Movatterモバイル変換

[0]ホーム
URL:

Skip to main content

Advertisement

Springer Nature Link
Log in

Core log integration: a hybrid intelligent data-driven solution to improve elastic parameter prediction

  • Original Article
  • Published:
Neural Computing and Applications Aims and scope Submit manuscript

Abstract

Current oil prices and global financial situations underline the need for the best engineering practices to recover remaining hydrocarbons. A good understanding of the elastic behavior of the reservoir rock is extremely imperative in avoiding the severe well drilling problems such as wellbore in-stability, differential sticking, kicks, and many more. Therefore, it is plausible to have a good estimation of the rock elastic behavior for successful well operations. This study presents a generalized empirical model to predict static Poisson’s ratio of the carbonate rocks. Petrophysical well logs were used as inputs, and the laboratory measured static Poisson’s ratio was used as an output. Three supervised artificial intelligence (AI) techniques were used, viz. artificial neural network (ANN), support vectors regression, and adaptive network-based fuzzy interference system. An extensive prediction comparison was made between these three AI techniques. Based on the lowest average absolute percentage error (AAPE) and highest coefficient of determination (R2), the ANN model proposed to be the best model to predict static Poisson’s ratio. To transform black box nature of AI model into a white box, ANN-based empirical correlation is also developed to predict the static Poisson’s ratio. Comparison of the developed empirical correlation with previously established approaches to find static Poisson’s ratio on an unseen published dataset revealed that the equation of ANN can predict the static Poisson’s ratio with implicitly less AAPE and with highR2 value. The proposed model with the empirical correlation can assist geo-mechanical engineers to predict the static Poisson’s ratio in the absence of core data. The novelty of the new equation is that it can be used without the need of any AI software.

This is a preview of subscription content,log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
¥17,985 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (Japan)

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

Abbreviations

APE:

Absolute percentage error

AAPE:

Average absolute percentage error

ANFIS:

Adaptive neuro-fuzzy inference system

ANN:

Artificial neural network

CC:

Correlation coefficient

FFNN:

Feedforward neural network

LVDT:

Linear variable differential transducer

MLP:

Multilayer perceptron

PR:

Poisson’s ratio

RBF:

Radial basis function

RMSE:

Root mean square error

SVR:

Support vectors regression

UCS:

Unconfined compressive strength

b1 :

Bias between input and hidden layer of neural network

b2 :

Bias between hidden and output layer of neural network

\(c_{1}\) :

Cognitive parameter\(\left( {0 \le c_{1} \le 1.2} \right)\)

\(c_{2}\) :

Cognitive parameter\(\left( {0 \le c_{2} \le 1.2} \right)\)

Edyn :

Dynamic Young’s modulus (MPsi)

Estatic :

Static Young’s modulus (MPsi)

Ed :

Dynamic Young’s modulus (MPsi)

i :

Index for neurons

j :

Index for number of input parameters

\(n\) :

Iteration number

Nh :

Total number of neurons

PRdyn :

Dynamic Poisson’s ratio

PRstatic :

Static Poisson’s ratio

P-wave:

Compressional wave

\(p_{i}\) :

Particle\(i\) position at any iteration

\(p_{i}^{\text{b}}\) :

Particle best solution

\(p_{\text{gb}}\) :

Global best solution

Rhob:

Bulk density (g/cc)

R2 :

Coefficient of determination

S-wave:

Shear wave

w :

Weight\(\left( {0 \le w \le 1.2} \right)\)

\(v_{i}\) :

Weight\(\left( {0 \le w \le 1.2} \right)\)

w1 :

Weights vector between input and hidden layer of neural network

w2 :

Weights vector between hidden and output layer of neural network

x :

Input parameters

y :

Output variable

\(\sigma_{\text{o}}\) :

Activation function between hidden and output layer of FFNN

\(\sigma_{\text{L}}\) :

Activation function between input and hidden layer of FFNN

Δtc :

Compressional wave transit time (µs/ft)

Δts :

S-wave transit time (µs/ft)

ρ :

Bulk density (g/cc)

\(\nu_{\text{dyn}}\) :

Dynamic Poisson’s ratio

References

  1. Anifowose F, Labadin J, Abdulraheem A (2015) Improving the prediction of petroleum reservoir characterization with a stacked generalization ensemble model of support vector machines. Appl Soft Comput 26:483–496.https://doi.org/10.1016/j.asoc.2014.10.017

    Article  Google Scholar 

  2. Anifowose F, Adeniye S, Abdulraheem A, Al-Shuhail A (2016) Integrating seismic and log data for improved petroleum reservoir properties estimation using non-linear feature-selection based hybrid computational intelligence models. J Pet Sci Eng 145:230–237.https://doi.org/10.1016/j.petrol.2016.05.019

    Article  Google Scholar 

  3. Anifowose FA, Labadin J, Abdulraheem A (2015) Ensemble model of non-linear feature selection-based extreme learning machine for improved natural gas reservoir characterization. J Nat Gas Sci Eng 26:1561–1572.https://doi.org/10.1016/j.jngse.2015.02.012

    Article  Google Scholar 

  4. Anifowose FA, Labadin J, Abdulraheem A (2017) Ensemble machine learning: an untapped modeling paradigm for petroleum reservoir characterization. J Pet Sci Eng 151:480–487.https://doi.org/10.1016/j.petrol.2017.01.024

    Article  Google Scholar 

  5. Helmy T, Hossain MI, Adbulraheem A et al (2017) Prediction of non-hydrocarbon gas components in separator by using hybrid computational intelligence models. Neural Comput Appl 28:635–649.https://doi.org/10.1007/s00521-015-2088-4

    Article  Google Scholar 

  6. Al-Bulushi NI, King PR, Blunt MJ, Kraaijveld M (2012) Artificial neural networks workflow and its application in the petroleum industry. Neural Comput Appl 21:409–421.https://doi.org/10.1007/s00521-010-0501-6

    Article  Google Scholar 

  7. Mohaghegh S (1995) Neural network: what it can do for petroleum engineers. J Pet Technol 47:42.https://doi.org/10.2118/29219-PA

    Article  Google Scholar 

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

    Article  Google Scholar 

  9. Tariq Z, Elkatatny S, Mahmoud M, Abdulraheem A (2016) A new artificial intelligence based empirical correlation to predict sonic travel time. In: International petroleum technology conference. International Petroleum Technology Conference

  10. Najibi AR, Ghafoori M, Lashkaripour GR, Asef MR (2015) Empirical relations between strength and static and dynamic elastic properties of Asmari and Sarvak limestones, two main oil reservoirs in Iran. J Pet Sci Eng 126:78–82.https://doi.org/10.1016/j.petrol.2014.12.010

    Article  Google Scholar 

  11. Abdulraheem A, Sabakhy E, Ahmed M et al (2007) Estimation of permeability from wireline logs in a middle eastern carbonate reservoir using fuzzy logic. In: SPE middle east oil and gas show and conference. Society of Petroleum Engineers

  12. Nooruddin HA, Anifowose F, Abdulraheem A (2013) Applying artificial intelligence techniques to develop permeability predictive models using mercury injection capillary-pressure data. In: SPE Saudi Arabia section technical symposium and exhibition. Society of Petroleum Engineers

  13. Anifowose F, Labadin J, Abdulraheem A (2013) A least-square-driven functional networks type-2 fuzzy logic hybrid model for efficient petroleum reservoir properties prediction. Neural Comput Appl 23:179–190.https://doi.org/10.1007/s00521-012-1298-2

    Article  Google Scholar 

  14. Helmy T, Rahman SM, Hossain MI, Abdelraheem A (2013) Non-linear heterogeneous ensemble model for permeability prediction of oil reservoirs. Arab J Sci Eng 38:1379–1395.https://doi.org/10.1007/s13369-013-0588-z

    Article  Google Scholar 

  15. Shujath Ali S, Hossain ME, Hassan MR, Abdulraheem A (2013) Hydraulic unit estimation from predicted permeability and porosity using artificial intelligence techniques. In: North Africa technical conference and exhibition. Society of Petroleum Engineers

  16. 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. Society of Petroleum Engineers

  17. 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 & conference. Society of Petroleum Engineers

  18. Tariq Z, Elkatatny S, Mahmoud M et al (2017) A new approach to predict failure parameters of carbonate rocks using artificial intelligence tools. In: SPE Kingdom of Saudi Arabia annual technical symposium and exhibition. Society of Petroleum Engineers

  19. Tariq Z, Elkatatny S, Mahmoud M et al (2017) A new technique to develop rock strength correlation using artificial intelligence tools. In: SPE reservoir characterisation and simulation conference and exhibition. Society of Petroleum Engineers

  20. Yang Y, Rosenbaum MS (2002) The artificial neural network as a tool for assessing geotechnical properties. Geotech Geol Eng 20:149–168.https://doi.org/10.1023/A:1015066903985

    Article  Google Scholar 

  21. Sonmez H, Tuncay E, Gokceoglu C (2004) Models to predict the uniaxial compressive strength and the modulus of elasticity for Ankara agglomerate. Int J Rock Mech Min Sci 41:717–729.https://doi.org/10.1016/j.ijrmms.2004.01.011

    Article  Google Scholar 

  22. Cevik A, Sezer EA, Cabalar AF, Gokceoglu C (2011) Modeling of the uniaxial compressive strength of some clay-bearing rocks using neural network. Appl Soft Comput 11:2587–2594.https://doi.org/10.1016/j.asoc.2010.10.008

    Article  Google Scholar 

  23. Elkatatny S, Tariq Z, Mahmoud M et al (2018) Development of new mathematical model for compressional and shear sonic times from wireline log data using artificial intelligence neural networks (white box). Arab J Sci Eng.https://doi.org/10.1007/s13369-018-3094-5

    Article  Google Scholar 

  24. Bazargan H, Adibifard M (2017) A stochastic well-test analysis on transient pressure data using iterative ensemble Kalman filter. Neural Comput Appl.https://doi.org/10.1007/s00521-017-3264-5

    Article  Google Scholar 

  25. Artun E (2017) Characterizing interwell connectivity in waterflooded reservoirs using data-driven and reduced-physics models: a comparative study. Neural Comput Appl 28:1729–1743.https://doi.org/10.1007/s00521-015-2152-0

    Article  Google Scholar 

  26. Fattahi H, Gholami A, Amiribakhtiar MS, Moradi S (2015) Estimation of asphaltene precipitation from titration data: a hybrid support vector regression with harmony search. Neural Comput Appl 26:789–798.https://doi.org/10.1007/s00521-014-1766-y

    Article  Google Scholar 

  27. Alimohammadi S, Sayyad Amin J, Nikooee E (2017) Estimation of asphaltene precipitation in light, medium and heavy oils: experimental study and neural network modeling. Neural Comput Appl 28:679–694.https://doi.org/10.1007/s00521-015-2097-3

    Article  Google Scholar 

  28. Adebayo AR, Abdulraheem A, Olatunji SO (2015) Artificial intelligence based estimation of water saturation in complex reservoir systems. J Porous Media 18:893–906.https://doi.org/10.1615/JPorMedia.v18.i9.60

    Article  Google Scholar 

  29. Baziar S, Shahripour HB, Tadayoni M, Nabi-Bidhendi M (2016) Prediction of water saturation in a tight gas sandstone reservoir by using four intelligent methods: a comparative study. Neural Comput Appl. 10:15–20.https://doi.org/10.1007/s00521-016-2729-2

    Article  Google Scholar 

  30. Gatens JM, Harrison CW, Lancaster DE, Guidry FK (1990) In-situ stress tests and acoustic logs determine mechanical propertries and stress profiles in the devonian shales. SPE Form Eval 5:248–254.https://doi.org/10.2118/18523-PA

    Article  Google Scholar 

  31. 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.https://doi.org/10.1016/j.petrol.2006.01.003

    Article  Google Scholar 

  32. Khaksar A, Taylor PG, Fang Z et al (2009) Rock strength from core and logs, where we stand and ways to go. In: EUROPEC/EAGE conference and exhibition. Society of Petroleum Engineers

  33. Nes O-M, Fjær E, Tronvoll J et al (2005) Drilling time reduction through an integrated rock mechanics analysis. In: SPE/IADC drilling conference. Society of Petroleum Engineers

  34. Chan T, Hood M, Board M (1982) Rock properties and their effect on thermally induced displacements and stresses. J Energy Resour Technol 104:384.https://doi.org/10.1115/1.3230433

    Article  Google Scholar 

  35. Cadwallader S, Wampler J, Sun T et al (2015) An integrated dataset centered around distributed fiber optic monitoring—key to the successful implementation of a geo-engineered completion optimization program in the eagle ford shale. In: Proceedings of the 3rd unconventional resources technology conference. American Association of Petroleum Geologists, Tulsa, OK, USA

  36. Wang C, Wu Y-S, Xiong Y et al (2015) Geomechanics coupling simulation of fracture closure and its influence on gas production in shale gas reservoirs. In: SPE reservoir simulation symposium. Society of Petroleum Engineers

  37. Nawrocki PA, Dusseault MB (1996) Modelling of damaged zones around boreholes using a radius dependent Young’S modulus. J Can Pet Technol.https://doi.org/10.2118/96-03-04

    Article  Google Scholar 

  38. Ameen MS, Smart BGD, Somerville JM et al (2009) Predicting rock mechanical properties of carbonates from wireline logs (a case study: arab-D reservoir, Ghawar field, Saudi Arabia). Mar Pet Geol 26:430–444.https://doi.org/10.1016/j.marpetgeo.2009.01.017

    Article  Google Scholar 

  39. Elkatatny S, Tariq Z, Mahmoud M et al (2018) An integrated approach for estimating static Young’s modulus using artificial intelligence tools. Neural Comput Appl.https://doi.org/10.1007/s00521-018-3344-1

    Article  Google Scholar 

  40. Tariq Z, Elkatatny SM, Mahmoud MA, Abdulraheem A, Abdelwahab AZ, Woldeamanuel M (2017) Estimation of rock mechanical parameters using artificial intelligence tools. American Rock Mechanics Association

  41. Mahmoud M, Elkatatny S, 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.https://doi.org/10.1016/j.petrol.2016.04.011

    Article  Google Scholar 

  42. Tariq Z, Elkatatny SM, Mahmoud MA et al (2017) Development of new correlation of unconfined compressive strength for carbonate reservoir using artificial intelligence techniques. In: 51st US rock mechanics/geomechanics symposium 2017

  43. D’Andrea D V., Fischer RL, Fogelson DE (1965) Prediction of compressive strength from other rock properties. United States Department of The Interior Bureau of Mines

  44. Kumar A, Jayakumar T, Raj B, Ray KK (2003) Correlation between ultrasonic shear wave velocity and Poisson’s ratio for isotropic solid materials. Acta Mater 51:2417–2426.https://doi.org/10.1016/S1359-6454(03)00054-5

    Article  Google Scholar 

  45. Phani KK (2008) Correlation between ultrasonic shear wave velocity and Poisson’s ratio for isotropic porous materials. J Mater Sci 43:316–323.https://doi.org/10.1007/s10853-007-2055-2

    Article  Google Scholar 

  46. Edimann K, Somerville JM, Smart BGD et al (1998) Predicting rock mechanical properties from wireline porosities. In: SPE/ISRM rock mechanics in petroleum engineering. Society of Petroleum Engineers

  47. Al-Shayea NA (2004) Effects of testing methods and conditions on the elastic properties of limestone rock. Eng Geol 74:139–156.https://doi.org/10.1016/j.enggeo.2004.03.007

    Article  Google Scholar 

  48. Singh V, Singh TN (2006) A neuro-fuzzy approach for prediction of Poisson’s ratio and young’s modulus of shale and sandstone. In: The 41st U.S. symposium on rock mechanics (USRMS), 17–21 June, Golden, Colorado

  49. Shalabi FI, Cording EJ, Al-Hattamleh OH (2007) Estimation of rock engineering properties using hardness tests. Eng Geol 90:138–147.https://doi.org/10.1016/j.enggeo.2006.12.006

    Article  Google Scholar 

  50. Al-Anazi A, Gates ID (2010) A support vector machine algorithm to classify lithofacies and model permeability in heterogeneous reservoirs. Eng Geol 114:267–277.https://doi.org/10.1016/j.enggeo.2010.05.005

    Article  Google Scholar 

  51. Baykasoğlu A, Dereli T, Tanış S (2004) Prediction of cement strength using soft computing techniques. Cem Concr Res 34:2083–2090.https://doi.org/10.1016/j.cemconres.2004.03.028

    Article  Google Scholar 

  52. ASTM D-04 (2005) Standard test method for triaxial compressive strength of undrained rock core specimens without pore pressure measurements

  53. Rao S, Ramamurti V (1993) A hybrid technique to enhance the performance of recurrent neural networks for time series prediction. In: IEEE international conference on neural networks. IEEE, pp 52–57

  54. Angelini E, Ludovici A (2009) CDS Evaluation model with neural networks. J Serv Sci Manag 02:15–28.https://doi.org/10.4236/jssm.2009.21003

    Article  Google Scholar 

  55. Monjezi M, Dehghani H (2008) Evaluation of effect of blasting pattern parameters on back break using neural networks. Int J Rock Mech Min Sci 45:1446–1453.https://doi.org/10.1016/j.ijrmms.2008.02.007

    Article  Google Scholar 

  56. 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

    Article MathSciNet MATH  Google Scholar 

  57. Lippmann R (1994) Book review: “Neural Networks, A Comprehensive Foundation”, by Simon Haykin. Int J Neural Syst 05:363–364.https://doi.org/10.1142/S0129065794000372

    Article  Google Scholar 

  58. 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 

  59. Yılmaz I, Yuksek AG (2008) An example of artificial neural network (ANN) application for indirect estimation of rock parameters. Rock Mech Rock Eng 41:781–795.https://doi.org/10.1007/s00603-007-0138-7

    Article  Google Scholar 

  60. Yagiz S, Sezer EA, Gokceoglu C (2012) Artificial neural networks and nonlinear regression techniques to assess the influence of slake durability cycles on the prediction of uniaxial compressive strength and modulus of elasticity for carbonate rocks. Int J Numer Anal Methods Geomech 36:1636–1650.https://doi.org/10.1002/nag.1066

    Article  Google Scholar 

  61. Mohaghegh SD (2017) Shale Analytics. Springer, Cham

    Book  Google Scholar 

  62. 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 

  63. Jang J-SR (1996) Input selection for ANFIS learning. In: Proceedings of IEEE 5th international fuzzy systems. IEEE, pp 1493–1499

  64. Jang J-SR, Sun Chuen-Tsai (1995) Neuro-fuzzy modeling and control. Proc IEEE 83:378–406.https://doi.org/10.1109/5.364486

    Article  Google Scholar 

  65. Ebrahimi M, Sajedian A (2010) Use of fuzzy logic for predicting two phase inflow performance relationship of horizontal oil wells. In: Trinidad and tobago energy resources conference. Society of Petroleum Engineers

  66. 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

    Article  Google Scholar 

  67. 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 

  68. El-Sebakhy EA, Hadi AS, Faisal KA (2007) Iterative least squares functional networks classifier. IEEE Trans Neural Networks 18:844–850.https://doi.org/10.1109/TNN.2007.891632

    Article  Google Scholar 

  69. Elhaj MA, Anifowose F, Abdulraheem A, Fahad K (2015) Single gas flow prediction through chokes using artificial intelligence techniques. SPE Saudi Arabia Section Annual Technical Symposium and Exhibition, 21–23 April, Al-Khobar, Saudi Arabia.https://doi.org/10.2118/177991-MS

  70. Anifowose F, Adeniye S, Abdulraheem A (2014) Recent advances in the application of computational intelligence techniques in oil and gas reservoir characterisation: a comparative study. J Exp Theor Artif Intell 26:551–570.https://doi.org/10.1080/0952813X.2014.924577

    Article  Google Scholar 

  71. Trontl K, Šmuc T, Pevec D (2007) Support vector regression model for the estimation of γ-ray buildup factors for multi-layer shields. Ann Nucl Energy 34:939–952.https://doi.org/10.1016/j.anucene.2007.05.001

    Article  Google Scholar 

  72. 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

    Article MathSciNet MATH  Google Scholar 

  73. Khoukhi A, Oloso M, Elshafei M et al (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 

  74. Guo G (2014) Support vector machines applications. Springer, Cham

    Google Scholar 

  75. Eberhart R, Kennedy J (1995) A new optimizer using particle swarm theory. In: MHS’95. Proceedings of the sixth international symposium on micro machine and human science. IEEE, pp 39–43

  76. Kennedy J (1997) The particle swarm: social adaptation of knowledge. In: Proceedings of 1997 IEEE international conference on evolutionary computation (ICEC’97). IEEE, pp 303–308

  77. Tariq Z, Abdulraheem A, Khan MR, Sadeed A (2018) New inflow performance relationship for a horizontal well in a naturally fractured solution gas drive reservoirs using artificial intelligence technique. In: Offshore technology conference Asia. Offshore Technology Conference

  78. Eberhart RC, Shi Y (1998) Comparison between genetic algorithms and particle swarm optimization. In: International conference on evolutionary programming, pp 611–616

    Google Scholar 

  79. Hagan MT, Menhaj MB (1994) Training feedforward networks with the Marquardt algorithm. IEEE Trans Neural Networks 5:989–993.https://doi.org/10.1109/72.329697

    Article  Google Scholar 

  80. Bello O, Asafa T (2014) A functional networks softsensor for flowing bottomhole pressures and temperatures in multiphase production wells. In: SPE intelligent energy conference & exhibition. Society of Petroleum Engineers

  81. Awadalla M, Yousef H (2016) Neural networks for flow bottom hole pressure prediction. Int J Electr Comput Eng 6:1839.https://doi.org/10.11591/ijece.v6i4.10774

    Article  Google Scholar 

  82. Memon PQ, Yong S-P, Pao W, Sean PJ (2014) Surrogate reservoir modeling-prediction of bottom-hole flowing pressure using radial basis neural network. In: 2014 Science and information conference. IEEE, pp 499–504

  83. Jahanandish I, Salimifard B, Jalalifar H (2011) Predicting bottomhole pressure in vertical multiphase flowing wells using artificial neural networks. J Pet Sci Eng 75:336–342.https://doi.org/10.1016/j.petrol.2010.11.019

    Article  Google Scholar 

  84. Osman E-SA, Ayoub MA, Aggour MA (2005) An artificial neural network model for predicting bottomhole flowing pressure in vertical multiphase flow. In: SPE middle east oil and gas show and conference. Society of Petroleum Engineers

  85. Ebrahimi A, Khamehchi E (2015) A robust model for computing pressure drop in vertical multiphase flow. J Nat Gas Sci Eng 26:1306–1316.https://doi.org/10.1016/j.jngse.2015.08.036

    Article  Google Scholar 

  86. Adebayo AR, Abdulraheem A, Al-Shammari AT (2013) Promises of artificial intelligence techniques in reducing errors in complex flow and pressure losses calculations in multiphase fluid flow in oil wells. In: SPE Nigeria annual international conference and exhibition. Society of Petroleum Engineers

Download references

Acknowledgements

The authors would like to acknowledge College of Petroleum & Geosciences (CPG), King Fahd University of Petroleum & Minerals for providing research opportunities to produce this paper.

Author information

Authors and Affiliations

  1. Department of Petroleum Engineering, King Fahd University of Petroleum and Minerals, Dhahran, 31261, Saudi Arabia

    Zeeshan Tariq, Mohamed Mahmoud & Abdulazeez Abdulraheem

Authors
  1. Zeeshan Tariq

    You can also search for this author inPubMed Google Scholar

  2. Mohamed Mahmoud

    You can also search for this author inPubMed Google Scholar

  3. Abdulazeez Abdulraheem

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence toZeeshan Tariq.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Appendix A

Appendix A

Average absolute percentage error (AAPE) is defined as follows:

$${\text{AAPE}} = \frac{{\sum {\left| {\left( {{\text{PRstatic}}_{\text{measured}} - {\text{PRstatic}}_{\text{predicted}} } \right)|| *\frac{100}{{{\text{PRstatic}}_{\text{measured}} }}} \right|} }}{k}$$
(26)

Root mean square error (RMSE) is defined as follows:

$${\text{RMSE}} = \sqrt { \frac{{\sum {\left( {{\text{PRstatic}}_{\text{measured}} - {\text{PRstatic}}_{\text{predicted}} } \right)^{2} } }}{k}}$$
(27)

where\({\text{PRstatic}}\)measured is the measured value of\({\text{PRstatic}}\) and\({\text{PRstatic}}\)predicted is the estimated value from the models.k is the total number of data points.

Pearson correlation coefficient CC is defined as follows:

$${\text{CC}} = \frac{{{{k}}\sum {{xy}} - \left( {\sum {{x}}} \right)\left( {\sum {{y}}} \right)}}{{\sqrt {{{k}}\left( {\sum {{x}}^{2} } \right) - \left( {\sum {{y}}} \right)^{2} } \sqrt {{{k}}\left( {\sum {{b}}^{2} } \right) - \left( {\sum {{b}}} \right)^{2} } }}$$
(28)

wherex andy are two variables.

Coefficient of determinationR2 is defined as follows:

$${{R}}^{2} = \left( {\frac{{{{k}}\sum {{xy}} - \left( {\sum {{x}}} \right)\left( {\sum {{y}}} \right)}}{{\sqrt {{{k}}\left( {\sum {{x}}^{2} } \right) - \left( {\sum {{y}}} \right)^{2} } \sqrt {{{k}}\left( {\sum {{b}}^{2} } \right) - \left( {\sum {{b}}} \right)^{2} } }}} \right)^{2} .$$
(29)

Rights and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Tariq, Z., Mahmoud, M. & Abdulraheem, A. Core log integration: a hybrid intelligent data-driven solution to improve elastic parameter prediction.Neural Comput & Applic31, 8561–8581 (2019). https://doi.org/10.1007/s00521-019-04101-3

Download citation

Keywords

Access this article

Subscribe and save

Springer+ Basic
¥17,985 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (Japan)

Instant access to the full article PDF.

Advertisement

[8]ページ先頭
©2009-2025 Movatter.jp