Using artificial neural networks to estimate the z-factor for natural hydrocarbon gases

Abstract

Gas compressibility factor ( z-factor) is an important parameter widely used in petroleum and chemical engineering. Accurate and fast calculation of this parameter is of crucial need and challenges a large number of simulators used in petroleum engineering. The Standing–Katz chart was published in 1942 and since then has been considered an industry standard. Several methods have been tried and developed to calculate z-factor by fitting models on the smoothed Standing–Katz data. Some of these models are the Dranchuk and Abou-Kassem (DAK), the Nishiumi–Saito, the Nishiumi, and the Brill–Beggs correlations. All models developed afterwards the Standing–Katz charts present some limitation like instability close to certain boundaries, convergence, and/or accuracy. In fact, different correlations tend to fit better to a particular area of the domain for P pr and T pr (pseudo-reduced pressure and temperature), but fail badly close and beyond to their limits. Also, most correlations require iterative procedures to obtain the corresponding z-factor, and may even present different results dependent on the initial guess for the initial iteration. The DAK correlation is one of the most widely used models. In this study we propose and develop a methodology to obtain z-factors for Natural Hydrocarbon Gases using Artificial Neural Networks (ANN). Data obtained directly from the Standing–Katz and Katz compressibility charts were used to train several topologies of ANN. The input parameters in the ANN are the pseudo-reduced pressure and temperature and the output is the z-factor. Two of the successful networks have two hidden layers. The first ANN uses five neurons in each hidden layer and the second ANN uses ten neurons in each hidden layer (called 2-5-5-1 and 2-10-10-1 networks respectively). These topologies were trained with the data from the charts using a back-propagation training algorithm. The results are compared with the charts (with values not used during the training section), along with the results obtained using DAK correlation. In addition, performance comparisons were made between the ANN model and the DAK correlation. In both situations, the ANN models are superior to the DAK correlation. In addition, the ANN model covers a wider range of P pr and T pr , which surpasses the limits of all other correlations together. Typically, the time needed to obtain results for a 2-5-5-1 network corresponds to the time of one single iteration needed for the DAK correlation. The paper discusses these results, and provides the weight sets (values of synapses and biases) needed to reproduce the ANN, which can be easily implemented in an electronic spreadsheet.