## 3 Results and Discussion
### Prediction of Optimal Salt Concentration for Diesel  
The phase behavior of the SDHS-AAE(6 EO4 PO) system with commercial diesel was investigated with different anionic-nonionic mixing ratios at reference temperature (25 \(\pm\) 2 \({}^{\circ}\)C). It was found that the middle phase appeared as a thin layer between the water and the oil phases. Table 2 shows the optimal salt concentration (S*) and the minimum IFT (IFT*) of the diesel system. The anionic-nonionic mixing ratio did not affect optimal salt concentration. All the ratios showed the same result for S*, which was 9% wt/v NaCl. However, the anionic-nonionic ratio affected the IFT* value. The IFT* tended to decrease when AAE(6 EO4 PO) increased. For example, the IFT* of 0.07 mN/m for the 9:1 ratio was reduced to 0.02 for the 5:5 ratio. The IFT* results did not reach ultralow interfacial tension [17,18]. The EACN of the commercial diesel in this study was 9.10 \(\pm\) 0.51, which was determined from our previous studies [51]. Due to our knowledge of the value of EACN, the optimal salt concentration could be predicted via the HLD and HLD\({}_{\text{N}}\) equations. The three  
Figure 8: The average interaction terms of each anionic-nonionic ratio of SDHS-AAE(6 EO4 PO) systems. Figure 7: The interaction terms of SDHS-AAE(6 EO4 PO) systems. scenarios were conducted, including HLD (Equation (9)), HLDN with average interaction term (Equation (12)), and HLDN based on nonionic mole fraction (Equation (13)). Figure 9 presents the optimal salt concentrations from the experiment, with three case predictions. It was found that the optimal salt concentration by HLD prediction did not fit with linear regression, while the other two predictions by HLDN (i.e., HLDN,average, HLDN,basedxn) could fit with the linear trends (R2 \(>\) 0.99). The HLD equation predicted optimal salt concentrations lower than in the actual experiment, in contrast to the HLDN based on mole fraction. Equations (9) and (13) were more precise when estimating the optimal salt concentrations at the low AAE(6 EO4 PO) fraction than regarding the high weight of AAE(6 EO4 PO). In the case of HLDN with an average interaction term, the results showed that it was close to the experimental value when AAE(6 EO4 PO) in the mixed system increased. The errors between experimental results and the predictions of salt concentrations were 1.89-7.44, 1.11-9.62, and 0.28-9.54% for HLD/HLDN with the average interaction term, and HLDN based on mole fraction, respectively. The precision in all cases was more than 90%. Thus, both HLDSDHS-AAE(6 EO4 PO) and HLDN, SDHS-AAE(6 EO4 PO) equations had high efficiency. As noted, the precisions of the optimal salt-concentration prediction between HLDSDHS-AAE(6 EO4 PO) and HLDN, SDHS-AAE(6 EO4 PO) differences cannot be compared because the K values (Ki and Kn) of SDHS and AAE(6 EO4 PO) are too close [29; 52]. Moreover, the effect of polydispersity of the EO and PO groups in the extended surfactant (i.e., industrial grade) on the prediction was not considered in this study. In this case, the HLD and HLDN equations are useful prediction tools to reduce the time-consuming nature and cost of the experimental process. They can be applied to many applications, especially petroleum oil-based cleaning/decontamination and soil remediation. Optimal conditions are crucial for environmental and economic considerations in large-scale clean-up--however, there is one important point to consider before applying the HLD equation. In the case of the mixed surfactant, the K values of each surfactant need to be determined. If the K values are close, both HLD and HLDN equations can be applied. When the K values are different, the HLDN equation might be better to use for more precision. For optimal prediction, the EACN of the targeted oil should be determined. Therefore, the time period was required when investigating the EACN of the targeted oil. In addition, the HLD and HLDN equations should be formulated from the oils, with EACNs covering the targeted oil.