Application of Machine Learning for Bit-Formation Matching in drilling operations

Application of Machine Learning for Bit-Formation Matching in drilling operations | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Application of Machine Learning for Bit-Formation Matching in drilling operations Shedrach Igemhokhai, Abiodun Olaoye, Kelani Bello, Ehigie Momodu, and 2 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5556031/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Efficient bit formation matching is imperative for the success and cost-effectiveness of drilling operations. At present, drill bit selection predominantly depends on historical data and experiential knowledge. While machine learning, particularly Artificial Neural Networks (ANNs), has gained prominence in bit selection, other diverse and impactful algorithms such as XGBOOST and Random Forest (RF), are often overlooked. This paper involves the systematic application and comparative analysis of XGBOOST, RF, and ANN, alongside an optimization approach using Genetic Algorithm. The study comprehensively considers various influential factors including formation properties, drilling fluid characteristics, bit design, and operational parameters. In this study, we achieved promising results with the highest classification accuracy for bit selection recorded at 0.97 using the XGBOOST model, while RF and ANN yielded accuracies of 0.91 and 0.93 respectively. Additionally, we obtained impressive R squared values of 0.991, 0.975, and 0.953 for predicting the Rate of Penetration (ROP) using the XGBOOST, ANN, and RF models respectively. These algorithms, coupled with the optimization techniques, aims to establish a robust framework for nuanced and accurate bit-formation matching. The results obtained hold significant potential for minimizing costs and optimizing resource allocation & utilization during the planning and execution of drilling projects in the oil and gas industry. Physical sciences/Energy science and technology/Fossil fuels/Crude oil Earth and environmental sciences/Solid earth sciences/Geology/Economic geology Machine Learning Bit-Formation Matching Drilling Artificial Neural Networks XGBOOST Random Forest Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 1. INTRODUCTION Efficient bit formation matching is a critical factor in the success and cost-effectiveness of drilling operations in the oil and gas industry. The selection of an appropriate drill bit tailored to the geological formation being penetrated significantly influences drilling performance, including rates of penetration, tool wear, and overall operational efficiency. However, traditional methods of bit selection often rely on historical data and subjective expert judgment, which may lead to suboptimal outcomes due to the complex and dynamic nature of geological formations and drilling environments. Moreover, the increasing diversity and heterogeneity of subsurface formations pose significant challenges to conventional decision-making processes. Variations in lithology, porosity, permeability, and other formation properties necessitate a more sophisticated approach to bit formation matching that can account for the intricate interplay between geological characteristics, drilling parameters, and tool design. In light of these challenges, there is a pressing need for advanced methodologies that can leverage the wealth of available data and provide actionable insights into bit-formation compatibility. Machine learning (ML) techniques offer a promising avenue for addressing this need by enabling the analysis of large and complex datasets to uncover hidden patterns and relationships that may inform more informed bit selection decisions. However, despite the growing interest in ML-driven approaches for bit formation matching, there exists a gap in the literature regarding the systematic evaluation and comparison of different ML algorithms and optimization techniques tailored specifically to this application. Drilling a well requires careful consideration of several important factors, including bit selection. Consequently, choosing the right bits is a difficult task because bit performance is affected by a number of variables, including ROP, revolutions per minute (RPM), mud weight (MW), and depth (D) (Momeni et al., 2018 ). Cost per foot is typically the basis for the most basic type of bit selection. With this approach, the bit that will offer the lowest cost per foot over the next interval is simply selected. Furthermore, other variables like offset, journal angle, and other design elements are also taken into account. This distinguishes one bit from another based on the unique surroundings (Watalingam, 2014 ). Using offset well performance data is the standard method for bit selection. The bit type with the highest penetration rate or the bit with the lowest cost per foot are the two most often utilised criteria for choosing the bit for the following interval. The selection procedure also takes into account elements like hydraulics, formation hardness, bit design, and operational characteristics. The selection process is a trial-and-error process because of the quantity of variables taken into account ((Bilgesu et al., 2001 ). This method frequently overlooks several crucial factors influencing bit performance and cannot ensure the best bit type is chosen 1.1 TYPES OF BITS Based on their design qualities, rotary drilling bits can be broadly categorised as either roller cutter bits or drag bits (Table 1 ). Fixed cutter blades are a frequent feature of drag bits. These blades are included into the bit's body. The drill string rotates as a single unit during the rotation. Conversely, the roller cutter bits typically feature two or more cones with fundamental cutting components. When the bottom-hole rotation occurs, these cutters revolve around the cone's axis (Fasheum, 1997 ) Table 1 Bit Types and Attributes Bit Type Characteristics Advantages Drag Bits • Fixed cutter blades integrated into the bit's body (Fasheunm, 1997) • Physically machine the drilling cuttings • Include PDC, diamond, and steel-cutting bits • No rolling components (Fasheunm, 1997) • Drills as a single unit (Margareth, 2017) • Reduces likelihood of bit breakage • Cost-effective and time-saving (Margareth, 2017) Roller Cutter Bits • Feature two or more cones with fundamental cutting components (Harrell, 1994) • Diverse tooth design and bearing types • Drilling motion depends on cone offset (Harrell, 1994) • Efficient in both soft and hard formations (Warren, 1984) • Accommodates broad range of formations • Increases drilling speed in various formation types (Harrell, 1994) 1.2 IADC BIT CLASSIFICATION SYSTEM 1.2.1 ROLLING CUTTER BIT CLASSIFICATION The world saw the introduction of the International Association of Drilling Contractors' (IADC) bit code categorization system in 1940. The IADC bit code categorization system for rolling cutter bits was created in 1987 and enhanced with additional features in 1992. An illustration of typical roller cone nomenclature is provided below in Fig. 1 and the standard nomenclature in Table 2 . Table 2 : Standard Nomenclature for Roller cone bits (McGehee et al., 1992) 1.2.2 CLASSIFICATION OF POLYCRYSTALLINE DIAMOND COMPACT (PDC) BITS One letter and three numbers make up the nomenclature for PDC drill bits. The letter, such as M for matrix, S for steel, or D for diamond, denotes the type of body. In the meantime, the type of formation that will be drilled is indicated by the first digit. The bit profile will be represented by digit number three, and the structure by digit number two. Table 3 shows the specifications for each of these digits. Table 3 Geological Formation Type Classification for Drilling (Brandon et al., 1992 ) S/N Type Description PDC Cutting Structure 1 Soft and soft sticky Highly drillable formations (Clay, marble, gumbo, unconsolidated sands) Normal size 2 Soft-medium Low compressive strength sands, shale and anhydrites with hard layers intermixed 3 Medium Moderate compressive strength sand, chalk, anhydrite and shale 4 Medium hard Higher compressive strength with non or semi sharp sand, shale, lime and anhydrite. 19mm cutters 5 Hard High compressive strength with sharp layers of sand or siltstone 13mm cutters 5 Extremely hard Dense and sharp formations, such as quartzite and volcanic rock 8mm cutters 1.3 BIT SELECTION METHODS Although bit performance may have a very small impact on overall well cost (about 5 percent of the budget), bit cost may have a significant overall impact (Jamshidi & Mostafavi, 2013 ) Bit selection can be broadly divided into three groups: : Evaluation of Costs (Cost Analysis) Analysis of Offset Well Logs 1.3.1 EVALUATION OF COSTS Typically, the cost analysis method is used to examine historical data from offset wells. Moreover, bit run monitoring uses it. An economical assessment of the bit's performance level will be made. But this approach takes up valuable time (Rabia et al., 1986). The estimation of bit cost is highlighted in the formula below: Because drilling characteristics are not taken into account, the aforementioned procedure is not regarded as an effective way to choose a bit. Thus, alternative approaches will be considered (Bataee et al., 2010) 1.3.2 ANALYSIS OF OFFSET WELL LOGS W. J. Hightower in 1964 created an intricate graphical depiction of the formation under study with the aid of gamma ray and spontaneous potential log data. This method, which is based on the compressive strength of the rock, compares various drilling bit types, drilling conditions, and lithology using sonic log and other lithology log data to be used in the selection of the suitable bit (Onyia, 1988). But bit selection is still based solely on past offset bit records, and current drilling data is still not taken into account. But current drilling data is still not taken into account, and bit selection is solely based on historical offset bit records. But current drilling data is still not taken into account, and bit selection is solely based on historical offset bit records. 2. METHODOLOGY 2.1 Data gathering and analysis The dataset utilized in this study comprises offset data from five oil wells located within the Niger Delta Field. The data were divided as follows: 70% for training, 15% for validation, and 15% for testing the Rate of Penetration (ROP) functions and conclusions drawn from the modelled bit. The first stage was using field data to determine the Targeted IADC bit code. Using the Targeted IADC bit code that was obtained in Stage 1, Stage 2 involved predicting the ROP values. The third stage involves reusing the predicted ROP value in the data set to obtain the optimized predicted IADC bit code value. 2.2. Machine Learning Model development The diagram below (Fig. 2 ) shows a flowchart representing the steps utilized for the development of the machine learning models used for this study. The data gathered was stored in an excel workbook format. The data was then exported to a python environment (Jupyter notebook), where all data processing and machine learning operations was carried out. The models adopted were ANN, Random Forest (RF) and Extreme Gradient Boosting (XGB), which were all implemented in the python environment (Jupyter Notebook) using different libraries and their appropriate versions. 2.2.1. Random Forest (RF): Random forest regression is an ensemble learning technique that builds multiple decision trees during training and combines their outputs to improve predictive performance and reduce overfitting (Breiman, 2001 ). Each tree is constructed using a randomly sampled subset of the training data and features, a process known as bootstrapping and feature bagging, respectively. This method ensures diversity among the trees, thereby enhancing the robustness and accuracy of predictions. In this study, random forest regression was employed due to its ability to handle non-linear relationships, accommodate high-dimensional datasets, and provide insight into feature importance (Loh, 2011 ). The hyperparameters, such as the number of trees (n_estimators) and maximum depth (max_depth), were optimized using grid search to ensure the model's performance was tailored to the dataset. The model's predictive capability was assessed using metrics such R squared and mean squared error (MSE), which are well-suited for evaluating the performance of regression models. Furthermore, feature importance rankings derived from the random forest were used to understand the relative contributions of input variables to the prediction, providing interpretability to the results (Louppe et al., 2013 ). Random forest's capability to effectively generalize across varying datasets while mitigating overfitting made it an ideal choice for this analysis. 2.2.2 Extreme Gradient Boosting (XGB) Classification Extreme Gradient Boosting (XGB) is a powerful machine learning technique used for predictive modelling in various research fields. The goal of XGB, like other prediction models, is to minimize the number of variables required for prediction, thereby reducing data collection burden and enhancing efficiency. In XGB, each decision tree is trained on the residuals (the difference between the predicted and actual values) of the previous tree. This iterative process allows the model to learn from the mistakes of the previous trees and improve the prediction accuracy. The primary reason for the accuracy of the XGB model is the cumulative effect of combining the predictions made by each decision tree. Mathematically, if we denote the current model as \(\:{f}_{m}\) ( X ) and the new tree as h(x) the updated model \(\:{f}_{m+1}\) ( X ) is given by: \(\:{f}_{m+1}\) ( X ) = \(\:{f}_{m}\) ( X ) + α⋅ h(x) …………………….……………………Eq. 2 where α is the learning rate. This process is repeated for a specified number of iterations or until the residuals can no longer be reduced. The final prediction is obtained by summing the predictions of all the trees. In the case of classification, a softmax function is applied to the sum to obtain the probabilities of each class, and the class with the highest probability is chosen as the prediction 2.2.3. Artificial Neural Network (ANN): ANN is a computational model inspired by the structure and function of the biological neural networks that make up the brain. The ANN model used for this study was a feed-forward neural network consisting of n hidden layers each with a set of neurons that can estimate a given output response (y) from provided input data (x) as shown in Fig. 3 . The mathematical concept of ANN involves a set of interconnected nodes or neurons that process and transmit information. Each neuron calculates a linear combination ( z ) of n input features ( \(\:{x}_{i}\) ) with corresponding weight ( \(\:{w}_{i}\) ) and bias ( b ) as shown in Eq. 3. The weights of the connections between the neurons are adjusted during training to minimize the error between the predicted output and the true output. The selection of the right activation function is very essential in the ANN modelling process as it is chiefly responsible for the mapping of the inputs to the outputs. z = \(\:\sum\:_{i=1}^{n}{x}_{i}{w}_{i}\) + b …………………….……………………Eq. 3 During the ANN process, the transformed version of the output data is forwarded from one hidden layer to another. The network is trained through an updating process that tunes the model weights to minimize model loss ( L ) which is typically taken as the root mean square error (RMSE) as shown in Eq. 4 where \(\:{\text{ŷ}}_{i}\) is the model prediction. The minimization is done through a gradient descent method where the weights are manipulated as a function of L and scaled using the learning rate (λ) as shown in Eq. 5. L = \(\:\sqrt{\frac{1}{n}\sum\:_{i=1}^{n}{({y}_{i}-{\text{ŷ}}_{i})}^{2}}\) ……………Eq. 4 \(\:{w}_{t+1}\) = \(\:{w}_{t}\) - λ \(\:\frac{\partial\:\text{L}}{\partial\:{w}_{t}}\) ……………Eq. 5 3. RESULTS AND DISCUSSION The results are as shown in the graphs below. In all the modelling, 70% of the data was used for training the model, 15% for validating the model performance, and another 15% testing the data. The correlation between the numerical features in the utilized dataset is shown in Fig. 4 below. Table 4 shows the performance of the different models utilized in the bit classification Table 4 Classification accuracies of the various models CLASSIFICATION MODEL CLASSIFICATION ACCURACY ANN 0.93 RANDOM FOREST 0.91 XGBOOST 0.97 3.1.1 Confusion Matrix The confusion matrix visually represents the model's performance in predicting the bit codes. Each row of the matrix corresponds to the actual bit codes, while each column represents the predicted bit code. Figure 5 shows the confusion matrix of the ANN model while Fig. 6 shows the confusion matrix of the Xgboost classification model. The next step utilised the predicted bit code as one of the inputs in order to predict the ROP values. In this step, various regression models were processed to predict the Rate of Penetration (ROP). Table 5 shows the tuned hyperparameters of the various models. Table 5 Optimal parameters of models utilised in the modelling Model Hyper parameters Final Optimized value Execution time (ms) ANN Kernel_initializer normal 10430.65 model optimizer adam epochs 300 layer 1 number of neurons 16 layer 1 activation function relu layer 2 number of neurons 64 layer 2 activation function relu layer 3 number of neurons 32 layer 3 activation function relu output layer number of neurons 1 output activation function softmax RF n estimators 1000 27.283 max depth 5 max features "sqrt" XGB max depth 5 210 ϒ 0.01 n estimators 100 subsample 0.8 random state 66 With an R squared value of 0.991, the Xgboost model proved to be the best prediction model, although Random forest and Artificial Neural Network, were accurate enough as well. Table 6 shows the evaluation of the different regression models Table 6 Evaluation of Regression Models Regression Models RMSE R Squared Xgboost 1.236 0.991 Random Forest 1.954 0.953 Ann 1.537 0.975 The plots below show the actual vs predicted values of ROP using the Xgboost model (Fig. 7), the ANN model (Fig. 8) and the Random forest model (Fig. 9 ) It is evident from the aforementioned graphs that we can optimize the ROP value through the modelling process by utilizing all of the available data. We can then utilize the optimized ROP value to get the optimized IADC bit code. The accuracy of the R value is roughly 99 percent based on the graph's numerical values. A tiny error still exists, and it has specific causes. 4. CONCLUSION This study investigated the application of machine learning techniques for bit - formation matching in drilling operations. The review identified gaps borne out of extensive literature, and highlighted the limitations of traditional methods reliant on historical data and expert judgment. The results obtained from the study provided opportunities on the potential of machine learning techniques to improve bit - formation matching in drilling operations. Comparative analysis of different algorithms provided insights into the performance and effectiveness in predicting bit-formation compatibility. Declarations Funding This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors. Availability of data and material Due to confidentiality agreements with the data provider, the field data used in this study are not publicly available. However, a summary of the data analysis and results is included in this published article. Specific data requests may be considered on a case-by-case basis and subject to approval from the data provider. For inquiries, please contact the corresponding author at [email protected] Authors Contribution Shedrach Igemhokhai: Conceptualization, Methodology, Formal analysis, Writing original draft, Software, Visualization, Data curation, Review and Editing. Kelani Bello : Review and Editing, Data curation. Abiodun Olaoye: Conceptualization, Review and Editing, Data curation. Ehigie Momodu: Review and Editing, Data curation. Nsisong Isuk : Review and Editing. Abayomi Adejumo: Review and Editing Competing interests The authors declare that they have no competing interest. References Bataee, M., Edalatkhah, S., & Ashna, R. (2010). Comparison between Bit Optimization Using Artificial Neural Network and Other Methods Base on Log Analysis Applied in Shadegan Oil Field. Society of Petroleum Engineers - International Oil and Gas Conference and Exhibition in China 2010, IOGCEC , 4 , 3097–3103. https://doi.org/10.2118/132222-MS Bilgesu, H. I., Al-Rashidi, A. F., Aminian, K., & Ameri, S. (2001). An Unconventional Approach for Drill-Bit Selection. Proceedings of the Middle East Oil Show , 198–203. https://doi.org/10.2523/68089-ms Brandon, B. D., Cerkovnik, J., Koskie, E., Bayoud, B. B., Colston, F., Clayton, R. I., Anderson, M. E., Hollister, K. T., Senger, J., & Niemi, R. (1992). Development of a New IADC Fixed Cutter Drill Bit Classification System . https://doi.org/10.2118/23940-MS Breiman, L. (2001). Random forests. Machine Learning , 45 (1), 5–32. https://doi.org/10.1023/A:1010933404324/METRICS Fasheum, M. (1997). THE UNIVERSITY OF NOTTINGHAM DEPARTMENT OF MINERAL RESOURCES ENGINEERING by . April . Hightower, W. J. (1964, March). Proper selection of drill bits and their use. In SPE Practical Aspects of Improved Recovery Techniques Symposium (pp. SPE-794). SPE. https://doi.org/10.2118/794-MS Jamshidi, E., & Mostafavi, H. (2013). Soft computation application to optimize drilling bit selection utilizing virtual inteligence and genetic algorithms. Society of Petroleum Engineers - International Petroleum Technology Conference 2013, IPTC 2013: Challenging Technology and Economic Limits to Meet the Global Energy Demand , 1 (October), 357–371. https://doi.org/10.2523/16446-ms Loh, W. Y. (2011). Classification and regression trees. Wiley Interdisciplinary Reviews: Data Mining and Knowledge Discovery , 1 (1), 14–23. https://doi.org/10.1002/WIDM.8 Louppe, G., Wehenkel, L., Sutera, A., & Geurts, P. (2013). Understanding variable importances in forests of randomized trees. Advances in Neural Information Processing Systems, 26, 431–439. McGehee, D. Y., Dahlem, J. S., Gieck, J. C., Kost, B., Lafuze, D., Reinsvold, C. H., & Steinke, S. C. (1992). The IADC Roller Bit Classification System . https://doi.org/10.2118/23937-MS Momeni, M., Hosseini, S. J., Ridha, S., Laruccia, M. B., & Liu, X. (2018). An optimum drill bit selection technique using artificial neural networks and genetic algorithms to increase the rate of penetration. Journal of Engineering Science and Technology , 13 (2), 361–372. Onyia, E. C. (1988). Relationships Between Formation Strength, Drilling Strength, and Electric Log Properties. Society of Petroleum Engineers of AIME, (Paper) SPE , OMEGA . https://doi.org/10.2118/18166-MS Rabia, H., Farrelly, M., & Barr, M. V. (1986). A New Approach to Drill Bit Selection. Society of Petroleum Engineers of AIME, (Paper) SPE , 421–428. https://doi.org/10.2118/15894-MS Watalingam, P. (2014). Bit Selection Using Drilling Data By Artificial Neural Networks . May . http://utpedia.utp.edu.my/id/eprint/14233 Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. 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2014)\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-5556031/v1/2d61cc38b6f8ad472a405339.png"},{"id":77121294,"identity":"b11a992d-5764-4568-bcfb-d98807ef8e30","added_by":"auto","created_at":"2025-02-25 10:26:02","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":318297,"visible":true,"origin":"","legend":"\u003cp\u003eCorrelation between numerical features in the dataset\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-5556031/v1/10e948702a3cdf814ea10f21.png"},{"id":77123064,"identity":"e16e0e0e-084c-40a4-89c0-3f2b8b4cdfdf","added_by":"auto","created_at":"2025-02-25 10:42:02","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":30212,"visible":true,"origin":"","legend":"\u003cp\u003eConfusion matrix of the ANN model\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-5556031/v1/ceb788da632f26bd98524c55.png"},{"id":77121608,"identity":"2b4bdd52-df75-4997-bfb8-71447afdfe15","added_by":"auto","created_at":"2025-02-25 10:34:02","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":25292,"visible":true,"origin":"","legend":"\u003cp\u003eConfusion matrix of the Xgboost Model\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-5556031/v1/95dc87e95c7d2a960d3b2230.png"},{"id":77120217,"identity":"daf6323f-4a8b-47b7-8aaa-7803b3d34516","added_by":"auto","created_at":"2025-02-25 10:18:02","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":42695,"visible":true,"origin":"","legend":"\u003cp\u003eActual vs Predicted ROP using Xgboost Model\u003c/p\u003e","description":"","filename":"7.png","url":"https://assets-eu.researchsquare.com/files/rs-5556031/v1/eafd6beaa1827ec7aeaf0225.png"},{"id":77120215,"identity":"8b3dbb57-3408-4f4d-a7d5-55bc0f99135b","added_by":"auto","created_at":"2025-02-25 10:18:02","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":42830,"visible":true,"origin":"","legend":"\u003cp\u003eActual vs Predicted ROP using ANN Model\u003c/p\u003e","description":"","filename":"8.png","url":"https://assets-eu.researchsquare.com/files/rs-5556031/v1/0fbf332cedf3c40c962ec644.png"},{"id":77120220,"identity":"ff5fb59b-b14a-48d6-b822-a3ef567cbd8f","added_by":"auto","created_at":"2025-02-25 10:18:02","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":58902,"visible":true,"origin":"","legend":"\u003cp\u003eActual vs Predicted ROP value using Random forest model\u003c/p\u003e","description":"","filename":"9.png","url":"https://assets-eu.researchsquare.com/files/rs-5556031/v1/56fd6f8e9230b291950cb441.png"},{"id":77123299,"identity":"b207cfa4-e642-4225-b202-6408904b1e24","added_by":"auto","created_at":"2025-02-25 10:50:08","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1512068,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5556031/v1/9f4766cf-2a74-4969-940d-9ae5de78e6c5.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Application of Machine Learning for Bit-Formation Matching in drilling operations","fulltext":[{"header":"1. INTRODUCTION","content":"\u003cp\u003eEfficient bit formation matching is a critical factor in the success and cost-effectiveness of drilling operations in the oil and gas industry. The selection of an appropriate drill bit tailored to the geological formation being penetrated significantly influences drilling performance, including rates of penetration, tool wear, and overall operational efficiency. However, traditional methods of bit selection often rely on historical data and subjective expert judgment, which may lead to suboptimal outcomes due to the complex and dynamic nature of geological formations and drilling environments.\u003c/p\u003e\n\u003cp\u003eMoreover, the increasing diversity and heterogeneity of subsurface formations pose significant challenges to conventional decision-making processes. Variations in lithology, porosity, permeability, and other formation properties necessitate a more sophisticated approach to bit formation matching that can account for the intricate interplay between geological characteristics, drilling parameters, and tool design.\u003c/p\u003e\n\u003cp\u003eIn light of these challenges, there is a pressing need for advanced methodologies that can leverage the wealth of available data and provide actionable insights into bit-formation compatibility. Machine learning (ML) techniques offer a promising avenue for addressing this need by enabling the analysis of large and complex datasets to uncover hidden patterns and relationships that may inform more informed bit selection decisions.\u003c/p\u003e\n\u003cp\u003eHowever, despite the growing interest in ML-driven approaches for bit formation matching, there exists a gap in the literature regarding the systematic evaluation and comparison of different ML algorithms and optimization techniques tailored specifically to this application.\u003c/p\u003e\n\u003cp\u003eDrilling a well requires careful consideration of several important factors, including bit selection. Consequently, choosing the right bits is a difficult task because bit performance is affected by a number of variables, including ROP, revolutions per minute (RPM), mud weight (MW), and depth (D) (Momeni et al., \u003cspan class=\"CitationRef\"\u003e2018\u003c/span\u003e). Cost per foot is typically the basis for the most basic type of bit selection. With this approach, the bit that will offer the lowest cost per foot over the next interval is simply selected. Furthermore, other variables like offset, journal angle, and other design elements are also taken into account. This distinguishes one bit from another based on the unique surroundings (Watalingam, \u003cspan class=\"CitationRef\"\u003e2014\u003c/span\u003e).\u003c/p\u003e\n\u003cp\u003eUsing offset well performance data is the standard method for bit selection. The bit type with the highest penetration rate or the bit with the lowest cost per foot are the two most often utilised criteria for choosing the bit for the following interval. The selection procedure also takes into account elements like hydraulics, formation hardness, bit design, and operational characteristics. The selection process is a trial-and-error process because of the quantity of variables taken into account ((Bilgesu et al., \u003cspan class=\"CitationRef\"\u003e2001\u003c/span\u003e). This method frequently overlooks several crucial factors influencing bit performance and cannot ensure the best bit type is chosen\u003c/p\u003e\n\u003cdiv id=\"Sec2\" class=\"Section2\"\u003e\n \u003ch2\u003e1.1 TYPES OF BITS\u003c/h2\u003e\n \u003cp\u003eBased on their design qualities, rotary drilling bits can be broadly categorised as either roller cutter bits or drag bits (Table \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e). Fixed cutter blades are a frequent feature of drag bits. These blades are included into the bit\u0026apos;s body. The drill string rotates as a single unit during the rotation. Conversely, the roller cutter bits typically feature two or more cones with fundamental cutting components. When the bottom-hole rotation occurs, these cutters revolve around the cone\u0026apos;s axis (Fasheum, \u003cspan class=\"CitationRef\"\u003e1997\u003c/span\u003e)\u003c/p\u003e\n \u003cdiv class=\"gridtable\"\u003e\u0026nbsp;\u003ctable id=\"Tab1\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eBit Types and Attributes\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003ccolgroup cols=\"3\"\u003e\u003c/colgroup\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eBit Type\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eCharacteristics\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eAdvantages\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eDrag Bits\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u0026bull; Fixed cutter blades integrated into the bit\u0026apos;s body (Fasheunm, 1997)\u003c/p\u003e\n \u003cp\u003e\u0026bull; Physically machine the drilling cuttings\u003c/p\u003e\n \u003cp\u003e\u0026bull; Include PDC, diamond, and steel-cutting bits\u003c/p\u003e\n \u003cp\u003e\u0026bull; No rolling components (Fasheunm, 1997)\u003c/p\u003e\n \u003cp\u003e\u0026bull; Drills as a single unit (Margareth, 2017)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u0026bull; Reduces likelihood of bit breakage\u003c/p\u003e\n \u003cp\u003e\u0026bull; Cost-effective and time-saving (Margareth, 2017)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRoller Cutter Bits\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u0026bull; Feature two or more cones with fundamental cutting components (Harrell, 1994)\u003c/p\u003e\n \u003cp\u003e\u0026bull; Diverse tooth design and bearing types\u003c/p\u003e\n \u003cp\u003e\u0026bull; Drilling motion depends on cone offset (Harrell, 1994)\u003c/p\u003e\n \u003cp\u003e\u0026bull; Efficient in both soft and hard formations (Warren, 1984)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u0026bull; Accommodates broad range of formations\u003c/p\u003e\n \u003cp\u003e\u0026bull; Increases drilling speed in various formation types (Harrell, 1994)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e\n \u003ch2\u003e1.2 IADC BIT CLASSIFICATION SYSTEM\u003c/h2\u003e\n \u003cdiv id=\"Sec4\" class=\"Section3\"\u003e\n \u003ch2\u003e1.2.1 ROLLING CUTTER BIT CLASSIFICATION\u003c/h2\u003e\n \u003cp\u003eThe world saw the introduction of the International Association of Drilling Contractors\u0026apos; (IADC) bit code categorization system in 1940. The IADC bit code categorization system for rolling cutter bits was created in 1987 and enhanced with additional features in 1992. An illustration of typical roller cone nomenclature is provided below in Fig. \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e and the standard nomenclature in Table \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e.\u003c/p\u003e\n \u003cp\u003eTable 2 : Standard Nomenclature for Roller cone bits (McGehee et al., 1992)\u0026nbsp;\u003c/p\u003e\n \u003cp\u003e\u003cimg 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\" width=\"604\" height=\"363\"\u003e\u003c/p\u003e\n \u003c/div\u003e\n \u003cdiv id=\"Sec5\" class=\"Section3\"\u003e\n \u003ch2\u003e1.2.2 CLASSIFICATION OF POLYCRYSTALLINE DIAMOND COMPACT (PDC) BITS\u003c/h2\u003e\n \u003cp\u003eOne letter and three numbers make up the nomenclature for PDC drill bits. The letter, such as M for matrix, S for steel, or D for diamond, denotes the type of body. In the meantime, the type of formation that will be drilled is indicated by the first digit. The bit profile will be represented by digit number three, and the structure by digit number two. Table \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e shows the specifications for each of these digits.\u003c/p\u003e\n \u003cdiv class=\"gridtable\"\u003e\u0026nbsp;\u003ctable id=\"Tab3\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eGeological Formation Type Classification for Drilling (Brandon et al., \u003cspan class=\"CitationRef\"\u003e1992\u003c/span\u003e)\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003ccolgroup cols=\"4\"\u003e\u003c/colgroup\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eS/N\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eType\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eDescription\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003ePDC Cutting Structure\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eSoft and soft sticky\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eHighly drillable formations (Clay, marble, gumbo, unconsolidated sands)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"3\"\u003e\n \u003cp\u003eNormal size\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eSoft-medium\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eLow compressive strength sands, shale and anhydrites with hard layers intermixed\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eMedium\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eModerate compressive strength sand, chalk, anhydrite and shale\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eMedium hard\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eHigher compressive strength with non or semi sharp sand, shale, lime and anhydrite.\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e19mm cutters\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eHard\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eHigh compressive strength with sharp layers of sand or siltstone\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e13mm cutters\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eExtremely hard\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eDense and sharp formations, such as quartzite and volcanic rock\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e8mm cutters\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003c/div\u003e\n \u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec6\" class=\"Section2\"\u003e\n \u003ch2\u003e1.3 BIT SELECTION METHODS\u003c/h2\u003e\n \u003cp\u003eAlthough bit performance may have a very small impact on overall well cost (about 5 percent of the budget), bit cost may have a significant overall impact (Jamshidi \u0026amp; Mostafavi, \u003cspan class=\"CitationRef\"\u003e2013\u003c/span\u003e) Bit selection can be broadly divided into three groups: :\u003c/p\u003e\n\u003c/div\u003e\n\u003col start=\"1\" type=\"1\"\u003e\n \u003cli\u003eEvaluation of Costs (Cost Analysis)\u003c/li\u003e\n \u003cli\u003eAnalysis of Offset Well Logs\u0026nbsp;\u003c/li\u003e\n\u003c/ol\u003e\n\u003cp\u003e\u003cstrong\u003e1.3.1 EVALUATION OF COSTS\u003c/strong\u003e\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eTypically, the cost analysis method is used to examine historical data from offset wells. Moreover, bit run monitoring uses it. An economical assessment of the bit\u0026apos;s performance level will be made. But this approach takes up valuable time (Rabia et al., 1986). The estimation of bit cost is highlighted in the formula below:\u003c/p\u003e\n\u003cp\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"432\" height=\"32\"\u003e\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eBecause drilling characteristics are not taken into account, the aforementioned procedure is not regarded as an effective way to choose a bit. Thus, alternative approaches will be considered (Bataee et al., 2010) \u0026nbsp;\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e1.3.2 ANALYSIS OF OFFSET WELL LOGS\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eW. J. Hightower in 1964 created an intricate graphical depiction of the formation under study with the aid of gamma ray and spontaneous potential log data. This method, which is based on the compressive strength of the rock, compares various drilling bit types, drilling conditions, and lithology using sonic log and other lithology log data to be used in the selection of the suitable bit (Onyia, 1988). But bit selection is still based solely on past offset bit records, and current drilling data is still not taken into account. But current drilling data is still not taken into account, and bit selection is solely based on historical offset bit records. But current drilling data is still not taken into account, and bit selection is solely based on historical offset bit records. \u0026nbsp;\u003c/p\u003e"},{"header":"2. METHODOLOGY","content":"\u003cdiv id=\"Sec12\" class=\"Section2\"\u003e\n \u003ch2\u003e2.1 Data gathering and analysis\u003c/h2\u003e\n \u003cp\u003eThe dataset utilized in this study comprises offset data from five oil wells located within the Niger Delta Field. The data were divided as follows: 70% for training, 15% for validation, and 15% for testing the Rate of Penetration (ROP) functions and conclusions drawn from the modelled bit.\u003c/p\u003e\n \u003cp\u003eThe first stage was using field data to determine the Targeted IADC bit code. Using the Targeted IADC bit code that was obtained in Stage 1, Stage 2 involved predicting the ROP values. The third stage involves reusing the predicted ROP value in the data set to obtain the optimized predicted IADC bit code value.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec13\" class=\"Section2\"\u003e\n \u003ch2\u003e2.2. Machine Learning Model development\u003c/h2\u003e\n \u003cp\u003eThe diagram below (Fig. \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e) shows a flowchart representing the steps utilized for the development of the machine learning models used for this study. The data gathered was stored in an excel workbook format. The data was then exported to a python environment (Jupyter notebook), where all data processing and machine learning operations was carried out.\u003c/p\u003e\n \u003cp\u003eThe models adopted were ANN, Random Forest (RF) and Extreme Gradient Boosting (XGB), which were all implemented in the python environment (Jupyter Notebook) using different libraries and their appropriate versions.\u003c/p\u003e\n \u003cdiv id=\"Sec14\" class=\"Section3\"\u003e\n \u003ch2\u003e2.2.1. Random Forest (RF):\u003c/h2\u003e\n \u003cp\u003eRandom forest regression is an ensemble learning technique that builds multiple decision trees during training and combines their outputs to improve predictive performance and reduce overfitting (Breiman, \u003cspan class=\"CitationRef\"\u003e2001\u003c/span\u003e). Each tree is constructed using a randomly sampled subset of the training data and features, a process known as bootstrapping and feature bagging, respectively. This method ensures diversity among the trees, thereby enhancing the robustness and accuracy of predictions.\u003c/p\u003e\n \u003cp\u003eIn this study, random forest regression was employed due to its ability to handle non-linear relationships, accommodate high-dimensional datasets, and provide insight into feature importance (Loh, \u003cspan class=\"CitationRef\"\u003e2011\u003c/span\u003e). The hyperparameters, such as the number of trees (n_estimators) and maximum depth (max_depth), were optimized using grid search to ensure the model's performance was tailored to the dataset.\u003c/p\u003e\n \u003cp\u003eThe model's predictive capability was assessed using metrics such R squared and mean squared error (MSE), which are well-suited for evaluating the performance of regression models. Furthermore, feature importance rankings derived from the random forest were used to understand the relative contributions of input variables to the prediction, providing interpretability to the results (Louppe et al., \u003cspan class=\"CitationRef\"\u003e2013\u003c/span\u003e).\u003c/p\u003e\n \u003cp\u003eRandom forest's capability to effectively generalize across varying datasets while mitigating overfitting made it an ideal choice for this analysis.\u003c/p\u003e\n \u003c/div\u003e\n \u003cdiv id=\"Sec15\" class=\"Section3\"\u003e\n \u003ch2\u003e2.2.2 Extreme Gradient Boosting (XGB) Classification\u003c/h2\u003e\n \u003cp\u003eExtreme Gradient Boosting (XGB) is a powerful machine learning technique used for predictive modelling in various research fields. The goal of XGB, like other prediction models, is to minimize the number of variables required for prediction, thereby reducing data collection burden and enhancing efficiency.\u003c/p\u003e\n \u003cp\u003eIn XGB, each decision tree is trained on the residuals (the difference between the predicted and actual values) of the previous tree. This iterative process allows the model to learn from the mistakes of the previous trees and improve the prediction accuracy. The primary reason for the accuracy of the XGB model is the cumulative effect of combining the predictions made by each decision tree.\u003c/p\u003e\n \u003cp\u003eMathematically, if we denote the current model as \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{f}_{m}\\)\u003c/span\u003e\u003c/span\u003e(\u003cem\u003eX\u003c/em\u003e) and the new tree as \u003cem\u003eh(x)\u003c/em\u003e the updated model \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{f}_{m+1}\\)\u003c/span\u003e\u003c/span\u003e(\u003cem\u003eX\u003c/em\u003e) is given by:\u003c/p\u003e\n \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u0026nbsp;\u003cspan class=\"mathinline\"\u003e\\(\\:{f}_{m+1}\\)\u003c/span\u003e\u0026nbsp;\u003c/span\u003e(\u003cem\u003eX\u003c/em\u003e) = \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{f}_{m}\\)\u003c/span\u003e\u003c/span\u003e(\u003cem\u003eX\u003c/em\u003e) + α⋅ \u003cem\u003eh(x) …………………….……………………Eq.\u0026nbsp;2\u003c/em\u003e\u003c/p\u003e\n \u003cp\u003ewhere α is the learning rate. This process is repeated for a specified number of iterations or until the residuals can no longer be reduced.\u003c/p\u003e\n \u003cp\u003eThe final prediction is obtained by summing the predictions of all the trees. In the case of classification, a softmax function is applied to the sum to obtain the probabilities of each class, and the class with the highest probability is chosen as the prediction\u003c/p\u003e\n \u003c/div\u003e\n \u003cdiv id=\"Sec16\" class=\"Section3\"\u003e\n \u003ch2\u003e2.2.3. Artificial Neural Network (ANN):\u003c/h2\u003e\n \u003cp\u003eANN is a computational model inspired by the structure and function of the biological neural networks that make up the brain. The ANN model used for this study was a feed-forward neural network consisting of n hidden layers each with a set of neurons that can estimate a given output response (y) from provided input data (x) as shown in Fig. \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e.\u003c/p\u003e\n \u003cp\u003eThe mathematical concept of ANN involves a set of interconnected nodes or neurons that process and transmit information. Each neuron calculates a linear combination (\u003cem\u003ez\u003c/em\u003e) of n input features (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{x}_{i}\\)\u003c/span\u003e\u003c/span\u003e) with corresponding weight (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{w}_{i}\\)\u003c/span\u003e\u003c/span\u003e) and bias (\u003cem\u003eb\u003c/em\u003e) as shown in Eq.\u0026nbsp;3. The weights of the connections between the neurons are adjusted during training to minimize the error between the predicted output and the true output. The selection of the right activation function is very essential in the ANN modelling process as it is chiefly responsible for the mapping of the inputs to the outputs.\u003c/p\u003e\n \u003cp\u003ez = \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\sum\\:_{i=1}^{n}{x}_{i}{w}_{i}\\)\u003c/span\u003e\u003c/span\u003e+\u003cem\u003eb …………………….……………………Eq.\u0026nbsp;3\u003c/em\u003e\u003c/p\u003e\n \u003cp\u003eDuring the ANN process, the transformed version of the output data is forwarded from one hidden layer to another. The network is trained through an updating process that tunes the model weights to minimize model loss (\u003cem\u003eL\u003c/em\u003e) which is typically taken as the root mean square error (RMSE) as shown in Eq. 4 where \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{ŷ}}_{i}\\)\u003c/span\u003e\u003c/span\u003e is the model prediction. The minimization is done through a gradient descent method where the weights are manipulated as a function of \u003cem\u003eL\u003c/em\u003e and scaled using the learning rate (λ) as shown in Eq. 5.\u003c/p\u003e\n \u003cp\u003e\u003cem\u003eL\u003c/em\u003e = \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\sqrt{\\frac{1}{n}\\sum\\:_{i=1}^{n}{({y}_{i}-{\\text{ŷ}}_{i})}^{2}}\\)\u003c/span\u003e\u003c/span\u003e \u003cem\u003e……………Eq.\u0026nbsp;4\u003c/em\u003e\u003c/p\u003e\n \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u0026nbsp;\u003cspan class=\"mathinline\"\u003e\\(\\:{w}_{t+1}\\)\u003c/span\u003e\u0026nbsp;\u003c/span\u003e = \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{w}_{t}\\)\u003c/span\u003e\u003c/span\u003e - λ\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\frac{\\partial\\:\\text{L}}{\\partial\\:{w}_{t}}\\)\u003c/span\u003e\u003c/span\u003e \u003cem\u003e……………Eq.\u0026nbsp;5\u003c/em\u003e\u003c/p\u003e\n \u003c/div\u003e\n\u003c/div\u003e"},{"header":"3. RESULTS AND DISCUSSION","content":"\u003cp\u003eThe results are as shown in the graphs below. In all the modelling, 70% of the data was used for training the model, 15% for validating the model performance, and another 15% testing the data. The correlation between the numerical features in the utilized dataset is shown in Fig. \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003e below.\u003c/p\u003e\u003cdiv class=\"gridtable\"\u003e\n \u003cdiv align=\"left\" class=\"colspec\"\u003eTable 4 shows the performance of the different models utilized in the bit classification\u003c/div\u003e\n \u003cdiv align=\"char\" class=\"colspec\"\u003e\u003c/div\u003e\u003ctable id=\"Tab5\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eClassification accuracies of the various models\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\u003ccolgroup cols=\"2\"\u003e\u003c/colgroup\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\"\u003e\n \u003cp\u003eCLASSIFICATION MODEL\u003c/p\u003e\n \u003c/th\u003e\u003cth align=\"left\"\u003e\n \u003cp\u003eCLASSIFICATION ACCURACY\u003c/p\u003e\n \u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\"\u003e\n \u003cp\u003eANN\u003c/p\u003e\n \u003c/td\u003e\u003ctd align=\"char\"\u003e\n \u003cp\u003e0.93\u003c/p\u003e\n \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\"\u003e\n \u003cp\u003eRANDOM FOREST\u003c/p\u003e\n \u003c/td\u003e\u003ctd align=\"char\"\u003e\n \u003cp\u003e0.91\u003c/p\u003e\n \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\"\u003e\n \u003cp\u003eXGBOOST\u003c/p\u003e\n \u003c/td\u003e\u003ctd align=\"char\"\u003e\n \u003cp\u003e0.97\u003c/p\u003e\n \u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/table\u003e\n \u003c/div\u003e\u003ch2\u003e3.1.1 Confusion Matrix\u003c/h2\u003e\u003cp\u003eThe confusion matrix visually represents the model's performance in predicting the bit codes. Each row of the matrix corresponds to the actual bit codes, while each column represents the predicted bit code. Figure 5 shows the confusion matrix of the ANN model while Fig. 6 shows the confusion matrix of the Xgboost classification model.\u003c/p\u003e\u003cp\u003eThe next step utilised the predicted bit code as one of the inputs in order to predict the ROP values. In this step, various regression models were processed to predict the Rate of Penetration (ROP). Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003e shows the tuned hyperparameters of the various models.\u003c/p\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable id=\"Tab6\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 5\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eOptimal parameters of models utilised in the modelling\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\u003ccolgroup cols=\"4\"\u003e\u003c/colgroup\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\"\u003e\n \u003cp\u003eModel\u003c/p\u003e\n \u003c/th\u003e\u003cth align=\"left\"\u003e\n \u003cp\u003eHyper parameters\u003c/p\u003e\n \u003c/th\u003e\u003cth align=\"left\"\u003e\n \u003cp\u003eFinal Optimized value\u003c/p\u003e\n \u003c/th\u003e\u003cth align=\"left\"\u003e\n \u003cp\u003eExecution time (ms)\u003c/p\u003e\n \u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" rowspan=\"11\"\u003e\n \u003cp\u003eANN\u003c/p\u003e\n \u003c/td\u003e\u003ctd align=\"left\"\u003e\n \u003cp\u003eKernel_initializer\u003c/p\u003e\n \u003c/td\u003e\u003ctd align=\"left\"\u003e\n \u003cp\u003enormal\u003c/p\u003e\n \u003c/td\u003e\u003ctd align=\"left\" rowspan=\"11\"\u003e\n \u003cp\u003e10430.65\u003c/p\u003e\n \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\"\u003e\n \u003cp\u003emodel optimizer\u003c/p\u003e\n \u003c/td\u003e\u003ctd align=\"left\"\u003e\n \u003cp\u003eadam\u003c/p\u003e\n \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\"\u003e\n \u003cp\u003eepochs\u003c/p\u003e\n \u003c/td\u003e\u003ctd align=\"left\"\u003e\n \u003cp\u003e300\u003c/p\u003e\n \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\"\u003e\n \u003cp\u003elayer 1 number of neurons\u003c/p\u003e\n \u003c/td\u003e\u003ctd align=\"left\"\u003e\n \u003cp\u003e16\u003c/p\u003e\n \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\"\u003e\n \u003cp\u003elayer 1 activation function\u003c/p\u003e\n \u003c/td\u003e\u003ctd align=\"left\"\u003e\n \u003cp\u003erelu\u003c/p\u003e\n \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\"\u003e\n \u003cp\u003elayer 2 number of neurons\u003c/p\u003e\n \u003c/td\u003e\u003ctd align=\"left\"\u003e\n \u003cp\u003e64\u003c/p\u003e\n \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\"\u003e\n \u003cp\u003elayer 2 activation function\u003c/p\u003e\n \u003c/td\u003e\u003ctd align=\"left\"\u003e\n \u003cp\u003erelu\u003c/p\u003e\n \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\"\u003e\n \u003cp\u003elayer 3 number of neurons\u003c/p\u003e\n \u003c/td\u003e\u003ctd align=\"left\"\u003e\n \u003cp\u003e32\u003c/p\u003e\n \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\"\u003e\n \u003cp\u003elayer 3 activation function\u003c/p\u003e\n \u003c/td\u003e\u003ctd align=\"left\"\u003e\n \u003cp\u003erelu\u003c/p\u003e\n \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\"\u003e\n \u003cp\u003eoutput layer number of neurons\u003c/p\u003e\n \u003c/td\u003e\u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\"\u003e\n \u003cp\u003eoutput activation function\u003c/p\u003e\n \u003c/td\u003e\u003ctd align=\"left\"\u003e\n \u003cp\u003esoftmax\u003c/p\u003e\n \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" rowspan=\"3\"\u003e\n \u003cp\u003eRF\u003c/p\u003e\n \u003c/td\u003e\u003ctd align=\"left\"\u003e\n \u003cp\u003en estimators\u003c/p\u003e\n \u003c/td\u003e\u003ctd align=\"left\"\u003e\n \u003cp\u003e1000\u003c/p\u003e\n \u003c/td\u003e\u003ctd align=\"left\" rowspan=\"3\"\u003e\n \u003cp\u003e27.283\u003c/p\u003e\n \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\"\u003e\n \u003cp\u003emax depth\u003c/p\u003e\n \u003c/td\u003e\u003ctd align=\"left\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\"\u003e\n \u003cp\u003emax features\u003c/p\u003e\n \u003c/td\u003e\u003ctd align=\"left\"\u003e\n \u003cp\u003e\"sqrt\"\u003c/p\u003e\n \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" rowspan=\"5\"\u003e\n \u003cp\u003eXGB\u003c/p\u003e\n \u003c/td\u003e\u003ctd align=\"left\"\u003e\n \u003cp\u003emax depth\u003c/p\u003e\n \u003c/td\u003e\u003ctd align=\"left\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\u003ctd align=\"left\" rowspan=\"5\"\u003e\n \u003cp\u003e210\u003c/p\u003e\n \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\"\u003e\n \u003cp\u003eϒ\u003c/p\u003e\n \u003c/td\u003e\u003ctd align=\"left\"\u003e\n \u003cp\u003e0.01\u003c/p\u003e\n \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\"\u003e\n \u003cp\u003en estimators\u003c/p\u003e\n \u003c/td\u003e\u003ctd align=\"left\"\u003e\n \u003cp\u003e100\u003c/p\u003e\n \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\"\u003e\n \u003cp\u003esubsample\u003c/p\u003e\n \u003c/td\u003e\u003ctd align=\"left\"\u003e\n \u003cp\u003e0.8\u003c/p\u003e\n \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\"\u003e\n \u003cp\u003erandom state\u003c/p\u003e\n \u003c/td\u003e\u003ctd align=\"left\"\u003e\n \u003cp\u003e66\u003c/p\u003e\n \u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/table\u003e\n \u003c/div\u003e\u003cp\u003eWith an R squared value of 0.991, the Xgboost model proved to be the best prediction model, although Random forest and Artificial Neural Network, were accurate enough as well. Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e6\u003c/span\u003e shows the evaluation of the different regression models\u003c/p\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable id=\"Tab7\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 6\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eEvaluation of Regression Models\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\u003ccolgroup cols=\"3\"\u003e\u003c/colgroup\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\"\u003e\n \u003cp\u003eRegression Models\u003c/p\u003e\n \u003c/th\u003e\u003cth align=\"left\"\u003e\n \u003cp\u003eRMSE\u003c/p\u003e\n \u003c/th\u003e\u003cth align=\"left\"\u003e\n \u003cp\u003eR Squared\u003c/p\u003e\n \u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\"\u003e\n \u003cp\u003eXgboost\u003c/p\u003e\n \u003c/td\u003e\u003ctd align=\"char\"\u003e\n \u003cp\u003e1.236\u003c/p\u003e\n \u003c/td\u003e\u003ctd align=\"char\"\u003e\n \u003cp\u003e0.991\u003c/p\u003e\n \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\"\u003e\n \u003cp\u003eRandom Forest\u003c/p\u003e\n \u003c/td\u003e\u003ctd align=\"char\"\u003e\n \u003cp\u003e1.954\u003c/p\u003e\n \u003c/td\u003e\u003ctd align=\"char\"\u003e\n \u003cp\u003e0.953\u003c/p\u003e\n \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\"\u003e\n \u003cp\u003eAnn\u003c/p\u003e\n \u003c/td\u003e\u003ctd align=\"char\"\u003e\n \u003cp\u003e1.537\u003c/p\u003e\n \u003c/td\u003e\u003ctd align=\"char\"\u003e\n \u003cp\u003e0.975\u003c/p\u003e\n \u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/table\u003e\n \u003c/div\u003e\u003cp\u003eThe plots below show the actual vs predicted values of ROP using the Xgboost model (Fig. 7), the ANN model (Fig. 8) and the Random forest model (Fig. \u003cspan class=\"InternalRef\"\u003e9\u003c/span\u003e)\u003c/p\u003e\u003cp\u003eIt is evident from the aforementioned graphs that we can optimize the ROP value through the modelling process by utilizing all of the available data. We can then utilize the optimized ROP value to get the optimized IADC bit code. The accuracy of the R value is roughly 99 percent based on the graph's numerical values. A tiny error still exists, and it has specific causes.\u003c/p\u003e"},{"header":"4. CONCLUSION","content":"\u003cp\u003eThis study investigated the application of machine learning techniques for bit - formation matching in drilling operations. The review identified gaps borne out of extensive literature, and highlighted the limitations of traditional methods reliant on historical data and expert judgment.\u003c/p\u003e \u003cp\u003eThe results obtained from the study provided opportunities on the potential of machine learning techniques to improve bit - formation matching in drilling operations. Comparative analysis of different algorithms provided insights into the performance and effectiveness in predicting bit-formation compatibility.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eFunding\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAvailability of data and material\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eDue to confidentiality agreements with the data provider, the field data used in this study are not publicly available. However, a summary of the data analysis and results is included in this published article. Specific data requests may be considered on a case-by-case basis and subject to approval from the data provider. For inquiries, please contact the corresponding author at [email protected]\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthors Contribution\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eShedrach Igemhokhai:\u003c/strong\u003e Conceptualization, Methodology, Formal analysis, Writing original draft, Software, Visualization, Data curation, Review and Editing. \u003cstrong\u003eKelani Bello\u003c/strong\u003e: Review and Editing, Data curation. \u003cstrong\u003eAbiodun Olaoye:\u003c/strong\u003e Conceptualization, Review and Editing, Data curation. \u003cstrong\u003eEhigie Momodu:\u003c/strong\u003e Review and Editing, Data curation. \u003cstrong\u003eNsisong Isuk\u003c/strong\u003e: Review and Editing. \u003cstrong\u003eAbayomi Adejumo:\u0026nbsp;\u003c/strong\u003eReview and Editing\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCompeting interests\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors declare that they have no competing interest.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eBataee, M., Edalatkhah, S., \u0026amp; Ashna, R. (2010). Comparison between Bit Optimization Using Artificial Neural Network and Other Methods Base on Log Analysis Applied in Shadegan Oil Field. \u003cem\u003eSociety of Petroleum Engineers - International Oil and Gas Conference and Exhibition in China 2010, IOGCEC\u003c/em\u003e, \u003cem\u003e4\u003c/em\u003e, 3097\u0026ndash;3103. https://doi.org/10.2118/132222-MS\u003c/li\u003e\n\u003cli\u003eBilgesu, H. I., Al-Rashidi, A. F., Aminian, K., \u0026amp; Ameri, S. (2001). An Unconventional Approach for Drill-Bit Selection. \u003cem\u003eProceedings of the Middle East Oil Show\u003c/em\u003e, 198\u0026ndash;203. https://doi.org/10.2523/68089-ms\u003c/li\u003e\n\u003cli\u003eBrandon, B. D., Cerkovnik, J., Koskie, E., Bayoud, B. B., Colston, F., Clayton, R. I., Anderson, M. E., Hollister, K. T., Senger, J., \u0026amp; Niemi, R. (1992). \u003cem\u003eDevelopment of a New IADC Fixed Cutter Drill Bit Classification System\u003c/em\u003e. https://doi.org/10.2118/23940-MS\u003c/li\u003e\n\u003cli\u003eBreiman, L. (2001). Random forests. \u003cem\u003eMachine Learning\u003c/em\u003e, \u003cem\u003e45\u003c/em\u003e(1), 5\u0026ndash;32. https://doi.org/10.1023/A:1010933404324/METRICS\u003c/li\u003e\n\u003cli\u003eFasheum, M. (1997). \u003cem\u003eTHE UNIVERSITY OF NOTTINGHAM DEPARTMENT OF MINERAL RESOURCES ENGINEERING by\u003c/em\u003e. \u003cem\u003eApril\u003c/em\u003e.\u003c/li\u003e\n\u003cli\u003eHightower, W. J. (1964, March). Proper selection of drill bits and their use. In SPE Practical Aspects of Improved Recovery Techniques Symposium (pp. SPE-794). SPE. https://doi.org/10.2118/794-MS\u003c/li\u003e\n\u003cli\u003eJamshidi, E., \u0026amp; Mostafavi, H. (2013). Soft computation application to optimize drilling bit selection utilizing virtual inteligence and genetic algorithms. \u003cem\u003eSociety of Petroleum Engineers - International Petroleum Technology Conference 2013, IPTC 2013: Challenging Technology and Economic Limits to Meet the Global Energy Demand\u003c/em\u003e, \u003cem\u003e1\u003c/em\u003e(October), 357\u0026ndash;371. https://doi.org/10.2523/16446-ms\u003c/li\u003e\n\u003cli\u003eLoh, W. Y. (2011). Classification and regression trees. \u003cem\u003eWiley Interdisciplinary Reviews: Data Mining and Knowledge Discovery\u003c/em\u003e, \u003cem\u003e1\u003c/em\u003e(1), 14\u0026ndash;23. https://doi.org/10.1002/WIDM.8\u003c/li\u003e\n\u003cli\u003eLouppe, G., Wehenkel, L., Sutera, A., \u0026amp; Geurts, P. (2013). Understanding variable importances in forests of randomized trees. Advances in Neural Information Processing Systems, 26, 431\u0026ndash;439.\u003c/li\u003e\n\u003cli\u003eMcGehee, D. Y., Dahlem, J. S., Gieck, J. C., Kost, B., Lafuze, D., Reinsvold, C. H., \u0026amp; Steinke, S. C. (1992). \u003cem\u003eThe IADC Roller Bit Classification System\u003c/em\u003e. https://doi.org/10.2118/23937-MS\u003c/li\u003e\n\u003cli\u003eMomeni, M., Hosseini, S. J., Ridha, S., Laruccia, M. B., \u0026amp; Liu, X. (2018). An optimum drill bit selection technique using artificial neural networks and genetic algorithms to increase the rate of penetration. \u003cem\u003eJournal of Engineering Science and Technology\u003c/em\u003e, \u003cem\u003e13\u003c/em\u003e(2), 361\u0026ndash;372.\u003c/li\u003e\n\u003cli\u003eOnyia, E. C. (1988). Relationships Between Formation Strength, Drilling Strength, and Electric Log Properties. \u003cem\u003eSociety of Petroleum Engineers of AIME, (Paper) SPE\u003c/em\u003e, \u003cem\u003eOMEGA\u003c/em\u003e. https://doi.org/10.2118/18166-MS\u003c/li\u003e\n\u003cli\u003eRabia, H., Farrelly, M., \u0026amp; Barr, M. V. (1986). A New Approach to Drill Bit Selection. \u003cem\u003eSociety of Petroleum Engineers of AIME, (Paper) SPE\u003c/em\u003e, 421\u0026ndash;428. https://doi.org/10.2118/15894-MS\u003c/li\u003e\n\u003cli\u003eWatalingam, P. (2014). \u003cem\u003eBit Selection Using Drilling Data By Artificial Neural Networks\u003c/em\u003e. \u003cem\u003eMay\u003c/em\u003e. http://utpedia.utp.edu.my/id/eprint/14233\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Machine Learning, Bit-Formation Matching, Drilling, Artificial Neural Networks, XGBOOST, Random Forest","lastPublishedDoi":"10.21203/rs.3.rs-5556031/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-5556031/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eEfficient bit formation matching is imperative for the success and cost-effectiveness of drilling operations. At present, drill bit selection predominantly depends on historical data and experiential knowledge. While machine learning, particularly Artificial Neural Networks (ANNs), has gained prominence in bit selection, other diverse and impactful algorithms such as XGBOOST and Random Forest (RF), are often overlooked. This paper involves the systematic application and comparative analysis of XGBOOST, RF, and ANN, alongside an optimization approach using Genetic Algorithm. The study comprehensively considers various influential factors including formation properties, drilling fluid characteristics, bit design, and operational parameters.\u003c/p\u003e \u003cp\u003eIn this study, we achieved promising results with the highest classification accuracy for bit selection recorded at 0.97 using the XGBOOST model, while RF and ANN yielded accuracies of 0.91 and 0.93 respectively. Additionally, we obtained impressive R squared values of 0.991, 0.975, and 0.953 for predicting the Rate of Penetration (ROP) using the XGBOOST, ANN, and RF models respectively.\u003c/p\u003e \u003cp\u003eThese algorithms, coupled with the optimization techniques, aims to establish a robust framework for nuanced and accurate bit-formation matching. The results obtained hold significant potential for minimizing costs and optimizing resource allocation \u0026amp; utilization during the planning and execution of drilling projects in the oil and gas industry.\u003c/p\u003e","manuscriptTitle":"Application of Machine Learning for Bit-Formation Matching in drilling operations","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-02-25 10:17:57","doi":"10.21203/rs.3.rs-5556031/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"8f65c97a-fa93-4b03-8d8e-e7c9b49a7974","owner":[],"postedDate":"February 25th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":44774175,"name":"Physical sciences/Energy science and technology/Fossil fuels/Crude oil"},{"id":44774176,"name":"Earth and environmental sciences/Solid earth sciences/Geology/Economic geology"}],"tags":[],"updatedAt":"2025-02-25T10:17:57+00:00","versionOfRecord":[],"versionCreatedAt":"2025-02-25 10:17:57","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-5556031","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-5556031","identity":"rs-5556031","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}