Method for Providing a Numerical Model of a Sample of Rock

A method for providing a numerical model of a sample of rock, in particular a plug sample taken from a sample of rock, said sample of rock taken from a vertical portion of the rock core, according to its longitudinal direction, extracted from a well of an oil or gas reservoir, the method comprising:

• performing a CT scan of the plug sample of rock;
• measuring a porosity ϕms of the plug sample of rock;
• measuring a permeability kms of the plug sample of rock;
• generating a 3D numerical model, at least comprising a cell discretization representing a volume of the plug sample of rock, according to the following steps:
• a) recovering data from the CT scan providing at least information on a statistical density function ƒ(ρ) of the value ρ, wherein ρ is an attenuation X-ray radiation in the volume of the plug sample of rock;
• b) generating a segmentation of the discretization of the first 3D model into sub-volumes responsive to the data retrieved in step a) from the plug sample of rock, said sub-volumes representing components of the plug sample of rock;
• c) identifying the components of each sub-volumes;
• d) determining a porosity statistical distribution function F(ϕ) for the cells of the 3D model at least responsive to the statistical density function ƒ(ρ);
• e) populating a porosity ϕ for each sub-volume of the 3D model, wherein the porosity is spatially distributed among the cells of said sub-volume by means of a Gaussian simulation algorithm responsive to the porosity statistical distribution function F(ϕ) as an approximation of a Gaussian density function;
• f) populating a permeability among the cells of each sub-volume comprising a component contributing to the porosity, wherein the permeability is defined as a scalar function responsive to the porosity of the cell k(ϕ);
• g) performing a numerical simulation of the 3D model according to conditions relating to the permeability kms in order to obtain a global permeability knum;
• h) iteratively repeating steps e) to g) until the global permeability measured on the plug sample of rock kms and the permeability knum calculated from the 3D model differ less than a threshold.