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Consolidation example based on fluid injection and production application

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.

Material properties

Property	Value	Unit
Fluid density	1,000	kg/m3
Porosity	0.3	–
Viscosity	10−3	Pa⋅s
Fluid compressibility	3.3332941333333e × 10−5	m −1
Intrinsic permeability	4.9346165e × 10−11	m2
Young’s modulus	5 × 108	Pa
Poisson ratio	0.3	–

The time duration is 8.64 ⋅10⁶ s, and the time step size is 8.64 ⋅10⁴ 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

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