anaflow.flow.ext_thiem_int

ext_thiem_int(rad, r_ref, cond_gmean, var, len_scale, roughness=1.0, dim=2.0, lat_ext=1.0, rate=-0.0001, h_ref=0.0, K_well='KH', prop=1.6)[source]

The extended Thiem solution for the intgeral variogram.

The extended Theis solution for steady flow under a pumping condition in a confined aquifer. The type curve is describing the effective drawdown in a d-dimensional statistical framework, where the conductivity distribution is following a log-normal distribution with an integral correlation function incorporating a roughness parameter.

The roughness parameter controls the field roughness of log-transmissivity. It’s limits are a pure nugget model for r -> 0 and the gaussian model for r -> infinity.

Parameters:

rad (numpy.ndarray) – Array with all radii where the function should be evaluated
r_ref (float) – Reference radius with known head (see h_ref)
cond_gmean (float) – Geometric-mean conductivity. You can also treat this as transmissivity by leaving ‘lat_ext=1’.
var (float) – Variance of the log-conductivity.
len_scale (float) – Corralation-length of log-conductivity.
roughness (float, optional) – Roughness of the model. Should be positive. Default: 1
dim (float, optional) – Dimension of space. Default: 2.0
lat_ext (float, optional) –

Lateral extend of the aquifer:
- sqare-root of cross-section in 1D
- thickness in 2D
- meaningless in 3D
Default: 1.0
rate (float, optional) – Pumpingrate at the well. Default: -1e-4
h_ref (float, optional) – Reference head at the reference-radius r_ref. Default: 0.0
K_well (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 and time-points.

Return type:

numpy.ndarray

Notes

If you want to use cartesian coordiantes, just use the formula r = sqrt(x**2 + y**2)