Method for representing a reservoir including three types of media

A computer-implemented method of building a model of a reservoir,

• the method comprising:
• obtaining a three-dimensional meshed model representing the reservoir, wherein the reservoir comprises three interlocking media including a porous matrix, surface discontinuities within the porous matrix, and conduits within the porous matrix, the three-dimensional meshed model comprising a plurality of three-dimensional polyhedrons conforming to the surface discontinuities and conduits of the reservoir, a surface discontinuity being represented in the three-dimensional meshed model by a two-dimensional (2D) meshed surface where each cell of the surface is a face of a three-dimensional (3D) polyhedron, and each conduit being represented by a one-dimensional (1D) meshed line where each cell of the line is an edge of a polyhedron;
• and
• generating a graph model from the three-dimensional meshed model, the graph model comprising a plurality of nodes and connections between adjacent nodes, wherein:
• each node corresponds to a selected one among the three interlocking media and is associated to a set of parameters including geometrical parameters and permeability;
• the connections between the adjacent nodes include connections between two nodes corresponding to the same medium and connections between nodes corresponding to any two different media;
• and
• each connection between two nodes is associated with a transmissibility value determined from the medium to which belong the two nodes linked by the connection and their respective associated set of parameters.