Method for determining an electrofacies interpretation of measurements carried out in a well

Abstract

The invention relates to a method for determining an electrofacies interpretation of measurements relating to at least one segment of least one well passing through an underground formation. The method includes applying a silhouette method to a plurality of classifications of the plurality of measurements determined by an unsupervised classification method applied for a plurality of values of the number of classes, in order to determine a first electrofacies interpretation and a corresponding number of classes. Next, an iterative stochastic relaxation method is applied to probabilities of each of the measurements belonging to each of the classes of the first electrofacies interpretation, and a second electrofacies interpretation is obtained when a predefined convergence criterion is met.

Description

[0001] METHOD FOR DETERMINING AN ELECTROFACIAL INTERPRETATION OF MEASUREMENTS TAKEN IN A WELL

[0002] technical field

[0003] The present invention relates to the field of interpretation of measurements made in a well drilled in an underground formation, such as well log measurements made along a well.

[0004] The invention can be applied, without limitation, to the fields of oil exploration and production, the characterization of an underground formation for the purpose of geological storage of a fluid such as CO2, the monitoring of a geological storage site for a fluid, geothermal energy, and energy storage in the subsurface. More generally, the invention can be applied to any field involving a geological characterization step of an underground formation.

[0005] In general, the exploration and development of geological petroleum reservoirs require the most precise knowledge possible of subsurface geology in order to effectively assess reserves, model production, and manage operations. Indeed, determining the location of a production and / or injection well within a hydrocarbon reservoir, the composition of the drilling mud, completion characteristics, the choice of a hydrocarbon recovery process (such as water injection), and the parameters necessary for implementing this process (such as injection pressure, production rate, etc.) all require a thorough understanding of the reservoir. Knowledge of a reservoir means having the most accurate possible description of its structure, petrophysical properties, fluid properties, and so on.

[0006] To acquire this knowledge, the oil industry combines field measurements (carried out in situ during seismic surveys, well logging, coring, etc.) with experimental modeling (performed in the laboratory) and numerical simulations (performed using software). The formalization of this knowledge then involves creating a model of the subsurface, represented on a computer as a gridded representation known as a geological model.

[0007] This geological model can be used (after scaling) in a flow simulation (or reservoir simulation) to predict (or even simulate) flows, pressure evolution within the reservoir, and fluid production at wells drilled into the reservoir. Clearly, the prediction of a flow simulation will be more representative of the actual flows in the underground formation of interest the more accurate the geological model of that formation. Well logs and core sampling provide precise local information about the rocks encountered by a well and are therefore highly valued for building a reliable geological model.

[0008] Well logging involves measuring the characteristics of the rocks through which a well passes using probes. A logging measurement results in a recording as a function of depth (or along a feature of a geological formation through which a well passes). Examples of well logging include gamma ray logging, sonic logging, bulk density logging, electrical logging, and well imaging logging.

[0009] The recordings resulting from well logs are then analyzed, that is, interpreted, most often jointly, to deduce the characteristics of the rocks. This interpretation involves, in particular, searching along these recordings for intervals (that is, successive sets of samples) exhibiting similar characteristics. These intervals, for which the characteristics are consistent from one sample to another, are called electrofacies.

[0010] Generally, the interpretation of at least some of the log measurements is carried out by an expert, who must cross-analyze the different types of log measurements. The result of such an interpretation is therefore subjective and can vary considerably from one interpreter to another. Furthermore, such a manual process can be lengthy and tedious, and cannot reasonably be considered for all log measurements. However, the quality of a human interpretation of log measurements is often superior to fully automated interpretations implemented by computer.

[0011] Previous technique

[0012] The following documents will be cited later in the description:

[0013] Serra O, Abbott HT (1980) The contribution of logging data to sedimentology and stratigraphy. In: SPE 9270, 55th Technical Conference, Dallas, TX, 19 pp.

[0014] Dubois, M. K., Bohling, G. C., & Chakrabarti, S. (2007). Comparison of four approaches to a rock facies classification problem. Computers & Geosciences, 33(5), 599-617.

[0015] Emelyanova, I., Pervukhina, M., Clennell, M., & Dyt, C. (2017, June). Unsupervised identification of electrofacies employing machine learning. In 79th EAGE Conference and Exhibition 2017-Workshops (pp. cp-519). European Association of Geoscientists & Engineers. Halotel, J., Demyanov, V., & Gardiner, A. (2020). Value of Geologically Derived Features in Machine Learning Facies Classification. Mathematical Geosciences, 52(1), 5-29.

[0016] Jeong, J., Park, E., Emelyanova, I., Pervukhina, M., Esteban, L, & Yun, S. T. (2020). Interpreting the Subsurface Lithofacies at High Lithological Resolution by Integrating Information from Well-Log Data and Rock-Core Digital Images. Journal of Geophysical Research: Solid Earth, 125(2), e2019JB018204.

[0017] Rosenfeld A., Hummel R.A. and Zucker S.W. (1976), Scene labeling by relaxation operations, IEEE Trans. Systems, Man, Cybernetics, vol. SMC-6, 420-433.

[0018] Rousseeuw, P.J. (1987), Silhouettes: A graphical aid to the interpretation and validation of cluster analysis, Journal of Computational and Applied Mathematics. 20:53-65. doi : 10.1016 / 0377-0427(87)90125-7.

[0019] Ruofei Zhao, Yuanzhi Li, Yuekai Sun, Statistical convergence of the EM algorithm on Gaussian mixture models. Electron. J. Statist. 14(1): 632-660 (2020). DOI: 10.1214 / 19- EJS1660.

[0020] Zucker S.W., Krishnamurthy E.V. and Haar R. L. (1978), Relaxation processes for Scene labeling: convergence, speed and stability, IEEE Trans, on Systems, Man and Cybernetics, vol. SMC-8, no. 1.

[0021] Among the computer-based methods used to interpret well electrofacies measurements, a classic distinction is made between fully automated methods, involving unsupervised classification, and partially automated methods, involving supervised classification. Unlike an unsupervised classification method, a supervised classification method aims to group samples into homogeneous classes based on predefined rules determined from training data. It is common practice in the prior art for the training data required by supervised classification methods to come from a manual interpretation by an expert (hence the term semi-automated method) of at least a subset of the well measurements.An electrofacies interpretation from a supervised classification method is generally more geologically realistic than an electrofacies interpretation from an unsupervised classification method, because it takes into account a pre-interpretation carried out by a specialist.

[0022] Among fully automated electrofacies interpretation methods, the document (Emelyanova et al., 2017) is well-known. The process described in this document combines three unsupervised classification methods to reach a classification consensus. In other words, the process described in this document applies three unsupervised automatic classification methods to well log data to determine three electrofacies interpretations, and then determines a final electrofacies interpretation from this plurality of interpretations by the majority of voters. Furthermore, the quality of the prediction is quantified by the proportion of majority votes relative to the total number of voters. However, this document does not describe the consideration of a criterion, such as a geological one, in determining its final interpretation. Moreover, the process described in this document does not propose any further improvements to its final interpretation.

[0023] We are also familiar with the document (Halotel et al., 2020) which describes the value of incorporating geological information into supervised classification methods to improve the facies interpretation of well logs, compared to data-driven classification methods. More specifically, this document outlines constraints based on advanced preliminary analyses, such as stratigraphic cycle analysis, depositional type analysis (marine or non-marine), and petrophysical analyses to determine grain size, pore size, clay content, etc. However, these geological and / or petrophysical analyses require specific expertise (from a sedimentologist and a petrophysicist, respectively) and are generally very rarely available during the electrofacies interpretation phase of well log data.Furthermore, the process described in this document does not propose to refine the interpretation in electrofacies resulting from a first classification, nor to combine different classification methods to arrive at a classification consensus.

[0024] We are also familiar with the paper (Jeong et al. 2020) that describes the combination of an unsupervised automatic classification method for core images and a supervised classification method for well data using a multi-layer neural network for improved automatic classification in lithofacies. More specifically, the process described in this paper uses a classification obtained by an unsupervised classification method applied to core images to create training information for a supervised classification method applied to log data. Thus, in this process, the training information is obtained only from the portions of the well for which cores, and moreover, core images, are available. In practice, cores are not available along the entire length of the well for which log records are available.Furthermore, the core samples are taken from preferred areas of the well (in other words, they are not taken randomly). For example, unlike reservoir areas, clay cover zones are rarely or only minimally cored (because their petrophysical properties are less important). Thus, the training information described in this document is not necessarily representative of all the electrofacies classes present in the well, which can negatively impact the results of the supervised classification subsequently implemented. In particular, the result of the supervised classification is inherently limited by the number of classes resulting from the unsupervised classification, which can lead to an erroneous interpretation of the well log measurements in terms of electrofacies.Furthermore, the procedure described in this document employs a single supervised classification method, namely a multi-layer neural network, to identify lithofacies at all depths, including those not cored. Therefore, this document does not teach how to combine different supervised classification methods to reach a classification consensus.

[0025] We are also familiar with the document (Dubois et al., 2007) that compares four conventional supervised classification methods for electrofacies of well logs on the same dataset. However, the procedure described in this document does not describe the use of a criterion, such as a geological one, to refine a classification. Furthermore, the procedure described in this document does not propose refining the electrofacies interpretation resulting from an initial classification, nor does it propose combining different classification methods to reach a consensus. Finally, this document does not describe the quantification of the probability of a point belonging to a class.

[0026] Furthermore, US document 2002 / 0052690 describes the application of supervised classification methods to determine an electrofacies interpretation of well logs. This document also describes a quantification of the probability of a point belonging to a class. However, it does not describe the consideration of a criterion, such as a geological one, to refine a classification. Moreover, the procedure described in this document does not propose refining the electrofacies interpretation resulting from an initial classification, nor does it propose combining different classification methods to reach a classification consensus.

[0027] Finally, we are familiar with document W02022 / 043051 A1, which concerns a method for determining an electrofacies interpretation of measurements relating to at least a portion of at least one well traversing an underground formation. More specifically, the method comprises applying a plurality of supervised or unsupervised classification methods to the measurements to determine training information. Then, a plurality of supervised classification methods is applied to the measurements, with the classification methods being trained using the training information. An ensemble classification method is then applied to the results of the plurality of supervised classification methods to determine the electrofacies interpretation of the measurements.

[0028] However, this method has the drawback of requiring an initial application of several supervised or unsupervised classification methods, followed by a second application of another set of supervised classification methods. This process can therefore be relatively complex to implement (requiring the automatic generation of training data for the supervised classification methods). Furthermore, when implementing the method using unsupervised classification methods (which has the advantage of not requiring a training database), the number of electrofacies (or classes) must be predefined by a user. This, on the one hand, prevents complete automation of the implementation of the process according to the invention, and on the other hand, can lead to results dependent on the user's expertise.

[0029] Thus, the processes described in the prior art describe either methods that can be fully automated but may lead to geologically implausible or even erroneous electrofacies interpretations, or partially automated methods, requiring information from an expert, which may lead to a more realistic but subjective electrofacies interpretation.

[0030] The present invention aims to overcome these drawbacks. In particular, the method according to the invention allows for fully automated implementation, requiring neither training data nor the predetermination of a number of classes. Indeed, the method according to the invention uses a statistical approach to classify measurements into automatically determined categories. Furthermore, a fully automated spatial smoothing of the interpretation, based on statistical considerations, eliminates the need for a reclassification step generally performed manually by a user—a process that can be lengthy, tedious, and also subjective.

[0031] Summary of the invention

[0032] The invention relates to a method for determining an electrofacies interpretation of measurements relating to at least a portion of at least one well passing through an underground formation. The method according to the invention comprises carrying out the following steps:

[0033] A) a plurality of measurements are carried out relating to at least said portion of said at least one well crossing said underground formation, said plurality of said measurements resulting at least from a well log and / or an image of at least one core taken from said at least one well;

[0034] (b) A first electrofacial interpretation of said plurality of said measurements relating to at least said portion of said at least one well is determined as follows: (a) for each value of a number of classes of a plurality of values ​​of said number of classes between a minimum number of classes and a maximum number of classes, an unsupervised classification method is applied to said plurality of said measurements; (b) a silhouette method is applied to said plurality of classifications of said plurality of measurements determined for each of said values ​​of said number of classes, and said first electrofacial interpretation and a corresponding number of classes are determined by selecting said classification and said value of said number of classes for which said silhouette score is closest to 1;(c) an iterative stochastic relaxation method is applied to the probabilities of each of said measures belonging to each of said classes of said first electrofacial interpretation, and a second electrofacial interpretation is obtained when a predefined convergence criterion of said iterative relaxation method is reached.

[0035] According to one embodiment of the invention, said well logging can be selected from among gamma ray logging, sonic logging, density logging, electrical logging or well imaging logging.

[0036] According to one implementation of the invention, said unsupervised classification method can be chosen from a family of exclusive partitioning methods or a family of probabilistic partitioning methods.

[0037] According to one implementation of the invention, said unsupervised classification method can be a Gaussian mixture model.

[0038] According to one implementation of the invention, the probabilities of belonging of each of the measures to each of the classes can be a function of a Mahalanobis distance.

[0039] According to one embodiment of the invention, said iterative stochastic relaxation method can implement a compatibility matrix measuring the compatibility of membership of a measure i to a class c and of a measure j to a class d expressed according to a formula of the type: r ijcd ~ / PidPjc where p id is a probability that a measure i belongs to a class d and p JC is a probability that a measure j belongs to a class c.

[0040] According to one embodiment of the invention, the predefined convergence criterion of the iterative relaxation method can be reached when, = 0, with: where 1^ = 1 if p c >1) = max p^ and 1^ = 0 otherwise, p c >1) is the probability that a measure i belongs to the class otherwise, is the probability that a measure i belongs to class d at iteration (n - 1), N is the number of said plurality of measures, and K is said number of classes.

[0041] The invention also relates to a computer program product downloadable from a communication network and / or recorded on a computer-readable medium and / or executable by a processor, comprising program code instructions for implementing the method as described above, when said program is executed on a computer.

[0042] The invention further relates to a method for exploiting a resource present in an underground formation and / or for storing a fluid in said underground formation, comprising the implementation of the method to determine an electrofacies interpretation of measurements relating to at least a portion of at least one well passing through an underground formation as described above.

[0043] According to one embodiment of the invention, from at least said interpretation in electrofacies of the measurements relating to at least said portion of at least said well crossing said subsurface formation, one can construct a mesh representation representative of said subsurface formation, one can determine at least one exploitation scheme of said resource and / or a scheme for injecting said fluid into said subsurface formation from at least said mesh representation representative of said subsurface formation, and one can exploit said resource of said subsurface formation according to said exploitation scheme and / or one can inject said fluid into said subsurface formation according to said scheme for injecting said fluid into said subsurface formation.

[0044] According to one embodiment of the invention, said resource exploitation scheme and / or fluid injection scheme may include at least one site of at least one injection well and / or at least one production well, and said wells of said site may be drilled and equipped with production infrastructure.

[0045] Other features and advantages of the process according to the invention will become apparent from the following description of non-limiting examples of implementations, with reference to the figures attached and described below.

[0046] List of figures

[0047] Figure 1 presents, as an illustration, a log of natural radioactivity as a function of depth.

[0048] Figure 2 presents, as an illustration, an electrofacies interpretation carried out manually by an expert geologist, for which 16 different classes were identified.

[0049] Figure 3A shows, by way of illustration, an electrofacies interpretation resulting from the implementation of steps 1 and 2 of the process according to the first aspect of the invention. Figure 3B shows, by way of illustration, an enlargement of Figure 3A between depths of 2200 m and 2600 m.

[0050] Figure 4A presents, by way of illustration, an electrofacies interpretation resulting from the implementation of all the steps of the process according to the first aspect of the invention.

[0051] Figure 4B shows, for illustrative purposes, an enlargement of Figure 4A between depths of 2200m and 2600m.

[0052] Description of the implementation methods

[0053] According to a first aspect, the invention relates to a method for determining an electrofacies interpretation of measurements relating to at least a portion of at least one well crossing an underground formation.

[0054] According to one embodiment of the invention, the method according to the first aspect of the invention may relate to a method for determining an electrofacies interpretation of measurements relating to at least a portion of at least one well passing through an underground formation in order to exploit a resource of an underground formation and / or to inject a fluid into the underground formation.

[0055] According to a second aspect, the invention relates to a method for exploiting a resource from an underground formation and / or for injecting a fluid into the underground formation, the method according to the second aspect comprising the implementation of the method to determine an electrofacies interpretation of measurements relating to at least a portion of at least one well according to the first aspect of the invention.

[0056] The underground formation being studied can be at any depth, and in particular be shallow (for example less than 3 km, as is mostly the case in the case of a geothermal, hydrogeological or mining resource), or deep or even ultra-deep and possibly under a layer of water (as is mostly the case in the case of an oil and / or gas resource and in the case of deep geothermal energy).

[0057] According to the invention, the plurality of measurements relating to at least a portion of at least one well results from at least one well log and / or an image of at least one core sample taken from the well in question, at the level of at least one portion of the well in question. According to one embodiment of the invention, the underground formation of interest may include an oil reservoir, preferably with its cap.

[0058] According to the invention, the well traversing the underground formation of interest can have any geometry, and in particular be a vertical or deviated well. This is referred to as the well trajectory.

[0059] By electrofacies, we mean a grouping of samples from the plurality of measurements (e.g., logs) according to the invention having homogeneous (measurement) values. In other words, two samples of measurements (e.g., logs) belong to the same group, or 'electrofacies', if their (e.g., log) responses, that is, if the (e.g., log) measurements taken at these points, do not differ significantly. The concept of electrofacies was introduced, in particular, in the document (Serra and Abbot, 1980). Determining the different electrofacies can be seen as seeking both to maximize the differences between the (e.g., log) responses at any two points belonging to two different electrofacies, and to minimize the differences between the (e.g., log) responses at any two points belonging to the same electrofacies.

[0060] Electrofacies interpretation of well measurements refers to the classification (or partitioning) of samples along the well's path for which measurements are available. In other words, following electrofacies interpretation, a class is assigned to each sample along the well's path for which measurements are available. An electrofacies class is a label, which can be any meaningless string (e.g., class 'CO', class 'C1') or a meaningful one (e.g., 'sandstone', 'clay', 'limestone'), a color, or simply a symbol (e.g., "*', "+', '%', etc.). This label is not a quantitative quantity, unlike quantities such as numbers that follow an order relation (i.e., lesser, greater, equal).In particular, when an electrofacies interpretation is available from a specialist, at least for some samples along at least a portion of at least one well, an electrofacies class can be a chain of characteristics representative of a lithological type (for example 'sandstone', 'limestone', 'clay', etc.). These are then referred to as lithofacies.

[0061] In general, the process according to the invention comprises at least the following steps:

[0062] 1) Acquisition of measurements relating to at least a portion of at least one well

[0063] 2) Determination of a preliminary electrofacies interpretation using an unsupervised classification method and a silhouette method

[0064] 3) Determination of a second electrofacies interpretation using an iterative stochastic relaxation method

[0065] 4) Exploitation of a resource and / or storage of a fluid in an underground formation The process according to the first aspect of the invention includes at least steps 1 to 3 described below.

[0066] The method according to the second aspect of the invention further comprises at least step 4 described below.

[0067] At least step 2) and / or step 3) can be implemented by computer means, including a computer, processor or calculator.

[0068] The various steps of the process according to the invention are detailed below. According to the invention, the steps of the process according to the invention are applied to at least a portion of at least one well penetrating the underground formation.

[0069] 1) Acquisition of measurements relating to at least a portion of at least one well

[0070] During this step, a plurality of measurements are taken relating to at least a portion of at least one well crossing the underground formation of interest, the plurality of measurements resulting at least from a well log and / or an image of at least one core taken from the well in question.

[0071] According to one embodiment of the invention, at least one well log can be selected from gamma ray logging, sonic logging, density logging, electrical logging, or well wall imaging logging. Advantageously, at least five different logs are performed for the same portion of the same well. The variety of logging types allows for more reliable electrofacies interpretation, due to the redundancy of information that can be derived from each type of log.

[0072] As is well known, well logging is performed using a probe that moves along the path (at least a portion, typically a few kilometers) of the well and measures a property (e.g., density, natural radioactivity, resistivity, etc.) of the rock surrounding the well at successive sampling intervals (on the order of tens of centimeters). Thus, a well logging measurement results in a series of samples (typically a few thousand to tens of thousands of measurement points) along the path of the well in question, each sample containing at least one value of a property (e.g., density, natural radioactivity, resistivity, etc.) of the surrounding rock.

[0073] According to one embodiment of the invention, well logs can undergo pretreatments, such as resampling well known to those skilled in the art, so that well logs of different types are "replaced" at the same measurement points along the well path.

[0074] According to the invention, at least one image of at least one core sample taken from at least one well is obtained by an imaging device, such as a CT scanner or any other imaging technique. Preferably, the image of the extracted core can be preprocessed, for example by textural analysis, to determine at least one measurement of a desired property (e.g., layer dip) for a series of samples along the wellbore. Advantageously, when a core image is used in conjunction with at least one well log, resampling can be performed so that the sample series of the core images and the well log are concordant in terms of the location of the measurement points. Information on core image processing methods can be found, for example, in the document (Jeong et al., 2020).

[0075] According to one embodiment of the invention, well logs and / or the image of at least one core taken from at least one well may have undergone principal component decomposition beforehand.

[0076] At the end of this step, at least two types of measurements are obtained from a well, i.e., measurements from at least one well log and / or an image of a core taken from the well, for a succession of samples along at least a portion of the trajectory of at least one well crossing the underground formation of interest.

[0077] At the end of this step, we have a table of size NxP, where N is the number of measurement points along the portion of at least one well (which is a function of the length of the portion of the well trajectory for which at least one measurement is made, which can be on the order of km for log measurements, and of the sampling step of the measurement, which can be on the order of tens of cm for a logging tool) and P is the number of types of measurements (sonic logs, resistivity, etc.) measured for this same portion of the well.

[0078] Subsequently, we denote X lt ...,X P the P vectors of size N corresponding to the N values ​​from the P measurements.

[0079] 2) Determination of a preliminary electrofacies interpretation using an unsupervised classification method and a silhouette method

[0080] During this step, a first electrofacies interpretation is determined of the plurality of measurements relating to at least one portion of at least one well according to the following two sub-steps:

[0081] 2.1) Application of an unsupervised classification method for a plurality of class numbers

[0082] 2.2) Application of a silhouette method to determine an optimal number of classes

[0083] In general, an unsupervised classification method is a method that seeks to partition, or segment, a set of samples into homogeneous and distinct classes. This is also referred to as "clustering" or "labeling." Unlike a supervised classification method, an unsupervised classification method is not trained using training data. However, unlike a supervised classification method, an unsupervised classification method requires a number of classes as input. The number of classes is generally defined by a user. The sequence of substeps 2.1) and 2.2) according to the invention aims to determine a classification using an unsupervised method (which, compared to a supervised classification method, avoids the need to create a training dataset) while also eliminating the need for a user to define the number of classes.These sub-steps are detailed below.

[0084] 2.1) Application of an unsupervised classification method for a plurality of class numbers

[0085] In this substep, starting from a predefined minimum and maximum number of classes, for each value of the number of classes between the predefined minimum and maximum numbers, an unsupervised classification method is applied to the plurality of measurements from step 1. According to one embodiment of the invention, the unsupervised classification method implemented can be a Gaussian Mixture Model (GMM). The Gaussian Mixture Model is based on an expectation maximization algorithm. A description of this method can be found in (Zhao et al., 2020). This model is advantageous for implementing the process according to the invention for the following reasons:

[0086] (i) This is a probabilistic model, which is consistent with the probabilistic aspect of stochastic relaxation which is implemented in step 3) of the process according to the invention;

[0087] (ii) It allows us to handle almost any type of point distribution, more precisely anything that can be approximated by a sum of weighted Gaussians;

[0088] (iii) It relies on an expectation-maximization algorithm that is fast and reliably converges to a local optimum provided that this optimum is not degenerate (i.e., that it is not an inflection or ripple point). Convergence is even faster when the data are easily separable into distinct groups. If the separation is very clear, it has even been shown that there is convergence to a global optimum.

[0089] Alternatively, the unsupervised classification method can be chosen from any exclusive (e.g., K-means) or probabilistic (including GMM) clustering algorithm. Exclusive clustering associates one and only one cluster with each data point. Probabilistic clustering assigns a probability to each pair (point, cluster), and the pair with the highest probability is retained.

[0090] According to one embodiment of the invention, the minimum predefined number of classes may be 2. According to one embodiment of the invention, the maximum predefined number of classes may be between 15 and 30, preferably between 20 and 25, and is most preferably 22. Such preferred values ​​allow a large number of classes to be tested in a reasonable amount of computation time.

[0091] At the end of this sub-step, we obtain a plurality of classifications of the measures from step 1), more precisely a classification for each of the values ​​of the number of classes between the minimum number of classes and the maximum number of classes.

[0092] 2.2) Application of a silhouette method to determine an optimal number of classes

[0093] During this sub-step, a silhouette method is applied to the plurality of classifications determined in sub-step 2.1), and a first electrofacies interpretation is determined by selecting, from among the plurality of classifications determined in sub-step 2.1), the classification for which the silhouette score is closest to 1.

[0094] The silhouette method is described, for example, in the document (Rousseeuw, 1987). Generally, in data clustering, the silhouette coefficient is a measure of the quality of a partition of a dataset in automatic classification, ranging from -1 to 1. For each point, its silhouette coefficient is the difference between the average distance to points in its own group (cohesion) and the average distance to points in other neighboring groups (separation). If this difference is negative, the point is, on average, closer to the neighboring group than to its own: it is therefore misclassified. Conversely, if this difference is positive, the point is, on average, closer to its own group than to the neighboring group: it is therefore well classified.In other words, a silhouette score close to 1 indicates that the classification is robust, with little ambiguity and well-defined classes, whereas a silhouette score close to -1 indicates that the boundaries between the classes are uncertain.

[0095] Thus, at the end of this step, by selecting the classification for which the silhouette score is closest to 1, an automated classification of the measurements from step 1) is obtained, without any predetermination of the number of classes by a person skilled in the art, using an unsupervised classification method. Indeed, the sequence of substeps 2.1) and 2.2) allows the number of classes for an unsupervised classification method to be determined by maximizing a statistical criterion. Subsequently, the measurements taken in at least one portion of at least one well for the classification thus obtained are referred to as the "first electrofacies interpretation." This could also be referred to as an "intermediate electrofacies interpretation."

[0096] 3) Determination of a second electrofacies interpretation by means of an iterative stochastic relaxation method. During this step, an iterative stochastic relaxation method is applied to the probabilities of belonging of each of said measurements to each of said classes of said first electrofacies interpretation, and a second electrofacies interpretation is obtained when a predefined convergence criterion of said iterative relaxation method is reached.

[0097] Even though the number of classes in the first electrofacies interpretation from step 2) was statistically optimally determined by implementing the silhouette method, the resulting classification may exhibit very strong spatial discontinuities along the portion of the well for which measurements are available. For example, some measurements classified in category c tmay find themselves isolated amidst measures belonging to another category c y Such a lithological distribution is clearly not realistic from a geological perspective. A person skilled in the art, observing such a geologically implausible distribution, would reclassify such isolated measurements into the dominant neighboring category. Similarly, measurements located on the boundary between two classes are often misclassified by unsupervised classification methods such as GMM, and manual relabeling may be necessary. Such reclassifications, carried out manually by a person skilled in the art, homogenize the entire classification, ensure realistic spatial continuity, and result in classes that are more geologically relevant and comparable to actual lithologies.

[0098] To avoid manual intervention by a skilled professional, which can be subjective and in any case requires considerable expertise, the invention applies an iterative stochastic relaxation method to the probabilities of each measurement belonging to each of the classes of the initial electrofacies interpretation. Generally, an iterative stochastic relaxation method allows for the homogenization of data, that is, the reduction of contrasts, in a robust, consistent, and statistically rigorous manner, without operator intervention. Thus, the method according to the invention implements an iterative stochastic relaxation method based on a rigorous probability calculation derived from the statistical analysis of the measurements, thereby avoiding arbitrary smoothing of the results.

[0099] According to one implementation of the invention, probabilities of belonging of each of the measurements to each of the classes of the first interpretation in electrofacies are determined first (initial conditions of the method of the iterative stochastic relaxation method), then an iterative stochastic relaxation algorithm is applied to these probabilities of belonging.

[0100] Subsequently, we denote p ic the probability of belonging that a measure i belongs to a class c, with ie {1, ... , N} and ce {1, ... , K}. Thereafter, the exponent (n) is used to signify the current iteration of the iterative relaxation method, the exponent (0) indicating that it is the initial condition (iteration 0) of the iterative relaxation method.

[0101] 3.1) Determination of initial membership probabilities

[0102] According to one implementation of the invention, during this substep, for each measurement ie {1, ...,1V} from step 1) and each class ce {1, (from step 2), we can determine the probability p^ that measure i belongs to class c. This results in a probabilistic classification, rather than a discrete one.

[0103] According to one embodiment of the invention, the probability of membership p can be determined 0) that the measure i belongs to class c as a function of the distance d ic from point i to class c in parameter space ( 1; ...,X P ) by a relationship of the type:

[0104] Advantageously, the distance of ic from point i to class c in parameter space (X n ...,X PThis corresponds to the Mahalanobis distance. Indeed, the Mahalanobis distance has the advantage of being invariant under changes of scale and of taking into account the variance and skewness of the data, that is, the shape of the underlying distribution. Generally, the Mahalanobis distance is often used for detecting outliers in a dataset, or for determining the consistency of data, such as that provided by a sensor. Thus, this distance is calculated between the received data and the data that can be used, but the latter may require prior knowledge of the distribution of the points, for example, a normal distribution.

[0105] 3.2) Application of an iterative stochastic relaxation method

[0106] This substep involves applying an iterative stochastic relaxation method to the membership probabilities determined above. The use of an iterative relaxation method in this context aims to smooth the initial electrofacies interpretation obtained in step 2.

[0107] According to one embodiment of the invention, the probabilities of belonging to iteration n + 1 of the iterative stochastic relaxation method can be determined from the probabilities of belonging to iteration n according to a formula of the type:

[0108] (n+l) _ p / (n)\ Pic ~ ic \ Pic )' where F ic is an update operator, is the probability of measure i belonging to class c at iteration n + 1, and p^ is the probability of measure i belonging to class c at iteration n. According to one embodiment of the invention, the expression of the function F can be used icaccording to a formula of the type: where a is a positive integer, preferably equal to 1, as defined in (Rosenfeld et al., 1976), which leads to the following notation: with q ic = SjeVi( / i) c ij 2d=i rijcd. Pjd' °where Vt(J ) is the neighborhood of height h around the point i, ctj is a contribution coefficient from the point j to the point i and r ijcd is a compatibility matrix measuring the compatibility of point i belonging to class c and point j to class d. Indeed, given the expression of the term q ic , which takes into account the probabilities of all possible point-class combinations (j, d), the compatibility matrix gives more or less weight to the pairs (j, d) that are more or less compatible with the pair (j, c) being updated by the

[0109] According to one embodiment of the invention, the height h can be chosen as follows: h = P * H, where H is the total length of the well, and P is between 0.003 and 0.01, preferably P = 0.005. In other words, the height h corresponds to a percentage of the well height between 0.3 and 1%, and preferably 0.5%. Such values ​​correspond to values ​​obtained from a plurality of tests carried out by the Applicant. It is clear that a person skilled in the art can also predefine the value of h.

[0110] According to one embodiment of the invention, the following expression can be used for the contribution coefficient c^- from point j to point i according to a formula of the type: where Dij is the spatial distance between points i and j. Such a formulation allows:

[0111] (i) to ensure that the contribution of point j to point i is relative to the contributions of the other points in the neighborhood V L (h);

[0112] (ii) to be well defined when the spatial distance 0^ = 0, which happens when i = j, but also when there are, by mistake, redundant measurements in the data.

[0113] According to a preferred embodiment of the invention, a compatibility matrix r can be used ijcd according to a formula of the type: ^ijcd jPidPjc

[0114] This compatibility matrix therefore involves the product of "crossed" probabilities, which is justified by the fact that if the class-point pairs (j, d) and (j, c) have low probabilities, they should have little weight in the probability of (j, d) when updating the probability of (j, c), and vice versa if the probabilities of (j, d) and (j, c) are high. In general, the choice of the expression for the compatibility matrix r ijcdThis is tricky because it essentially involves integrating prior information about the interactions between the data that the operator must control. Furthermore, its calculation requires a significant amount of memory because the compatibility matrix is ​​of size N. 2 x K 2 The formulation of the compatibility matrix defined above by the Applicant, directly based on probabilities, has the advantage of being simple to calculate.

[0115] Furthermore, the above formulation, including a square root in the definition of r ijcd , ensures the following two points:

[0116] (i) Similarity (denoted a LJ lower for the similarity between an individual i and an individual j) of an individual i with itself is maximal.

[0117] (ii) This maximum is always equal to 1 (that is, taking another distribution of log measurements, this maximum will always be equal to 1).

[0118] If we do not take the square root, the similarity of an individual i with itself will always be maximal, so point (i) above will indeed be verified, but this similarity will not always be equal to 1, regardless of the underlying distribution, and therefore point (ii) will be refuted. This choice, including the square root, thus homogenizes the notion of similarity across all possible distributions of measurements.

[0119] According to a preferred embodiment of the invention, the quantity q ic can be more simply rewritten as follows:

[0120] OR

[0121] The term has l}represents the current element of the symmetric similarity graph between individuals i and j relative to their respective probabilities of assignment to the K classes. This term is closer to 0 the more individuals i and j are assignable to different classes, and closer to 1 the more they are assignable to the same classes. Thus, it measures, in a certain way, the agreement (similarity) or disagreement (dissimilarity) between the two individuals i and j. In summary, the first term, c^, represents the spatial contribution of i's neighbors, and the second term, a i} , represents the probabilistic contribution of these same neighbors, calculated as the product of the square roots of the probabilities for all classes. In general, the stochastic relaxation algorithm is an iterative Picard algorithm for the continuous function F ic : [0,1] [0,1], It is known from the document (Zucker et al.,

[0122] 1978) that such an algorithm does indeed converge to a fixed point of F icHowever, convergence can be more or less rapid depending on the type and quantity of data. Furthermore, convergence can be numerically unstable, meaning that fluctuations may occur when approaching a fixed point due to rounding errors or divisions by very small numbers, which can make the results less reliable. Moreover, the criterion proposed in the document (Zucker et al., 1978) for measuring the rate of convergence proves difficult to implement for log-type measurements. Indeed, the large number of individuals makes it impossible to define such a criterion in a meaningful way, and since this criterion is defined locally (point by point), it becomes virtually impossible to use it globally to control the rate of convergence of the process.To resolve this problem and to control the reliability of the results, the Applicant has developed a convergence criterion adapted to the measurements of the process according to the invention. According to the invention, the iterative stochastic relaxation method is applied to the probabilities of each measurement belonging to each of the classes of the first electrofacies interpretation, and a second electrofacies interpretation is obtained when a predefined convergence criterion of said iterative stochastic relaxation method is met.

[0123] According to one embodiment of the invention, the predefined convergence criterion of the iterative relaxation method is reached when, at iteration n', "') = 0, with: a measure i belongs to class c = 1 if p^ l ' 1 = rnax Pie = 0 otherwise, p^ -1)is the probability that a measure i belongs to class d at iteration (n - 1), N is the number of measures, and K is the number of classes. In other words, at each iteration n of the iterative stochastic relaxation method, the parameter An is determined. (n), which is the number (as a percentage) of class assignment changes between consecutive iterations n - 1 and n, and we stop the iterative stochastic relaxation method at the first iteration n* for which = 0. This criterion, based on the number of class assignment changes between two consecutive iterations, guarantees (within numerical errors) that the algorithm no longer generates assignment changes and that it is therefore no longer necessary to continue the relaxation from the user's point of view. Note that this criterion applies to (discrete) class memberships and not to (continuous) membership probabilities; it is therefore possible that the algorithm may not yet have converged in probabilities when our criterion has already been met. This approach allows us to:

[0124] (i) exit relaxation more quickly than if one had to wait for convergence in probabilities, which, as already mentioned, can be slow;

[0125] (ii) monitor the stability of the result in terms of membership rather than probability, more easily achieved and quantified by the number An.

[0126] Alternatively, the predefined convergence criterion for the iterative stochastic relaxation method can consist of a maximum number of iterations, for example, 50. After numerous trials conducted by the Applicant, such a value ensures that the iterative stochastic relaxation method is reasonably close to convergence. Thus, at the end of this step, a second electrofacies interpretation is obtained for the plurality of measurements relating to at least the portion of at least one well. This second interpretation is spatially smoothed with respect to the first interpretation, automatically and based on rigorous statistical criteria.

[0127] Thus, the method according to the invention allows for the automated determination of an electrofacies interpretation, benefiting from the advantages of an unsupervised classification method (i.e., one that does not require a training set) but without having to predefine a number of classes to perform the classification. Furthermore, the spatial smoothing of the result from the unsupervised classification, often necessary and performed manually, is here carried out automatically and reliably, by exploiting statistical information contained in the measurements.

[0128] Furthermore, the invention relates to a computer program product downloadable from a communication network and / or stored on a computer-readable medium (e.g., an embedded computer) and / or executable by a processor. This program includes program code instructions for implementing the method according to the first aspect as described above, in particular steps 2) and / or 3) described above, when the program is executed on a computer.

[0129] 4) Exploitation of a resource and / or storage of a fluid in an underground formation

[0130] This step is implemented within the framework of the process according to a second aspect of the invention, which relates to a process for exploiting a resource from an underground formation, such as a geothermal resource, an oil and / or gas resource, a mineral resource, or a hydrogeological resource, or for storing a fluid in the underground formation, such as the storage (or sequestration) of CO2.

[0131] During this step of the process according to the second aspect of the invention, from at least the electrofacies interpretation of at least a portion of at least one well determined at the end of the previous step, a resource of the underground formation is exploited, and / or a fluid is stored in the underground formation.

[0132] According to one embodiment of the invention, from at least the electrofacies interpretation of at least a portion of at least one well, a representative mesh representation of the underground formation of interest can be determined, and at least one exploitation scheme for the resource present in the underground formation and / or a scheme for injecting a fluid into the underground formation can be determined from this mesh representation, then the resource of interest and / or the fluid of interest is exploited according to the exploitation scheme.

[0133] In general, an operating scheme and / or a scheme for injecting a fluid into a formation includes a number, geometry and location, position and spacing, of the injection and / or production wells to be drilled in the underground formation under study and to be equipped.

[0134] According to one embodiment of the invention in which the resource to be exploited is geothermal, the aim is to determine at least one exploitation scheme allowing the injection of a predominantly aqueous fluid into the studied underground formation and its subsequent recovery. Indeed, in the field of geothermal energy, the heat or energy of the fluid injected into the formation and recovered is exploited.

[0135] According to an implementation of the invention in which the resource to be exploited is of an oil and / or gas nature, it is necessary to determine at least one scheme for exploiting the hydrocarbons contained in the underground formation studied.

[0136] According to an embodiment of the invention in which the method aims to store a fluid in the underground formation, it is necessary to determine at least one scheme for injecting a fluid into a formation, with a view to its storage.

[0137] Conventionally, a representative mesh representation of an underground formation of interest is constructed, as according to the invention, from at least the electrofacies interpretation of at least a portion of at least one well, but advantageously is also constructed from measurements taken on rock samples from the wells, information deduced from seismic surveys, and production data such as oil and water flow rates, pressure variations, etc. Those skilled in the art are well-versed in methods for constructing a representative mesh representation of an underground formation. A particular embodiment of the invention in which the fluid comprises hydrocarbons is described below in a non-limiting manner.In general, in oil production, a production plan includes the number, geometry, and location (position and spacing) of injection and production wells to be drilled and equipped in the reservoir under study. A production plan may also include a type of enhanced recovery of hydrocarbons contained in the reservoir, such as recovery by injecting a solution containing one or more polymers, CO2 foam, etc. An optimal hydrocarbon reservoir production plan should, for example, allow for a high recovery rate of hydrocarbons trapped in the geological reservoir over a long production period, requiring a limited number of wells. In other words, the specialist predefines evaluation criteria according to which a geological reservoir fluid production plan is considered sufficiently efficient to be implemented on the reservoir under study.

[0138] According to one embodiment of the invention, determining a hydrocarbon production scheme for the studied geological reservoir can be achieved using a flow simulator (or reservoir simulator). An example of a reservoir simulator is the PumaFlow® simulator (IFP Energies nouvelles, France). Generally, at any time t during the simulation, a flow simulator solves all the flow equations specific to each cell and provides solution values ​​for the unknowns (saturations, pressures, concentrations, temperature, etc.) predicted at that time t. From this solution, the quantities of oil produced and the state of the reservoir (pressure distribution, saturations, etc.) at the time considered are determined.Using a mesh representation, determined from at least one electrofacies interpretation for at least a portion of at least one well, the flow simulator makes it possible to reliably predict productions, particularly of oil and gas, for a given operating scheme.

[0139] According to one embodiment of the invention, different exploitation schemes for the fluid contained in the geological reservoir under study can be defined, and at least one criterion is estimated using the flow simulator, such as the quantity of hydrocarbons produced according to each of the different exploitation schemes, the curve representing the evolution of production over time at each well, the oil-to-gas ratio (OGR), etc. The scheme according to which the hydrocarbons contained in the reservoir are actually exploited can then correspond to the one satisfying at least one of the evaluation criteria for the different exploitation schemes.According to the invention, a plurality of flow simulations are carried out for a plurality of injector-producer well sites, using the simulator according to the invention and using a mesh representation determined from at least one electrofacies interpretation for at least a portion of at least one well, and the operating scheme is determined according to which the fluid from the geological reservoir is exploited for each of the sites and the site satisfying at least one of the predefined evaluation criteria is selected.

[0140] Advantageously, a plurality of flow simulations can be carried out for a plurality of assisted recovery types, using the simulator according to the invention and a mesh representation determined from at least one electrofacies interpretation of at least one portion of at least one well, and the operating scheme is determined according to which the fluid from the geological reservoir is to be exploited for each of the assisted recovery types, and the assisted recovery satisfying at least one of the predefined evaluation criteria is selected.

[0141] Once the production plan is determined, the hydrocarbons trapped in the oil reservoir are exploited according to this plan, specifically by drilling the injection and production wells of the plan thus determined, in order to produce the hydrocarbons, and by installing the production infrastructure necessary for the development of this reservoir. If the production plan has also been determined by estimating reservoir production associated with different types of enhanced recovery, the selected additive(s) (polymer, surfactants, CO2 foam) as described above are injected into the injection well.

[0142] It is understood that the exploitation scheme can evolve over the duration of hydrocarbon exploitation of a geological reservoir, depending on knowledge of the reservoir acquired during exploitation, and on improvements in the various technical fields occurring during the exploitation of a hydrocarbon deposit (improvements in the field of drilling, enhanced recovery for example).

[0143] Application example

[0144] The advantages of the process according to the invention are presented below in an example of application.

[0145] For this application example, we have well log measurements taken in a section ranging from approximately 1800m to 3300m deep of a vertical well through an underground formation consisting mainly of sandstone and clay, located in the offshore of Western Australia.

[0146] The available log measurements are of five types: natural radioactivity in gamma rays (GR), sonic logging, density logging, neutron logging, and electrical logging. Figure 1 illustrates a natural radioactivity log (GR in IPA units, standard in this field) as a function of depth Z.

[0147] Figure 2 illustrates an IE-M electrofacies interpretation performed manually by an expert geologist, for which 16 different classes were identified (labeled C1 to C16). Figure 3A illustrates an IE-INV-PART electrofacies interpretation resulting from the implementation of steps 1 and 2 of the process according to the first aspect of the invention (in other words, without the iterative stochastic relaxation step), and Figure 3B is an enlargement of Figure 3A between depths of 2200 m and 2600 m. Figure 4A illustrates an IE-INV electrofacies interpretation resulting from the implementation of all the steps of the process according to the first aspect of the invention, and Figure 4B is an enlargement of Figure 4A between depths of 2200 m and 2600 m. For figures 3A, 3B, 4A, and 4B, a number of distinct classes equal to 7 was determined automatically by implementing the method according to the invention; the classes for these figures are noted C1 to C7.For figures 2, 3A, 3B, 4A, and 4B, the classes determined along the well (here we only present the result of the interpretation for one sample out of 10 along the well, for visualization purposes) are represented by colors varying on a color scale in shades of gray, and are placed (for illustration purposes) on the x-axis at the level of the corresponding value of the GR log.

[0148] It can be observed that the classes determined by implementing all the steps of the process according to the invention (Figures 4A and 4B) are geologically plausible, in that the classes remain stable with depth, whereas interrupting the implementation of the process according to the invention after step 2 (Figures 3A and 3B) can lead to isolated classifications within a dominant classification (see Figure 3B in particular). Such lithological distributions are clearly not realistic from a geological point of view. A person skilled in the art, observing such a geologically implausible distribution, would reclassify such isolated measurements into the neighboring dominant category. Implementing all the steps of the process according to the invention, and in particular the iterative stochastic relaxation step, avoids manual reclassification.

[0149] Furthermore, comparing Figure 2 with Figures 4A and 4B, it can be observed that, even though manual interpretation resulted in a greater number of classes than with automatic determination of this number of classes by implementing the method according to the invention (16 classes instead of 7 classes), there is consistency between the result of the method according to the invention and manual labeling in terms of spatial continuity. However, electrofacies interpretation performed fully automatically by the method according to the invention can be obtained in about ten minutes on an Intel(R) Core(TM) i7-8850H CPU @ 2.60GHz (2.59 GHz), whereas manual interpretation performed by the expert can take several days.Thus, the method according to the invention allows for the automated determination of an electrofacies interpretation, benefiting from the advantages of an unsupervised classification method (i.e., one that does not require a training set) but without having to predefine a number of classes to perform the classification. Furthermore, the spatial smoothing of the result from the unsupervised classification, often necessary and performed manually, is here carried out automatically and reliably, by exploiting statistical information contained in the measurements.

Claims

DEMANDS 1. A method for determining an electrofacies interpretation of measurements relating to at least a portion of at least one well passing through an underground formation, with a view to exploiting a resource of said underground formation and / or injecting a fluid into said underground formation, characterized in that at least the following steps are carried out: A) a plurality of measurements are carried out relating to at least said portion of said at least one well crossing said underground formation, said plurality of said measurements resulting at least from a well log and / or an image of at least one core taken from said at least one well; (b) A first electrofacial interpretation of said plurality of said measurements relating to at least said portion of said at least one well is determined as follows: (a) for each value of a number of classes of a plurality of values ​​of said number of classes between a minimum number of classes and a maximum number of classes, an unsupervised classification method is applied to said plurality of said measurements; (b) a silhouette method is applied to said plurality of classifications of said plurality of measurements determined for each of said values ​​of said number of classes, and said first electrofacial interpretation and a corresponding number of classes are determined by selecting said classification and said value of said number of classes for which said silhouette score is closest to 1; C) an iterative stochastic relaxation method is applied to probabilities of belonging of each of said measures to each of the classes of said first interpretation in electrofacies, and a second interpretation in electrofacies is obtained when a predefined convergence criterion of said iterative relaxation method is reached.

2. Method according to claim 1, wherein said at least one well log is selected from gamma ray logs, sonic logs, density logs, electrical logs or well imaging logs.

3. A method according to any one of the preceding claims, wherein said unsupervised classification method is chosen from a family of exclusive partitioning methods or a family of probabilistic partitioning methods.

4. A method according to claim 3, wherein said unsupervised classification method is a Gaussian mixture model.

5. A method according to any one of the preceding claims, wherein said probabilities of belonging of each of said measures to each of said classes are a function of a Mahalanobis distance.

6. A method according to any one of the preceding claims, wherein said iterative stochastic relaxation method implements a compatibility matrix measuring the compatibility of membership of a measure i to a class c and of a measure j to a class d expressed according to a formula of the type: ^ijcd jPidPjc where p id is a probability that a measure i belongs to a class d and p jc is a probability that a measure j belongs to a class c.

7. A method according to any one of the preceding claims, wherein said predefined convergence criterion of said iterative relaxation method is met when, at a measure i belongs to the class 0 otherwise, is the probability that a measure i belongs to class d at iteration (n - 1), N is the number of said plurality of measures, and K is said number of classes.

8. A method for exploiting a resource present in an underground formation and / or for storing a fluid in said underground formation, comprising implementing the method for determining an electrofacies interpretation of measurements relating to at least a portion of at least one well passing through an underground formation according to any one of the preceding claims.

9. A method according to claim 8, wherein, based on at least said electrofacial interpretation of measurements relating to at least said portion of at least said well traversing said subsurface formation, a representative mesh representation of said subsurface formation is constructed, at least one resource exploitation scheme and / or a scheme for injecting said fluid into said subsurface formation is determined based on at least said representative mesh representation of said subsurface formation, and said resource is exploited from said formation underground according to said operating scheme and / or said fluid is injected into said underground formation according to said scheme to inject said fluid into said underground formation.

10. A method according to any one of claims 8 or 9, wherein said resource exploitation scheme and / or fluid injection scheme comprises at least one planting of at least one injection well and / or at least one production well, and wherein said wells of said planting are drilled and equipped with production infrastructure.

11. Product computer program downloadable from a communication network and / or recorded on a computer-readable medium and / or executable by a processor, comprising program code instructions for implementing the method according to any one of claims 1 to 7, when said program is executed on a computer.

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