Modeling A
==============


Characteristics of modeling A
-------------------------------------

The global coordinate system is chosen so that the discontinuity is horizontal in this coordinate system (:math:`\alpha =0°` therefore an Euler angle of :math:`90°`).

The modeling is carried out in plane deformation with 1092 elements QU4 for the mass and 91 elements QU4 for the discontinuity.

Discretization in time:


* 25 time steps for the first :math:`\mathrm{7,5}` years


* 25 time steps for the next :math:`\mathrm{12,5}` years.


Tested sizes and results
------------------------------

The results obtained with*Code_Aster* are compared with those obtained by the code *LAGAMINE*.

We present the pressure profile along the discontinuity at :math:`\mathrm{7,5}` and :math:`20` years (figure), the variations in the opening along the discontinuity at :math:`\mathrm{7,5}` and :math:`20` years (figure) and the flow leaving the crack at the well per day (figure).


.. image:: images/10000000000003980000028038EC468F3E07BBC9.jpg
    :width: 5.2819in
    :height: 3.6744in


.. _RefImage_10000000000003980000028038EC468F3E07BBC9.jpg:

Figure 3.2.1: Pressure along the discontinuity at 7.5 years and 20 years and comparison with the results of *LAGAMINE*


.. image:: images/10000000000003980000027BAC4044696631F394.jpg
    :width: 4.7756in
    :height: 3.2957in


.. _RefImage_10000000000003980000027BAC4044696631F394.jpg:

Figure 3.2.2: Opening of the discontinuity along the reservoir after 7.5 and 20 years and comparison with the results of *LAGAMINE*

The results are almost identical to those obtained with *LAGAMINE*.


.. image:: images/100000000000037F0000027A70FF5A1E13094534.jpg
    :width: 5.3366in
    :height: 3.7807in


.. _RefImage_100000000000037F0000027A70FF5A1E13094534.jpg:

Figure 3.2.3: Mass flow out of the crack at the well per day over the time obtained with *Code_Aster*

The reference values are those obtained with *LAGAMINE*.


.. csv-table::

    ":math:`X(m)` "," :math:`Y(m)` ", "**Time (years)**", "**Time (years)**", "**Reference** :math:`\mathrm{PRE1}` **(** :math:`\mathrm{MPa}` **)**", "**Tolerance (** :math:`\text{\%}` **)**"
    "256.97", "0", "7.5", "7.5", "39.95"," 1.0%"
    "516,51", "0", "7,5", "42,68"," 1.0%"
    "256,97", "0", "20", "20", "38.45"," 1.0%"
    "516,51", "0", "20", "40,98"," 1.0%"



.. csv-table::

    ":math:`X(m)` "," :math:`Y(m)` ", "**Time (years)**", "**Reference** :math:`\mathrm{V1}`
    **(** :math:`m` **)**", "**Tolerance (** :math:`\text{\%}` **)**"
    "516,51", "0", "7,5", "2,20E-04"," 1.0%"
    "516,51", "0", "20", "2,04E-04"," 1.0%"


We add a case of non-regression:


.. csv-table::

    ":math:`X(m)` "," :math:`Y(m)` ", "**Time (years)**", "**Reference** :math:`\mathrm{FH11X}` :math:`({\mathrm{kg.m}}^{-1}\mathrm{.}{s}^{-1})` ", "**Tolerance (** :math:`\text{\%}` **)**"
    "516,51", "0", "7,5", "-7,0189E-03"," 0.10%"
    "516,51", "0", "20", "-5,3847E-03"," 0.10%"