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## Consolidation example based on fluid injection and production application

## References

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 ^{2}
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.

Property | Value | Unit |
---|---|---|

Fluid density | 1,000 | kg/m^{3} |

Porosity | 0.3 | – |

Viscosity | 10^{−3} |
Pa⋅s |

Fluid compressibility | 3.3332941333333e × 10^{−5} |
m ^{−1} |

Intrinsic permeability | 4.9346165e × 10^{−11} |
m^{2} |

Young’s modulus | 5 × 10^{8} |
Pa |

Poisson ratio | 0.3 | – |

The time duration is 8.64 ⋅10^{6} s,
and the time step size is 8.64 ⋅10^{4} 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.

Kim, J. and
Tchelepi, H.A. and
Juanes, R
(2011):
*Stability and convergence of sequential methods for coupled flow and geomechanics: Drained and undrained splits*.
Computer Methods in Applied Mechanics and Engineering,
vol. 200,
p. 2094--2116,
DOI:
https://doi.org/10.1016/j.cma.2011.02.011
https://www.sciencedirect.com/science/article/pii/S0045782511000466

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