About revisiting Domain Decomposition Methods for Poroelasticity
Abstract and Figures
We revisit herein well-established domain decomposition (DD) schemes to perform realistic simulations of coupled flow and poroelasticity problems on parallel computers. We define distinct solution schemes to take into account different transmission conditions amongst subdomain boundaries. Indeed, we examine two different approaches, i.e., Dirichlet-Neumann (DN) and the mortar finite element method (MFEM), and we recognize their advantages and disadvantages. The MFEM significantly lessens the computational cost of reservoir compaction and subsidence calculations by dodging the conforming Cartesian grids that arise from the pay-zone onto its vicinity. There is a manifest necessity of producing non-matching interfaces between the reservoir and its neighborhood. We thus employ MFEM over NURBS surfaces to stick these non-conforming subdomain parts. We then decouple the mortar saddle-point problem (SPP) using the DNDD scheme. We confirm that this procedure is proper for calculations at the field level. We also carry comprehensive comparisons between the conventional and non-matching solutions to prove the method's accuracy. Examples encompass linking finite element codes for slightly compressible single-phase and poroelasticity. We have used this program to a category of problems ranking from near-borehole applications to whole field subsidence estimations.
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The mortar finite element method (MFEM) significantly reduces the computational cost of subsidence computations by avoiding conforming Cartesian meshes arising from the pay-zone (PZ) towards its surroundings, where we may employ instead unstructured meshes to represent complex geological features correctly. There is thus an apparent necessity of
having non-conforming interfaces between the reservoir (RS) and its surroundings. To glue these non-matching subdomain problems, we utilize MFEM on curved 3-D boundaries represented by NURBS surfaces. We extend the approaches that we
presented in ARMA papers 12-313 and 13-475. We decouple the mortar saddle-point problem (SPP) using standard domain decomposition techniques to exploit current parallel machine architectures. We demonstrate that this approach is suitable for field
level computations. We conduct detailed benchmarks between the conforming and non-conforming solutions to validate the procedure. Examples involve coupling a continuous Galerkin finite element program for mechanics with a slightly compressible single-phase code.
To tackle general sub-domains problems in geomechanics, we present an MFEM scheme on curved interfaces based on NURBS curves and surfaces. The goal is to have a more robust geometrical representation for mortar spaces, which allows gluing non-conforming interfaces on realistic geometries. The resulting mortar saddle-point problem is decoupled using standard domain decomposition techniques such as Dirichlet-Neumann, to exploit current parallel machine architectures. Two- and three-dimensional examples ranging from near-wellbore applications to field level subsidence computations show that the proposed scheme can handle problems of practical interest.
In order to tackle general sub-domains problems in geomechanics, a MFEM scheme on curve interfaces based on NURBS curves is presented in this paper. The goal is having a more robust geometrical representation for mortar spaces, which allows gluing non-conforming interfaces on realistic geometries. The resulting mortar saddle-point problem is decoupled by means of standard Domain Decomposition techniques such as Dirichlet-Neumann and Neumann-Neumann, in order to exploit current parallel machine architectures. Examples ranging from near-wellbore applications to field level subsidence computations show that the proposed scheme can handle problems of practical interest. Extensions to three-dimensional problems are also discussed.
The authors start with an introduction to the concepts involved in physics giving the equations of flow through porous media and the deformation characteristics of soils and rocks. Succeeding chapters deal with the practical implications of these phenomena and explain the application of theory in both experimental and field work. Details are given of actual incidents, such as the subsidence experienced in Venice and Ravenna. The authors have also formulated a consolidation code, which is detailed at the end of the book, and provide instructions on how to modify the given program.
In this paper, the geometry of oil reservoirs is reconstructed by using B-splines surfaces. The technique exploits the reservoir’s static model’s simplicity to build a robust piecewise continuous geometrical representation by means of Bèzier bicubic patches. Interpolation surfaces can manage the reservoir’s topology while translational surfaces allow extrapolating it towards its sideburdens. After that, transfinite interpolation (TFI) can be applied to generate decent hexahedral meshes. In order to test the procedure, several open-to-the-public oil reservoir datasets are reconstructed and hexahedral meshes around them are generated. This reconstruction workflow also allows having different meshes for flow and mechanics by computing a projection operator in order to map pressures from the original flow mesh to the generated reference mechanics mesh. As an update respect to a previous version of this research, we already incorporate blending functions to the TFI procedure in order to attract the mesh towards the reservoir, which allows grading the hexahedral meshes in the appropriate manner. Finally, field scale reservoir compaction and subsidence computations are carried out by using continuous Galerkin FEM for both flow and mechanics in order to demonstrate the applicability of the proposed algorithm.
