# Solubility/Insolubility: A Possible Option for Recycling Polystyrene
## 3 Results
### Process Simulation Results  
The thermodynamic model used for this design was the Non-Random Two Liquids (NRTL) model. The binary interaction parameters for the ethanol and D-limonene mixture were adjusted based on experimental data using the regression analysis tool included in the process simulator. The Interior Point Optimizer (IPOPT) method was employed, and the Objective Function (_OF_) was as follows [40]:  
\[OF=\text{min}{\sum\limits_{i=1}^{NP}\sum\limits_{j=1}^{NC}\left[\frac{y_{i,j}^{ exp}-y_{i,j}^{cal}}{y_{i,j}^{exp}}\right]^{2}} \tag{13}\]  
Two isobaric databases for the ethanol + D-limonene mixture have been found in the literature, one at a pressure of 40 kPa [25] and another at a pressure of 101.3 kPa [41]. The parameter values are presented in Table 1. The Root-Mean-Square Deviation (RMSD) for the vapor composition was 0.017 at 40 kPa and 0.038 at 101.3 kPa. The RMSD for temperature was 2.3 K at 40 kPa and 3.7 K at 101.3 kPa. \begin{table}
\begin{tabular}{c c} \hline
**Parameter** & **Value** \\ \hline \(A_{12}\) & 1182.40 cal/mol \\ \(A_{21}\) & \(-\)48.956 cal/mol \\ \(\alpha_{12}\) & 6.1 \(\times\) 10\({}^{-3}\) \\ \end{tabular}
\end{table} 
Table 1: Binary interaction parameters of the NRTL equation of state for ethanol (1) + D-limonene (2) mixture. Figure 4: The influence of ethanol in a stirred tank on the behavior of a polystyrene (PS) composition in extract and mass flow in raffinate. The solid line represents the flow of PS in the raffinate, while the dashed line represents the mass composition of PS in the extract. The dotted line indicates a flow rate of 15 kg/s of ethanol, with a recovery efficiency of 99% for solid PS in the raffinate. The DWSIM process simulator does not have specific features for polymer processes, but it is still possible to utilize the Compound Creator wizard for this purpose. The PS was defined by incorporating data on the molecular weight determined in this study, and the standard boiling point was supposed to be 673.15 K, considering that polymers start to boil before decomposition [42], the melting temperature (513.15 K) [43], and the density of the solid phase (0.92 g/cm\({}^{3}\)) [42]. The conceptual design of the process considered the results from the previous section, which included a flow of a mixture consisting of 100 kg/s of PS (52% \(w/w\)) and D-limonene (48% \(w/v\)), as well as a fresh ethanol feed of 15 kg/s. The initial scheme examined consisted of a mixer to merge the feed streams and a compound separator. The design variable for the separator was set to achieve a recovery rate of 99%. The resulting solvent mixture consists of 75.6% w of D-limonene, 23.6% w of ethanol, and 0.8% w of PS. A distillation column was designed using the shortcut method module, with ethanol selected as the light key component and D-limonene as the heavy key component. A proposal was made to achieve a recovery rate of 99.99% for the key components located in both the dome and bottom. The specified pressure for the condenser was 206.8 kPa (30 psia), while for the reboiler it was 241.3 kPa (35 psia), with the utilization of a total condenser. A sensitivity analysis was conducted to determine the minimum reflux ratio (R\({}_{\text{min}}\). The reflux ratio was varied from 1.2 to 20 times R\({}_{\text{min}}\). It was found that a reflux ratio of 1.5 reduces the number of stages without impacting the quality of the distillate. The findings are displayed in Table 2.  
The final design of the distillation column was determined using the rigorous method, which involved six equilibrium stages and feeding on plate four. After achieving convergence, the proposal for the recirculation of solvents was presented, as depicted in Figure 5. The temperature in Stream 16 is extremely high. This is because the property dataset for PS is not sufficient. Because the amount of PS in other currents is insignificant, this does not affect the thermodynamic properties of other streams.