Reference problem
=====================


Geometry
---------

The field studied consists of two porous masses (:math:`\mathrm{AEFD}` and :math:`\mathrm{EBCF}`) separated by a hydraulic joint. The play between the structure and the gas injection wall (:math:`\mathrm{AGIB}`) is also modelled.


.. image:: images/10000000000003B1000002E924AC5B574423F534.jpg
    :width: 5.2555in
    :height: 4.1429in


.. _RefImage_10000000000003B1000002E924AC5B574423F534.jpg:

Point coordinates (in meters):


.. csv-table::

    "", ":math:`x` "," :math:`y` ", "", ":math:`x` "," "," "," :math:`y` ", "", ":math:`x` "," :math:`y`"
    ":math:`A` ", "0.4", "7.5"," :math:`D` "," "," ", "20", "7.5"," :math:`G` ", "0", "7.5"
    ":math:`B` ", "0.4", "-7.5"," -7.5", ":math:`E` "," ", "0.4", "0", "0" :math:`H`
    ":math:`C` ", "20", "-7.5"," :math:`F` "," ", "20", "0"," :math:`I` ", "0", "-7.5"



Material properties
----------------------


* Properties of intersticial fluid (dihydrogen):


.. csv-table::

    "Molar mass", ":math:`\mathrm{0,002}{\mathrm{kg.m}}^{-3}`"
    "Viscosity", ":math:`{9.10}^{-6}\mathrm{Pa.s}`"



* Properties of the upper rock matrix:

The matrix is elastic and has the following properties:


.. csv-table::

    "Young's module", ":math:`\mathrm{3,0}\mathrm{GPa}`"
    "Poisson's Ratio", ":math:`\mathrm{0,12}`"
    "Porosity", ":math:`\mathrm{0,18}`"
    "Intrinsic permeability", ":math:`\mathrm{2,75}{.10}^{-20}{m}^{2}`"



* Properties of the lower rock matrix:

The lower rock matrix has the same mechanical characteristics as the upper matrix, but has an intrinsic permeability that is ten times lower.


.. csv-table::

    "Young's module", ":math:`\mathrm{3,0}\mathrm{GPa}`"
    "Poisson's Ratio", ":math:`\mathrm{0,12}`"
    "Porosity", ":math:`\mathrm{0,18}`"
    "Intrinsic permeability", ":math:`\mathrm{2,75}{.10}^{-21}{m}^{2}`"



* Properties of the discontinuity:

The mechanical behavior of discontinuity is described by Bandis's law. Hydraulic flow is given by cubic law.


.. csv-table::

    "Initial normal stiffness", ":math:`{1.10}^{9}{\mathrm{Pa.m}}^{-1}`"
    "Initial asymptotic opening", ":math:`\mathrm{0,4}\mathrm{mm}`"
    "Coefficient :math:`\gamma` "," :math:`2`"



* Game Properties:

The play between the emission wall of the dihydrogen flow and the rock is an elastic medium that is very inrigid and has very high permeability.


.. csv-table::

    "Young's module", ":math:`\mathrm{3,0}\mathrm{MPa}`"
    "Poisson's Ratio", ":math:`\mathrm{0,12}`"
    "Porosity", ":math:`1`"
    "Intrinsic permeability", ":math:`{1.10}^{-8}{m}^{2}`"



Boundary conditions and loading
------------------------------------

The hydraulic boundary conditions are as follows:

On :math:`[\mathrm{GD}]` zero hydraulic flow

On :math:`[\mathrm{DC}]` :math:`{p}_{g}={p}_{0}=\mathrm{0,1}\mathrm{MPa}`

On :math:`[\mathrm{CI}]` zero hydraulic flow

On :math:`[\mathrm{IG}]` gas flow :math:`{F}_{g}={1.10}^{-10}\mathrm{kg.}{s}^{-1}\mathrm{.}{m}^{-2}`

The mechanical boundary conditions are given by the figure below.


.. image:: images/1000000000000350000002D137D2EFA22C341F16.jpg
    :width: 4.8138in
    :height: 4.0929in


.. _RefImage_1000000000000350000002D137D2EFA22C341F16.jpg:


Initial conditions
--------------------

The initial conditions are as follows:


* initial opening: :math:`\mathrm{3,48}{.10}^{-6}m`


* initial pressure in the massif: :math:`{p}_{0}=\mathrm{0,1}\mathrm{MPa}`


* compressive stress in direction :math:`y`: :math:`\mathrm{12,3}\mathrm{MPa}`


* temperature: :math:`303°K`