Abstract: The invention is a method for exploring and exploiting a fluid in a subterranean formation comprising a network of fractures. On the basis of measurements of properties relating to the formation, a meshed representation of the formation, and statistical parameters relating to the network of fractures, each mesh of the meshed representation is broken down into at least one unfractured matrix block and an equivalent permeability tensor of the network of fractures in the mesh concerned is determined. A matrix block characteristic dimension is then determined according to a relation that is a function at least of the eigenvalues of the equivalent permeability tensor. Based on the meshed representation, the characteristic dimension and a flow simulator, there is defined an optimum exploitation scheme for the fluid of the formation and said fluid is exploited as a function of the optimum exploitation scheme.

Abstract: Method for exploiting a fluid in a subterranean formation comprising a network of fractures. On the basis of measurements of properties relating to the formation, a meshed representation of the formation, and statistical parameters relating to the network of fractures, each mesh of the meshed representation is broken down into at least one unfractured matrix block and an equivalent permeability tensor of the network of fractures in the mesh concerned is determined. A matrix block characteristic dimension is then determined according to a relation that is a function at least of the eigenvalues of the equivalent permeability tensor. On the basis of the meshed representation, the characteristic dimension and a flow simulator, there is defined an optimum exploitation scheme for the fluid of the formation and said fluid is exploited as a function of the optimum exploitation scheme. Application notably to oil exploration and exploitation.

Abstract: The method of the invention optimizes the development of a heterogeneous porous medium using enhanced recovery of a fluid by fast determination of position of a front separating a sweeping fluid and the fluid in the medium having application for development of oil reservoirs or gas. The velocity field of the front is determined only once with a flow simulator. A relation describing the position of the front in the heterogeneous medium is defined. Velocity fluctuations are accounted for in the direction of the front and the velocity fluctuations in the direction perpendicular to the direction of the front. For each time interval, the position of the front is reconstructed with a fast Fourier transform and injection of the sweeping fluid is optimized according to the position of the front.

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: The invention relates to a method for determining the zones of a stratified porous medium whose physical properties are known, wherein the front or interface between fluids in place and injected flushing fluids moves in a stationary manner, without using a complete flow simulation. Starting from an a priori defined front form which separates two zones of uniform saturation, assumed to have a stationary displacement, the pressure field is determined independently in each zone. The pressure jump on either side of the front is then evaluated for any point of the interface. If it is zero, the form of the front is such that it can move in a stationary manner in the medium. If the pressure jump is not zero, the user deforms the interface and resumes the process until a stationary form is obtained. This process may not converge. In this case, we consider that a stationary front cannot form through the total thickness of the medium and the medium is divided so as to seek solutions in intermediate zones.

Abstract: The method optimizes the development of a heterogeneous porous medium within the context of enhanced recovery of a fluid in place, by fast determination of the position of the front separating a sweeping fluid and the fluid in places having application for development of oil reservoirs or gas. The velocity field in the neighbourhood of the front is determined only once by means of a flow simulator. Then a relation describing the position of the front in the heterogeneous medium is defined by freedom from the viscous coupling by means of the perturbation theory, and by accounting for the velocity fluctuations in the front advance direction and the velocity fluctuations in the direction perpendicular to the front advance direction. Finally, for each time interval, the position of the front is reconstructed by means of a fast Fourier transform and injection of the sweeping fluid is optimized according to the position of said front.

Abstract: The invention is a method of determining all the components of an absolute permeability tensor of a porous medium sample from permeability measurements, obtained for example by placing the sample in a permeameter which is useful for fast determination of permeability anisotropies of rocks and detention of internal heterogeneities. A pressure difference ?P is applied between the inlet and outlet faces of a laboratory rock sample, with zero flow conditions on the edges parallel to the mean flow obtained by confining it in a sheath under pressure. Starting from conventional permeability measurements in three directions and from the measurements of the two components of the viscous forces transverse to the sample, a permeability tensor k can be “inverted” by numerical solution of the corresponding boundary-value problem.

Abstract: The invention relates to a method for determining the zones of a stratified porous medium whose physical properties are known, wherein the front or interface between fluids in place and injected flushing fluids moves in a stationary manner, without using a complete flow simulation. Starting from an a priori defined front form which separates two zones of uniform saturation, assumed to have a stationary displacement, the pressure field is determined independently in each zone. The pressure jump on either side of the front is then evaluated for any point of the interface. If it is zero, the form of the front is such that it can move in a stationary manner in the medium. If the pressure jump is not zero, the user deforms the interface and resumes the process until a stationary form is obtained. This process may not converge. In this case, we consider that a stationary front cannot form through the total thickness of the medium and the medium is divided so as to seek solutions in intermediate zones.

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: The invention is a method of determining all the components of an absolute permeability tensor of a porous medium sample from permeability measurements, obtained for example by placing the sample in a permeameter which is useful for fast determination of permeability anisotropies of rocks and detention of internal heterogeneities. A pressure difference ?P is applied between the inlet and outlet faces of a laboratory rock sample, with zero flow conditions on the edges parallel to the mean flow obtained by confining it in a sheath under pressure. Starting from conventional permeability measurements in three directions and from the measurements of the two components of the viscous forces transverse to the sample, permeability tensor k can be “inverted” by numerical solution of the corresponding boundary-value problem. Since these quantities can be alternatively obtained from numerical solutions of the same flow in a heterogeneous medium, the method can also be used as an upscaling tool in a reservoir simulator.

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: Method for determining, from a 3D image, the values of hydraulic parameters such as the large-scale equivalent permeability, the permeability of blocks and the matrix-fracture exchange coefficient .alpha. of a fractured porous medium such as a geologic formation. The method mainly comprises discretization of the medium by means of a grid pattern and fast and approximate solution, in this grid pattern, of equations modelling diffusion of the fluids in the medium, determination of the variation with time of a large-scale transfer function (f(t), f(s)) characterizing the fluid flows from the matrix to the fractures, by simulation of the movement of particles performing random walks in continuous time on said grid pattern and suitable processing of a state function (.epsilon.(.tau.)) indicative of the presence thereof either in the matrix or in a fracture. The method can be applied for large-scale modelling of fractured oil reservoirs allowing well test interpretation.