... preconditioner united states government europe government iteration convergence neighborhood transmissibility coarse grid equation linear solver convergence multistage preconditioner Introduction Since the introduction of reservoir simulation, engineers have used simulation to understand how...

... on the GPU architecture. reservoir simulation scaling method gpu implementation scalability basis function multiscale method operator upstream oil & gas computational physics multiscale solver tchelepi scientific computing msrsb implementation coarse grid application jenny parallel...

... reconstruction from the coarse-grid solution. The first method uses the vertical equilibrium concept. The second method performs a 1D solution for the fine-scale pressure. A spatially variable multi-porosity permeability model can also be accommodated. In parallel implementation, besides the load balancing...

.... scaling method resolution algorithm transmissibility Artificial Intelligence indicator function geologic feature Durlofsky reservoir simulation accuracy partition Upstream Oil & Gas admissible neighbor grid permeability coarse grid coarse block partition vector reduced-order model...

... are constructed using a non-overlapping partition of the fine grid. Second, the prolongation operator is composed of a set of basis functions, each of which has compact support within a support region that contains a coarse grid block. Finally, the basis functions form a partition of unity. Through a series...

..., a Schwarz overlapping method is used on the primal coarse grid (see Fig. 1 ). Governing Equations and Discretized Formulation. The standard black-oil model has two hydrocarbon phases (i.e., oil and gas) and one aqueous phase (water), rock and fluid compressibility, gravity effects, and capillary...

... associated with the coarse grid blocks. These mappings are constructed by restricted smoothing: starting from a constant, a localized iterative scheme is applied directly to the fine-scale discretization to give prolongation operators that are consistent with the local properties of the differential...

... scaling method node Lunati Cartesian grid category iteration primal coarse grid basis function Modeling & Simulation spe 163649 MsFV method grid permeability coarse grid formulation fine cell neighbor dual grid algorithm pressure solution Multiscale Method coarse block...

... and accuracy compared with coarse-scale models. scaling method Simulation basis function coarse grid reservoir simulation relative permeability Multiscale Method spe 163669 porous media Modeling & Simulation multiscale basis function flux solver coarse block formulation permeability...

... method is compact and generic for a large class of grids, and thereby, suitable for discretizations of reservoir models with complex geologic architecture. Flow equations are solved on a coarse grid where basis functions with subgrid resolution accurately account for subscale variations from...

... triangulation single phase flow simulation coarse grid permeability tessellation voronoi tessellation grid optimization problem flow information streamline algorithm centroidal voronoi tessellation Introduction Geological models describing fine-scale heterogeneities are generally upscaled...

... local preconditioner iteration coarse grid grid upstream oil & gas convergence mass conservation operator modeling & simulation tam prolongation operator matrix reservoir simulation boundary condition spe 141473 spectra restriction operator preconditioner permeability...

... that the proposed strategy results in efficient and accurate simulation of multiphase flow in heterogeneous porous media. reservoir simulation pressure equation modeling & simulation fluid dynamics comput flow in porous media hajibeygi iteration coarse grid i-msfv method jenny equation scaling...

.../pressure fields based on local proper orthogonal decompositions (PODs) glued together using the Multiscale Mixed FEM (MsMFEM) framework on a coarse grid. Based on snapshots from one or more simulation run, we perform singular value decompositions (SVDs) for the flux distribution over coarse grid...

... Abstract The multiscale finite volume (MSFV) method is extended to account for non-matching coarse grids arising from faulted porous media. To obtain accurate quantities at the coarse scale, basis and correction functions are computed in extended local domains near the fault regions...

... Abstract Previous research has shown that multiscale methods are robust and capable of providing more accurate solutions than traditional upscaling methods. Multiscale methods solve the pressure equation on a coarse grid, but capture the effects from fine-scale heterogeneities through basis...

... & Simulation near-well region iteration non-darcy effect reservoir simulation completion Computation productivity procedure transmissibility darcy-forchheimer flow scaling method Upstream Oil & Gas boundary condition darcy-forchheimer equation perforation wellbore coarse grid grid...

...-scale simulation. scaling method reference solution upscaled model coarse grid operator reservoir simulation Lee multiphase flow Jenny Upstream Oil & Gas boundary condition saturation transmissibility Modeling & Simulation reconstruction grid adaptive reconstruction...

.... scaling method Upstream Oil & Gas stencil velocity field Modeling & Simulation VCMP refinement reservoir simulation accuracy Cartesian grid Artificial Intelligence approximation boundary condition CCAR grid grid permeability field coarse grid total flow flux approximation lamber...

... history matching Evensen state vector ensemble Kalman filter accurate model update grid permeability field pressure increase reservoir simulation unknown model error ensemble member mean permeability coarse grid society of petroleum engineers Introduction and (11) q 0 ∼ N...