Supporting plots and tables on vapour–liquid equilibrium prediction for synthesis gas conversion using artificial neural networks

This article contains data on vapor–liquid equilibrium modeling of 1533 gas-liquid solubilities divided over sixty binary systems viz. carbon monoxide, carbon dioxide, hydrogen, water, ethane, propane, pentane, hexane, methanol, ethanol, 1-propanol, 1-butanol, 1-pentanol, and 1-hexanol in the solvents phenanthrene, 1-hexadecanol, octacosane, hexadecane and tetraethylene glycol at pressures up to 5.5 MPa and temperatures from 293 to 553 K using literature data. The solvents are considered to be potentially significant in the conversion of synthesis gas through gas-slurry processes. Artificial neural networks limited to one hidden layer and up to five neurons in the hidden layer were used to predict the binary plots.


Value of the data
This data could be used by the broader scientific community as it shows the training and testing of artificial neural networks for a number of binary systems.
Different training algorithms could be used and compared with the performance described here.
Other computational methods and techniques could be used and compared with the data presented here.

Data
The data presented here is generated in preparation of a manuscript on vapour-liquid equilibrium (VLE) prediction for synthesis gas conversion using artificial neural networks (ANN) [1]. The experimental VLE data used in this study was obtained from Breman et al. [2]. Phase equilibrium modeling is a crucial element in describing the behavior of the Fischer-Tropsch (FT) reaction [3][4][5][6][7][8][9][10][11][12]. The FT reaction produces a range of hydrocarbons from light olefins and paraffins to heavy wax. Since we are comparing too many binaries to easily visualize, data for each binary is presented here. Then the summary of the overall results is published on the related paper [1]. The tables and figures presented here are unique; there is no duplication.

Experimental design, materials, and methods
An artificial neural network with input, hidden, and output layers was generated. The network was limited to one hidden layer and a maximum of five neurons in the hidden layer. A small network with the required accuracy is desirable for the speed of computation.
To validate the networks, the performance plots were generated for all the binary systems. The training and test curves for one representative system is presented in Fig. 1.
The performance plot does not indicate any major problems with the training. The training and test curves are very similar. If the test curves had increased significantly before the training curve increased, then it is possible that some overfitting might have occurred. The best training performance which is represented by the property tr.best_epoch indicates the iteration at which the validation performance reached a minimum. The training continued for 18 more iteration before the training stopped.
The next step is to evaluate the training state plot. The training record is used to plot the training state plot.
Another plot used to validate the network performance is the error histogram presented in Fig. 2. The error histogram plots a histogram of error values. It computes the error values as the difference between target values and predicted values, helping us to visualize the networks error.
The low values in the error histogram are an indication of a good network performance. The final step in validating the network results is by plotting a regression plot shown in Fig. 3. The solid line in the plot represents the best linear fit regression between outputs and targets.   Fig. 3, it can be observed that training was perfect. The R value of 1 for the training and test data indicates that there is an exact linear relationship between our inputs and targets.
It is important to note that the plots in Figs. 1-3 were obtained after training one of the binary system, and is used to represent the plots obtained when training the entire binary system since similar plots were also obtained for each binary system.
The percentage MAE, and RMSE across each system are presented in Table 1.
The experimental values versus the predicted values for the X i and Y i for all the 60 binaries denoted (A1-A60) are presented in Figs. 4-15.