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The Flow Analysis of Fiuids in Fractal Reservoir with the Fractional Derivative
Tian J; Tong DK; Tian, J (reprint author), Chinese Acad Sci, Inst Mech, Beijing 100080, Peoples R China.
Source PublicationJOURNAL OF HYDRODYNAMICS
2006
Volume18Issue:3Pages:287-293
ISSN1001-6058
AbstractIn 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.
KeywordFractional Calculus Porous Media Fractal Integral Transform Exact Solution
DOI10.1016/S1001-6058(06)60005-X
Indexed BySCI
Language英语
WOS IDWOS:000208248300005
WOS Research AreaMechanics
WOS SubjectMechanics
Funding OrganizationChina National 973 Program [2002CB211708] ; Natural Science Foundation of Shandong Province [Y2003F01]
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Document Type期刊论文
Identifierhttp://dspace.imech.ac.cn/handle/311007/58456
Collection力学所知识产出(1956-2008)
Corresponding AuthorTian, J (reprint author), Chinese Acad Sci, Inst Mech, Beijing 100080, Peoples R China.
Recommended Citation
GB/T 7714
Tian J,Tong DK,Tian, J . The Flow Analysis of Fiuids in Fractal Reservoir with the Fractional Derivative[J]. JOURNAL OF HYDRODYNAMICS,2006,18(3):287-293.
APA Tian J,Tong DK,&Tian, J .(2006).The Flow Analysis of Fiuids in Fractal Reservoir with the Fractional Derivative.JOURNAL OF HYDRODYNAMICS,18(3),287-293.
MLA Tian J,et al."The Flow Analysis of Fiuids in Fractal Reservoir with the Fractional Derivative".JOURNAL OF HYDRODYNAMICS 18.3(2006):287-293.
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