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Machine Learning Approach to Model Rock Strength: Prediction and Variable Selection with Aid of Log Data

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Abstract

Comprehensive knowledge and analysis of in situ rock strength and geo-mechanical characteristics of rocks are crucial in hydrocarbon and mineral exploration stage to maximize wellbore performance, maintain wellbore stability, and optimize hydraulic fracturing process. Due to the high cost of laboratory-based measurements of rock mechanics properties, the log-based prediction is a viable option. Nowadays, the machine learning tools are being used for estimation of the in situ rock properties using wireline log data. This paper proposes a machine learning approach for rock strength (uniaxial compressive strength) prediction. The main objectives are to investigate the performance of data-driven predictive model in determining this vital parameter and to select features of predictor log variables in the model. The backpropagation multilayer perception (MLP) artificial neural network (ANN) with Levenberg–Marquardt training algorithm as well as the least squares support vector machine (LS-SVM) with coupled simulated annealing (CSA) optimization technique is employed to develop the dynamic data-driven models. Capturing nonlinear, high dimensional, and complex nature of real field log data, the rock strength models’ performances are evaluated using statistical criteria to ensure concerning the model reliability and accuracy. The model predictions are compared and validated against the measured values as well as the results obtained from existing log-based correlations. Both the MLP-ANN and the CSA-based LS-SVM connectionist strategies are able to predict the rock strength so that there is a very good match between the model results and corresponding measured values. The input log parameters are ranked based on their contributions in prediction performance. The acoustic travel time and gamma ray are found to have the highest relative significance in estimating rock strength. New correlations are also developed to obtain the in situ rock strength of the siliciclastic sedimentary rocks using the most important log parameters such as dynamic sonic slowness, formation electron density, and shalyness effect. The developed correlations can be used to obtain quick estimation of dynamic uniaxial compressive strength profile using wireline logging data, instead of static data from the surface measurements or laboratory data. It is expected that the proposed models and tools will enable oil and gas engineers to better predict rock strength and thus enhance wellbore performance.

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Abbreviations

AAPE:

Average absolute percentage error

ANN:

Artificial neural network

BTS:

Brazilian tensile strength

DT:

Sonic travel time (µs/ft)

FL:

Fuzzy logic

GEP:

Gene expression programming

GR:

Gamma ray (API)

LS-SVM:

Least square support vector machine

LM:

Levenberg–Marquardt

MAPE:

Maximum absolute error percentage

MSE:

Mean square error

MLP:

Multilayer perception

MVRE:

Multivariate regression analysis

RBF:

Radial basis kernel function

RMSE:

Root mean square error

UCS:

Unconfined compressive strength (MPa), rock strength

b :

Bias

dd:

Dry density

E :

Young’s modulus (MPa)

G :

Shear modulus (MPa)

\({\text{GR}}_{\log }\) :

Gamma-ray value of the zone of interest

\({\text{GR}}_{\max }\) :

Maximum value of gamma-ray log over the entire log

\({\text{GR}}_{\min }\) :

Minimum value of gamma-ray log over the entire log

I d :

Slake durability index

Is(50) :

Point load index test

I GR :

Shale Index (Clay index)

K :

Bulk modulus (MPa)

N :

Number of neurons

NPHI:

Neutron porosity

PHI:

Effective porosity

PHIN:

Neutron porosity (frac.)

PHIND:

Porosity from the combination of density and neutron log

R 2 :

Coefficient of determination

RB:

Formation bulk density

RT:

True (Deep) resistivity (Ω m), Rt

SRn:

Schmidt hammer rebound number harness number (SRn)

Vp:

Compressional wave velocity (km/s)

Vs:

Shear wave velocity (km/s)

Vsh:

Shale volume (shaliness)

wc:

Water content

x i :

Input variables

y p :

Predicted value (y)

y m :

Target (actual) output variable (y)

ϕ :

True porosity (frac.)

ϕ e :

Effective porosity (frac.)

ϕ D,e :

Effective density porosity (frac.)

ϕ N,e :

Effective neutron porosity (frac.)

\(\phi_{{\text{N,sh}}}\) :

Neutron porosity of the adjacent shale zone (frac.)

\(\nu\) :

Poison’s ratio

\(\rho_{{\text{b}}}\) :

Bulk density (g/cm3)

\(\rho_{{{\text{b}} \cdot {\text{c}}}}\) :

Clay corrected density porosity (g/cm3)

\(\rho_{{{\text{fl}}}}\) :

Fluid density (g/cm3)

\(\rho_{{{\text{ma}}}}\) :

Matrix density (g/cm3)

ω ij :

Connected weight between the ith neuron and jth neuron

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Acknowledgements

We thank Equinor (formerly Statoil) Canada Ltd., Natural Sciences and Engineering Research Council of Canada (NSERC), and InnovateNL for providing financial support to accomplish this study at the Memorial University, St. John’s, NL, Canada.

Funding

The funding was funded by Equinor (formerly Statoil) Canada Ltd., CA (211162).

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Authors and Affiliations

  1. Department of Process Engineering, Memorial University, St. John’s, NL, Canada

    Mohammad Islam Miah, Salim Ahmed, Sohrab Zendehboudi & Stephen Butt

  2. Department of Petroleum and Mining Engineering, Chittagong University of Engineering and Technology, Chittagong, 4349, Bangladesh

    Mohammad Islam Miah

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  1. Mohammad Islam Miah
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Contributions

MIM: conceptualization, modeling/simulation, validation, and original draft; SZ: supervision, technical discussion, and writing—reviewing and editing; SA: supervision, technical discussion, and writing—reviewing and editing; SB: technical discussion and reviewing, manuscript editing.

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Correspondence to Mohammad Islam Miah.

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Miah, M.I., Ahmed, S., Zendehboudi, S. et al. Machine Learning Approach to Model Rock Strength: Prediction and Variable Selection with Aid of Log Data. Rock Mech Rock Eng 53, 4691–4715 (2020). https://doi.org/10.1007/s00603-020-02184-2

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  • DOI: https://doi.org/10.1007/s00603-020-02184-2

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