- ext_theis_3d(time, rad, storage, cond_gmean, var, len_scale, anis=1.0, lat_ext=1.0, rate=- 0.0001, r_well=0.0, r_bound=inf, h_bound=0.0, K_well='KH', prop=1.6, far_err=0.01, struc_grid=True, parts=30, lap_kwargs=None)¶
The extended Theis solution in 3D.
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 3D statistical framework, where the transmissivity distribution is following a log-normal distribution with a gaussian correlation function and taking vertical anisotropy into account.
numpy.ndarray) – Array with all time-points where the function should be evaluated
numpy.ndarray) – Array with all radii where the function should be evaluated
float) – Storage of the aquifer.
float) – Geometric-mean conductivity.
float) – Variance of the log-conductivity.
float) – Corralation-length of log-conductivity.
float, optional) – Anisotropy-ratio of the vertical and horizontal corralation-lengths. Default: 1.0
float, optional) – Lateral extend of the aquifer (thickness). Default:
float, optional) – Pumpingrate at the well. Default: -1e-4
float, optional) – Radius of the pumping-well. Default:
float, optional) – Radius of the outer boundary of the aquifer. Default:
float, optional) – Reference head at the outer boundary as well as initial condition. Default:
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:
float, optional) – Proportionality factor used within the upscaling procedure. Default:
float, optional) – Relative error for the farfield transmissivity for calculating the cutoff-point of the solution. Default:
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:
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:
head – Array with all heads at the given radii and time-points.
- Return type
If you want to use cartesian coordiantes, just use the formula
r = sqrt(x**2 + y**2)
>>> ext_theis_3d([10,100], [1,2,3], 0.001, 0.001, 1, 10, 1, 1, -0.001) array([[-0.32756786, -0.16717569, -0.09141211], [-0.5416396 , -0.36982684, -0.27798614]])