On the simulation of fracking processes in porous media by use of a phase-field approach

摘要

The theoretical and numerical description of hydraulic fracturing processes in porous soil or rock is a very interesting topic in engineering sciences. Following this, the well-known phase-field approach applied to fracturing solids was recently embedded in the Theory of Porous Media for the description of hydraulic fracturing scenarios. This method has been found very convenient not only for the description of solid deformation and fracture but also for the transition of Darcy-type flow in the saturated porous-media domain towards Navier-Stokes-type flow in fractured zones. However, the monotonic evolution of the phase-field variable as it is used in purely solid-mechanical scenarios does not allow for the description of pre-existing closed fractures or of fractures closing after generation, where either only Darcy-type flow occurs or where Navier-Stokes-type flow turns back to Darcy-type flow. Taking this into account, the present study also concerns the introduction of a crack-opening indicator as an additional variable governed by the current deformation. By use of this procedure, not only opening but also closing fractures as well as pre-fractured domains can easily be included into the numerical simulation of fracking scenarios in saturated porous media. Proceeding from the finite-element analysis, the numerical results are found consistent with experimental observations presented in the literature.