anaflow.flow.ext_thiem_3d¶
- ext_thiem_3d(rad, r_ref, cond_gmean, var, len_scale, anis=1.0, lat_ext=1.0, rate=- 0.0001, h_ref=0.0, K_well='KH', prop=1.6)[source]¶
The extended Thiem solution in 3D.
The extended Thiem solution for steady-state flow under a pumping condition in a confined aquifer. The type curve is describing the effective drawdown in a 3D statistical framework, where the conductivity distribution is following a log-normal distribution with a gaussian correlation function and taking vertical anisotropy into account.
- Parameters
rad (
numpy.ndarray
) – Array with all radii where the function should be evaluatedr_ref (
float
) – Reference radius with known head (see h_ref)cond_gmean (
float
) – Geometric-mean conductivity.var (
float
) – Variance of the log-conductivity.len_scale (
float
) – Corralation-length of log-conductivity.anis (
float
, optional) – Anisotropy-ratio of the vertical and horizontal corralation-lengths. Default: 1.0lat_ext (
float
, optional) – Lateral extend of the aquifer (thickness). Default:1.0
rate (
float
, optional) – Pumpingrate at the well. Default: -1e-4h_ref (
float
, optional) – Reference head at the reference-radius r_ref. Default:0.0
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
- Returns
head – Array with all heads at the given radii.
- Return type
References
- Zech2013
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
Notes
If you want to use cartesian coordiantes, just use the formula
r = sqrt(x**2 + y**2)
Examples
>>> ext_thiem_3d([1,2,3], 10, 0.001, 1, 10, 1, 1, -0.001) array([-0.48828026, -0.31472059, -0.22043022])