Relative Permeability Modeling Using Extra Trees, ANFIS, and Hybrid LSSVM–CSA Methods.

Determination of the essential properties of petroleum reservoir rocks and parameters of fluid flow in the porous media is a challenging part of reservoir characterization. Among other reservoir rock and two-phase flow properties, the relative permeabilities of gas–oil and water–oil systems are required as critical inputs for reservoir simulation models. Generally, laboratory experiments are considered the best way to obtain accurate information on reservoir rock and flow properties. However, due to the high costs and lengthy procedures of laboratory analyses of reservoir rocks and due to other reasons such as unavailability of the required rock samples, particularly during the early stages of reservoir life, the use of other techniques to predict these properties is inevitable. In this study, three advanced machine learning methods were used to predict relative permeability of oil in the presence of water (k_row), relative permeability of water (k_rw), relative permeability of oil in the presence of gas (k_rog), and relative permeability of gas (k_rg). These methods are adaptive network-based fuzzy inference system (ANFIS), the hybrid of least square support vector machine (LSSVM) with coupled simulated annealing (CSA), and extremely randomized trees, also known as extra trees (ET). We used two extensive sets of experimental data on relative permeabilities in the water–oil and gas–oil systems to develop models with good generalization and universality. The prediction accuracy and reliability of the developed models were evaluated using two standard statistical quality measures, i.e., root mean square deviation (RMSD) and the regression coefficient (R²). The results show that while all the developed models were capable of matching the experimental results with reasonable accuracies, the ET and hybrid LSSVM–CSA models provided better prediction performance and superior correlations between the measured and predicted values. Moreover, this study shed light on to what degree each rock-flow property is important in the estimation of water–oil and gas–oil relative permeabilities. In this regard, we applied feature reduction based on the ET feature importance rankings for developing new ET models to estimate water–oil relative permeabilities using only two input features, i.e., S_w and S_wc, for prediction of k_row, and S_w and wettability type for prediction of k_rw, instead of the seven input parameters used in development of the main models. [ABSTRACT FROM AUTHOR]