anaflow.flow.ext_grf_model

Anaflow subpackage providing the extended GRF Model.

The following functions are provided

ext_grf(time, rad, S_part, K_part, R_part[, …]) The extended “General radial flow” model for transient flow.
ext_grf_steady(rad, r_ref, conductivity[, …]) The extended “General radial flow” model for steady flow.
ext_grf(time, rad, S_part, K_part, R_part, dim=2, lat_ext=1.0, rate=-0.0001, h_bound=0.0, K_well=None, struc_grid=True, lap_kwargs=None)[source]

The extended “General radial flow” model for transient flow.

The general radial flow (GRF) model by Barker introduces an arbitrary dimension for radial groundwater flow. We introduced the possibility to define radial dependet conductivity and storage values.

This solution is based on the grf model 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
  • S_part (numpy.ndarray) – Given storativity values for each disk
  • K_part (numpy.ndarray) – Given conductivity values for each disk
  • R_part (numpy.ndarray) – Given radii separating the disks (including r_well and r_bound).
  • 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
  • h_bound (float, optional) – Reference head at the outer boundary R_part[-1]. Default: 0.0
  • K_well (float, optional) – Conductivity at the well. Default: K_part[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:

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
ext_grf_steady(rad, r_ref, conductivity, dim=2, lat_ext=1.0, rate=-0.0001, h_ref=0.0, arg_dict=None, **kwargs)[source]

The extended “General radial flow” model for steady flow.

The general radial flow (GRF) model by Barker introduces an arbitrary dimension for radial groundwater flow. We introduced the possibility to define radial dependet conductivity.

This solution is based on the grf model presented in [Barker88].

Parameters:
  • rad (numpy.ndarray) – Array with all radii where the function should be evaluated
  • r_ref (float) – Radius of the reference head.
  • conductivity (float or callable) – Conductivity. Either callable function taking kwargs or float.
  • 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
  • h_ref (float, optional) – Reference head at the reference-radius r_ref. Default: 0.0
  • arg_dict (dict or None, optional) – Keyword-arguments given as a dictionary that are forwarded to the conductivity function. Will be merged with **kwargs. This is designed for overlapping keywords in grf_steady and conductivity. Default: None
  • **kwargs – Keyword-arguments that are forwarded to the conductivity function. Will be merged with arg_dict
Returns:

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