Use of neural networks for prediction of vapor-liquid equilibrium k-values for light hydrocarbon mixtures

Abstract

A new method for prediction of vapor-liquid equilibrium ratios (K-values) was developed. The new method is based on the new technology of neural networks, and predicts K-values of a component in a mixture as a function component identity, mixture pressure, temperature, and convergence pressure. About 8000 experimentally determined K-values were collected from different publications. The data represent K-values for Methane through normal-Decane in different binary, ternary, and multicomponent mixtures. The collected data was used to train a neural network. Input to the network were: component's molecular weight and specific gravity, mixture pressure, temperature, and convergence pressure. The output of the network was the component's K-value for the required pressure and temperature. The average absolute error for training data (8000 points) was at about 4.7%. After training the network, the final network was tested. Five sample tests were obtained from the literature that were not part of the training data. Each sample consisted of experimental K-values, compositional analysis, and dew-point pressure data. The samples represented three mixtures at different temperatures. The neural network predicted K-values for every component in all mixtures, with an overall average absolute error of about 8%. The experimental data did not include convergence pressure, and was calculated using the dew point pressure. Neural network K-value predictions were compared to different published Kvalue methods and are shown to have better accuracy for the samples used in testing. Furthermore the neural network method is explicit and doesn't involve iterations to determine K-values. eccentricity causing a decreased seal effectiveness is examined, along with the corresponding increase of blade root/retainer and cavity averaged temperature. It is found that the minimum coolant flow C,,.i,, required to prevent the ingress increases markedly with rotor eccentricity, even for small eccentricity values, in an almost linear fashion. For 25 percent eccentricity, the highest blade root/retainer adiabatic temperature for C,, = 3600 is 49 percent higher than that for Cv = 7200. whereas for 12.5 percent eccentricity it is only 20 percent higher. In addition, the circumferential location of the maximum ingress velocity was found at a 30' retarded phase angle (measured from the circumferential location of maximum seal clearance).