Algebraic Multiscale Solver for Elastic Geomechanical Deformation

Abstract:

Predicting the geomechanical response of geological formations to thermal, pressure, and mechanical loading is important in many engineering applications. The mathematical formulation that describes deformation of a reservoir coupled with flow and transport entails heterogeneous coefficients with a wide range of length scales. Such detailed heterogeneous descriptions of reservoir properties impose severe computational challenges for the study of realistic-scale (km) reservoirs. To deal with these challenges, we developed an Algebraic Multiscale Solver for ELastic geomechanical deformation (EL-AMS). Constructed on finite element fine-scale system, EL-AMS imposes a coarse-scale grid, which is a non-overlapping decomposition of the domain. Then, local (coarse) basis functions for the displacement vector are introduced. These basis functions honor the elastic properties of the local domains subject to the imposed local boundary conditions. The basis form the Restriction and Prolongation operators. These operators allow for the construction of accurate coarse-scale systems for the displacement. While the multiscale system is efficient for resolving low-frequency errors, coupling it with a fine-scale smoother, e.g., ILU(0), leads to an efficient iterative solver. Numerical results for several test cases illustrate that EL-AMS is quite efficient and applicable to simulate elastic deformation of large-scale heterogeneous reservoirs.