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Effective Thermal Conductivity Modeling of Sandstones: SVM Framework Analysis

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Abstract

Among the most significant physical characteristics of porous media, the effective thermal conductivity (ETC) is used for estimating the thermal enhanced oil recovery process efficiency, hydrocarbon reservoir thermal design, and numerical simulation. This paper reports the implementation of an innovative least square support vector machine (LS-SVM) algorithm for the development of enhanced model capable of predicting the ETCs of dry sandstones. By means of several statistical parameters, the validity of the presented model was evaluated. The prediction of the developed model for determining the ETCs of dry sandstones was in excellent agreement with the reported data with a coefficient of determination value (\({R}^{2})\) of 0.983 and an average absolute relative deviation of 0.35 %. Results from present research show that the proposed LS-SVM model is robust, reliable, and efficient in calculating the ETCs of sandstones.

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Abbreviations

\(A^{T}\) :

Transpose of matrix A

AARD :

Average absolute relative deviation

ARD :

Average relative deviation

ANN :

Artificial neural network

B :

Bias term

ETC :

Effective thermal conductivity

\(I_N\) :

\(N\times N\) identity matrix

\(K(x_i ,x_j )\) :

Kernel function

L :

Lagrangian

LS-SVM:

Least square support vector machine

RMSE :

Root mean squared error

w :

Weight vector

\(\alpha _i \) :

Lagrange multipliers

\(\varPhi \) :

Map from input space into feature space

\(\gamma \) :

regularization constant

\(\varSigma \) :

width of the RBF kernel

\(\varOmega \) :

Kernel matrix

\(\lambda \) :

The effective thermal conductivity (W\({\cdot }\)m\(^{-1}{\cdot }\mathrm{K}^{-1}\))

T :

Temperature (K)

P :

Pressure (MPa)

\(\emptyset \) :

Porosity (%)

\(\rho \) :

Density (\(\hbox {g}{\cdot }\hbox {cm}^{-3})\)

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Authors and Affiliations

  1. Department of Petroleum Engineering, Petroleum University of Technology (PUT), Ahwaz, Iran

    Alireza Rostami & Mohammad Masoudi

  2. Institute of Petroleum Engineering (IPE), Tehran University, Tehran, Iran

    Alireza Ghaderi-Ardakani

  3. Young Researchers and Elites Club, North Tehran Branch, Islamic Azad University, Tehran, Iran

    Milad Arabloo

  4. Petroleum Engineering Program, Texas A&M University at Qatar, Doha, Qatar

    Mahmood Amani

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  1. Alireza Rostami
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  2. Mohammad Masoudi
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  3. Alireza Ghaderi-Ardakani
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  4. Milad Arabloo
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  5. Mahmood Amani
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Correspondence to Milad Arabloo.

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Rostami, A., Masoudi, M., Ghaderi-Ardakani, A. et al. Effective Thermal Conductivity Modeling of Sandstones: SVM Framework Analysis. Int J Thermophys 37, 59 (2016). https://doi.org/10.1007/s10765-016-2057-x

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