Thermo-hydrodynamic Crack Propagation in Porous Media

  • al Khoury, Rafid (Delft university of Technology)
  • Arzanfudi, Mehdi Musivand (DIANA FEA BV)

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We introduce a fully coupled thermo-hydrodynamic-mechanical computational model for multiphase flow in a deformable porous solid exhibiting crack propagation arising from fluid hydrodynamics. The fluid flow in the porous matrix domain is governed by Darcy’s law, and that in the crack by the Navier-Stokes equations. We utilize the averaging theory for the porous matrix, and the drift-flux model for the fluid dynamics in the fracture. The numerical solution is conducted using a mixed finite element discretization scheme combining the standard Galerkin finite element method (FEM) and the extended finite element method (XFEM). Several features typify the novelty of the model. Among others, the fluid in the crack is compressible and exhibits phase change, buoyancy, and convective heat transfer. The mass and energy inside the crack are conserved due to imposition of the isentropic expansion process. Keeping entropy constant at the moment of crack propagation would cause the fluid volume to expand, leading its pressure and density to drop, as physically occurring in reality. The figure below highlights this point and shows the projection of the fluid into its phase diagram at a point inside the crack. It exhibits a clear snapback of pressure and density with every crack propagation instant.