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A robust Gaussian process regression-based model for the determination of static Young’s modulus for sandstone rocks

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Abstract

Static Young’s modulus (Es) is one of the leading mechanical rock properties. The Es can be measured from experimental lab methods. However, these methods are costly, time-consuming, and challenging to collect samples. Thus, some researchers have proposed alternative techniques, such as empirical correlations, to determine the Es. However, the previous studies have limitations: lack of accuracy, the need for specific data, and improper validation to prove the proper relationships between the inputs and outputs to show the correct physical behavior. In addition, most previous models were based on the dynamic Young’s modulus. Therefore, this study aims to use the Gaussian process regression (GPR) method for Es determination using 1853 real global datasets. The utilization of global data to develop the Es prediction model is unique. The GPR model was validated by applying trend analysis to show that the correct relationships between the inputs and output are attained. Furthermore, different statistical error analyses, namely an average absolute percentage relative error (AAPRE), were performed to assess the GPR accuracy compared to current methods. This study confirmed that the GPR model has robustly and accurately predicted the Es with AAPRE of 5.41%, surpassing all the existing studied models that have AAPRE of more than 10%. The trend analysis results indicated that the GPR model follows the proper physical behaviors for all input trends. The GPR model can accurately predict the Es at different ranges of inputs.

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Data availability

The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

Abbreviations

E s :

Static Young’s modulus

E d :

Dynamic Young’s modulus

GPR:

Gaussian process regression

AVO:

Amplitude variations with offset

RHOB:

Bulk formation density

DTs:

Shear time

DTc:

Compressional time

IQR:

Interquartile range

CF:

Covariance function

T analysis :

Trend analysis

APRE:

Average percent relative error

AAPRE:

Average absolute percent relative error

R :

Correlation coefficient

RMSE:

Root mean square error

SD:

Standard deviation

\(E_{\max .}\) :

Maximum absolute percent relative error

\(E_{\min .}\) :

Minimum absolute percent relative error

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Acknowledgements

The authors would like to express their profound gratitude to the Universiti Teknologi PETRONAS (UTP) for supporting this study under YUTP-Grant cost centers 15LC0-098 and 15LC0-226.

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Authors and Affiliations

  1. Petroleum Engineering Department, Universiti Teknologi PETRONAS, 32610, Seri Iskandar, Perak Darul Ridzuan, Malaysia

    Fahd Saeed Alakbari, Mysara Eissa Mohyaldinn & Mohammed Abdalla Ayoub

  2. Institute of Hydrocarbon Recovery, Universiti Teknologi PETRONAS, 32610, Seri Iskandar, Perak Darul Ridzuan, Malaysia

    Fahd Saeed Alakbari, Mysara Eissa Mohyaldinn & Mohammed Abdalla Ayoub

  3. Mechanical Engineering Department, Universiti Teknologi PETRONAS, 32610, Seri Iskandar, Perak Darul Ridzuan, Malaysia

    Ali Samer Muhsan

  4. Gas Processing Center, College of Engineering, Qatar University, P.O. Box 2713, Doha, Qatar

    Ibnelwaleed A. Hussein

  5. Chemical Engineering Department, College of Engineering, Qatar University, P.O. Box 2713, Doha, Qatar

    Ibnelwaleed A. Hussein

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  1. Fahd Saeed Alakbari
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  2. Mysara Eissa Mohyaldinn
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Correspondence to Fahd Saeed Alakbari or Mysara Eissa Mohyaldinn.

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Alakbari, F.S., Mohyaldinn, M.E., Ayoub, M.A. et al. A robust Gaussian process regression-based model for the determination of static Young’s modulus for sandstone rocks. Neural Comput & Applic 35, 15693–15707 (2023). https://doi.org/10.1007/s00521-023-08573-2

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