Deterministic Modeling to Predict the Natural Gas Density Using Artificial Neural Networks

During the past decades, several research studies have been made to unfold the immense and diversified benefits of the innovative applications of machine learning (ML) techniques in the petroleum industry. For instance, machine learning algorithms were applied to estimate the various physical properties of natural gas. Natural gas density is considered an indispensable metric that influences the determination of several variables necessary for analyzing natural gas systems. In this work, the Artificial neural network (ANN), a machine learning technique, was applied to estimate natural gas density incorporating the influencing factors. The ANN model was also compared with another ML technique, namely the Adaptive Neuro-Fuzzy Inference System (ANFIS). A mathematical form has been also presented using ANN. A real data set was taken from the literature, comprised of about 4500 data points assimilating three influencing input variables, including pseudo-reduced pressure (PPr), pseudo-reduced temperature (TPr), and molecular weight (Mw). The PPr and TPr are obtained by calculating the averages of the sample gas critical pressures and critical temperatures. A complicated nonlinear relationship exists between the three influencing variables and the gas density. The data set was divided into a 70:30 ratio for training and testing the model, respectively. Adaptive Neuro-Fuzzy Inference System (ANFIS) and Artificial Neural Networks (ANN) were applied to train and test the model. Absolute average percentage error (AAPE), coefficient of determination (R2), and root mean squared error (RMSE) were considered in the error metrics to acquire the best possible model. Levenberg–Marquardt backpropagation algorithm was employed for ANN, while subtractive clustering was used for ANFIS. Results showed that natural gas density can be well correlated with numerous inputs using machine learning tools (ANN and ANFIS). The input parameters include Ppr, Tpr, and Mw, as mentioned above. ANN performed better than ANFIS. The network was adjusted against the training sub-set to set-up weights and biases covering each node. R2 for both testing and training data was more than 99%, while AAPE was around 4% for both cases. Moreover, a detailed mathematical scheme for the ANN model is also provided in this paper.