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Darcy's Law for Immiscible Two-Phase Flow: A Theoretical Development

巻 8, 発行 6, 2005, pp. 557-567
DOI: 10.1615/JPorMedia.v8.i6.20
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要約

The aim of this paper is to show how the method of volume averaging can be used to obtain a closed set of averaged equations for bubbling flow. The Navier-Stokes equations are considered as the starting point for the volume-averaging method. The closure was formulated as an associated problem with the deviations around averaged values of the local variables. When the traditional length-scale restrictions are imposed, the volume-averaged momentum equation can be given by 〈Vkk − 〈Vmm = Kk · (−∇ 〈pkk + ρkgk), which is equivalent to Darcy's law. The tensor Kk is determined by closure problems that must be solved using a spatially periodic model of a two-phase flow medium.

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  2. Peng Xiaolong, Liu Yong, Liang Baosheng, Du Zhimin, Dao Ming, Interface condition for the Darcy velocity at the water-oil flood front in the porous medium, PLOS ONE, 12, 5, 2017. Crossref

  3. Aguilar-Madera C.G., Flores-Cano J.V., Matías-Pérez V., Briones-Carrillo J.A., Velasco-Tapia F., Computing the permeability and Forchheimer tensor of porous rocks via closure problems and digital images, Advances in Water Resources, 142, 2020. Crossref

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