A method for building a reservoir model according to a sequence of geological events

Abstract

It is disclosed a method and device for building a model of a geological reservoir from a predetermined geological calendar, the method comprising: - defining a plurality of computer models (Mi) representing respectively a plurality of formation states of the reservoir, wherein the respective computer models comprise at least: o a last model in chronological order, corresponding to a present-day deformation state of the reservoir, and o a first model in chronological order, corresponding to an earlier deformation state of the reservoir, o at least one transient model, corresponding to an intermediate formation state of the reservoir, and - simulating the formation of the reservoir, comprising: o performing numerical simulation, in a computer model a period of time, of all geological events occurring within the period of time, to generate numerical simulation outputs, and o integrating the simulation outputs in the computer-model associated to the period of time ti+1.

Description

[0001] A METHOD FOR BUILDING A RESERVOIR MODEL ACCORDING TO A SEQUENCE OF GEOLOGICAL EVENTS

[0002] TECHNICAL FIELD

[0003] The present disclosure relates to the field of geological modelling, in particular to a computer-implemented method for building a model of a geological reservoir according to a present-day state and in accordance with a determined geological calendar of the formation of the reservoir. The disclosure finds notable applications in the field of Carbon Capture and Storage (CCS) and / or hydrocarbon production.

[0004] BACKGROUND OF THE INVENTION

[0005] In the study of underground geological formations, and in a perspective of exploiting the geological formations for managing resources (e.g. extracting resources such as hydrocarbon production, or storing Carbon Dioxide or water), it is necessary to have good knowledge of the geometry of the sedimentary structures and distribution of the geological and petrophysical properties of the underground. These properties enable for instance to better determine the geometry of a geological formation, for instance an oil or gas reservoir, estimate the quantity and distribution of resources stored therein, or the volume of carbon that could be stored in depleted oil and gas reservoirs, saline formations or the like.

[0006] In order to characterize a geological formation, it is well known to acquire on-site data for instance by campaigns or seismic reflections and / or by drilling exploration wells. This on-site data however only provides reduced, local, hindsight about the configuration of the reservoir, the geometry of horizons and the distribution of geological and / or petrophysical properties over the whole domain of interest.

[0007] Accordingly, according to standard geostatistical approaches, it is known to build a structural model of a reservoir, comprising a set of geological surfaces comprising horizons, corresponding to iso-chronological surfaces that are determined from the on-site data, and faults, which are also observable on-site.

[0008] Based on the structural model, a three-dimensional mesh is then built which conforms to the horizons and faults, and which is then populated by geological and / or petrophysical parameters, according to geostatistical algorithms. The geostatistical algorithms enable filling the mesh from the sparsely acquired, on-site data. An important downside of these approaches is that the result is obtained without taking into account the complexity of geological phenomena having occurred successively during the formation of the reservoir. Hence the result is not necessarily related to geological chronology. Indeed, apart from the main horizons which are present in the structural model, and which are associated to relative, and sometimes absolute geological times, there is no relationship, in the obtained model, between a cell and an age corresponding to that cell. As a consequence, the geological phenomena leading to the formation of the reservoir in its present-day state, and the causality between these phenomena, are ignored. It results in possible inconsistencies between the model and the corresponding existing structures, as well as errors in the geological and petrophysical parameters which populate the model, and hence errors in the determination of the reservoir’s properties.

[0009] DESCRIPTION OF THE INVENTION

[0010] The present disclosure aims at improving the prior art.

[0011] In particular, an aim of the present disclosure is enabling to build models of a reservoir having increased accuracy, in particular having increased consistency with the succession of geological events having led to the present-day, observable state of the reservoir.

[0012] Another aim of the invention is to enable better prediction of petrophysical properties of a reservoir.

[0013] To this end, a method for building a model of a geological reservoir according to a present-day state of the reservoir, from a predetermined geological calendar of the formation of the reservoir, is disclosed, wherein the geological calendar covers a determined period of time T and comprises a sequence of geological events occurring within said determined period of time, each geological event being associated to a geological time within the determined period of time T, the method being implemented by a computer and comprising: defining a plurality of computer models representing respectively a plurality of formation states of the reservoir, where each computer model is associated to a subperiod of time tj within the period of time T, wherein the respective computer models comprise at least: o a last model in chronological order, corresponding to a present-day deformation state of the reservoir, and o a first model in chronological order, corresponding to an earlier deformation state of the reservoir, o at least one transient model, corresponding to an intermediate formation state of the reservoir, and simulating formation of the reservoir, comprising, for each subperiod of time tj within the period of time T, considered in chronological order: o performing numerical simulation, in the computer model corresponding to the subperiod of time tj, of all geological events occurring within the subperiod of time, to generate numerical simulation outputs, and o integrating the simulation outputs in the computer-model associated to the next subperiod of time tj+i.

[0014] In embodiments, numerical simulation outputs comprise at least one of: geological parameters, mechanical parameters, petrophysical parameters, discrete flow drivers, structural elements.

[0015] In embodiments, performing numerical simulation of geological events in a computer model comprises performing numerical simulation of a sequence of geological events chronologically in accordance to the respective geological time of each geological event, wherein the numerical simulation of each geological event generates respective numerical simulation outputs which are integrated in the computer model for the numerical simulation of the next geological event.

[0016] In embodiments, the computer models comprise at least one common horizon, corresponding to a iso-chronological surface, and said at least one common horizon exhibits different folding configurations in computer models associated to at least two different subperiods of time.

[0017] In embodiments, the computer models comprise at least one common fault, separating areas of the reservoir in relative displacement with respect to each other, and wherein the slip between the areas separated by the faults has at least two different values in computer models associated to at least two different subperiods of time. In embodiments, the geological events comprise sedimentation events, performing numerical simulation of a sedimentation event comprises generating, on an iso- chronological surface of a computer model, a plurality of horizons, and the outputs of numerical simulation of a sedimentation event comprise said additional horizons.

[0018] In embodiments, the geological events comprise fracturation events, performing numerical simulation of a fracturation event comprises generating, in a computer model, at least one fault, and the outputs of numerical simulation of a fracturation event comprise said at least one fault.

[0019] In embodiments, the geological events comprise diagenetic events, performing numerical simulation of a diagenetic event comprises generating or modifying properties of at least one conduit or fault in a computer model, and the outputs of numerical simulation of a diagenetic event comprises said generated conduit or fault or said modified properties of a conduit or fault.

[0020] In embodiments, the method further comprises a preliminary step of computing, for each computer model, a respective parametric representation, in which an horizon is represented by a constant value of time, and computing a mapping between the parametric representations, and wherein integrating the simulation outputs of a numerical simulation performed in a computer-model associated to a first subperiod of time in a computer-model corresponding to a next subperiod of time comprises: determining coordinates of points of the first computer model in the corresponding parametric representation,

[0021] Inducing, from the mapping between the parametric representations, coordinates of equivalent points in the parametric representation associated to the next subperiod of time, and

[0022] Inferring the coordinates of equivalent points in the model corresponding to the next subperiod of time.

[0023] In embodiments, the computer models corresponding to earlier states of deformation of the reservoir, as compared to the present-day state, are obtained from the computer model corresponding to the present-day state by implementation of a well restoration algorithm. In embodiments, defining the computer models comprises receiving ground data relative to the reservoir, and defining the computer model corresponding to the present-day deformation state of the reservoir from the received ground data.

[0024] According to another object, a computer program product is disclosed, having stored thereon code instructions for implementing the method according to the description above, when it is executed by a computer.

[0025] According to another object, it is disclosed a computer configured for implementing the method according to the description above.

[0026] The disclosed method enables building a model corresponding to a present-day state of a reservoir, according to a determined sequence of events that led to the present- day, observable state of the reservoir. This method comprises defining a plurality of models of the same reservoir at different stages of formation, and simulating the determined sequence of geological events where each geological event is simulated in the model corresponding to the geological time of occurrence of said event, and the outputs of the simulation of the geological event are added as inputs in the model corresponding to the next stage of formation of the reservoir.

[0027] Accordingly, the succession of geological events and the consequences of each event on the next may be respected. For instance, when a fault occurs before a sedimentation event, then the fault only extends between the layers of rock formed before the sedimentation event. According to another example, deformation of the Earth crust may alter the relative disposition of sedimentary layers.

[0028] BRIEF DESCRIPTION OF THE DRAWINGS

[0029] The present disclosure is illustrated by way of example, and not by way of limitation, in the figures of the accompanying drawings, in which like reference numerals reference to similar elements and in which:

[0030] Figure 1 is a flow chart schematically describing the main steps of a method for building a model of a reservoir.

[0031] Figure 2 represents an example of an excerpt of a geological calendar including a succession of geological events having occurred during the formation of a reservoir, Figure 3 represents an example of a set of structural models Mj corresponding to different stages of formation of a reservoir,

[0032] Figure 4 schematically represents an embodiment of integrating outputs of a geological event simulated in a model corresponding to a deformation state of a reservoir into a model corresponding to a next deformation state.

[0033] Figure 5 is extracted from [Mallet, 2004] and represents a (u,v,t) parametrization performed by the Geochron™ model.

[0034] Figures 6a to 6c represents the normalized values of the u, v and t coordinates of the structural models, respectively for three models corresponding to different stages of formation of a reservoir.

[0035] Figure 6 schematically represents an exemplary method for implementing the transition from one model to a next,

[0036] Figure 7 schematically represents an exemplary device for implementing the method.

[0037] DETAILED DESCRIPTION OF AT LEAST AN EMBODIMENT

[0038] With reference to the attached drawings, a method for building a model of a geological reservoir according to a present-day state will now be described.

[0039] With reference to figure 8, this method may be implemented by a device 10 comprising a computer, this computer comprising a memory 15 to store program instructions loadable into a circuit and adapted to cause circuit 14 to carry out the steps of the present invention when the program instructions are run by the circuit 14. The memory 15 may also store data and useful information for carrying the steps of the present invention as described above.

[0040] The circuit 14 may be for instance: a processor or a processing unit adapted to interpret instructions in a computer language, the processor or the processing unit may comprise, may be associated with or be attached to a memory comprising the instructions, or the association of a processor I processing unit and a memory, the processor or the processing unit adapted to interpret instructions in a computer language, the memory comprising said instructions, or an electronic card wherein the steps of the invention are described within silicon, or a programmable electronic chip such as a FPGA chip (for « Field- Programmable Gate Array »).

[0041] This computer comprises an input interface 13 for the reception of several data used for the above method according to the invention, for instance a geological calendar of the formation of a reservoir, an initial structural model of the reservoir, parameters involved in simulating geological events, such as parameters involved in simulating sedimentation, fracturation or diagenetic events, ground data relative to the actual reservoir, for comparison with the obtained model, etc. This computer also comprises an output interface 16 for outputting the reservoir model, for example for transmitting the model to another computing device, or a storage device, via a telecommunication network or using a connector for plugging an output device such as a disk drive, a memory card, a USB flash drive, etc.

[0042] The computer may also include a display 11 for displaying a three-dimensional representation of the model, or any data derived therefrom, such as for instance a 2D representation of a stratigraphic column, etc.

[0043] To ease the interaction with the computer, the device may also comprise human input means such as a keyboard 12, mouse, and / or a tactile screen which are connected to the computer circuit 14. The various components described above may be remotely connected to one another, i.e. the memory storing the data and / or the circuit implementing the method may be remotely located with reference to the user and accessible through any suitable network.

[0044] A geological reservoir is a subsurface rock formation enabling the accumulation and storage of oil, natural gas, water or other types of resources. Modelling a geological reservoir may be performed in order to determine key features of the actual reservoir, such as its geometry, its petrophysical properties, including porosity and permeability, and perform simulation of fluid flows within the reservoir, in view of assessing the potential for resource extraction from the reservoir, or storage in the reservoir (such as carbon dioxide).

[0045] As known to the skilled person, the formation of a geological reservoir is a phenomenon extending over millions of years, during which a succession of geological events may occur, including events of sedimentation, diagenesis, erosion, deformation, faulting, etc. Considering the very long time-scales of these phenomena, the structure of a reservoir is considered constant during periods of time ranging from at least 100 years to several thousand years. Therefore, the notion of “present-day state” of a geological reservoir refers to the geological structure of the reservoir that is observable by Man in modern times and that may be analyzed with a view to operating that reservoir. In particular, the present-day state of a geological reservoir relates to a state that can be at least partly described by collecting ground data, and performing fluid flow computations in order to simulate the actual behavior of the reservoir, if the latter was exploited. The ground data that may be collected by the reservoir include data collectable either by observation of the geological formation (configuration of faults, dips etc.), by performing seismic acquisition campaigns, or by drilling exploration wells and extracting rock core samples enabling the establishment of stratigraphic logs.

[0046] The method disclosed herein enables building a model of a reservoir according to a present-day state, and in accordance with a geological calendar of the formation of the reservoir.

[0047] With reference to figure 2 is shown an example of an excerpt of a geological calendar of the formation of a reservoir that may be used within the scope of the present disclosure.

[0048] A geological calendar is a timeline that extends far beyond human history, and is used to represent the major events in Earth’s evolution. A geological calendar typically divides Earth’s history into several eons, which are further subdivided into eras, period, epochs and ages. The most recent eon, the Phanerozoic, is the one in which complex life forms, including humans, have evolved. It is divided into the Paleozoic, Mesozoic and Cenozoic eras which in turn, are further divided into periods. For instance, the Mesozoic era is divided into the Cretaceous, Jurassic and Triassic periods, which are further divided into epochs and ages. The exemplary excerpt of figure 2 shows some ages from the end of the Jurassic era to the Cenozoic era (i.e. from 134 million years to 5 million years ago). These various divisions of Earth’s history, namely eons, eras, periods, epochs and ages, are further associated to respective geological times defining the beginning and the end of each division.

[0049] Within the context of the present disclosure, the geological calendar of the formation of the reservoir further comprises a plurality of successive geological events believed to have occurred during the formation of the reservoir and having contributed to shaping the reservoir according to its present-day state. The geological events are sequenced according to a determined chronology. In particular, each geological event may be associated to at least one geological time, at which the even occurred, or started. In embodiments, the geological events are associated to a duration determined by two successive geological times, or they may be associated to at least one determined age or epoch of the geological calendar. The sequence of successive geological events is comprised within a period of time T covered by the geological calendar.

[0050] In the example of figure 2, one sedimentation event is represented, extending over the Barremian age, between 128 and 126 million years before present. Also three fracturing events are represented, one during the Upper Aptian age (between 65 and 121 million years before present), one at 33 million years before present and the last at 20.5 million years before present. Last, two diagenesis event are shown, having occurred over the Upper Aptian age and the Oligocene.

[0051] The geological calendar of the formation of a reservoir, and in particular the sequence of geological events, may be defined by geologists from the study of the actual reservoir, ground data derived therefrom, and the knowledge of the geological history of the region within which is formed the reservoir.

[0052] With reference to figures 1 and 3, the method for forming a model of the present-day state of a reservoir comprises a step 100 of defining a plurality of computer models Mj, i=1..P, where P is a natural number superior or equal to 3, representing respectively different formation stages of the reservoir, where each computer model is associated to a subperiod of time tj, i=1..P, within the period of time T covered by the geological calendar of formation of the reservoir. The number P of computer models and the duration of their associated subperiods of time is determined such that the sum of the subperiods of time is equal to T, and such that two subperiods of time associated with two models do not overlap.

[0053] The computer models generated at step 100 may be structural models of the reservoir. A structural model is a numerical representation of the three-dimensional arrangement of rock structures forming the reservoir, which is defined at least by a boundary volume Vi, and a plurality of surfaces extending within said volume and partitioning the volume into a plurality of areas. The plurality of surfaces may include one or more horizons H, where each horizon is an iso-chronological surface associated to a determined geological time. In the present-day state, the one or more horizons of the structural model may be faulted or tilted due to tectonic forces or other geological processes.

[0054] The plurality of surfaces may also include one or more major faults F extending transversely to one or more horizons. A major fault separates two areas of the reservoir which are thus enabled a relative displacement called slip.

[0055] In embodiments, the structural models Mj generated at step 100 represent the evolution over time of a same sedimentary deposit, until reaching its present-day configuration.

[0056] Each model may be defined by the following parameters, which may vary from one model to another:

[0057] Number of horizons, and hence of layers of sediments between consecutive horizons,

[0058] Shape of each horizon (including folding or tilting of the horizons)

[0059] Slip of each major fault.

[0060] With reference to figure 3, the computer models generated at step 100 include at least:

[0061] A last model MP, in chronological order, corresponding to a present-day, observable state of the reservoir,

[0062] A first model Mi, in chronological order, corresponding to an earlier state of formation of the reservoir, which may in particular be a state prior to deformations and apparitions of faults present in the present-day state of the reservoir, and

[0063] At least one transient model Mj, 1 < i < P, corresponding to at least one intermediate formation state of the reservoir, between the first model and the last model.

[0064] The last model MP, corresponding to a present-day state of the reservoir, may include a plurality of horizons, with a deformation state that has been observed on-site. It may also include a plurality of faults and a slip between areas of the reservoir separated by a major fault; where the slip may also have been observed on site or deduced from on-site data. Said last model MP can be defined from ground data, which can notably include, or be derived from, campaigns of seismic reflections, in-situ observations of geologists, satellite or aerial images, or wellbore data, including well logs, cores and plugs.

[0065] The first model Mi, corresponding to a pre-deformation state of the reservoir is a model wherein some or all faults may have been removed, and their slip has been reduced or brought to zero and / or the deformations of the horizons may have been partially or totally removed. In embodiments, the horizons, in this model, are horizontal and the slip of all faults present in the last model MP is brought to zero. In addition, the first model MO may include less horizons than the subsequent models.

[0066] The at least one transient model corresponding to an intermediate formation state of the reservoir is different from the model Mi and the model MP, in at least:

[0067] The number and / or shape of the horizons, and / or

[0068] The slip of each fault.

[0069] In particular, at least one transient model may comprise a common fault with the last model MP, with a slip of said fault that may be reduced or brought to zero in the transient model.

[0070] The initial model and the transient models may be derived from the final model by one or more of the following changes: removing or reducing the slip of at least one fault, and / or reducing the number of horizons and / or reducing a deformation of horizons of the model corresponding to the present- day state.

[0071] This may be performed by implementing a so-called restoration algorithm, known to the skilled person. For instance, one can refer to EP2880465.

[0072] Last, the number of structural models, and their respective configurations, may be defined such that the general structure of the reservoir, namely the configuration of the horizons and the slip of the major faults, is considered to be sensibly stationary over the period of time tj associated to a model Mj.

[0073] According to the non-limiting example represented in figure 3, a set of four successive models is defined, where M4 represents a present-day state of a reservoir, and M3 to Mi represent successive restored stages of the reservoir at earlier geological times, with progressive unfolding of the layers of rocks and removal of the horizons deposited last.

[0074] Each structural model Mj of the reservoir is a three-dimensional model defined in a Cartesian space, where any point of the model can be defined by three coordinates (x,y,z), where x and y may be coordinates on perpendicular axes corresponding to a horizontal plane, and z may be a coordinate on a vertical axis.

[0075] With reference to figure 3, the structural models of the reservoir comprise a plurality of control points CPk, corresponding to geological features of the reservoir that are identical across at least two different models, even though they may not have the same coordinates (x,y,z), for instance due to a deformation of the reservoir. In other words, control points correspond to identical sediments, which position can be tracked across a plurality of structural models even though it is not constant. The control points may be identified by their position with respect to stratigraphy and to faults.

[0076] Back to figure 1 , the method further comprises simulating 300 the formation of the reservoir according to the geological calendar of formation of the reservoir. This comprises, for each subperiod of time tj within the period of time T covered by the geological calendar, considered in chronological order, i.e. starting from the earliest subperiod of time:

[0077] Performing 310 a numerical simulation, in the computer model Mj associated to said subperiod of time, of all geological events defined in the geological calendar and occurring within said subperiod of time, to generate numerical simulation outputs, and

[0078] Integrating 320 said simulation outputs in the computer model Mj+i associated to the next subperiod of time.

[0079] In embodiments, the subperiod of time tj associated to a computer model Mj may cover a plurality of geological events. With reference to figure 2, is shown an example wherein four computer models are defined: a first model Mi corresponding to a subperiod of time ti during which a sedimentation event Sed 1 occurs, thus a sedimentation event is simulated in the model Mi then a first transient model M2, in which are simulated a sequence of events comprising a fracturation event Frad and a diagenesis event D1 , a second transient model M3, in which is simulated a sequence of events comprising a fracturation event Frac2 and a diagenesis event D2, and, a last model M4, in which is simulated a third fracturing event Frac 3.

[0080] When a plurality of geological events are simulated in a same computer model Mi, corresponding to a sub-period of time ti, a numerical simulation of the sequence of geological events is performed chronologically in accordance with the respective geological time of each geological event, and the simulation outputs of each event are integrated in the model Mj before simulating the next event.

[0081] In embodiments, step 300 comprises simulating at least one geological event per model Mj, except for the present-day state model MP which may only receive the outputs of the events simulated in the previous models.

[0082] The outputs of the numerical simulation of geological events may comprise at least one among the following:

[0083] Deformation of the model, resulting in updated positions of a plurality of points of the model,

[0084] New or changed mechanical parameters,

[0085] New or changed geological parameters

[0086] New or changed petrophysical parameters,

[0087] New structural elements, including additional faults or horizons absent from the considered computer model before performing the numerical simulation, New or changed discrete flow drivers, such as karstic conduits or fractures.

[0088] The geological events that may be simulated within a computer model may comprise at least one of: a sedimentation event, an erosive event, a tectonic event, or a diagenetic event, such as dissolution.

[0089] In particular, simulating a sedimentation event may comprise simulating the formation, on a considered iso-chronological surface of the considered computer model, of a plurality of layers of sediments, where each layer of sediments represents a quantity of sediments deposited over a determined period of sedimentation.

[0090] The iso-chronological surface on which are deposited the layers of sediments may be a horizon of the model. Alternatively, it may be another iso-chronological surface, which geological time may be inferred from the geological time associated to a neighboring horizon by considering a hypothesis of linearity of the thickness of the rock with time. The surface defined between two consecutive layers of sediments corresponds to an additional horizon generated in the model.

[0091] In embodiments, the layers of sediments that are deposited during the sedimentation simulation may be partitioned into a plurality of cells, and the sedimentation simulation further enables assigning geological parameters to each cell, such that the mineral type and granulometric distribution of the elements deposited in each cell, and / or petrophysical parameters such as interparticular porosity or permeability. The skilled person may refer for instance to the patent applications WO2020 / 229863 or WO2020 / 229866 filed by the applicant, for a method for performing simulation of sedimentation, and to the patent application PCT / IB2023 / 000437 also filed by the applicant, for a method for performing simulation of sedimentation followed by computation of petrophysical parameters.

[0092] Diagenesis relates to the physical and chemical changes in sediments caused by water-rock interactions, microbial activity and compaction after deposition of the sediments. Diagenetic events can thus include compaction, cementation, dissolution, and others.

[0093] Depending on the type of diagenetic event that is simulated, the simulation of a diagenetic event may lead to:

[0094] A mineralogic change of a cell of the model, leading to a change in petrophysical parameters,

[0095] A geometric change of a cell, for example a reduction of thickness due to compaction, or erosion, which may also lead to a change in mechanical parameters, Apparition or modification of discrete flow drivers, such as conduits or fractures, due to erosion, which may also impact the petrophysical parameters of the model.

[0096] The skilled person may refer for instance to the patent application PCT / IB2023 / 000218 filed by the applicant, for a detailed method for simulating dissolution within a reservoir.

[0097] Tectonic events notably include fracturing events, which relate to deformation of the Earth crust resulting in fractures appearing within the model. Fractures may exhibit various configurations according to the mode of deformation, and may strongly influence the behavior of a reservoir, in particular with respect to permeability and hence to fluid flows within the reservoir. The simulation of a fracturation event may thus lead to apparition of fractures within the reservoir model, where each fracture may be represented as a bounded surface, and which may further be associated with geometric parameters and also petrophysical parameters (e.g. permeability). The skilled person may refer for instance to the patent application PCT / FR2024 / 050560 filed by the applicant, for a detailed method for simulating fracturation within a reservoir.

[0098] In any case, propagating the features output by the simulation of the geological events, e.g. the geological or petrophysical parameters, to the later stages of the model, and at correct locations complying with the evolution of the formation of the reservoir, enables obtaining, in the present-day state model of the reservoir MP, an accurate distribution of these parameters.

[0099] A possible embodiment for implementing the transition from one computer model Mj representing a state of formation of the reservoir to a next computer model Mj+i, in order to integrate 320 the outputs generated by the simulation of a geological event in a model Mj into the next computer Mj+i will now be described.

[0100] According to said embodiment, the method comprises a preliminary step 200 of computing, a mapping function enabling to determine, for each point having coordinates (x,y,z) in a first model Mj, the corresponding coordinates of the same point in a subsequent model Mj+i . This step 200 comprises a substep 210 of computing, for each structural model Mj of the reservoir generated at step 100, a respective parametric representation Pj of the model Mj, where time is a parameter. In said parametric representation, each horizon is represented by a surface having a constant value of time, i.e. an iso-chronological value. In what follows, a parametric representation Pj of a structural model Mi is referred to as “parametric model” Pj.

[0101] Computing, for a structural model in cartesian coordinates, a corresponding parametric model Pj, may be performed by computing a coordinate transformation from the cartesian coordinates (x,y,z) of the structural model Mj to parametric coordinates (u,v,t), where t (x,y,z) is a relative geological time of deposition of a particle and {u(x,y,z), v(x,y,z)} are the coordinates representing the spatial position of a particle or point of the reservoir at said relative geological time t(x,y,z). Because at the original depositional time, sedimentary layers are typically deposited in uniform layers, the image of the structural model in the parametric space may be represented by a stack of flat, horizontal layers, where each horizon is a surface having a constant value of t.

[0102] In embodiments, the computation of the coordinate transformation towards the (U,V,T) parameterization is performed by application of the Geochron™ model disclosed in the publication by [Mallet, 2004], and which may be generated by the SKUA™ software.

[0103] Employing the same notations as used in this publication, and referring to figure 5, each structural model of the reservoir Mj corresponds to a G-space in the 3D Cartesian space. Any point belonging to that space is denoted x such that: x = x. X + y. Y + z. Z

[0104] Where (X,Y,Z) is a given right-handed orthogonal frame of unit vectors.

[0105] The (U,V,T) parameterization corresponds to the parametric space (designated as Geo-Chronological space and denoted G-space in said publication). Let be a plane orthogonal to the vector T and corresponding to the surface of the earth at geological time t, Htis parallel to the pair of orthogonal unit vectors (U,V) which can thus be used as a frame for Ht. As a consequence, for any reference point po belonging to Ht, the pair of vectors (U,V) induces a coordinate system (u,v) on Htsuch that : Any particle of sediments observable today at a location x within a structural model of the reservoir, was deposited at some location (u,v) on a plane Htand can thus be characterized in a unique way by its coordinates (u,v,t) in the parametric space.

[0106] As a consequence, computing 210 a (U,V,T) parameterization of a model of a reservoir in a Cartesian space corresponds to determining a transform function u defined as:

[0107] -x u(x) u

[0108] X = y E G -> U(X) = v(x) e G z t(x) for which the norm of the gradient of t must be constant:

[0109] | |V(t) | | . N = C

[0110] The constant C can be arbitrarily defined. N is a vector field orthogonal to the horizons of the structural model, that points from the older horizon toward the most recent. An inverse function u'1exists for all points of the G space transformed into the G using u, such that:

[0111] Moreover, each parametric model is normalized so that all coordinates rest between 0 and 1 .

[0112] With reference to figures 6a to 6c, are shown respectively three structural models corresponding to successive stages of formation of a reservoir, where the axes are Cartesian axes, and each pixel is associated to a color corresponding to the value of a parametric coordinate t, u, v.

[0113] As can be appreciated from this example, since all parametric models Pj are generated independently from respective structural geological models Mi, these respective sets of coordinates (u,v,t)j are also independent, meaning that equal coordinates in different parametric models Pj do not correspond to a same particle of the reservoir. Thus, during a step 220, a mapping of the coordinate t among the various parametric models is performed. In what follows, a mapping corresponds to a function or computation that enables finding a value of t in a model Mj that corresponds to a given value of t in a model Mj. This mapping is performed based on the assumption that two distinct structural models Mj comprise at least two horizons in common, denoted Ho and Hi, where each horizon is associated with respective absolute geological times To and Ti. Each horizon is associated with relative geological times to and tu in each parametric model Pj. The t coordinates to and tu of the explicit horizons in each parametric model can be directly retrieved from the application of the Geochron model.

[0114] Using the constant gradient constraint of the relative geological time t in the parametric space, the value of a relative geological time tbj in a parametric model Pj corresponding to an absolute geological time Tb can be deduced from the value of a relative geological time tb in a parametric model Pj by a linear regression based on :

[0115] The relative to and toj values in each parametric model Pj and the absolute time To of the horizon Ho,

[0116] The relative J?,, and R values in each parametric model Pj and the absolute time Ti of the horizon Hi,

[0117] The fact that tbj and tb correspond to the same absolute time Tb. Indeed, the following equation applies:

[0118] Hence

[0119] With reference to figure 7, during a step 230, a mapping of the u and v coordinates among the various parametric models Pj is also performed. Since the u and v axes are orthogonal to each other, and orthogonal to the t axis, the mapping of the u and v axes between two parametric models corresponds to determining a rotation matrix and a translation vector enabling the determination of coordinates (u , v,t)j of a point Ptj in a parametric model Pj from its coordinates (u,v,t)j in a parametric model Pj as follows:

[0120] Pt -

[0121] Where R, '• is the rotation matrix from the parametric model Pj to the parametric model Pj at the point Ptj, expressed as: cos 0 — sin 0 0

[0122] Pt-

[0123] Rj_.lj = sind cos 9 0

[0124] 0 0 0

[0125] And 0 is the rotation angle between ui and Uj at point Ptj, the translation vector from the parametric model Pj to the parametric model Pj at point i, expressed as:

[0126] TransPi=d.u, dv, 0)

[0127] The determination of the parameters du, dv and 0 is performed based on control points introduced above, which correspond to identical particles, thus deposited at a same absolute geological time and same initial location. For a given control point CP, its coordinates in a parametric model Pj are (Ucp,vcp,tcp)i, and its coordinates in the parametric model Pj are (uCp,Vcp,tCp)j.

[0128] The equations of rotation and translation provided above apply when the t coordinate of the two considered parametric spaces is mapped according to the description of step 220 above. Thus, for each control point, the coordinate tcpj in the parametric model Pj is derived from the coordinate tcpin the parametric model P, by application of the mapping disclosed above.

[0129] As these coordinates correspond to the same location (or same particle), it results that: du. — ^CP juCP,i

[0130] DV= ^CP,J ~vcp,i Thus, for each control point, values of du, dv and 6 can be determined. From then, values of du, dv and 0, and hence of the rotational matrix and translation vectors, can be determined for each point of a parametric model by linear interpolation between the position of the point and the position of the control points.

[0131] With reference to figure 4, once the parametric models Pj and the mapping between the t and u,v coordinates of these models are computed, the step of integrating 320 the simulation outputs of a numerical simulation performed in a structural model Mj into a next structural model Mj+i comprises, for a plurality of points - and for instance, for all of them - of the computer model Mi:

[0132] Determining (u,v,t)j coordinates 321 of the points in the corresponding parametric model Pj,

[0133] Inducing 222, from the mapping between the parametric models, coordinates (u ,v,t),i+i of equivalent points in the parametric model Pj+i corresponding to the next subperiod of time i+1 , and

[0134] Inferring 223 the coordinates of the equivalent points in the structural model Mj+i corresponding to said next subperiod of time. This can be performed by applying the inverse function u-1of the function u that was computed for determining the parametric model Pj+i from the structural model Mj+i .

[0135] This enables transferring not only the position of points, but also of segments, surfaces and volumes, delimited by said points, as well as any parameter associated to them. Parameters, in particular geological or petrophysical parameters may thus be transferred from one model to the next, be modified by the simulation of geological events, and be again transferred until obtaining a modified version of the computer model corresponding to the present-day state of the reservoir, which have been enriched of the outputs of the various simulations.

[0136] The method thus enables obtaining a model of a reservoir according to a present-day state, having a structure and parameters which are the result of the simulation of a sequence of geological phenomena replicating the actual sequence of phenomena having led to the formation of the reservoir. In embodiments, the model may thus be associated to parameters such as geological or petrophysical parameters, resulting from said sequence. Therefore the distribution of parameters populating the model is more relevant and enables assessing more reliably the operating potential of the reservoir.

[0137] Accordingly, the method may further comprise a step 400 of performing at least one among the following applications: - Performing fluid flow computation within the obtained model of the reservoir, which enables establishing plans regarding exploitation or management of a resource stored within the reservoir, or storage of carbon dioxide, positioning wells, etc.

[0138] Extracting, from the obtained model, a stratigraphic column or a statistic distribution of at least one parameter populating the model, and comparing the stratigraphic column or statistic distribution to equivalents obtained from the actual reservoir by on-site data acquisition. This may in turn enable to correct or validate input parameters of the simulation, such as the sequence of geological events, or the input parameters of said events.

Claims

CLAIMS1 . A method for building a model of a geological reservoir according to a present- day state of the reservoir, from a predetermined geological calendar of the formation of the reservoir, wherein the geological calendar covers a determined period of time T and comprises a sequence of geological events occurring within said determined period of time, each geological event being associated to a geological time within the determined period of time T, the method being implemented by a computer and comprising: defining (100) a plurality of computer models (Mj) representing respectively a plurality of formation states of the reservoir, where each computer model is associated to a subperiod of time tj within the period of time T, wherein the respective computer models comprise at least: o a last model (MP) in chronological order, corresponding to a present-day deformation state of the reservoir, and o a first model (Mi) in chronological order, corresponding to an earlier deformation state of the reservoir, o at least one transient model, corresponding to an intermediate formation state of the reservoir, and simulating (300) formation of the reservoir, comprising, for each subperiod of time tj within the period of time T, considered in chronological order: o performing numerical simulation (310), in the computer model (M / ) corresponding to the subperiod of time tj, , of all geological events occurring within the subperiod of time (tj), to generate numerical simulation outputs, and o integrating (320) the simulation outputs in the computer-model (Mj+i ) associated to the next subperiod of time tj+i .

2. The method according to claim 1 , wherein numerical simulation outputs comprise at least one of: geological parameters, mechanical parameters, petrophysical parameters, discrete flow drivers, structural elements.

3. The method according to claim 1 or 2, wherein performing numerical simulation of geological events (310) in a computer model comprises performing numerical simulation of a sequence of geological events chronologically in accordance to the respective geological time of each geological event, wherein the numerical simulation of each geological event generates respective numerical simulation outputs which are integrated in the computer model for the numerical simulation of the next geological event.

4. The method according to any of claims 1 to 3, wherein the computer models comprise at least one common horizon (H), corresponding to a iso- chronological surface, and said at least one common horizon exhibits different folding configurations in computer models (Mj ) associated to at least two different subperiods of time (tjj).

5. The method according to any of the preceding claims, wherein the computer models comprise at least one common fault (F), separating areas of the reservoir in relative displacement with respect to each other, and wherein the slip between the areas separated by the faults has at least two different values in computer models (Mi j) associated to at least two different subperiods of time (tij).

6. The method according to any of the preceding claims, wherein the geological events comprise sedimentation events, performing numerical simulation of a sedimentation event comprises generating, on an iso-chronological surface of a computer model, a plurality of horizons, and the outputs of numerical simulation of a sedimentation event comprise said additional horizons.

7. The method according to any of the preceding claims, wherein the geological events comprise fracturation events, performing numerical simulation of a fracturation event comprises generating, in a computer model, at least one fault, and the outputs of numerical simulation of a fracturation event comprise said at least one fault.

8. The method according to any of the preceding claims, wherein the geological events comprise diagenetic events, performing numerical simulation of a diagenetic event comprises generating or modifying properties of at least one conduit or fault in a computer model, and the outputs of numerical simulation of a diagenetic event comprises said generated conduit or fault or said modified properties of a conduit or fault.

9. The method according to any of the preceding claims, further comprising a preliminary step of computing (210), for each computer model (Mi), a respective parametric representation (Pi), in which an horizon is represented by a constant value of time, and computing a mapping (220, 230) between the parametric representations (Pi), and wherein integrating the simulation (320) outputs of a numerical simulation performed in a computer-model (Mi) associated to a first subperiod of time (ti) in a computer-model (Mj+i) corresponding to a next subperiod of time (tj+i) comprises:Determining (321 ) coordinates of points of the first computer model (M / ) in the corresponding parametric representation (Pi),Inducing (322), from the mapping between the parametric representations (Pi), coordinates of equivalent points in the parametric representation (Dj+i) associated to the next subperiod of time (ti+i ), andInferring (323) the coordinates of equivalent points in the model corresponding to the next subperiod of time (ti+i).

10. The method according to any of the preceding claims, wherein the computer models corresponding to earlier states of deformation of the reservoir, as compared to the present-day state, are obtained from the computer model corresponding to the present-day state by implementation of a well restoration algorithm.

11. The method according to any of the preceding claims, wherein defining the computer models comprises receiving ground data relative to the reservoir, and defining the computer model corresponding to the present-day deformation state of the reservoir from the received ground data.

12. A computer program product, having stored thereon code instructions for implementing the method according to any of the preceding claims, when it is executed by a computer.

13. A computer, configured for implementing the method according to any of claims 1 to 11.

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