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relative permeability : ウィキペディア英語版
relative permeability

In multiphase flow in porous media, the relative permeability of a phase is a dimensionless measure of the effective permeability of that phase. It is the ratio of the effective permeability of that phase to the absolute permeability. It can be viewed as an adaptation of Darcy's law to multiphase flow.
For two-phase flow in porous media given steady-state conditions, we can write
:q_i = -\frac \nabla P_i \qquad \text \quad i=1,2
where q_i is the flux, \nabla P_i is the pressure drop, \mu_i is the viscosity. The subscript i indicates that the parameters are for phase i.
\kappa_i is here the phase permeability (i.e., the effective permeability of phase i), as observed through the equation above.
Relative permeability, \kappa_}\kappa, as
:\kappa_{\mathit{ri}} = \kappa_i / \kappa
where \kappa is the permeability of the porous medium in single-phase flow, i.e., the absolute permeability. Relative permeability must be between zero and one.
In applications, relative permeability is often represented as a function of water saturation; however, owing to capillary hysteresis one often resorts to a function or curve measured under drainage and another measured under imbibition.
Under this approach, the flow of each phase is inhibited by the presence of the other phases. Thus the sum of relative permeabilities over all phases is less than 1. However, apparent relative permeabilities larger than 1 have been obtained since the Darcean approach disregards the viscous coupling effects derived from momentum transfer between the phases (see assumptions below). This coupling could enhance the flow instead of inhibit it. This has been observed in heavy oil petroleum reservoirs when the gas phase flows as bubbles or patches (disconnected).〔M.C. Bravo, M. Araujo / International Journal of Multiphase Flow 34 (2008) 447–460〕
==Assumptions==
The above form for Darcy's law is sometimes also called Darcy's extended law, formulated for horizontal, one-dimensional, immiscible multiphase flow in homogeneous and isotropic porous media. The interactions between the fluids are neglected, so this model assumes that the solid porous media and the other fluids form a new porous matrix through which a phase can flow, implying that the fluid-fluid interfaces remain static in steady-state flow, which is not true, but this approximation has proven useful anyway.
Each of the phase saturation must be larger than the irreducible saturation, and each phase is assumed continuous within the porous medium.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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