[butterfly1]

Hey guys,

I'm modeling a two-phase (gas-water) flow through porous media (laminar flow). I calculated the permeability with the Blake-Kozeny equation.
First there is only gas in the porous media which should be replaced by water, so far so good.
The problem is: I have to consider two different permeabilities don't I? One for the gas, the other for water. Is there a way to connect the permeability with for example the volume fraction of water? There is no further explanation in the theory guide concerning the permeability in two-phase flow.

Thank you for reading and (hopefully) answering!

[jhabriel]

Hi butterfly,

I'm simulating a similar system (in my case I have first only water and later a NAPL (Non aqueous phase liquid) enters and push out the water). There are two types of permeabilities (if we can say so), an intrinsic permeability [L^2] and relative permeabilities [dimensionless],

The intrinsic permeability only depends on the properties of the porous media (and can only change in space) and is a second order tensor, if the direction of the flow is aligned with the stratification path of the media you'll have a diagonal tensor, of course you can consider an isotropic media and it would be simply a scalar (in 1D). If you are dealing with an heterogeneous media you must calculate a mean permeability on every face (I recommend that you use the harmonic mean).

The relative permeabilities are very important in two-phase flow, they represent the tortousity and cross sectional area available for each phases. You must use a correlation in order to calculate the relative permeability for the wetting phase and for the non wetting phase, basically they are a function of the saturation of the wetting phase, you can use the Brooks-Corey correlation, or the van-Genuchten correlation. Also, you must evaluate the mean values of the relative permeabilities on every faces of the cells, I recommend to use the upstream weighting, so, it would depends also on the pressures values of each phases. See, that the relative permeabilities changes with space and time, because the saturation changes with space and time.

I hope I have been helpful.

Best Regards
Jhabriel Varela
National University of Asuncion
jhabriel@gmail.com