InjectionProduction.pandoc

+++
date = "2017-12-29"
title = "StaggeredScheme"
weight = 151
project = "HydroMechanics/StaggeredScheme/InjectionProduction1D/InjectionProduction1D.prj"
author = "Wenqing Wang"

[menu]
  [menu.benchmarks]
    parent = "hydro-mechanics"

+++

{{< data-link >}}

---
#     Consolidation example based on fluid injection and production    application

{{< img src="../InjectionProduction.png" >}}

Based on one of  the examples about injection and
production well that is present by Kim et al. \cite kimTchJua2011, this benchmark
 is used to verify the staggered scheme, which
  is implemented in OGS-6 for modelling of the coupled hydro-mechanical (HM)
 processes in the porous media. The problem of the example is defined
 in a 10 x 150 m  <span class="math inline"><em></em><sup>2</sup></span>
domain (as shown in the figure). The deformation is solved under the plane strain
 assumption. Initially, the pore pressure and the
 stress are set to zero. On all boundaries no fluid flux condition is
 applied for the hydraulic process. On the lateral
and the bottom boundaries, zero normal displacement is prescribed. On
the top surface a vertical traction boundary condition of 2.125 MP is
applied. The gravity related terms are neglected in both: the Darcy velocity
 and the momentum balance equation.

The material properties are shown in the following table.
<table>
<caption>Material properties</caption>
<thead>
<tr class="header">
<th align="left">Property</th>
<th align="left">Value</th>
<th align="left">Unit</th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td align="left">Water density</td>
<td align="left">1,000</td>
<td align="left">kg/m<span class="math inline"><em></em><sup>3</sup></span></td>
</tr>
<tr class="even">
<td align="left">Porosity</td>
<td align="left">0.3</td>
<td align="left">–</td>
</tr>
<tr class="odd">
<td align="left">Viscosity</td>
<td align="left"><span class="math inline">10<sup>−3</sup></span></td>
<td align="left">Pa<span class="math inline">⋅</span>s</td>
</tr>
<tr class="even">
<td align="left">Specific storage</td>
<td align="left"><span class="math inline">10<sup>−4</sup></span></td>
<td align="left">m <span class="math inline"><em></em><sup>−1</sup></span></td>
</tr>
<tr class="odd">
<td align="left">Intrinsic permeability</td>
<td align="left"><span class="math inline">4.9346165<em>e</em> × 10<sup>−11</sup></span></td>
<td align="left">m<span class="math inline"><em></em><sup>2</sup></span></td>
</tr>
<tr class="even">
<td align="left">Young’s modulus</td>
<td align="left"><span class="math inline">5 × 10<sup>8</sup></span></td>
<td align="left">Pa</td>
</tr>
<tr class="odd">
<td align="left">Poisson ratio</td>
<td align="left">0.3</td>
<td align="left">–</td>
</tr>
</tbody>
</table>

The time duration is 8.64 <span class="math inline">⋅10<sup>6</sup></span> s, 
and the time step size is 8.64 <span class="math inline">⋅10<sup>4</sup></span> s.
 For the verification the example is also solved by the monolithic
scheme. The displacement solution at the last
time step is shown in the enclosed figure too.

## References

{{< bib id="kimTchJua2011" >}}