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Journal of Porous Media
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ISSN Druckformat: 1091-028X
ISSN Online: 1934-0508

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Journal of Porous Media

DOI: 10.1615/JPorMedia.v8.i6.20
pages 557-567

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

Francisco J Valdes-Parada
Universidad Autonoma, Metropolitana-Iztapalapa, Col. Vicentino, Mexico
Gilberto Espinosa-Paredes
Área de Ingeniería en Recursos Energéticos, Universidad Autónoma Metropolitana-Iztapalapa, Av. San Rafael Atlixco No. 186, Col. Vicentina, C.P. 09340, Cd. de México, México

ABSTRAKT

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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