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:maxdepth: 3 | ||
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index | ||
tutorials | ||
examples/index | ||
package |
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{ | ||
"cells": [ | ||
{ | ||
"cell_type": "code", | ||
"execution_count": null, | ||
"metadata": { | ||
"collapsed": false | ||
}, | ||
"outputs": [], | ||
"source": [ | ||
"%matplotlib inline" | ||
] | ||
}, | ||
{ | ||
"cell_type": "markdown", | ||
"metadata": {}, | ||
"source": [ | ||
"\n# The Theis solution\n\nIn the following the well known Theis function is called an plotted for three\ndifferent time-steps.\n\nReference: `Theis 1935 <https://doi.org/10.1029/TR016i002p00519>`__\n\n" | ||
] | ||
}, | ||
{ | ||
"cell_type": "code", | ||
"execution_count": null, | ||
"metadata": { | ||
"collapsed": false | ||
}, | ||
"outputs": [], | ||
"source": [ | ||
"import numpy as np\nfrom matplotlib import pyplot as plt\nfrom anaflow import theis\n\n\ntime = [10, 100, 1000]\nrad = np.geomspace(0.1, 10)\n\nhead = theis(time=time, rad=rad, storage=1e-4, transmissivity=1e-4, rate=-1e-4)\n\nfor i, step in enumerate(time):\n plt.plot(rad, head[i], label=\"Theis(t={})\".format(step))\n\nplt.legend()\nplt.tight_layout()\nplt.show()" | ||
] | ||
} | ||
], | ||
"metadata": { | ||
"kernelspec": { | ||
"display_name": "Python 3", | ||
"language": "python", | ||
"name": "python3" | ||
}, | ||
"language_info": { | ||
"codemirror_mode": { | ||
"name": "ipython", | ||
"version": 3 | ||
}, | ||
"file_extension": ".py", | ||
"mimetype": "text/x-python", | ||
"name": "python", | ||
"nbconvert_exporter": "python", | ||
"pygments_lexer": "ipython3", | ||
"version": "3.6.9" | ||
} | ||
}, | ||
"nbformat": 4, | ||
"nbformat_minor": 0 | ||
} |
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r""" | ||
The Theis solution | ||
================== | ||
In the following the well known Theis function is called an plotted for three | ||
different time-steps. | ||
Reference: `Theis 1935 <https://doi.org/10.1029/TR016i002p00519>`__ | ||
""" | ||
import numpy as np | ||
from matplotlib import pyplot as plt | ||
from anaflow import theis | ||
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time = [10, 100, 1000] | ||
rad = np.geomspace(0.1, 10) | ||
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head = theis(time=time, rad=rad, storage=1e-4, transmissivity=1e-4, rate=-1e-4) | ||
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for i, step in enumerate(time): | ||
plt.plot(rad, head[i], label="Theis(t={})".format(step)) | ||
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plt.legend() | ||
plt.tight_layout() | ||
plt.show() |
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b1aeb7d2930d746b1355d09b73b76480 |
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.. DO NOT EDIT. | ||
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. | ||
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: | ||
.. "examples/01_call_theis.py" | ||
.. LINE NUMBERS ARE GIVEN BELOW. | ||
.. only:: html | ||
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.. note:: | ||
:class: sphx-glr-download-link-note | ||
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Click :ref:`here <sphx_glr_download_examples_01_call_theis.py>` | ||
to download the full example code | ||
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.. rst-class:: sphx-glr-example-title | ||
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.. _sphx_glr_examples_01_call_theis.py: | ||
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The Theis solution | ||
================== | ||
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In the following the well known Theis function is called an plotted for three | ||
different time-steps. | ||
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Reference: `Theis 1935 <https://doi.org/10.1029/TR016i002p00519>`__ | ||
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.. GENERATED FROM PYTHON SOURCE LINES 10-26 | ||
.. image:: /examples/images/sphx_glr_01_call_theis_001.png | ||
:alt: 01 call theis | ||
:class: sphx-glr-single-img | ||
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.. code-block:: default | ||
import numpy as np | ||
from matplotlib import pyplot as plt | ||
from anaflow import theis | ||
time = [10, 100, 1000] | ||
rad = np.geomspace(0.1, 10) | ||
head = theis(time=time, rad=rad, storage=1e-4, transmissivity=1e-4, rate=-1e-4) | ||
for i, step in enumerate(time): | ||
plt.plot(rad, head[i], label="Theis(t={})".format(step)) | ||
plt.legend() | ||
plt.tight_layout() | ||
plt.show() | ||
.. rst-class:: sphx-glr-timing | ||
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**Total running time of the script:** ( 0 minutes 0.325 seconds) | ||
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.. _sphx_glr_download_examples_01_call_theis.py: | ||
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.. only :: html | ||
.. container:: sphx-glr-footer | ||
:class: sphx-glr-footer-example | ||
.. container:: sphx-glr-download sphx-glr-download-python | ||
:download:`Download Python source code: 01_call_theis.py <01_call_theis.py>` | ||
.. container:: sphx-glr-download sphx-glr-download-jupyter | ||
:download:`Download Jupyter notebook: 01_call_theis.ipynb <01_call_theis.ipynb>` | ||
.. only:: html | ||
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.. rst-class:: sphx-glr-signature | ||
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`Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_ |
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{ | ||
"cells": [ | ||
{ | ||
"cell_type": "code", | ||
"execution_count": null, | ||
"metadata": { | ||
"collapsed": false | ||
}, | ||
"outputs": [], | ||
"source": [ | ||
"%matplotlib inline" | ||
] | ||
}, | ||
{ | ||
"cell_type": "markdown", | ||
"metadata": {}, | ||
"source": [ | ||
"\n# The extended Theis solution in 2D\n\nWe provide an extended theis solution, that incorporates the effectes of a\nheterogeneous transmissivity field on a pumping test.\n\nIn the following this extended solution is compared to the standard theis\nsolution for well flow. You can nicely see, that the extended solution represents\na transition between the theis solutions for the geometric- and harmonic-mean\ntransmissivity.\n\nReference: `Zech et. al. 2016 <http://dx.doi.org/10.1002/2015WR018509>`__\n\n" | ||
] | ||
}, | ||
{ | ||
"cell_type": "code", | ||
"execution_count": null, | ||
"metadata": { | ||
"collapsed": false | ||
}, | ||
"outputs": [], | ||
"source": [ | ||
"import numpy as np\nfrom matplotlib import pyplot as plt\nfrom anaflow import theis, ext_theis_2d" | ||
] | ||
}, | ||
{ | ||
"cell_type": "markdown", | ||
"metadata": {}, | ||
"source": [ | ||
"We use three time steps: 10s, 10min, 10h\n\n" | ||
] | ||
}, | ||
{ | ||
"cell_type": "code", | ||
"execution_count": null, | ||
"metadata": { | ||
"collapsed": false | ||
}, | ||
"outputs": [], | ||
"source": [ | ||
"time_labels = [\"10 s\", \"10 min\", \"10 h\"]\ntime = [10, 600, 36000] # 10s, 10min, 10h" | ||
] | ||
}, | ||
{ | ||
"cell_type": "markdown", | ||
"metadata": {}, | ||
"source": [ | ||
"Radius from the pumping well should be in [0, 4].\n\n" | ||
] | ||
}, | ||
{ | ||
"cell_type": "code", | ||
"execution_count": null, | ||
"metadata": { | ||
"collapsed": false | ||
}, | ||
"outputs": [], | ||
"source": [ | ||
"rad = np.geomspace(0.05, 4)" | ||
] | ||
}, | ||
{ | ||
"cell_type": "markdown", | ||
"metadata": {}, | ||
"source": [ | ||
"Parameters of heterogeneity, storage and pumping rate.\n\n" | ||
] | ||
}, | ||
{ | ||
"cell_type": "code", | ||
"execution_count": null, | ||
"metadata": { | ||
"collapsed": false | ||
}, | ||
"outputs": [], | ||
"source": [ | ||
"var = 0.5 # variance of the log-transmissivity\nlen_scale = 10.0 # correlation length of the log-transmissivity\nTG = 1e-4 # the geometric mean of the transmissivity\nTH = TG * np.exp(-var / 2.0) # the harmonic mean of the transmissivity\n\nS = 1e-4 # storativity\nrate = -1e-4 # pumping rate" | ||
] | ||
}, | ||
{ | ||
"cell_type": "markdown", | ||
"metadata": {}, | ||
"source": [ | ||
"Now let's compare the extended Theis solution to the classical solutions\nfor the near and far field values of transmissivity.\n\n" | ||
] | ||
}, | ||
{ | ||
"cell_type": "code", | ||
"execution_count": null, | ||
"metadata": { | ||
"collapsed": false | ||
}, | ||
"outputs": [], | ||
"source": [ | ||
"head_TG = theis(time, rad, S, TG, rate)\nhead_TH = theis(time, rad, S, TH, rate)\nhead_ef = ext_theis_2d(time, rad, S, TG, var, len_scale, rate)\ntime_ticks = []\nfor i, step in enumerate(time):\n label_TG = \"Theis($T_G$)\" if i == 0 else None\n label_TH = \"Theis($T_H$)\" if i == 0 else None\n label_ef = \"extended Theis\" if i == 0 else None\n plt.plot(\n rad, head_TG[i], label=label_TG, color=\"C\" + str(i), linestyle=\"--\"\n )\n plt.plot(\n rad, head_TH[i], label=label_TH, color=\"C\" + str(i), linestyle=\":\"\n )\n plt.plot(rad, head_ef[i], label=label_ef, color=\"C\" + str(i))\n time_ticks.append(head_ef[i][-1])\n\nplt.xlabel(\"r in [m]\")\nplt.ylabel(\"h in [m]\")\nplt.legend()\nylim = plt.gca().get_ylim()\nplt.gca().set_xlim([0, rad[-1]])\nax2 = plt.gca().twinx()\nax2.set_yticks(time_ticks)\nax2.set_yticklabels(time_labels)\nax2.set_ylim(ylim)\nplt.tight_layout()\nplt.show()" | ||
] | ||
} | ||
], | ||
"metadata": { | ||
"kernelspec": { | ||
"display_name": "Python 3", | ||
"language": "python", | ||
"name": "python3" | ||
}, | ||
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"codemirror_mode": { | ||
"name": "ipython", | ||
"version": 3 | ||
}, | ||
"file_extension": ".py", | ||
"mimetype": "text/x-python", | ||
"name": "python", | ||
"nbconvert_exporter": "python", | ||
"pygments_lexer": "ipython3", | ||
"version": "3.6.9" | ||
} | ||
}, | ||
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"nbformat_minor": 0 | ||
} |
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