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Setting permeability anisotropy with Voronoi elements

I'm trying to define proper permeability values for each connection in my Voronoi mesh file.  Essentially, my PER(1) and PER(2) values are constant and equal to one another, and I have another constant value for PER(3), but it does not necessarily equal PER(1) and PER(2). 

First, is it correct that the flow equations solved by TOUGH2 don't treat permeability as a tensor directly, but rely on the ISOT value provided in columns 26-30 from each line of the CONNE block?  If I'm wrong about this, then I shouldn't have a problem just using the MESH file I've generated as-is. 

However, if I'm not wrong:

Assuming the XYZ axes to be the principal axes of permeability, it should be fairly straightforward to calculate with the equivalent permeability should be for each connection based on the value of BETAX, but I'm not sure what the best way to set that up with permeability modifiers.   I'd particularly be interested in solutions that don't involve me having to change my MESH file each time I change the values of PER(1), PER(2), and PER(3) in the ROCKS block.

Thanks!

4 replies

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    • Mikey_Hannon
    • 7 yrs ago
    • Reported - view

    Just for clarity, I should say that PER(1) and PER(2) are the permeabilities I'm associating with the x and y axes, and PER(3) is the permeability associated with the z-axis (parallel to gravity).

    • Finsterle GeoConsulting
    • Stefan_Finsterle
    • 7 yrs ago
    • Reported - view

    Mikey,

    I'm not sure I followed your post, but as you know, TOUGH2 does NOT use a permeability tensor (for an exception, see Arnaldsson, A., Berthet, J.-C., Kjaran, S., Sigurðsson, S. Þ., Numerical scheme to simulate flow through anisotropic rocks in TOUGH2. Computers & Geosciences, 65, 2014, doi:10.1016/j.cageo.2013.08.002), but assigns permeabilities simply by the value of ISOT, regardless of the orientation of a connection.

    Also note that in iTOUGH2 you can assign permeability modifiers separately for each PER.

    Stefan

    • Jin_Wu
    • 6 yrs ago
    • Reported - view

    Hi!

    Have your found an answer to your question? I am really confused with ISOT. The ISOT means permeability direction. Its value can be 1, 2 or 3. If I have a three dimensional mesh which is generated by another software, how can I know ISOT for every connection between two blocks? 

    Thanks!

      • Mikey_Hannon
      • 6 yrs ago
      • Reported - view

      Jin Wu 

      This may require input from people more experienced than I in TOUGH2 pre-processors, but as I understand it there is no additional routine to parse your MESH file and select the appropriate ISOT for each connection listed in your CONNE block.  This would be the responsibility of your mesh generator. 

      The issue I was raising is that for Voronoi meshes, the direction of each connection may not (and likely will not) align with the principal directions of permeability.  Technically, ISOT doesn't indicate a permeability direction.  Rather, it simply chooses which of the three permeabilities listed in the ROCKS block to associate with each connection.  For rectilinear grids that align with the principal permeability tensor, ISOT is equivalent to the permeability direction.

      If you have the patience to do this by hand, you'll need to determine the direction of each connection to determine which of the permeabilities you should use for it.  Depending on the simplicity of your mesh, you can determine from BETAX which of your connections are vertical (BETAX=+/-1) or horizontal (BETAX=0).  So, if you have a rectilinear grid, and if you have a system that is isotropic in all horizontal directions but has a different permeability in the permeability direction, you can choose ISOT=1 (typically) for all horizontal connections and ISOT=3 (typically) for all vertical connections.

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