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The Flow Analysis of Fiuids in Fractal Reservoir with the Fractional Derivative

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Abstract

In this paper, fractional order derivative, fractal dimension and spectral dimension are introduced into the seepage flow mechanics to establish the flow models of fluids in fractal reservoirs with the fractional derivative. The flow characteristics of fluids through a fractal reservoir with the fractional order derivative are studied by using the finite integral transform, the discrete Laplace transform of sequential fractional derivatives and the generalized Mittag-Leffler function. Exact solutions are obtained for arbitrary fractional order derivative. The long-time and short-time asymptotic solutions for an infinite formation are also obtained. The pressure transient behavior of fluids flow through an infinite fractal reservoir is studied by using the Stehfest’ s inversion method of the numerical Laplace transform. It shows that the order of the fractional derivative affect the whole pressure behavior, particularly, the effect of pressure behavior of the early-time stage is larger The new type flow model of fluid in fractal reservoir with fractional derivative is provided a new mathematical model for studying the seepage mechanics of fluid in fractal porous media.

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Authors and Affiliations

  1. Institute of Mechanics, Chinese Academy of Science, Beijing, 100080, China

    Ji Tian

  2. Gudong Petroleum Factory of Shengli Petroleum Administration, Dongying, 256504, China

    Ji Tian

  3. Department of Applied Mathematics, China University of Petroleum, Dongying, 257061, China

    Deng-ke Tong

Authors
  1. Ji Tian
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  2. Deng-ke Tong
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Correspondence to Deng-ke Tong.

Additional information

Project supported by the China National 973 Program (Grant No: 2002CB211708) and the Natural Science Foundation of Shandong Province (Grant No: Y2003F01).

Boigraphy: TIAN Ji (1964-), Male, Senior Engineering

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Tian, J., Tong, Dk. The Flow Analysis of Fiuids in Fractal Reservoir with the Fractional Derivative. J Hydrodyn 18, 287–293 (2006). https://doi.org/10.1016/S1001-6058(06)60005-X

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  • DOI: https://doi.org/10.1016/S1001-6058(06)60005-X

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