Journal of Petroleum Science and Technology

Journal of Petroleum Science and Technology

Development of an Artificial Neural Network Model to Calculate Static Young’s Modulus Based on a Log-derived Data Base

Document Type : Research Paper

Authors
Samir Khaled 1
Sayed Gomaa 2
Karim Nasr 2
Mohamed Elwageeh 3
Salah Badr 2
1 1:Mining and Petroleum Engineering Department, Faculty of Engineering, Al-Azhar University, Cairo, Egypt
2 Mining and Petroleum Engineering Department, Faculty of Engineering, Al-Azhar University, Cairo, Egypt
3 Petroleum Engineering and Gas Technology Department, Faculty of Energy and Environmental Engineering, British University in Egypt (BUE), El Sherouk City, Cairo, Egypt
10.22078/jpst.2023.4879.1821
Abstract
Static Young’s Modulus is a measure of reservoir rock stiffness and is best determined by experimental studies on cores. However, the experimental procedures are demanding with considerable cost. On the other hand, a dynamic Young’s modulus can easily be estimated from readily available petrophysical data. The static young’s modulus can easily be obtained from the dynamic counterpart by empirical relationships. This research attempts to use AI techniques to predict Static Young’s modulus. Two thousand three hundred fifty data sets were collected from several wells in the Middle East with sandstone and limestone lithology and used to build an AI model. Each data set contains static Young’s Modulus as a function of the bulk density, shear wave arrival time, and compressional wave arrival time. An artificial neural network (ANN) model was developed to predict the static young’s modulus with high accuracy of R2 = 0.999 and AARE of 0.028%. The proposed model was validated with measured reservoir rock data and was compared with four different correlations. The results showed that the model provided the highest coefficient of determination (R2) and the lowest standard deviation.
Keywords
Young’s Modulus
Neural Network
Bulk Density
Shear Wave Arrival Time
Compressional Wave Arrival Time
  1. Abdulraheem A, Ahmed M, Vantala A, Parvez T (2009) Prediction of rock mechanical parameters for hydrocarbon reservoirs using different artificial intelligence techniques, In SPE Saudi Arabia Section Technical Symposium, OnePetro, doi.org/10.2118/126094-MS.##
  2. Alramahi B A, Alshibli K A, Attia A M (2005) Influence of grain size and consolidation pressure on porosity of rocks, In Site Characterization and Modeling, 1-13, doi.org/10.1061/40785(164)41.‏ ##
  3. Alshibli K A, Alramahi B A, Attia A M (2006) Assessment of spatial distribution of porosity in synthetic quartz cores using microfocus computed tomography (µCT), Particulate science and technology, 24, 4: 369-380, doi.org/10.1080/02726350600934606.‏ ##
  4. Nes O M, Fjær E, Tronvoll J, Kristiansen T G, Horsrud P (2012) Drilling time reduction through an integrated rock mechanics analysis, Journal of Energy Resources Technology, 134: 3, doi.org/10.1115/1.4006866. ##
  5. Fjar E, Holt R M, Raaen A, Horsrud P (2008) Petroleum related rock mechanics, Elsevier. ##
  6. Lacy L L (1997) Dynamic rock mechanics testing for optimized fracture designs, In SPE Annual Technical Conference and Exhibition, OnePetro, doi.org/10.2118/38716-MS. ##
  7. Brandas L T, Fjaer E, Tokle K, Tronvoll J (2012) Relating acoustic wave velocities to formation mechanical properties, In 46th US Rock Mechanics/Geomechanics Symposium, OnePetro. ##
  8. Zisman, W. (1933) Comparison of the statically and seismologically determined elastic constants of rocks, Proceedings of the National Academy of Sciences of the United States of America, 19, 7: 680, doi.org/10.1073/pnas.19.7.680. ##
  9. Belikov B (1962). Elastic properties of rocks, Studia Geophysica et Geodaetica 6, 1: 75-85. ##
  10. Goryainov N N, Lyakhovitskii F M (1979) Seismic methods in engineering geology, Seismicheskie metody v inzhenernoi geologii. ##
  11. King M S (1983) Static and dynamic elastic properties of igneous and metamorphic rocks from the Canadian shield. ##
  12. Eissa E, Kazi A (1988) Relation between static and dynamic Young's moduli of rocks, International Journal of Rock Mechanics and Mining and Geomechanics Abstracts, 25: 6. ##
  13. McCann D, Entwisle D (1992) Determination of Young's modulus of the rock mass from geophysical well logs, Geological Society, London, Special Publications, 65, 1: 317-325, doi.org/10.1144/GSL.SP.1992.065.01.2. ##
  14. Morales R H, Marcinew R P (1993) Fracturing of high-permeability formations: mechanical properties correlations, In SPE Annual Technical Conference and Exhibition, OnePetro, doi.org/10.2118/26561-MS. ##
  15. Wang Z (2000) Dynamic versus static elastic properties of reservoir rocks, Seismic and acoustic velocities in reservoir rocks, 3: 531-539. ##
  16. Fei W, Huiyuan B, Jun Y, Yonghao Z (2016) Correlation of dynamic and static elastic parameters of rock, Electronic Journal of Geotechnical Engineering, 21, 04: 1551-1560. ##
  17. Najibi A R, Ghafoori M, Lashkaripour G R, Asef M R (2015) Empirical relations between strength and static and dynamic elastic properties of Asmari and Sarvak limestones, two main oil reservoirs in Iran, Journal of Petroleum Science and Engineering, 126: 78-82, doi.org/10.1016/j.petrol.2014.12.010. ##
  18. Elkatatny S, Mahmoud M, Mohamed I, Abdulraheem A (2018) Development of a new correlation to determine the static Young's modulus, Journal of Petroleum Exploration and Production Technology, 8, 1: 17-30, doi.org/10.1007/s13202-017-0316-4. ##
  19. Mahmoud A A, Elkatatny S, Al-Shehri D (2020) Application of machine learning in evaluation of the static young's modulus for sandstone formation, Sustainability, 12, 5: 1880, doi.org/10.3390/su12051880. ##
  20. Elkatatny S, Tariq Z, Mahmoud M, Abdulraheem A, Mohamed I (2019) An integrated approach for estimating static Young's modulus using artificial intelligence tools, Neural Computing and Applications, 31, 8: 4123-4135, doi.org/10.1007/s00521-018-3344-1. ##
  21. Tariq Z, Elkatatny S, Mahmoud M, Abdulraheem A (2016) A holistic approach to develop new rigorous empirical correlation for static Young's modulus, In Abu Dhabi International Petroleum Exhibition and Conference, OnePetro, doi.org/10.2118/183545-MS. ##
  22. Rashidi M, Hajipour M, Asadi A (2018) Correlation between static and dynamic elastic modulus of limestone formations using artificial neural networks, In 52nd US Rock Mechanics/Geomechanics Symposium, OnePetro. ##
  23. Mahmoud A A, Elkatatny S, Ali A, Moussa T (2019) Estimation of static young's modulus for sandstone formation using artificial neural networks, Energies, 12, 11: 2125, doi.org/10.3390/en12112125. ##
  24. Badrouchi F, Badrouchi N, Rabiei M, Rasouli V (2019) Estimation of elastic properties of bakken formation using an artificial neural network model, In 53rd US Rock Mechanics/Geomechanics Symposium, OnePetro.##