## 4 Methodology
### Feature Creation  
When creating features for our models, Raoult's law and the gas molar weight equation in Section 3.3 assume that all the components and proportions of a given gas are known to compute the final pressure and molar weight. Although specifications indicate that no more than 2% of the LPG volume is compound by C5 hydrocarbons and that the sum of C2+C5 hydrocarbons must not exceed 5% of the LPG volume, a wide range of possible mixture proportions is observed in reality. In some scenarios, the C5 proportion exceeds the specifications, which is detrimental to propane and butane content. The same is observed for C2 content. In our model, we decided to consider five hypothetical LPG compositions as described in Table 2. Our hypothesis is that such simplifications could be useful towards understanding the real LPG composition given temperature and pressure sensor readings. To compute specific pressures given [PERSON]'s equations, and given the wide variety of C2 and C5 components, we approximated them with a single type of chemical compound: methyl-disulfide (C\({}_{2}\)H\({}_{6}\)S\({}_{2}\)), and pentane (C\({}_{5}\)H\({}_{12}\)). The constants for [PERSON]'s equations were obtained from the National Institute of Standards and Technology ([[https://webbook.nist.gov/](https://webbook.nist.gov/)]([https://webbook.nist.gov/](https://webbook.nist.gov/)) (accessed on 23 October 2021)), and the University of Maryland ([[https://user.eng.umd.edu/~nsw/chbe250/anto.dat](https://user.eng.umd.edu/~nsw/chbe250/anto.dat)]([https://user.eng.umd.edu/~nsw/chbe250/anto.dat](https://user.eng.umd.edu/~nsw/chbe250/anto.dat)) (accessed on 23 October 2021)), which cite the following scientific literature sources: [74; 75; 76; 77; 78; 79; 80; 81]. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline  & & & \multicolumn{3}{c}{**Unit A**} & & & & & **Unit B** & & & \\ \cline{2-13}  & **Mean** & **Stdev** & **min** & **25\%** & **50\%** & **75\%** & **Max** & **Mean** & **Stdev** & **min** & **25\%** & **50\%** & **75\%** & **Max** \\ \hline P1 (kg/cm\({}^{2}\)) & 7.42 & 0.29 & 6.54 & 7.28 & 7.43 & 7.60 & 8.32 & 4.98 & 3.84 & 0.00 & 0.00 & 7.61 & 8.02 & 8.78 \\ \hline T2 (\({}^{\circ}\)C) & 62.66 & 19.82 & 0.00 & 66.17 & 67.41 & 69.13 & 89.70 & 35.99 & 30.84 & 0.00 & 0.00 & 58.20 & 61.38 & 80.36 \\ \hline C5 (\%) & 0.63 & 1.15 & 0.00 & 0.02 & 0.17 & 0.70 & 6.52 & 0.04 & 0.11 & 0.00 & 0.00 & 0.00 & 0.03 & 0.74 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Description statistics for sensor and laboratory analysis data obtained for debutanizer _Unit A_ and _Unit B_. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**LPG Sample Mixture** & **C2H6S2** & **C3H8** & **C4H10** & **CSH12** \\ \hline
1 & 0.000 & 0.485 & 0.505 & 0.010 \\ \hline
2 & 0.000 & 0.480 & 0.500 & 0.020 \\ \hline
3 & 0.030 & 0.465 & 0.485 & 0.020 \\ \hline
4 & 0.000 & 0.465 & 0.485 & 0.050 \\ \hline
5 & 0.000 & 0.455 & 0.475 & 0.070 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Description of sample mixtures considered to compute expected pressure for certain temperature, given the mixture composition and constants from [PERSON]’s equations. For each of these scenarios, we estimated the T1 values using the Clausius-Clapeyron relation based on the enthalpy of vaporization we computed for a snapshot of data provided in debutanizer unit diagrams (see Figure 4). By analyzing temperature and pressure for three segments of measurements, we identified that high or low C5 content is likely associated with certain pressure thresholds. We thus created dummy variables considering those thresholds. In Table 3 we describe some of the features we developed for our machine learning models. We grouped then in _Feature Groups_, based on their common characteristics. Although features from _Features Group 1_ correspond to raw sensor readings, the rest of the features was developed based on physical principles and equations presented in Section 3.3.