Darcy's law is applicable for low velocity flow through porous Media; Re nearly about 1 . For higher velocity you must apply Modified Darcy Forchheimer Brinkman Model. You can find the details of this model in my papers:

Two-phase flow and heat transfer in porous media-Part 1: Theoretical Model and Validation

Deleted research item The research item mentioned here has been deleted

More details in the second paper:

Two-phase flow and heat transfer in porous media-Part II: Effect of Inertia, Friction, Porosity Variation and Saturation

Deleted research item The research item mentioned here has been deleted

I will reiterate what Dr. Gamal B. Abdelaziz mentioned. Permeability is a property of the porous medium that measures the capacity and ability of the formation to transmit fluids (gas or liquid). But measuring absolute permeability can be a challenge because of,

1. The velocity of the fluid in porous media may cause Klinkenberg effect or may require non-linear correction.

2. If another fluid is already present in the porous media, you will be measuring relative permeability, which is different from absolute permeability.

Hope this helped. Thank you

Let me consider Ishtiaque Anwar answer and add:

1- Relative permeability of a fluid is the ratio of its effective permeability to the medium permeability.

2- Darcy's law is of limited applicability and the post-Darcy flow is affected by inertia and turbulence

3- Forschheimer is the first suggesting a nonlinear relationship between the pressure and the fluid velocity modeled by adding a velocity square term to the Darcy's law.

4- An alternative to Darcy's equation is what is commonly known as Brinkman's equation. It aims to account for friction due to the macroscopic shear by adding a term allows no-slip boundary condition at the walls.

5- Forscliheimer- Brinkman extended Darcy formulation is the most commonly used equation for representing the conservation of momentum for single phase flow through porous media

Dr. Gamal B. Abdelaziz nicely clarified.

Ishtiaque Anwar Thank you for your respond and I hope a continuous cooperation

Please tell me what you need in this subject, do not hesitate to contact me any time for more details. my Ph D. was about the same point

Two phase flow and heat transfer in porous media Arjun Jayakumar

The flow through the porous duct experiences in general the boundary frictional drag “fv”, a bulk frictional drag induced by the solid matrix (designed as Darcy’s pressure drop) “fD”, the drag induced by gravity effect “fg”, and a flow inertia drag “fi” induced by the solid matrix at high velocities (designed as Forschheimer’s form drag). Under the present assumptions, fv and fi are neglected and Equation can be written as a function of the dimensionless parameters as:

fD =φ/DaRe

You can find details in the attached file

TWO-PHASE FLOW AND HEAT TRANSFER IN POROUS MEDIA

Part 1: Theoretical Model and Validation.

The Influence of fluid property on permeability and form drag coefficient is characterized by the friction factors fv, fD, fi and ft. The total friction factor ft depends mainly on both Reynolds number Re, and Darcy number (Dp and φ). Three regions for the behavior appear

 Re≤100, fi is negligible, fD and fv shares with the main part.

 100≤ Re≤10000 , transition region in which the two types of friction factors fD and fv decrease sharply while the inertia friction factor fi increases sharply.

 Re>10000 , ft curve overlaps with the line of fi, the two types of friction fD and fv are neglected and fi/ft asymptotes to the value 1. i.e. the flow depends mainly on the inertia friction fi which is constant with Re.

You can find additional details in the attached file