Abstract: The invention relates to a method for history matching a facies geostatistical model using the ensemble Kalman filter (EnKF) technique. The EnKF is not normally appropriate for discontinuous facies models such as multiple point simulation (MPS). In the method of the invention, an ensemble of realizations are generated and then uniform vectors on which those realizations are based are transformed to Gaussian vectors before applying the EnKF to the Gaussian vectors directly. The updated Gaussian vectors are then transformed back to uniform vectors which are used to update the realizations. The uniform vectors may be vectors on which the realizations are based directly; alternatively each realization may be based on a plurality of uniform vectors linearly combined with combination coefficients. In this case each realization is associated with a uniform vector made up from the combination coefficients, and the combination coefficient vector is then transformed to Gaussian and updated using EnKF.

Abstract: A multiple point simulation technique for generating a model realization of a subterranean formation having different facies is described which uses a non-stationary training image which reflects facies spatial trends across the formation. The realization is formed by sequentially populating each cell; a facies pattern of neighboring cells is identified for each cell in the model grid, and then corresponding facies patterns identified in the training image. The probability of a target cell in the model grid having a given facies is calculated based on the proportion of occurrences of the corresponding facies pattern where the central cell has that facies. The contribution of each corresponding facies pattern occurrence in the training image to this proportion or probability is weighted according to the distance between its central cell and the training image cell corresponding in location to the target cell in the model grid.

Abstract: The present disclosure describes a method that improves the long-range geobody continuity in Multiple Point Statistical methods, wherein the coarsest multi-grid level cells are simulated in a regular path, and the subsequent level cells are simulated in a random path as usual. The method is general and is applicable to different cases: such as hard data conditioning, soft data conditioning, non-stationarity modeling, 2 or more than 2 types of facies modeling, and 2D and 3D modeling. The method is particularly useful in reservoir modeling, especially for the channelized systems, but can be generally applied to other geological environments.

Abstract: The present disclosure describes a method that improves the long-range geobody continuity in Multiple Point Statistical methods, wherein the coarsest multi-grid level cells are simulated in a regular path, and the subsequent level cells are simulated in a random path as usual. The method is general and is applicable to different cases: such as hard data conditioning, soft data conditioning, non-stationarity modeling, 2 or more than 2 types of facies modeling, and 2D and 3D modeling. The method is particularly useful in reservoir modeling, especially for the channelized systems, but can be generally applied to other geological environments.

Abstract: Estimating in-situ stress of an interval having drilling response data is described. Estimating involves obtaining drilling response data of a data rich interval with available data. Estimating relative rock strength as a composite value that includes in-situ stress and rock strength. Estimating a Poisson's ratio from the relative rock strength. Generating a stress model that includes uniaxial strain model using the Poisson's ratio. Verifying the stress model with the available data. Applying the stress models in a non-data rich interval.

Abstract: A method of computer modeling a reservoir using multiple-point statistics from non-stationary training images is provided.

Abstract: A method for creating a modified realization of a geostatistical model of a subterranean hydrocarbon reservoir is described, which may be used in a history matching process. The modified realization is based on a current realization which is a function of a first uniform random number field. At least one further uniform random number field Ui is created and a linear combination made of the first uniform random number field and the further uniform random number field or fields Ui, together with combination coefficients ri, to derive a modified non-uniform random number field V. A uniform score transformation procedure is then performed, e.g. using an empirical cumulative distribution function, on the modified non-uniform number field V, to derive a modified uniform random number field Umod. A modified realization of the model can then be derived from the uniform random number field Umod.

Abstract: A multiple point simulation technique for generating a model realization of a subterranean formation having different facies is described which uses a non-stationary training image which reflects facies spatial trends across the formation. The realization is formed by sequentially populating each cell; a facies pattern of neighboring cells is identified for each cell in the model grid, and then corresponding facies patterns identified in the training image. The probability of a target cell in the model grid having a given facies is calculated based on the proportion of occurrences of the corresponding facies pattern where the central cell has that facies. The contribution of each corresponding facies pattern occurrence in the training image to this proportion or probability is weighted according to the distance between its central cell and the training image cell corresponding in location to the target cell in the model grid.

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.

Abstract: The invention relates to a method for history matching a facies geostatistical model using the ensemble Kalman filter (EnKF) technique. The EnKF is not normally appropriate for discontinuous facies models such as multiple point simulation (MPS). In the method of the invention, an ensemble of realizations are generated and then uniform vectors on which those realizations are based are transformed to Gaussian vectors before applying the EnKF to the Gaussian vectors directly. The updated Gaussian vectors are then transformed back to uniform vectors which are used to update the realizations. The uniform vectors may be vectors on which the realizations are based directly; alternatively each realization may be based on a plurality of uniform vectors linearly combined with combination coefficients. In this case each realization is associated with a uniform vector made up from the combination coefficients, and the combination coefficient vector is then transformed to Gaussian and updated using EnKF.

Abstract: A method for creating a modified realization of a geostatistical model of a subterranean hydrocarbon reservoir is described, which may be used in a history matching process. The modified realization is based on a current realization which is a function of a first uniform random number field. At least one further uniform random number field Ui is created and a linear combination made of the first uniform random number field and the further uniform random number field or fields Ui, together with combination coefficients r to derive a modified non-uniform random number field V. A uniform score transformation procedure is then performed, e.g. using an empirical cumulative distribution function, on the modified non-uniform number field V, to derive a modified uniform random number field Umod. A modified realization of the model can then be derived from the uniform random number field Umod.

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.

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 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 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: 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: 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 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, for example, a hydrodynamic type having applications of geostatistical modelling of heterogeneous reservoirs of various objects: fracture, channels, vesicles, etc., for example. The objects are distributed in a zone of a heterogeneous medium according to a Poisson point process in form of figurative points with a point density ?(x) that varies according to their position (x) in the zone, a realization of a uniform random vector according to which the position of each object is defined while respecting density ?(x) is formed, and the uniform random vector is gradually modified according to a gradual deformation process so as to obtain gradual migration of each object until a final realization best adjusted to parameters relative to the structure of the medium, such as hydrodynamic parameters, is obtained.

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.