K_CG(rad, cond_gmean, var, len_scale, anis, K_well='KH', prop=1.6)[source]

The coarse-graining conductivity.

This solution was presented in ‘’Zech 2013’’[R8].

This functions gives an effective conductivity for 3D pumpingtests in heterogenous aquifers, where the conductivity is following a log-normal distribution and a gaussian correlation function and taking vertical anisotropy into account.

  • rad (numpy.ndarray) – Array with all radii where the function should be evaluated

  • cond_gmean (float) – Geometric-mean conductivity.

  • var (float) – Variance of the log-conductivity.

  • len_scale (float) – Corralation-length of log-conductivity.

  • anis (float) – Anisotropy-ratio of the vertical and horizontal corralation-lengths.

  • K_well (string/float, optional) – Explicit conductivity value at the well. One can choose between the harmonic mean ("KH"), the arithmetic mean ("KA") or an arbitrary float value. Default: "KH"

  • prop (float, optional) – Proportionality factor used within the upscaling procedure. Default: 1.6


K_CG – Array containing the effective conductivity values.

Return type




Zech, A. ‘’Impact of Aqifer Heterogeneity on Subsurface Flow and Salt Transport at Different Scales: from a method determine parameters of heterogeneous permeability at local scale to a large-scale model for the sedimentary basin of Thuringia.’’ PhD thesis, Friedrich-Schiller-Universität Jena, 2013


>>> K_CG([1,2,3], 0.001, 1, 10, 1, 2)
array([0.00063008, 0.00069285, 0.00077595])