anaflow.flow.homogeneous

Anaflow subpackage providing flow solutions in homogeneous aquifers.

The following functions are provided

thiem(rad, r_ref, transmissivity[, rate, h_ref]) The Thiem solution.
theis(time, rad, storage, transmissivity[, …]) The Theis solution.
grf(time, rad, storage, conductivity[, dim, …]) The general radial flow (GRF) model for a pumping test.
thiem(rad, r_ref, transmissivity, rate=-0.0001, h_ref=0.0)[source]

The Thiem solution.

The Thiem solution for steady-state flow under a pumping condition in a confined and homogeneous aquifer. This solution was presented in [Thiem1906].

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).
  • transmissivity (float) – Transmissivity of the aquifer.
  • 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
Returns:

head – Array with all heads at the given radii.

Return type:

numpy.ndarray

References

[Thiem1906]Thiem, G., ‘’Hydrologische Methoden, J.M. Gebhardt’‘, Leipzig, 1906.

Notes

The parameters rad, r_ref and transmissivity will be checked for positivity. If you want to use cartesian coordiantes, just use the formula r = sqrt(x**2 + y**2)

Examples

>>> thiem([1,2,3], 10, 0.001, -0.001)
array([-0.3664678 , -0.25615   , -0.19161822])
theis(time, rad, storage, transmissivity, rate=-0.0001, r_well=0.0, r_bound=inf, h_bound=0.0, struc_grid=True, lap_kwargs=None)[source]

The Theis solution.

The Theis solution for transient flow under a pumping condition in a confined and homogeneous aquifer. This solution was presented in [Theis35].

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 coefficient of the aquifer.
  • conductivity (float) – Conductivity of the aquifer.
  • rate (float, optional) – Pumpingrate at the well. Default: -1e-4
  • r_well (float, optional) – Inner radius of the pumping-well. Default: 0.0
  • r_bound (float, optional) – Radius of the outer boundariy of the aquifer. Default: np.inf
  • h_bound (float, optional) – Reference head at the outer boundary, as well as initial condition. 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
  • lap_kwargs (dict or None optional) – Dictionary for get_lap_inv containing method and method_dict. The default is equivalent to lap_kwargs = {"method": "stehfest", "method_dict": None}. Default: None
Returns:

head – Array with all heads at the given radii and time-points.

Return type:

numpy.ndarray

References

[Theis35]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
grf(time, rad, storage, conductivity, dim=2, lat_ext=1.0, rate=-0.0001, r_well=0.0, r_bound=inf, h_bound=0.0, struc_grid=True, lap_kwargs=None)[source]

The general radial flow (GRF) model for a pumping test.

This solution was presented in [Barker88].

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 coefficient of the aquifer.
  • conductivity (float) – Conductivity of the aquifer.
  • dim (float, optional) – Fractional dimension of the aquifer. Default: 2.0
  • lat_ext (float, optional) – Lateral extend of the aquifer. Default: 1.0
  • rate (float, optional) – Pumpingrate at the well. Default: -1e-4
  • r_well (float, optional) – Inner 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
  • 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
  • lap_kwargs (dict or None optional) – Dictionary for get_lap_inv containing method and method_dict. The default is equivalent to lap_kwargs = {"method": "stehfest", "method_dict": None}. Default: None
Returns:

head – Array with all heads at the given radii and time-points.

Return type:

numpy.ndarray

References

[Barker88]Barker, J. ‘’A generalized radial flow model for hydraulic tests in fractured rock.’‘, Water Resources Research 24.10, 1796-1804, 1988