Abstract: A method of constraining a stochastic model of Gaussian or related type, representing a porous medium such as an underground reservoir, to data characteristic of the displacement of the fluids is disclosed. The method is based on an iterative development in two stages. The first stage carries out a flow simulation, in identifying zones inside the reservoir and in estimating the modification to be brought to the effective permeabilities of these zones so as to improve calibration between the real data and the corresponding responses obtained with the flow simulator. The second stage involves an intermediate optimization problem intended to minimize an intermediate objective function (implemented from a gradual deformation technique) measuring the difference between the effective permeabilities calculated for the zones and the effective permeabilities identified during the first stage for better calibration.

Abstract: A computer implemented 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, based upon measured dynamic data, representative of fluid displacements in a medium, using a continuous distribution parameterization technique is disclosed. The method has application for elaboration of an underground reservoir model by simulating the configuration of various heterogeneities: permeability, porosity, fractures, channels, etc.

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: A method of constraining a stochastic model of Gaussian or related type, representing a porous medium such as an underground reservoir, to data characteristic of the displacement of the fluids is disclosed. The method is based on an iterative development in two stages. The first stage carries out a flow simulation, in identifying zones inside the reservoir and in estimating the modification to be brought to the effective permeabilities of these zones so as to improve calibration between the real data and the corresponding responses obtained with the flow simulator. The second stage involves an intermediate optimization problem intended to minimize an intermediate objective function (implemented from a gradual deformation technique) measuring the difference between the effective permeabilities calculated for the zones and the effective permeabilities identified during the first stage for better calibration.