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


Geometry
---------

F

D

C

E

B

A

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


.. csv-table::

    "**Point**", ":math:`X` "," :math:`Y`"
    ":math:`A` ", "0.425", "-10"
    ":math:`B` ", "1,1225", "-10"
    ":math:`C` ", "1,1225", "0"
    ":math:`D` ", "0.425", "0"
    ":math:`E` ", "10", "-10"
    ":math:`F` ", "10", "0"


The part delimited by :math:`\mathit{ABCD}` will be called :math:`\mathit{BO}` and the part :math:`\mathit{BEFC}`, :math:`\mathit{BG}`.

For the 3D version of the wtnv125 test, the geometry is extruded with a thickness of :math:`\mathrm{5,181}m`.


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

The properties of the material are shown in the table below.


+----------------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
|Liquid water                                  |Density (:math:`{\mathit{kg.m}}^{\mathrm{-}3}`) 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}`)                        |103 4180 10-4 10-3                                                                                                                                                                                                                                                                                                                                                                                                       |
+----------------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
|Gaz                                           |Specific heat (:math:`{\mathit{J.K}}^{\mathrm{-}1}`) Molar mass (:math:`{\mathit{kg.mol}}^{\mathrm{-}1}`)                                                                                                                                                                |1000 0.02896 1.8. 10-5                                                                                                                                                                                                                                                                                                                                                                                                   |
+----------------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
|Sturdy (:math:`\mathit{BO}`)                  |Density (:math:`{\mathit{kg.m}}^{\mathrm{-}3}`) Drained Young's Modulus :math:`E` (:math:`\mathit{Pa}`) Poisson's Ratio                                                                                                                                                  |2670 1.9.1020 0.2                                                                                                                                                                                                                                                                                                                                                                                                        |
+----------------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
|Initial state (:math:`\mathit{BO}`)           |Porosity Temperature (:math:`K`) Gas Pressure (:math:`\mathit{Pa}`) Vapor Pressure (:math:`\mathit{Pa}`) Initial Capillary Pressure (:math:`\mathit{Pa}`)                                                                                                                |0.35 293 1E5 2320 5.107 (:math:`S\mathrm{=}\mathrm{0,57}`)                                                                                                                                                                                                                                                                                                                                                               |
+----------------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
|                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  |
+----------------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
|Homogenized coefficients (:math:`\mathit{BO}`)|Homogenized density (:math:`{\mathit{kg.m}}^{\mathrm{-}3}`) Saturation Intrinsic permeability (:math:`{m}^{2}`) Relative liquid permeability () Relative liquid permeability Relative gas permeability (:math:`{\mathit{J.K}}^{\mathrm{-}1}`) Biot Thermal conductivities|:math:`2670` :math:`S({P}_{c})\mathrm{=}0.99(1\mathrm{-}{6.10}^{\mathrm{-}9}{P}_{c})` :math:`{10}^{\mathrm{-}20}` :math:`{\mathit{kr}}_{w}(S)\mathrm{=}S` :math:`{\mathit{kr}}_{\mathit{gz}}(S)\mathrm{=}1\mathrm{-}S` :math:`482` :math:`1` :math:`\begin{array}{c}{\lambda }_{S}^{T}(S)\mathrm{=}0.35\mathrm{\cdot }S\\ {\lambda }_{T}^{T}(S)\mathrm{=}0.6\\ {\lambda }_{\mathit{CT}}^{T}(S)\mathrm{=}0.728\end{array}`|
+----------------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
|Solid (BG)                                    |Density (:math:`{\mathit{kg.m}}^{\mathrm{-}3}`) Drained Young's Modulus :math:`E` (:math:`\mathit{Pa}`) Poisson's Ratio                                                                                                                                                  |:math:`2670` :math:`\mathrm{1,9}{.10}^{20}` :math:`0.2`                                                                                                                                                                                                                                                                                                                                                                  |
+----------------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
|Initial state (BG)                            |Porosity Temperature (:math:`K`) Gas Pressure (:math:`\mathit{Pa}`) Vapor Pressure (:math:`\mathit{Pa}`) Initial Capillary Pressure (:math:`\mathit{Pa}`)                                                                                                                |:math:`\mathrm{0,05}` :math:`293` :math:`1E5` :math:`2320` :math:`{7.10}^{7}` (:math:`S\mathrm{=}\mathrm{0,81}`)                                                                                                                                                                                                                                                                                                         |
+----------------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
|Homogenized coefficients (BG)                 |Homogenized density (:math:`{\mathit{kg.m}}^{\mathrm{-}3}`) Saturation Intrinsic permeability (:math:`{m}^{2}`) Relative liquid permeability () Relative liquid permeability Relative gas permeability (:math:`{\mathit{J.K}}^{\mathrm{-}1}`) Biot Thermal conductivity  |:math:`2670` :math:`S({P}_{c})\mathrm{=}0.99(1\mathrm{-}{6.10}^{\mathrm{-}9}{P}_{c})` :math:`{10}^{\mathrm{-}19}` :math:`{\mathit{kr}}_{w}(S)\mathrm{=}S` :math:`{\mathit{kr}}_{\mathit{gz}}(S)\mathrm{=}1\mathrm{-}S` :math:`706` :math:`1` :math:`\begin{array}{c}{\lambda }_{S}^{T}(S)\mathrm{=}0.05\mathrm{\cdot }S\\ {\lambda }_{T}^{T}(S)\mathrm{=}0.6\\ {\lambda }_{\mathit{CT}}^{T}(S)\mathrm{=}1.539\end{array}`|
+----------------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+


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

On all edges: Zero hydraulic flow

The only driver here is the saturation of one medium by another.