Unstedy fluid flow in Porous media
 

In unsteady 2D modelling water flow in a rectangular porous media (10 meter length and 5 meters wide) with permeability of 1e-10 m/s and porosity 0.3, with 50000 pascal pressure for water inlet (left side) and 0 pascal for outlet (right side), I have chosen 1000 seconds for fluid flow (time step size 1, number of time step 1000), but the results showed that the water have passed through the medium about 5 meters (more than half of the medium) which does not make sense!!!
I was wondering to know if some one could tell me what is wrong whit my modelling?

Hi,

Did you mean 1E-10 m² for permeability? (instead of m/s)

When I estimate the Darcy velocity I obtain so that after 1000 seconds the water front should be at 0.5 m. Are you sure there is not an extra 0 somewhere?

Hi
Thank you for your comment:
yes I mean 1E-10 m² which is 1/permeability (m/s) and the permeability magnitude is 1e10 m/s.

would you please tell me what is the difference in the results?

that doesn't make sense


I don't understand your question. What I meant in my post is that it looks like there is an error of 1 order of magnitude in your numbers.

For modeling of porous media fluent uses viscous resistant in terms of 1/m² which is equal to 1/α.
And α is permeability of the medium (m/s), so if you want to model a porous media with permeability of 1e-10 m/s you should insert the viscous resistant of 1e10 (1/1e-10).
Would you please tell me if I am right?

You can't abracadabra m² units from m/s units. Googling for 10 seconds makes me think you're confusing hydraulic conductivity (expressed in m/s) with permeability (expressed in m²). In Fluent User's Guide, permeability is in m² and viscous resistance is in 1/m².

In my first post I did a quick estimation with the help of Darcy's law and I mysteriously got the same result than your simulation, but 1 order of magnitude off. That made me think that maybe one of your numbers is wrong by 1 order.

The isotropic permeability coefficient, k (e.g., m2/(Pa/sec) in SI units), is the coefficient of the pressure term in Darcy’s law and is related to the hydraulic conductivity, kh (e.g., m/s), by the expression

kh = kgρf

where g is the gravitational acceleration.
The intrinsic permeability, κ (e.g., in m2), is related to k and kh, as follows:

κ = μ kh/gρf = μk

http://www.cfd-online.com/Forums/dat...BJRU5ErkJggg==where μ is the dynamic viscosity.

It seems that FLUENT uses the intrinsic permeability. And if the if the isotropic permeability of medium is 1e-10, to have Darcy velocity of 0.5 m/s in the mentioned modelling , the value of 1e13 should be inserted as viscous resistance (Dynamic viscosity of water is 0.001 kg/(m-sec)).


Am I right?
Best regards

: viscous resistance (1/m²)
: permeability (m²)


If permeability is 1E-10, viscous resistance is 1E10!

Look at the attached excerpt from User's Guide 15.0, the viscosity is not included in the viscous resistance.

Now we have returned to the beginning
Inserting the viscous resistance 1e10 (1/α) where α = 1e-10 m2 for my model, results in the water transport about 5 meters!!!
What else do you think that might be its reason?