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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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.
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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