Document Type : Original Research Paper
Authors
- Ali Nemati vardin 1
- Masoud Monjezi 1
- Hasel Amini Khoshalan 2
- Jafar Hamidi Khademi 1
- Mojtaba Rezakhah 1
1 Department of Mining Engineering, Faculty of Engineering, Tarbiat Modares University, Tehran, Iran
2 Department of Mining Engineering, Faculty of Engineering, University of Kurdistan, Sanandaj, Iran
10.22044/jme.2025.15933.3065
Abstract
Drilling is one of the most important operations in open-pit mining, and the penetration rate of drill bits is a key performance measure. This paper presents research on the penetration rate of drill bits based on mining rock mass rating, thrust pressure (weight on bit), rotational pressure, and Schmidt hammer rebound hardness. To achieve this, a dataset comprising the drilling operations of 85 blastholes from the Sungun copper mine in Iran was prepared and analyzed using statistical and intelligent methods. Multivariate regression analysis and artificial neural networks developed in Python, utilizing optimization algorithms such as gradient descent, stochastic gradient descent, and adaptive moment estimation, were applied to predict the penetration rate of drill bits in this study. The coefficient of determination (R²), mean absolute error (MAE), and root mean square error (RMSE) served as performance indicators to evaluate the methods employed. Among these, the adaptive moment estimation (Adam)-based model exhibited superior performance compared to alternative models, achieving values of R² = 0.96, MAE = 4.55, and RMSE = 4.30. Furthermore, the sensitivity analysis revealed that mining rock mass rating is the most influential factor on the rate of penetration, while thrust pressure has the least impact.
Keywords
- Drilling
- Rate of Penetration
- Intelligent Methods, Adaptive Moment Estimation
- stochastic gradient descent
Main Subjects
[1]. Graham, J. W., & Muench, N. L. (1959). Analytical determination of optimum bit weight and rotary speed combinations. SPE ATCE,1349-G.
[2]. Maurer, W. C. (1962). The Perfect-Cleaning theory of rotary drilling. Journal of Petroleum Exploration and Production Technology, 14 (11): 1270–1274.
[3]. Galle, E. M., & Woods, H. B. (1963). Best Constant Weight and Rotary Speed for Rotary Rock Bits. API Drilling and Production Practice, New York, API-63-048.
[4]. Bourgoyne, A. T., & Young, F. S. (1974). A Multiple Regression Approach to Optimal Drilling and Abnormal Pressure Detection. Society of Petroleum Engineers journal, 14(04):371-384.
[5]. Fear, M. J. (1999). How to Improve Rate of Penetration in Field Operations, SPE Drilling & Completion, 14 (1), 42-49, SPE-55050-PA
[6]. Bilgin, N., Copur, H., & Balci, C. (2013). Mechanical excavation in mining and civil industries. CRC press.
[7]. Hosseini, S. H., Ataie, M., & Aghababaie, H. (2014). A laboratory study of rock properties affecting the penetration rate of pneumatic top hammer drills. Journal of mining and environment, 5(1), 25-34.
[8]. Motahhari, H. R., Hareland, G., Nygaard, R., & Bond, B. (2009). Method of Optimizing Motor and Bit Performance for Maximum ROP. Journal of Canadian Petroleum Technology, 48 (6), PETSOC-09-06-44-TB.
[9]. Ritto, T. G., Christian, S., & Sampaio, R. (2010). Robust optimization of the rate of penetration of a drill-string using a stochastic nonlinear dynamical model, Computational Mechanics, 45 (5), 415-427.
[10]. Yi, P., Kumar, A., & Samuel, R. (2014). Realtime Rate of Penetration Optimization Using the Shuffled Frog Leaping Algorithm. Journal of Energy Resources Technology, 137(3), 032902.
[11]. Yarali, O., & Soyer, E. (2013). Assessment of relationships between drilling rate index and mechanical properties of rocks. Tunnelling and Underground Space Technology, 33, 46-53.
[12]. Nazir, R., Momeni, E., Armaghani, D. J., & Amin, M. M. (2013). Correlation between unconfined compressive strength and indirect tensile strength of limestone rock samples. Electronic Journal of Geotechnical Engineering, 18(1), 1737-1746.
[13]. Tiryaki, B. (2008). Predicting intact rock strength for mechanical excavation using multivariate statistics, artificial neural networks, and regression trees. Engineering Geology, 99(1-2):51-60.
[14]. Karakus, M., & Tutmez, B. (2006). Fuzzy and multiple regression modelling for evaluation of intact rock strength based on point load, Schmidt hammer and sonic velocity. Rock Mechanics and Rock Engineering, 39, 45-57.
[15]. Moradian, Z. A., & Behnia, M. (2009). Predicting the uniaxial compressive strength and static Young’s modulus of intact sedimentary rocks using the ultrasonic test. International Journal of Geomechanics, 9(1), 14-19.
[16]. Yagiz, S. (2011). Correlation between slake durability and rock properties for some carbonate rocks. Bulletin of Engineering Geology and the Environment, 70, 377-383.
[17]. Kahraman, S. (2014). The determination of uniaxial compressive strength from point load strength for pyroclastic rocks. Engineering Geology, 170, 33-42.
[18]. Kahraman, S., Fener, M., & Gunaydin, O. (2017). Estimating the uniaxial compressive strength of pyroclastic rocks from the slake durability index. Bulletin of Engineering Geology and the Environment, 1107-1115.
[19]. Basarir, H., Tutluoglu, L., & Karpuz, C. (2014). Penetration rate prediction for diamond bit drilling by adaptive neuro-fuzzy inference system and multiple regressions. Engineering Geology, 173, 1-9.
[20]. Saeidi, O., Torabi, S. R., Ataei, M., & Rostami, J. (2014). A stochastic penetration rate model for rotary drilling in surface mines. International Journal of Rock Mechanics and Mining Sciences, 68, 55-65.
[21]. Kivade, S. B., Murthy, C.S., & Vardhan, H. (2015). Experimental investigations on penetration rate of percussive drill. Procedia Earth and Planetary Science, 11, 89-99.
[22]. Kahraman, S. (2016). The prediction of penetration rate for percussive drills from indirect tests using artificial neural networks. Journal of the Southern African Institute of Mining and Metallurgy, 116 (8), 793-800.
[23]. Khosravimanesh, Sh., Esmaeilzadeh, A., Akhyani, M., Mikaeil, R., & Mokhtarian Asl, M. (2024). Accurate prediction of drill bit penetration rate in rock using supervised machine learning techniques base on laboratory test data. Rudarsko-geološko-naftni zbornik, 39(1), 115-130.
[24]. Gokceoglu, C., & Zorlu, K. (2004). A fuzzy model to predict the uniaxial compressive strength an the modulus of elasticity of a problematic rock. Engineering Applications of Artificial Intelligence, 17(1), 61-72.
[25]. Mishra, D. A., & Basu, A. (2013). Estimation of uniaxial compressive strength of rock materials by index tests using regression analysis and fuzzy inference system. Engineering Geology, 160, 54-68.
[26]. Hashmi, K., Graham, I. D., & Mills, B. (2000). Fuzzy logic-based data selection for the drilling process. Journal of Materials Processing Technology, 108 (1), 55-61.
[27]. Nandi, A. K., & Davim, J. P. (2009). A study of drilling performances with minimum quantity of lubricant using fuzzy logic rules. Mechatronics,19 (2), 218-232.
[28]. Sujatha Therese, P., & Kesavan Nair, N. (2012). Application of self-tuning fuzzy PI controllers for drilling process. ICCEET, India, 69-73.
[29]. Bilgesu, H., Tetrick, L., Altmis, U., Mohaghegh, S., & Ameri, S. (1997). A new approach for the prediction of rate of penetration (ROP) values. In: SPE Eastern Regional Meeting (Society of Petroleum Engineers).
[30]. Shad, H. I. A., Sereshki, F., Ataei, M., & Karamoozian, M. (2018). Prediction of rotary drilling penetration rate in iron ore oxides using rock engineering system. International Journal of Mining Science and Technology, 28(3), 407- 413.
[31]. Barbosa, L. F., Nascimento, A., Hugo Mathias, M., & Carvalho, J. A. (2019). Machine learning methods applied to drilling rate of penetration prediction and optimization: A review. Journal of Petroleum Science and Engineering, 183, 1–20.
[32]. Zhao, Y., Noorbakhsh, A., Koopialipoor, M., Azizi, A., & Tahir, M. M. (2020). A new methodology for optimization and prediction of rate of penetration during drilling operations. Engineering with Computers, 36, 587-595.
[33]. Elkatatny, S., Al-AbdulJabbar, A., & Abdelgawad, K. (2020). A new model for predicting rate of penetration using an artificial neural network. Sensors, 20 (7), 2058.
[34]. Lawal, A. I., Kwon, S., & Onifade, M. (2021). Prediction of rock penetration rate using a novel antlion optimized ANN and statistical modelling. Journal of African Earth Sciences, 104287.
[35]. Ayoub, M., Shien, G., Diab, D., & Ahmed, Q. (2017). Modeling of drilling rate of penetration using adaptive neuro-fuzzy inference system. International Journal of Applied Engineering Research, 12(22),12880-12891
[36]. Yavari, H., Sabah, M., Khosravanian, R., & Wood, D. (2018). Application of an Adaptive Neuro-fuzzy Inference System and Mathematical Rate of Penetration Models to Predicting Drilling Rate. Iranian Journal of Oil & Gas Science and Technology, 7(3), 73-100.
[37]. Hamdi, Z., Haldavnekar, A., Momeni, M., & Bataee, M. (2020). Improving Drilling Rate of Penetration Modelling Performance Using Adaptive Neuro-Fuzzy Inference Systems. Abu Dhabi International Petroleum Exhibition & Conference, SPE-203427-MS.
[38]. Kamran, M. (2021). A Probabilistic Approach for Prediction of Drilling Rate Index using Ensemble Learning Technique. Journal of Mining and Environment, 12 (2), 327-337.
[39]. Pacis, F. J., Ambrus, A., Alyaev, A., Khosravanian, R., Kristiansen, T. G., & Wiktorski, T. (2023). Improving predictive models for rate of penetration in real drilling operations through transfer learning. Journal of Computational Science, 72, 102100.
[40]. Heydari, S., Hoseinie, S. H., & Bagherpour, R. (2024). Prediction of jumbo drill penetration rate in underground mines using various machine learning approaches and traditional models. Scientific Reports, 14, 8928.
[41]. Mebarkia, M., Abdelmalek, A., Aoulmi, Z., Louafi, M., Tabet, A., & Benselhoub, A. (2024). Synergistic prediction of penetration rate in Boukhadhra mining using regression, design of experiments, fuzzy logic, and artificial neural networks. Technology audit and production reserves, 4 (78), 32-42.
[42]. Kazemi, M. M. K., Nabavi, Z., & Armaghani, D. J. (2024). A novel hybrid XGBoost methodology in predicting penetration rate of rotary based on rock-mass and material properties. Arabian Journal for Science and Engineering, 49(4), 5225-5241.
[43]. Shi, F., Liao, H., Wang, S., Alfarisi, O., & Qu, F. (2025). Optimization of Drilling Rate Based on Genetic Algorithms and Machine Learning Models. Geoenergy Science and Engineering, 213747.
[44]. Lawal, A. I., Kwon, S., & Onifade, M. (2021). Prediction of rock penetration rate using a novel antlion optimized ANN and statistical modelling. Journal of African Earth Sciences, 182, 104287.
[45]. Sharma, A., Burak, T., Nygaard, R., Hoel, E., Kristiansen, T., & Welmer, M. (2025). Hybrid ROP modeling: Combining analytical and data-driven approaches for drilling. Geoenergy Science and Engineering, 213877.
[46]. Amini, H., Gholami, R., Monjezi, M., Torabi, S. R., & Zadhesh, J. (2012). Evaluation of flyrock phenomenon due to blasting operation by support vector machine. Neural Computing and Applications, 21, 2077-2085.
[47]. Karpuz, C., et al. (1990). Drillability studies on the rotary blasthole drilling of lignite overburden series. International journal of surface mining, reclamation and environment, 4(2), 89-93.
[48]. Kahraman, S., et al. (2000). Prediction of the penetration rate of rotary blast hole drills using a new drillability index. International Journal of Rock Mechanics and Mining Sciences, 37(5), 729-743.
[49]. Huang, S.L., & Wang, Z. W. (1997). The mechanics of diamond core drilling of rocks. International Journal of Rock Mechanics and Mining Sciences, 34 (3), 1-14.
[50]. Bauer, A. (1971). Open pit drilling and blasting. Journal of the Southern African Institute of Mining and Metallurgy, 71(6), 115-121.
[51]. Kahraman, S. (1999). Rotary and percussive drilling prediction using regression analysis. International Journal of Rock Mechanics and Mining Sciences, 36(7), 981-989.
[52]. Maurer, W. (1966). The state of rock mechanics knowledge in drilling. In: ARMA US Rock Mechanics/Geomechanics Symposium, ARMA.
[53]. Prasad, B. S., Murthy, B., & Pandey, S. (2016). Investigations on rock drillability applied to underground mine development vis-à-vis drill selection. In: Recent Advances in Rock Engineering (RARE 2016). Atlantis Press.
[54]. Jakubec, J., & Laubscher, D. H. (2000). The MRMR rock mass rating classification system in mining practice. In: Proceedings of the 3rd international conference and exhibition on mass mining. Brisbane, Australia.
[55]. Aydin, A. (2009). ISRM Suggested method for determination of the Schmidt hammer rebound hardness: Revised version. International Journal of Rock Mechanics and Mining Sciences, 46 (3), 627-634.
[56]. Ali Abd Al-Hameed, K. (2022). Spearman's correlation coefficient in statistical analysis. International Journal of Nonlinear Analysis and Applications, 13(1), 3249-3255.
[57]. Gupta, N. (2013). Artificial neural network. Netw complex systems, 3(1), 24-28.
[58]. Haykin, S. (2004). Neural Networks: A comprehensive foundation. Pearson Education, Inc. Singapore.
[59]. Koopialipoor, M., Fahimifar, A., Ghaleini, E. N., et al. (2020). Development of a new hybrid ANN for solving a geotechnical problem related to tunnel boring machine performance. Engineering with Computers, 36, 345-357.
[60]. Adebayo, B., Opafunso, Z. O., & Akande, J. M. (2010). Drillability and strength characteristics of selected rocks in Nigeria. AU Journal of Technology, 14(1), 56-60.
[61]. Amini Khoshalan, H., Shakeri, J., Dehghani, H., & Bascompta Massanes, M. (2022). Developing new models for flyrock distance assessment in open-pit mines. Journal of Mining and Environment, 13 (2), 377-391.
[62]. Ghasemi, E., Amini, H., & Ataei, M. (2014). Application of artificial intelligence techniques for predicting flyrock distance caused by blasting operation. Arabian Journal of Geosciences, 7(1), 193–202.
[63]. Madhu, G., Kautish, S., Alnowibet, K. A., Zawbaa, H. M., & Mohamed, A. W. (2023). NIPUNA: A Novel Optimizer Activation Function for Deep Neural Networks. Axioms, 12(3), 246.
[64]. Zhang, J., Li, C., Yin, Y., et al. (2023). Applications of artificial neural networks in microorganism image analysis: a comprehensive review from conventional multilayer perceptron to popular convolutional neural network and potential visual transformer. Artificial Intelligence Review, 56(2), 1013-1070.
[65]. Tian, Y., Zhang, Y., & Zhang, H. (2023). Recent advances in stochastic gradient descent in deep learning. Mathematics, 11(3), 682.
[66]. Duchi, J., Hazan, E., & Singer, Y. (2011). Adaptive sub gradient methods for online learning and stochastic optimization. Journal of Machine Learning Research, 12(7), 2121-2159.
[67]. Kingma, D. P., & Ba, L. J. (2015). Adam: A method for stochastic optimization. International Conference on Learning Representations (ICLR), 1412.6980.
[68]. Hyndman, R. J., & Koehler, A. B. (2006). Another look at measures of forecast accuracy. International Journal of Forecasting, 22(4), 679-688.
[69]. Shirani Faradonbeh, R., & Monjezi, M. (2017). Prediction and minimization of blast-induced ground vibration using two robust meta-heuristic algorithms. Engineering with Computers, 33 (4), 835-851.
)