.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "examples/02_call_ext_theis2d.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_examples_02_call_ext_theis2d.py>`
        to download the full example code.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_examples_02_call_ext_theis2d.py:


The extended Theis solution in 2D
=================================

We provide an extended theis solution, that incorporates the effectes of a
heterogeneous transmissivity field on a pumping test.

In the following this extended solution is compared to the standard theis
solution for well flow. You can nicely see, that the extended solution represents
a transition between the theis solutions for the geometric- and harmonic-mean
transmissivity.

Reference: `Zech et. al. 2016 <http://dx.doi.org/10.1002/2015WR018509>`__

.. GENERATED FROM PYTHON SOURCE LINES 15-21

.. code-block:: Python


    import numpy as np
    from matplotlib import pyplot as plt

    from anaflow import ext_theis_2d, theis








.. GENERATED FROM PYTHON SOURCE LINES 22-23

We use three time steps: 10s, 10min, 10h

.. GENERATED FROM PYTHON SOURCE LINES 23-27

.. code-block:: Python


    time_labels = ["10 s", "10 min", "10 h"]
    time = [10, 600, 36000]  # 10s, 10min, 10h








.. GENERATED FROM PYTHON SOURCE LINES 28-29

Radius from the pumping well should be in [0, 4].

.. GENERATED FROM PYTHON SOURCE LINES 29-32

.. code-block:: Python


    rad = np.geomspace(0.05, 4)








.. GENERATED FROM PYTHON SOURCE LINES 33-34

Parameters of heterogeneity, storage and pumping rate.

.. GENERATED FROM PYTHON SOURCE LINES 34-43

.. code-block:: Python


    var = 0.5  # variance of the log-transmissivity
    len_scale = 10.0  # correlation length of the log-transmissivity
    TG = 1e-4  # the geometric mean of the transmissivity
    TH = TG * np.exp(-var / 2.0)  # the harmonic mean of the transmissivity

    S = 1e-4  # storativity
    rate = -1e-4  # pumping rate








.. GENERATED FROM PYTHON SOURCE LINES 44-46

Now let's compare the extended Theis solution to the classical solutions
for the near and far field values of transmissivity.

.. GENERATED FROM PYTHON SOURCE LINES 46-71

.. code-block:: Python


    head_TG = theis(time, rad, S, TG, rate)
    head_TH = theis(time, rad, S, TH, rate)
    head_ef = ext_theis_2d(time, rad, S, TG, var, len_scale, rate)
    time_ticks = []
    for i, step in enumerate(time):
        label_TG = "Theis($T_G$)" if i == 0 else None
        label_TH = "Theis($T_H$)" if i == 0 else None
        label_ef = "extended Theis" if i == 0 else None
        plt.plot(rad, head_TG[i], label=label_TG, color="C" + str(i), linestyle="--")
        plt.plot(rad, head_TH[i], label=label_TH, color="C" + str(i), linestyle=":")
        plt.plot(rad, head_ef[i], label=label_ef, color="C" + str(i))
        time_ticks.append(head_ef[i][-1])

    plt.xlabel("r in [m]")
    plt.ylabel("h in [m]")
    plt.legend()
    ylim = plt.gca().get_ylim()
    plt.gca().set_xlim([0, rad[-1]])
    ax2 = plt.gca().twinx()
    ax2.set_yticks(time_ticks)
    ax2.set_yticklabels(time_labels)
    ax2.set_ylim(ylim)
    plt.tight_layout()
    plt.show()



.. image-sg:: /examples/images/sphx_glr_02_call_ext_theis2d_001.png
   :alt: 02 call ext theis2d
   :srcset: /examples/images/sphx_glr_02_call_ext_theis2d_001.png
   :class: sphx-glr-single-img






.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 0.608 seconds)


.. _sphx_glr_download_examples_02_call_ext_theis2d.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: 02_call_ext_theis2d.ipynb <02_call_ext_theis2d.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: 02_call_ext_theis2d.py <02_call_ext_theis2d.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: 02_call_ext_theis2d.zip <02_call_ext_theis2d.zip>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_