Method of generating a hybrid 3D grid a heterogenous formation crossed by a geometric discontinuity in order to carry out simulations

摘要

The hybrid grillage is generated in 3 dimensions by defining the cavity in a way that ensures its Delaunay admissibility. The transition grillage is built taking into account at least one of the following constraints: conformity, convexity, orthogonality and grillage auto-centering. The resulting grillage is optimised for at least one quality criterion determined from the numerical schema : At least a first structured grillage is formed for at least part of the heterogenous medium, a second grillage is formed for at least part of the geometric discontinuity, a cavity is formed around the second grillage and an unstructured transition grillage is formed to cover the transition between the first and second structured grillages. The numerical schema includes an approximation of the flow of fluids at two points and is of a final volume type. The geometric discontinuity is a well shaft and the second structured grillage is radial circular type. The first grillage is a non-uniform Cartesian type with parallelepiped elements. The transition grillage is made of convex polyhedric elements pressing on the border quadrilaterals of the cavity. Construction of the cavity involves a dilation of the geometric discontinuity using a local dilation coefficient (alpha ) defined to ensure the Delaunay admissibility of the cavity. The dilation colefficient alpha is expressed as a function of parameters describing the discontinuity, parameters describing the grillage of the discontinuity and/or parameters connected to the size of the local corner of the reservoir. Construction of the transition grillage involves defining the sites of the grillage by Delaunay triangulation of the peaks of the cavity and the topology of the cavity's borders; correcting the sites of the cavity to obtain non-empty and auto-centered cells; constructing the power diagram for the sites from a regular three-dimensional triangulation of all the sites of the cavity, and correcting the diagram to obtain a conforming hybrid grillage. The Delaunay triangulation and/or the regular triangulation are formed by an incremental method. The hybrid grillage is optimised by suppressing small corners with a size less than a value depending on at least one global parameter (delta ) and at least one local parameter (h 1) by suppression and/or dilation of these corners under control of quality criteria for the numerical schema (orthogonality, planarity and auto-centering), to improve the regularity of shape of the hybrid grillage, and moving the sites of the cavity towards their centre of mass under the control of quality criteria for the numerical schema (orthogonality). The quality criteria are applicable to polyhedric meshes, defined as orthogonality (a transition element is called orthogonal if its orthogonality is greater than or equal to a fixed threshold); planarity (a transition element is called planar if its planarity is less than or equal to a fixed threshold, and auto-centering (an element is called auto-centered if its site is inside itself).