Water-based mud properties quantification using dielectric dispersion measurements and artificial intelligence

Abstract

Embodiments presented provide for a quantification of mud properties used in hydrocarbon recovery operation. In certain embodiments, artificial intelligence and dielectric dispersion measurements are used for quantification of mud properties.

Description

ATTORNEY DOCKET IS23.1034-WO-PCT WATER-BASED MUD PROPERTIES QUANTIFICATION USING DIELECTRIC DISPERSION MEASUREMENTS AND ARTIFICIAL INTELLIGENCE CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims the benefit of U.S. Provisional Application No. 63 / 607,173, filed December 7, 2023. FIELD OF THE DISCLOSURE

[0002] Aspects of the disclosure relate to mud properties used in hydrocarbon recovery operations. More specifically, aspects of the disclosure relate to using artificial intelligence for quantification of dielectric dispersion measurements. BACKGROUND

[0003] Quantification of mud properties for hydrocarbon recovery projects is an important step in development of a productive wellbore. The processing and interpretation of dielectric dispersion logs in wells drilled with water-based muds require the knowledge of the borehole mud properties, and in particular, its whole mud conductivity and permittivity and mud filtrate salinity. The knowledge of the former is necessary to apply the so-called borehole corrections to the measurements, i.e., to remove the effect of the borehole in the permittivity and conductivity that are measured. The latter is an important parameter when interpreting the dielectric dispersion in terms of petrophysical quantities. Indeed, dielectric measurements at high frequencies are shallow, and most of the time the zone that is illuminated by the tool is invaded with mud filtrate. The knowledge of the properties of this filtrate increases the interpretation robustness.

[0004] Today, the mud is characterized mostly through surface measurements, either from mud and mud filtrate conductivity measured by the field engineer on a mud sample, or from mud company reports, and the properties of the mud downhole are extrapolated from these surface measurements. Surface mud samples; however, or mud reports mayATTORNEY DOCKET IS23.1034-WO-PCT WATER-BASED MUD PROPERTIES QUANTIFICATION USING DIELECTRIC DISPERSION MEASUREMENTS AND ARTIFICIAL INTELLIGENCE not allow for an accurate estimation of the mud conditions and properties downhole, either from surface measurement biases, no representativeness, or because events occurred in-between these measurements and the actual log (for example sending a fresh mud pill downhole). A direct estimation of mud properties at the exact time of the dielectric logging is required.

[0005] Modern dielectric tools may possess an external mud sensor, but experience has shown that these sensors are difficult to calibrate and not always quantitative. In the presence of washouts, either located below the casing shoe, at well bottom, or due to geomechanically effects within the logging interval, it is sometimes possible to estimate the mud properties directly from the dielectric dispersion propagation array measurements. Today, experienced analysts will scrutinize the full logging interval searching and then provide a guestimate of the mud conductivity and permittivity.

[0006] There is a need to provide an apparatus and methods that are easier to operate than conventional apparatus and methods to provide for analysis of water-based mud properties.

[0007] There is a further need to provide apparatus and methods that do not have drawbacks such as improper analysis of water-based mud properties.

[0008] There is a still further need to reduce economic costs associated with operations and apparatus described above with conventional tools to allow for correct identification of water-based mud properties. SUMMARYATTORNEY DOCKET IS23.1034-WO-PCT WATER-BASED MUD PROPERTIES QUANTIFICATION USING DIELECTRIC DISPERSION MEASUREMENTS AND ARTIFICIAL INTELLIGENCE

[0009] So that the manner in which the above recited features of the present disclosure can be understood in detail, a more particular description of the disclosure, briefly summarized below, may be had by reference to embodiments, some of which are illustrated in the drawings. It is to be noted that the drawings illustrate only typical embodiments of this disclosure and are therefore not to be considered limiting of its scope, for the disclosure may admit to other equally effective embodiments without specific recitation. Accordingly, the following summary provides just a few aspects of the description and should not be used to limit the described embodiments to a single concept.

[0010] In one embodiment, a method is disclosed. The method may comprise obtaining a log of mud properties of a wellbore. The method may further comprise annotating the log of mud properties with intervals. The method may further comprise estimating mud properties from the intervals. The method may further comprise obtaining mud properties based upon the estimated mud properties and permittivity and conductivity at different frequencies. BRIEF DESCRIPTION OF THE DRAWINGS

[0011] So that the manner in which the above recited features of the present disclosure can be understood in detail, a more particular description of the disclosure, briefly summarized above, may be had by reference to embodiments, some of which are illustrated in the drawings. It is to be noted; however, that the appended drawings illustrate only typical embodiments of this disclosure and are therefore not be considered limiting of its scope, for the disclosure may admit to other equally effective embodiments.

[0012] FIG.1 is a decision tree structure in one example embodiment of the disclosure.ATTORNEY DOCKET IS23.1034-WO-PCT WATER-BASED MUD PROPERTIES QUANTIFICATION USING DIELECTRIC DISPERSION MEASUREMENTS AND ARTIFICIAL INTELLIGENCE

[0013] FIG.2 is a parallel ensemble learning method.

[0014] FIG.3 is a sequential ensemble learning method.

[0015] FIG.4 is a leaf-wise tree growth structure in one example embodiment of the disclosure.

[0016] FIG.5 is a model design flow in one example embodiment of the disclosure.

[0017] FIG.6 is a side view of a dielectric scanner.

[0018] FIG.7 is a view of a dielectric scanner.

[0019] FIG. 8 is a data generation workflow in one example embodiment of the disclosure.

[0020] FIG.9 is an example of ^^^^80variations as function of mud conductivity.

[0021] FIG.10 is supervised model training workflow.

[0022] FIG.11 is a prediction models training workflow.

[0023] FIG.12 is inference workflow.

[0024] FIG.13 is an example of J function for conductivity.ATTORNEY DOCKET IS23.1034-WO-PCT WATER-BASED MUD PROPERTIES QUANTIFICATION USING DIELECTRIC DISPERSION MEASUREMENTS AND ARTIFICIAL INTELLIGENCE

[0025] FIG.14 is an example of most probable standoff thickness estimation at a single depth.

[0026] FIG.15 is an example of depth sample optimization based on unconstrained estimated standoff.

[0027] FIG.16 is a mud conductivity quantification workflow.

[0028] FIG.17 is an inverse model training workflow.

[0029] FIG.18 is an example of a log with the mud conductivity quantification through different methods.

[0030] FIG.19 is a method to estimate mud solid fraction.

[0031] FIG.20 is mud properties resulting from embodiments of the disclosure.

[0032] To facilitate understanding, identical reference numerals have been used, where possible, to designate identical elements that are common to the figures (“FIGS”). It is contemplated that elements disclosed in one embodiment may be beneficially utilized on other embodiments without specific recitation. DETAILED DESCRIPTION

[0033] In the following, reference is made to embodiments of the disclosure. It should be understood, however, that the disclosure is not limited to specific described embodiments. Instead, any combination of the following features and elements, whether related to different embodiments or not, is contemplated to implement and practice theATTORNEY DOCKET IS23.1034-WO-PCT WATER-BASED MUD PROPERTIES QUANTIFICATION USING DIELECTRIC DISPERSION MEASUREMENTS AND ARTIFICIAL INTELLIGENCE disclosure. Furthermore, although embodiments of the disclosure may achieve advantages over other possible solutions and / or over the prior art, whether or not a particular advantage is achieved by a given embodiment is not limiting of the disclosure. Thus, the following aspects, features, embodiments and advantages are merely illustrative and are not considered elements or limitations of the claims except where explicitly recited in a claim. Likewise, reference to “the disclosure” shall not be construed as a generalization of inventive subject matter disclosed herein and should not be considered to be an element or limitation of the claims except where explicitly recited in a claim.

[0034] Although the terms first, second, third, etc., may be used herein to describe various elements, components, regions, layers and / or sections, these elements, components, regions, layers and / or sections should not be limited by these terms. These terms may be only used to distinguish one element, components, region, layer or section from another region, layer or section. Terms such as “first”, “second” and other numerical terms, when used herein, do not imply a sequence or order unless clearly indicated by the context. Thus, a first element, component, region, layer or section discussed herein could be termed a second element, component, region, layer or section without departing from the teachings of the example embodiments.

[0035] When an element or layer is referred to as being “on,” “engaged to,” “connected to,” or “coupled to” another element or layer, it may be directly on, engaged, connected, coupled to the other element or layer, or interleaving elements or layers may be present. In contrast, when an element is referred to as being “directly on,” “directly engaged to,” “directly connected to,” or “directly coupled to” another element or layer, there may be no interleaving elements or layers present. Other words used to describe the relationshipATTORNEY DOCKET IS23.1034-WO-PCT WATER-BASED MUD PROPERTIES QUANTIFICATION USING DIELECTRIC DISPERSION MEASUREMENTS AND ARTIFICIAL INTELLIGENCE between elements should be interpreted in a like fashion. As used herein, the term “and / or” includes any and all combinations of one or more of the associated listed terms.

[0036] Some embodiments will now be described with reference to the figures. Like elements in the various figures will be referenced with like numbers for consistency. In the following description, numerous details are set forth to provide an understanding of various embodiments and / or features. It will be understood; however, by those skilled in the art, that some embodiments may be practiced without many of these details, and that numerous variations or modifications from the described embodiments are possible. As used herein, the terms “above” and “below”, “up” and “down”, “upper” and “lower”, “upwardly” and “downwardly”, and other like terms indicating relative positions above or below a given point are used in this description to more clearly describe certain embodiments.

[0037] Aspects of the disclosure provide an automated workflow that is usually performed by an experienced analyst. The aspects allow the workflow to be performed by non-specialists. To achieve this goal, a combination of physics and artificial intelligence (“AI”) techniques are performed together, leading to creation of an automatic dielectric mud property advisor.

[0038] In one example embodiment, a first step is to use AI to label intervals in logs having the potential to provide accurate mud properties. The second step is to estimate the mud properties on the selected intervals, either through an explicit model inversion process or through AI.

[0039] The last step is to use the knowledge of mud conductivity at different frequencies, coupled with the measure of mud temperature and mud density to obtain a full effectiveATTORNEY DOCKET IS23.1034-WO-PCT WATER-BASED MUD PROPERTIES QUANTIFICATION USING DIELECTRIC DISPERSION MEASUREMENTS AND ARTIFICIAL INTELLIGENCE description of mud properties, including permittivity and conductivity at different frequencies, and mud filtrate salinity. Supervised Learning

[0040] Supervised learning algorithms use a set of data to model relationships between the target prediction output (label) and the input features such that one can predict the output values for new data based on those relationships. These algorithms are two-step processes composed of a learning (training) step and a prediction step. In the training step, the model is developed based on given training data. In the prediction step, the model is used to predict the label for new (test) data. In the aspects described, two different types of supervised learning algorithms are used to solve two different tasks. 1. Classification: In the classification problem, the goal is to predict discrete values. A binary classification algorithm is used to detect mud patterns (label = 1 if the pattern is present, label = 0 otherwise). 2. Regression: The goal of regression problems is to predict continuous variables. A regression algorithm may be used to predict mud conductivity from detected mud patterns. Decision Trees

[0041] A decision tree, referring to FIG. 1 , is one of the easiest and most popular classification algorithms to understand and interpret. The goal of using a decision tree is to create a training model that can predict the class or value of the target variable by learning simple decision rules inferred from training data.

[0042] To predict a label for an input, the process is started at the root of the tree. Values of the root attribute are compared with the input’s attribute (feature). The branch is then followed corresponding to that value and jump to the next node.ATTORNEY DOCKET IS23.1034-WO-PCT WATER-BASED MUD PROPERTIES QUANTIFICATION USING DIELECTRIC DISPERSION MEASUREMENTS AND ARTIFICIAL INTELLIGENCE Training process 1. Initially, an original set is used as the root node. 2. On each iteration of the algorithm, iteration is conducted through the very unused attribute of the set and calculates entropy and information gain of this attribute. 3. The process then selects the attribute which has the smallest entropy or largest information gain. 4. The set is then split by the selected attribute to produce a subset of the data. 5. The algorithm continues to recur on each subset, considering only attributes never selected before. If the dataset consists of N attributes, then deciding which attribute to place at the root or at different levels of the tree as internal nodes is a complicated step. By just randomly selecting any node to be the root can’t solve the issue. If a random approach is followed, such an approach may give bad results with low accuracy

[0043] For solving this attribute selection problem, various criteria may be used: Entropy, Information gain, Gini index, Gain Ratio, Reduction in Variance, and Chi-Square. These criterions will calculate values for every attribute. The values are sorted, and attributes are placed in the tree by following the order i.e., the attribute with a high value (in case of information gain) is placed at the root. Ensemble Methods

[0044] Ensemble models are a machine learning technique that combines several base models to produce one optimal prediction. There are different types of ensemble learning methods. The most common one is known as “bagging”. Bagging involves fitting many models on different samples of the same dataset and combining the predictions. Boosting ModelsATTORNEY DOCKET IS23.1034-WO-PCT WATER-BASED MUD PROPERTIES QUANTIFICATION USING DIELECTRIC DISPERSION MEASUREMENTS AND ARTIFICIAL INTELLIGENCE

[0045] Bagging is shown in FIG.2. In classifications, it takes their majority vote, while in regression it averages the predictions. Instead of simple averaging, the prediction can also be obtained by weighting each prediction according to model accuracy for instance. In any of these cases, the base models are trained in parallel. Another possibility is to train them sequentially, which leads to a different type of ensemble learning called boosting Boosting is a very popular variant of ensemble methods where base models are obtained by training decision trees sequentially (FIG.3). These training decision trees are then combined to get better performance. It can be used for both regression and classification problems. In embodiments, a gradient boosting classifier may be used.

[0046] Boosting models have three main components: loss function, weak learners, and additive model. The role of the loss function is to estimate how good the model is at making predictions with the given data and its form could vary depending on the problem at hand. A weak learner is a model that classifies the data but does so very poorly (it has a high error rate). These are typically decision trees. The additive model is a sequential approach of adding the trees. After each iteration, the model is closer to its final version, meaning that each iteration will reduce the value of the loss function. Boosting methods have different variants such as AdaBoost, Gradient Boosting (GB), XGBoost, LightGBM, CatBoost, and NGBoost. Gradient boosting algorithms are composed of following steps: 1. Initialize model with a constant value: ^^^^ ^^^^argmin−)2. For m=1 to M (number of weak learners)ATTORNEY DOCKET IS23.1034-WO-PCT WATER-BASED MUD PROPERTIES QUANTIFICATION USING DIELECTRIC DISPERSION MEASUREMENTS AND ARTIFICIAL INTELLIGENCE a. Compute residuals ^^^^^^^^^^^(^^^^^^^^,^^^^(^^^^^^^^))^^^^^^^^^ = −�^^^^^^^^(^^^^^^^^)�, for ^^^^ = 1, … ,^^^^^^^^(^^^^)=^^^^^^^^−1(^^^^)b. Train decision tree with terminal node reasons ^^^^ f^^^^^^^^ or ^^^^ = 1, … ,c.L(^^^^^^^^ ,^^^^^^^^−1 (^^^^^^^^) + Υ), for ^^^^ = 1, … , ^^^^^^^^d. Update^^^^^^^^(^^^^) = ^^^^^^^^−1(^^^^) + ^^^^�Υ^^^^^^^^1(^^^^ ∈ ^^^^^^^^^^^^)

[0047] Decisionon feature values. In these embodiments, the algorithm looks for the best split which results in the highest information gain. Finding the best split turns out to be the most time-consuming part of the learning process of decision trees. The two algorithms by other GBDT implementations to find the best splits are: 1. Pre-sorted: Feature values are pre-sorted, and all possible split points are evaluated. 2. Histogram-based: Continuous features are divided into discrete bins which are used to create feature histograms.

[0048] Aspects of the disclosure use a variant of gradient boosting called Light Gradient Boosting Machine (LightGBM). The starting point for LightGBM is the histogram-based algorithm since it performs better than the pre-sorted algorithm. For each feature, all the data instances are scanned to find the best split with regards to the information gain. Thus, the complexity of the histogram-based algorithm is dominated by the number of data instances and features.ATTORNEY DOCKET IS23.1034-WO-PCT WATER-BASED MUD PROPERTIES QUANTIFICATION USING DIELECTRIC DISPERSION MEASUREMENTS AND ARTIFICIAL INTELLIGENCE

[0049] To overcome this issue, LightGBM uses two techniques: • Gradient One-Side Sampling (GOSS) - computes gradients which give a valuable insight into the information gain and select only the data with high gradients (large error). • Exclusive Feature Bundling (EFB) – combines mutually exclusive features (do not have non-zero values simultaneously) into a single feature which reduces training time without affecting the accuracy.

[0050] Finally, contrary to other boosting algorithms that grow tree level-wise, LightGBM splits the tree leaf-wise by choosing the leaf with maximum delta loss to grow (FIG.4). Since the leaf is fixed, the leaf-wise algorithm has a lower loss compared to the level-wise algorithm. Model Design Flow

[0051] The model design flow includes three different steps as shown in FIG.5. 1. The data generation is done by running a physics-based generator for predefined set of parameters. 2. Data labelling is performed by setting a label parameter to 1 when mud pattern is observed and 0 otherwise. 3. The modelling is the selection, the design, and the application of the machine learning algorithm to build the binary classification model (supervised models). Data generation-Real Measurements

[0052] The synthetic data is obtained in a way to imitate the real data measured with Dielectric Scanner tool (FIG.6). Dielectric Scanner features:ATTORNEY DOCKET IS23.1034-WO-PCT WATER-BASED MUD PROPERTIES QUANTIFICATION USING DIELECTRIC DISPERSION MEASUREMENTS AND ARTIFICIAL INTELLIGENCE • two 2-polararization magnetic-dipole transmitters, located at the center of the pad • eight 2-polararization (longitudinal and transverse) magnetic-dipole receivers, distributed in 2 sets of 4 receivers, symmetrically positioned around the transmitter. • two electric-dipole receivers, located each side of the transmitters, at a very narrow distance. • 4 discrete operating frequencies from about 20MHz up to about 1 GHz.

[0053] High-resolution measurements may be obtained by combining transmitter and symmetrically positioned receivers to form array measurements, that are compensated from transmitter and receiver gains. Each array is operated with two polarizations. In embodiments, four frequencies are interpreted to obtain apparent permittivity and conductivity.

[0054] In embodiments, the tool measures amplitude (AMP) and phase (PHA) of the emitted electromagnetic wave at the receivers. In total, the tool provides 4^^^^^^^^^^^^^^^^ × 2^^^^^^^^ × (8^^^^^^^^ × 2^^^^^^^^^^^^ + 2^^^^^^^^ × 1^^^^^^^^^^^^) = 144 (AMP, PHA) measurements. After combining into arrays, as described above (FIG.7), the number of apparent permittivity and conductivity may be reduced.

[0055] The so-called apparents represent bulk permittivity and conductivity as if a geological formation were homogenous. One apparent permittivity and apparent conductivity are obtained for each spacing, polarization, and frequency. Consequently, from FIG. 7, Frequency (4) multiplied by Spacing and Polarization (9) results in the number of different arrays (36): 36 apparent permittivities and 36 apparent conductivities. These 36 apparent signals will be used to detect mud patterns. Longitudinal (LG) are the arrays recorded with longitudinal polarization, transverse (TR) are the arrays recorded with transverse polarization, and finally transverse-electric (TE) are the single arrayATTORNEY DOCKET IS23.1034-WO-PCT WATER-BASED MUD PROPERTIES QUANTIFICATION USING DIELECTRIC DISPERSION MEASUREMENTS AND ARTIFICIAL INTELLIGENCE recoded with the electric dipole. Each spacing is labelled from 1 to 4 for increasing transmitter to receiver spacing. Synthetic Data

[0056] In embodiments, synthetic data may be used to train versions of artificial intelligence. The generation is performed based on underlying physical laws for dielectric data.

[0057] As shown in FIG. 8, a first step is to generate mud permittivity and mud conductivity for given frequency, mud salinity, drilling fluid density (DFD), and temperature. Then, for given a formation salinity, formation porosity, pressure, and temperature, the simulator will output corresponding formation permittivity and formation conductivity. With mud and formation properties, a bit size and standoff of the tool are chosen to simulate amplitude and phase of the measured signals. In the next step, the amplitude and phase are used to compute attenuation and phase shift that are finally used to generate apparent permittivity and apparent conductivity. In embodiments, to simulate field data a noise may be added by controlling noise level as additional parameter. It should be noted that only apparent conductivities are used to detect mud patterns.

[0058] In addition to the apparents, mud and formation priors may be generated. These may be obtained by adding Gaussian noise to the mud conductivity and formation conductivity values. Data labelling

[0059] The data labelling described above may be based on data physics. The data labeling may be composed of two main steps: 1. Computing standoff for which 80% of the signal is coming from the mud 2. Adding constraints for maximum measurable conductivityATTORNEY DOCKET IS23.1034-WO-PCT WATER-BASED MUD PROPERTIES QUANTIFICATION USING DIELECTRIC DISPERSION MEASUREMENTS AND ARTIFICIAL INTELLIGENCE Cutoff Standoff computing

[0060] The standoffs above which 80 percent of the signal comes from the mud, and only 20 percent from the formation, the J&K-function formalism is used. It consists in expressing the apparent conductivity ^^^^ or permittivity ^^^^ as: ^^^^^^^^^^^^ = ^^^^^^^^^^^^ + ^^^^(^^^^)(^^^^^^^^^^^^ − ^^^^^^^^^^^^) − ^^^^^^^^0^^^^(^^^^)(^^^^^^^^^^^^ − ^^^^^^^^^^^^)^^^^^^^^ ^^^^^^^^ − ^^^^^^^^^^^^^^^^^ = ^^^^^^^^^^^^ + ^^^^(^^^^)� ^^^^^^^^ ^^^^^^^^ ( ) ^^^ ^^^^ − ^^^^ � + ^^^^ ^^^^ ��, ^^^^^^^^0where ^^^^ is thesubscripts md and fm describe the mud and formation, and where J and K define the direct and cross radial response function. In addition to standoff ^^^^, J and K depend on the array spacing, and actual mud and formation properties. ^^^^ stands for the circular frequency at which the electromagnetic waves are emitted.conductivity and permittivity contrasts between mud and formation affect the conductivity and permittivity apparents, leading to possible complexity in their interpretation. As the K term in the conductivity equation is scaled by frequency, the effect of the K term may be omitted at first order at low frequency. Simplification of the formula results in: ^^^^^^^^^^^^= ^^^^^^^^^^^^+ ^^^^(^^^^)(^^^^^^^^^^^^^^^^− ^^^^^^^^^^^^). Equation 1

[0061] The standoff is defined at which 80% of the signal comes from the formation,^^^^80, such that ^^^^(^^^^80) = 0.8.

[0062] The functions J and K are computed based on the simulated data. The form and values depend on the actual formation properties, and a functional providing ^^^^80as function of formation properties is defined. FIG.9 presents an example of ^^^^80variationsATTORNEY DOCKET IS23.1034-WO-PCT WATER-BASED MUD PROPERTIES QUANTIFICATION USING DIELECTRIC DISPERSION MEASUREMENTS AND ARTIFICIAL INTELLIGENCE as function of mud conductivity for frequency 2, for the 9 different arrays. Constraints

[0063] The propagation of electromagnetic wave in a media is subject to attenuation, and for increasing formation or mud conductivity. The waves are increasingly attenuated from transmitter to receiver, up to a threshold where the amplitude measured at receiver is lower than electronic thermal noise and hence is dominated by noise. This conductivity threshold depends on the transmitter to receiver distance, and on the frequency. Table 1 provides the mud conductivity thresholds above which the array measurement is not representative of the formation properties anymore. Above this threshold, the noisy array measurement is excluded from the training and modelling steps. Max cond F0 F1 F2 F3Combining Two Labels

[0064] The standoff used for data simulation is compared to the four standoff thresholds obtained in the first step (for each frequency). If the standoff is higher than the threshold, the channels with that frequency can be used to detect the mud pattern. Accordingly, the label for that frequency is set to 1. Otherwise, it is 0. After this step, four labels are present, one per frequency. The next step is then to add constraints. As it can be concluded from the previous discussion, there is one constraint per frequency. To obtain constrained labelATTORNEY DOCKET IS23.1034-WO-PCT WATER-BASED MUD PROPERTIES QUANTIFICATION USING DIELECTRIC DISPERSION MEASUREMENTS AND ARTIFICIAL INTELLIGENCE an operation is performed to the labels and constraints and get label equal to 1 only when both label and constraint are equal to 1. Finally, we will have one label per frequency. To set the final label to 1 it is enough to have all these labels equal to 1. This is the output that we want to predict with the model. However, the information about the label per frequency can be used to label difficulty of the detection for given sample Modelling

[0065] Modelling is based on a supervised machine learning model. The problem is defined as a binary classification problem. The classification model is based on receiving values as input and generating as output the class to which the values belong. The input values represent 36 conductivity channels values and 0 or 1 as output.

[0066] FIG. 10 illustrates a workflow when training a supervised machine learning model. First, data is split into training and testing datasets. The training data is used for model training. Once the model is trained, test data are used to evaluate model pe4rformance.

[0067] Additional method steps are represented in FIG.11. The data may be split into 4 different datasets with different number of inputs: 1. Dataset with only one frequency (F0) – 9 inputs 2. Dataset with two frequencies (F0 and F1) – 18 inputs 3. Dataset with three frequencies (F0, F1, and F2) – 27 inputs 4. Dataset with four frequencies (F0, F2, F3 and F4) – 36 inputs Moreover, due to its high sensitivity to noise, the signal measured by electric-dipole receivers for frequency F0 is excluded from inputs. As we have previously said, not all the data can be used to any value of the mud conductivity. This is restricted by the frequency of the emitted electromagnetic waves (FIG.7). Since we don’t know the true mud conductivity value (this is what we want to predict) we can use priors to get an ideaATTORNEY DOCKET IS23.1034-WO-PCT WATER-BASED MUD PROPERTIES QUANTIFICATION USING DIELECTRIC DISPERSION MEASUREMENTS AND ARTIFICIAL INTELLIGENCE about the range of conductivity values we expect to get. These priors can tell us if we are rather positioned close to low conductivity values when we can use all the inputs or higher values where some of the channels should be excluded.”

[0068] After the data splitting, 4 models are trained as shown in FIG. 11. Each of 4 datasets is split into a training dataset and testing dataset and separate models are trained. The models are trained by using LightGBM approach. Inference

[0069] An inference workflow is presented in FIG.12. The inference is done on real data. In one real data file, 36 arrays indexed by depth value are present. These arrays can have from a few thousands to hundreds of thousands of samples with constant mud properties. Due to an unpredictable noise behavior, the samples are independently analyzed. The steps in the inference process are the following. Firstly, the prior obtained from mud reports or any external input such as laterolog or induction tools is compared to the constraints to select input frequencies. Once the channels are selected, the corresponding model is used to predict mud pattern presence. In addition to a binary label, the model will also output the probability of the detection meaning that for the low probability values (lower than 0.5) the pattern will not be detected, while for high probabilities (higher than or equal to 0.5) the mud pattern will be detected. This probability value is crucial for the last step which is the prediction postprocessing.

[0070] This step concerns mainly the cases when too little or too many patterns are detected. The postprocessing goes as follows: 1. Set the number of desired mud patterns per file (currently equal to 1000, but can be modified),ATTORNEY DOCKET IS23.1034-WO-PCT WATER-BASED MUD PROPERTIES QUANTIFICATION USING DIELECTRIC DISPERSION MEASUREMENTS AND ARTIFICIAL INTELLIGENCE 2. Verify if the number of detected mud patterns (with ML model) is higher or lower that preset threshold, 3. If higher → take first 1000 patterns with highest prediction probabilities, 4. If lower → add 0-prediction samples with highest probabilities until one of two conditions is satisfied: a. Number of samples is equal to 1000 b. Sample prediction probability is lower than 10% Quantification of Mud Conductivity

[0073] On real data, the depths at which inference workflow identified high sensitivity to mud properties are then subject to a second workflow to quantity the mud properties.

[0074] The previous inference workflow acts as an accelerator (only select a limited number of depths) and as a stabilization boost (only depth at which chances of success to estimate mud properties are high).

[0075] There are different ways to estimate mud properties, and two different methods are discussed below: a method based on the model of the tool response function as explained in the subsection “Cutoff Standoff computing”, and a method based on AI.

[0076] The first method utilizes the simplification of the response to standoff of the apparent conductivities, as shown in Equation 1.

[0077] Each frequency is treated independently of the other, as mud and formation conductivities vary with frequency. For a given frequency, Equation 1 represents a system to solve, with 9 sub-equations, one per array. For example, ^^^^^^^^0,^^^^^^^^1= ^^^^^^^^^^^^+ ^^^^^^^^0,^^^^^^^^1(^^^^)(^^^^^^^^^^^^− ^^^^^^^^^^^^)ATTORNEY DOCKET IS23.1034-WO-PCT WATER-BASED MUD PROPERTIES QUANTIFICATION USING DIELECTRIC DISPERSION MEASUREMENTS AND ARTIFICIAL INTELLIGENCE ^^^^^^^^0,^^^^^^^^2= ^^^^^^^^^^^^+ ^^^^^^^^0,^^^^^^^^2(^^^^)(^^^^^^^^^^^^− ^^^^^^^^^^^^)^^^^^^^^0,^^^^^^^^3= ^^^^^^^^^^^^+ ^^^^^^^^0,^^^^^^^^3(^^^^)(^^^^^^^^^^^^− ^^^^^^^^^^^^)⋮=⋮ re-written in a matrix form as^^^^^^^^0,^^^^^^^^1 1 − ^^^^^^^^0,^^^^^^^^1(^^^^) ^^^^^^^^0,^^^^^^^^1(^^^^)^^^^ � ^^^^^^^^^^^^^^^^0,^^^^^^^^2� =� 1 − (^^^^) (^^^^)� ^^^^� ^^^^^^^^^^^^�Or^^^^ � ^^^^� = ^^^^ (^^^^)� ^^^^^^^^^^^^0,^^^^^^^^2 ^^^^0 ^^^^^^^^^^^^�.

[0078] FIG.13 shows ana given a priori mud conductivity of 2S / m. Each colored line in each plot corresponds to a different array for a given frequency.

[0079] For a given standoff STOF, or ^^^^, and a priori mud properties based on user input and a priori formation properties based on deeper reading arrays, an approximate response matrix ^^^^^^^^0(^^^^) can be constructed and the system can be inverted. However, the actual standoff at a given depth is unknown.

[0080] To overcome this challenge, the possible range of standoff variations (bounded by tool radius and hole radius) is successively scanned. For each standoff, the system is solved through a fast unconstrained system inversion method, and the norm of the reconstruction error is computed. The norms for each valid frequency are added and the standoff minimizing the sum of norms is selected by depth point as the optimal standoff. This process is illustrated for a single depth in FIG.14.ATTORNEY DOCKET IS23.1034-WO-PCT WATER-BASED MUD PROPERTIES QUANTIFICATION USING DIELECTRIC DISPERSION MEASUREMENTS AND ARTIFICIAL INTELLIGENCE

[0081] At this stage, the mud properties are not yet evaluated, as unconstrained inversion, although fast, can lead to negative, i.e. non-physical values for the mud conductivity.

[0082] A more time consuming, non-negative, solver is then used in a second step, but only on the depths where the optimal standoff obtained previously passes a certain threshold corresponding at 80 percent DOI for the highest valid frequency, and only for the approximately best 5000 depths showing the larger most probable standoff. This second optimization of the depth samples is necessary to mitigate the time-consuming feature of non-negative solvers. The process is illustrated in FIG.15.

[0083] In addition, the response function is modified to ensure that the mud conductivity values are increasing for increasing frequency. This is achieved by using all frequencies together in a single inversion and inverting for the lowest frequency conductivity and for positive increment per increasing frequency.

[0084] The non-negative linear solver is the time-consuming step of the workflow, and this is why the acceleration provided by the previous inference step is necessary, coupled by the first inversion process.

[0085] The full quantification workflow is shown in FIG.16.

[0086] The workflow based on AI can be seen in FIG.17.

[0087] For a given frequency, inverse model is trained by using LGBM to estimate mud conductivity. Contrary to the previous task where a binary label was predicted, this label is a continuous variable and a regression model is used. The first step in the workflow is to select only datapoints where mud patterns are present, since these are the cases where inversion should be done. After that, four different models are trainedATTORNEY DOCKET IS23.1034-WO-PCT WATER-BASED MUD PROPERTIES QUANTIFICATION USING DIELECTRIC DISPERSION MEASUREMENTS AND ARTIFICIAL INTELLIGENCE to estimate mud conductivity at each frequency.

[0088] FIG.18 shows an example of log where the mud conductivity quantification is achieved through the 2 different methods, response function-based, and AI-based. The last 4 tracks show the apparent conductivities at different frequencies together with the quantification. The choice between one or the other method depends on the need to have some advanced quality controls, as such provided by the response-based approach. Mud Conductivities to mud properties

[0089] Once the mud conductivities at different frequencies and different depth are estimated, they can be transformed into the petrophysics value of interest. Those petrophysics values of interest are the mud permittivity and conductivity, that will be sued for borehole corrections, and the mud filtrate salinity that will be used to support the petrophysical interpretation.

[0090] To enable accurate borehole corrections, both conductivity and permittivity are need for the mud. The current workflow only provides conductivities. The main reason is that for high conductivities typical of water-based muds, 1 S / m and above, the conductivity term dominates in the response of permittivity apparents as explained above, and it becomes difficult to extract the value of the mud permittivity. The solution to estimate mud permittivity is then to rely on a mud property model. Typically, a mud property model takes in input the fraction of solids in the mud, and the water phase, or filtrate, salinity. Auxiliary inputs are operational frequency, borehole temperature and borehole pressure. While mud reports do provide values for the fraction of solids, the former are not always available, and an alternate method to estimate this value is required. Dielectric Scanner tool does measure the borehole hydrostatic pressureATTORNEY DOCKET IS23.1034-WO-PCT WATER-BASED MUD PROPERTIES QUANTIFICATION USING DIELECTRIC DISPERSION MEASUREMENTS AND ARTIFICIAL INTELLIGENCE (BHPR_ADT) and from its differential, a depth-based mud density measurement (DFD_ADT) is extracted. From mud density, assuming the density of solids is known and having filtrate salinity as parameter, (mostly a binary choice depending on the presence of barite), the fraction of solids can be estimated. The process to obtain mud density is described in FIG.19.

[0091] Finally, the mud property model (MPM) writes: ^^^^ �^^^^^^^^^^^^^^^^^^^^^^^^^^^^� = ^^^^^^^^^^^^�^^^^^^^^^^^^_^^^^^^^^^^^^, ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^,^^^^,^^^^,^^^^�,where ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ is the filtrate salinity, and ^^^^, ^^^^ the borehole temperature and pressure respectively.

[0092] The workflow for this application contains 2 steps: 1. Estimate filtrate salinity ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ using the estimated ^^^^^^^^^^^^^^^^ at different frequencies ^^^^ and different depths, and the measured ^^^^^^^^^^^^, ^^^^, ^^^^^^^^^^^^ ^^^^, by inverting the MPM for ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^parameter. 2. Reconstruct the expected mud permittivity values using the ^^^^^^^^^^^^. Example of application

[0093] In one embodiment, a well contains 190241 depth points. The number of points selected by the ML-based inference is reduced to 32265 depth points, which corresponds to a 6 times acceleration. These depth points are processed with the unconstrained fast R-system inversion scan providing the most probable standoff associated with each of these depths. The standoff threshold that was set to 1.2-in for the given conditions is then increased up to 1.9-inch leading to only 5012 points where mud conductivity quantificationATTORNEY DOCKET IS23.1034-WO-PCT WATER-BASED MUD PROPERTIES QUANTIFICATION USING DIELECTRIC DISPERSION MEASUREMENTS AND ARTIFICIAL INTELLIGENCE is done via nonnegative R-system inversion. Compared to the initial 190241 points, we obtained a 38 time acceleration in this example.

[0094] Finally, the mud conductivities at each frequency for each of these depths is used together with the mud density estimation (DFD) to obtain a single mud filtrate salinity, and in a last step whole mud permittivity is reconstructed.

[0093] FIG.20 shows the mud properties resulting for the method described. Track 1 illustrates the solid fraction in the mud estimated from mud density. As illustrated, there is a settling of mud solids at the bottom of the well. Track 2 shows the mud conductivities at 4 different frequencies (x-axis), as a function of mud temperature (y-axis). It may be observed that the mud conductivities are increasing with increasing temperature. Track 3 show the mud filtrate salinity estimated (x-axis) as function of mud temperature (y- axis). The mud filtrate salinity is in fact constant. This mud filtrate salinity can be used to support the invaded zone petrophysics interpretation for dielectric dispersion tools, but also for other shallow tools such as micro-resistivity. Finally, track 4 shows the reconstructed mud permittivity, to be used in conjunction with mud conductivities to perform optimal borehole corrections for dielectric dispersion tools.

[0094] Embodiments of the disclosure are presented next. Aspects of the disclosure should not be considered limiting through the recitation of the features of the claims. In one embodiment, a method is disclosed. The method may comprise obtaining a log of mud properties of a wellbore. The method may further comprise annotating the log of mud properties with intervals. The method may further comprise estimating mud properties from the intervals. The method may further comprise obtaining mud properties based upon the estimated mud properties and permittivity and conductivity at different frequencies.ATTORNEY DOCKET IS23.1034-WO-PCT WATER-BASED MUD PROPERTIES QUANTIFICATION USING DIELECTRIC DISPERSION MEASUREMENTS AND ARTIFICIAL INTELLIGENCE

[0095] In another example embodiment, the method may be performed wherein the annotating of the log of mud properties is performed through artificial intelligence.

[0098] In another example embodiment, the method may be performed wherein the estimating the mud properties from the intervals is through a model inversion process.

[0097] In another example embodiment, the method may be performed wherein the estimating the mud properties from the intervals is through artificial intelligence.

[0098] In another example embodiment, the method may be performed wherein mud filtrate salinity is used in the obtaining of the mud properties.

[0099] In another example embodiment, a method is disclosed. The method may comprise obtaining a log of mud properties of a wellbore. The method may further comprise annotating the log of mud properties with intervals. The method may further comprise obtaining mud density from the log of mud properties from the intervals. The method may further comprise obtaining mud conductivity based upon the mud density.

[0100] In another example embodiment, the method may be performed wherein the mud conductivity is mud filtrate conductivity.

[0101] In another example embodiment, the method may be performed wherein the obtained mud conductivity is obtained at different frequencies of evaluation.

[0102] In another example embodiment, the method may be performed wherein the mud properties are non-electromagnetic mud properties.ATTORNEY DOCKET IS23.1034-WO-PCT WATER-BASED MUD PROPERTIES QUANTIFICATION USING DIELECTRIC DISPERSION MEASUREMENTS AND ARTIFICIAL INTELLIGENCE

[0103] The foregoing description of the embodiments has been provided for purposes of illustration and description. It is not intended to be exhaustive or to limit the disclosure. Individual elements or features of a particular embodiment are generally not limited to that particular embodiment, but, where applicable, are interchangeable and can be used in a selected embodiment, even if not specifically shown or described. The same may be varied in many ways. Such variations are not to be regarded as a departure from the disclosure, and all such modifications are intended to be included within the scope of the disclosure.

[0104] While embodiments have been described herein, those skilled in the art, having benefit of this disclosure, will appreciate that other embodiments are envisioned that do not depart from the inventive scope. Accordingly, the scope of the present claims or any subsequent claims shall not be unduly limited by the description of the embodiments described herein.

Claims

ATTORNEY DOCKET IS23.1034-WO-PCT WATER-BASED MUD PROPERTIES QUANTIFICATION USING DIELECTRIC DISPERSION MEASUREMENTS AND ARTIFICIAL INTELLIGENCE CLAIMS What is claimed is:

1. A method, comprising: obtaining a log of mud properties of a wellbore; annotating the log of mud properties with intervals; estimating mud properties from the intervals; and obtaining mud properties based upon the estimated mud properties and permittivity and conductivity at different frequencies.

2. The method according to claim 1, wherein the annotating of the log of mud properties is performed through artificial intelligence.

3. The method according to claim 1, wherein the estimating the mud properties from the intervals is through a model inversion process.

4. The method according to claim 1, wherein the estimating the mud properties from the intervals is through artificial intelligence.

5. The method according to claim 1, wherein mud filtrate salinity is used in the obtaining of the mud properties.

6. A method, comprising: obtaining a log of mud properties of a wellbore; annotating the log of mud properties with intervals; obtaining mud density from the log of mud properties from the intervals; and obtaining mud conductivity based upon the mud density.ATTORNEY DOCKET IS23.1034-WO-PCT WATER-BASED MUD PROPERTIES QUANTIFICATION USING DIELECTRIC DISPERSION MEASUREMENTS AND ARTIFICIAL INTELLIGENCE 7. The method according to claim 6, wherein the mud conductivity is mud filtrate conductivity.

8. The method according to claim 6, wherein the obtained mud conductivity is obtained at different frequencies of evaluation.

9. The method according to claim 6, wherein the mud properties are non-magnetic mud properties.

10. The apparatus as illustrated and described.

11. The method as illustrated and described.

Images