New Correlation for the Gas Deviation Factor for High-Temperature and High-Pressure Gas Reservoirs Using Neural Networks

The gas deviation factor (Z-factor) is an effective thermodynamic property required to address the deviation of real gas behavior from that of an ideal gas. Empirical models and correlations to compute Z-factor based on equation of states are often implicit because they needed a huge number of iterations and thus were computationally very expensive. Many explicit empirical correlations are also reported in the literature to improve the simplicity; yet, no individual explicit correlation was formulated for the complete full range of pseudoreduced temperatures and pseudoreduced pressures, which demonstrates a significant research gap. The inaccuracy in determining the gas deviation factor will result in a huge error in computing subsequent natural gas engineering properties such as gas expansion factor (E g ), formation volume factor (B g ), gas compressibility (c g ), and original gas in place. Previously reported empirical correlations provide better estimation of the gas deviation factor at lower pressures, but at higher reservoir pressures, their accuracies become questionable. One of the examples of high-pressure reservoirs is the abnormal pressured reservoir, where the reservoir pressure exists up to 20 000 psia. In this study, an improved Z-factor empirical correlation is presented in a linear fashion using a robust artificial intelligence tool, the artificial neural network (ANN). The new correlation is trained on more than 3000 data points from laboratory experiments obtained from several published sources. The proposed correlation is only a function of pseudoreduced temperature (T pr ) and pseudoreduced pressure (p pr ) of the gases, which makes it easier to implement than the reported implicit and complicated explicit correlations. The proposed correlation can be valid for p pr ranges between 0.1 and 40 and T pr ranges between 1.05 and 3.05. The accuracy and generalization capabilities of the proposed ANN-based correlation are also tested against previously published correlations at low and high gas reservoir pressures on an unseen published dataset. The comparative results on a published dataset show that the new correlation outperformed other methods of predicting Z-factor by giving less average absolute percentage error, less root-mean-square error, and high coefficient of determination (R 2 ). The error obtained was less than 3% compared to the measured data, while the other correlations predicted the gas deviation factor with an error up to 4% at low pressure and up to 20% at high pressure. The new proposed ANN-based correlation can be utilized to estimate the Z-factor at any pressure range (on which the model is trained) especially for high pressures. The new proposed correlation is very easy to be used, and it requires only the gas-specific gravity that is needed to determine the pseudocritical properties of the real gas and from which the Z-factor can be determined.