  In fractured natural formations, the equations governing fluid flow and
geomechanics are strongly coupled. Hydrodynamical properties depend on the
mechanical configuration, and they are therefore difficult to accurately
resolve using uncoupled methods. In recent years, significant research has
focused on discretization strategies for these coupled systems, particularly in
the presence of complicated fracture network geometries. In this work, we
explore a finite-volume discretization for the multiphase flow equations
coupled with a finite-element scheme for the mechanical equations. Fractures
are treated as lower dimensional surfaces embedded in a background grid.
Interactions are captured using the Embedded Discrete Fracture Model (EDFM) and
the Embedded Finite Element Method (EFEM) for the flow and the mechanics,
respectively. This non-conforming approach significantly alleviates meshing
challenges. EDFM considers fractures as lower dimension finiten volumes which
exchange fluxes with the rock matrix cells. The EFEM method provides, instead,
a local enrichment of the finite-element space inside each matrix cell cut by a
fracture element. Both the use of piecewise constant and piecewise linear
enrichments are investigated. They are also compared to an Extended Finite
Element (XFEM) approach. One key advantage of EFEM is the element-based nature
of the enrichment, which reduces the geometric complexity of the implementation
and leads to linear systems with advantageous properties. Synthetic numerical
tests are presented to study the convergence and accuracy of the proposed
method. It is also applied to a realistic scenario, involving a heterogeneous
reservoir with a complex fracture distribution, to demonstrate its relevance
for field applications.
