Abstract: The invention is a method of developing a petroleum reservoir employing a technique for selection of the position of the wells to be drilled. A production indicator map is utilized comprising a set of cells each associated with a production indicator defining impact on fluid production of addition of a well in this cell. The production indicator map is constructed by selecting cells from among the set of cells of the map; determining production indicators in the selected cells; and interpolating the production indicators on the set of cells of the map, by an interpolation model accounting for a distance between the cell to be interpolated and the closest well to the cell to be interpolated. The position of the well to be drilled is defined by the cell where the production indicator is a maximum.

Abstract: The invention is a method for real-time updating of a geological model using dynamic data while maintaining the coherence thereof with static observations. An initial set of reservoir property maps, obtained from stochastic simulations of a random function, are available. Parameters providing new realizations of the random function when applied to the set are selected. New maps are created using initial values of the parameters. As soon as new dynamic data are available, the parameters are modified to reduce a difference between the simulated data for perturbed models and the measured data. Finally, the reservoir is developed using a modified development scheme to account for the deformed maps.

Abstract: A method is disclosed for operating an oil pool based on a reservoir model gradually deformed by means of cosimulations. A map of a property of the pool is obtained by a stochastic simulation of a first random function. A correlation coefficient is chosen between the first random function and a second random function with an identical mean and covariance. The map is modified by a cosimulation of the two random functions by using the correlation coefficient. The correlation coefficient is modified and the cosimulation step is reiterated to deform the map and minimize a matching objective function. Finally, the pool is operated by implementing an operating scheme accounting for the deformed map.

Abstract: Method for optimizing the development of an underground reservoir, wherein a geological model is updated using dynamic data and well tests. A reservoir model is constructed by performing a geological model scale change. Dynamic data are simulated from this reservoir model. Influence zones are identified within the geological model where the well tests induce a pressure variation during well testing. Well tests are then simulated for each influence zone. An objective function measuring the difference between the simulated data and the measured data is calculated. The geological model is then modified so as to reduce to the maximum the objective function using a geostatistical parametrizing technique. Finally, development of the underground reservoir is optimized by evaluating, by means of a flow simulator, the reservoir production for various production schemes. Application: notably oil reservoir development.

Abstract: A method of developing a petroleum reservoir, wherein a facies map representative of the reservoir is constructed from petrophysical property maps. A grid cell visiting order is defined by selecting the visiting order that first passes through the cells where the facies are the most discriminated. Then, in each cell i, according to the visiting order, and for various facies values k, the likelihood defined by the probability of obtaining in cell i the values of observed petrophysical properties is calculated, knowing that the facies in cell i is facies k, and knowing on the one hand already identified facies values V<i* and, the values of the petrophysical properties of the previously visited cells. The facies value that maximizes the likelihood in cell i is associated with each cell i of the grid.

Abstract: A method of developing a petroleum reservoir according to a given development scheme, from a facies map representative of the reservoir. New measurements are taken in the reservoir to better characterize it. A geostatistical simulator is selected. A set of random numbers is then identified which are provided to the geostatistical simulator to provide a facies representation identical to the initial map by inverting a random number generation algorithm of the simulator. The map is then modified to account for the new measurements, by carrying out a geostatistical simulation constrained by the measurements, with the geostatistical simulator and the set of random numbers. Finally, the reservoir development scheme is modified by accounting for the modified map, and the reservoir is developed using the modified development scheme.

Abstract: A method of modifying a geological model representative of an underground reservoir is disclosed which respects average proportions of the lithologic facies imposed by a production data calibration process which has application to petroleum reservoir development. A geographical zone Z is defined within the geological model and an average proportion in zone Z allowing the production data to be calibrated is determined for k facies, with an optimization process. The proportions of these facies are modified using a block indicator cokriging method constrained by the average proportions to be respected. A new geological model constrained by the modified facies proportions is simulated and the development of the underground medium is optimized by the simulated model.

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: The invention relates to a method having applications for oil exploration and CO2 storage of determining the three-dimensional distribution of the absolute permeability of a heterogeneous sample. The method includes: determining a 3D porosity map of the sample; carrying out a viscous miscible displacement experiment during which the evolution of the differential pressure on either side of the sample is determined; from this evolution, determining a 1D absolute permeability profile along the sample and constructing a first 3D permeability map from the 3D porosity map; estimating a simulated differential pressure by simulating numerically a viscous miscible test from the first permeability map and from the 1D permeability profile; determining the three-dimensional distribution of the absolute permeability of the sample by modifying at least once the first permeability map so as to minimize the difference between the simulated differential pressure and the differential pressure measured over the course of time.

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: Method for optimizing the development of an underground reservoir, wherein a geological model is updated using dynamic data and well tests. A reservoir model is constructed by performing a geological model scale change. Dynamic data are simulated from this reservoir model. Influence zones are identified within the geological model where the well tests induce a pressure variation during well testing. Well tests are then simulated for each influence zone. An objective function measuring the difference between the simulated data and the measured data is calculated. The geological model is then modified so as to reduce to the maximum the objective function using a geostatistical parametrizing technique. Finally, development of the underground reservoir is optimized by evaluating, by means of a flow simulator, the reservoir production for various production schemes. Application: notably oil reservoir development.

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 predicting petrophysical characteristics of an underground reservoir by constructing a geologic model consistent with seismic measurements is disclosed which permits optimization of oil reservoir development schemes. A geologic model, from which seismic data are simulated in depth, is constructed in depth. The geologic model is made consistent with seismic measurements acquired in time by minimization of an objective function by comparing the seismic measurements with seismic data simulated from the geologic model and converted to time. During minimization, the interval velocities used for conversion are updated by comparing, within the objective function, an observed thickness in time ?Tobsm,n between two markers with a thickness in time ?Tsimm,n simulated from the seismic data, and by modifying simulation parameters such as the error ?simm,n on the thickness of the two markers estimated in depth.

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: The invention relates to a method having applications for oil exploration and CO2 storage of determining the three-dimensional distribution of the absolute permeability of a heterogeneous sample. The method includes: determining a 3D porosity map of the sample; carrying out a viscous miscible displacement experiment during which the evolution of the differential pressure on either side of the sample is determined; from this evolution, determining a 1D absolute permeability profile along the sample and constructing a first 3D permeability map from the 3D porosity map; estimating a simulated differential pressure by simulating numerically a viscous miscible test from the first permeability map and from the 1D permeability profile; determining the three-dimensional distribution of the absolute permeability of the sample by modifying at least once the first permeability map so as to minimize the difference between the simulated differential pressure and the differential pressure measured over the course of time.

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 of predicting petrophysical characteristics of an underground reservoir by constructing a geologic model consistent with seismic measurements is disclosed which permits optimization of oil reservoir development schemes. A geologic model, from which seismic data are simulated in depth, is constructed in depth. The geologic model is made consistent with seismic measurements acquired in time by minimization of an objective function by comparing the seismic measurements with seismic data simulated from the geologic model and converted to time. During minimization, the interval velocities used for conversion are updated by comparing, within the objective function, an observed thickness in time ?Tobsm,n between two markers with a thickness in time ?Tsimm,n simulated from the seismic data, and by modifying simulation parameters such as the error ?simm,n on the thickness of the two markers estimated in depth.

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.