Numerical modeling of fractured porous media subject to compaction

In this work, carried out in collaboration with the computational geoscience group of MOX, starting from previous analysis of the flow through fractured porous rock media, we extend the model taking into account the compaction phenomenon that characterizes the sedimentary layers subject to a progressive burial. The compaction process, determining changes of the porosity of the rock medium and, in particular, of the fracture aperture, impacts the fluid dynamic behaviour within the sediment, whose pore space is usually filled by water or fluid resulting from the chem- ical transformation of the organic component of the rock. Through our analysis we investigate how the presence of an highly permeable fracture and its different physical properties affect the overall flow behaviour, highlighting, moreover, the influence of the choice of the fracture boundary conditions. The physical problem is characterized by a significant separation of spacial scales, since the aperture of the fracture is considerably smaller compared to size of the domain. Thus, to represent this strong localized heterogeneity we employ a reduced model for the fracture fluid dynamics, avoiding an extremely high computational effort to resolve the scale of the fracture with the grid. Furthermore to treat the fracture as an immersed interface, thanks to the reduced model, we exploit the Extended Finite Elements (XFEM), that, with a proper enrich- ment of the element cut by the interface, allow the use of more flexible non-conforming meshes. We built a suitable solver based on the C++ finite element library GetFEM++ to carry out the simulations that are performed in a two dimensional section of a sedimentary layer. We consider the differential problems formulated in an auxiliary fixed domain, derived from the completely compacted configuration of the physical one that, instead, deforms as time elapses. In this way the mesh is built just once at the beginning along with the basis function of the finite element method, reducing the computational costs.