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

  • Salaheldin Elkatatny
  • Zeeshan Tariq
  • Mohamed Mahmoud
  • Abdulazeez Abdulraheem
  • Ibrahim Mohamed
Original Article

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.

Keywords

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

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

List of symbols

b1

Bias between input and hidden layers of neural network

b2

Bias between hidden and output layers of neural network

E

Young’s modulus, MPsi

Estatic

Static Young’s modulus, MPsi

Edynamic

Dynamic Young’s modulus, MPsi

Emax

Maximum error between actual and predicted

Emin

Minimum error between actual and predicted

J

Total number of input parameters

N

Total number of neurons

R

Correlation coefficient

R2

Coefficient of determination

x

Input parameters

y

Output variable

w1

Weights vector between input and hidden layers of neural network

w2

Weights vector between hidden and output layers of neural network

Subscripts and superscripts

i

Index for neurons

j

Index for number of input parameters

n

Normalized value

Notes

Compliance with ethical standards

Conflict of interest

The authors declare that there is no conflict of interests regarding the publication of this paper.

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Copyright information

© The Natural Computing Applications Forum 2018

Authors and Affiliations

  1. 1.Department of Petroleum EngineeringKing Fahd University of Petroleum and MineralsDhahranSaudi Arabia
  2. 2.Petroleum Engineering DepartmentCairo UniversityCairoEgypt
  3. 3.Petroleum Engineering DepartmentSuez UniversitySuezEgypt
  4. 4.Advantek International Corp.HoustonUSA

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