Modeling study of sandstone permeability under true triaxial stress based on backpropagation neural network, genetic programming, and multiple regression analysis

doi:10.1016/j.jngse.2020.103742

Journal of Natural Gas Science and Engineering

Volume 86, February 2021, 103742

https://doi.org/10.1016/j.jngse.2020.103742 Get rights and content

Highlights

•
The permeability prediction models are built by BPNN, GP, and regression analysis.
•
The permeability prediction data fit well with the experimental data.
•
The pore pressure has the greatest influence on sandstone permeability.
•
Under true triaxial stress, the influence on permeability follows σ₁ > σ₂ > σ₃.
•
The BPNN model is more accurate than the GP and multiple regression models.

Abstract

Permeability evolution of sandstone is of great significance in the development of tight sandstone gas reservoirs. Traditional laboratory tests have the disadvantages of high cost and long testing time. Therefore, the present study employed use artificial intelligence systems, i.e., backpropagation neural network (BPNN), genetic programming (GP), and multiple regression analysis to construct prediction models of sandstone permeability based on the coupling effect of true triaxial stress field and pore pressure. The results showed that the permeability prediction obtained from the systems fit well with the experimental data, and evidenced that permeability increased with pore pressure and decreased with increase in principal stress. Sensitivity analysis showed that the pore pressure has the greatest influence on sandstone permeability under different true triaxial stress. The effect of anisotropic principal stress on permeability exhibited σ₁ > σ₂ > σ₃ under fixed pore pressure. Further assessment based on a combination of five evaluation indexes showed that the prediction accuracy of the BPNN model was better.

Introduction

As a new, clean, and efficient energy source, tight sandstone gas has become a new area of focus in the exploration and development of unconventional natural gas worldwide, and it plays an important role in oil and gas production in China as well (Zhang, 2008; Zhang et al., 2009, 2012; Dai et al., 2012; Li et al., 2012). In the exploitation of tight sandstone gas reservoirs, multiphysics coupling problems, such as fluid-solid coupling, are frequently encountered with the rock mass (Yang et al., 2012; Tian et al., 2018). The initial in situ stress and pore pressure significantly affect the seepage characteristics of fluid in the rock mass (Zou et al., 2012; Chen et al., 2019; Peng et al., 2020). Permeability is the key parameter determining the development of tight sandstone gas and reflects the difficulty of fluid migration in sandstone reservoirs. The evolution law of reservoir rock permeability has long been the focus of domestic and foreign scholars. Gray and Fatt (1963) studied the influence of pore pressure and confining pressure on the permeability of sandstone cores, and found that permeability increased with pore pressure and decreased with increase in confining pressure. Zoback and Byerlee (1975) further verified the relationship between the permeability, confining pressure, and pore pressure of Berea sandstone, and found that the effect of pore pressure on permeability was more significant than that of confining pressure. Liu et al. (2015) conducted laboratory experiments to study the seepage characteristics of sandstone along the complete stress-strain curve under different confining pressure and pore pressure combinations, and field tests to study the seepage law of sandstone in the vertical direction, and obtained the relationships between permeability and volumetric strain, pore pressure, and confining pressure. Zhang et al. (2017) studied the effect of stress concentration on the seepage characteristics of sandstone and established an exponential relationship between peak gas flow and volume strain of sandstone after failure. Yu et al. (2019) predicted sandstone permeability using scanning electron microscopy and studied its relationship with microscopic characteristics using fractal dimensions. The research results showed that the predicted permeability fit well with the measured data.

Currently, the most commonly used method for testing the permeability of rock mass is laboratory testing. However, precision instruments and equipment are frequently required to obtain more realistic permeability results; this often entails significant investment of time and energy to obtain the permeability of rock mass under the combined effect of principal stress and pore pressure via experiments (Gokceoglu, 2002; Taylor and Appleby, 2006). The use of artificial intelligence systems, such as neural networks, GP, and regression analysis, to solve such highly nonlinear, complex, and fuzzy geomechanical problems has become a global trend (Grima and Babuška, 1999; Ni and Wang, 2000; Özcan et al., 2009; Asadi et al., 2011; Cevik et al., 2011). Ali and Chawathé (2000) established an artificial neural network (ANN) model to predict the permeability of arkosic sandstone using its porosity and mineral composition, and the model exhibited good applicability in predicting the permeability of the South Lucky Lake field. Yin et al. (2013) constructed a BPNN model to predict the gas permeability of coal at various effective stresses and temperatures; they found that the predicted permeability was very close to the experimental permeability and that the maximum relative error did not exceed 5%. Rezaee et al. (2006) used regression analysis to obtain a permeability prediction formula for carbonate rock based on porosity and pore throat radius. The accuracy evaluation showed that the formula had good permeability prediction ability. Nazari and Riahi (2011) established ANN and GP models to predict the tensile strength and water permeability of high-strength concrete. The training results showed that both models had good prediction abilities, but GP had less dependence on users and more reasonable prediction results. These artificial intelligence technologies have strong robustness, generalization error ability, and nonlinear dynamic processing ability, which provide a new way to solve the seepage problem of reservoir rock with multi-factor, complexity, randomness, and nonlinearity.

At present, the experimental testing and prediction modeling for sandstone permeability are usually based on the conventional triaxial stress path or uniaxial stress condition, which belong to the simple stress state. The actual reservoir rock is in an unequal three-dimensional pressure state (σ₁ > σ₂ > σ₃). The significant influence of the intermediate principal stress on the strength, deformation, seepage, and other characteristics of rock has been confirmed (Mogi, 1971; Liu et al., 2018, 2019). In the present study, cubic sandstones are taken as the research objects, and the large number of permeability test data obtained from seepage experiments under the true triaxial stress path are used to construct the sandstone permeability prediction models under the coupling effect of true triaxial stress field and pore pressure using BPNN, GP, and multiple regression analysis to study the seepage law of sandstone.

Section snippets

Sample data from true triaxial seepage experiments

The sandstone for the specimens used in this study was obtained from the outcrop of Chayuan, Chongqing. The Young's modulus, E, of the sandstone is 10.6 GPa and its Poisson's ratio, v, is 0.31. The nuclear magnetic resonance (NMR) test of the sandstone used showed that the porosity is 4.6% and the permeability is 0.3638 mD, the sandstone is mainly composed of quartz and feldspar and possesses relatively stronger homogeneity, with no obvious joints and fissures on the surface. After they were

BPNN

Artificial neural network is a type of nonlinear data modeling technology based on neuron design. It originated from the study of the thought process of the human brain (Sietsma and Dow, 1991; Basheer and Hajmeer, 2000). It contains three main parameters: weight, bias, and activation function. The most widely used neural network model is the BPNN (Rezaee et al., 2006; Özcan et al., 2009; Ding et al., 2011; Yin et al., 2013). The gradient descent algorithm is used by reducing the slope of the

Sensitivity analysis

From the comparison between the experimental and predicted permeability results of the three models, it can be seen that σ₁, σ₂, σ₃, and p affect the variation in permeability. When each principal stress increases, the pores and fractures in the sandstone are compressed and the seepage channel narrows, causing permeability to decline.

Gas injection causes the effective stress in the pores and fractures to decrease; hence, the pore space increases and leads to the expansion of sandstone. This

Conclusion

In this research, BPNN, GP, and multiple regression analysis were used to construct the prediction models for sandstone permeability under true triaxial stress conditions. The conclusions are as follows:

(1)
The permeability predicted by the BPNN, GP, and multiple regression analysis models were in good agreement with the experimental data, and showed the variation of sandstone permeability with principal stress and pore pressure.
(2)
Based on the cosine amplitude method, we investigated the effect of

Credit author statement

Beichen Yu: Conceptualization, Methodology, Writing - Original Draft, Writing - Review & Editing; Honggang Zhao: Investigation, Methodology; Jiabao Tian: Investigation, Software; Chao Liu: Methodology, Resources, Project administration, Writing - Review & Editing; Zhenlong Song: Software; Yubing Liu: Formal analysis; Minghui Li: Supervision.

Declaration of competing interest

We declare we have no competing interests.

Acknowledgments

This study was financially supported by the National Natural Science Foundation of China (51874053), the Graduate Research and Innovation Foundation of Chongqing, China (CYS19013, CYB19046, CYB19045).

References (55)

M. Ali et al.
Using artificial intelligence to predict permeability from petrographic data
Comput. Geosci.
(2000)
M. Asadi et al.
Evaluating the strength of intact rocks through genetic programming
Appl. Soft Comput.
(2011)
I.A. Basheer et al.
Artificial neural networks: fundamentals, computing, design, and application
J. Microbiol. Methods
(2000)
A. Baykasoglu et al.
Prediction of compressive and tensile strength of limestone via genetic programming
Expert Syst. Appl.
(2008)
M. Beiki et al.
Application of genetic programming to predict the uniaxial compressive strength and elastic modulus of carbonate rocks
Int. J. Rock Mech. Min. Sci.
(2013)
A. Cevik et al.
Modeling of the uniaxial compressive strength of some clay-bearing rocks using neural network
Appl. Soft Comput.
(2011)
T.Y. Chen et al.
Experimental study of permeability change of organic-rich gas shales under high effective stress
J. Nat. Gas Sci. Eng.
(2019)
M. De Simone et al.
Estimating DEM microparameters for uniaxial compression simulation with genetic programming
Int. J. Rock Mech. Min. Sci.
(2019)
C. Gokceoglu
A fuzzy triangular chart to predict the uniaxial compressive strength of the Ankara agglomerates from their petrographic composition
Eng. Geol.
(2002)
Y.H. Jong et al.
Influence of geological conditions on the powder factor for tunnel blasting
Int. J. Rock Mech. Min. Sci.
(2004)

C. Liu et al.

Deformation and permeability evolution of coals considering the effect of beddings

Int. J. Rock Mech. Min. Sci.

(2019)

Y.B. Liu et al.

Permeability evolution of anthracite coal considering true triaxial stress conditions and structural anisotropy

J. Nat. Gas Sci. Eng.

(2018)

A. Majdi et al.

Evolving neural network using a genetic algorithm for predicting the deformation modulus of rock masses

Int. J. Rock Mech. Min. Sci.

(2010)

A. Nazari et al.

Prediction split tensile strength and water permeability of high strength concrete containing TiO2 nanoparticles by artificial neural network and genetic programming

Compos. B Eng.

(2011)

K.M. Neaupane et al.

Prediction of tunneling-induced ground movement with the multi-layer perceptron

Tunn. Undergr. Space Technol.

(2006)

H.G. Ni et al.

Prediction of compressive strength of concrete by neural networks

Cement Concr. Res.

(2000)

F. Özcan et al.

Comparison of artificial neural network and fuzzy logic models for prediction of long-term compressive strength of silica fume concrete

Adv. Eng. Software

(2009)

S. Palani et al.

An ANN application for water quality forecasting

Mar. Pollut. Bull.

(2008)

H.H. Peng et al.

Computed tomography analysis on cyclic fatigue and famage properties of rock salt under gas pressure

Int. J. Fatig.

(2020)

J. Sietsma et al.

Creating artificial neural networks that generalize

Neural Network.

(1991)

H. Sonmez et al.

Estimation of rock modulus: for intact rocks with an artificial neural network and for rock masses with a new empirical equation

Int. J. Rock Mech. Min. Sci.

(2006)

W.B. Tian et al.

The threshold pressure gradient effect in the tight sandstone gas reservoirs with high water saturation

Fuel

(2018)

B. Tiryaki

Predicting intact rock strength for mechanical excavation using multivariate statistics, artificial neural networks, and regression trees

Eng. Geol.

(2008)

C.N. Zou et al.

Tight gas sandstone reservoirs in China: characteristics and recognition criteria

J. Petrol. Sci. Eng.

(2012)

W. Banzhaf et al.

Genetic Programming: an Introduction: on the Automatic Evolution of Computer Programs and its Applications

(1998)

J.F. Chenard et al.

Stream temperature modelling using artificial neural networks: application on Catamaran Brook, New Brunswick, Canada

Hydrol. Process.

(2008)

J.X. Dai et al.

Tight gas in China and its significance in exploration and exploitation

Petrol. Explor. Dev.

(2012)

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Modeling study of sandstone permeability under true triaxial stress based on backpropagation neural network, genetic programming, and multiple regression analysis

Highlights

Abstract

Introduction

Section snippets

Sample data from true triaxial seepage experiments

BPNN

Sensitivity analysis

Conclusion

Credit author statement

Declaration of competing interest

Acknowledgments

Comput. Geosci.

Appl. Soft Comput.

J. Microbiol. Methods

Expert Syst. Appl.

Int. J. Rock Mech. Min. Sci.

Appl. Soft Comput.

J. Nat. Gas Sci. Eng.

Int. J. Rock Mech. Min. Sci.

Eng. Geol.

Int. J. Rock Mech. Min. Sci.

Int. J. Rock Mech. Min. Sci.

J. Nat. Gas Sci. Eng.

Int. J. Rock Mech. Min. Sci.

Compos. B Eng.

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Neural Network.

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