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.. "examples/04_call_ext_theis_tpl.py"
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.. only:: html

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

        :ref:`Go to the end <sphx_glr_download_examples_04_call_ext_theis_tpl.py>`
        to download the full example code.

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

.. _sphx_glr_examples_04_call_ext_theis_tpl.py:


The extended Theis solution for truncated power laws
====================================================

We provide an extended theis solution, that incorporates the effectes of a
heterogeneous conductivity field following a truncated power law.
In addition, it incorporates the assumptions of the general radial flow model
and provides an arbitrary flow dimension.

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 well- and farfield-conductivity.

Reference: (not yet published)

.. GENERATED FROM PYTHON SOURCE LINES 16-22

.. code-block:: Python


    import numpy as np
    from matplotlib import pyplot as plt

    from anaflow import ext_theis_tpl, theis








.. GENERATED FROM PYTHON SOURCE LINES 23-24

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

.. GENERATED FROM PYTHON SOURCE LINES 24-28

.. code-block:: Python


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








.. GENERATED FROM PYTHON SOURCE LINES 29-30

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

.. GENERATED FROM PYTHON SOURCE LINES 30-33

.. code-block:: Python


    rad = np.geomspace(0.05, 4)








.. GENERATED FROM PYTHON SOURCE LINES 34-35

Parameters of heterogeneity, storage and pumping rate.

.. GENERATED FROM PYTHON SOURCE LINES 35-45

.. code-block:: Python


    var = 0.5  # variance of the log-conductivity
    len_scale = 20.0  # upper bound for the length scale
    hurst = 0.5  # hurst coefficient
    KG = 1e-4  # the geometric mean of the conductivity
    KH = KG * np.exp(-var / 2)  # the harmonic mean of the conductivity

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








.. GENERATED FROM PYTHON SOURCE LINES 46-48

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

.. GENERATED FROM PYTHON SOURCE LINES 48-83

.. code-block:: Python


    head_KG = theis(time, rad, S, KG, rate)
    head_KH = theis(time, rad, S, KH, rate)
    head_ef = ext_theis_tpl(
        time=time,
        rad=rad,
        storage=S,
        cond_gmean=KG,
        len_scale=len_scale,
        hurst=hurst,
        var=var,
        rate=rate,
    )
    time_ticks = []
    for i, step in enumerate(time):
        label_TG = "Theis($K_G$)" if i == 0 else None
        label_TH = "Theis($K_H$)" if i == 0 else None
        label_ef = "extended Theis TPL 2D" if i == 0 else None
        plt.plot(rad, head_KG[i], label=label_TG, color="C" + str(i), linestyle="--")
        plt.plot(rad, head_KH[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.xscale("log")
    plt.xlabel("r in [m]")
    plt.ylabel("h in [m]")
    plt.legend()
    ylim = plt.gca().get_ylim()
    plt.gca().set_xlim([rad[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_04_call_ext_theis_tpl_001.png
   :alt: 04 call ext theis tpl
   :srcset: /examples/images/sphx_glr_04_call_ext_theis_tpl_001.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 0.416 seconds)


.. _sphx_glr_download_examples_04_call_ext_theis_tpl.py:

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

      :download:`Download Python source code: 04_call_ext_theis_tpl.py <04_call_ext_theis_tpl.py>`

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

      :download:`Download zipped: 04_call_ext_theis_tpl.zip <04_call_ext_theis_tpl.zip>`


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