Method for simplifying the modeling of a geological porous medium

Abstract

A method of exploring a heterogeneous geological porous original medium, such as a reservoir crossed by an irregular network of fractures, by means of a transposed medium be equivalent to the original medium with respect to a determined type of physical transfer function known for the original medium. The method includes (a) analyzing the original medium to acquire data as to its physical characteristics; (b) forming an image of at least two dimensions of the original medium as an array of pixels, based on the acquired data; (c) associating with each pixel of the array an initial value for the physical transfer function, (d) assigning values for the physical transfer function at each pixel of the array, such as the minimum distance separating the pixel from the nearest fracture, by reference to values of the function assigned to neighboring pixels of the image, (e) determining a physical property of the transposed or equivalent medium by identifying a volume portion of the equivalent medium based on the physical transfer function for the corresponding volume portion of the original medium, and (f) physically exploring the original reservoir based on the determined physical property. The physical transfer function can represent variations between different parts of the original medium, for example distance or transmissivities or heat transfers, such as between a reservoir and a well crossing the reservoir, etc. The method can be applied to determine a transposed medium providing the same recovery of a fluid during a capillary imbibition process as the actual medium.