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    Modeling Flow in Porous Media With Double Porosity/Permeability: Mathematical Model, Properties, and Analytical Solutions

    Source: Journal of Applied Mechanics:;2018:;volume( 085 ):;issue: 008::page 81009
    Author:
    Nakshatrala, Kalyana B.
    ,
    Joodat, Seyedeh Hanie S.
    ,
    Ballarini, Roberto
    DOI: 10.1115/1.4040116
    Publisher: The American Society of Mechanical Engineers (ASME)
    Abstract: Geomaterials such as vuggy carbonates are known to exhibit multiple spatial scales. A common manifestation of spatial scales is the presence of (at least) two different scales of pores with different hydromechanical properties. Moreover, these pore-networks are connected through fissures and conduits. Although some models are available in the literature to describe flows in such media, they lack a strong theoretical basis. This paper aims to fill this gap in knowledge by providing the theoretical foundation for the flow of incompressible single-phase fluids in rigid porous media that exhibit double porosity/permeability. We first obtain a mathematical model by combining the theory of interacting continua and the maximization of rate of dissipation (MRD) hypothesis, and thereby provide a firm thermodynamic underpinning. The governing equations of the model are a system of elliptic partial differential equations (PDEs) under a steady-state response and a system of parabolic PDEs under a transient response. We then present, along with mathematical proofs, several important mathematical properties that the solutions to the model satisfy. We also present several canonical problems with analytical solutions which are used to gain insights into the velocity and pressure profiles, and the mass transfer across the two pore-networks. In particular, we highlight how the solutions under the double porosity/permeability differ from the corresponding ones under Darcy equations.
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      Modeling Flow in Porous Media With Double Porosity/Permeability: Mathematical Model, Properties, and Analytical Solutions

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    contributor authorNakshatrala, Kalyana B.
    contributor authorJoodat, Seyedeh Hanie S.
    contributor authorBallarini, Roberto
    date accessioned2019-02-28T11:01:11Z
    date available2019-02-28T11:01:11Z
    date copyright6/4/2018 12:00:00 AM
    date issued2018
    identifier issn0021-8936
    identifier otherjam_085_08_081009.pdf
    identifier urihttp://yetl.yabesh.ir/yetl1/handle/yetl/4251787
    description abstractGeomaterials such as vuggy carbonates are known to exhibit multiple spatial scales. A common manifestation of spatial scales is the presence of (at least) two different scales of pores with different hydromechanical properties. Moreover, these pore-networks are connected through fissures and conduits. Although some models are available in the literature to describe flows in such media, they lack a strong theoretical basis. This paper aims to fill this gap in knowledge by providing the theoretical foundation for the flow of incompressible single-phase fluids in rigid porous media that exhibit double porosity/permeability. We first obtain a mathematical model by combining the theory of interacting continua and the maximization of rate of dissipation (MRD) hypothesis, and thereby provide a firm thermodynamic underpinning. The governing equations of the model are a system of elliptic partial differential equations (PDEs) under a steady-state response and a system of parabolic PDEs under a transient response. We then present, along with mathematical proofs, several important mathematical properties that the solutions to the model satisfy. We also present several canonical problems with analytical solutions which are used to gain insights into the velocity and pressure profiles, and the mass transfer across the two pore-networks. In particular, we highlight how the solutions under the double porosity/permeability differ from the corresponding ones under Darcy equations.
    publisherThe American Society of Mechanical Engineers (ASME)
    titleModeling Flow in Porous Media With Double Porosity/Permeability: Mathematical Model, Properties, and Analytical Solutions
    typeJournal Paper
    journal volume85
    journal issue8
    journal titleJournal of Applied Mechanics
    identifier doi10.1115/1.4040116
    journal fristpage81009
    journal lastpage081009-18
    treeJournal of Applied Mechanics:;2018:;volume( 085 ):;issue: 008
    contenttypeFulltext
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    DSpace software copyright © 2002-2015  DuraSpace
    نرم افزار کتابخانه دیجیتال "دی اسپیس" فارسی شده توسط یابش برای کتابخانه های ایرانی | تماس با یابش
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