METHOD FOR DETERMINING UNCERTAINTIES ASSOCIATED WITH A MODEL OF A SEDIMENTARY BASIN

Description

Technical field

[0001] The present invention relates to the field of exploration and exploitation of oil deposits or geological gas storage sites. The present invention also relates to the field of new energies such as geothermal energy or energy storage in the subsoil. In general, the present invention can be used in any field requiring characterization of the geometry, the nature of the sedimentary layers composing the subsoil, and optionally the nature of the hydrocarbons present in the subsoil.

[0002] Oil exploration involves searching for hydrocarbon deposits within a sedimentary basin. The general approach to assessing the petroleum potential of a sedimentary basin involves going back and forth between a prediction of the petroleum potential of the sedimentary basin, based on measured information relating to the basin studied (outcrop analysis, seismic surveys, drilling for example), and exploratory drilling in the different areas with the best potential, in order to confirm or refute the previously predicted potential, and to acquire new information to refine the predictions of the petroleum potential of the basin studied.

[0003] The oil exploitation of a deposit consists, from the information gathered during the oil exploration phase, of selecting the areas of the deposit presenting the best oil potential, of defining exploitation schemes for these areas (for example using a reservoir simulation, in order to define the number and positions of the exploitation wells allowing maximum hydrocarbon recovery), of drilling exploitation wells and, in general, of setting up the production infrastructures necessary for the development of the deposit.

[0004] The assessment of the petroleum potential of a sedimentary basin is most often implemented using computer-based software that allows the synthesis of available data and the simulation of the geological history of the basin studied. This software can allow the simulation in one, two or three dimensions of the sedimentary, tectonic, thermal, hydrodynamic, organic and inorganic chemistry processes that occur during the formation of an oil basin.

[0005] In particular, stratigraphic simulation aims to simulate the evolution of a sedimentary basin over geological time in order to quantify in particular the geometry of the sedimentary layers, the type of sediments deposited, the water depth at the time of deposition, etc. Basin simulation makes it possible to simulate, over geological time, the formation of hydrocarbons, in particular from the organic matter initially buried with the sediments, and the transport of these hydrocarbons from the rocks in which they were formed to those where they are trapped.Following a stratigraphic simulation or a basin simulation, a model of the basin is obtained, in the form of a digital representation such as a grid or a mesh, each mesh comprising at least one value of a property relating to the basin (geometry of the sedimentary layers, composition of the sediments, pressure, temperature, content and nature of hydrocarbons, etc.). The values ​​of these properties are then analyzed in particular to evaluate the petroleum potential of the basin studied.

[0006] Generally speaking, basin models must at least reproduce the measurements made on the basin, such as measurements acquired at wells or data from seismic acquisitions. The result of a simulation, however, is directly dependent on the simulation input parameters (such as the initial bathymetry, sediment transport coefficients or sediment inputs for stratigraphic simulation, or the type of organic matter, petrophysical properties of rocks, physicochemical properties of fluids, temperatures and pressures for basin simulation). These simulation parameters are generally estimated from different in situ measurements, but the available data are generally not sufficiently informative to characterize the input parameters of these simulations in a unique way.Thus, it may happen that different models reproduce the measurements made on a basin, while corresponding to a different state of the basin than the current one. It therefore appears important to quantify the uncertainties associated with the values ​​of the basin properties resulting from a simulation in order to integrate them into the process of evaluating the petroleum potential of the basin, and in particular in the evaluation of the exploration risk.

[0007] One way to carry out such studies is to place oneself in the probabilistic framework and to consider the input parameters of the numerical simulations involved in a basin modeling as random variables having a given probability distribution (for example, uniform in a certain interval or Gaussian). These distributions are chosen by the user according to his expertise and knowledge of the basin, and can be derived for example from the calibration of the model on the available data (measurements). One can then seek to estimate the corresponding distribution of the properties of interest. One can use Monte Carlo type sampling methods for this: a large set of models is generated according to the parameter distributions (set of values ​​for the input parameters) and the evolution of these models over time is simulated.This provides a sample of values ​​for the simulated properties that can then be analyzed and used to estimate the probability distribution of a given event and / or situation given the uncertainty assumed in the input parameters. These events are characterized by a target range of values ​​for a given property, or by the joint presence of several properties in target ranges. This type of analysis can be performed on scalar properties, which represent, for example, regional characteristics of the basin such as the average of a property, or on the spatial distribution of properties in a set of grid cells (3D block, map, 2D section, etc.). For example, we can estimate a probability map of the presence of a reservoir defined by the probability in each column of grid cells of the basin that the thickness of deposited sediment and the sand concentration are greater than a certain threshold.This map can then be used to estimate an exploration risk. It should also be noted that approaches, also based on sampling of input parameters and associated basin properties, provide an estimate of the impact of these parameters on the simulated properties considered (sensitivity analysis).

[0008] However, such analyses require the performance of a large number of simulations (several thousand for example) to obtain representative samples, which is difficult to envisage in the context of an operational study due to the long simulation times and the short deadlines for carrying out such studies. Prior art

[0009] The following documents will be cited during the description: 1. Douarche, F., Da Veiga, S., Feraille, M., Enchéry, G., Touzani, S. and Barsalou, R. (2014) Sensitivity Analysis and Optimization of Surfactant-Polymer Flooding under Uncertainties: Oil & Gas Science and Technology - Rev. IFP Energies nouvelles, v. 69, no. 4, p. 603-617. 2. Gervais, V., Ducros, M., Granjeon, D. (2018) Probability maps of reservoir presence and sensitivity analysis in stratigraphic forward modeling. AAPG Bulletin, 102(4) 3. Ducros, M., Nader F. (2020) Map-based uncertainty analysis for exploration using basin modeling and machine learning techniques applied to the Levant Basin petroleum systems, Eastern Mediterranean. Marine and Petroleum Geology, 120. 4. Jin, R., Chen, W., Sudjianto, A. (2002), On sequential sampling for global metamodeling in engineering design. Proceedings of DETC'02, ASME 2002 Design Engineering Technical Conference and Computers and Information in Engineering Conference, Montreal, Canada, September 29-October 2, 2002. 5. Sacks, J., Welch, W.J., Mitchell, T.J., Wynn, H.P. (1989) Design and Analysis of Computer Experiments. Stat. Sci. 4(4), 409-423. 6. Le Gratiet, L., Cannamela, C. (2015). Cokriging-based sequential design strategies using fast cross-validation techniques for multi-fidelity computer codes. Technometrics, 57(3), pp. 418-427. 7. Picheny, V., Ginsbourger, D., Roustant, O., Haftka, R., Kim N-H (2010). Adaptive designs of experiments for accurate approximation of a target region. Journal of Mechanical Design, 132(7), pp. 071008-1 - 071008-9 8. Busby, D. (2009). Hierarchical adaptive experimental design for Gaussian process emulators. Reliability Engineering and System Safety 94, pp 1183-1193. 9. Granjeon, D. and P. Joseph (1999) Concepts and applications of a 3-D multiple lithology, diffusive model in stratigraphic modeling, in J. W. Harbaugh, W. L. Watney, E. C. Rankey, R. Slingerland, and R. H.Goldstein, eds, Numerical Experiments in Stratigraphy: recent advances in stratigraphic and sedimentologic computer simulations, SEPM Special Publication 62, p. 197-210 10. Scheichl R., Masson R., Wendebourg J. (2003), Decoupling and Block Preconditioning for Sedimentary Basin Simulations, Computational Geosciences 7(4), pp. 295-318. 11. Steckler, MS and Watts, AB (1978) Subsidence of the Atlantic Type Continental Margin off New York. Earth and Planetary Science Letters, 41, 1-13 12. Sobol', IM (1990) On sensitivity estimation for nonlinear mathematical models: Mathematical Modeling & Computational Experiment, vol. 1, no. 4, p. 407-414. .

[0010] We know the document "Arthur Thenon. Use of multi-fidelity meta-models for the optimization of reservoir production. Earth Sciences. Pierre and Marie Curie University - Paris VI, 2017" which concerns the use of multi-fidelity meta-models for the optimization of reservoir production.

[0011] To overcome this problem, it is possible to rely on meta-models that approximate the relationship between the model's input parameters and the scalar outputs of interest. These are also referred to as response surfaces or approximate analytical models. Each of these meta-models is constructed from a set of values ​​of the desired property - a simulator during risk or sensitivity analyses. In this case, the only simulations to be carried out are those allowing the construction of the training set.

[0012] Different techniques exist to build such meta-models, such as polynomial regression, Gaussian processes or neural networks. In some cases, the outputs of interest are called functional because they depend, for example, on time or position in the basin. This could be, for example, the distribution of the thickness of sediments deposited in each column of the grid, or the distribution of temperature in the basin. For this type of output, the meta-model approach can be applied to each time or location of interest. One way to reduce the number of variables to be predicted, and therefore the computation times, is to introduce dimension reduction techniques into the process (see document [1] for example).More precisely, a reduced basis decomposition (e.g., PCA type) is applied to all simulated values ​​for the experimental design models in the area of ​​interest (maps, blocks, sections). Meta-modeling is then applied not to the simulated outputs directly but to the weights associated with each vector of the reduced basis. The simulation outputs are then estimated by linear combination of the reduced basis with the predicted values ​​for the associated weights.

[0013] The use of meta-models for carrying out risk analyses and sensitivity analyses is a widespread technique in many applications. In basin-scale subsurface modelling, we can cite in particular the work presented in documents [2,3]. The limited number of simulations to be carried out makes this type of analysis accessible in the context of operational studies.

[0014] However, the main difficulty lies in the choice of the training set. Ideally, one wants to generate an experimental design that is as small as possible and leads to satisfactory estimates in terms of accuracy. However, it is difficult to know in advance the number of simulations necessary to obtain such estimators, or the adequate value of the simulation parameters in the experimental design. This will depend in particular on the number of uncertain parameters and the complexity of the relationship between these parameters and the response. In order to optimize the process of building the training set, different methods have been proposed, in the field of engineering in general but not specifically in the field of basin simulation or stratigraphic simulation, to sequentially complete an experimental design with new simulations according to a given criterion.Some only use the position of the points already simulated in the parameter space to propose new ones. These are called methods without adaptation. For example, we can cite the maximin criterion (see document [4]) which aims to best cover the parameter space according to geometric criteria.

[0015] Other approaches, called adaptation approaches, use both the already simulated sample and the information provided by the current meta-model to select new points. The criterion used then depends on the objective of the study. For risk analyses and sensitivity analyses, the aim is to identify predictive estimators across the entire space of uncertain parameters. At each iteration, one or more new complementary points are proposed, which can then be simulated simultaneously, on a computational cluster (which can be translated as "grouping") for example.

[0016] However, these methods, from the field of engineering in general, only apply to a single meta-model, approaching a single scalar output, the quality of which they will seek to improve thanks to the new point chosen. They can therefore be directly applied to estimate a physical quantity, for example a property of interest in a given mesh. If we wish to predict this property in a set of meshes without going through a decomposition into a reduced basis (functional output), adaptive methods can be applied in each mesh. However, if many meshes are considered, this will lead to adding to the experimental design as many simulations as meshes, which may not be optimal in terms of computation time and computer memory used.

[0017] The present invention overcomes these drawbacks. The present invention relates to an automatic and efficient method for quantifying uncertainties for spatial outputs in basin modeling in the broad sense (stratigraphic simulation and basin simulation). The present invention is based on the coupling of sequential planning methods with adaptation to the processing of functional outputs by reduced base decomposition. It makes it possible both to limit the number of meta-models to be calculated, and therefore the calculation times and computer memory, and to supplement the experimental design at each iteration with new points aimed at globally improving the estimation of the property of interest in all the cells considered. Furthermore, the training set is built in real time, until relevant stopping criteria are reached, in particular representative of the quality of the estimations of the spatial properties of interest. Summary of the invention

[0018] The present invention relates to a method for determining uncertainties relating to at least one physical property of a sedimentary basin, by means of a numerical simulation executed from simulation parameters, said numerical simulation being a stratigraphic simulation or a basin simulation executed on a computer, said physical property of the basin being chosen from the thickness of a stratigraphic unit, the sand concentration, the clay concentration in a stratigraphic unit, the temperature, the pressure, the porosity, the density, the saturation, or the concentration of the rock in organic matter, said stratigraphic simulation simulating the evolution of a sedimentary basin over geological time in order to quantify in particular the geometry of the sedimentary layers, the type of sediments deposited, the water depth at the time of deposition, and said basin simulation simulating over geological time,the formation of hydrocarbons, particularly from organic matter initially buried with the sediments, and the transport of these hydrocarbons from the rocks in which they formed to those where they are trapped.

[0019] The method according to the invention is characterized in that at least the following steps are carried out: A) Measurements of physical quantities relating to said basin are carried out by means of sensors, and at least values ​​of said simulation parameters are determined, said simulation parameters being chosen from the initial bathymetry, the sediment inputs, their transport for each time step, petrophysical properties associated with the basin studied; B) Uncertain simulation parameters are selected, and a plurality of combinations of the possible values ​​of said uncertain simulation parameters are defined; C) A plurality of meshed representations of said basin are determined by means of said numerical simulation, each of said meshed representations being obtained for one of said combinations of said plurality of combinations of the possible values ​​of said uncertain parameters, each of the meshes of one of said meshed representations comprising at least one value making it possible to determine said property; and in that, for at least one of said physical properties of said sedimentary basin, at least the following steps are carried out: D) For each of said mesh representations, a realization of a spatial distribution of said property is determined, a principal component analysis is applied to the plurality of realizations of said spatial distribution of said property, said components are selected whose sum of the associated eigenvalues ​​is greater than a predefined threshold, and an approximate analytical model of said spatial distribution of said property is determined by constructing an approximate analytical model for each of said selected components;E) As long as a stopping criterion is not satisfied, the accuracy of said approximate analytical model of said spatial distribution of said property is improved iteratively by determining, at each iteration, at least one additional combination of said plurality of combinations of the possible values ​​of said uncertain parameters by means of a sequential planning method with adaptation, said sequential planning method with adaptation being applied to said approximate analytical models of said selected components, by considering the components in the decreasing order of their eigenvalues ​​and until reaching a value of an accuracy indicator relating to at least said component considered at the current iteration, and by repeating steps C) and D); ; and in that, from said improved approximate analytical model of said spatial distribution of said at least one improved physical property, said uncertainties relating to at least said spatial distribution of said property of said sedimentary basin model are determined.

[0020] According to an implementation of the invention, said at least one stopping criterion may be a function of at least one precision indicator on said approximate analytical models of said components.

[0021] According to one implementation of the invention, an approximate analytical model can be determined by means of Gaussian process regression.

[0022] According to an implementation of the invention, said sequential planning method with adaptation can be chosen from the following list: a method for estimating the maximum kriging variance, a method for estimating the maximum kriging variance weighted by the cross-validation error, a method by integrating the kriging variance, or hierarchical experimental designs.

[0023] According to one implementation of the invention, in the case of a plurality of physical properties of said basin, steps C) to E) can be applied for each of said physical properties of said basin.

[0024] The invention further relates to a computer program product downloadable from a communication network and / or recorded on a computer-readable medium and / or executable by a processor, comprising program code instructions for implementing the method as described above, when said program is executed on a computer.

[0025] The invention also relates to a method for exploiting hydrocarbons present in a sedimentary basin, said method comprising at least the implementation of the method for determining uncertainties relating to at least one physical property of a sedimentary basin as described above, and in which, from at least said improved approximate analytical model and / or said uncertainties relating to at least said physical property, an exploitation scheme for said basin is determined comprising at least one installation of at least one injection well and / or at least one production well, and said hydrocarbons from said basin are exploited at least by drilling said wells of said installation and equipping them with exploitation infrastructures.

[0026] Other characteristics and advantages of the method according to the invention will appear on reading the following description of non-limiting examples of embodiments, with reference to the figures appended and described below. List of figures

[0027] There figure 1 illustrates the evolution, as a function of the number of simulations, of a first indicator of precision for four components of an approximate analytical model of a spatial distribution of interest. The figure 2 illustrates the evolution, as a function of the number of simulations, of a second indicator of precision of an approximate analytical model of a spatial distribution of interest. The figure 3 illustrates the distribution of the values ​​of the first precision indicator of an approximate analytical model of a spatial distribution of interest in each mesh of the spatial distribution of interest. Description of the embodiments

[0028] According to a first aspect, the invention relates to a method for determining uncertainties relating to at least one physical property relating to a sedimentary basin, by means of a numerical simulation carried out from simulation parameters. The numerical simulation according to the invention may be a stratigraphic simulation or a basin simulation. The numerical simulations according to the invention are described in more detail in section 3) below. The method according to the first aspect of the invention comprises at least steps 1 to 6 described below.

[0029] According to a second aspect, the invention relates to a method for exploiting hydrocarbons present in a sedimentary basin, using uncertainties relating to at least the physical property of the basin. The method according to the second aspect of the invention further comprises at least step 7 described below.

[0030] The steps of the methods according to the first and second aspects are described below in the non-limiting case of a single physical property of interest. In the case of a set of physical properties of interest, it is possible, in a non-limiting manner, to repeat steps 4 and 5 sequentially for each physical property of interest.

[0031] Physical properties of the basin include, for example, the thickness of a stratigraphic unit, the sand concentration, the clay concentration in a stratigraphic unit, the temperature, the pressure, the porosity, the density, the saturation, or the TOC (or concentration of organic matter in the rock). 1) Measurements of physical quantities relating to the pelvis

[0032] During this step, measurements of physical quantities relating to the sedimentary basin considered are carried out using sensors, and at least values ​​of the parameters of the numerical simulation considered are deduced from them.

[0033] According to one implementation of the invention, the measurements of physical quantities comprise at least logging measurements and seismic measurements. Advantageously, the measurements of physical quantities may also comprise measurements carried out on outcrops, petrophysical and / or geochemical analyses of cores taken in situ.

[0034] Logging measurements are understood to mean measurements carried out in at least one well drilled in a basin, by means of a logging device or probe moving along the well to measure a physical quantity relating to the geological formation close to the well. Logging measurements make it possible to estimate, for example, the water and hydrocarbon content at each measurement step in the well, the dominant lithology (or lithological facies) and in particular the sand and / or clay content of the rocks crossed, but also the dip and thickness of the layers. According to one implementation of the invention, the physical quantities measured may include electrical resistivity, natural gamma radioactivity, spontaneous polarization. The logging measurement is a local measurement, along the well and of limited lateral extension.

[0035] Seismic measurements are understood to mean measurements carried out by means of a seismic measurement acquisition device, conventionally comprising at least one seismic source (for example a water gun in marine seismic, or a vibrating truck in terrestrial seismic) to generate seismic waves in the basin and a plurality of seismic wave receivers (such as accelerometers, hydrophones) placed so as to record at least seismic waves having been reflected on impedance contrasts of the basin (such as erosion surfaces, limits of stratigraphic units). Conventionally the seismic acquisition device is mobile so as to cover a large area (2D or 3D) on the surface of the basin.

[0036] Without limitation, the sensors may further consist of fluid samplers and analyzers, core samplers and analyzers or any sample taken.

[0037] From these measurements, it is possible to estimate the geometry of the stratigraphic units of the basin at the present time, to qualify the different inorganic sedimentary deposits (mineralogical composition or at least the type of deposit, thicknesses, ages, deposition conditions, etc.), to estimate petrophysical properties such as facies (lithology), porosity, permeability, fluid saturation or even the organic matter content at measurement points in the basin. It is also possible to deduce the geological events undergone by the basin over geological time (erosion, subsidence, eustatism, etc.). This information deduced from the measurements is, however, uncertain, because it results from measurements, possibly pre-processed (in particular seismic measurements), or from an interpretation of the measurements (for example, the estimation of the geometry of the stratigraphic units on the basis of seismic measurements).

[0038] According to one implementation of the invention, from the measurements thus carried out, it is possible to define the input parameters of a stratigraphic simulation, such as the initial bathymetry, the sediment inputs (inorganic, such as the production of different carbonates, and possibly organic), their transport for each time step. According to one implementation of the invention, the initial bathymetry can be estimated by an interpretation in depositional environments (fluvial, coastal, deep marine, etc.) of the well measurements and / or the seismic measurements. According to one implementation of the invention, the transport coefficients can be defined from modern sedimentary environments (i.e. observed in the present time), for example by comparing the sediment flux transported by rivers to the flow rate of these rivers. According to one implementation of the invention, the sediment inputs can be evaluated from the volume of sediment deposited in the basin.

[0039] From these measurements, we can also define the input parameters of a basin simulation, in particular petrophysical properties associated with the basin studied, such as facies (lithology), porosity, permeability, or even the organic matter content at measurement points in the basin. We can also deduce information on the properties of the fluids present in the basin, such as saturation values ​​in the different fluids present in the basin. Also, we can measure temperatures at different points in the basin (bottomhole temperatures in particular).

[0040] In the case of a basin simulation, these measurements can also be used to construct a mesh representation representative of the basin in its current state. More precisely, the construction of a mesh representation of a basin consists of discretizing the basin architecture in three dimensions, and assigning properties to each of the cells of this mesh representation. To do this, we use in particular measurements of physical quantities carried out at different points in the basin described above, which we extrapolate and / or interpolate, into the different cells of the mesh representation, according to more or less restrictive hypotheses. Most often, the spatial discretization of a sedimentary basin is organized into layers of cells, each representing the different geological layers of the basin studied.

[0041] At the end of this step, we therefore obtain, from the measurements of physical quantities carried out on the basin, at least the values ​​of input parameters of the numerical simulation considered. 2) Definition of a plurality of combinations of values ​​of uncertain simulation parameters

[0042] In this step, uncertain simulation parameters are selected and a plurality of combinations of the possible values ​​of said uncertain simulation parameters are defined.

[0043] An uncertain simulation parameter is a simulation parameter whose value for the basin under consideration is not known with certainty. In other words, these are simulation parameters for which the uncertainties are greater than a predefined threshold, for example greater than 10%. Advantageously, among the set of uncertain parameters, we choose those whose variation in the interval of their plausible values ​​leads to a significant variation in the simulation results, in particular the values ​​of the physical property of interest. In other words, we will select from the set of uncertain parameters those for which it appears important to study the impact on the values ​​of the physical property of interest.

[0044] Generally speaking, a person skilled in the art is perfectly aware of how to identify uncertain simulation parameters among the set of parameters of a simulation.

[0045] According to an implementation of the invention, uncertainties in the simulation parameters can be determined from uncertainties in the measurements of physical quantities relating to said basin described in the previous step.

[0046] According to another implementation of the invention, the uncertainties on the simulation parameters can be estimated from bibliographic information, relating to the basin studied or on analogues.

[0047] According to an implementation of the invention, in order to identify the uncertain parameters having a strong impact on the simulation, a few (for example 3 to 5 per uncertain parameter) numerical simulations can be carried out beforehand for different predefined values ​​of simulation parameters, and a first sensitivity analysis is carried out based on the result of these simulations. For example, if only one parameter is varied and an equivalent simulation result is obtained regardless of the value of this parameter, it can be assumed that it is not necessary to consider this parameter in the analysis. Conversely, if different values ​​of the parameter give a very different simulation result, then it may be important to quantify the uncertainties on the property of interest associated with this parameter.

[0048] According to one implementation of the invention, a plurality of combinations of the possible values ​​of said uncertain simulation parameters can be defined from probability distribution laws associated with said uncertain parameters. The probability law can, for example, be uniform between a minimum value and a maximum value.

[0049] Advantageously, a plurality of combinations of the possible values ​​of the uncertain simulation parameters can be defined by means of a sampling method. These sampling techniques are also known as experimental designs. According to one implementation of the invention, factorial designs, composite designs, maximin distance designs, etc. can be used in a non-limiting manner. Advantageously, the Latin Hypercube sampling method can be used, as described in document [8].

[0050] In the following, we assume that we have generated an experimental design noted D = ( θ j ) j =1.. n , including a number n of combinations of possible values ​​of the uncertain parameters. 3) Determination of a plurality of mesh representations of the basin

[0051] During this step, a plurality of mesh representations representative of the basin are determined by means of the numerical simulation considered, each of the mesh representations being obtained for one of the combinations of the plurality of combinations of the possible values ​​of said uncertain parameters. According to an implementation of the invention, the mesh representation in question here is a mesh representation at the current time, but the method according to the invention can be applied to a mesh representation determined for any geological time.

[0052] According to one implementation of the invention, the numerical simulation is a stratigraphic simulator. This is a software program executed on a computer aimed at reconstructing the sedimentary processes that have affected the basin from a previous geological time to the present time. Thus, a numerical stratigraphic simulation is generally implemented discretely in time, that is to say that a stratigraphic simulation simulates the stratigraphic state of the basin for a succession of time steps. A time step of a stratigraphic simulator corresponds to a geological period during which sedimentary deposits or erosions have modified the basin. The properties (including porosity and mineralogy) of these deposits can be relatively heterogeneous at the basin level. The simulation of the history of the filling of a sedimentary basin is carried out from input parameters representative of the sedimentary history of the basin studied.According to one implementation of the invention, the input parameters of a stratigraphic simulation may be at least (1) the space available for sedimentation, linked to tectonic and / or eustatic movements and to the mechanical compaction of the sediments (or settlement of the sediments under the effect of the weight of the overlying layers), (2) the supply of sediments in the basin, either by the boundaries, or via in situ production or precipitation, (3) the transport of these sediments (transport capacity estimated from the characteristics of the sediment such as the size of the grains or their density, the flow of water flowing on the ground surface and the local slope of the basin) in the available space created. The system of equations describing these processes may for example be solved by a spatial discretization in finite volumes, and an explicit scheme in finite volumes.According to an implementation of the invention, the result of a stratigraphic simulation for a time step can correspond to a mesh representation for which each mesh is at least filled with the following information: the sediment content (sand, clay, carbonates, organic matter, etc.), and the depositional environments (in particular the bathymetry at the time of deposition). In a very conventional manner, the mesh representation resulting from a stratigraphic simulation is also filled with characteristic properties of the depositional environment (water depth, basin elevation, etc.). A description of such a stratigraphic simulator can be found in document [9]. An example of such a stratigraphic simulator is the DIONISOS FLOW ® software (IFP Energies nouvelles, France).

[0053] According to one implementation of the invention, the numerical simulation may be a basin simulation. Conventionally, a basin simulator makes it possible to reconstruct geological and / or geochemical processes that have affected the basin from a geological time t to the present time. Conventionally, the period over which the history of this basin is reconstructed is discretized into geological events, also called states. Thus, two states are separated by a geological event (corresponding for example to a particular sedimentary deposit and which can extend between a hundred years and a few million years). A basin simulator is based on a mesh representation of the basin, also called a basin model, and the basin simulator makes it possible to determine such a model for each state. Thus, a basin simulator makes it possible to calculate physical properties relating to the basin studied in each cell of the mesh representation associated with each state.Among the physical properties estimated by a basin simulator, we generally find the temperature, pressure, porosity and density of the rock contained in the considered mesh, saturation, and TOC (or concentration of the rock in organic matter). Classically, a basin simulator also allows to calculate the quantity and composition of hydrocarbons of thermogenic origin, by means of a kinetic model which is fed by kinetic parameters. Thus, basin simulation consists of the resolution of a system of differential equations describing the evolution over time of the physical properties studied. To do this, we can for example use a discretization by the finite volume method, as described for example in the document

[10] . For each state, it is necessary to solve the equations in small time increments (i.e. with a small time step. dt) to the next state. In accordance with the principle of cell-centered finite volume methods, the unknowns are discretized by a constant value per cell and the conservation equations (mass or heat) are integrated in space on each cell and in time between two successive time steps. The discrete equations then express that the quantity conserved in a cell at a given time step is equal to the quantity contained in the cell at the previous time step, increased by the flows of quantities entering the cell and reduced by the flows of quantities leaving the cell through its faces, plus external inputs. An example of such a basin simulator is the TemisFlow ™ software (IFP Énergies nouvelles, France).

[0054] Still according to an implementation of the invention according to which said numerical simulation is a basin simulation, it is also possible to reconstruct the past architectures of the basin beforehand for different states of the basin. To do this, the mesh representation constructed in the previous step, which represents the basin at the current time, is deformed in order to represent the anti-chronological evolution of the architecture of the subsoil over geological time, and this for the different states of the basin. At the end of this step, a mesh representation is available for each state. According to a first embodiment, the structural reconstruction can be particularly simple if it is based on the hypothesis that its deformation results solely from a combination of vertical movements by compaction of the sediment or by uplift or subsidence of its basement.This technique, known as "back stripping" (or "progressive decompaction of the basin" in French) is described for example in document

[11] . According to another embodiment, in the case of basins with a complex tectonic history, particularly in the case of basins with faults, it is appropriate to use techniques with less restrictive assumptions, such as structural restoration. Such structural restoration is described for example in document FR 2 930 350 A1 (US 2009 / 0265152 A1). Structural restoration consists of calculating the successive deformations that the basin has undergone, by integrating the deformations due to compaction and those resulting from tectonic forces.

[0055] Thus, at the end of this step, whatever the numerical simulation used, we obtain at least one mesh representation of the basin (in particular at the current level) for each of the combinations of the possible values ​​of the uncertain parameters. Each of the meshes of these mesh representations contains at least one value of the physical property of interest or property values ​​allowing the determination of a value of the property of interest (for example by linear combination of several property values ​​in the mesh considered). 4) Construction of an approximate analytical model of a spatial distribution of the physical property

[0056] In this step, a realization of a spatial distribution of the physical property of interest is determined for each of the meshed representations of the plurality of meshed representations, a principal component analysis is applied to the plurality of realizations of the spatial distribution of the physical property, and the components resulting from the principal component analysis whose sum of the associated eigenvalues ​​is greater than a predefined threshold are selected. Then, an approximate analytical model relating to the spatial distribution of the property is determined by constructing an approximate analytical model for each of the selected components.

[0057] According to one implementation of the invention, the production of a spatial distribution of the physical property of interest of a mesh representation may correspond to the distribution of the values ​​of the physical property of interest for at least a subset of the cells of the mesh representation, such as for example a column of cells in the mesh representation, a group of cells of the mesh representation corresponding to the same geological layer, or any other group of cells. It is clear that this step can also be applied to all the cells of the mesh representation, that is to say that the distribution of the values ​​of the physical property of interest is considered for all the cells of the mesh representation.

[0058] According to another implementation of the invention, the realization of a spatial distribution of the physical property of interest of a mesh representation can be determined from the values ​​of one or more physical properties of the mesh representation, such as for example from a linear combination of one or more physical properties.

[0059] Subsequently, we note y ( u , θ j ) the spatial distribution of the physical property y for the combination of uncertain parameters θ j , with j varying from 1 to n, and where u is the position of the mesh in the basin. We also note y ( D ) = ( y ( u , θ j )) j =1.. n the set of spatial distributions of the physical property y of interest for the experimental design D . This is the training set. Furthermore, we note Nthe number of meshes of the spatial distribution.

[0060] According to the invention, a principal component analysis (PCA) is applied to the plurality of realizations of the spatial distribution of the physical property of interest, obtained for each of the combinations of values ​​of the uncertain parameters. Generally speaking, a principal component analysis of a geostatistical variable consists of representing it in a basis formed from the eigenvectors of its covariance operator. A functional representation of the random field is thus obtained. From such an analysis, an approximation of the random field can be defined which represents a quantifiable part of the variance of the process while retaining only a limited number of components in this representation.

[0061] With the notations defined previously, the decomposition into principal components of spatial distributions y ( D ) can be written as follows: y u θ j = ∑ k = 1 M α k θ j ϕ k u Or ϕ k ( u ) are the basis vectors, equal to the eigenvectors of the covariance matrix, α k ( θ j ) are the projection coefficients on this basis, also called components, and M is such that M = min ( N, n ). In this decomposition, it is clear that the basis vectors are orthogonal and sorted in decreasing order of the associated eigenvalues, corresponding to the decreasing order of variance explained by these basis vectors (variance of the components according to each vector).

[0062] Advantageously, we can keep only the first m components of the base corresponding to a given minimal percentage of the total variance of the response y(usually at least 95%). This percentage is equal to the normalized sum of the corresponding eigenvalues. This generally allows the spatial distributions of the physical property to be satisfactorily reproduced y ( D ) while capturing most of the variance of this set. Equation (1) can then be modified as follows: y u θ j ≈ ∑ k = 1 m α k θ j ϕ k u

[0063] According to the invention, an approximate analytical model of the spatial distribution of the physical property of interest is then constructed, the approximate analytical model being a function of the uncertain parameters. An approximate analytical model, also called a meta-model or response surface, is a model that approximates the relationship between the input parameters of the simulation (in particular the uncertain parameters) and an output of this simulation or any other variable calculated from the outputs of the simulation.

[0064] According to one implementation of the invention, the meta-model ŷ of the physical property of interest can be written, for any combination of parameters θ (and not only for the plurality of combinations of uncertain parameters predefined in step 2) in the following manner: y ^ u θ = ∑ k = 1 m α ^ k θ ϕ k u Or â k ( θ ) represents the meta-model approximating the component α u ( θ ) , constructed from the values ​​calculated for this component on the training set y(D).

[0065] According to an implementation of the invention, a meta-model can be constructed that approximates a scalar variable of interest by means of polynomial regression, Gaussian process regression, or neural networks, or any similar method.

[0066] Thus, during this step, an approximate analytical model of the physical property of interest is constructed by constructing an approximate analytical model for each principal component selected according to a threshold on the variance as described above. In general, an approximate analytical model makes it possible to approach a large number of simulations at a lower cost, and therefore to be able to explore the space of uncertain parameters. 5) Improvement of the approximate analytical model of the spatial distribution of the physical property

[0067] This step is iterative, i.e. it can be repeated several times, as long as at least one stopping criterion is not satisfied. During this step, for a given iteration, the aim is to improve the approximate analytical model of the spatial distribution of the physical property of interest by applying a sequential planning method with adaptation in order to determine at least one additional combination of the possible values ​​of the uncertain parameters. By "improving the approximate analytical model" is meant improving its accuracy. Once an additional combination has been determined, steps 3) and 4) described above are reapplied to the new plurality of combinations of the values ​​of the uncertain parameters, formed by the plurality of combinations of values ​​of the uncertain parameters at the previous iteration and at least one additional combination of values ​​of the uncertain parameters determined at the current iteration.

[0068] In other words, during this step, we evaluate whether the approximate analytical model of the spatial distribution of the physical property of interest is satisfactory, and if this is not the case, we automatically add additional data to the training set in order to build a more accurate approximate analytical model, taking into account enriched data. An improved approximate analytical model makes it possible to predict the physical property of interest more accurately.

[0069] Generally speaking, a sequential planning method with adaptation enriches a given training set (and more specifically the set of combinations of values ​​of uncertain simulation parameters) by using both the definition of this set and the information provided by the meta-model built on this set.

[0070] Advantageously, if we use a Gaussian process regression method to build an approximate analytical model of a given scalar property, we can use a sequential planning method with adaptation based on different criteria, such as: maximum kriging variance (in English "Maximum Mean Squared Error" or MMSE, see document [5]), maximum kriging variance weighted by the cross-validation error (in English "Adjusted variance", see document [6]); integration of the kriging variance (in English "Integrated Mean Square Error" or IMSE, see document [7]), or hierarchical adaptive experimental designs (in English "Hierarchical adaptive experimental design", see document [8]).

[0071] According to the invention, a sequential planning method is applied with adaptation to the approximate analytical models of the components resulting from the decomposition into principal components, starting with the components associated with the largest eigenvalues. More precisely, at the first iteration, the component is identified α k associated with the largest eigenvalue whose meta-model α̂ k does not satisfy the target quality defined by a value of a precision indicator. Then we apply a sequential planning method to the meta-model α̂ k until the target quality is reached, iteration after iteration. We then move on to the next component in an additional iteration, and so on until a target quality is reached for all the meta-models of the components. The objective here is to primarily improve the prediction on the components corresponding to the highest variances of the response.

[0072] According to the invention, at least one stopping criterion is evaluated at each iteration.

[0073] According to an implementation of the invention, a stopping criterion relating to the precision of the approximate analytical model can be predefined, i.e. a precision beyond which it is no longer considered useful to improve the approximate analytical model.

[0074] According to a variant of this implementation of the invention, it is possible to define a precision indicator relating to the approximate analytical models of the components resulting from the principal component analysis at the current iteration.

[0075] According to an implementation of the invention, a precision indicator can be determined, noted Q2 , relating to an analytical model approximated by a component in the following manner: Q 2 = 1 − ∑ i = 1 n α θ i − α ^ − i θ i 2 ∑ i = 1 n α θ i − α ¯ 2 Or α̂ - i is the approximate analytical model obtained for α from the experimental plan D - i = ( θ j ) 1≤ j ≠ i ≤ n , And α̂ represents the average of the values α ( D ) . More precisely, this approach consists of using the so-called "leave-one-out" cross-validation technique (known by the acronym LOO-CV), in which we consider complementary meta-models obtained by ignoring one of the points in the training set, and calculating the error between the simulated value at this point and the value predicted by the meta-model. The prediction errors thus calculated are then grouped into a global indicator. The precision indicator Q 2 has a value all the closer to 1 as the error it quantifies is small.

[0076] According to another implementation of the invention, which can however be combined with the implementation described previously, it is also possible to estimate a precision indicator of an approximate analytical model of a component from an additional experimental plan, for example noted D test = ( θ ' j ) 1 ≤ j ≤ ntest , independent of the training set of the current iteration. We can then define a precision indicator, noted R2, as follows: R 2 = 1 − ∑ j = 1 ntest α θ ′ j − α ^ θ ′ j 2 ∑ j = 1 ntest α θ ′ j − α ¯ 2 Or α̂ is the meta-model obtained for α from the experimental plan D And α represents the average of the values α ( D test ).

[0077] According to an implementation of the invention, it is also possible to define a general stopping criterion for the iterative process, which may correspond to a threshold relating to the precision indicators Q2 and / or R2 associated with each or some of the components. Alternatively or cumulatively, it is also possible to define a stopping criterion in the form of a threshold relating to the average, over all the meshes of the spatial distribution, of the indicators Q2 and / or R2, and / or to their median, to their maximum or minimum value, etc. In a complementary manner, it is also possible to define a stopping criterion based on monitoring the evolution of such indicators during the iterations: for example, it may be concluded that adding additional combinations is no longer effective if a stagnation of the precision indicators is observed with the iterations.Finally, a predefined stopping criterion may consist of a maximum number of iterations of steps 3 to 5 of the method according to the invention, or even a maximum number of simulations carried out.

[0078] These criteria aim to ensure the efficiency of the method according to the invention, that is to say to automatically plan new simulations to be carried out and to avoid unnecessary simulations as far as possible. 6) Estimation of uncertainties associated with the spatial distribution of the physical property

[0079] In this step, based on the improved approximate analytical model obtained by applying the previous steps, uncertainties associated with the spatial distribution of the physical property are determined. Advantageously, uncertainties associated with the spatial distribution of the physical property are quantified by means of a sensitivity analysis and / or a risk analysis.

[0080] According to an implementation of the invention, from the improved approximate analytical model, a sensitivity analysis can be carried out relating to the spatial distribution of the physical property of interest. In general, a sensitivity analysis makes it possible to analyze the impact of the uncertainty of each parameter on the simulator responses. Such a technique is for example described in document [2].

[0081] According to an implementation of the invention, from the improved approximate analytical model, a global sensitivity analysis based on the variance can be carried out, for example according to the Sobol index method, described for example in document

[12] . To do this, a large sample of the space of uncertain parameters is generated, the corresponding realizations of the spatial distribution of the property of interest are estimated using the improved approximate analytical model, and the share of the variance of the property of interest due to the variability of each parameter alone (main effect) or in interaction with other parameters is quantified in each cell of this spatial distribution. This gives the influence of each parameter in each cell of the spatial distribution of the property of interest.

[0082] Alternatively or cumulatively, from the improved approximate analytical model, a risk analysis can be performed on the spatial distribution of the physical property of interest. For example, a large sample of the uncertain parameters can be generated (Monte Carlo type) and the corresponding realizations of the spatial distribution of the property of interest can be estimated using the improved approximate analytical model. This provides a large sample of the property of interest in each grid cell of the spatial distribution that can be analyzed. For example, percentiles for this property can be calculated, or the probability that the physical property in this grid cell is in a given target interval can be estimated. This gives a spatial distribution of percentiles or probabilities of occurrence (see for example document [2]). 7) Exploitation of hydrocarbons in the basin

[0083] This optional step is to be implemented, at the end of the previous steps, in the case of the method according to the second aspect of the invention, which consists of a method for exploiting hydrocarbons from a sedimentary basin.

[0084] At the end of the implementation of the previous steps, we have at least one precise approximate analytical model of at least one physical property of interest in the sedimentary basin and an estimate of the uncertainties associated with at least this physical property of interest.

[0085] An accurate analytical model of at least one physical property of interest is advantageous for quickly estimating the petroleum potential of the basin. In particular, it can be used to estimate probabilities of occurrence of events related to the basin properties, characterized by the joint presence of several properties in target intervals. In particular, it can be used to estimate a probability of presence of the desired resources, such as an accumulation of hydrocarbons. For example, a probability map of the presence of a reservoir can be estimated, defined by the probability in each column of the basin that the thickness of deposited sediments and the sand concentration are greater than a certain threshold. These probabilities can be integrated into the decision-making process regarding the drilling of new exploration wells, which will provide data to enrich the basin model.Thus, based on such analyses, a reservoir can be identified in the basin, and at least one exploitation scheme for the hydrocarbons contained in the sedimentary basin studied can be determined.

[0086] According to one implementation of the invention, from at least the uncertainties associated with the spatial distribution of the physical property, it is possible to identify a potential reservoir in the basin, and at least one exploitation scheme for the hydrocarbons contained in the sedimentary basin studied can be determined.

[0087] Generally speaking, an exploitation scheme includes a number, geometry and location (position and spacing) of the injection and production wells to be drilled in the basin. An exploitation scheme may also include a type of enhanced recovery of the hydrocarbons contained in the reservoir(s) of the basin, such as enhanced recovery by means of the injection of a solution comprising one or more polymers, CO2 foam, etc. An exploitation scheme for a hydrocarbon reservoir in a basin must, for example, allow a high recovery rate of the hydrocarbons trapped in this reservoir, over a long exploitation period, and requiring a limited number of wells. In other words, the specialist predefines evaluation criteria according to which a hydrocarbon exploitation scheme for a sedimentary basin is considered sufficiently efficient to be implemented.

[0088] According to one embodiment of the invention, a plurality of exploitation schemes for the hydrocarbons contained in one or more geological reservoirs of the basin studied can be defined and at least one evaluation criterion for these exploitation schemes is estimated using a reservoir simulator (such as the PUMA FLOW ® software (IFP Energies nouvelles, France)). These evaluation criteria can include the quantity of hydrocarbons produced for each of the different exploitation schemes, the curve representing the evolution of production over time at each of the wells considered, the oil-to-gas ratio (GOR) at each well considered, etc. The scheme according to which the hydrocarbons contained in the reservoir(s) of the basin studied are actually exploited can then correspond to that satisfying at least one of the evaluation criteria for the different exploitation schemes.Note that the definition of the plurality of operating diagrams to be tested can itself be determined automatically, for example using the COUGAR FLOW ® software (IFP Energies nouvelles, France).

[0089] Then, once an exploitation scheme has been determined, the hydrocarbons trapped in the oil reservoir(s) of the sedimentary basin studied are exploited according to this exploitation scheme, in particular at least by drilling the injection and production wells of the exploitation scheme thus determined, and by installing the production infrastructures necessary for the development of this or these reservoirs. In the case where the exploitation scheme has also been determined by estimating the production of a reservoir associated with different types of enhanced recovery, the selected type(s) of additives (polymers, surfactants, CO2 foam) are injected into the injection well.

[0090] It is understood that a hydrocarbon exploitation plan for a basin may evolve over the duration of the exploitation of the hydrocarbons in this basin, depending for example on additional knowledge relating to the basin acquired during this exploitation, improvements in the different technical fields occurring during the exploitation of a hydrocarbon deposit (improvements in the field of drilling, assisted recovery for example).

[0091] As an alternative to hydrocarbon recovery, the process steps can also be implemented as part of a geothermal process, underground energy storage, or underground gas storage.

[0092] For these applications, following the implementation of the previous steps, we have at least one precise approximate analytical model of at least one physical property of interest in the sedimentary basin and an estimate of the uncertainties associated with at least this physical property of interest.

[0093] An accurate analytical model of at least one physical property of interest is advantageous for quickly estimating the potential for geothermal energy, or for underground storage of gas or energy (e.g. compressed gas). Computer equipment and program product

[0094] The method according to the invention is implemented by means of equipment (for example a computer workstation) comprising data processing means (a processor) and data storage means (a memory, in particular a hard disk), as well as an input and output interface for entering data and restoring the results of the method.

[0095] The data processing means are configured to carry out in particular steps 2 to 6 described above.

[0096] Furthermore, the invention relates to a computer program product downloadable from a communication network and / or recorded on a computer-readable medium and / or executable by a processor, comprising program code instructions for implementing the method as described above, when said program is executed on a computer. Examples

[0097] The characteristics and advantages of the method according to the invention will appear more clearly on reading the application example below.

[0098] For this application example, we consider a sedimentary basin in a passive margin context. This margin is characterized by a supply of sediments composed of sand and clay at a point located to the west of the margin at the time of its formation. The numerical simulation according to the invention is a stratigraphic simulation and the physical property of interest is the total thickness of sediments deposited in each column of the stratigraphic model.

[0099] The 9 uncertain parameters considered are linked to the different processes involved in the formation of the sedimentary basin: accommodation, sediment supply and transport. They are associated with a uniform distribution law in a given interval.

[0100] The method according to the invention is then applied to the total thickness of sediments deposited in each column of the mesh representation. The physical property of interest is therefore the total thickness of sediments deposited in each column of the mesh representation. More precisely, for this example, the spatial distribution of interest is a map of size 1000km X 1000km in a horizontal plane, discretized into a mesh of 100 X 100 cells. We consider an initial LHS type experimental design of 20 combinations of the possible values ​​of the uncertain simulation parameters to which we add at each iteration one (case 1) or five (case 2) new combinations of the possible values ​​of the uncertain simulation parameters. The meta-models approximating the components are built by Gaussian processes, and the addition of combinations is done according to the maximum kriging variance method.Principal component analysis leads to retaining 4 components (noted Comp1, Comp2, Comp3, Comp4) corresponding to 95% of the variance.

[0101] The stopping criteria considered are: value of the precision indicator Q2 (as defined in section 5) greater than 0.95 for the meta-models of the components; value of the median R2 coefficient (as defined in section 5) over the area of ​​interest for the total thickness of sediments greater than 0.95; two stagnation criteria as iterations progress for the median R2 coefficient over the area of ​​interest for the total thickness of sediments;

[0102] In addition, a maximum number of simulations is set at 98.

[0103] The implementation of the method according to the invention is repeated for 5 different initial experimental designs Exp1, Exp2, Exp3, Exp4, Exp5. The quality of the predictions is estimated using an independent set of 50 points.

[0104] There figure 1 illustrates the evolution of the precision indicator Q2 for the 4 components Comp1, Comp2, Comp3, Comp4 as a function of the number of NS simulations, in case 1 (left figure) and in case 2 (right figure) and for the first experimental design Exp1. The figure 2 illustrates the evolution of the median R2 precision indicator on the spatial distribution of the total sediment thickness for the 5 different experimental designs Exp1, Exp2, Exp3, Exp4, and Exp5, with the addition of 1 combination per iteration (case 1), at least one of the stopping criteria relating to this indicator being satisfied after approximately 58 simulations (see the delimitation between the portions of curves "<CRIT" et "> CRIT"). The figure 3illustrates the distribution of the values ​​of the precision indicator R2 for the total thickness of sediments in each mesh (in total 100x100 meshes) of the spatial distribution considered for the 5 experimental designs Exp1, Exp2, Exp3, Exp4, Exp5 with addition of 1 point per iteration (case 1), for the training set (column "APP" on the left), until satisfying at least one of the predefined stopping criteria (column "<CRIT" du milieu), et en poursuivant les itérations jusqu'à atteindre 98 simulations (colonne "> CRIT" on the right).

[0105] We can observe on the figure 1 that the method of iterative point additions according to the invention makes it possible to generally increase the quality of the prediction of the approximate analytical models for the different components. In addition, it can be observed that adding 5 points simultaneously during an iteration does not degrade the results. It can also be observed on the figure 2that this improvement is also accompanied by an overall increase in the median R2 indicator. Finally, we can observe on the figure 3 that the stopping criteria relating to the precision indicators (criteria 2 and 3 above) are satisfactory. Indeed, the value of the coefficient R2 in the meshes is generally satisfactory once one of these criteria is reached, and increases only very little if the iterations continue.

Claims

1. Method for determining uncertainties relating to at least one physical property of a sedimentary basin, by means of a numerical simulation executed based on simulation parameters, said numerical simulation being a computer-executed stratigraphic simulation or basin simulation, said physical property of the basin being selected from the thickness of a stratigraphic unit, sand concentration, clay concentration in a stratigraphic unit, temperature, pressure, porosity, density, saturation, and concentration of the rock in respect of organic matter, said stratigraphic simulation simulating the evolution of a sedimentary basin over geological time in order in particular to quantify the geometry of the sedimentary layers, the type of sediments deposited, and the water depth at the time of deposition, and said basin simulation simulating, over geological time, the formation of hydrocarbons in particular from organic matter initially buried with the sediments, and the transport of these hydrocarbons from the rocks in which they were formed to those in which they are trapped, wherein at least the following steps are carried out: A) measurements of physical quantities relating to said basin are carried out by means of sensors, and at least values of said simulation parameters are determined, said simulation parameters being selected from the initial bathymetry, the inflows of sediments, their transport for each time increment and petrophysical properties associated with the studied basin; B) uncertain simulation parameters are selected, and a plurality of combinations of possible values of said uncertain simulation parameters are defined; C) a plurality of mesh representations of said basin are determined by means of said numerical simulation, each of said mesh representations being obtained for one of said combinations of said plurality of combinations of possible values of said uncertain parameters, each of the mesh cells of one of said mesh representations having at least one value allowing said property to be determined; and wherein, for at least one of said physical properties of said sedimentary basin, at least the following steps are carried out: D) for each of said mesh representations, a realization of a spatial distribution of said property is determined, a principal component analysis is applied to the plurality of realizations of said spatial distribution of said property, said components the sum of the associated eigenvalues of which is greater than a predefined threshold are selected, and an approximate analytical model of said spatial distribution of said property is determined by constructing an approximate analytical model for each of said selected components; E) as long as a stop criterion is not met, the accuracy of said approximate analytical model of said spatial distribution of said property is improved iteratively by determining, in each iteration, at least one additional combination of said plurality of combinations of possible values of said uncertain parameters by means of an adaptive sequential planning method, said adaptive sequential planning method being applied to said approximate analytical models of said selected components, the components being considered in descending order of their eigenvalues until a value of an accuracy indicator relating at least to said component considered in the current iteration is reached, steps C) and D) being repeated; and wherein, based on said improved approximate analytical model of said spatial distribution of said at least one physical property, said uncertainties relating to at least said spatial distribution of said property of said sedimentary basin model are determined.

2. Method according to Claim 1, wherein said at least one stop criterion is dependent on at least one indicator of the accuracy on said approximate analytical models of said components.

3. Method according to either of the preceding claims, wherein an approximate analytical model is determined by means of a Gaussian process regression.

4. Method according to any of the preceding claims, wherein said adaptive sequential planning method is selected from the following list: a method for estimating MMSE (MMSE standing for Maximum Mean Squared Error), a method for estimating adjusted variance, an IMSE-based method (IMSE standing for Integrated Mean Square Error), and hierarchical experimental design.

5. Method according to any of the preceding claims, wherein, in the case of a plurality of physical properties of said basin, steps C) to E) are applied for each of said physical properties of said basin.

6. Computer program product that is downloadable from a communication network and / or recorded on a medium that is readable by computer and / or executable by a processor, comprising program code instructions for implementing the method according to any of the preceding claims, when said program is executed on a computer.

7. Method for extracting hydrocarbons present in a sedimentary basin, said method comprising at least implementing the method for determining uncertainties relating to at least one physical property of a sedimentary basin according to any of Claims 1 to 5, and wherein, on the basis at least of said improved approximate analytical model and / or said uncertainties relating to at least said physical property, an extraction scheme is determined for said basin, said extraction scheme comprising at least a placement of at least one injection well and / or at least one production well, and said hydrocarbons of said basin are extracted at least by drilling said wells of said placement and equipping them with extraction infrastructures.