anaflow.tools.special.well_solution
- well_solution(time, rad, storage, transmissivity, rate=-0.0001, h_bound=0.0, struc_grid=True)[source]
The classical Theis solution.
The classical Theis solution for transient flow under a pumping condition in a confined and homogeneous aquifer.
This solution was presented in ‘’Theis 1935’’[R9].
- Parameters
time (
numpy.ndarray
) – Array with all time-points where the function should be evaluated.rad (
numpy.ndarray
) – Array with all radii where the function should be evaluated.storage (
float
) – Storage of the aquifer.transmissivity (
float
) – Transmissivity of the aquifer.rate (
float
, optional) – Pumpingrate at the well. Default: -1e-4h_bound (
float
, optional) – Reference head at the outer boundary at infinity. Default:0.0
struc_grid (
bool
, optional) – If this is set to “False”, 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
- Returns
head – Array with all heads at the given radii and time-points.
- Return type
- Raises
ValueError – If
rad
is not positiv.ValueError – If
time
is negative.ValueError – If shape of
rad
andtime
differ in case ofstruc_grid
isTrue
.ValueError – If
transmissivity
is not positiv.ValueError – If
storage
is not positiv.
References
- R9
Theis, C., ‘’The relation between the lowering of the piezometric surface and the rate and duration of discharge of a well using groundwater storage’’, Trans. Am. Geophys. Union, 16, 519-524, 1935
Notes
The parameters
rad
,T
andS
will be checked for positivity. If you want to use cartesian coordiantes, just use the formular = sqrt(x**2 + y**2)
Examples
>>> well_solution([10,100], [1,2,3], 0.001, 0.001, -0.001) array([[-0.24959541, -0.14506368, -0.08971485], [-0.43105106, -0.32132823, -0.25778313]])