Strictly hyperbolic models of co-current three-phase flow withgravity

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We study the character of the equations in the traditional formulation of one-dimensional immiscible three-phase flow with gravity, in the limit of negligible capillarity. We restrict our analysis to co-current flow required for a displacement process; in cases of mixed co-current and counter-current flow, capillarity effects cannot be dropped from the formulation. The model makes use of the classical multiphase extension of Darcy's equation. It is well known that, if relative permeabilities are taken as fixed functions of saturations, the model yields regions in the saturation space where the system of equations is locally elliptic. We regard elliptic behavior as ... continued below

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Juanes, Ruben & Patzek, Tadeusz W. November 18, 2002.

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We study the character of the equations in the traditional formulation of one-dimensional immiscible three-phase flow with gravity, in the limit of negligible capillarity. We restrict our analysis to co-current flow required for a displacement process; in cases of mixed co-current and counter-current flow, capillarity effects cannot be dropped from the formulation. The model makes use of the classical multiphase extension of Darcy's equation. It is well known that, if relative permeabilities are taken as fixed functions of saturations, the model yields regions in the saturation space where the system of equations is locally elliptic. We regard elliptic behavior as a nonphysical artifact of an incomplete formulation, and derive conditions on the relative permeabilities that ensure strict hyperbolicity of the governing equations. The key point is to acknowledge that a Darcy-type formulation is insufficient to capture all the physics of three-phase flow and that, consequently, the relative permeabilities are functionals that depend on the fluid viscosity ratio and the gravity number. The derived conditions are consistent with the type of displacements that take place in porous media. By means of an illustrative example, we show how elliptic behavior can be removed, even when using simplistic relative permeability models.

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  • Journal Name: Transport in Porous Media; Journal Volume: 55; Journal Issue: 1; Related Information: Journal Publication Date: 2004

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  • Report No.: LBNL--51845
  • Grant Number: DE-AC02-05CH11231
  • Office of Scientific & Technical Information Report Number: 861190
  • Archival Resource Key: ark:/67531/metadc777275

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  • November 18, 2002

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  • Dec. 3, 2015, 9:30 a.m.

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  • April 1, 2016, 8:17 p.m.

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Juanes, Ruben & Patzek, Tadeusz W. Strictly hyperbolic models of co-current three-phase flow withgravity, article, November 18, 2002; Berkeley, California. (digital.library.unt.edu/ark:/67531/metadc777275/: accessed August 18, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.