Abstract: Method for mapping a 3D grid or mesh from a faulted subsurface domain to a continuous design domain, wherein the grid may be used to represent a discrete model of a subsurface material property (such as permeability) to use, for example, in a reservoir simulator. The mapping is geometry-based, not physics-based. The mapping is determined by an iterative optimization procedure designed to penalize deformation of tessellated mesh cells (703) in the design domain compared to their geometric quality in the faulted domain (701), but subject to stitching constraints (702) appearing as a penalty term or Lagrange multiplier term in the optimization objective function to influence the final mesh to co-locate pairs of points identified on opposite sides of a fault as having been located together before the fault occurred.

Abstract: Method for generating a 3D grid, and for defining a material property model on the grid, to use, for example, in a reservoir simulator. A mapping is defined (61,71) to a design space in which the material property is described as a piecewise smooth implicit or explicit function in three dimensions. Grid geometry is constructed only in the physical space of the model (62-65, 73-76), and no grid is required in the design space. The material property, for example permeability, is sampled in the design space (66,77) to populate the cells in the grid constructed in the physical domain. Prismatic grid cells may be truncated based on faults and horizons (65), or maybe conformed to fault surfaces using a 3D parameterization of the model (76). Only forward mapping, i.e. from the physical domain to the design space, is required.

Abstract: A method and system are described for generating a geologic model having material properties for a faulted subsurface region. The method and system involve parameterizing corresponding fault surfaces and solving an energy optimization equation and/or conservation law equation for the corresponding fault surfaces based on parameterized nodes on the fault surfaces to generate a displacement map. The displacement map is used to map a geologic model from the physical space to the design space, where it is populated with material properties. The resulting populated geologic model may be used for hydrocarbon operations associated with the subsurface region.

Abstract: A method and apparatus for generating a simulation grid for a reservoir model based on a geological model comprising horizons, constraints and multiple geological grid cells. A pre-image is generated corresponding to the geological grid cells, the pre-image comprising a surface and the modeling constraints being mapped onto the surface. A constrained two-dimensional grid is generated on the pre-image, the two-dimensional grid comprising multiple grid cells. Simulation layer boundaries are selected from the geological model and the constrained two-dimensional grid is projected onto the simulation layer boundaries. Prismatic cells are then generated to form the three-dimensional simulation grid. The method of generating a grid as herein described may be incorporated in existing reservoir simulators.

Abstract: A method and system are described for creating a subsurface model. The method and system may include updating a subsurface model having objects associated with a subsurface region. The method includes obtaining a subsurface model having a mesh formed from various nodes and forming blocks or mesh elements, which have mesh shapes. Then, areas of the mesh that need repair are identified and one or more of a local re-meshing operation, an edge-flipping operation, a collapsing operation and any combination thereof are applied to the identified areas. The resulting updated subsurface model is then outputted.

Abstract: A method and system are described for creating a subsurface model. The method involves forming a volumetric representation having objects associated with the subsurface region; computing a value for each of the blocks based on an object priority function; and removing one or more blocks based on constraints and the object priority function to create the watertight model. Then, using the watertight model to perform simulations and in performing hydrocarbon operations.

Abstract: A method and system are described for generating a geologic model having material properties for a faulted subsurface region. The method and system involve parameterizing corresponding fault surfaces and solving an energy optimization equation and/or conservation law equation for the corresponding fault surfaces based on parameterized nodes on the fault surfaces to generate a displacement map. The displacement map is used to map a geologic model from the physical space to the design space, where it is populated with material properties. The resulting populated geologic model may be used for hydrocarbon operations associated with the subsurface region.

Abstract: Method for mapping a 3D grid or mesh from a faulted subsurface domain to a continuous design domain, wherein the grid may be used to represent a discrete model of a subsurface material property (such as permeability) to use, for example, in a reservoir simulator. The mapping is geometry-based, not physics-based. The mapping is determined by an iterative optimization procedure designed to penalize deformation of tessellated mesh cells (703) in the design domain compared to their geometric quality in the faulted domain (701), but subject to stitching constraints (702) appearing as a penalty term or Lagrange multiplier term in the optimization objective function to influence the final mesh to co-locate pairs of points identified on opposite sides of a fault as having been located together before the fault occurred.

Abstract: Method for generating a 3D grid, and for defining a material property model on the grid, to use, for example, in a reservoir simulator. A mapping is defined (61,71) to a design space in which the material property is described as a piecewise smooth implicit or explicit function in three dimensions. Grid geometry is constructed only in the physical space of the model (62-65, 73-76), and no grid is required in the design space. The material property, for example permeability, is sampled in the design space (66,77) to populate the cells in the grid constructed in the physical domain. Prismatic grid cells may be truncated based on faults and horizons (65), or maybe conformed to fault surfaces using a 3D parameterization of the model (76). Only forward mapping, i.e. from the physical domain to the design space, is required.

Abstract: A method and apparatus for generating a simulation grid for a reservoir model based on a geological model comprising horizons, constraints and multiple geological grid cells. A pre-image is generated corresponding to the geological grid cells, the pre-image comprising a surface and the modeling constraints being mapped onto the surface. A constrained two-dimensional grid is generated on the pre-image, the two-dimensional grid comprising multiple grid cells. Simulation layer boundaries are selected from the geological model and the constrained two-dimensional grid is projected onto the simulation layer boundaries. Prismatic cells are then generated to form the three-dimensional simulation grid. The method of generating a grid as herein described may be incorporated in existing reservoir simulators to improve their accuracy.

Abstract: A computer-implemented method for generating a constrained Delaunay triangulation for a planar domain with boundaries and internal features. The boundaries and internal features of the domain are approximated with polylines. Unconstrained Delaunay triangulation is constructed for the domain. The unconstrained Delaunay triangulation is modified to conform triangle sides to the polylines. The modified triangulation is corrected to make it a constrained Delaunay triangulation. At least one of the steps of the method is implemented using a computer.

Abstract: A computer-implemented method for generating a constrained Delaunay triangulation for a planar domain with boundaries and internal features. The boundaries and internal features of the domain are approximated with polylines. Unconstrained Delaunay triangulation is constructed for the domain. The unconstrained Delaunay triangulation is modified to conform triangle sides to the polylines. The modified triangulation is corrected to make it a constrained Delaunay triangulation. At least one of the steps of the method is implemented using a computer.

Abstract: A method for generating constrained Voronoi grids in a plane with internal features and boundaries is disclosed. The disclosed method generally includes approximation of internal features and boundaries with polylines based on plane geometry. Protected polygons or points are generated around the polylines, and Delaunay triangulation of protected points or protected polygon vertices is constructed. Delaunay triangulation that honors protected polygons or points is generated in the rest of the gridding domain. The constrained Voronoi grid is then generated from the Delaunay triangulation, which resolves all of the approximated features and boundaries with the edges of Voronoi cells. Constrained Voronoi grids may be generated with adaptive cell sizes based on specified density criterion.

Abstract: A method for generating constrained Voronoi grids in a plane with internal features and boundaries is disclosed. The disclosed method generally includes approximation of internal features and boundaries with polylines based on plane geometry. Protected polygons or points are generated around the polylines, and Delaunay triangulation of protected points or protected polygon vertices is constructed. Delaunay triangulation that honors protected polygons or points is generated in the rest of the gridding domain. The constrained Voronoi grid is then generated from the Delaunay triangulation, which resolves all of the approximated features and boundaries with the edges of Voronoi cells. Constrained Voronoi grids may be generated with adaptive cell sizes based on specified density criterion.