Abstract: Method for constructing a continuous design space for generating a physical property model in a faulted subsurface medium. The matching relationship of the fault traces on the two sides of each fault is used in a systematic way to determine the location of the fault traces in the design space. The location of any other point in the design space may then be determined by interpolation of the locations of fault traces. The fault traces are thus used as control points for the mapping. The method involves: (a) identifying the control points and determining their location in both physical and design space and (b) using selected control points, mapping any point from physical space to design space, preferably using the moving least squares method.

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 transforming a discontinuous, faulted subsurface reservoir into a continuous, fault-free space where a complete geological model based on selected geological concepts can be built and updated efficiently. Faults are removed in reverse chronological order (62) to generate a pseudo-physical continuous layered model, which is populated with information according to the selected geological concept (68). The fault removal is posed as an optimal control problem where unknown rigid body transformations and relative displacements on fault surfaces are found such that deformation of the bounding horizons and within the volume near the fault surface are minimized (63). A boundary-element-method discretization in an infinite domain is used, with boundary data imposed only on fault surfaces. The data populated model may then be mapped back to the original faulted domain such that a one-to-one mapping between continuous and faulted spaces may be found to a desired tolerance (72).

Abstract: A variable discretization method for general multiphase flow simulation in a producing hydrocarbon reservoir. For subsurface regions for which a regular or Voronoi computational mesh is suitable, a finite difference/finite volume method (“FDM”) is used to discretize numerical solution of the differential equations governing fluid flow (101). For subsurface regions with more complex geometries, a finite element method (“FEM”) is used. The invention combines FDM and FEM in a single computational framework (102). Mathematical coupling at interfaces between different discretization regions is accomplished by decomposing individual phase velocity into an averaged component and a correction term.

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 constructing a continuous design space for generating a physical property model in a faulted subsurface medium. The matching relationship of the fault traces on the two sides of each fault is used in a systematic way to determine the location of the fault traces in the design space. The location of any other point in the design space may then be determined by interpolation of the locations of fault traces. The fault traces are thus used as control points for the mapping. The method involves: (a) identifying the control points and determining their location in both physical and design space and (b) using selected control points, mapping any point from physical space to design space, preferably using the moving least squares method.

Abstract: Method for transforming a discontinuous, faulted subsurface reservoir into a continuous, fault-free space where a complete geological model based on selected geological concepts can be built and updated efficiently. Faults are removed in reverse chronological order (62) to generate a pseudo-physical continuous layered model, which is populated with information according to the selected geological concept (68). The fault removal is posed as an optimal control problem where unknown rigid body transformations and relative displacements on fault surfaces are found such that deformation of the bounding horizons and within the volume near the fault surface are minimized (63). A boundary-element-method discretization in an infinite domain is used, with boundary data imposed only on fault surfaces. The data populated model may then be mapped back to the original faulted domain such that a one-to-one mapping between continuous and faulted spaces may be found to a desired tolerance (72).

Abstract: A variable discretization method for general multiphase flow simulation in a producing hydrocarbon reservoir. For subsurface regions for which a regular or Voronoi computational mesh is suitable, a finite difference/finite volume method (“FDM”) is used to discretize numerical solution of the differential equations governing fluid flow (101). For subsurface regions with more complex geometries, a finite element method (“FEM”) is used. The invention combines FDM and FEM in a single computational framework (102). Mathematical coupling at interfaces between different discretization regions is accomplished by decomposing individual phase velocity into an averaged component and a correction term.