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Neural Computing and Applications

, Volume 31, Issue 12, pp 8561–8581 | Cite as

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

  • Zeeshan TariqEmail author
  • Mohamed Mahmoud
  • Abdulazeez Abdulraheem
Original Article

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 high R2 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.

Keywords

Static Poisson’s ratio Carbonate rocks Triaxial tests Well logs Artificial intelligence Particle swarm optimization Mathematical model 

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

List of symbols

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

Notes

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.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

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© Springer-Verlag London Ltd., part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Petroleum EngineeringKing Fahd University of Petroleum and MineralsDhahranSaudi Arabia

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