The adsorption of methane on the gas shale has been studied with shale physical parameters such as porosity, pressure and temperature. In this study, the statistical analysis on three (3) different morphological and mineralogical Marcellus shale samples has been investigated. The experimental adsorption measurements were conducted at three different temperatures up to 60°C and pressure up to 200bar. The variation of adsorption on shale fabric has been conducted using different machine learning approaches. The multivariate analysis is carried out using the partial least square (PLS) method and support vector regression (SVR), along with random forest regression method. The PLS is a mathematical optimization method and is employed in this study along with SVR and random forest method due to its ability to incorporate the correlation between the independent variables, which decrease the influence of noise, and identifies the system information in linear regression study. The model perdition and correlation analysis are carried out using the fitting durability of R2Y and Q2Y coefficients. The R2Y coefficient represents the correlation in terms of variance of all the dependent variables. Whereas Q2Y explains model accuracy in terms of predictability. The machine learning based SVR method is incorporated for its ability to handle the regression model for linear and nonlinear input data based on mathematical formulation called kernels. The poly-kernels in SVR methods re-arrange the input data based on its high dimensional space. The SVR methods utilize the iteration approach to sequential minimal optimization. The accuracy of the different models is calculated by correlation coefficient (R), root mean square error (RMSE) and mean absolute error (MAE). The variation in different input parameters with adsorption was not increased or decreased synchronically. It has suggested that the variation in shale fabric has not affected the adsorption changes. The PLS analysis has concluded that there is no linear relationship between the adsorption variation with shale fabric total organic content but may have some correlation with mineralogical configurations, such as clay and quartz content and compositions. The data has been divided into the training and testing data. The correlation calculation from the PLS method gives the value of 0.451 R2 and the predictability values are 10.695 RMSE. The analysis from machine learning SVR method shows the good predictability of the adsorption in the variation with shale fabric parameters. Fabric and adsorption have 0.35 R squared obtained from SVR method. The SVR method has given the adsorption and TOC output of RMSE value of 13.995 with R2 ≈ 0.10. The model prediction capabilities using random forest regression was the highest accuracy with R squared value of 0.75 with RMSE value of 8.756. This indicates that shale TOC has a small impact on the adsorption in variation, and therefore on desorption after pressure and porosity. The statistical analysis presented in this study incorporated one of the best regression models algorithms based on machine learning approach to study the adsorption variation with shale fabric this study

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