An integrated approach for estimating static Young’s modulus using artificial intelligence tools

Abstract

Elastic parameters play a key role in managing the drilling and production operations. Determination of the elastic parameters is very important to avoid the hazards associated with the drilling operations, well placement, wellbore instability, completion design and also to maximize the reservoir productivity. A continuous core sample is required to be able to obtain a complete profile of the elastic parameters through the required formation. This operation is time-consuming and extremely expensive. The scope of this paper is to build an advanced and accurate model to predict the static Young’s modulus using artificial intelligence techniques based on the wireline logs (bulk density, compressional time, and shear time). More than 600 measured core data points from different fields were used to build the AI models. The obtained results showed that ANN is the best AI technique for estimating the static Young’s modulus with high accuracy [R2 was 0.92 and the average absolute percentage error (AAPE) was 5.3%] as compared with ANFIS and SVM. For the first time, an empirical correlation based on the weights and biases of the optimized ANN model was developed to determine the static Young’s modulus. The developed correlation outperformed the published correlations for static Young’s modulus prediction. The developed correlation enhanced the accuracy of predicting the static Young’s modulus. (R2 was 0.96 and AAPE was 6.2%.) The developed empirical correlation can help geomechanical engineers determine the static Young’s modulus where laboratory core samples are not available.

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Abbreviations

AAPE:

Average absolute percentage error

ANFIS:

Adaptive neuro-fuzzy inference system

ANN:

Artificial neural network

CC:

Correlation coefficient

MAE:

Maximum absolute error

RMSE:

Root-mean-square error

RHOB:

Bulk density, g/cm3

SVM:

Support vector machines

b 1 :

Bias between input and hidden layers of neural network

b 2 :

Bias between hidden and output layers of neural network

E :

Young’s modulus, MPsi

E static :

Static Young’s modulus, MPsi

E dynamic :

Dynamic Young’s modulus, MPsi

E max :

Maximum error between actual and predicted

E min :

Minimum error between actual and predicted

J :

Total number of input parameters

N :

Total number of neurons

R :

Correlation coefficient

R 2 :

Coefficient of determination

x :

Input parameters

y :

Output variable

w 1 :

Weights vector between input and hidden layers of neural network

w 2 :

Weights vector between hidden and output layers of neural network

i:

Index for neurons

j :

Index for number of input parameters

n :

Normalized value

References

  1. 1.

    Chang C, Zoback MD, Khaksar A (2006) Empirical relations between rock strength and physical properties in sedimentary rocks. J Pet Sci Eng 51:223–237

    Article  Google Scholar 

  2. 2.

    Howard GC, Fast CR (1970) Hydraulic fracturing. Monograph, volume 2 of SPE, Henry L. Doherty Memorial Fund of AIME, Society of Petroleum Engineers of AIME

  3. 3.

    Gatens JM, Harrison CW, Lancaster DE, Guldry FK (1990) In-situ stress tests and acoustic logs determine mechanical properties and stress profiles in the Devonian shales. SPE Form Eval 5(3):248–254

    Article  Google Scholar 

  4. 4.

    Ameen MS, Smart BG, Somerville JM, Hammilton S, Naji NA (2009) Predicting rock mechanical properties of carbonates from wireline logs (a case study: Arab-D reservoir, Ghawar field, Saudi Arabia). Mar Petrol Geol 26(4):430–444

    Article  Google Scholar 

  5. 5.

    Al-Anazi AF, Gates ID (2010) A support vector machine algorithm to classify lithofacies and model permeability in heterogeneous reservoirs. Eng Geol 114(3–4):267–277

    Article  Google Scholar 

  6. 6.

    Barree RD, Gilbert JV, Conway MW (2009) Stress and rock property profiling for unconventional reservoir stimulation. Paper SPE 118703 presented at the SPE hydraulic fracturing technology conference, The Woodlands, Texas, 19–21 January

  7. 7.

    Colin C, Potter S, Darren F (1997) Formation elastic parameters by deriving S-wave velocity logs. CREWES Research 9:1–10

    Google Scholar 

  8. 8.

    Larsen I, Fjær E, Renlie L (2000) Static and dynamic Poisson’s ratio of weak sandstones. Paper ARMA-2000-0077 presented at the 4th North American rock mechanics symposium, Seattle, Washington, 31 July–3 August

  9. 9.

    Abdulraheem A, Ahmed M, Vantala A, Parvez T (2009) Prediction of rock mechanical parameters for hydrocarbon reservoirs using different artificial intelligence techniques. Paper SPE 126094 presented at Saudi Arabia section technical symposium, Al-Khobar, Saudi Arabia, 9–11 May

  10. 10.

    Fjaer E, Holt RM, Horsrud P, Raaen AM, Risnes R (1992) Petroleum Related Rock Mechanics. Elsevier, Amsterdam

    Google Scholar 

  11. 11.

    King MS (1970) Static and dynamic elastic moduli of rocks under pressure. In: Proceedings of 11th U.S. symposium on rock mechanics, pp 329–351

  12. 12.

    Ledbetter H (1993) Dynamic vs static Young’s moduli a case study. Mater Sci Eng 165(1):9–10

    Article  Google Scholar 

  13. 13.

    Canady WJ (2011) A method for full-range Young’s Modulus correction. Paper SPE presented at 143604 North American unconventional gas conference and exhibition, The Woodlands, Texas, USA, 14–16 June

  14. 14.

    Khaksar A, Taylor PG, Fang Z, Kayes T, Salazar A, Rahman K (2009) Rock strength from core and logs, where we stand and ways to go. Paper SPE 121972 presented at the EUROPEC/EAGE conference and exhibition, Amsterdam, The Netherlands

  15. 15.

    Belikov BP, Alexandrov TW, Rysova TW (1970) Elastic properties of rock minerals and rocks. Nauka, Moscow

    Google Scholar 

  16. 16.

    Gorjainov NL (1979) Seismic methods in engineering geology. Nedra, Moscow

    Google Scholar 

  17. 17.

    McCann, DM, Entwisle DC (1992) Determination of Young’s Modulus of the rock mass from geophysical well logs. In: Hurst A, Giffiths CM, Worthington PF (eds) Geological applications of wireline logs II: Geological Society of Special Publications, vol 65, pp 317–325

  18. 18.

    Morals RH, Marcinew RP (1993) Fracturing of high-permeability formations: mechanical properties correlations. SPE paper 26561, Presented in SPE annual technical conference and exhibition, Houston, Texas, 3–6 October

  19. 19.

    Bradford IDR, Fuller J, Thompson PJ, Walsgrove TR (1998) Benefits of assessing the solids production risk in a North Sea reservoir using elastoplastic modeling. Paper SPE-47360 presented at SPE/ISRM rock mechanics in petroleum engineering, Trondheim, Norway, 8–10 July

  20. 20.

    King MS (1983) Static and dynamic elastic properties of rocks from the canadian shield. Int J Rock Mech Min Sci 20(5):237–241

    Article  Google Scholar 

  21. 21.

    Eissa EA, Kazi A (1988) Relation between static and dynamic Young’s modulus of rocks. Int J Rock Mech Min Sci Geomech 25(6):479–482

    Article  Google Scholar 

  22. 22.

    Wang Z (2000) Dynamic versus static elastic properties of reservoir rocks, in seismic and acoustic velocities in reservoir rocks. SEG Geophys Reprint Ser 19:531–539

    Google Scholar 

  23. 23.

    Najibi AR, Mohammad G, Gholam RL, Mohammad RA (2015) Empirical relations between strength and static and dynamic elastic properties of Asmari and Sarvak limestones, two main oil reservoirs in Iran. J Petrol Sci Eng 126(2015):78–82

    Article  Google Scholar 

  24. 24.

    Elkatatny SM, Mahmoud MA, Moahmed I, Abdulraheem A (2017) Development of a new correlation to determine the static Young’s modulus. J Pet Explor Prod Technol, pp 1–10

  25. 25.

    Mahmoud MA, Elkatatny SA, Ramadan E, Abdulraheem A (2016) Development of lithology-based static Young’s modulus correlations from log data based on data clustering technique. J Pet Sci Eng 146:10–20

    Article  Google Scholar 

  26. 26.

    Álvarez del Castillo A, Santoyo E, García-Valladares O (2012) Α new void fraction correlation inferred from artificial neural networks for modeling two-phase flows in geothermal wells. Comput Geosci 41:25–39. https://doi.org/10.1016/j.cageo.2011.08.001

    Article  Google Scholar 

  27. 27.

    Lippman RP, Lippman RP (1987) An introduction to computing with neural nets. In: Mag A (ed) IEEE ASSP magazine IEEE, pp 4–22. https://doi.org/10.1109/massp.1987.1165576

  28. 28.

    Vineis P, Rainoldi A (1997) Neural networks and logistic regression: analysis of a case-control study on myocardial infarction. J Clin Epidemiol 50:1309–1310. https://doi.org/10.1016/S0895-4356(97)00163-7

    Article  Google Scholar 

  29. 29.

    Burbidge R, Trotter M, Buxton B, Holden S (2001) Drug design by machine learning: support vector machines for pharmaceutical data analysis. Comput Chem 26:5–14. https://doi.org/10.1016/S0097-8485(01)00094-8

    Article  Google Scholar 

  30. 30.

    Hinton GE, Osindero S, Teh Y-W (2006) A fast learning algorithm for deep belief nets. Neural Comput 18:1527–1554. https://doi.org/10.1162/neco.2006.18.7.1527

    MathSciNet  Article  MATH  Google Scholar 

  31. 31.

    Cranganu C, Breaban ME, Luchian H (2015) Artificial intelligent approaches in petroleum geosciences, Artificial intelligent approaches in petroleum geosciences. Springer International Publishing, Cham. https://doi.org/10.1007/978-3-319-16531-8

  32. 32.

    Jang J-SR (1993) ANFIS: adaptive-network-based fuzzy inference system. IEEE Trans Syst Man Cybern 23:665–685. https://doi.org/10.1109/21.256541

    Article  Google Scholar 

  33. 33.

    Tahmasebi P, Hezarkhani A (2012) A hybrid neural networks-fuzzy logic-genetic algorithm for grade estimation. Comput Geosci 42:18–27. https://doi.org/10.1016/j.cageo.2012.02.004

    Article  Google Scholar 

  34. 34.

    Walia N, Singh H, Sharma A (2015) ANFIS: adaptive neuro-fuzzy inference system—a survey. Int J Comput Appl 123:32–38. https://doi.org/10.5120/ijca2015905635

    Google Scholar 

  35. 35.

    Uçar T, Karahoca A, Karahoca D (2013) Tuberculosis disease diagnosis by using adaptive neuro fuzzy inference system and rough sets. Neural Comput Appl 23:471–483. https://doi.org/10.1007/s00521-012-0942-1

    Article  Google Scholar 

  36. 36.

    Guo G (2014) Support vector machines applications. In: Ma Y, Guo G (eds) Support vector machines applications. Springer International Publishing, Cham. https://doi.org/10.1007/978-3-319-02300-7

  37. 37.

    Jeng J-T, Chuang C-C, Su S-F (2003) Support vector interval regression networks for interval regression analysis. Fuzzy Sets Syst 138:283–300. https://doi.org/10.1016/S0165-0114(02)00570-5

    MathSciNet  Article  MATH  Google Scholar 

  38. 38.

    Khoukhi A, Oloso M, Elshafei M, Abdulraheem A, Al-Majed A (2011) SUPPORT vector regression and functional networks for viscosity and gas/oil ratio curves estimation. Int J Comput Intell Appl 10:269–293. https://doi.org/10.1142/S1469026811003100

    Article  Google Scholar 

  39. 39.

    Elkatatny SM, Tariq Z, Mahmoud MA (2016) Real time prediction of drilling fluid rheological properties using artificial neural networks visible mathematical model (white box). J Petrol Sci Eng 146:1202–1210

    Article  Google Scholar 

  40. 40.

    Elkatatny SM (2017) Real time prediction of rheological parameters of KCl water-based drilling fluid using artificial neural networks. Arab J Sci Eng 42(4):1655–1665

    Article  Google Scholar 

  41. 41.

    Elkatatny SM, Mahmoud M (2017) Development of new correlations for the oil formation volume factor in oil reservoirs using artificial intelligent white box technique. Petroleum (in press)

  42. 42.

    Elkatatny SM, Mahmoud M (2017) Development of a new correlation for bubble point pressure in oil reservoirs using artificial intelligent white box technique. Arab J Sci Eng. https://doi.org/10.1007/s13369-017-2589-9

    Google Scholar 

  43. 43.

    Elkatatny SM, Mahmoud MA, Tariq Z, Abdulraheem A (2017) New insights into the prediction of heterogeneous carbonate reservoir permeability from well logs using artificial intelligent network. Neural Comput Appl. https://doi.org/10.1007/s00521-017-2850-x

    Google Scholar 

  44. 44.

    Bandar AD, Algarni MT, Tale M, Almushiqeh I (2011) Prediction of Poisson’s ratio and Young’s modulus for hydrocarbon reservoirs using alternating conditional expectation algorithm. Paper SPE 138841 presented at SPE Middle east oil and gas show and conference, Manama, Bahrain, 25–28 September

  45. 45.

    Madhubabu N, Singh PK, Kainthola A, Mahanta B, Tripathy A, Singh TN (2016) Prediction of compressive strength and elastic modulus of carbonate rocks. Measurement 88:202–213

    Article  Google Scholar 

  46. 46.

    Beiki M, Majdi A, Givshad AD (2013) Application of genetic programming to predict the uniaxial compressive strength and elastic modulus of carbonate rocks. Int J Rock Mech Min Sci 63:159–169

    Article  Google Scholar 

  47. 47.

    Dehghan S, Sattari G, Chelgani SC, Aliabadi M (2010) Prediction of uniaxial compressive strength and modulus of elasticity for Travertine samples using regression and artificial neural networks. Min Sci Technol 20(1):41–46

    Google Scholar 

  48. 48.

    Yin S, Ding W, Shan Y, Zhou W, Wang R, Zhou X, Li A, He J (2016) A new method for assessing Young’s modulus and Poisson’s ratio in tight interbedded clastic reservoirs without a shear wave time difference. J Nat Gas Sci Eng 36:267–279

    Article  Google Scholar 

  49. 49.

    Ghasemi E, Kalhori H, Bagherpour R, Yagiz S (2016) Model tree approach for predicting uniaxial compressive strength and Young’s modulus of carbonate rocks. Bull Eng Geol Environ (in press)

  50. 50.

    Aboutaleb S, Behnia M, Bagherpour R, Bluekian B (2017) Using non-destructive tests for estimating uniaxial compressive strength and static Young’s modulus of carbonate rocks via some modeling techniques. Bull Eng Geol Environ 1–17. https://doi.org/10.1007/s10064-017-1043-2

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Correspondence to Salaheldin Elkatatny.

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Elkatatny, S., Tariq, Z., Mahmoud, M. et al. An integrated approach for estimating static Young’s modulus using artificial intelligence tools. Neural Comput & Applic 31, 4123–4135 (2019). https://doi.org/10.1007/s00521-018-3344-1

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Keywords

  • Static Young’s modulus
  • Artificial intelligence
  • Artificial neural network
  • Adaptive neuro-fuzzy inference system
  • Support vector machine
  • Log data
  • Core data