Comparison of Permeability Estimation Models Through Bayesian Model Averaging and LASSO Regression

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Abstract To capture the most realistic reservoir description in terms of heterogeneity, it is essential to find out the most accurate approach for formation permeability estimation in non-cored intervals. The simplest and most common approach of data modeling is multiple linear regression that adopts stepwise elimination for model variables selection. However, that elimination has shown its weakness to efficiently handle the high number of predictors in a physical process. In this research, we adopt two modern statistical leaning algorithms for core permeability modeling given well log attributes and prediction in non-cored intervals of a sandstone formation. The Bayesian Model Averaging (BMA) was adopted as a stochastic approach of data modeling and parameter selection in formation permeability modeling. Based on Bayes' theorem, BMA integrates prior distribution given the observed data in order to produce a posterior distribution of how likely the model is assimilating the data. In the computed BMA Occam's window, the best selected model has maximum posterior probability and minimum BIC; meanwhile, the non-influential predictors are eliminated when the probability of a nonzero predictor coefficient is less than 50% for the best sampled model. Conversely, the same procedure was done through the LASSO regression that considers penalized least squared equation for data modeling and non-influential factors removal. Results of the two algorithms were illustrated, discussed, and depicted for efficiency comparison in terms of their modeling and prediction accuracy. In addition, the two models were statistically validated based on observed-predicted response matching. Both BMA and LASSO have led to very accurate modeling and excellent matching between the observed and predicted core permeability. The adjusted R-squared and root mean squared error are highly encouraging with slight preferrnece of LASSO on BMA. The novelty of Bayesian Model Averaging comes from its stochastic design to generate multiple models taking into account the data uncertainty which leads to finding find the optimal fit between core permeability and well log attributes. Also, the LASSO regression has led to better results than BMA with the same observed-predicted response matching. Both of them have overcome the multicollinearity between two pairs of predictors. Consequently, BMA and LASSO are efficient approaches for multisource permeability modeling with high dimensional predictors.