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: 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: 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 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.