Abstract: The invention is a method for calculating the inter-cell absolute permeability values associated with a reservoir model at the scale of the flow simulations representative of the porous medium from the absolute permeability values associated with a geologic model representative of the same porous medium.

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: The invention is a computer implemented method for fast simulation of the flow of a single and incompressible fluid in a heterogeneous porous medium such as an aquifer or a petroleum reservoir having application such as, for example, to the development of petroleum reservoirs. After discretizing the medium with a grid, a permeability field is determined from which a diffusivity equation is directly solved in the spectral domain by an iterative procedure involving fast Fourier transforms. A first algorithm directly manages the pressures and velocities, but it may be slow for great permeability contrasts. A second algorithm, which introduces an intermediate variable updated at each iteration, allows faster processing of greater permeability contrasts than the first algorithm. The third algorithm, based on increased Lagrangian, allows consideration of infinite permeability contrasts. The algorithms allow simulation of flows in weakly to highly heterogeneous media, with a reduced computing time.

Abstract: A method of reconstructing a stochastic realization, continuous or discrete, resulting from a random function representing a numerical model, can be representative of a porous heterogeneous medium such as an underground reservoir. It is based on identification, for a given realization, of a random function and of a set of random numbers allowing, from a given geostatistical simulator, to reconstruct the reference realization. The reconstruction techniques proposed are either general or specific to a type of geostatistical simulator. They concern the sphere of optimization, relaxation, filtering and sequential approaches. The reconstruction method allows to estimate a set of random numbers for regenerating the reference realization, this reference realization can then be locally or globally modified, by gradual deformation, so as to better reproduce newly acquired dynamic data (production data for example). The method is applicable notably to oil reservoir development for example.

Abstract: A method intended for gradual deformation of a Boolean model allowing best simulation of 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 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 the objects in size, number, positions, within the model, a combined realization obtained by combining on the one hand an initial realization comprising a 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. An application is construction of a Boolean underground reservoir model allowing simulation of the configuration of heterogeneities such as fractures, channels, etc.

Abstract: A method for more rapidly forming a stochastic model of Gaussian or Gaussian-related type, representative of a porous heterogeneous medium such as an underground reservoir, constrained by data characteristic of the displacement of fluids and punctual observations, these observations being uncertain and characterized by a probability law. The method transforms static information, given in form of probability laws, into Gaussian punctual pseudo-data which has the advantage of being compatible with a gradual deformation method. An objective function J measuring the difference between the dynamic data (production data for example) and the corresponding responses simulated for the reservoir model considered may be minimized.

Abstract: A method having application notably to the development of petroleum reservoirs for fast generation of a geostatistical reservoir model on flexible grid, representative of a porous heterogeneous medium. A flexible grid best discretizing the medium is first generated. A regular Cartesian grid whose cell size, in a given direction, is greater than or equal to the largest size of the cell of the flexible grid in the same direction is then generated. On this Cartesian grid, at least one realization of petrophysical quantities characteristic of the heterogeneous medium is simulated from a geostatistical simulator. Then, this realization is resampled with a smaller discretization interval in order to know the petrophysical value associated with the realization at any point of the medium. Finally, the values of the simulated petrophysical properties are assigned to the center of the cells of the flexible grid.

Abstract: A 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. The method comprises construction of a chain of realizations representative of a stochastic model (Y) by gradually combining an initial realization of (Y) and one or more other realization(s) of (Y) referred to as a composite realization, and minimizing an objective function (J) measuring the difference between a set of non-linear data deduced from the combination by means of a simulator simulating the flow in the medium and the data measured in the medium, by adjustment of the coefficients of the combination.

Abstract: The invention is a method for calculating the inter-cell absolute permeability values associated with a reservoir model at the scale of the flow simulations representative of the porous medium from the absolute permeability values associated with a geologic model representative of the same porous medium.

Abstract: Method of reconstructing a stochastic realization, continuous or discrete, resulting from a random function representing a numerical model, that can be representative of a porous heterogeneous medium such as an underground reservoir. It is based on identification, for a given realization, of a random function and of a set of random numbers allowing, from a given geostatistical simulator, to reconstruct the reference realization. The reconstruction techniques proposed are either general or specific to a type of geostatistical simulator. They concern the sphere of optimization, relaxation, filtering and sequential approaches. The reconstruction method allows to estimate a set of random numbers for regenerating the reference realization, this reference realization can then be locally or globally modified, by gradual deformation, so as to better reproduce newly acquired dynamic data (production data for example). Application: notably oil reservoir development for example.

Abstract: Method for more rapidly forming a stochastic model of Gaussian or Gaussian-related type, representative of a porous heterogeneous medium such as an underground reservoir, constrained by data characteristic of the displacement of fluids and punctual observations, these observations being uncertain and characterized by a probability law. It is based on a method for transforming static information, given in form of probability laws, into Gaussian punctual pseudo-data. This transformation technique has the advantage of being fully compatible with a gradual deformation method. In fact, it makes it possible to minimize an objective function J measuring the difference between the dynamic data (production data for example) and the corresponding responses simulated for the reservoir model considered. Minimization is carried out by combining realizations of a stochastic model on the one hand for the reservoir model and, on the other hand, for the Gaussian pseudo-data representative of the static information.

Abstract: A method having application notably to the development of petroleum for fast generation of a geostatistical reservoir model on flexible grid, representative of a porous heterogeneous medium. A flexible grid best discretizing the medium is first generated. A regular Cartesian grid whose cell size, in a given direction, is greater than or equal to the largest size of the cell of the flexible grid in the same direction is then generated. On this Cartesian grid, at least one realization of petrophysical quantities characteristic of the heterogeneous medium is simulated from a geostatistical simulator. Then, this realization is resampled with a smaller discretization interval in order to know the petrophysical value associated with the realization at any point of the medium. Finally, the values of the simulated petrophysical properties are assigned to the center of the cells of the flexible grid.

Abstract: The invention is a method for fast simulation of the flow of a single and incompressible fluid in a heterogeneous porous medium such as an aquifer or a petroleum reservoir having application to the development of petroleum reservoirs. After discretizing the medium by means of a grid, a permeability field is determined from which a diffusivity equation is directly solved in the spectral domain by an iterative procedure involving fast Fourier transforms. A first algorithm directly manages the pressures and velocities, but it may be slow for great permeability contrasts. A second algorithm, which introduces an intermediate variable updated at each iteration, allows faster processing of greater permeability contrasts than the first algorithm. The third algorithm, based on increased Lagrangian, allows consideration of infinite permeability contrasts. The algorithms allow simulation of flows in weakly to highly heterogeneous media, with a reduced computing time.

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 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: 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.