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 steadystate 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: 1e4  h_ref (
float
, optional) – Reference head at the referenceradius r_ref. Default:0.0
Returns: head – Array with all heads at the given radii.
Return type: References
[Thiem1906] Thiem, G., ‘’Hydrologische Methoden, J.M. Gebhardt’’, Leipzig, 1906. Notes
The parameters
rad
,r_ref
andtransmissivity
will be checked for positivity. If you want to use cartesian coordiantes, just use the formular = sqrt(x**2 + y**2)
Examples
>>> thiem([1,2,3], 10, 0.001, 0.001) array([0.3664678 , 0.25615 , 0.19161822])
 rad (

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 timepoints 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: 1e4  r_well (
float
, optional) – Inner radius of the pumpingwell. 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 toFalse
, the rad and time array will be merged and interpreted as single, rt points. In this case they need to have the same shapes. Otherwise a structured rt grid is created. Default:True
 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 timepoints.
Return type: 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, 519524, 1935  time (

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 timepoints 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: 1e4  r_well (
float
, optional) – Inner radius of the pumpingwell. 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, rt points. In this case they need to have the same shapes. Otherwise a structured rt grid is created. Default:True
 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 timepoints.
Return type: References
[Barker88] Barker, J. ‘’A generalized radial flow model for hydraulic tests in fractured rock.’’, Water Resources Research 24.10, 17961804, 1988  time (