Stability analysis of sequential implicit strategies for fluid-structure interactions in fractured porous media
Keywords: Sustainability.
Energy Resources Engineering.

In naturally-fractured subsurface reservoirs, fluid withdrawal and injection alter reservoir pressure, which causes mechanical deformation of rock matrix and fractures. In turn, the induced slip and opening of fractures can significantly affect the hydraulic properties of fractures. Coupling fluid flow and geomechanics in numerical simulations is essential for the accurate representation of the dynamics of fractured reservoirs. Therefore, it is important to develop a computational framework with an accurate fracture model and an efficient simulation scheme for a coupled hydromechanical problem. For coupled fractured reservoir simulation, previous studies have extensively utilized am embedded fracture modeling due to their localization within an element. The embedded fracture treatment consists of the Embedded Discrete Fracture Model (EDFM) for a flow domain and the Strong Discontinuity Approach (SDA) for a mechanical domain. The study will investigate three main ideas to improve the embedded fracture simulation strategy: a mechanical fracture intersection modeling with the EDFM, a stability analysis of the fully implicit scheme (FIM), and enhancement of the fixed stress scheme (FSS) with the EDFM. The mechanical modeling of fracture intersection is based on the superposition of local enrichment to fractures. The proposed modeling tunes the number of local nonlinear constraints to avoid any singularity from linear dependency between fracture jump vectors. In addition, the model prevents any overlap of the facing corners of material at an intersection. Two- and three-dimensional synthetic cases represent the robustness and reliability of our model with comparison with analytical solutions and the Discrete Fracture Model. While the FIM is known for its unconditional stability theoretically, various discretizations with the FIM are shown as unstable in practice. The numerical experiments indicate that the FIM for a coupled problem has lower and upper stability limits of the time step. The lower limit is related to the violation of the inf-sup condition of the Q1P0 element. The upper time step limit is caused by the finite machine precision of floating-point variables. This study investigates and derives analytical expressions for both stability bounds using inspectional analysis. The numerical experiments indicate that the proposed stability criteria capture the simulation stability time step window. A sequential implicit scheme is known for its flexibility in computational framework development and the capability of multiscale simulation for coupled problems. As an extension of the FSS, a fixed total normal traction scheme (FTS) is proposed for the EDFM framework. The FTS updates the SDA-modeled hydraulic fracture aperture during flow iterations based on the fixed total normal traction assumption. The numerical sensitivity experiments demonstrate the convergence performance of the FTS. The FTS achieves better convergence performance with a smaller time step and a larger grid size. Non-linearity from significant fracture compressibility worsens the convergence performance of the FSS without fracture jump update, which requires six times more iterations than the FTS. A fixed effective normal traction scheme (FETS) is proposed for an opening fracture because the FTS violates a yield condition of the opening fracture during flow iterations. While the FETS mitigates the convergence issue from the opening fracture, more analysis is required on how to define a damping parameter β which indicates a deformation ratio between a fracture and a pore volume