FR2926379A1 - METHOD, PROGRAM AND COMPUTER SYSTEM FOR CONSTRUCTING A 3D GEOLOGICAL MODEL - Google Patents

Abstract

The present invention relates to a method, a program and a computer system for constructing three-dimensional geological models, for example a reservoir, the method comprising the steps of: providing a set of models in proportions, each of the models in proportions comprising uvw cells associated with respective values of likelihood of occurrence of facies, said values forming a set of estimation probability values (S100), for each of the cells, of a distribution law of facies probabilities, from the sets of values of the probabilities, so that each of the estimated laws reflects the set of models provided: - extraction, from models in proportions provided initially, or supply of spatial coherence data; S200) of a new proportional model set, based on the estimated facies probability distribution laws, including a drawing new probabilities of facies for each of the cells, the draw being further constrained according to the spatial coherence data; and- creating (S300) a new set of geological models, by stochastic simulation of facies and petrophysical properties from the new set of proportionally created models.

Description

METHOD, PROGRAM AND COMPUTER SYSTEM FOR CONSTRUCTING A 3D GEOLOGICAL MODEL

The present invention relates to a method, a program and a computer system for constructing a three-dimensional or 3D geological model, and in particular to take into account a geological uncertainty in the construction of this model. This invention is particularly suited to the oil field. Before the exploitation of an oil field, it is desirable to be able to evaluate the volume of hydrocarbons present in the reservoir, and the capacity of the field, ie the volume of hydrocarbons that can be produced according to a certain development plan. The capacity of the field depends on the spatial distribution of the reservoir (envelope of the deposit), the porosity (which translates the volume likely to be occupied by fluids), the saturation in hydrocarbons (fraction of the quantity of fluid in oil or in gas), permeability (ability of the medium to be passed through by a fluid). In order to better evaluate the key quantities of a reservoir, the industry uses spatial numerical models symbolizing the reservoir. The construction of these 3D numerical models, also called geomodels, typically comprises one or more of the following steps: defining an internal mesh from the general structure of the zone; -teach each cell of the mesh in probability of occurrence of facies; - assign by stochastic simulation to each cell lithological properties (facies) and petrophysical properties (porosity, permeability, saturations ...); and - realize a dynamic flow model. Production profiles are ultimately defined By definition, a model in proportions consists of a geometric support, realized by discretization of a region or zone into a set of cells, to which are assigned probabilities of occurrence of facies. In other words, the proportional model is a discretized model of space. which gives at each point a (or cell of index uvw) a probability vector p (a): [p, (a), p2 (ct) pf (a)] with nF components where nF denotes the number of facies considered and pk (a) the probability of occurrence of facies Fk. Such a model is illustrated in Fig. 1. R B ,, ets76; rür ^ 6521 - r1 & III Incennudes 1 cl 2 - teh the doctment - I V ~ - Irr'rl. 1 17 The geological model is a model obtained from the model in proportions, in which each cell is assigned a facies and petrophysical properties, by stochastic simulation. From a single model in proportions, one generally simulates several geological models.

Describing the underground environment and its dynamic behavior is an arduous and particularly uncertain exercise. Important decisions related to heavy investments (business license purchases, etc.) are made on the basis of these uncertain representations of the field. Thus, a neglected uncertainty that escapes identification can lead to the ruin of a development project.

We classically distinguish three major families of uncertainties according to the stage of construction of the geomodel where they intervene, and the type of information used. We speak of: - structural uncertainties when defining the geometry of the reservoir; - geological uncertainties for the construction of the internal mesh and the filling in probabilities of occurrence of facies then in lithological and petrophysical properties; and - dynamic uncertainties for the design of the flow model. Of all the sources of uncertainty encountered in reservoir modeling, geology plays a major role because it leads to the understanding of the internal architecture of the subsoil. Indeed, it is a question of integrating into the models certain hypotheses and certain concepts of geology, which make it possible to establish a link between the data and the points where no measurement has been made. Although there is a great deal of variability in the underground environment, the geological structures that compose it make it not completely chaotic. It presents, on the contrary, a geological coherence or spatial continuity, that the modeler, informed by the knowledge brought by the geology, tries to translate into its interpretation of the available observations. This source of information is introduced through what is known as the geological scenario. It comes from the sedimentologist's interpretation of the available data (seismic data, cores, logs, etc.). The geological scenario specifies the parameters governing the position of the various deposits, such as, for example, the direction of sandy inputs, paleogeography, the size of the heterogeneities, lateral evolutions of facies. the position of the shoreline, wave energy, correlations, etc. The scenario

R 'R, e, cls' 6: an ^ _6571 - OX) I 11 6rcennudcs I and 2 - irae doc -11,11 08 - 111.01 - 2.27 geological ruler, in a way, the geological image of the reservoir, since it reflects a choice of geological continuity of the underground environment. The establishment of the geological scenario is based on a small number of spatially dispersed measurements that provide a framework for extrapolating basement features. This scenario is therefore derived from different choices and modeling assumptions that are inherently subjective. The imprecise, partial and subjective nature of the geological knowledge of the subterranean environment confers in fact a highly uncertain character to the geological scenario, as well as to the geomodel that results from it.

Currently, the assessment of geological uncertainty consists mainly in reproducing all the possible states of the environment, compatible with the observations. We proceed conventionally by varying, in a probabilistic framework and from a model in proportions, the lithological and petrophysical parameters on which the recoverable volumes and the production profiles depend. Thanks to the development of computer resources, it is now possible to quickly generate not only a single geomodel but a series of alternative modelizations of the reservoir, all of which will respect the same starting data (geological interpretation, wells, seismic information, etc.). Examination of all the simulations makes it possible to delimit a range in which the total volume of hydrocarbons or the production profile fluctuates, and thus to quantify the uncertainties associated with these quantities. As a general rule, a set of equiprobable achievements is generated on the basis of a single geological scenario. One uses only one model in proportions. In doing so, the present inventors have realized that the statistical variability of the state of the medium around the selected scenario is actually represented. However, the quality and quantity of the collected data leave an essential place for geological interpretation that can result in a profusion of scenarios, all compatible with the available information. Such an approach is therefore not sufficient to describe the geological space of uncertainties in its entirety. Indeed, this approach ignores the variability of the geological scenario To better specify this area, an object of the present invention is to return to

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4 the source of the uncertainties that weigh on the definition of the sedimentary scheme, in other words geology. We know, in this respect, the works of A. HAAS & P. FORMERY, in particular the article Uncertainties in facies proportion estimation. Theoretical framework: the Dirichlet distribution, Mathematical Geology (2002). In this paper, the authors evaluate the uncertainty of facies proportions using a Bayesian approach. The uncertainty evaluated here is of a statistical nature on the available data (well data). This approach is based on a single geological scenario and does not fully integrate the uncertainty associated with the variability of models in proportions from different geological scenarios. In accordance with the above. there is therefore a need for a process that allows a better integration of the geological uncertainty during the modeling of reservoirs, in particular hydrocarbon reservoirs. This goal is achieved through a computer implemented method of constructing three-dimensional geological models, for the evaluation of geological quantities, comprising the steps of: providing a set of models in proportions. each of the models in proportions comprising uvw cells associated with respective values of likelihood of occurrence of facies, said values forming a set of probability values; estimating, for each of the cells, a distribution law of facies probabilities, from the sets of values of the probabilities, so that each of the estimated laws reflects the set of models provided; extracting, from the models in proportions initially provided, spatial coherence data; - creation of a new set of proportional models, based on the estimated facies probability distribution laws, including a draw of new facies probabilities for each of the cells, the draw being further constrained according to the spatial coherence data extracted; and - creation of a new set of geological models, by stochastic simulation of facies and petrophysical properties from the new set of proportionally created models.

R rr, e, Incentives 1 and 2 - This is done in the same way. Alternatively, the spatial coherence data are not extracted from the models in proportions provided initially but are provided in parallel. models in proportions. According to variants, the method according to the invention is capable of comprising one or more of the following characteristics: the laws of distribution of probability of facies are of Dirichlet type, of parameters {cl, ..., CnF}, V ,, . where nF is the number of facies; the creation step comprises: the simulation of a set of intermediate random variables (F1), n ,, and (äF) ,,,,, ^ according to the gamma laws of parameters (I, c) 7n ,, 4 and (l, cnF) ,,,. ,,, respectively, the new facies probabilities of the new set of models in proportion corresponding to the ratio of the realizations of these intermediate random variables; at the creation stage, the draw of the new facies probabilities is constrained according to the spatial coherence data, during the simulation of the set of intermediate random variables; at the step of creating a new set of models: quantile values, u1, ... u ,, are associated with each of the intermediate random variables and (FnF) ,,,. ,,, a value of quantile ui being defined according to an inequality 1P (T'j) <ui, in which P (f) is a cumulative probability; and the draw of the new probabilities of facies is constrained via a draw of quantile values, the draw of the quantile values being itself constrained according to the spatial coherence data; spatial coherence data include variograms associated with facies; - at the stage of creation of the new set of models in proportion, the constrained drawing of quantiles is done by stochastic simulation; - stochastic simulation is done by Gaussian sequential simulation or SGS methods; the spatial coherence data comprise a variogram of infinite range and of zero threshold; and at the step of creating the new set of models in proportion, the drawing of the quantile values respects said variogram of infinite range and zero threshold;

R, Br, is'2c, 5Um26521 - u% nl It Incennudes 1 el 2 - teNte dipoi doc - 11 I'ns II. - at the stage of creation of the new set of models, the drawing of the new probabilities of facies is also constrained according to different directions of anisotropy spatial coherence data; in the data supplying step, each of the provided models comprises uvw cells which are associated with the same facies probability value, for a given facies; the method according to the invention furthermore comprises a step of weighting the models provided and, at the estimation step, the distribution laws of facies probabilities are estimated so as to reflect the set of weighted models; The steps of estimation and creation of the new set of templates are performed iteratively, so that at least one of the templates created during the creation step is used to determine parameters of at least one one of said distribution laws; the step of creating a new set of models further comprises a step 15 for simulating petrophysical properties for each of the facies cells; and the method according to the invention further comprises a step of deducing accumulations in hydrocarbons. The invention also relates to a computer program product, the program comprising routines for executing the steps of the method according to the invention, when said program is executed on a computer. The invention also relates to a computer system comprising a memory containing a program comprising routines for executing the steps of the method according to the invention, when said program is executed. Other characteristics and advantages of the invention will become apparent on reading the following detailed description of the embodiments of the invention, given by way of example only and with reference to the appended drawings, which illustrate: FIG. : an illustration of a model in proportions; - Figure 2: an illustration of different steps of the method, according to one embodiment of the invention; Figure 3: an illustration of three models in MA, MB, MC proportions associated with three distinct geological scenarios; FIGS. 4A-C: an illustration of the simulation method of the distribution function inversion ratio (CDF) vectors;

In this case, there were 6,21-o lul Uncertainty> 1 and 2 - text of the document - 11 II - I - I. FIG. 5A-B: a graphical representation of typical variograms obtained along two axes, in one embodiment of the invention; and FIGS. 6A-B: a graphical representation of facies variograms, in different directions, as used in one embodiment of the invention (FIG.6A), mapped to an 8f direction of these variograms. (FIG 6B). The invention relates broadly to a method of constructing geological models. This method relies on a set of initial proportion models and spatial coherence data, reflecting distinct geological scenarios. It leads to the creation of a new set of geological models, integrating the variability of the models in initial proportions and respecting spatial coherence data. Initial proportion models and spatial coherence data reflect real situations, at least to the extent possible. The models in proportions are typically filled in according to probability of occurrence values of facies resulting from experimental observations or extrapolation of these observations. The different models in proportions provided have the same geometric support, that is to say the same mesh structure. The spatial coherence data are preferably provided in the form of variograms, specific to each facies and which. where appropriate. report spatial 20 correlations and directions of anisotropy. The process involves, in particular, a step of creating new models in proportions, from which will be generated, by stochastic simulation of facies and petrophysical properties, new geological models. The step of creating new proportional models passes in particular by estimating a distribution law of probability of occurrence of facies, cell by cell. This point is particularly important and original: the aim of the invention is notably to estimate the way in which the probabilities relating to various facies are distributed within each of the cells of the model. So we have to somehow do probabilities of probabilities. The method according to the invention therefore makes it possible to scan, from a few basic geological scenarios, all the statistically compatible geological scenarios. An interest of such a technique lies in the transition from discrete hypotheses (the various geological scenarios) to a continuous phenomenon. This process k Bi e 'cry] a rn ~ 26521u080111 Inceruwdes I el 2 - tome dep.), Doc - 11'01 08 - 10 01 - 7:27 allows to generate all the alternative images of the tank from some geological scenarios. each corresponding to a plausible interpretation of the reservoir. To do this, the method according to the invention provides a practical scheme for integrating geological uncertainty in the construction of the geological model. The method according to one embodiment of the invention will now be described in outline. with reference to Figure 2. which illustrates different steps of the process. The method relies on a set of models in distinct proportions, typically provided by the geologist (step S 10) and spatial coherence data. These last ones typically translate the spatial coherence of the probabilities of occurrence of facies. They can be provided by the geologist or extracted from the models provided. This alternative bases two distinct embodiments which will be detailed later.

Proportional models and spatial coherence data reflect different geological scenarios. Indeed, from the measurements collected and its geological knowledge of the region. the geologist can define several appropriate geological scenarios. In a first embodiment, the various possible geological scenarios are translated only in the models in proportions provided. In other words, the information relating to the spatial coherence of the geological scenarios is implicitly contained in the models in proportions provided; it can be extracted from it. The model game in proportions synthesizes in this case all the knowledge and information available. In some cases, the different geological scenarios have a certain continuity between them and can be considered as variants around the same landscape. They are thus particularly suitable for being translated by models in proportions from which spatial coherence data will be extracted. The spatial coherence data are preferably extracted in the form of variograms. It should be noted that the step of extracting the spatial coherence data can take place at any time before the step of simulating the new probabilities of occurrence of facies, which will be detailed later.

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In a second embodiment, the various possible geological scenarios are translated both by models in provided proportions and spatial coherence data provided independently of the models. This embodiment is particularly advantageous when the available data are fragmentary. These spatial coherence data can be for example variograms, specific to each of the facies, and which account for spatial correlations and, where appropriate, directions of anisotropy. The directions of anisotropy generally correspond to privileged directions of sedimentary inputs. The uncertainty of the geological scenario is then translated both by the proportional models and the spatial coherence data. Moreover, in a case described as extreme, the proportional models do not contain any information on the spatial distribution of the different facies. This amounts to saying that each of the models initially supplied includes uinv cells which are associated with the same facies probability value, for a given facies. These different cases and other variants will be explained later, in particular through examples. The implementation of the method assumes the existence of a parametric probability law able to govern the proportions of facies in the population constituted by the set of models in proportion. It is thus, from the models in proportion, to estimate (step S100) for each of the cells, a law of distribution of proportions of facies. This may involve, in practice, determining the first moments of the distribution law in question. Knowing the parameters of the distribution law, it is possible to simulate, for each of the cells of the model, probabilities of occurrence of facies so as to create a new set of models in proportions (step S200). However, the medium has a spatial structure whose coherence in each of the newly created proportions is necessary. In other words, simulated proportion models must respect spatial coherence data.

To do this, the simulations of the new probabilities of occurrence of facies are not done independently for each of the cells but are constrained according to these spatial coherence data.

Finally, from the new proportional models simulated in step S200, new geological models can be generated (step S300). typically by facies simulation and petrophysical properties. Simulation of facies and petrophysical properties is preferably done by stochastic simulation, according to the Gaussian sequential simulation (SGS) method, known per se. As shown in Figure 2, typically hundreds of models are simulated in proportions, and as many new geological models are generated (typically a facies simulation is performed for each model in proportion).

From these geological models it will be possible for example to obtain hydrocarbon accumulations in a conventional manner. Taking into account the geological uncertainty makes it possible to better estimate these accumulations in hydrocarbons. The subsequent exploitation of the reservoir is concretely improved.

These objectives being fixed, a computer program can, for this purpose, be developed according to the knowledge of those skilled in the art. This program should include the routines necessary for carrying out the steps of the method according to the invention. This program can then be executed on a suitable computer system, such as a conventional workstation or any suitable computer system, also according to the invention. Some aspects of the invention will now be detailed, with reference to FIGS. 1 to 6. For clarity, a model reservoir is used as an explanatory support. In the following context, the geologist provides three models in MA, MB, MC proportions associated with three distinct geological scenarios (Figures 2 and 3). An example of a model in standard proportion is shown in FIG. 1. Each of the models in MA-MC proportions corresponds to a discretization of the reservoir according to a sugar box grid which comprises 70 × 60 × 1 cells with a square section of 100 meters. aside (a layer). In this example. the modeled environment corresponds to that of a carbonated platform. For example, the following geological scenarios can be considered, as shown in Figure 3:

Rrterets] o5wr26521 - noon 1 1 Incertnudes 1 and 2 - te, ie doc po - Il, I mi - 11,1) 1 - 1727 II - Geological scenario A: the carbonate platform has a beach profile, translated by the model in MA proportions; - Geological scenario B: the carbonate platform has a promontory of north-south axis, translated by the model in proportions MB; and - Geological Scenario C: the carbonate platform has a northwesterly / southeasterly promontory, expressed as the MC proportions model. The uncertainty relating to the geological scenario relates here to the morphology of the carbonate ramp. It has repercussions on the lateral extension of the facies and their proportions.

The studied reservoir lists three categories of facies (nF = 3), which are respectively designated fi, f2 and f2, ranging for example from the best to the least good reservoir rock. According to the method according to the invention, each of the cells of each of the models is assigned a probability of occurrence of each facies. Thus, for a model in given proportions, for example MA, each cell of index uvw is indicated by a nf-tuple of proportions of facies (P) A ,,,,, = {p ,,

, pfF f, nF corresponding to the number of lithofacies taken into account. This is illustrated schematically in Figure 1. Guidance as to the details of implementation can be found in the following references: P. CHAUVET, Aide-mémoire of linear geostatistics, Les Presses (1999) and D. MARCOTTE, Written notes: mining geostatistics, GLQ3401 course, École Polytechnique de Montréal (May 2003). It is then assumed that there is a probability law capable of governing the probabilities of occurrence of facies in the population constituted by the set of models in proportion MA, MB and MC. The probabilities of occurrence of facies in each cell of models in initial proportions can be considered as particular achievements of this law of probability. One way to do this is to determine the first moments of the probability law from models in initial proportions that constitute particular realizations. This point will be discussed again later. However, since a proportional model usually involves more than one million cells, it is difficult to consider a random vector. DTD: R, Brecels 2450.'26521u08.'111 Iceruwdes 1 and 2 - Iule dcpol doc - 1 1 IInN - Io pl - I 1 27 encompassing the model in proportions in its entirety. It is therefore more advantageous to study the vector (P), n, of facies proportion for each of the cells, for example, if we consider the cell scale uvw, but considering the population constituted by the M models in proportions, we can group in a numerical table of dimension nM x nF the probabilities of occurrence of facies.This matrix is interpreted as the realization of a sample of size nM (number of models in proportions) of a random vector of nF dimensions (number of facies) .We can then, in step S200 (FIG. 2), assign to each of the uvw cells of the whole population of models in proportion, a vector proportion of facies (P ) ,,, b ,, which follows a parametric probability law, and whose components are defined by the random variables (Pi) ä ,,,, (P2) ,,,,,,, (P3) uäI .. for example, the hypothesis that this law of probability is a Dirichlet law. n of facies follows a Dirichlet distribution of parameters {ci, c2, c3}. Indeed, for a model in given proportions, for example MA, the vector proportion of facies (P) ", n ,, = {pl, p2, P3} associated follows a uniform law, it is thus advantageous to infer for law a posteriori of the proportions of facies a distribution of Dirichlet.

This procedure is then repeated at step 5200 (FIG. 2). for all the cells of the models in proportions. In this hypothesis, each cell of the model in proportions has its own Dirichlet law which one notes ..., cnF]. ci, ..., cr, F being the parameters of the law in the cell uvw. The nM models in initial proportions thus make it possible to estimate the first statistical moments of the Dirichlet's law, from which the parameters derive. The first moments of the Dirichlet's law are, in known manner, established as follows: E (p1) = c E (p) 2) = cl + 1) c (c + 1) cIxci E (PIp,) ùc c + I), with cIc; R Rte, ets 205tpt 26921 - nXnl l l Uncertainties 1 e1 2 - tlt this doct - Il tlt 1 - lu tt! The next step is to create the new models in proportions (step S200 in FIG. 2). To do this. for each uvw cell, it is possible to calculate an embodiment of the vector proportion of facies (P) ä ,,,, according to a Dirichlet law of parameter {ci, c2, c3}, for example by simulation of a set of intermediate random variables (F1), n ,,. (r2) ,,,,,., (r3) ,,,, .. .. Indeed, to simulate a Dirichlet distribution of parameters ci, c2, c3 amounts to randomly drawing three numbers ri, 1-'2 and 1 ' 3 in three Gamma laws of respective parameters (1, ci); (I, c2) and (1, e3). The components (P1) ,,., 1., (P2) ,, 1, (P3) u ,, ä of the facies proportion vector correspond to the realization ratio of these variables, according to the following equations: PI = r, / (r, + r2 + r3); P2 = F2 / (r1 + 1-2 + r3), and P3 = r3 / (r, + F2 + 1-33). In addition, models in facies proportions must respect spatial coherence data. Indeed, the subterranean environment presents a spatial structure whose spatial coherence is wished to preserve in each model in proportions generated. More exactly, it is a question of translating the idea that two vectors of proportions relative to points situated near each other must, on average, be more similar to each other than two vectors corresponding to distant points. For that, one can constrain the simulation of the vector of proportion (P) u,. ,,, for example according to his entourage. In this respect, a spatial coherence constraint may advantageously be introduced during the drawing of the intermediate variables (F 1) ,,,, (r 2) u ,,,. (R3) ,,,. ,,. Preferably, the intermediate variables (F1), n1, .- (f2) u, 1, (r3) n, are generated by the inverse transform method, as illustrated in FIGS. 4A-C. each of the cells of the model in proportions the parameters ci, e2 and c3 of the associated Dirichlet law, one can determine the cumulative probability curve (or CDF, of the English "cumulative distribution function") for each of the parameters Gamma laws respectively (1, ci), (l C2) and (1, e3). Thus, for the parameter Gamma law (1. ci). Using the cumulative probability curve, it is possible to establish a correspondence between a number u1 previously simulated according to a uniform law over the interval [0; 1], and an intermediate random variable r 1. The quantity ui refers to the cumulative probability IP (r1) <u1, whence R'-R e6 '22n50n46521--0% 0l1 i rnceruludes 1 and 2 -veve dipoi doc - II, ^ II - lo r ~ l - 13.27

14 the name of quantile for the value u1. The quantile vector is then called the nuplet (ui, U2 U3), each of whose components is associated with a Gamma law. Thus, the creation of a model in proportions that respects the spatial coherence data passes here by a constrained simulation of the intermediate variables F ,, r2, r3, itself obtained from a constrained simulation of the n-tuples (u1, u2, u3) 2 ,, ^ w or quantile vectors for all the cells of the model in proportions. To summarize the first steps of the method according to the invention, it is desired to create (step 5200) a new model in proportions that respect the spatial coherence data. For this, it is possible to constrain, at any point in the discretized space (for each cell), the simulation of the new probabilities of occurrence of facies, or the vector of proportions (P) ,,,,, with those from his neighborhood. The algorithm used for this simulation introduces for example the spatial coherence constraint when drawing the independent intermediate variables and (ä F) ,,, w. In this example, these variables are preferably introduced for the realization of the Dirichlet laws previously estimated for each cell. Their simulation is performed for example by inverting their respective distribution function. For each cell, a quantile vector is drawn in a uniform multidimensional distribution over the set [0; 1] ° F (where nF is the total number of cells). Its components determine the simulated values of the independent intermediate variables, and then the proportion vector (P) ,,,. ,,. As a result, how to simulate quantile vectors in space. and in particular from a cell to a contiguous cell, influences the spatial coherence of the embodiments. While independently derived quantile vectors will generally produce incoherent proportions, the introduction of a correlation (via the spatial coherence constraint) results in locally consistent proportion vectors. To respect spatial coherence data when simulating new models in proportions, one way is to simulate, for all the cells of the model, quantile vectors (u1, u2, u3) ,,,., • whose variograms are close to facies variograms of spatial coherence data. This amounts to saying that the quantiles are simulated under stress, the constraint being derived from the spatial coherence data. The simulation of the vectors R 'L3 e eis ^ bic "2 21-401111 Incerutude, 1 and 2 - quantum doc - 11'111 Y) N - In ~~ l - 1. 27 head is typically done by stochastic simulation. For example, according to Gaussian sequential simulation (SGS) methods, what will be discussed now are various alternatives as to how to introduce the spatial coherence constraint As discussed above, spatial coherence data are provided preferentially under form of variograms, associated with each of the facies According to a possible definition, the variogram y (h) measures, for the random function Q, the mean squared difference observed between the values that the function Q takes for pairs of points { a, a + h), separated by a vector h, i.e. y (h) = E (Q (a) - Q (a + h)) 21 '2 where E [Z] defines the mathematical expectation of the random variable Z. A graphical representation of a variogram is given in Figure 5A-B or 6A - B. It should be noted that the nature and degree of knowledge of the subsoil is reflected in the choice of facies variograms to be used for quantile simulation. For the sake of clarity, it should be remembered that in a first embodiment mentioned above, the spatial coherence data are extracted from the models in proportions provided by the geologist. This means that the geological uncertainty is translated only by the models in proportions. In practice. this implies a preliminary analysis of the spatial continuity of the models in proportions provided initially. in order to extract the spatial coherence data that will make it possible to carry out the stress-constrained simulation. In contrast, in the second embodiment discussed above, the spatial coherence data is provided by the geologist. This means that the geological uncertainty is translated by both proportional models and spatial coherence data. Note, however, that in a variant of this embodiment, the new proportional models will be simulated using a single quantile for all the cells of the model in proportions, which amounts to considering spatial coherence data, variograms of infinite range and zero threshold. These points will be discussed again later. R 8teteis'205ott.2 (: 1 - OR'I 11 Uncertainties 1 and 2 - land deposit doc - Il r'IrR - Io ol - F27

Concerning the first embodiment: the variograms used to simulate the quantile vectors can for example be constrained as a function of variograms of facies extracted from the models in proportions provided initially. This embodiment is particularly well suited for modeling so-called carbonated platform environments. Indeed, in this type of environment, the nature of the sediments generally follows a certain polarity, and varies gradually along the carbonated ramp. Such a distribution is characterized by a relatively smooth spatial variation of facies proportions, according to a certain trend map.

A methodology is for example the following. Knowing the Dirichlet laws attached to each of the cells of the model in proportions, one determines for a model in proportion given (for example the model MA) and a given cell (uvw), the vector quantile (ui, u2, u3) At, ,, t which, once transformed, provides the proportions of facies observed for this model.

Since each component is known everywhere in space, its variographic analysis is traditionally done. First of all, the values of an experimental variogram are calculated for increasing distances and a certain number of directions. Then, we try to adjust to these series of experimental points an analytical model of variogram, for example chosen from the Gaussian, spherical and exponential models. These make it possible to deduce the covariance between any two points as a function of their spacing and, possibly, of the direction they define. Therefore, for each quantile, we have Nm analytic expressions of the variogram yt (h) associated with it, each resulting from models in initial proportions. For example, the successive study of models in proportions MA, MB and MC (illustrated in FIG. 3A) leads to define for a given quantile component, a theoretical variogram model. For example, for the MA model, a range is obtained. of 2810 meters and a bearing S = 0.02 along the North - South axis (Figure 5A) and, for the East - West direction (Figure 5B), a span of 2290 m and a bearing S = 0.02. For the MB model (not shown), the variogram has a range of 2030 m and a range of 0.01 in North - South orientation. According to the East-West axis, it reveals a range of 1650 puts a threshold of 0.03. For the MC model (not shown), its range is 2860

R $ rereis 265 ') o'2 (21 - ORBI Il Incerulude, 1 and 2 - such droplet doc - Il n1 ux - to t - IG ?? m and 2320 m and the steps of 0.02 and 0.02, according to In order to avoid any correlation model, we can combine, for each quantile, the Nm variograms drawn from variographic analysis of the models in initial proportions. corresponds to a weighted average of the various variograms possible, then a weighted average of the different possible variograms is made, and the variograms obtained are then used to constrain the simulation of the quantiles necessary for calculating new probabilities of occurrence of facies. thus to generate new models in facies proportions The constraint simulation of the quantiles is done in a conventional way by stochastic simulation, for example by using the simulation method At a later stage (S300, (Figure 2), stochastic simulations of facies and petrophysical properties will be carried out from proportional models, so as to obtain geological models that correspond to alternative images of tanks. It should be noted that the alternative set out above opens the way to certain sophistications. In particular, spatial coherence can be introduced by learning on already existing models. In other words, the newly simulated proportions models can be taken into consideration to determine parameters of the distribution distributions estimated in step 5100 (FIG. 2). Steps S100 and S200 are then called iterative or interleaved. In the second embodiment mentioned above, the variograms T, (h) used to simulate the components of the quantile vectors can be constrained according to variograms provided by the geologist. according to his knowledge of the environment. This embodiment is particularly advantageous when it comes to modeling silico-clastic environments, characterized by relatively abrupt changes of facies.

We will then be able to "approximate" a quantile variogram of a variogram of facies provided by the geologist. FIG. 1 and 2-iule depoi doc-1 1 01'0 -Ions-17'27 According to a first variant of this embodiment, the models in proportions provided initially do not include indications of variations in the distribution of different facies in space. Thus, for a given model, we will assign to all uvw cells the same probability value of occurrence of facies. The fact of assigning, for all the cells of a model, the same values of probabilities of occurrence of facies assumes a so-called stationarity hypothesis. By modifying the probability values of occurrence of facies, we can decline the model in several versions, for example a median version, a minimal version (called pessimistic version), and a maximum version (so-called optimistic version). For example, in the optimistic version, one will have the values pj ° pt, p2 ° pt p3OPt of probabilities of occurrence of facies for all the cells of the model in proportions. For the pessimistic version one will have the values plpess, p2pess p3pess of probabilities of occurrence of facies for all the cells of the model in proportions. In step S100 (FIG. 2) estimation of probability distribution laws, a single law will then be obtained for all the cells of the model. When creating new models in proportions, the degree of continuity and anisotropy of the new probabilities of occurrence of facies will thus come exclusively from spatial coherence data provided by the geologist. To do this, we will compare the variograms of each of the quantile vector components of the variograms relative to the spatial coherence data provided. Several simulations can be made according to directions of anisotropy different from the variogram. Thus, while the initial distribution assumes a hypothesis of stationarity, the taking into account of spatial coherence data nevertheless leads to a "non-stationarity" of the facies, only carried by the spatial coherence data provided. Another variant of this embodiment consists in producing a single simulation of the quantile vectors (ut, u2, u3) m ,, t for all the cells of the model. We will speak here of uniform draw of quantiles. Assuming again three initial models, the intermediate values F1, 1 -2, and F3 are obtained from the same quantile vector (u1, u2, u3) for each of the cells of the model. In order to carry out a single simulation of the vectors (u ,, u2, u3) for each R-e, cl, `6i0o26521 - oanl IlIItCeOtlUdC, and 2 -test document doc - Il .1n8 - In r, l - [S.27 cell, one can use, in the SGS methods, a variogram of infinite range and of zero threshold during the simulation of the quantile values. Thus, if we perform four simulations from four different quantiles, we obtain four more or less optimistic models.

Various variants of this embodiment will now be illustrated from examples. In a first example, very little information is available and there is substantial uncertainty about the proportions of the facies and the direction of the inputs. This example is an extreme case, for which we have very little data. These data concern only the relative proportions of the facies, and the preferential directions according to which the sandy contributions are made. More precisely, it involves modeling a channelized environment with three facies varieties typical of stream deposits: - coarse sands of channels; - leavening silts; and - clays. In the present case, the geological uncertainty affects precisely: - The overall value of the proportion of facies, which can vary according to the following proportions: o In the case of an optimistic scenario: 60% coarse sands. 30% silts, and 10% agile; o In the case of a pessimistic scenario: 20% coarse sands, 50% silts, and 30% agile. - The direction of sandy inputs, which. in the absence of preferential azimuth, can define an angle with the North between 45 ° and 135 °. The extension of the preferential zones, whose characteristics (width, length) are naturally linked to those of the facies, but remain difficult to evaluate. Here, only the width is indeterminate but remains between 800 m and 2 km. In order to model this environment, we define a basic geological scenario, which is declined in two models in proportions, a model in optimistic proportions and a model in pessimistic proportions. whose proportions are defined

R R e eers 26j) o 26 21--080111 Incem rudes 1 and 2. leme dtpot doc - I1 1 I - Ir, 01 - I'F27

20 above. Moreover, we do not associate these two models in proportions with a spatial distribution a priori. On the contrary, we consider that, for each of these models in proportions, a uniform distribution of the proportions of facies is the hypothesis of stationarity.

A variogram is further provided by the geologist for each facies, depending on his knowledge of the environment. The geologist thus translates the different geological scenarios compatible with the data and information at his disposal, both by proportional models and variograms of facies. From these models in proportion, we then determine the parameters of a Dirichlet's law, as explained above. We can then weight these models in proportions to determine the parameters of the Dirichlet's law. Due to the hypothesis of stationarity, the proportion vectors associated with each of the cells of the model in proportions follow the same Dirichlet law. We can then simulate quantile vectors for each cell of the model according to the methodology described above. We will then be able to "bring closer" the anisotropy of the variogram yf (h) associated with a given quantile of that of the corresponding facies. Examples of such variograms are illustrated in Figure 6A. The main direction 8f (FIG. 6B) of the variogram yf (h) (FIG. 6A) naturally coincides with the direction in which the facies shows preferential elongations. and therefore offers the most continuity. In the present case, this amounts to considering the azimuth of the sedimentary inputs. The main direction 9f (FIG.6B) is therefore drawn into a support distribution [45; 135], because the orientation of the contributions is unknown (but can define an angle with the North between 45 ° and 135 °). The range Rf-n, according to the main direction of the variogram, is set to a value larger than the length of the model. The range Rte, according to the second direction of the variogram and perpendicular to the first, expresses the uncertainty as to the width of the preferential zones. It is simulated in a triangular support distribution [800 m; 2 km] and fashion 1400 m. Several proportional models will be created, corresponding to several anisotropy directions, from which several geological models will be generated by stochastic simulation of facies and petrophysical properties. R - • BRIEF 2 I I I I I lncerttludes 1 and - teele d2pot dot, - 11'111 'iltl - 1 t nl - 2t, 27

In a second example, the reservoir is oriented along an east-west axis and delimits an area 5 km wide by 10 km long. It is discretized into a stratigraphic grid of 100 x 50 x 1 cells. There are three facies varieties, typical of stream deposits: coarse channel sands (FI facies), leavening silts (facies F2), and clays (facies F3) of lowlands. A seismic campaign has defined two contrasting zones that share the reservoir from north to south: In the west, an area (hereinafter Fw) with high channel proportions: it corresponds to the channeling belt. In the east a domain (hereinafter Ovb) with the proportions of weaker channels. The direction of the sedimentary inputs is determined (it comes from the North). Geological uncertainty concerns here: - The overall value of facies proportions; - the distribution of the proportions of facies in the channel belt, because one generally observes lithology changes as one moves away from the axis of the belt; and - the lateral limits of the channeling belt, since the transition to the overflow zone can not be "clean". In order to model this environment, we define a basic geological scenario, which is divided into two models in proportions, a model in optimistic proportions and a model in pessimistic proportions, whose proportions are defined below: In the optimistic scenario we have: - domain (Fw): 60% of coarse sands, 30% of silts, 10% of clays - domain (Ovb): 10% of coarse sands, 50% of silts, 40% of clays. pessimistic scenario we have domain (Fw): 20% of coarse sands, 50% of silts. 30% clay domain (Ovb): 0% of coarse sands, 20% of silts, 80% of clays In each scenario (pessimistic or optimistic) is associated a model in proportions. The two models are combined in proportions by giving them a similar weight. We then define stationary Dirichlet laws, respectively, in the domains (Fw) and (Ovb). The variability of the proportions of facies is thus carried on the one hand by the laws of Dirichlet (since they delimit the regions), on the other hand

RR, eveix "o5on26521 - i18nl 1 1 Incernmde, 1 e1 2 - temI depot dot, - II t'l Ux - n1 - 21121 'by variograms y (h), which introduce the non-stationarity of the facies to the In each facies, the variogram yt (h) used is of Gaussian type, in order to obtain variations of smooth proportions in space.The orientation of the contributions being here known, the main direction y1 (h) the variogram corresponds to this axis, its range Rt1 in this direction is deterministic and equal to 15 km, it exceeds the length of the model because it simulates traversing objects Its range Rte according to the second direction of the variogram, perpendicular to the first, is simulated in a triangular support distribution [800 m; 2 km] and 1400 m mode.

The simulation of the quantiles is constrained so as to respect the variograms of facies. This will create new models in proportions, from which geological models will be generated by stochastic simulation of facies and petrophysical properties. It should be noted that the methodologies outlined above are based on the assumption that the vector proportion of facies (P), follows a Dirichlet distribution. These methodologies could, however, use other probability laws. Other laws have been tested. However, these resulted in, in the end, less good simulations. It should also be noted that the choice of variogram parameters strongly depends on the deposition environment considered. From one medium to another. spatial continuity does not translate in the same way, which requires a particular treatment for each environment. In the end, the definition of the geological scenario governs the distribution in space of proportions. The method according to the invention makes it possible to take account of the uncertainty on the geological interpretation. At this stage of modeling, this type of hazard is proving to be a source of significant variability that the processes of the prior art deal with, at best, in a non-exhaustive manner. As a result, the present invention allows for improved modeling of a reservoir. The subsequent exploitation of the reservoir is also improved. Finally, the invention may relate to a method, implemented by computer. construction of three-dimensional geological models, for the evaluation of hydrocarbon volumes in a reservoir. R Brel ers 2t50n, 26> 2 I - OXn111 Incernludes I erg - the Depth doc.

Claims (4)

A method implemented by computer for constructing three-dimensional geological models, for the evaluation of geological quantities, comprising the steps of: providing (S10) a set of models in proportions, each of the models in proportions comprising uvw cells to which respective values of likelihood of occurrence of facies are associated, said values forming a set of probability values; estimation (S 100), for each of the cells, of a distribution law of facies probabilities. from the sets of values of probabilities, so that each of the estimated laws reflects the set of models provided; - Extraction, from models in proportions provided initially. spatial coherence data; - creation (S200) of a new set of proportional models, based on the estimated facies probability distribution laws, including a draw of new probabilities of facies for each of the cells, the draw being further constrained according to the data spatial coherence extracted; and - creating (S300) a new set of geological models, by stochastic simulation of facies and petrophysical properties from the new set of proportionally created models. 2. Method implemented by computer for constructing three-dimensional geological models, for the evaluation of geological quantities, comprising the steps of: providing a set of models in proportions, each of the models in proportion comprising uvw cells with associated respective values of probability of occurrence of facies, said values forming a set of probability values; - providing spatial coherence data; -of estimation (Sl00), for each of the cells, of a distribution law of probability of facies, from the sets of values of the probabilities, so R t ec 1 5ntt 265221--0001 II Uncertainties I and 2 - that each of the estimated laws reflects the set of models provided; - of creation (S200) of a new set of models in proportions, starting from the distribution distributions of probabilities of facies estimated, including a draw of new probabilities of facies for each of the cells, the draw being further constrained according to the data spatial coherence provided; - creation (S300) of a new set of geological models, by stochastic simulation of facies and petrophysical properties, from the new set of models in created proportions. 3. The method according to claim 1 or 2, wherein the distribution laws 10 of facies probabilities are Dirichlet type. of parameters {cl cnF} ,,,. ,, where nF is the number of facies. 4. The method according to claim 3, wherein the creation step (S200) comprises: the simulation of a set of intermediary random variables (F1) ,,,,,,,,, .... and (Fä F) ,,,. ,, 15 according to gamma laws of parameters (l, c,), n..w .... and (l, cnF), n. ,,. respectively, the new facies probabilities of the new set of models in proportion corresponding to the ratio of the realizations of these intermediate random variables. 6. The method according to claim 4, wherein, at the creation step (S200), the draw of the new facies probabilities is constrained according to the spatial coherence data, during the simulation of the set of intermediate random variables. 7. The method according to claim 5, wherein in step (S200) of creating a new set of models: quantile values, u1, ... F are associated with each of the random variables. intermediates (F1) ,,,,, and (FnF) ,,, a quantile value uj being defined according to an inequality 1P (FF) <in which IP (F1) is a cumulative probability; and - the draw of the new probabilities of facies is constrained via a draw of values R B'es and C'.5OII 2 (21--0X'1111 Uncertainties 1 el 2 - test of doc - 11 lrt'nX - Iu ' 11 - 2-1: 27 25 quantile values being constrained according to the spatial coherence data 7. The method according to claim 6, wherein: the spatial coherence data comprises associated variograms 8. The method according to claim 9, wherein: at the creation step (S200) of the new set of models in proportion, the constrained drawing of quantiles is done by stochastic simulation. claim 8, wherein the stochastic simulation is by Gaussian sequential simulation or SGS methods 11. The method according to one of claims 6 to 9, wherein: the spatial coherence data comprises an infinite range variogram. and zero threshold: and - the creating step (S200) the new set of models in proportion, the draw quantile values meets said variogram infinite range and zero threshold. 14. The method according to one of claims 1 to 10, wherein, at the creation step (S200) of the new set of models, the draw of the new facies probabilities is further constrained according to different directions of anisotropy of the spatial coherence data. 15. The method according to one of claims 1 to 11, wherein at the data supply step, each of the provided templates comprises uni cells. associated with the same facies probability value, for a given facies. The method of any one of claims 1 to 12, further comprising a step of weighting the provided templates and wherein. in step R Bret et. '_ 65O't6571 - tiX0111 Uncertainties 1 and 2 - such as dem doc - II oi VN - I ntm -? 5!? 7 26 estimation (SI 00), the distribution laws facies probabilities are estimated to reflect the set of weighted models. The method according to any one of claims 1 to 13, wherein the estimation (S100) and creating (S200) steps are performed iteratively, so that at least one of the templates created during the creation step (S200) is used to determine parameters of at least one of said distribution laws (SI 00). The method according to one of claims 1 to 14, wherein the step of creating (S300) a new set of models further comprises a step of simulating petrophysical properties for each of the facies cells. 16. The method according to one of claims 1 to 15, further comprising a step of deducting hydrocarbon accumulations. 17. A computer program product, the program comprising routines for executing the steps of the method according to one of claims 1 to 16 when said program is executed on a computer. 18. A computer system comprising a memory containing a program comprising routines for performing the steps of the method according to one of claims 1 to 16, during the execution of said program on the system. R 'Dies ets 2 5 "2 (2 I - -)) l 1 1 Incetutudes 1 and 2 - text of document doc - Il o I u I - I c - t'tI - 2 (27