anaflow.flow.ext_theis_tpl_3d¶
- ext_theis_tpl_3d(time, rad, storage, cond_gmean, len_scale, hurst, var=None, c=1.0, anis=1, 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)[source]¶
The extended Theis solution for truncated power-law fields in 3D.
The extended Theis solution for transient flow under a pumping condition in a confined aquifer with anisotropy in 3D. The type curve is describing the effective drawdown in a 3-dimensional statistical framework, where the conductivity distribution is following a log-normal distribution with a truncated power-law correlation function build on superposition of gaussian modes.
- 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.cond_gmean (
float
) – Geometric-mean conductivity.len_scale (
float
) – Corralation-length of log-conductivity.hurst (
float
) – Hurst coefficient of the TPL model. Should be in (0, 1).var (
float
) – Variance of the log-conductivity. If var is given, c will be calculated accordingly. Default:None
c (
float
, optional) – Intensity of variation in the TPL model. Is overwritten if var is given. Default:1.0
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-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
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
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)