Unstedy fluid flow in Porous media

sirpolar · May 29, 2014, 03:06

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?

macfly · May 29, 2014, 11:04

Hi,

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

When I estimate the Darcy velocity I obtain $v_x=\frac{\alpha}{\mu}\frac{\Delta p}{\Delta x}=\frac{1\text{E-}10 \text{ m}^2}{1\text{E-3} \text{ Pa-s}}\frac{50000\text{ Pa}}{10\text{ m}}=5\text{E-4} \text{m/s}$ so that after 1000 seconds the water front should be at 0.5 m. Are you sure there is not an extra 0 somewhere?

sirpolar · May 29, 2014, 13:13

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?

macfly · May 29, 2014, 14:00

Quote:

Originally Posted by sirpolar

yes I mean 1E-10 m² which is 1/permeability (m/s) and the permeability magnitude is 1e10 m/s.

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.

sirpolar · May 29, 2014, 15:08

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?

macfly · May 29, 2014, 15:25

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.

sirpolar · May 30, 2014, 07:08

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

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

macfly · May 30, 2014, 12:19

Quote:

Originally Posted by sirpolar

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)
$\alpha$ : permeability (m²)
$D=\frac{1}{\alpha}$

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.

sirpolar · May 31, 2014, 04:18

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?

May 29, 2014, 03:06	Unstedy fluid flow in Porous media	#1
sirpolar Member Ebrahim Join Date: Feb 2014 Posts: 57 Rep Power: 12	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?

May 29, 2014, 11:04		#2
macfly Senior Member François Grégoire Join Date: Jan 2010 Location: Canada Posts: 392 Rep Power: 17	Hi, Did you mean 1E-10 m² for permeability? (instead of m/s) When I estimate the Darcy velocity I obtain $v_x=\frac{\alpha}{\mu}\frac{\Delta p}{\Delta x}=\frac{1\text{E-}10 \text{ m}^2}{1\text{E-3} \text{ Pa-s}}\frac{50000\text{ Pa}}{10\text{ m}}=5\text{E-4} \text{m/s}$ so that after 1000 seconds the water front should be at 0.5 m. Are you sure there is not an extra 0 somewhere? sirpolar likes this.

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May 29, 2014, 13:13		#3
sirpolar Member Ebrahim Join Date: Feb 2014 Posts: 57 Rep Power: 12	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?

May 29, 2014, 15:08		#5
sirpolar Member Ebrahim Join Date: Feb 2014 Posts: 57 Rep Power: 12	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?

May 29, 2014, 15:25		#6
macfly Senior Member François Grégoire Join Date: Jan 2010 Location: Canada Posts: 392 Rep Power: 17	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.

May 30, 2014, 07:08		#7
sirpolar Member Ebrahim Join Date: Feb 2014 Posts: 57 Rep Power: 12	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 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

May 31, 2014, 04:18		#9
sirpolar Member Ebrahim Join Date: Feb 2014 Posts: 57 Rep Power: 12	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?