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


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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Average absolute percentage error


Adaptive neuro-fuzzy inference system


Artificial neural network


Correlation coefficient


Maximum absolute error


Root-mean-square error


Bulk density, g/cm3


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


Index for neurons

j :

Index for number of input parameters

n :

Normalized value


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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).

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