WO2021130512A1

WO2021130512A1 - Device and method for predicting values of porosity lithofacies and permeability in a studied carbonate reservoir based on seismic data

Info

Publication number: WO2021130512A1
Application number: PCT/IB2019/001442
Authority: WO
Inventors: Fei Hong
Original assignee: Total SE
Current assignee: TotalEnergies SE
Priority date: 2019-12-23
Filing date: 2019-12-23
Publication date: 2021-07-01
Anticipated expiration: 2022-06-23

Abstract

The invention relates to a method (100) for predicting values of porosity, lithofacies and/or permeability in a studied carbonate reservoir based on seismic data, the method comprising: - Loading (130) an ensemble prediction model, said ensemble prediction model having been trained with: o values of elastic attributes, said elastic attributes comprising V p, V s, density or their mathematic transformations, and o values of porosity, lithofacies and/or permeability; - Acquiring (170) values of inverted elastic attributes calculated from seismic data generated on a studied carbonate reservoir, said inverted elastic attributes comprising Vp, Vs, density or their mathematic transformations; and - Generating (180) predicted values of porosity, lithofacies and/or permeability of the studied carbonate reservoir, said predicted values being calculated from the acquired values of inverted elastic attributes and the ensemble prediction model.

Description

DEVICE AND METHOD FOR PREDICTING VALUES OF POROSITY LITHOFACIES AND PERMEABILITY IN A STUDIED CARBONATE RESERVOIR BASED ON SEISMIC

DATA

Field of the invention

The present invention relates to the field of exploration and appreciation of reservoirs. In particular, the invention relates to the field of exploration and appreciation of carbonate reservoirs using machine learning techniques on seismic data. More particularly, the invention provides a new method for predicting values of porosity, lithofacies and/or permeability, in a studied carbonate reservoir.

Description of Related Art

Reservoir characterization has become increasingly important to hydrocarbon exploration Lithology and reservoir properties prediction from seismic data plays an essential role in reservoir quality evaluation, reservoir architecture delineation, and reservoir model building, which is of long-standing interest for petroleum reservoir exploration, development and production. Reservoir characterization attempts to describe petroleum deposits and the nature of the rocks that contain hydrocarbons, producing detailed geological reconstructions of both its geometry and of its lithological properties. This can provide important decision support, in particular in the highly competitive segment of carbonate reservoirs.

Reservoir characterization relies on expertise from petroleum engineering, geology, and geophysics and can benefit from well logging. Conventionally, deterministic method and geostatistical method are both employed to estimate lithofacies and reservoir properties, such as porosity, from seismic data. Lithology and texture identification are usually performed using either a core sample or cutting analysis and the borehole log methods. Core samples are collected during the well-drilling process and are analyzed directly by experts, i.e., geologists, but this technique is costly. Indirect methods, i.e. well logs, provide information that can be used for rock characterization with relatively lower costs. The lithofacies and reservoir parameter determination problem entails some important issues to be considered: data are intrinsically noisy and imperfect; the physics between the reservoir properties and seismic responses are highly complex and nonlinear. This is especially true for the heterogeneous carbonate reservoirs. However, well log is at one-point location for exploration stage and is incapable of proposition a 3D analysis. Hence, a need exists to find alternatives for interpretation of reservoir characteristics to minimize costs, including the time spent by specialists and improve the precision of prediction, in particular for carbonate reservoirs.

Standard methodologies are already employed in predicting geological features, or any spatially varying physical properties. However, such methodology such as linear regression or non-linear regression did not proved to be efficient due to heterogeneity of carbonate reservoirs. Machine learning provides an intelligent and practical means of predicting geological features, or any spatially varying physical properties, from multi-dimensional geophysical data sets. In particular, the basic premise of supervised learning is that it requires training data containing labeled samples representing what is known about the inference target. T rained classification models are then applied to input variables with similar geological context to predict classes present within the training data.

Recently, machine learning algorithms have achieved attractive results in solving classification problems such as lithology identification. For example, Peipei et al 2016, proposed a method based on machine learning techniques to characterize facies of a reservoir using seismic data (Peipei Li & Yuran Zhang, Facies Characterization of a Reservoir in the North Sea Using Machine Learning Techniques; Project Final Report for CS229 (Aut 2016-17)). With 80% of the data used for training they obtained a testing error of about 0.1 using Support Vector Machine which achieved best classification results among Support Vector Machine, Random Forest, Softmax Regression and Gaussian Discriminant Analysis. However, when used with seismic data available for use they were able to obtain a testing error of about 0.2 with Softmax Regression. In a context of reservoir characterization, there has also been proposed a method for predicting mineralogical, textural, petrophysical and/or petrophysics properties based on well log data using the prediction model (US2019/0266501). However, such a method is based on a prediction model trained with values obtained by rock sample analysis with laboratory level of details. Considering that values obtained from rock sample analysis with laboratory level of details are not systematically acquired, the amount of data available used to train a model may seem inadequate to obtain predictions that are really relevant.

Moreover, currently, most of those studies concerning machine learning applications for lithofacies and reservoir properties such as porosity focus on clastic reservoirs with few lithology variations whereas the investigation of machine learning approaches on carbonate reservoirs are sparsely documented. Yet, it is difficult to apply methodology effective on clastic reservoirs to carbonate depositional environments. This is in part due to the strong heterogeneities present in carbonate reservoirs, which have constantly undergone physical, chemical, and biological changes during sedimentation and post depositional diagenesis, thereby causing significant heterogeneities in rock properties.

Silva et al. (2015) applied a back-propagation neural network algorithm in lithology identification in a carbonate reservoir and achieved good fit (R = 85.62%) with the petrographic class prediction (Silva et al. Artificial neural networks to support petrographic classification of carbonate-siliciclastic rocks using well logs and textural information; Journal of Applied Geophysics 117 - June 2015). However, the neural network algorithm was trained with nineteen input parameters to predict lithofacies with the use of a data set that is primarily composed of laboratory measurements. Moreover, error in classification between Limestone classes were observed. Hence, the neural network algorithm encounters certain difficulties with respect to the classification of samples with the same texture but from different petrographic classes because the attribute values are highly similar for the same texture.

For pre-salt oilfields, owing to the complex porosity distribution in carbonate reservoirs, predicting a reliable porosity is a fundamental step for reservoir modelling. In general, pre salt carbonates are very heterogeneous reservoirs, in terms of facies, and consequently, in terms of porosity and permeability. Processes such as diagenesis and recrystallization can modify the primary porosity and make the lithofacies heterogeneous. However, applying a porosity volume derived from seismic data directly to the geological model is not an easy task since the difference between the seismic and geological grid could create upscaling issues both in vertical and lateral domains. Mori et al. 2018 proposed a method to predict porosity values of a carbonate reservoir through an artificial neural network method applied to the integration of well log and seismic data (Mori et al. Porosity Prediction of a Carbonate Reservoir in Campos Basin Based on the Integration of Seismic Attributes and Well Log Data; 10.5772/intechopen.82490, 2018/12/24). This method, when based on 12 attributes of seismic data, predicted porosity with a correlation coefficient of about 0.7 and, when based on 17 attributes of seismic data, predicted porosity with a correlation coefficient of about 0.9. However, they did not propose a lithofacies prediction based on this artificial neural network. Moreover, none of these studies proposed permeability predictions derived from seismic data.

Hence, a need exists for a solution dedicated to carbonate reservoirs and based on machine learning to determine lithofacies, porosity and permeability from seismic data. Summary of the invention

The following sets forth a simplified summary of selected aspects, embodiments and examples of the present invention for the purpose of providing a basic understanding of the invention. However, the summary does not constitute an extensive overview of all the aspects, embodiments and examples of the invention. The sole purpose of the summary is to present selected aspects, embodiments and examples of the invention in a concise form as an introduction to the more detailed description of the aspects, embodiments and examples of the invention that follow the summary.

The invention aims to overcome the disadvantages of the prior art. In particular, the invention proposes a method for predicting values of porosity, lithofacies and/or permeability in a studied carbonate reservoir based on seismic data, said method allowing to directly connect lithology and reservoir properties to seismic data. Advantageously, such a method based on machine learning techniques allows to predict the spatial distribution of porosity, lithofacies and/or permeability from seismic data.

The invention also proposes a computer device configured to predict values of porosity, lithofacies and/or permeability in a carbonate reservoir based on seismic data. Advantageously, a solution according to the invention can produce reliable values from a complex and heterogeneous carbonate reservoir.

Hence, according to an aspect of the present invention, it is provided a method for predicting values of porosity, lithofacies and/or permeability in a studied carbonate reservoir based on seismic data, the method comprising:

Loading an ensemble prediction model, said ensemble prediction model having been trained with: o values of elastic attributes, said elastic attributes comprising V_p, V_s, density or their mathematic transformations, and o values of porosity, lithofacies and/or permeability;

Acquiring values of inverted elastic attributes calculated from seismic data generated on a studied carbonate reservoir, said inverted elastic attributes comprising V_p, V_s, density or their mathematic transformations; and

Generating predicted values of porosity, lithofacies and/or permeability of the studied carbonate reservoir, said predicted values being calculated from the acquired values of inverted elastic attributes and the ensemble prediction model. Instead of directly employing seismic data gathered to infer lithofacies or reservoir properties, a method according to the invention is based on elastic attributes that are more sensitive to variations of lithofacies and reservoir properties. Advantageously, the ensemble prediction model used in this method has been trained with well logging data to generate a model that represent the complex nonlinear relationship between lithofacies/porosity/permeability and elastic attributes. Then the invention comprises the combination of the trained ensemble prediction model with inverted seismic cubes from seismic data (P-impedance and Vp/Vs ratio) to predict the spatial distribution of porosity, lithofacies and/or permeability from seismic data.

According to other optional features of the method:

- values of porosity, lithofacies and/or permeability used to train the ensemble prediction model have been calculated using a petrophysics methodology, preferably from well logs data. Indeed, the use of calculated values, for example thanks to petrophysics methodology, rather than measured values for example from cuttings makes it possible to support the analyze with a much larger amount of data and therefore improve the accuracy.

- it comprises a step of training the ensemble prediction model with values of elastic attributes comprising V_p, V_s, density or their mathematic transformations, and values of porosity, lithofacies and/or permeability;

- the step of training the ensemble prediction model comprises a resampling of the values of porosity, lithofacies and/or permeability in order to reduce the frequency of data used in training. Preferably, this comprises the use of substantially identical frequencies between data used in training and inverted elastic attributes generated from seismic data. More preferably, the use of a moving average filter to smooth the values of porosity, lithofacies and/or permeability. Such treatments which match the frequency of the data of log and seismic domain and proved to increase the prediction accuracy of the method.

- the elastic attributes comprise elastic attributes selected from the group consisting of: V_p, V_s, density, V_p/V_s ratio, shear modulus, bulk modulus, P-impedance, S- impedance, Poisson’s ratio and Lame’s coefficient;

- values of elastic attributes include: P-lmpedance and V_p/V_s ratio. Indeed, these attributes give the best prediction accuracy.

- the ensemble prediction model includes any one of: a boosting such as gradient boosting or adaptative boosting, a bagging and a stacking. Preferably, the ensemble prediction model includes any one of: random forest, adaboost and xgboost. Such machine learning methods give the best results in term of accuracy of lithofacies, permeability and porosity predictions for carbonate reservoir.

- the ensemble prediction model has been trained on one, preferably several, carbonate reservoirs that are different from the studied carbonate reservoir on which seismic data are generated. Hence, the method according to the invention do not need to realize log well on the studied reservoir to generate the predicted data. However, well log can be integrated on the studied carbonate reservoir to enhance the prediction model. Preferably the ensemble prediction model has been trained on one, preferably several, carbonate reservoirs that have a similar geological context.

- it comprises a step of determining lithofacies, porosity, permeability and elastic attributes values from a well log conducted on the studied carbonate reservoir and a step of retraining the ensemble prediction model with a set of data comprising determined values of lithofacies, porosity, permeability and elastic attributes; these steps can be used to enhanced the ensemble prediction model. Preferably, the step of retraining can comprise the use of key information on the formation of the reservoir such as water contact or gamma ray.

- the lithofacies, porosity, permeability and elastic attributes values determined from the well log conducted on the studied carbonate reservoir were calculated using a petrophysics methodology,

- the ensemble prediction model also includes reservoir type as input data, for example said reservoir type being selected from: lacustrine carbonates reservoir, cold-water carbonate reservoir, and warm-water carbonate reservoir. Indeed, such reservoirs can present relatively heterogeneous history and context and the ensemble prediction model can benefit from a distinction of those formations, combining the lithology and porosity prediction results.

- the seismic data acquired for a carbonate reservoir correspond to 2D or 3D seismic data,

- the seismic data have been collected via a plurality of transmitters and geophones,

- generating predicted values of porosity, lithofacies and/or permeability comprises a generation of predicted values of porosity, lithofacies and/or permeability for all intersections of a resolution grid corresponding to 2D seismic data acquired,

- generating predicted values of porosity, lithofacies and/or permeability comprises a generation of predicted values of porosity, lithofacies and/or permeability for each 3D voxel of a 3D model of the carbonate reservoir, According to another aspect of the present invention, it is provided a computer device for predicting values of porosity, lithofacies and/or permeability in a studied carbonate reservoir based on seismic data, the computer device comprising:

A data memory configured to store an ensemble prediction model, said ensemble prediction model having been trained with: o values of elastic attributes, said elastic attributes comprising V_p, V_s, density or their mathematic transformations, and o values of porosity, lithofacies and/or permeability;

A communication interface configured to acquire values of inverted elastic attributes calculated from seismic data generated on a studied carbonate reservoir, said inverted elastic attributes comprising V_p, V_s, density or their mathematic transformations; and

A processor configured to: o Load the ensemble prediction model, and o Generate predicted values of porosity, lithofacies and/or permeability in the studied carbonate reservoir, said predicted values being calculated from the acquired values of inverted elastic attributes and the ensemble prediction model.

According to another aspect of the present invention, it is provided a non-transitory computer readable medium storing executable instructions which, when executed by a processor, implements a method according to the invention.

In particular, it is provided a non-transitory computer readable medium storing executable instructions which, when executed by a processor of a computer device, implements a method for predicting values of porosity, lithofacies and/or permeability in a studied carbonate reservoir based on seismic data, the method comprising:

Acquiring values of inverted elastic attributes calculated from seismic data generated on a studied carbonate reservoir, said inverted elastic attributes comprising V_p, V_s, density or their mathematic transformations; and Generating predicted values of porosity, lithofacies and/or permeability of the studied carbonate reservoir, said predicted values being calculated from the acquired values of inverted elastic attributes and the ensemble prediction model.

Brief description of the drawings

The foregoing and other objects, features and advantages of the present invention will become more apparent from the following detailed description when taken in conjunction with the accompanying drawings in which:

FIG. 1 is a schematic view of a process flow diagram of the method according to an aspect of the invention.

FIG. 2 is a schematic view of a specific step of the method according to an embodiment of the invention.

FIG. 3 is a schematic view of a process flow diagram of a specific step of the method according to an embodiment of the invention.

FIG. 4 is a schematic view showing a process flow diagram of a method according to another embodiment of the invention.

FIG. 5 is a schematic block diagram of a computer device for predicting values according to an aspect of the invention.

FIG. 6 is an illustration of a comparison of lithofacies prediction using different machine learning algorithms (6A: Fuzzy Logic, probabilistic neural network (PNN), support vector machine (SVM) - 6B : deep neural network (DNN), Naive Bayes, Random Forest, extreme gradient boosting (XGBOOST)). Each grey level corresponds to different lithofacies.

FIG. 7 is an illustration of a confusing matrix of prediction results of five lithofacies (igneous, anhydrite, dolomitic limestone, silica-rich limestone, and limestone) using different machine learning algorithms: Random Forest (7A) ; extreme gradient boosting (7B); Fuzzy Logic (7C); Deep Neural Network (7D); Probabilistic Neural Network (7E); Naive Bayes (7F); Support Vector Machine (7G)).

FIG. 8 is a schema of a comparison of different machine learning algorithm for porosity prediction: Support Vector Machine (8A); Deep Neural Network (8B) ; Linear regression (8C); Nonlinear regression (8D) ; Random Forest (8E) ; extreme gradient boosting (8F) of 3 wells (A1 , A2, A3).

Several aspects of the present invention are disclosed with reference to flow diagrams and/or block diagrams of methods, devices and computer program products according to embodiments of the invention.

On the figures, the flow diagrams and/or block diagrams show the architecture, the functionality and possible implementation of devices or systems or methods and computer program products, according to several embodiments of the invention.

For this purpose, each box in the flow diagrams or block diagrams may represent a system, a device, a module or code which comprises several executable instructions for implementing the specified logical function(s).

In some implementations, the functions associated with the box may appear in a different order than indicated in the figures.

For example, two boxes successively shown, may be executed substantially simultaneously, or boxes may sometimes be executed in the reverse order, depending on the functionality involved.

Each box of flow diagrams or block diagrams and combinations of boxes in flow diagrams or block diagrams, may be implemented by special systems that perform the specified functions or actions or perform combinations of special equipment and computer instructions.

Detailed description

A description of example embodiments of the invention follows.

In the following description, “ensemble prediction method” means a type of machine learning method that uses a series of learners to learn and uses some rules to integrate the learning results so as to achieve better learning effects than a single learner. The main idea of ensemble learning is to first generate a number of learners according to certain rules and then combine them by some integration strategies, and eventually output the final results by comprehensive judgment. Briefly, what ensemble learning does is to integrate multiple weak learners into one strong learner. Such ensemble prediction method can for example be selected from: Random Forest (RF, Breiman, 1996; 2001) and Extreme Gradient Boosting (XGBOOST, Chen and Guestrin, 2016). An ensemble prediction method is used to produce an ensemble prediction model.

As used herein, the term "reservoir" or "petroleum reservoir" can refers to a subsurface group of sedimentary rocks capable of storing a pool of hydrocarbons. This is commonly a porous sandstone or limestone.

By “process”, “compute", “determine”, “display”, “extract”, “compare” or more broadly “executable operation” is meant, within the meaning of the invention, an action performed by a computer device or a processor unless the context indicates otherwise. In this regard, the operations relate to actions and/or processes of a data processing system, for example a computer system or an electronic computing device, which manipulates and transforms the data represented as physical (electronic) quantities in the memories of the computer system or other devices for storing, transmitting or displaying information. In particular, calculation operations are carried out by the processor of the device, the produced data are entered in a corresponding field in a data memory and this field or these fields can be returned to a user for example through a Human Machine Interface formatting such data. These operations may be based on applications or software.

The terms or expressions “application”, “software”, “program code”, and “executable code” mean any expression, code or notation, of a set of instructions intended to cause a data processing to perform a particular function directly or indirectly (for example after a conversion operation into another code). Exemplary program codes may include, but are not limited to, a subprogram, a function, an executable application, a source code, an object code, a library and/or any other sequence of instructions designed for being performed on a computer system.

By “processor” is meant, within the meaning of the invention, at least one hardware circuit configured to perform operations according to instructions contained in a code. The hardware circuit may be an integrated circuit. Examples of a processor include, but are not limited to, a central processing unit, a graphics processor, an application-specific integrated circuit (“ASIC” according to Anglo-Saxon terminology), and a programmable logic circuit. A single processor or several other units may be used to implement the invention. By “coupled” is meant, within the meaning of the invention, connected, directly or indirectly, with one or more intermediate elements. Two elements may be coupled mechanically, electrically or linked by a communication channel.

The expression “human-machine interface”, within the meaning of the invention, corresponds to any element allowing a human being to communicate with a computer, in particular and without that list being exhaustive, a keyboard and means allowing in response to the commands entered on the keyboard to perform displays and optionally to select with the mouse or a touchpad items displayed on the screen. Another embodiment is a touch screen for selecting directly on the screen the elements touched by the finger or an object and optionally with the possibility of displaying a virtual keyboard.

By “computer device”, it should be understood any device comprising a processing unit or a processor, for example in the form of a microcontroller cooperating with a data memory, possibly a program memory, said memories possibly being dissociated. The processing unit cooperates with said memories by means of internal communication bus.

The term "about" as used herein can allow for a degree of variability in a value or range, for example, within 10%, within 5%, or within 1 % of a stated value or of a stated limit of a range.

The term "substantially" as used herein refers to a majority of, or mostly, as in at least about 50%, 60%, 70%, 80%, 90%, 95%, 96%, 97%, 98%, 99%, 99.5%, 99.9%, 99.99%, or at least about 99.999% or more.

As mentioned, carbonate reservoirs constitute a highly competitive segment for which physics between the reservoir properties and seismic responses are highly complex and nonlinear.

Machine learning methods have been proposed for lithofacies prediction or porosity prediction. However, most methods are based on rock sample analysis or show a high level of confusion between lithofacies such as limestone classes. Moreover, no machine learning methods have been proposed for permeability prediction from inverted seismic data.

To answer these issues, the inventor developed solutions dedicated to carbonate reservoirs and based on machine learning to determine porosity, lithofacies and/or permeability from seismic data. In particular according to the invention, well log data are used to build an ensemble prediction model to classify lithofacies using elastic attributes. Inverted elastic attributes coming from seismic data, preferably 2D or 3D, are processed by the trained prediction model to generate lithofacies, permeability and porosity prediction for example on the whole 3D area.

Hence, according to a first aspect, the invention relates to a method 100 for predicting values of porosity, lithofacies and/or permeability in a studied carbonate reservoir based on seismic data.

As shown in figure 1 , said method comprising the steps of: loading 130 an ensemble prediction model, acquiring 170 values of inverted elastic attributes calculated from seismic data generated on a studied carbonate reservoir, and generating 180 predicted values of porosity, lithofacies and/or permeability of the studied carbonate reservoir.

As it will be described hereafter, a method 100 for predicting values of porosity, lithofacies and/or permeability according to the invention is mainly based on:

- an ensemble prediction model previously trained, and

- on acquired values of inverted elastic attributes calculated from seismic data.

This method is particularly adapted for carbonate reservoirs and, as illustrated by example, produces better results than other prediction methods already proposed on clastic or shale reservoirs for example.

In an embodiment, the ensemble prediction model has been previously trained. However, the invention set out herein can also comprise an embodiment where the ensemble prediction model is trained as part of the method according to the invention.

In that case, as shown in figure 1 , a method 100 for predicting values of porosity, lithofacies and/or permeability according to the invention can comprise a facultative step of collecting 110 data from a well log.

Well logging is a powerful tool to obtain information from the subsurface. Typically, a wireline tool is lowered into a borehole and measurements are taken so that rock properties, such as elastic attributes, can be inferred from the measured data. Common rock properties inferred from well logs include P-wave velocity V_p, S-wave velocity V_s, density, etc. As shown in figure 1 , a method 100 for predicting values of porosity, lithofacies and/or permeability according to the invention can comprise a step of training 120 the ensemble prediction model.

Machine learning is now widely adopted in various industrial fields. For example, Bayesian classification has been used for years in seismic data analysis. Prediction models can be divided into unsupervised learning methods and supervised learning methods. The unsupervised learning methods make it possible to determine groups of observations without a priori. Hence, those groups will be formed without a need for a label value on input data. On the contrary, the supervised learning methods link an input to an output based on example input-output pairs.

Preferably, in the present invention, a machine learning technique is used to build a supervised prediction model configured to estimate lithofacies, permeability and/or porosity from inverted elastic attributes. Among supervised learning methods, neural networks, classification or regression trees, nearest neighbor search, and random forest are some of the most robust and efficient machine learning techniques according to the invention. For example, the Bayesian classification which has been used for years in seismic data analysis shows lower prediction result than ensemble methods evaluated.

In particular, in the present invention, an ensemble prediction model that estimates lithofacies, permeability and/or porosity from elastic attributes, preferably inverted elastic attributes, is used. The training of said ensemble prediction model is preferably done with values of elastic attributes, as input data, and with values of lithofacies, permeability and/or porosity, as target data. These values used to train the ensemble prediction model can be considered as reference data. They have advantageously been produced on a carbonate reservoir and have been inferred from a well log. Elastic attributes used to train the ensemble prediction model can be inverted elastic attributes, namely elastic attributes calculated with inversion of geophysical data, or elastic attributes generated from well log data.

Preferably, the ensemble prediction model has been trained on one, preferably several, carbonate reservoirs that are different from the studied carbonate reservoir on which seismic data is generated.

The ensemble prediction model has been trained at least with the attribute to be predicted (i.e. porosity, lithofacies and permeability). For example, if the invention is used to predict porosity and lithofacies values, the ensemble model should have been trained at least with porosity and lithofacies values.

As already mentioned, there is a high heterogeneity in lithofacies, permeability and porosity of a carbonate reservoir. However, due to the possible variation in post depositional diagenesis history of a carbonate reservoir, there has been shown a high heterogeneity between carbonate reservoirs. Hence, the ensemble prediction model preferably can also include reservoir types as input data, for example said reservoir types being selected from: lacustrine carbonates formation, cold-water carbonate formation, and warm-water carbonate formation. When training the ensemble prediction model, carbonate reservoirs may have been grouped into at least three different classes of carbonate reservoirs.

Advantageously, the ensemble prediction model is not calibrated/trained based on rock analysis of samples and preferably uses only well logs for training. As illustrated in the figure 2, the training 120 of the ensemble prediction model can be based on key information values 121 , elastic attributes values 122, porosity values 123, permeability values 125 and lithofacies values 124. Preferably, the training 120 of the ensemble prediction model is at least based on elastic attributes values, porosity values, permeability values and lithofacies values. Key information values 121 can for example correspond to reservoirs typology type, a priori geological information, gamma ray values or water-contact values. Such key information without being essential can enhance the accuracy of the prediction.

As proved in the example, ensemble prediction models proved to be the best performers for permeability, lithofacies and porosity predictions on carbonate reservoirs. Indeed, while artificial neural networks have already been proposed for porosity prediction and lithofacies predictions, ensemble prediction models outperformed several other methods of machine learning in this context of carbonate reservoirs.

Ensemble prediction model refers to a machine learning paradigm where multiple models (i.e. “weak learners”) are trained to solve the same problem and are combined to obtain better results. The main hypothesis is that when weak models are correctly combined, more accurate and/or robust models can be obtained. Ensemble prediction models can be combined in a “homogeneous ensemble prediction model”, homogeneous weak learners that are trained in different ways. Alternatively, an ensemble prediction model can use different types of base learning algorithms to combine heterogeneous weak learners into a “heterogeneous ensemble prediction model”. Ensemble prediction methods can also be divided into sequential ensemble prediction methods, where the base learners are generated sequentially (e.g. xgboost), and parallel ensemble prediction methods, where the base learners are generated in parallel (e.g. Random Forest).

Stacking is an ensemble learning technique that combines multiple classification or regression models via a meta-classifier or a meta-regressor. The base level models are trained based on a complete training set, then the meta-model is trained on the outputs of the base level model as features. The base level often consists of different learning algorithms and therefore stacking ensembles are often heterogeneous.

Bagging (or bootstrap aggregation) uses bootstrap sampling to obtain the data subsets for training the base learners. Hence, each model in the ensemble is trained on a random sample of the dataset, where preferably each random sample is the same size as the dataset and sampling with replacement is used. For aggregating the outputs of base learners, bagging uses voting for classification and averaging for regression. For example, the random forest approach can be considered as being a bagging method where decision trees, fitted on bootstrap samples, are combined to produce an output with lower variance.

Boosting refers to a family of algorithms that can fit a sequence of weak learners (such as small decision trees) to weighted versions of the data. In particular, each new model added to an ensemble is biased to pay more attention (more weight) to instances that previous model misclassified. The predictions are then combined through a weighted majority vote or a weighted sum to produce the final prediction. The principal difference between boosting and bagging, is that boosting works by iteratively creating models and adding them to the ensemble. Boosting comprise for example adaptative boosting and gradient boosting.

Preferably, the ensemble prediction model includes a method selected from: stacking, boosting, such as gradient boosting or adaptative boosting, and bagging such as random forest.

More preferably, the ensemble prediction model is selected from: random forest, xgboost, adaboost. Even more preferably, the ensemble prediction model is selected from xgboost and adaboost.

Moreover, the step of training 120 the ensemble prediction model can comprise the use of a moving average filter to smooth the values of permeability, lithofacies and/or porosity calculated from well logs. This will make it comparable to the scale of the inverted elastic attributes from pre-stack seismic data. Hence it significantly improves the resolution and prediction accuracy. Also, values of lithofacies, permeability and porosity used for the training are preferably calculated using a petrophysics methodology, for example by log data directly (porosity) and a definition of lithofacies by the lithology content and petrophysics properties. For example, a petrophysics methodology can correspond to a deterministic petrophysics methodology or a stochastic petrophysics methodology. Preferably, a petrophysics methodology corresponds to a deterministic petrophysics methodology. Such methodologies are well known to the person skilled in the art, they also include knowhow and geoscientist expertise.

As mentioned, the ensemble prediction model according to the invention, and in particular its training, is based at least partly on elastic attributes. Elastic attributes are preferably generated from well logs (in particular for the training) or seismic data with standard inversion methods (in particular for the prediction).

In particular, elastic attributes comprise P-wave velocity V_p, S-wave velocity V_s, density or their mathematic transformations. Preferably, the elastic attributes comprise elastic attributes selected from the group consisting of:

P-wave velocity V_p,

- S-wave velocity V_s,

Density,

- Vp/Vs ratio,

- shear modulus: density^*V_s ²,

- bulk modulus: density^*(V_p ² - (4/3^*V_s ²)

P-impedance: V_p ^* density,

- S-impedance: V_s ^* density,

Poisson’s ratio: (V_p ²-2V_s ²)/(2^*(V_p ²-V_s ²));and

Lame’s coefficient: density^*(V_p ²-4/3V_s ²) - (2/3^*density^*V_s ²).

More preferably, the elastic attributes comprise elastic attributes selected from the group consisting of P-lmpedance and V_p/V_s ratio. Even more preferably, the elastic attributes consist of P-lmpedance and V_p/V_s ratio.

Back to the figure 1 , a method 100 for predicting values of porosity, permeability and/or lithofacies according to the invention comprises a step of loading 130 an ensemble prediction model. Preferably, the loaded ensemble prediction model has been trained according to the step of training 120 describe above, more preferably with data collected according to the step of collecting 110 data from well logs. Advantageously, as it has already been described, the ensemble prediction model includes any one of a stacking, a bagging such as random forest, a gradient boosting such as xgboost or an adaptative boosting such as adaboost. Preferably, the ensemble prediction model includes any one of a random forest or a xgboost.

In particular, the ensemble prediction model have been trained with values of elastic attributes and values of lithofacies, permeability and/or porosity. Such values can be considered as reference values. In particular, elastic attributes values are classically described as input data, whereas lithofacies, permeability and/or porosity values can be considered as target values. Advantageously, as mentioned, those reference values have been obtained from well logs. They are not based on rock sample analysis.

As shown in figure 1 , a method 100 for predicting values of porosity, lithofacies and/or permeability according to the invention comprises a step of acquiring 170 values of inverted elastic attributes calculated from seismic data generated on a studied carbonate reservoir.

Generally, inverted elastic attributes are elastic attributes obtained from the inversion of seismic data. The preferably comprise V_p, V_s, density or their mathematic transformations.

In particular, the inverted elastic attributes comprise inverted elastic attributes selected from the group consisting of: V_p, V_s, density, V_p/V_s ratio, shear modulus, bulk modulus, P- impedance, S-impedance, Poisson’s ratio and Lame’s coefficient.

Preferably values of inverted elastic attributes include: P-lmpedance and V_p/V_s ratio. More preferably values of inverted elastic attributes consist in: P-lmpedance and V_p/V_s ratio.

Whereas, the inverted elastic attributes have been generated before the implementation of the method according to the invention, in some embodiments, the method according to the invention can include the generation of those inverted elastic attributes.

Hence, as shown in figure 1 , a method 100 for predicting values of porosity, lithofacies and/or permeability according to the invention can comprise a step of collecting 140 seismic data.

The seismic data generated on a carbonate reservoir preferably corresponds to 2D or 3D seismic data. For example, the seismic data can be collected via several of transmitters and geophones. As shown in figure 1 , a method 100 for predicting values of porosity, lithofacies and/or permeability according to the invention can also comprise a step of inversion 150 of seismic data. Indeed, whereas seismic data do not contain direct facies information, it can be used to obtain P-wave velocity, S-wave velocity, density, and other reservoir properties using seismic inversion techniques.

As shown in figure 1 , a method 100 for predicting values of porosity, lithofacies and/or permeability according to the invention can comprise a step of pretreatment 160 of inverted seismic data. Indeed, inverted seismic data may be pretreated 160 so as to facilitate future operations. A pretreatment according to the invention may be: normalization of data, re-sampling, aggregation of data, and/or re-coding variables.

As already described, inverted elastic attributes can comprise V_p, V_s, density or mathematic transformations based on these elastic attributes.

As shown in figure 1 , a method 100 for predicting values of porosity, lithofacies and/or permeability according to the invention comprises a step of generating 180 predicted values of porosity, lithofacies and/or permeability of the studied carbonate reservoir.

This step can comprise treating or processing the acquired values of inverted elastic attributes with the ensemble prediction model.

A method 100 for predicting values of porosity, lithofacies and/or permeability according to the invention can comprise a step of generating 180 predicted values of porosity, lithofacies or permeability of the studied carbonate reservoir. However, no machine learning methods have been proposed for simultaneous prediction of porosity and lithofacies whereas both of this information are of utmost importance for carbonate reservoir characterization. Hence, a method 100 for predicting values of porosity, lithofacies and/or permeability according to the invention preferably comprises a step of generating 180 predicted values of porosity and lithofacies of the studied carbonate reservoir. More preferably, the method according to the invention comprises a step of generating 180 predicted values of porosity and lithofacies, or permeability of the studied carbonate reservoir.

Alternatively, a method 100 according to the invention can comprise a step of generating 180 predicted values of:

- porosity,

- lithofacies,

- permeability, - porosity and permeability,

- lithofacies and permeability, or

- porosity, lithofacies and permeability.

As illustrated in the figure 3, the generation 180 of predicted values of porosity and lithofacies is based on a trained ensemble prediction model 181 , inverted elastic attributes 184 and it can also be based on key information 185 value. Key information 185 values can for example correspond to reservoirs typology type, a priori geological information, gamma ray values or water-contact values. Such key information without being essential can enhance the accuracy of the prediction. Hence, while seismic data 182 and inverted seismic data 183 can be processed in a method according to the invention, such data are not injected in the trained ensemble prediction model 181 .

In particular, generating 180 predicted values of porosity, lithofacies and/or permeability comprises a generation of predicted values of porosity, lithofacies and/or permeability for each pixel of a 2D model of the carbonate reservoir. Preferably, generating 180 predicted values of porosity, lithofacies and/or permeability comprises a generation of predicted values of porosity, lithofacies and/or permeability for each 3D voxel of a 3D model of the carbonate reservoir. Advantageously, the invention generates lithological probability cubes from seismic

In some embodiments, the methods and devices of the present disclosure may facilitate determining how much hydrocarbon is in place in a subterranean carbonate reservoir. The methods and devices of the present disclosure may also help for positioning a well position.

This method based on seismic data and a prediction model trained with well logs, can determine lithofacies collocated with the 3D seismic elastic attribute to build an accurate subsurface reservoir model and this without the need of any well log on this reservoir.

It has been stated that the ensemble prediction model has been trained preferably from well logs generated from different carbonate reservoirs than the studied carbonate reservoir. Again, this is advantageous because without any well log data, the method according to the invention can produce relevant predicted values of porosity, lithofacies or permeability in similar geological context. However, the accuracy of prediction can be further enhanced.

As illustrated in figure 4, the method according to the invention can comprise a process 200 of retraining the trained ensemble prediction model.

A process 200 of retraining the trained ensemble prediction model will be based on the trained 231 ensemble prediction model or on data used to train the trained ensemble prediction model (e.g. elastic attributes values, porosity values, lithofacies values, permeability values, reservoir typology values).

Moreover, those data will be advantageously completed with permeability, lithofacies and/or porosity 232 values and elastic attributes 233 generated from at least one well log 210 of the studied carbonate reservoir. As previously, well log will be analyzed 220, preferably according to a petrophysics methodology, more preferably a deterministic petrophysics methodology in order to determine lithofacies, permeability and porosity 232 values and elastic attributes 233. Moreover, the value of the key information 234 such as reservoir typology can be advantageously used for the retraining 230 step. Key information values 234 can for example correspond to reservoirs typology types, a priori geological information, gamma ray values or water-contact values. Such key information without being essential can enhance the accuracy of the prediction.

The well log received via a logging tool can be transmitted to a separate system used to perform the workflow steps dedicated to the elastic attributes, lithofacies and porosity calculation. To determine these elastic attributes, lithofacies and porosity, the well log data may be input into a petrophysical model stored in a device according to the invention or another device. The petrophysical model may incorporate a multi-mineral analysis with classification techniques such as Bayesian classification.

Hence, the method according to the invention can comprise the determination of lithofacies, permeability, porosity and elastic attributes values from a well log conducted on the studied carbonate reservoir and a step of retraining 230 the ensemble prediction model with a set of data comprising determined values of lithofacies, permeability, porosity and elastic attributes.

This is particularly advantageous and can be of use in many situations. For example, from the predicted values of porosity, lithofacies and/or permeability, one will be able to select a relevant location for the realization of a first well location. Log data calculated from this well location will be used in combination with the trained ensemble prediction model or data used to train this model to re-train 230 an ensemble prediction model. Hence, be so by putting again the method according to the invention with the retrained prediction model 186, then it will be possible to obtain more accurate data.

Alternatively, one or more well logs of the studied carbonate reservoir can be available before the first implementation of the method according to the invention. One will be able to use data from those well logs in combination with the trained ensemble prediction model or data used to train this model to re-train 230 an ensemble prediction model.

The present invention uses an ensemble prediction model. As stated, whereas much of the focus of machine learning is on developing the single most accurate prediction model possible for a given task, those ensemble prediction model generate a set of models and then make prediction by aggregating the outputs of these models.

Such a feature can be advantageously use when performing a retraining of the ensemble prediction model. Indeed, it is possible to give more importance to data generated from the studied carbonate reservoir than data generated from other carbonate reservoir when performing the step of 230 retraining the ensemble prediction model.

In another aspect, the invention relates to a device 1 for predicting values of porosity, lithofacies and/or permeability in a studied carbonate reservoir based on seismic data.

For purposes of this disclosure, a device 1 according to the invention may include any instrumentality or aggregate of instrumentalities operable to compute, classify, process, transmit, receive, retrieve, originate, switch, store, display, manifest, detect, record, reproduce, handle, or utilize any form of information, intelligence, or data.

For example, an information handling system may be a personal computer, a network storage device, or any other suitable device and may vary in size, shape, performance, functionality, and price. The information handling system may include random access memory (RAM), one or more processing resources such as a central processing unit (CPU) or hardware or software control logic, ROM, and/or other types of nonvolatile memory. Additional components of the information handling system may include one or more disk drives, one or more network ports for communication with external devices as well as various input and output (I/O) devices, such as a keyboard, a mouse, and a video display. The information handling system may also include one or more buses operable to transmit communications between the various hardware components.

Figure 5 is a schematic block diagram illustrating various hardware components that may be utilized in the device 1 according to the invention to predict values of porosity, lithofacies and/or permeability in a studied carbonate reservoir based on seismic data.

In particular, as illustrated in figure 5, the device 1 comprises: one or more memory components 10 configured to store an ensemble prediction model, one or more communication interfaces 20 configured to acquire values of inverted elastic attributes calculated from seismic data; and one or more processors 30 configured to process the acquired values of inverted elastic attributes with the ensemble prediction model to generate predicted values of porosity, lithofacies and/or permeability in the studied carbonate reservoir. It can also comprise one or more user interfaces.

A device 1 for predicting values of porosity, lithofacies and/or permeability in a studied carbonate reservoir based on seismic data may comprise a memory component 10.

The memory component 10 may comprise any computer readable medium known in the art including, for example, a volatile memory, such as a static random access memory (SRAM) and a dynamic random access memory (DRAM) , and / or a non-volatile memory, such as read-only memory, flash memories, hard disks, optical disks and magnetic tapes. The memory component 10 may include a plurality of instructions or modules or applications for performing various functions. Thus, the memory component 10 can implement routines, programs, or matrix-type data structures. Preferably, the memory component 10 may comprise a medium readable by a computer system in the form of a volatile memory, such as a random-access memory (RAM) and / or a cache memory. The memory component 10, like the other modules, can for example be connected with the other components of the device 1 via a communication bus and one or more data carrier interfaces.

The memory component is preferably configured to store an ensemble prediction model. As already mentioned, the ensemble prediction model has been in particular trained with: o values of elastic attributes, said elastic attributes comprising V_p, V_s, density or their mathematic transformations, and o values of porosity, lithofacies and/or permeability.

The memory component 10 can be configured to store all data and values generated during the step of collecting 110 data from well logs.

The memory component 10 can be configured to store all data and values such as reservoir typology values, values of elastic attributes and values of porosity, lithofacies and/or permeability, in particular those used to train the ensemble prediction model.

Moreover, the memory component 10 is preferably configured to store instructions capable of implementing the method according to the invention.

Furthermore, the device 1 can also comprise a communication interface 20. The communication interface 20 is preferably configured to transmit data on at least one communication network and may implement a wired or wireless communication. The device 1 can communicate with other devices or computer systems and in particular with clients 2 thanks to the communication interface 20. For example, communication interfaces 20 enable the device 1 to receive data from the various sensing components on location (e.g., 3D seismic data from geophones). Preferably, the communication is operated via a wireless protocol such as Wi-Fi, 3G, 4G, and/or Bluetooth. These data exchanges may take the form of sending and receiving files. For example, the communication interface 20 may be configured to transmit a printable file. The communication interface may in particular be configured to allow the communication with a remote terminal, including a client. The client is generally any hardware and/or software capable of communication with the device 1 .

A communication interface 20 according to the invention is, in particular, configured to exchange data with third party devices or systems.

A communication interface 20 configured to acquire values of inverted elastic attributes calculated from seismic data generated on a studied carbonate reservoir, said inverted elastic attributes comprising V_p, V_s, density or their mathematic transformations.

The device 1 may be communicatively coupled to another computing system, such as the client 2 that is configured to execute an inversion modeling software.

The device 1 may include a communication interface 20 through which another computing system, such as the client 2, sends the inverted elastic attributes as an input into the ensemble prediction model.

It should be noted that, in other embodiments, the inversion modeling software may be included in the device 1 according to the invention, or the components of the illustrated control systems may be distributed throughout a greater number of control systems.

Such devices may all be located at the reservoir site, or at a location remote from the reservoir site.

A device 1 for predicting values of porosity, lithofacies and/or permeability in a studied carbonate reservoir based on seismic data may comprise a processor 30. The processor 30 may be operably coupled to the memory component 10 to execute instructions, encoded in programs, for carrying out the presently disclosed techniques, more particularly to perform the method according to the invention.

The encoded instructions may be stored in any suitable article of manufacture (such as the memory component 10) that includes at least one tangible non-transitory, computer- readable medium that at least collectively stores these instructions or routines. In this manner, the memory component 10 may contain a set of instructions that, when executed by the processor 30, performs the disclosed method.

The memory component 10 may include any number of databases or similar storage media that can be queried from the processor 30 as needed to perform the disclosed method.

In particular, the processor 30 is configured to: load the ensemble prediction model and process the acquired values of inverted elastic attributes with the ensemble prediction model to generate predicted values of porosity, lithofacies and/or permeability in the studied carbonate reservoir.

These different modules or components are separated in Figure 5, but the invention may provide various types of arrangement, for example a single module cumulating all the functions described here. Similarly, these modules or components may be divided into several electronic boards or gathered on a single electronic board.

A device 1 according to the invention can be incorporated into a computer system and able to communicate with one or several external devices such as a keyboard, a pointer device, a display, or any device allowing a user to interact with the device 1 .

The device 1 may also be configured to communicate with or via a human-machine- interface. Thus, in one embodiment of the present invention, the device 1 can be coupled to a human interface machine (HMI). The HMI may be used to allow the transmission of parameters to the devices or conversely make available to the user the values of the data measured or calculated by the device.

In general, the HMI is communicatively coupled to a processor and includes a user output interface and a user input interface. The user output interface may include an audio and display output interface and various indicators such as visual indicators, audible indicators and haptic indicators.

The user input interface may include a keyboard, a mouse, or another navigation module such as a touch screen, a touchpad, a stylus input interface, and a microphone for inputting audible signals such as a user speech, data and commands that can be recognized by the processor.

The user interface may include various input/output devices that enable an operator to, for example, input values of inverted elastic attributes, or visualize an output image of the predicted values of porosity, lithofacies and/or permeability in the studied carbonate reservoir such as a 3D reservoir model on a digital display.

In another aspect, the invention relates to a non-transitory computer readable medium storing executable instructions which, when executed by a processor, implement a method according to the invention.

For the purposes of this disclosure, computer-readable media may include any instrumentality or aggregation of instrumentalities that may retain data and/or instructions for a period of time. Computer-readable media may include, for example, without limitation, storage media such as a direct access storage device (e.g., a hard disk drive or floppy disk drive), a sequential access storage device (e.g., a tape disk drive), compact disk, CD-ROM, DVD, RAM, ROM, electrically erasable programmable read-only memory (EEPROM), and/or flash memory; as well as communications media such as wires, optical fibers, microwaves, radio waves, and other electromagnetic and/or optical carriers; and/or any combination of the foregoing.

In particular, the invention relates to a non-transitory computer readable medium storing executable instructions which, when executed by a processor, implement a method for predicting values of porosity, lithofacies and/or permeability in a studied carbonate reservoir based on seismic data, the method comprising:

- Acquiring values of inverted elastic attributes calculated from seismic data generated on a studied carbonate reservoir, said inverted elastic attributes comprising Vp, Vs, density or their mathematic transformations; and

- Generating predicted values of porosity, lithofacies and/or permeability of the studied carbonate reservoir, said predicted values being calculated from the acquired values of inverted elastic attributes and the ensemble prediction model.

Thus, as will be appreciated by the one skilled in the art, aspects of the present invention may be embodied as a device, system, method or computer program product. Accordingly, aspects of the present invention may take the form of a fully hardware embodiment, a fully software embodiment (including firmware, resident software, microcode, etc.) or a mode of operation. In addition, aspects of the present invention may take the form of a computer program product incorporated into one or more computer readable media having a computer readable program code embedded therein.

Any combination of one or more computer readable media may be used. In the context of this document, a computer readable medium may be any tangible medium that may contain, or store, a program for use by or in connection with an instruction execution system, apparatus, or device. A computer readable medium may be, for example, but not limited to, an electronic, magnetic, optical, electromagnetic, infrared or semiconductor system, apparatus or device, or any suitable combination of the foregoing. More specific examples (a non-exhaustive list) of the computer-readable storage medium would include: a hard disk, a random-access memory (RAM).

Computer program code for performing operations for aspects of the present invention may be written in any combination of one or more programming languages, including an object- oriented programming language such as Java, C ++, or similar, the programming language "C" or similar programming languages, a scripting language such as Perl, or similar languages, and / or functional languages such as Meta Language. Program code can run entirely on a user's computer, partly on a user's computer, and partly on a remote computer or entirely on the computer or remote server. In the latter scenario, the remote computer can be connected to a user's computer by any type of network, including a local area network (LAN) or a wide area network (WAN).

These computer program instructions may be stored on a computer readable medium that can direct a computing device (i.e. computer, server ...), so that the instructions stored in the computer readable medium produce a computing device configured to implement the invention.

EXAMPLE Data preparation

The data used to test the machine learning workflow includes logging data from 7 wells labeled A1 to A7 and 2D inverted seismic data (P-impedance and V_p/V_s ratio) from presalt carbonate, offshore Brazil.

Data has been prepared from well logging data. The input variable (mainly P-impedance and Vp/V_s ratio) and target variable (reservoir properties to be predicted, i.e. permeability, lithofacies or porosity) were prepared based on petrophysics methodology and in particular on the basis of geological constraints and petrophysical interpretation. In each well, the petrophysics logs (required for training and testing) have been derived using standard deterministic petrophysics methodology.

Prediction models traininq

Machine learning models were used to determine patterns in the relationship between the input variable (P-impedance and V_p/V_s ratio) and the target variable (lithofacies and porosity) based on the labelled logging data. These patterns were trained to be applied on the seismic inversion results. Whereas seven machine learning models were trained (cf. Table 1), machine learning used in this study were mainly two ensemble learning approaches: Random Forest and XGBoost.

Table 1 . Machine learning algorithm (MLA) parameter used for the training model of lithofacies prediction for well A6.

MLA Parameter

Fuzzy Logic Fuzzy Gamma, gamma=0.9 PNN spread=0.4 SVM c=1024, g=1024 DNN hidden_units=[10, 20, 10]

Naive Bayes type=’linear’ Random Forest ntree=50, mtry=1 XGBOOST objective=’multi:softmax’, max_depth=9, eta=0.02

Lithofacies Prediction

The prediction results of different machine learning classifiers are presented in Figure 6. 50% of the data from each well were randomly extracted to compose the training data set. The grey levels indicate the lithofacies of limestone, silica-rich limestone, dolomitic limestone, anhydrite, and igneous rock.

The comparisons of the multiclass confusion matrix and the overall accuracy are shown in Figure 7 and Table 2, respectively. It can be seen that, in terms of prediction accuracy, Random Forest (Figure 7A) and XGBoost (Figure 7B) rank top 2, show obvious advantages over the rest of the machine learning algorithms. Indeed, Fuzzy Logic (figure 7C), DNN (figure 7D), PNN (figure 7E), Naive Bayes (figure 7F), SVM (figure 7G), , have generated lower predictions accuracies (Table 2). Moreover, when it comes to time consumed, XGBoost has a non-negligible time-consuming problem, while Random Forest shows high efficiency. This suggests that ensemble learning method can be considered as a good first choice algorithm for the supervised classification of lithofacies.

Table. 2. A comparison of different machine learning algorithms for the lithofacies prediction in terms of overall accuracy and time consumed.

ML Algorithm Prediction Accuracy Time Consumed

Fuzzy Logic 54.68% 2s

PNN 78.52% 11s

SVM 76.66% 123s

DNN 69.80% 360s

Naive Bayes 55.46% 52s

Random Forest 84.28% 4s

XGBOOST 83.32% 120s

Random Forest and XGBoost perform better with prediction accuracy above 80%. In particular, DNN (Figure 7D) predicted accurately anhydrite with only 33.5% of accuracy while Random Forest and XGBoost predicted it respectively with 70.5% and 68.3% of accuracy; Domolitic with 34% of accuracy while Random Forest and XGBoost were above 55%; and Silica-rich with 37% of accuracy while Random Forest and XGBoost predicted it respectively with 73.8% and 72.7% of accuracy. Similarly, Naive Bayes (Figure 7F) predicted domolitic with only 34% of accuracy while Random Forest and XGBoost were above 55%; and Silica-rich with 32% of accuracy while Random Forest and XGBoost predicted it with 73.8% and 72.7% of accuracy respectively.

Porosity Prediction The essence of porosity prediction is essentially a regression problem, while lithofacies prediction is essentially a classification problem. Hence there is a need to find a prediction model that will perform in both regression problem and classification problem. Therefore, not all machine learning algorithms can be employed to solve this regression problem. Ensemble learning methods were compared with four other methods for porosity prediction: SVM, DNN, linear and nonlinear regression. Here we took all the 7 wells into account. Similarly, 50% of the data from each well was randomly extracted to compose the training set which produces a generalized network. Then the generalized network was applied on each well to predict the porosity. We used correlation coefficients as the criteria to measure the performance of different machine learning algorithms.

Results of four machine learning algorithms and two regression methods for porosity prediction of three wells (A1 , A2 and A3) are presented in Figure 8: Support Vector Machine (8A); Deep Neural Network (8B) ; Linear regression (8C); Nonlinear regression (8D) ; Random Forest (8E); extreme gradient boosting (8F).

These figures from 8A to 8D show visible differences between the predicted porosity and the actual porosity with really little difference for the figure 8E. On the contrary, the differences between the two curves for figure 8F are almost not visible.

Also, the comparisons of corresponding correlation coefficients are listed in Table 3. Similar as lithofacies prediction, Random Forest and XGBoost had significantly better performances for porosity prediction. It is worth noting that XGBoost ranks first in terms of correlation coefficients, but it still suffers from the time-consuming problem.

Table 3. A comparison of different machine learning algorithms and regression methods for the porosity prediction in terms of overall accuracy and time consumed.

Time Correlation Coefficient

MLA

Consumed A1 A2 A3 A4 A5 A6 A7 Average

SVM 253s 0.84 0.85 0.75 0.74 0.84 0.94 0.84 0.83

DNN 550s 0.85 0.86 0.79 0.79 0.85 0.94 0.87 0.85

Linear

69s 0.84 0.72 0.67 0.72 0.83 0.93 0.81 0.79

Regression

Nonlinear

73s 0.83 0.68 0.66 0.68 0.82 0.94 0.79 0.77

Regression

Random

84s 0.92 0.92 0.91 0.88 0.91 0.97 0.93 0.92

Forest

XGBOOST 120s 0.96 0.96 0.95 0.95 0.95 0.98 0.95 0.95 To confirm the superiority of ensemble models, the impact of data abundance on the lithofacies prediction accuracy of the each well have also been evaluated. As expected, the more data is accounted for classifier training, the higher the validation accuracy for lithofacies prediction. Overall, when the portion of the training data is over 50%, the two ensemble learning classifiers can well predict the lithofacies (i.e. with 80 % of training data 94,5% for Random Forest and 89,2% for XGBoost).

For the purpose of comparison, it can be noticed that the predicted seismic lithofacies distribution at the well location roughly match with the lithofacies profile from wells A1 to A7. The silica-rich limestone is also fairly well delineated in the seismic profile. For example, the section of silica-rich limestone partially occurring at wells A1 , A2, A4, and A6 can be captured by seismic prediction to a certain degree.

The impact of data abundance on the porosity prediction accuracy of the each well have also been evaluated. It appears that the results of the porosity prediction are not very sensitive to the data completeness. This might suggest that, even if only 20% of the training sample is accounted, the relationship of elastic attributes versus porosity can still be fairly well captured. Also, comparatively speaking, the XGBoost predicts porosity with relatively higher accuracy than Random Forest. This in general make senses, since XGBoost has a better model construction ability in terms of regression problems.

Hence, the present invention describes how to combine, for carbonate reservoir characterization, machine learning with a successful ensemble prediction model, elastic attribute from well log, and inverted seismic attributes.

The ensemble train networks based on well logging data applied to seismic inversion results proved to be efficient in effectively mapping the spatial distribution of lithofacies and porosity. In particular, ensemble learning shows its potential in lithofacies, permeability and porosity prediction in terms of accuracy and efficiency, in comparison with other machine learning algorithm and industry tools.

Hence, a fast and efficient method for predicting values of porosity, lithofacies and/or permeability in a studied carbonate reservoir based on seismic data been described. Moreover, such a method for predicting values of porosity, lithofacies and/or permeability in a studied carbonate reservoir based on seismic data can be continually improve through learning.

Claims

1 . A method (100) for predicting values of porosity, lithofacies and/or permeability in a studied carbonate reservoir based on seismic data, the method comprising:

Loading (130) an ensemble prediction model, said ensemble prediction model having been trained with: o values of elastic attributes, said elastic attributes comprising V_p, V_s, density or their mathematic transformations, and o values of porosity, lithofacies and/or permeability;

- Acquiring (170) values of inverted elastic attributes calculated from seismic data generated on a studied carbonate reservoir, said inverted elastic attributes comprising V_p, V_s, density or their mathematic transformations; and

- Generating (180) predicted values of porosity, lithofacies and/or permeability of the studied carbonate reservoir, said predicted values being calculated from the acquired values of inverted elastic attributes and the ensemble prediction model.

2. The method of claim 1 , wherein values of porosity, lithofacies and/or permeability used to train the ensemble prediction model have been calculated using a petrophysics methodology.

3. The method of claim 1 , wherein said method comprises a step of training (120) the ensemble prediction model with values of elastic attributes comprising V_p, V_s, density or their mathematic transformations, and values of porosity, lithofacies and/or permeability.

4. The method of claim 3, wherein the step of training (120) the ensemble prediction model comprises a resampling of the values of porosity, lithofacies and/or permeability in order to reduce the frequency of data used in training.

5. The method according to anyone of claims 1 to 4, wherein the elastic attributes comprise elastic attributes selected from the group consisting of: V_p, V_s, density, Vp/V_s ratio, shear modulus, bulk modulus, P-impedance, S-impedance, Poisson’s ratio and Lame’s coefficient.

6. The method according to anyone of claims 1 to 5, wherein the values of elastic attributes include: P-lmpedance and V_p/V_s ratio.

7. The method according to anyone of claims 1 to 6, wherein the ensemble prediction model includes any one of: a boosting such as gradient boosting or adaptative boosting, a bagging and a stacking.

8. The method according to anyone of claims 1 to 7, wherein the ensemble prediction model has been trained on one, preferably several, carbonate reservoirs that are different from the studied carbonate reservoir on which seismic data are generated.

9. The method according to anyone of claims 1 to 8, wherein said method comprises a step of determining lithofacies, porosity, permeability and elastic attributes values from a well log conducted on the studied carbonate reservoir and a step of retraining the ensemble prediction model with a set of data comprising determined values of lithofacies, porosity, permeability and inverted elastic attributes.

10. The method of claim 9, wherein the lithofacies, porosity, permeability and elastic attributes values determined from the well log conducted on the studied carbonate reservoir were calculated using a petrophysics methodology.

11 . The method according to anyone of claims 1 to 10, wherein the ensemble prediction model also includes reservoir types as input data, for example said reservoir types being selected from: lacustrine carbonates reservoir, cold-water carbonate reservoir, and warm-water carbonate reservoir.

12. The method according to anyone of claims 1 to 11 , wherein the seismic data acquired for a carbonate reservoir correspond to 2D or 3D seismic data.

13. The method according to anyone of claims 1 to 12, wherein the seismic data have been collected via a plurality of transmitters and geophones.

14. The method according to anyone of claims 1 to 13, wherein generating (180) predicted values of porosity, lithofacies and/or permeability comprises a generation of predicted values of porosity, lithofacies and/or permeability for all intersections of a resolution grid corresponding to 2D seismic data acquired.

15. The method according to anyone of claims 1 to 14, wherein generating (180) predicted values of porosity, lithofacies and/or permeability comprises a generation of predicted values of porosity, lithofacies and/or permeability for each 3D voxel of a 3D model of the carbonate reservoir.

16. A computer device (1 ) for predicting values of porosity, lithofacies and/or permeability in a studied carbonate reservoir based on seismic data, said computer device comprising:

- A data memory (10) configured to store an ensemble prediction model, said ensemble prediction model having been trained with: o values of elastic attributes, said elastic attributes comprising V_p, V_s, density or their mathematic transformations, and o values of lithofacies, porosity and/or permeability;

- A communication interface (20) configured to acquire values of inverted elastic attributes calculated from seismic data generated on a studied carbonate reservoir, said inverted elastic attributes comprising V_p, V_s, density or their mathematic transformations; and

- A processor (30) configured to: o Load the ensemble prediction model, and o Generate predicted values of porosity, lithofacies and/or permeability in the studied carbonate reservoir, said predicted values being calculated from the acquired values of inverted elastic attributes and the ensemble prediction model.

17. A non-transitory computer readable medium storing executable instructions which, when executed by a processor of a computer device, implement a method according to anyone of claims 1 to 15.