No dispersivity?


Does anybody knows how can i justify the use of T2VOC for TCE tranpport without the inclusion of hydrodynamic dispersivity?


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  • Standard TOUGH2 does not include the standard hydrodynamic dispersion model.  T2DM is a special module of TOUGH2 that does include velocity-dependent longitudinal and transverse dispersion, but it is limited to 2D flow problems.

    As for your question, I believe you can justify using T2VOC for TCE transport without modeling formally hydrodynamic dispersion.  I say this because TOUGH2 is always producing some amount of error of the same form as hydrodynamic dispersion, i.e., velocity-dependent numerical dispersion. 

    One thing to note is that numerical dispersion does not have longitudinal and transverse components, so it will tend to be more isotropic than standard-model hydrodynamic dispersion, i.e., more like molecular diffusion.  Nevertheless, numerical dispersion is velocity-dependent just like standard-model hydrodynamic dispersion.

    If you can estimate the dispersivity of your field site, you could make a model domain with discretization that would produce dispersion very similar to the actual dispersion.  For a rectangular grid, the gridblock sizes dx/2, dy/2, and dz/2 are the length scales that you would want to match to the longitudinal dispersivity to make numerical dispersion approximately the same as hydrodynamic dispersion.

    If there were a case where your grid was very fine and actual hydrodynamic dispersion was larger than the grid would produce by numerical diffusion, you could increase molecular diffusivity to increase effective dispersion to match what you thought the physical behavior should be. 

    You may find all of the above very approximate and not all that satisfying.  But I would say the standard model for hydrodynamic dispersion is not very satisfying either.  E.g., under the standard model, it is possible to get upstream mechanical dispersion, which is completely non-physical. 

  • Thank you for the clear answer!
  • Just to add to Curt's reply:

    (1) In addition to T2DM (which is released as part of the standard TOUGH2 V2(.1) package), hydrodynamic dispersion is also handled by EOS9nT (released as a stand-alone package) and T2R3D (released as a module of TOUGH2-MP).

    (2) The concept of hydrodynamic dispersion treated as a Fickian diffusion process has recently been questioned (see Curt's comment and the vast literature on "non-normal" transport); it should thus be used with caution.

    (3) One "brute-force" approach to explicitly include hydrodynamic dispersion effects would be to generate a high-resolution model with stochastic heterogeneity in permeability (and porosity, adsorption coefficients, etc.). It is this small-scale heterogeneity that causes the spreading of a contaminant plume (forget about the often-cited pore-scale effect - it is negligible in almost all applications).

    (4) Relying on numerical dispersion as a proxy for modeling hydrodynamic dispersion has - in my opinion - serious limitations.

    Hope this is useful...
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