anaflow.flow.ext_theis_2d¶
- ext_theis_2d(time, rad, storage, trans_gmean, var, len_scale, rate=- 0.0001, r_well=0.0, r_bound=inf, h_bound=0.0, T_well=None, prop=1.6, struc_grid=True, far_err=0.01, parts=30, lap_kwargs=None)[source]¶
The extended Theis solution in 2D.
The extended Theis solution for transient flow under a pumping condition in a confined aquifer. The type curve is describing the effective drawdown in a 2D statistical framework, where the transmissivity distribution is following a log-normal distribution with a gaussian correlation function.
- Parameters
time (
numpy.ndarray
) – Array with all time-points where the function should be evaluatedrad (
numpy.ndarray
) – Array with all radii where the function should be evaluatedstorage (
float
) – Storage of the aquifer.trans_gmean (
float
) – Geometric-mean transmissivity.var (
float
) – Variance of log-transmissivity.len_scale (
float
) – Correlation-length of log-transmissivity.rate (
float
, optional) – Pumpingrate at the well. Default: -1e-4r_well (
float
, optional) – Radius of the pumping-well. Default:0.0
r_bound (
float
, optional) – Radius of the outer boundary of the aquifer. Default:np.inf
h_bound (
float
, optional) – Reference head at the outer boundary as well as initial condition. Default:0.0
T_well (
float
, optional) – Explicit transmissivity value at the well. Harmonic mean by default.prop (
float
, optional) – Proportionality factor used within the upscaling procedure. Default:1.6
far_err (
float
, optional) – Relative error for the farfield transmissivity for calculating the cutoff-point of the solution. Default:0.01
struc_grid (
bool
, optional) – If this is set toFalse
, the rad and time array will be merged and interpreted as single, r-t points. In this case they need to have the same shapes. Otherwise a structured r-t grid is created. Default:True
parts (
int
, optional) – Since the solution is calculated by setting the transmissivity to local constant values, one needs to specify the number of partitions of the transmissivity. Default:30
lap_kwargs (
dict
orNone
optional) – Dictionary forget_lap_inv
containing method and method_dict. The default is equivalent tolap_kwargs = {"method": "stehfest", "method_dict": None}
. Default:None
- Returns
head – Array with all heads at the given radii and time-points.
- Return type
Notes
If you want to use cartesian coordiantes, just use the formula
r = sqrt(x**2 + y**2)
Examples
>>> ext_theis_2d([10,100], [1,2,3], 0.001, 0.001, 1, 10, -0.001) array([[-0.33737576, -0.17400123, -0.09489812], [-0.58443489, -0.40847176, -0.31095166]])