A scalable fully implicit framework for reservoir simulation on parallel computers

Abstract

Computer Methods in Applied Mechanics and Engineering Rights NOTICE: this is the author's version of a work that was accepted for publication in Computer Methods in Applied Mechanics and Engineering. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Computer Methods in Applied Mechanics and Engineering, [, , (2017-11-10)]

Fully implicit hybrid two-level domain decomposition algorithms for two-phase flows in porous media on 3D unstructured grids

“…However, their stability may degrade on unstructured grids that are necessary for complex geometries [20]. Other widely used discretization methods for subsurface systems include finite volume methods [28,41,46] and mixed finite element methods [11,24,60,62]. In the past decade, discontinuous Galerkin (DG) finite element methods have been shown to be competitive with respect to other standard methods for transport problems, such as single phase flows [47], miscible displacement [48] and reactive transport [53,54].…”

“…Efforts have been made in employing Newton method and its variants to solve the two-phase flow problems [16,42,39,60,61,62,63,64]. Good candidates for solving the linear Jacobian system are preconditioned Krylov subspace methods [50].…”

“…Alternatively, the class of Schwarz-type preconditioners [52,55] based on overlapping domain decomposition is considered as a physics-coupled approach, where all the variables associated with a subdomain are solved together in a coupled way. A one-level restricted additive Schwarz (RAS) method [10] was 4 used in [60,61,62,63] to build the preconditioner for the Jacobian system arise from an active-set reduced-space version of Newton method for the two-phase flow on uniform grids. The RAS preconditioner is naturally suitable to parallel computing since communication occurs only between neighboring subdomains during the restriction process.…”

A two-stage preconditioner for multiphase poromechanics in reservoir simulation

“…Using a multigrid reduction (MGR) approach [11], the CPR method has been generalized in a broader multigrid framework and successfully applied to multiphase flow and transport with phase transitions in [12,13]. Recent solution alternatives to CPR can be found in [14,15].…”

A fully mass-conservative iterative IMPEC method for multicomponent compressible flow in porous media

“…Modeling and simulation of compositional flow in subsurface media are prevalent and of interest in hydrogeology and hydrocarbon reservoirs (cf. [8,28,29,20,37,36,18,26,27,40,31,32,33,34] and references therein). Mathematical model of multicomponent compressible flow in porous media includes the Darcy's law, the conservation of mass and the equation of state, which is a coupled nonlinear system.…”