Abstract: Method for forming an optimum stochastic model representative of the spatial distribution, in a heterogeneous underground zone, of physical quantities such as permeability and porosity, constrained by measured dynamic data, representative of fluid displacements in the medium, using a continuous distribution parametrization technique. The model is calibrated with the dynamic data by means of an iterative process of minimization of an objective function measuring, on each iteration, the difference between the dynamic data measured and dynamic data simulated by means of a flow simulator, obtained from a realization interpolated between a reference realization (initial or obtained at the end of the previous iteration) and another independent realization, by adjustment of a perturbation parameter, the iterative adjustment process being continued until an optimum realization of the stochastic model is obtained.

Abstract: Method intended for gradual deformation of a Boolean model allowing to best simulate the spatial configuration, in a heterogeneous underground zone, of geologic objects defined by physical quantities. The model is optimized by means of an iterative optimization process from realizations including each objects whose number is a random Poisson variable of determined mean, and by minimizing an objective function. In order to impose a continuity in the evolution of said objects in size, number, positions, within the model, a combined realization obtained by combining on the one hand an initial realization comprising a certain number of objects corresponding to a first mean value and at least another independent realization having another number of objects corresponding to a second mean value is constructed, this combination being such that the resulting number of objects has a mean value equal to the sum of the first and of the second mean value and that this mean value is also that defined by the model.

Abstract: A method of gradual deformation of representations or realizations, generated by sequential simulation, not limited to a Gaussian stochastic model of a physical quantity z in a meshed heterogeneous medium, in order to adjust the model to a set of data relative to the structure or the state of the medium which are collected by previous measurements and observations. The method comprises applying a stochastic model gradual deformation algorithm to a Gaussian vector with N mutually independent variables which is connected to a uniform vector with N mutually independent uniform variables by a Gaussian distribution function so as to define realizations of the uniform vector, and using these realizations to generate representations of the physical quantity z that are adjusted to the data.

Abstract: Method for rapidly forming a stochastic model of Gaussian or related type, representative of a porous heterogeneous medium such as an underground reservoir, constrained by data characteristic of the displacement of fluids.

Abstract: Method for gradually deforming, totally or locally, a Gaussian or similar type stochastic model of a heterogeneous medium such as an underground zone, constrained by a series of parameters relative to the structure of the medium. The method comprises drawing a number p, at least equal to two, of independent realizations of at least part of the selected medium model from all the possible realizations, and linear combination of these p realizations with p coefficients such that the sum of their squares is equal to 1. This linear combination constitutes a new realization of the stochastic model and it gradually deforms when the p coefficients are gradually modified. More generally, the method can comprise several iterative gradual deformation stages, with combination at each stage of a composite realization obtained at the previous stage with q new independent realizations drawn from all the realizations.

Abstract: Geostatistical method for gradually deforming an initial distribution of objects, of geologic type for example, from measurements or observations, so as to best adapt it to imposed physical constraints of hydrodynamic type for example.