Relative Permeability

For two-phase flow in porous media given steady-state conditions, we can write

:

q_i = -rac{\kappa_i}{\mu_i} 
abla P_i \qquad 	ext{for} \quad i=1,2

where

q_i

is the flux,

abla 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, as observed through the equation above.

Relative permeability is then defined from

\kappa_i = \kappa_{\mathit{ri}}\kappa

as

:

\kappa_{\mathit{ri}} = \kappa_i / \kappa

where

\kappa

is the Permeability of the porous medium in single-phase flow. 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.

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 throughout 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 called Corey type, and is Polynomial in the water saturation

S_w

. If

S_\mathit{wc}

is the irreducible (minimal, critical) water saturation and

S_\mathit{or}

is the residual (minimal, critical) oil saturation, we can define a scaled saturation value

= rac{S_w - S_\mathit{wc}}{1-S_\mathit{wc} - S_{or}}

)^n and $\kappa_\mathit{ro}=(1-S^---)^m$

$\kappa_\mathit{rw}(S_\mathit{wc}) = 0$ and $\kappa_\mathit{rw}(S_\mathit{or}) = 1$

$\kappa_\mathit{ro}(S_\mathit{wc}) = 1$ and $\kappa_\mathit{ro}(S_\mathit{or}) = 0$

n

m

m=n=2

	APPAREL
	BABY
	BEAUTY
	BOOKS
	CAR TOYS
	CELL PHONES
	DVD'S
	ELECTRONICS
	GOURMET FOOD
	GROCERIES
	HEALTH & PERSONAL
	HOME & GARDEN
	JEWELRY
	MUSIC
	MUSIC INSTRUMENTS
	OFFICE PRODUCTS
	SOFTWARE
	SPORTING GOODS
	TOOLS & HARDWARE
	TOYS
	VIDEO GAMES
	SHOPPING HOME

	MORE SHOPPING...

Information About

Relative Permeability