Effective Conductivity for Complex, Random Heterogeneities

When averaging over any spatial arrangement of discrete K values, the upscaling or averaging result depends on orientation of the arrangement relative to the direction of the hydraulic head gradient:

• Flow along highly stratified layers: Arithmetic mean, highest effective value 
• Flow perpendicular to stratified layers: Harmonic mean, lowest effective value
• Flow in isotropic, heterogeneous media: Geometric mean, yields an intermediate effective value between arithmetic and harmonic means
• Flow in anisotropic, heterogeneous media:  yields an intermediate effective value between arithmetic and harmonic means

Use MAGNET to simulate the flow in heterogeneous porous media in the following 4 cases and compute and compare the specific discharge and effective conductivity values. Are your results consistent with the above conclusions?   

MAGNET/Modeling Hints:

• Use ‘Synthetic mode’ in MAGNET to create a model domain.
• Choose a mean hydraulic conductivity to use for each realization.
• Use a zone feature of the entire aquifer area to assign the hydraulic conductivity as a random field described by statistical parameters (lnK variance, correlation scales).
• Use line or zone features as prescribed head boundaries to generate the head difference from the left edge to the rightedge of the model.