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Rate of penetration modeling using hybridization extreme learning machine and whale optimization algorithm

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Abstract

Modeling the rate of penetration (ROP) plays a fundamental role in drilling optimization since the achievement of an optimum ROP can drastically reduce the overall cost of drilling activities. Evolved Extreme learning machine (ELM) with the evolutionary algorithms and multi-layer perceptron with Levenberg-Marquardt training algorithm (MLP-LMA) were proposed in this study to predict ROP. This paper focused mainly on two aspects. The first one was the investigation of the whale optimization algorithm (WOA) to optimize the weights and biases between input and hidden layers of ELM to enhance its prediction accuracy. The other was to adopt a prediction methodology that seeks to update the predictive model at each formation in order to reduce the dimension of input data and mitigate the effect of non real-time data such as the formation properties on the bit speed prediction. The prediction models were trained and tested using 3561 data points gathered from an Algerian field. The statistical and graphical evaluation criteria show that the ELM-WOA exhibited higher accuracy and generalization performance compared with the ELM-PSO and MLP-LMA. Furthermore, ELM-WOA was compared with two well-known ROP correlations in the literature, and the comparison results reveal that the proposed ELM-WOA model is superior to the pre-existing correlations. The findings of this study can help for the achievement of an optimum ROP and the reduction of the non-productive time. In addition, the outputs of this study can be used as an objective function during the real-time optimization of the drilling operation.

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Abbreviations

AI:

artificial intelligence

ANN:

artificial neural network

BBO:

biogeography-based optimizer

EIA:

Energy Information Agency

ELM:

extreme learning machine

GA:

genetic algorithm

ICA:

imperialist competitive algorithm

K:

drillability constant

LMA:

Levenberg-Marquardt algorithm

MLP:

Multi-layer perceptron

MSE:

mean square error

PSO:

particle swarm optimization

Q:

flow rate

R2 :

coefficient of determination

RMSE:

root means square error

ROP:

rate of penetration

RPM:

revolution per minute

RTOM:

real time drilling operations monitoring

SPP:

stand pipe pressure

SVM:

support vector machine

T:

drilling torque

UCS:

unconfined compressive strength

WAG:

water alternating gas

WOA:

whale optimization algorithm

WOB:

weight on bit

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Authors and Affiliations

  1. Laboratory of Petroleum Equipment’s Reliability and Materials, Faculty of Hydrocarbons and Chemistry, University M’hamed Bougara of Boumerdes, Avenue de l’Indépendance, 35000, Boumerdes, Algeria

    Mohamed Riad Youcefi, Ahmed Hadjadj, Abdelhak Bentriou & Farouk Said Boukredera

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  1. Mohamed Riad Youcefi
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  2. Ahmed Hadjadj
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  4. Farouk Said Boukredera
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Appendix 1. Statistical formulas

Appendix 1. Statistical formulas

The mathematical formula for the statistical indexes considered in this study are shown below:

$$ RMSE=\sqrt{\frac{1}{N}{\sum}_{i=1}^N{\left({ROP}_{real,i}-{ROP}_{predicted,i}\right)}^2} $$
$$ {R}^2=1-\frac{\sum \limits_i^N\left({ROP}_{real,i}-{ROP}_{predicted,i}\right)}{\sum \limits_i^N\left({ROP}_{predicted,i}-\overline{ROP}\right)} $$

In the aforementioned expressions, N represents the number of data points, ROPreal is the measured rate of penetration value, ROPpredicted is the calculated ROP value by the developed models and \( \overline{ROP} \) is the average of the measured rate of penetration values.

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Youcefi, M.R., Hadjadj, A., Bentriou, A. et al. Rate of penetration modeling using hybridization extreme learning machine and whale optimization algorithm. Earth Sci Inform 13, 1351–1368 (2020). https://doi.org/10.1007/s12145-020-00524-y

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