Numerical simulations of the anomalous solute transport in a fractured porous aquifer

Ryuichi Chiba, Takashi Okaze, Sergei Fomin, Vladimir Chugunov, Yuichi Niibori, Hisao Fukunaga, Toshiyuki Hashida

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

2 Citations (Scopus)


A computer program, which enables us to calculate the anomalous non-Fickian contaminant transport in complex medium, has been developed. In recent years, prediction of mass transport in fractured porous media is becoming increasingly more important for the development of subsurface energy and material systems such as geothermal energy system and the geological disposal of radioactive wastes. Solute transport simulation can serve as an effective tool for predicting subsurface fluid flow but requires accurate model derivation and reliable values of physical parameters. The conventional mathematical model of contaminant transport in the aquifer is based on the Fick's law of diffusion. However, for the fractured porous media, where solute moves primarily through open channels and slowly diffuses into the porous blocks, the conventional model tends to predict smaller solute travel distance than that in the actual transport process. In contrast, the non-Fickian diffusion model can provide realistic representation of actual fluid flow in the heterogeneous media, such as fractured porous rocks. In the non-Fickian diffusion model, the governing equation is written in terms of fractional derivatives. In this study, in order to expand the applicability of the non-Fickian diffusion model to a variety of practical engineering problems, a numerical method has been developed. We provide a numerical solution of the equations by using implicit-finite difference method. The results obtained by numerical solution of the fractional differential equations were shown to be in a good agreement with analytical solutions.

Original languageEnglish
Title of host publicationGeothermal Resources Council Annual Meeting 2008
Subtitle of host publication"Geothermal - Gaining Steam"
Number of pages3
Publication statusPublished - 2008
EventGeothermal Resources Council Annual Meeting 2008: "Geothermal - Gaining Steam" - Reno, NV, United States
Duration: 2008 Oct 52008 Oct 8

Publication series

NameTransactions - Geothermal Resources Council
ISSN (Print)0193-5933


OtherGeothermal Resources Council Annual Meeting 2008: "Geothermal - Gaining Steam"
Country/TerritoryUnited States
CityReno, NV


  • Anomalous contaminant transport
  • Fractional derivative
  • Fractured porous media
  • Non-Fickian diffusion

ASJC Scopus subject areas

  • Renewable Energy, Sustainability and the Environment
  • Energy Engineering and Power Technology
  • Geophysics


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