Skip to main content
SpringerLink
Log in

Conformable Derivative Modeling of Pressure Behavior for Transport in Porous Media

  • Conference paper
  • First Online:
Proceedings of China-Europe Conference on Geotechnical Engineering

Part of the book series: Springer Series in Geomechanics and Geoengineering ((SSGG))

  • 3134 Accesses

Abstract

A mathematical model is developed for studying the pressure behavior in porous media which is a modification of the diffusivity equation in concept of conformable derivative. The solution of the new model is semi-analytically obtained for constant-rate flow condition. Type curves of the dimensionless pressure are plotted by the Stehfest algorithm. The effects of conformable derivative order parameters on the pressure responses are discussed in detail.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 259.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 329.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 329.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Metzler, R., Glöckle, W.G., Nonnenmacher, T.F.: Phys. A Stat. Mech. Appl. 211, 13–24 (1994)

    Article  Google Scholar 

  2. Fomin, S., Chugunov, V., Hashida, T.: Transp. Porous Media 81, 187–205 (2009)

    Article  Google Scholar 

  3. Mendes, G.A., Lenzi, E.K., Mendes, R.S., da Silva, L.R.: Phys. A Stat. Mech. Appl. 34, 6271–6283 (2005)

    Google Scholar 

  4. Zhou, H., Wang, C., Mishnaevsky Jr., L., Duan, Z., Ding, J.: Mech. Time Depend. Mater. 17, 413–425 (2013)

    Article  Google Scholar 

  5. Wu, W., Bauer, E., Kolymbas, D.: Mech. Mater. 23, 45–69 (1996)

    Article  Google Scholar 

  6. Zhang, Y., Benson, D.A., Meerschaert, M.M., LaBolle, E.M., Scheffler, H.P.: Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74, 026706 (2006)

    Article  Google Scholar 

  7. Magdziarz, M., Weron, A., Burnecki, K., Klafter, J.: Phys. Rev. Lett. 103, 180602 (2009)

    Article  Google Scholar 

  8. Gorenflo, R., Mainardi, F., Vivoli, A.: Chaos Solitons Fractals 34, 87–103 (2007)

    Article  MathSciNet  Google Scholar 

  9. Park, H.W., Choe, J., Kang, J.M.: Energy Sources 22, 881–890 (2000)

    Article  Google Scholar 

  10. Raghavan, R.: J. Petrol. Sci. Eng. 80, 7–13 (2011)

    Article  Google Scholar 

  11. Razminia, K., Razminia, A., Torres, D.F.: Appl. Math. Comput. 257, 374–380 (2015)

    MathSciNet  Google Scholar 

  12. Khalil, R., Al Horani, M., Yousef, A., Sababheh, M.: J. Comput. Appl. Math. 264, 65–70 (2014)

    Article  MathSciNet  Google Scholar 

  13. Abdeljawad, T.: J. Comput. Appl. Math. 279, 57–66 (2015)

    Article  MathSciNet  Google Scholar 

  14. Atangana, A., Baleanu, D., Alsaedi, A.: Open Math. 13, 889–898 (2015)

    Article  MathSciNet  Google Scholar 

  15. Zhou, H.W., Yang, S., Zhang, S.Q.: Phys. A Stat. Mech. Appl. 491, 1001–1013 (2018)

    Article  Google Scholar 

  16. Barker, J.A.: Water Resour. Res. 24, 1796–1804 (1988)

    Article  Google Scholar 

  17. Stehfest, H.: Commun. ACM 13, 47–49 (1970)

    Article  Google Scholar 

Download references

Acknowledgments

The present work is supported by the National Natural Science Foundation of China (51674266), and the State Key Research Development Program of China (2016YFC0600704). The financial supports are gratefully acknowledged.

Author information

Authors and Affiliations

  1. School of Mechanics & Civil Engineering, China University of Mining and Technology, Xuzhou, China

    R. Wang, H. W. Zhou, S. Yang & Z. Zhuo

Authors
  1. R. Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. H. W. Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. S. Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Z. Zhuo
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to H. W. Zhou .

Editor information

Editors and Affiliations

  1. Institut für Geotechnik, Universität für Bodenkultur, Vienna, Austria

    Wei Wu

  2. Faculty of Engineering, University of Leeds, Leeds, United Kingdom

    Hai-Sui Yu

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Wang, R., Zhou, H.W., Yang, S., Zhuo, Z. (2018). Conformable Derivative Modeling of Pressure Behavior for Transport in Porous Media. In: Wu, W., Yu, HS. (eds) Proceedings of China-Europe Conference on Geotechnical Engineering. Springer Series in Geomechanics and Geoengineering. Springer, Cham. https://doi.org/10.1007/978-3-319-97112-4_96

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-97112-4_96

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-97111-7

  • Online ISBN: 978-3-319-97112-4

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation