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

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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.

Original languageEnglish
Title of host publicationProceedings of 2006 ASME International Mechanical Engineering Congress and Exposition, IMECE2006 - Fluids Engineering Division
PublisherAmerican Society of Mechanical Engineers (ASME)
ISBN (Print)0791837904, 9780791837900
DOIs
Publication statusPublished - 2006 Jan 1
Event2006 ASME International Mechanical Engineering Congress and Exposition, IMECE2006 - Chicago, IL, United States
Duration: 2006 Nov 52006 Nov 10

Publication series

NameAmerican Society of Mechanical Engineers, Fluids Engineering Division (Publication) FED
ISSN (Print)0888-8116

Other

Other2006 ASME International Mechanical Engineering Congress and Exposition, IMECE2006
CountryUnited States
CityChicago, IL
Period06/11/506/11/10

ASJC Scopus subject areas

  • Engineering(all)

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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). https://doi.org/10.1115/IMECE2006-16138