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


Geometry
---------


.. image:: images/Object_1.svg
    :width: 250
    :height: 242


.. _RefImage_Object_1.svg:

Coordinates of the points (:math:`m`):


.. csv-table::

    ":math:`A` ", "-0.5", "-0.5", "-0.5"," :math:`C` ", "0.5", "0.5"
    ":math:`B` ", "0.5", "-0.5"," -0.5", ":math:`D` ", "-0.5", "0.5"



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

We only give here the properties on which the solution depends, knowing that the command file contains other material data (elasticity modules, thermal conductivity...) which ultimately play no role in the solution of the problem being treated.


+------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
|Liquid water            |Density (                                                                                                                                                                                                                                                                                                |103                                                                                                                                                                                                                                                                                                                                        |
+                        + :math:`{\mathit{kg.m}}^{\mathrm{-}3}`                                                                                                                                                                                                                                                                   +                                                                                                                                                                                                                                                                                                                                           +
|                        |)                                                                                                                                                                                                                                                                                                        | 4180 0. 0.001                                                                                                                                                                                                                                                                                                                             |
+                        +                                                                                                                                                                                                                                                                                                         +                                                                                                                                                                                                                                                                                                                                           +
|                        | Heat at constant pressure (:math:`{\mathit{J.K}}^{\mathrm{-}1}`) coefficient of thermal expansion of liquid (:math:`{K}^{\mathrm{-}1}`) Dynamic viscosity of liquid water (:math:`\mathit{Pa.s}`) Relative permeability to water                                                                        | .. image:: images/Object_2.svg                                                                                                                                                                                                                                                                                                            |
+                        +                                                                                                                                                                                                                                                                                                         +    :width: 250                                                                                                                                                                                                                                                                                                                            +
|                        |                                                                                                                                                                                                                                                                                                         |    :height: 242                                                                                                                                                                                                                                                                                                                           |
+                        +                                                                                                                                                                                                                                                                                                         +                                                                                                                                                                                                                                                                                                                                           +
|                        |                                                                                                                                                                                                                                                                                                         |                                                                                                                                                                                                                                                                                                                                           |
+                        +                                                                                                                                                                                                                                                                                                         +                                                                                                                                                                                                                                                                                                                                           +
|                        |                                                                                                                                                                                                                                                                                                         |                                                                                                                                                                                                                                                                                                                                           |
+------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
|Vapeur                  |Specific heat (                                                                                                                                                                                                                                                                                          |1900                                                                                                                                                                                                                                                                                                                                       |
+                        + :math:`{\mathit{J.K}}^{\mathrm{-}1}`                                                                                                                                                                                                                                                                    +                                                                                                                                                                                                                                                                                                                                           +
|                        |)                                                                                                                                                                                                                                                                                                        | 2.5E6. 0.018                                                                                                                                                                                                                                                                                                                              |
+                        +                                                                                                                                                                                                                                                                                                         +                                                                                                                                                                                                                                                                                                                                           +
|                        | Initial enthalpy (latent heat of vaporization) :math:`J\mathrm{/}\mathit{Kg}` Molar mass (:math:`{\mathit{kg.mol}}^{\mathrm{-}1}`)                                                                                                                                                                      |                                                                                                                                                                                                                                                                                                                                           |
+                        +                                                                                                                                                                                                                                                                                                         +                                                                                                                                                                                                                                                                                                                                           +
|                        |                                                                                                                                                                                                                                                                                                         |                                                                                                                                                                                                                                                                                                                                           |
+------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
|Gaz                     |Specific heat (                                                                                                                                                                                                                                                                                          |1900                                                                                                                                                                                                                                                                                                                                       |
+                        + :math:`{\mathit{J.K}}^{\mathrm{-}1}`                                                                                                                                                                                                                                                                    +                                                                                                                                                                                                                                                                                                                                           +
|                        |)                                                                                                                                                                                                                                                                                                        | 0.018                                                                                                                                                                                                                                                                                                                                     |
+                        +                                                                                                                                                                                                                                                                                                         +                                                                                                                                                                                                                                                                                                                                           +
|                        | Molar mass (:math:`{\mathit{kg.mol}}^{\mathrm{-}1}`) Relative gas permeability Gas viscosity (:math:`{\mathit{kg.m}}^{\mathrm{-}{\mathrm{1.s}}^{\mathrm{-}1}}`)                                                                                                                                         | .. image:: images/Object_3.svg                                                                                                                                                                                                                                                                                                            |
+                        +                                                                                                                                                                                                                                                                                                         +    :width: 250                                                                                                                                                                                                                                                                                                                            +
|                        |                                                                                                                                                                                                                                                                                                         |    :height: 242                                                                                                                                                                                                                                                                                                                           |
+                        +                                                                                                                                                                                                                                                                                                         +                                                                                                                                                                                                                                                                                                                                           +
|                        |                                                                                                                                                                                                                                                                                                         |                                                                                                                                                                                                                                                                                                                                           |
+                        +                                                                                                                                                                                                                                                                                                         +                                                                                                                                                                                                                                                                                                                                           +
|                        |                                                                                                                                                                                                                                                                                                         | 1,8E-5                                                                                                                                                                                                                                                                                                                                    |
+                        +                                                                                                                                                                                                                                                                                                         +                                                                                                                                                                                                                                                                                                                                           +
|                        |                                                                                                                                                                                                                                                                                                         |                                                                                                                                                                                                                                                                                                                                           |
+------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
|Dissolved air           |Specific heat (                                                                                                                                                                                                                                                                                          |1900                                                                                                                                                                                                                                                                                                                                       |
+                        + :math:`{\mathit{J.K}}^{\mathrm{-}1}`                                                                                                                                                                                                                                                                    +                                                                                                                                                                                                                                                                                                                                           +
|                        |)                                                                                                                                                                                                                                                                                                        | 50000                                                                                                                                                                                                                                                                                                                                     |
+                        +                                                                                                                                                                                                                                                                                                         +                                                                                                                                                                                                                                                                                                                                           +
|                        | Henry's constant (:math:`{\mathit{Pa.m}}^{3.}{\mathit{mol}}^{\mathrm{-}1}`)                                                                                                                                                                                                                             |                                                                                                                                                                                                                                                                                                                                           |
+                        +                                                                                                                                                                                                                                                                                                         +                                                                                                                                                                                                                                                                                                                                           +
|                        |                                                                                                                                                                                                                                                                                                         |                                                                                                                                                                                                                                                                                                                                           |
+------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
|Skeleton                |Heat capacity at constant stress (:math:`{\mathit{J.K}}^{\mathrm{-}1}`)                                                                                                                                                                                                                                  |1050                                                                                                                                                                                                                                                                                                                                       |
+------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
|Initial state           |Porosity                                                                                                                                                                                                                                                                                                 |0.3                                                                                                                                                                                                                                                                                                                                        |
+                        +                                                                                                                                                                                                                                                                                                         +                                                                                                                                                                                                                                                                                                                                           +
|                        | Temperature (:math:`K`) Gas Pressure (:math:`\mathit{Pa}`) Gas Pressure () Vapor Pressure (:math:`\mathit{Pa}`) Initial Liquid Saturation (:math:`\mathit{Pa}`)                                                                                                                                         | 300 1E5 3700 0.5                                                                                                                                                                                                                                                                                                                          |
+                        +                                                                                                                                                                                                                                                                                                         +                                                                                                                                                                                                                                                                                                                                           +
|                        |                                                                                                                                                                                                                                                                                                         |                                                                                                                                                                                                                                                                                                                                           |
+------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
|Constants               |Ideal gas constant                                                                                                                                                                                                                                                                                       |8,315                                                                                                                                                                                                                                                                                                                                      |
+------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
|Homogenized coefficients|Homogenized density (                                                                                                                                                                                                                                                                                    |2200                                                                                                                                                                                                                                                                                                                                       |
+                        + :math:`{\mathit{kg.m}}^{\mathrm{-}}`                                                                                                                                                                                                                                                                    +                                                                                                                                                                                                                                                                                                                                           +
|                        | 3)                                                                                                                                                                                                                                                                                                      |                                                                                                                                                                                                                                                                                                                                           |
+                        +                                                                                                                                                                                                                                                                                                         + .. image:: images/Object_4.svg                                                                                                                                                                                                                                                                                                            +
|                        | Sorption isothermal                                                                                                                                                                                                                                                                                     |    :width: 250                                                                                                                                                                                                                                                                                                                            |
+                        +                                                                                                                                                                                                                                                                                                         +    :height: 242                                                                                                                                                                                                                                                                                                                           +
|                        |                                                                                                                                                                                                                                                                                                         |                                                                                                                                                                                                                                                                                                                                           |
+                        +                                                                                                                                                                                                                                                                                                         +                                                                                                                                                                                                                                                                                                                                           +
|                        |                                                                                                                                                                                                                                                                                                         |                                                                                                                                                                                                                                                                                                                                           |
+                        +                                                                                                                                                                                                                                                                                                         +                                                                                                                                                                                                                                                                                                                                           +
|                        |                                                                                                                                                                                                                                                                                                         |                                                                                                                                                                                                                                                                                                                                           |
+                        +                                                                                                                                                                                                                                                                                                         + With                                                                                                                                                                                                                                                                                                                                      +
|                        |                                                                                                                                                                                                                                                                                                         |                                                                                                                                                                                                                                                                                                                                           |
+                        +                                                                                                                                                                                                                                                                                                         +                                                                                                                                                                                                                                                                                                                                           +
|                        |                                                                                                                                                                                                                                                                                                         | .. image:: images/Object_5.svg                                                                                                                                                                                                                                                                                                            |
+                        +                                                                                                                                                                                                                                                                                                         +    :width: 250                                                                                                                                                                                                                                                                                                                            +
|                        |                                                                                                                                                                                                                                                                                                         |    :height: 242                                                                                                                                                                                                                                                                                                                           |
+                        +                                                                                                                                                                                                                                                                                                         +                                                                                                                                                                                                                                                                                                                                           +
|                        |                                                                                                                                                                                                                                                                                                         |                                                                                                                                                                                                                                                                                                                                           |
+                        +                                                                                                                                                                                                                                                                                                         +                                                                                                                                                                                                                                                                                                                                           +
|                        |                                                                                                                                                                                                                                                                                                         |                                                                                                                                                                                                                                                                                                                                           |
+                        +                                                                                                                                                                                                                                                                                                         +                                                                                                                                                                                                                                                                                                                                           +
|                        |                                                                                                                                                                                                                                                                                                         |                                                                                                                                                                                                                                                                                                                                           |
+                        +                                                                                                                                                                                                                                                                                                         + .. image:: images/Object_6.svg                                                                                                                                                                                                                                                                                                            +
|                        |                                                                                                                                                                                                                                                                                                         |    :width: 250                                                                                                                                                                                                                                                                                                                            |
+                        +                                                                                                                                                                                                                                                                                                         +    :height: 242                                                                                                                                                                                                                                                                                                                           +
|                        |                                                                                                                                                                                                                                                                                                         |                                                                                                                                                                                                                                                                                                                                           |
+                        +                                                                                                                                                                                                                                                                                                         +                                                                                                                                                                                                                                                                                                                                           +
|                        |                                                                                                                                                                                                                                                                                                         |                                                                                                                                                                                                                                                                                                                                           |
+                        +                                                                                                                                                                                                                                                                                                         +                                                                                                                                                                                                                                                                                                                                           +
|                        |                                                                                                                                                                                                                                                                                                         |                                                                                                                                                                                                                                                                                                                                           |
+------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+



Boundary conditions and loads
-------------------------------------

On all sides:

Heat flow

.. image:: images/Object_7.svg
    :width: 250
    :height: 242


.. _RefImage_Object_7.svg:

Zero hydraulic flow