New Vision into Relative Permeability Estimation Using Artificial Neural Networks

Artificial intelligence (AI) has proven to be the smartest predicting tool in the oil and gas industry. In this paper, Artificial Neural Network (ANN) algorithm was applied to build two new empirical correlations to predict relative permeability profiles of oil-water two phase flow in the reservoir for both sandstone and carbonate reservoirs. The proposed model evaluates the relative permeability as a function of porosity, rock absolute permeability, initial water saturation, residual oil saturation, wettability index and water saturation. Accordingly, relative permeability to water and oil are respective outputs. Real data of both sandstone and carbonate reservoirs taken from literature were used in the development of the new empirical correlations. Multiple realizations with various hidden layer neurons were run to find the best scenario; and maximum coefficient of determination (R²) was designated as the finest case. The weights and biases values were found for the models of relative permeability to water and oil after proper training and are presented in this paper. Tan-sigmoid and linear transfer functions were utilized in the hidden and output layers, respectively. Neural Network was trained using Levenberg-Marquardt back-propagation algorithm. The novel ANN model was able to accurately estimate relative permeability to oil and water for an unseen data set of 319 real data points. Root mean squared error for both models are near to zero, while R² for relative permeability to oil and water is 0.92 and 0.98, respectively. The relative permeability models are presented in the form of an actual mathematical correlation. The use of the developed ANN models significantly saves time and cost for conducting experiments for relative permeability measurements.