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Analysis and modelling of gas relative permeability in reservoir by hybrid KELM methods

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Abstract

Petroleum reservoirs are often influenced by various flow behaviours including the mixture of gas, water and oil. The gas relative permeability is used to estimate how much of the gas in the reservoir is producible at a given water saturation level. Therefore, the gas relative permeability is a significant parameter to characterize the behaviour of petroleum reservoirs. However, the measurement of gas relative permeability by traditional methods tends to be comparatively expensive and time-consuming. In the recent years, the machine learning techniques provided new alternatives for predicting the gas relative permeability. For this purpose, five new methods were proposed based on kernel extreme learning machine (KELM) technique. Five meta-heuristic algorithms were adopted to tune the model hyper-parameters of KELMs, i.e., butterfly optimization algorithm (BOA), tunicate swarm algorithm (TSA), Multi-verse optimizer (MVO), Golden jackal optimization (GJO) and Harris hawk’s optimization (HHO). Five-fold cross validation was used to increase the model generalization. An extensive dataset from the experiments which contain 1024 data were taken to develop models. Four classical statistical indicators were used to measure the model performance, i.e., root mean squared error (RMSE), coefficient of determination (R2), variance accounted for (VAF) and mean absolute error (MAE). In addition, two comprehensive manners, overall evaluation index (GI) and Taylor Diagram, were evaluated to provide overall model assessments. Proposed hybrid KELM models performed better than several other machine learning techniques. BOA-KELM model with swarm size 150 generated the best generalization for the testing set and could be recommended to predict the gas relative permeability with the same inputs used in this study. The detailed performance of BOA-KELM includes: training set (GI:0.1736; R2: 0.9902; RMSE: 0.7477; VAF: 99.0218; MAE: 10.6636), testing set (GI:0.4164; R2: 0.9789; RMSE: 0.5314; VAF: 97.8917; MAE: 4.1706). The mutual information technique was employed to examine the influence of influential factors to the model interpretation and it can be found that the gas saturation had a larger influence on the hybrid KELM models. When it was used as an individual input, the overall prediction decreased but acceptable prediction performance still can be obtained by hybrid KELM models. In the case of the gas saturation to be the only input, the best testing R2 (0.94) could be generated by MVO-KELM which is higher than the R2 from the empirical method named Corey-Brooks model and several other machine learning techniques. The main novelty of this study is that five new machine learning methods were proposed to predict the gas relative permeability and performed better than other empirical or machine learning techniques.

Highlights

Five new methods based on KELM were proposed to predict gas relative permeability in reservoir.

Meta-heuristic algorithms were used to tune the hyper-parameters in KELM.

BOA-KELM model with swarm size 150 brought the best generalization ability.

Hybrid KELM models performed better than other classical and machine learning model for multi-inputs.

Mutual information was used to explore the interpretation of inputs.

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Data availability

No datasets were generated or analysed during the current study.

Abbreviations

AGS:

Average grain size

ANFIS:

Adaptive neuro-fuzzy inference system)

ANN:

Artificial neural network

APBD:

Absolute permeability before desalination

BK:

Bulk density

BOA:

Butterfly optimization algorithm

CALI:

Caliper logs

CALO:

Calorimetry

COA:

Cuckoo optimization algorithm

COLOR:

Color

CP:

Core porosity

CWT:

Time of compression wave travel

CWV:

Velocity of compression wave

DEN:

Density

DENC:

Density correction

DENL:

Density log

DENTR:

Density tool reading

DEP:

Depth

DEPH:

Depth horizon

DEPI:

Depth interval

DR:

Deep resistivity

ELM:

Extreme learning machine

ER:

Electrical resistivity

FBD:

Formation bottom depth

FIS:

Fuzzy interface system

FR:

Focused resistivity

FTD:

Formation top depth

GA:

Genetic algorithm

GI:

Overall evaluation index

GJO:

Golden jackal optimization

GR:

Gamma ray

GWO:

Grey wolf optimization

HGAPSO:

Hybrid genetic algorithm and particle swarm optimization

HHO:

Harris hawk’s optimization

K:

Derived core permeability

KELM:

Kernel extreme learning machine

Krg:

Relative gas permeability

LIGHTGBM:

Light gradient boosting machine

LM:

Levenberg–Marquardt

LSSVM:

Least square support vector machine

MAE:

Mean absolute error

MSE:

Mean squared error

MFR:

Microspherical focused resistivity

MLPNN:

Multilayer perception neural network

MVO:

Multi-verse optimizer

NNAW:

Neural network adaptive wavelet

NT:

Neutron

NTP:

Neutron porosity

P:

Porosity

PBD:

Porosity before desalination

PC:

Principal component

PCA:

Principal component analysis

PEF:

Photoelectric log

R2:

Coefficient of determination

RF:

Random forest

RL:

Resistivity log

RMSE:

Root mean squared error

RVR:

Relevance vector regression

SaDE:

Self-adaptive differential evolution

SC:

Salt concentration

Sg:

Gas saturation

SGB:

Stochastic Gradient Boosting

Sgc:

Critical gas saturation

SOP:

Secondary porosity

Sorg:

Residual oil saturation

SSD:

Social ski-driver

STT:

Sonic transit time

SVM:

Support vector machine

Swc:

Connate water saturation

TOP:

Total porosity

TRR:

True resistance

TSA:

Tunicate swarm algorithm

VAF:

Variance accounted for

WS:

Water saturation

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Acknowledgements

Enming Li and Bin Xi want to acknowledge the funding supported by China Scholarship Council under grant No. 202006370006 and 202008440524, respectively.

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Authors and Affiliations

Authors

Contributions

E.L. conceptualized the study, developed software, and drafted the original manuscript. N.Z. handled visualization and investigation. B.X. contributed to methodology, validation, software development, and the initial drafting of the manuscript. Y.Z. provided conceptualization and conducted a critical review. Y.F. wrote the original draft of the manuscript. B.O.T. was involved in the methodology. P.S. supervised the project. H.F. contributed to writing and validation. J.Z. participated in the review process and provided supervision.

Corresponding authors

Correspondence to Bin Xi or Jian Zhou.

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Competing interests

The authors declare no competing interests.

Additional information

Communicated by Hassan Babaie.

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Li, E., Zhang, N., Xi, B. et al. Analysis and modelling of gas relative permeability in reservoir by hybrid KELM methods. Earth Sci Inform 17, 3163–3190 (2024). https://doi.org/10.1007/s12145-024-01326-2

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  • DOI: https://doi.org/10.1007/s12145-024-01326-2

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