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
where qi is the flux, 
is the pressure drop, μi is the viscosity. The subscript i indicates that the parameters are for phase i.
κi is here the phase permeability (i.e., the effective permeability of phase i), as observed through the equation above.
Relative permeability, κri, for phase i is then defined from κi = κriκ as
- κri = κi / κ
where κ 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 due to capillary hysteresis, one often resorts to one function or curve measured under drainage and one measured under imbibition.
As the flow of each phase is inhibited by the presence of the other phases, the sum of relative permeabilities over all phases is always less than 1.
Contents |
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.
Approximations
Based on experimental data, simplified models of relative permeability as a function of water saturation can be constructed.
Corey-type
An often used approximation is the so-called Corey type, and is polynomial in the water saturation Sw[1][2] . If Swc is the irreducible (minimal, critical) water saturation and Sor is the residual (minimal, critical) oil saturation, we can define a scaled saturation value
and approximations of Corey type of the relative permeabilities of water and oil are then
- κrw = (S * )n and κro = (1 − S * )m
with the properties
- κrw(Swc) = 0 and κrw(Sor) = 1
- κro(Swc) = 1 and κro(Sor) = 0
and where n and m can be obtained from measured data. m = n = 2 is sometimes appropriate.
See also
References
 |
This fluid dynamics-related article is a stub. You can help Wikipedia by expanding it. |
This entry is from Wikipedia, the leading user-contributed encyclopedia. It may not have been reviewed by professional editors (see full disclaimer)
