with different physical properties are modeled and analyzed.",

author = "Sergei Fomin and Vladimir Chugunov and Toshiyuki Hashida",

year = "2006",

doi = "10.1115/IMECE2006-16138",

language = "English",

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series = "American Society of Mechanical Engineers, Fluids Engineering Division (Publication) FED",

publisher = "American Society of Mechanical Engineers (ASME)",

booktitle = "Proceedings of 2006 ASME International Mechanical Engineering Congress and Exposition, IMECE2006 - Fluids Engineering Division",

note = "2006 ASME International Mechanical Engineering Congress and Exposition, IMECE2006 ; Conference date: 05-11-2006 Through 10-11-2006",

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Fomin, S, Chugunov, V & Hashida, T 2006, Application of fractional derivatives for simulating diffusion into porous matrix in mathematical modeling of the contaminant transport in a confined fractured porous aquifer. in Proceedings of 2006 ASME International Mechanical Engineering Congress and Exposition, IMECE2006 - Fluids Engineering Division. American Society of Mechanical Engineers, Fluids Engineering Division (Publication) FED, American Society of Mechanical Engineers (ASME), 2006 ASME International Mechanical Engineering Congress and Exposition, IMECE2006, Chicago, IL, 米国, 06/11/5. https://doi.org/10.1115/IMECE2006-16138

Application of fractional derivatives for simulating diffusion into porous matrix in mathematical modeling of the contaminant transport in a confined fractured porous aquifer. / Fomin, Sergei; Chugunov, Vladimir; Hashida, Toshiyuki.
Proceedings of 2006 ASME International Mechanical Engineering Congress and Exposition, IMECE2006 - Fluids Engineering Division. American Society of Mechanical Engineers (ASME), 2006. (American Society of Mechanical Engineers, Fluids Engineering Division (Publication) FED).

研究成果: 書籍の章/レポート/Proceedings › 会議への寄与 › 査読

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N2 - Solute transport in the fractured porous confined aquifer is modeled by the advection-dispersion equation with fractional time derivative of order γ, which may vary from 0 to 1. Accounting for diffusion in the surrounding rock mass leads to the introduction of an additional fractional time derivative of order 1/2 in the equation for solute transport. The closed-form solutions for concentrations in the aquifer and surrounding rocks are obtained for the arbitrary time-dependent source of contamination located in the inlet of the aquifer. Based on these solutions, different regimes of contamination of the aquifers with different physical properties are modeled and analyzed.

AB - Solute transport in the fractured porous confined aquifer is modeled by the advection-dispersion equation with fractional time derivative of order γ, which may vary from 0 to 1. Accounting for diffusion in the surrounding rock mass leads to the introduction of an additional fractional time derivative of order 1/2 in the equation for solute transport. The closed-form solutions for concentrations in the aquifer and surrounding rocks are obtained for the arbitrary time-dependent source of contamination located in the inlet of the aquifer. Based on these solutions, different regimes of contamination of the aquifers with different physical properties are modeled and analyzed.

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Fomin S, Chugunov V, Hashida T. Application of fractional derivatives for simulating diffusion into porous matrix in mathematical modeling of the contaminant transport in a confined fractured porous aquifer. In Proceedings of 2006 ASME International Mechanical Engineering Congress and Exposition, IMECE2006 - Fluids Engineering Division. American Society of Mechanical Engineers (ASME). 2006. (American Society of Mechanical Engineers, Fluids Engineering Division (Publication) FED). doi: 10.1115/IMECE2006-16138