Abstract: The invention is a method for exploiting a subterranean medium, according to an exploitation scheme defined on a representation of the medium based on a two-dimensional grid representing the subterranean medium. The quality of the mesh cells of the grid is optimized by displacing the nodes of the grid by a procedure for minimizing the deformation of the grid by generating a reference grid; imposing a displacement of at least one node, termed a rigid node, of the reference grid on a corresponding node in the grid to be optimized; and constructing an optimized two-dimensional grid by displacement of the other nodes of the reference grid, while minimizing the displacement field of the nodes.

Abstract: Process for constructing a volume mesh of a subsurface formation comprising at least one sedimentary layer traversed by at least one fault. On the basis of a representation in a closed domain of the geometry of the horizons and of the faults in a parametric space before deformation and rupture, the bounds of the blocks delimited by the faults, the horizons and the boundaries of the domain are projected onto a reference surface. Next a surface mesh is constructed constrained by the projections thus obtained on the reference surface. At each node of the surface mesh, a vertical polygonal line passing through this node is defined. Next a volume mesh is constructed by vertical extrusion of the surface mesh along the polygonal lines. Application in particular to exploration and to exploitation of oilfields.

Abstract: Process for constructing a volume mesh of a subsurface formation comprising at least one sedimentary layer traversed by at least one fault. On the basis of a representation in a closed domain of the geometry of the horizons and of the faults in a parametric space before deformation and rupture, the bounds of the blocks delimited by the faults, the horizons and the boundaries of the domain are projected onto a reference surface. Next a surface mesh is constructed constrained by the projections thus obtained on the reference surface. At each node of the surface mesh, a vertical polygonal line passing through this node is defined. Next a volume mesh is constructed by vertical extrusion of the surface mesh along the polygonal lines. Application in particular to exploration and to exploitation of oilfields.

Abstract: A method having application for petroleum exploration or geological storage of generating a mesh of a faulted underground medium, comprising generating a hex-dominant mesh from faults and horizons in a form of a 3D triangulated surfaces. Each 3D triangulated surface is converted to a 2D triangulated surface onto which the faults are projected by an isometric unfolding technique. A regular two-dimensional grid pattern is generated for each 2D triangulated surface. The faults are accounted for by deforming quadrilaterals of the grid pattern intersected by projected faults. The deformed regular grid pattern is then converted to a 3D gridded surface and each quadrilateral which is crossed by a fault is converted into two triangles at a level of a diagonal. Finally, after iterating for all the 3D triangulated surfaces, the mesh is generated by creating links between the nodes of neighboring three-dimensional gridded surfaces with respect to the faults.

Abstract: A method for generating a mesh of a subterranean medium comprising at least one sedimentary layer crossed by at least one fault. The at least one layer is delimited vertically by two geological horizons discretized by two triangulated three-dimensional surfaces. For each horizon, a three-dimensional gridded surface is constructed by means of isometric unfolding accounting for the presence of the fault. Next, the mesh of the subterranean medium is generated by generating cells by creating links between the three-dimensional gridded surfaces. To do this, nodes of the first gridded surface that are situated on one side of the fault which differs from the side of a node of the second gridded surface having the same coordinates i, j are detected. Each non-detected node is joined with a node of the second gridded surface having the same coordinates i, j, and each detected node is joined with the fault by considering a direction of a neighboring node.

Abstract: The invention is a method for exploiting a subterranean medium, according to an exploitation scheme defined on a representation of the medium based on a two-dimensional grid representing the subterranean medium. The quality of the mesh cells of the grid is optimized by displacing the nodes of the grid by a procedure for minimizing the deformation of the grid by generating a reference grid; imposing a displacement of at least one node, termed a rigid node, of the reference grid on a corresponding node in the grid to be optimized; and constructing an optimized two-dimensional grid by displacement of the other nodes of the reference grid, while minimizing the displacement field of the nodes.

Abstract: This method for evaluating fluid flows in a heterogeneous medium, uses a hybrid grid constructed from a CPG type structured grid and from a radial grid. The first stage includes locally deforming a CPG type grid into a non-uniform Cartesian grid. These local grid cell deformations correspond to the change from a “CPG” frame to a “Cartesian” frame defined by the deformation. These deformations are then quantified, by a deformation function ?, and applied to the radial grid so as to shift to the “Cartesian” frame. The second stage includes locally correcting the definition of this deformation function around the radial grid, so that the radial grid, in the “Cartesian” frame, keeps its geometrical characteristics. A hybrid grid is then generated in the “Cartesian” frame from the two grids thus deformed. Finally, this hybrid grid is deformed to return to the “CPG” frame, using the inverse of deformation function ?.

Abstract: A method for generating a mesh of a subterranean medium comprising at least one sedimentary layer crossed by at least one fault. The at least one layer is delimited vertically by two geological horizons discretized by two triangulated three-dimensional surfaces. For each horizon, a three-dimensional gridded surface is constructed by means of isometric unfolding accounting for the presence of the fault. Next, the mesh of the subterranean medium is generated by generating cells by creating links between the three-dimensional gridded surfaces. To do this, nodes of the first gridded surface that are situated on one side of the fault which differs from the side of a node of the second gridded surface having the same coordinates i, j are detected. Each non-detected node is joined with a node of the second gridded surface having the same coordinates i, j, and each detected node is joined with the fault by considering a direction of a neighboring node.

Abstract: A method for evaluating fluid flows within a heterogeneous formation, crossed by one or more geometric discontinuities, comprising generating a hybrid grid from a CPG type grid and from structured grids having application, for example, in simulation of hydrocarbon reservoirs. The first stage locally deforms a CPG type grid into a non-uniform Cartesian grid. These local grid cell deformations correspond to the change from a so-called “CPG” frame of reference to a so-called “Cartesian” frame of reference defined by the deformation. These deformations are then quantified and applied to the structured grids so as to shift to the “Cartesian” frame. A hybrid grid is then generated in the “Cartesian” frame from the two thus deformed grids. Finally, the hybrid grid is deformed to return to the “CPG” frame, prior to improving the grid quality, by optimization under quality control in the numerical scheme sense.

Abstract: Method for evaluating fluid flows in a heterogeneous medium, by means of a hybrid grid constructed from a CPG type structured grid and from a radial grid. The first stage consists in locally deforming the CPG type grid into a non-uniform Cartesian grid. These local grid cell deformations correspond to the change from a reference frame referred to as “CPG” frame to a reference frame referred to as “Cartesian” frame defined by the deformation. These deformations are then quantified, by a deformation function ?, and applied to the radial grid so as to shift to the “Cartesian” frame. The second stage consists in locally correcting the definition of this deformation function around the radial grid, so that the radial grid, in the “Cartesian” frame, keeps its geometrical characteristics necessary for generation of a transition grid. A hybrid grid is then generated in the “Cartesian” frame from the two grids thus deformed.

Abstract: A method, having application for hydrocarbon reservoir simulation, generates a hybrid grid, in order to carry out simulations in accordance with a defined numerical scheme, in three dimensions in a numerical scheme, of a heterogeneous formation crossed by at least one geometric discontinuity such as, an underground formation where at least one well has been drilled, or a fractured formation, by combining structured grids and unstructured grids. The hybrid grid includes a first structured grid for gridding the heterogeneous medium with second structured grids for gridding a zone around each discontinuity. A cavity of minimum size is automatically generated, with cells of the transition grid being an intermediate size between the size of the cells of the first grid and the size of the cells of the second grids.

Abstract: A method for evaluating fluid flows within a heterogeneous formation, crossed by one or more geometric discontinuities, comprising generating a hybrid grid from a CPG type grid and from structured grids having application, for example, in simulation of hydrocarbon reservoirs. The first stage locally deforms a CPG type grid into a non-uniform Cartesian grid. These local grid cell deformations correspond to the change from a so-called “CPG” frame of reference to a so-called “Cartesian” frame of reference defined by the deformation. These deformations are then quantified and applied to the structured grids so as to shift to the “Cartesian” frame. A hybrid g rid is then generated in the “Cartesian” frame from the two thus deformed grids. Finally, the hybrid grid is deformed to return to the “CPG” frame, prior to improving the grid quality, by optimization under quality control in the numerical scheme sense.

Abstract: Method of generating a hybrid grid, in order to carry out simulations in accordance with a defined numerical scheme, in three dimensions and admissible in the numerical scheme sense, of a heterogeneous formation crossed by one or more geometric discontinuities such as, for example, an underground formation where one or more wells have been drilled, or a fractured formation, by combining structured grids and unstructured grids. The hybrid grid is achieved by associating a first structured grid for gridding the heterogeneous medium with second structured grids for gridding a zone around each discontinuity. A cavity of minimum size, allowing the cells of the transition grid to have an intermediate size between the size of the cells of the first grid and the size of the cells of the second grids, is first generated, entirely automatically. A transition grid meeting the constraints of the numerical scheme used for simulation is then constructed.