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Time-space fractional derivative models for CO2 transport in heterogeneous media

  • AiLian Chang EMAIL logo and HongGuang Sun
Published/Copyright: March 13, 2018
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Fractional Calculus and Applied Analysis
From the journal Fractional Calculus and Applied Analysis Volume 21 Issue 1

Abstract

This study is mainly to explore gas transport process in heterogeneous media, which is to lay the foundation for oil-gas exploitation and development. Anomalous transport is observed to be ubiquitous in complex geological formations and has a paramount impact on petroleum engineering. Simultaneously, the random motion of particles usually exhibits obvious path- and history- dependent behaviors. This paper investigates the time-space fractional derivative models as a potential explanation for the time memory of long waiting time and the space non-locality of large regional-scale. A one-dimensional fractional advection-dispersion equation (FADE) based on fractional Fick’s law is firstly used to accurately describe the transport of Carbon dioxide (CO2) in complex media. The new fractional Darcy-advection-dispersion equation (FDADE) model has subsequently been proposed to make a comparison with FADE model and demonstrate its physical mechanism. Finally, the priori estimation of the parameters (fractional derivative index) in fractional derivative models and corresponding physical explanation are presented. Combined with experimental data, the numerical simulations show the fractional derivative models can well characterize the heavy-tailed and early breakthrough phenomenon of CO2 transport.

MSC 2010: Primary 26A33; Secondary 34A08; 65C20; 65N06; 74E05; 76A02; 76N15
Key Words and Phrases: heterogeneous media; CO2 transport; fractional derivative model; heavy-tail; numerical simulation

Acknowledgements

The work was supported by the National Natural Science Foundation of China (Grant Nos. 41330632, 11572112, 41628202). This paper does not necessarily reflect the view of the funding agency.

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Received: 2017-10-15
Published Online: 2018-3-13
Published in Print: 2018-2-23

© 2018 Diogenes Co., Sofia

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  1. Frontmatter
  2. Editorial Note
  3. FCAA related news, events and books (FCAA–volume 21–1–2018)
  4. Survey Paper
  5. From continuous time random walks to the generalized diffusion equation
  6. Survey Paper
  7. Properties of the Caputo-Fabrizio fractional derivative and its distributional settings
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  9. Exact and numerical solutions of the fractional Sturm–Liouville problem
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  11. Some stability properties related to initial time difference for Caputo fractional differential equations
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  17. Time-fractional diffusion with mass absorption under harmonic impact
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  19. Optimal control of linear systems with fractional derivatives
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  21. Time-space fractional derivative models for CO2 transport in heterogeneous media
  22. Research Paper
  23. Improvements in a method for solving fractional integral equations with some links with fractional differential equations
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  25. On some fractional differential inclusions with random parameters
  26. Research Paper
  27. Initial boundary value problems for a fractional differential equation with hyper-Bessel operator
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  33. Differential and integral relations in the class of multi-index Mittag-Leffler functions
https://doi.org/10.1515/fca-2018-0010
Keywords for this article
heterogeneous media; CO2 transport; fractional derivative model; heavy-tail; numerical simulation

Articles in the same Issue

  1. Frontmatter
  2. Editorial Note
  3. FCAA related news, events and books (FCAA–volume 21–1–2018)
  4. Survey Paper
  5. From continuous time random walks to the generalized diffusion equation
  6. Survey Paper
  7. Properties of the Caputo-Fabrizio fractional derivative and its distributional settings
  8. Research Paper
  9. Exact and numerical solutions of the fractional Sturm–Liouville problem
  10. Research Paper
  11. Some stability properties related to initial time difference for Caputo fractional differential equations
  12. Research Paper
  13. On an eigenvalue problem involving the fractional (s, p)-Laplacian
  14. Research Paper
  15. Diffusion entropy method for ultraslow diffusion using inverse Mittag-Leffler function
  16. Research Paper
  17. Time-fractional diffusion with mass absorption under harmonic impact
  18. Research Paper
  19. Optimal control of linear systems with fractional derivatives
  20. Research Paper
  21. Time-space fractional derivative models for CO2 transport in heterogeneous media
  22. Research Paper
  23. Improvements in a method for solving fractional integral equations with some links with fractional differential equations
  24. Research Paper
  25. On some fractional differential inclusions with random parameters
  26. Research Paper
  27. Initial boundary value problems for a fractional differential equation with hyper-Bessel operator
  28. Research Paper
  29. Mittag-Leffler function and fractional differential equations
  30. Research Paper
  31. Complex spatio-temporal solutions in fractional reaction-diffusion systems near a bifurcation point
  32. Research Paper
  33. Differential and integral relations in the class of multi-index Mittag-Leffler functions
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