Method for exploitation of a subterranean medium in accordance with an exploitation scheme defined by an optimized representation
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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.
29 Citations
54 Claims
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1-16. -16. (canceled)
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17. A method for exploiting a subterranean medium, in which the subterranean medium is exploited according to an exploitation scheme defined using a representation of the medium, including a two-dimensional grid representing the subterranean medium, with quality of mesh cells of the grid being optimized by displacing nodes of the grid by minimizing deformation of the grid, comprising:
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(1) generating a reference grid comprising solely regular mesh cells which entirely covers the grid to be optimized; (2) imposing a displacement of at least one rigid node of the reference grid on a corresponding node in a grid to be optimized; and (3) constructing an optimized two-dimensional grid by displacement of other nodes of the reference grid while minimizing a displacement field of the nodes. - View Dependent Claims (18, 19, 20, 22, 23, 24, 25, 27, 28, 29, 30, 32, 33, 34, 36, 37, 38, 39, 40, 42, 43, 44, 46, 48, 50, 51, 53)
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21. A method for exploiting a subterranean medium according to an exploitation scheme using a representation of the medium, comprising a three-dimensional mesh with the subterranean medium comprising at least one sedimentary layer traversed by at least one fault with the at least one sedimentary layer being limited vertically by two geological horizons, comprising:
a) constructing a representation of the medium by; i) discretizing the geological horizons with two triangulated three-dimensional surfaces; ii) transforming each triangulated three-dimensional surface into a triangulated two-dimensional surface onto which the at least one fault is projected by an isometric unfolding with the projected at least one fault forming segments describing an open curve; iii) generating a regular two-dimensional grid for each triangulated two-dimensional surface; (iv) optimizing quality of the mesh cells of each regular two-dimensional grid by displacing nodes of the grid by a procedure minimizing deformation of the grid which comprises; (1) generating a reference grid comprising solely regular mesh cells and entirely covering the two-dimensional grid; (2) displacing nodes of the reference grid corresponding to rigid nodes of the grid to be optimized toward the rigid nodes with the rigid nodes being nodes of boundaries of the regular two-dimensional grid; (3) constructing an optimized two-dimensional grid by displacing other nodes of the reference grid while minimizing a displacement field of the nodes; v) deforming each optimized regular two-dimensional grid to fit nodes of the grid on a curve; vi) optimizing quality of the mesh cells of each deformed two-dimensional grid by displacing the nodes of the grid by minimizing deformation of the grid which comprises; (1) generating a reference grid comprising solely regular mesh cells which entirely covers the two-dimensional grid; (2) optimizing the nodes of the reference grid corresponding to the rigid nodes of the grid to be optimized by displacement toward the rigid nodes with the rigid nodes being nodes of boundaries of the regular two-dimensional grid and nodes of the curve; (3) constructing an optimized two-dimensional grid by displacement of the other nodes of the reference grid, while minimizing a displacement field of the nodes; vii) performing a change of reference frame to transform each optimized deformed grid into a three-dimensional gridded surface and transforming each quadrilateral traversed by the fault into two triangles at a diagonal; viii) generating the mesh of the representation of the subterranean medium linking each node of each quadrilateral and of each triangle of the two three-dimensional gridded surfaces and cutting each mesh cell traversed by the fault of the mesh of the subterranean medium; b) simulating at least one exploitation scheme with a representation of the medium and a flow simulator; and c) exploiting the medium by implementing an optimal exploitation scheme. - View Dependent Claims (26, 31, 35, 41, 45, 47, 49, 52)
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54. A computer program product downloadable from at least one of a communication network and a recording on a support readable by computer, comprising program code instructions for exploiting a subterranean medium, in which the subterranean medium is exploited according to an exploitation scheme defined using a representation of the medium, including a two-dimensional grid representing the subterranean medium, with quality of mesh cells of the grid being optimized by displacing nodes of the grid by minimizing deformation of the grid when the program is executed on a computer, the method comprising:
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(1) generating a reference grid comprising solely regular mesh cells which entirely covers the grid to be optimized; (2) imposing a displacement of at least one rigid node of the reference grid on a corresponding node in a grid to be optimized; and (3) constructing an optimized two-dimensional grid by displacement of other nodes of the reference grid while minimizing a displacement field of the nodes.
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Specification