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 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 for updating a geological reservoir model by integration of dynamic data having application, for example, to petroleum reservoir development. An initial map (y) of petrophysical properties is constructed by means of a geostatistical simulator and of static data. Then an initial set of gradual pilot points (PPi) and at least one complementary set of gradual pilot points (PPc) are constructed. A combined set of gradual pilot points (PP(t)) is then constructed by combining these sets of gradual pilot points according to the gradual deformation method wherein at least one deformation parameter is a characteristic parameter of said pilot points (position and/or value). The initial map (y) is then modified, the deformation parameters are modified according to the dynamic data and the procedure is repeated until a stop criterion is reached and the geological reservoir model is updated by associating the map thus optimized with the grid of the model.
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. The composite realization results from the projection of the direction of descent of the objective function, calculated by the flow simulator for the initial realization, in the vector subspace generated by P realizations of (Y), randomly drawn and independent of one another, and of the initial realization. During optimization, the chain is explored so as to identify a realization that allows minimizing the objective function (J). In order to sufficiently reduce the objective function, sequentially constructed chains are explored by taking as the initial realization the optimum realization determined for the previous chain. The method may be used for development of oil reservoirs.
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 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. The method makes it possible to gradually deform realizations of a model representative of the medium while modifying the statistical parameters relative to the structure of the medium. The method also allows gradual individual deformations of various parts of the model while preserving continuity between these parts. The method can be applied for construction of stochastic reservoir models constrained by non-linear data (data linked with the flow of fluids).
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. The method applies in particular to Gaussian sequential simulations and, in particular, to Gaussian white noises, from which any type of stochastic models (continuous, facies or object models, etc.) can be constructed. Application: elaboration of an underground reservoir model allowing to simulate the configuration of various heterogeneities: permeability, porosity, fractures, channels, etc.
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. Furthermore, the size of the objects is associated with the procedure for generating the number of objects so as to make an object appear or disappear progressively. Application: construction of a Boolean underground reservoir model allowing to simulate the configuration of various heterogeneities: fractures, channels, etc.
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:
A method of constructing an image representing the distribution of a categorical physical property representative of an underground zone having applications for petroleum reservoir development. A first training image representative of a geometrical structure of the categorical property is constructed. Training images representative of the distributions of several auxiliary properties are then constructed from the first training image. A probability law of the categorical property and a probability law of each auxiliary property are determined, from each training image, for a given pixel according to the values of the neighboring pixels. A probability law of the categorical property is calculated from these laws and from the images representative of the distribution of the auxiliary physical properties in the zone, and for each pixel of the image to be constructed. Finally, the value of the categorical property is determined by carrying out a random selection for the calculated probability law.