The following results will present the revised UNIFAC Dortmund binary interaction parameters for NaCl and KCl, the two sets of calculated VLE obtained for systems with salt using the existing parameters from the literature and the revised parameters of this study, the comparison of the two sets of calculated VLE with the experimental VLE of the systems, and the comparison of error values obtained for both sets of calculated VLE.
5.3.1 Revised UNIFAC Dortmund Parameters for Interactions with NaCl and KCl
The revised UNIFAC Dortmund parameters for binary interactions involving the ions of NaCl and KCl are presented as follows in Table 5.32:
Table 5.32. Revised UNIFAC Dortmund bmk Parameters for Binary Interactions with NaCl and KCl
Main Group 1 Main Group 2 Binary Interaction Parameters
b12 b21
Cl- OH -13.027 NR*
H2O -0.29409 NR*
Na+ -1.0938 NR*
K+ -1.5551 NR*
Na+ OH 9.2317 14.412
H2O 0.32527 2.0391
K+ OH 1.4813 0.67464
H2O 0.37276 1.3684
* Not revised
It is observed that only the bmk parameters are presented which are the only constants that were successfully revised from the parameters provided by Aznar & Telles (2001). It is because in the parameter estimation process, only these parameters have been observed to have significant changes in the iterations. As shall be discussed in the following sections, these revised parameters are more reliable in the prediction of VLE of systems with NaCl and KCl than the existing parameters of the previous authors.
5.3.2 Comparison of Experimental and Calculated VLE for Systems with NaCl and KCl
The experimental and calculated VLE for systems with NaCl and KCl, as well as the results of the comparison of the VLEs are presented in this section. The greater reliability of the revised parameters than the existing parameters from the literature will be shown in this section which will be supported by the discussion of molecular interactions.
5.3.2.1 Binary Systems with Salt
The experimental and calculated values for the binary systems with salt and the results of the comparison are as follows:
Table 5.33. Experimental and Calculated Bubble Points of Water (2) + NaCl (8) System
Bubble Point (T, K) Experimental Aznar & Telles
(2001) This Study
(2020) Experimental Aznar & Telles
(2001) This Study (2020)
326.55 325.79 325.79 345.95 346.42 345.47
327.65 327.23 327.22 352.45 353.01 352.04
331.95 332.13 332.13 357.85 358.52 357.54
337.55 337.65 337.65 362.05 362.70 361.70
345.35 345.16 345.16 365.85 366.49 365.48
350.45 350.61 350.60 371.25 372.02 370.98
356.85 356.90 356.90 335.35 336.92 334.66
361.65 361.92 361.91 343.65 345.19 342.86
364.25 364.42 364.42 350.95 352.61 350.21
370.15 370.38 370.38 356.65 358.24 355.79
326.95 326.56 326.28 361.15 362.77 360.27
330.85 330.50 330.21 365.35 366.91 364.38
338.15 338.03 337.74 369.15 370.79 368.21
342.05 342.18 341.88 372.65 374.34 371.74
351.75 351.93 351.63 337.55 341.95 336.86
356.95 357.25 356.94 346.65 351.10 345.79
361.35 361.81 361.50 353.85 358.34 352.85
364.85 365.28 364.96 359.05 363.53 357.91
370.45 370.99 370.67 363.55 368.10 362.37
Table 5.33. Experimental and Calculated Bubble Points of Water (2) + NaCl (8) System (continued)
Bubble Point (T, K) Experimental Aznar & Telles
(2001) This Study
(2020) Experimental Aznar & Telles
(2001) This Study (2020)
328.25 328.10 327.20 368.05 372.53 366.68
331.95 331.95 331.04 371.55 376.14 370.20
338.25 338.45 337.53 375.15 379.75 373.71
338.45 338.73 337.81
Table 5.34. Calculated Error Values for Water (2) + NaCl (8) System
Metrics Bubble Point Errors (K)
Aznar & Telles (2001) This Study (2020)
SE 2.14 0.74
RMSE 2.04 0.71
AAD 1.31 0.59
%AARD 0.37% 0.17%
Table 5.35. Calculated Squared Errors and Coefficients of Determination for Water (2) + NaCl (8) System
Metrics Values for Bubble Point
Aznar & Telles (2001) This Study (2020)
SSE 102.52 10.51
MSE 2.38 0.24
r2 0.9902 0.9989
r2 (adj.) 0.9900 0.9989
For water (2) + NaCl (8) system, the experimental as well as the calculated bubble points using the parameters of Aznar & Telles (2001) and the revised parameters of this study are shown in Table 5.33. The calculated bubble points using the revised parameters are shown to be closer to the experimental bubble points than those obtained from the parameters of the previous authors. This can be supported using the calculated error values and coefficients of determination in Tables 5.34-5.35, where the bubble point deviations resulted from the application of the revised parameters are lower than those of the parameters of the previous authors.
Figure 5.22. Comparison of Experimental and Calculated Bubble Points of Water (2) + NaCl (8) System
Figure 5.23. Pressure-Temperature Diagram for Water (2) + NaCl (8) System Using the Revised Parameters 320
325 330 335 340 345 350 355 360 365 370 375 380
320 325 330 335 340 345 350 355 360 365 370 375 380
T (Calculated, K)
T (Experimental, K) This Study (2020)
Aznar & Telles (2001)
320 325 330 335 340 345 350 355 360 365 370 375 380
10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95
Temperature, K
Pressure, kPa
w = 0 w = 0.00356 w = 0.04015
w = 0.07981 w = 0.14365 w = 0.25618
The qualitative comparison of experimental and calculated bubble points for water (2) + NaCl (8) system is shown in Figure 5.22-5.23. There are two sets of data points which corresponds to the revised parameters of this study and the parameters of Aznar & Telles (2001). As can be observed, the data points for the revised parameters are closer to the diagonal line than those of the parameters of the previous authors. This is because as shown in Table 5.34, lower error values are obtained for the revised parameters than the existing parameters from the literature. Thus, the revised parameters are more reliable for the calculation of bubble points in this system than the existing parameters.
A pressure-temperature diagram in Figure 5.23 was constructed to see whether the UNIFAC Dortmund model can show the increase in the bubble point with the increase in the concentration of NaCl across different pressures. A good depiction of the bubble point elevation upon the addition of salt can be observed, showing the reliability of the UNIFAC Dortmund model for this system.
It has been reported from the experimental data that NaCl increases the bubble point of the solution, hence also lowering the vapor pressure of water. This is mainly because of the strong attraction of water molecules with Na+ and Cl- ions, where the electrostatic field around ions causes a constant number of water molecules to surround them. Furthermore, it has been observed experimentally for alkali chloride solutions that Na+ is surrounded by water molecules which are twice as many as that of Cl- ions. This is because of the small size of Na+ which causes it to have greater charge density per unit volume and hence a higher number of attracted water molecules. Therefore, this ion is mainly responsible for the increase in the bubble point of the solution.
The UNIFAC Dortmund model using the revised parameters also showed that the same interactions are present in the solution. Based on the 𝜏𝑚𝑘 values, the interaction of ions with water is stronger than the interaction of water molecules with each other. Hence, the model also predicted the hydration of ions in the solution. Furthermore, the 𝜏𝑚𝑘 value for Na+-H2O is higher than Cl--H2O, which confirms that Na+is surrounded by more water
experimental data is the reason why the UNIFAC Dortmund model and the revised parameters are reliable in the prediction of the bubble points of the system.
Using the parameters of Aznar & Telles (2001), the same interactions can also be observed except that the Na+-H2O was predicted to be slightly stronger due to higher calculated 𝜏𝑚𝑘 value, which leads to a slight overestimation of the bubble points as shown by the points that are above the diagonal line in Figure 5.22. Because of the resulting deviation from the experimental bubble points, the revised parameters become more reliable for estimation than the parameters of the previous authors.
Table 5.36. Experimental and Calculated Bubble Points for Water (2) + KCl (9) System
Bubble Point (T, K) Experimental Aznar & Telles
(2001) This Study
(2020) Experimental Aznar & Telles
(2001) This Study (2020)
327.55 327.26 327.26 359.65 360.29 359.62
333.45 333.29 333.28 363.75 364.45 363.77
342.45 342.34 342.33 367.25 367.92 367.23
349.15 349.11 349.10 371.05 371.77 371.07
354.55 354.58 354.57 328.45 329.57 327.96
359.15 359.19 359.18 334.45 335.65 334.00
363.05 363.20 363.19 343.65 344.79 343.08
366.55 366.76 366.75 350.55 351.63 349.88
370.15 370.36 370.35 356.05 357.16 355.37
327.45 327.65 327.48 360.85 361.87 360.05
333.45 333.69 333.51 364.85 365.96 364.11
342.55 342.75 342.58 368.45 369.52 367.64
349.25 349.54 349.36 371.95 373.07 371.16
354.65 354.97 354.79 330.45 332.13 328.54
359.25 359.65 359.46 336.55 338.27 334.57
363.25 363.67 363.48 345.65 347.49 343.63
366.75 367.24 367.05 352.55 354.40 350.41
370.35 370.88 370.69 358.15 359.98 355.89
Table 5.36. Experimental and Calculated Bubble Points for Water (2) + KCl (9) System (continued)
Bubble Point (T, K) Experimental Aznar & Telles
(2001) This Study
(2020) Experimental Aznar & Telles
(2001) This Study (2020)
327.65 328.28 327.67 362.75 364.69 360.52
333.85 334.55 333.93 366.95 368.83 364.58
342.75 343.34 342.71 370.45 372.42 368.11
349.45 350.11 349.46 374.15 376.23 371.85
355.15 355.73 355.07
Table 5.37. Calculated Error Values for Water (2) + KCl (9) System
Metrics Bubble Point Errors (K)
Aznar & Telles (2001) This Study (2020)
SE 1.08 1.08
RMSE 1.03 1.03
AAD 0.82 0.63
%AARD 0.23% 0.18%
Table 5.38. Calculated Squared Errors and Coefficients of Determination for Water (2) + KCl (9) System
Metrics Values for Bubble Point
Aznar & Telles (2001) This Study (2020)
SSE 18.60 34.10
MSE 0.43 0.79
r2 0.9980 0.9962
r2 (adj.) 0.9980 0.9962
For water (2) + KCl (9) system, the experimental and calculated values at VLE are presented in Table 5.36. Approximately the same agreement with the experimental values can be observed from the two sets of calculated values obtained using the revised parameters and the parameters of Aznar & Telles (2001). This can also be seen in the error values and coefficients of determination in Tables 5.37-5.38, where the values for both parameters are almost equal with each other.
Figure 5.24. Comparison of Experimental and Calculated Bubble Points of Water (2) + KCl (9) System
Figure 5.25. Pressure-Temperature Diagram for Water (2) + KCl (9) System Using the Existing Parameters from the Literature
320 325 330 335 340 345 350 355 360 365 370 375 380
320 325 330 335 340 345 350 355 360 365 370 375 380
T (Calculated, K)
T (Experimental, K) This Study (2020)
Aznar & Telles (2001)
320 325 330 335 340 345 350 355 360 365 370 375 380
10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95
Temperature, K
Pressure, kPa
w = 0 w = 0.00807 w = 0.0393
w = 0.07943 w = 0.14234 w = 0.23466
The comparison of experimental and calculated bubble points for the binary system for water (2) + KCl (9) system are shown in Figure 5.24. It can be seen that both the revised parameters and the parameters of Aznar & Telles (2001) calculated bubble points that are equally close to the experimental bubble points, which is consistent with the approximately equal errors obtained in Table 5.37. Hence, any of these parameters can be used to accurately predict the bubble points of the system at different pressures. A good representation of the increase in the bubble point with the increase in salt concentration is also provided by the UNIFAC Dortmund model as shown in the pressure-temperature diagram in Figure 5.25.
It is also observed that the addition of KCl increases the bubble point of the solution and decreases the vapor pressure of water. This is also because of the electrostatic field of the ions that attract the water molecules. Moreover, the cation K+ is surrounded by more water molecules than Cl- with the same reason as that of Na+ in the previous system, which is due to its smaller size and hence greater charge density per unit volume. However, since K+ is larger than Na+, it is only surrounded by less water molecules than Na+. Hence, this is the reason why based on the experimental data, the bubble point elevation caused by KCl is lower than that of NaCl.
Similar descriptions of the interactions were also obtained using the UNIFAC Dortmund model and the revised parameters of this study. The 𝜏𝑚𝑘 values show that K+- H2O is stronger than Cl--H2O, hence, K+ is surrounded by more water molecules than Cl-. It has also been observed by the comparison of 𝜏𝑚𝑘 values of two binary systems with salt that Na+-H2O is stronger than K+-H2O. Therefore, the UNIFAC Dortmund model and the revised parameters also confirms that the smaller the ionic size, the greater the number of water molecules that will surround a given ion.
The parameters of Aznar & Telles (2001) also predicted the same interactions except that the bubble points are still slightly overestimated due to higher 𝜏𝑚𝑘 values calculated for the K+-H2O interaction. Nevertheless, good prediction of bubble points was still obtained using these parameters.
5.3.2.2 Ternary Systems with Salt
The experimental and calculated values at VLE for the ternary systems with salt as well as the results of their comparison are shown as follows:
Table 5.39. Experimental and Calculated Bubble Points for Ethanol (1) + Glycerol (3) + NaCl (8) System
Bubble Point (T, K) Experimental Aznar & Telles
(2001) This Study
(2020) Experimental Aznar & Telles
(2001) This Study (2020)
353.35 352.21 352.21 378.75 384.49 384.49
354.95 356.84 356.85 381.65 390.61 390.61
358.55 362.03 362.03 396.05 404.05 404.05
364.15 369.64 369.64 408.15 412.43 412.44
372.35 377.98 377.98 424.35 426.09 426.09
Table 5.40. Calculated Error Values for Ethanol (1) + Glycerol (3) + NaCl (8) System
Metrics Bubble Point Errors (K)
Aznar & Telles (2001) This Study (2020)
SE 9.62 9.62
RMSE 5.27 5.27
AAD 4.63 4.64
%AARD 1.22% 1.22%
Table 5.41. Calculated Squared Errors and Coefficients of Determination for Ethanol (1) + Glycerol (3) + NaCl (8) System
Metrics Values for Bubble Point
Aznar & Telles (2001) This Study (2020)
SSE 78.95 78.93
MSE 9.87 9.87
r2 0.9856 0.9856
r2 (adj.) 0.9838 0.9838
For ethanol (1) + glycerol (3) + NaCl (8) system, the experimental and calculated values at VLE are shown in Table 5.39. The calculated bubble points using the revised parameters and the parameters of Aznar & Telles (2001) are almost equal with each other, which is the reason why almost equal values of the error values and coefficients of determination from the experimental data are also obtained as shown in Tables 5.40-5.41.
Figure 5.26. Comparison of Experimental and Calculated Bubble Points of Ethanol (1) + Glycerol (3) + NaCl (8) System
350 360 370 380 390 400 410 420 430
350 360 370 380 390 400 410 420 430
T (Calculated, K)
T (Experimental, K) This Study (2020)
Aznar & Telles (2001)
Figure 5.27. Temperature-Concentration Diagram for Ethanol (1) + Glycerol (3) + NaCl (8) System
The comparison of the experimental and the calculated bubble points for ethanol (1) + glycerol (3) + NaCl (8) are shown in Figure 5.26. It can be seen that the calculated bubble points using both the revised parameters of this study and the parameters of Aznar & Telles (2001) are close to the experimental bubble points of the system. Since the corresponding data points for both sets of parameters coincide with each other, both sets of parameters can provide the same bubble point predictions for the given system. A temperature- concentration diagram in Figure 5.27 was also constructed which also shows the same results mentioned.
When the experimental bubble points of this system are compared to those of the same ethanol and glycerol system but without the presence of salt, the bubble points are almost equal with each other. This seems to shows that the addition of salt has a negligible effect on the bubble point and the salting-out phenomenon in the mixture. According to Faggion et al. (2016), this is because of the low solubility of the salt in the mixture of organic solvents.
350 360 370 380 390 400 410 420 430
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Temperature, K
Mass Fraction of Ethanol (NaCl-Free Basis) Faggion et al. (2016) This Study (2020) Aznar & Telles (2001)
Using the UNIFAC Dortmund model and the revised parameters of this study, an increase in the bubble point and a preferential salting-out of ethanol is observed upon the addition of NaCl. The increase in the bubble point is primarily caused by the strong interaction of ions with the OH subgroups, which have high 𝜏𝑚𝑘 values in the mixture. Since glycerol has several OH subgroups, then ions could have strong interactions with glycerol than with ethanol. As a result, glycerol is predicted to be preferentially salted-in into the solution while the ethanol is preferentially salted-out as a consequence.
However, based from the model, the increase in the bubble point upon the addition of salt is only about 0.01°C. It is found out that the small elevation in the bubble point is due to the negligible solubility of the salt in the solvent mixture, which is the same as the one reported in the experimental results. The same results can also be obtained using the parameters of Aznar & Telles (2001) in the UNIFAC Dortmund model.
Table 5.42. Experimental and Calculated Bubble Points for Water (2) + Glycerol (3) + NaCl (8) System
Bubble Point (T, K) Experimental Aznar & Telles
(2001) This Study
(2020) Experimental Aznar & Telles
(2001) This Study (2020)
372.05 371.91 370.50 379.85 373.72 373.60
372.95 372.43 371.41 381.45 373.56 373.66
373.75 372.66 371.90 384.05 373.57 373.86
375.35 372.81 372.51 387.25 373.89 374.31
379.85 372.41 372.68 392.15 374.80 375.32
381.85 372.36 372.69 395.55 376.25 376.82
385.05 372.48 372.88 411.55 387.43 388.07
387.55 372.73 373.15 375.95 376.09 371.76
388.75 372.97 373.40 376.05 376.12 371.83
391.85 373.86 374.29 376.45 376.30 372.42
395.55 375.09 375.52 377.05 376.40 372.97
400.55 376.85 377.29 377.55 376.41 373.62
373.05 373.58 370.82 380.75 375.74 374.62
Table 5.42. Experimental and Calculated Bubble Points for Water (2) + Glycerol (3) + NaCl (8) System (continued)
Bubble Point (T, K) Experimental Aznar & Telles
(2001) This Study
(2020) Experimental Aznar & Telles
(2001) This Study (2020)
373.65 373.81 371.31 382.35 375.38 374.81
373.95 373.98 371.73 385.85 375.22 375.29
374.65 374.19 372.40 388.95 375.68 376.03
375.05 374.24 372.71 392.65 376.21 376.68
375.65 374.25 372.98 398.35 380.31 381.04
376.55 374.17 373.30 402.95 383.69 384.48
378.15 373.98 373.50 419.15 413.13 414.03
Table 5.43. Calculated Error Values for Water (2) + Glycerol (3) + NaCl (8) System
Metrics Bubble Point Errors (K)
Aznar & Telles (2001) This Study (2020)
SE 12.46 12.30
RMSE 11.32 11.17
AAD 8.32 8.99
%AARD 2.12% 2.30%
Table 5.44. Calculated Squared Errors and Coefficients of Determination for Water (2) + Glycerol (3) + NaCl (8) System
Metrics Values for Bubble Point
Aznar & Telles (2001) This Study (2020)
SSE 847.78 677.37
MSE 22.31 17.83
r2 0.5179 0.6617
r2 (adj.) 0.5053 0.6528
Table 5.45. Experimental and Calculated Bubble Points for Water (2) + Glycerol (3) + KCl (9) System
Bubble Point (T, K) Experimental Aznar & Telles
(2001) This Study
(2020) Experimental Aznar & Telles
(2001) This Study (2020)
371.85 372.10 370.44 373.75 374.07 370.87
372.65 372.24 370.76 374.75 374.13 371.78
373.45 372.46 371.44 375.85 374.02 372.41
374.05 372.53 371.81 377.25 373.69 372.92
374.95 372.51 372.14 380.35 373.05 373.25
375.75 372.44 372.29 383.35 372.95 373.54
378.45 372.09 372.40 387.45 373.80 374.61
383.75 371.98 372.53 389.55 374.36 375.22
389.55 372.94 373.54 395.35 376.47 377.40
395.85 375.10 375.72 398.05 379.65 380.63
401.65 377.49 378.12 405.85 386.35 387.38
406.55 380.41 381.04 408.35 388.50 389.55
415.05 383.50 384.13 420.25 406.48 407.60
421.75 388.15 388.79 420.55 407.06 408.18
433.45 398.55 399.21 451.95 501.25 503.04
446.75 402.99 403.66
Table 5.46. Calculated Error Values for Water (2) + Glycerol (3) + KCl (9) System
Metrics Bubble Point Errors (K)
Aznar & Telles (2001) This Study (2020)
SE 22.64 22.31
RMSE 19.92 19.63
AAD 14.99 14.97
%AARD 3.64% 3.64%
Table 5.47. Calculated Squared Errors and Coefficients of Determination for Water (2) + Glycerol (3) + KCl (9) System
Metrics Values for Bubble Point
Aznar & Telles (2001) This Study (2020)
SSE 7467.80 7365.92
MSE 257.51 254.00
r2 0.5773 0.6007
r2 (adj.) 0.5627 0.5870
For water and glycerol systems with salt, the experimental and calculated bubble points are shown in Tables 5.42 and 5.45. For both water (2) + glycerol (3) + NaCl (8) and water (2) + glycerol (3) + KCl (9) systems, the calculated bubble points are equally close to the experimental bubble points at lower temperatures for both the revised parameters and the parameters of Aznar & Telles (2001). However, this is not the case for most of the calculated bubble points at higher temperatures, which even exceed 10 K difference from the experimental bubble points. This is the reason why high calculated errors and low coefficients of determination in Tables 5.43-5.44 and 5.46-5.47 are obtained for both systems.
Figure 5.28. Comparison of Experimental and Calculated Bubble Points of Water (2) + Glycerol (3) + NaCl (8) System
360 365 370 375 380 385 390 395 400 405 410 415 420
360 365 370 375 380 385 390 395 400 405 410 415 420
T (Calculated, K)
T (Experimental, K) This Study (2020)
Aznar & Telles (2001)
Figure 5.29. Comparison of Experimental and Calculated Bubble Points of Water (2) + Glycerol (3) + KCl (9) System
Figure 5.30. Temperature Concentration Diagram for Water (2) + Glycerol (3) + NaCl (8) System Using the Revised Parameters
370 380 390 400 410 420 430 440 450 460 470 480 490 500
370 380 390 400 410 420 430 440 450 460 470 480 490 500
T (Calculated, K)
T (Experimental, K) This Study (2020)
Aznar & Telles (2001)
360 365 370 375 380 385 390 395 400 405 410 415 420
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Temperature, K
Mass Fraction of Water (NaCl-Free Basis)
w = 0 w = 10.98 w = 18.44 w = 28.58
Figure 5.31. Temperature-Concentration Diagram for Water (2) + Glycerol (3) + KCl (9) System Using the Revised Parameters
The comparison of the experimental and calculated bubble points for both water (2) + glycerol (3) + NaCl (8) and water (2) + glycerol (3) + KCl (9) systems are shown in Figures 5.28-5.29. It is observed that both calculated bubble points using the parameters of Aznar &
Telles (2001) and the revised parameters are close to the experimental bubble points at temperatures of 372-378 K, while this is not true for the majority of the bubble points that lie beyond 378 K. The deviation of the bubble points from the experimental data can be seen to increase as the temperature increases or in other words, as the percentage of glycerol increases. In general, the UNIFAC Dortmund model using any of the parameters may not be suitable for the prediction of bubble points of water and glycerol systems with salt. The deviations can also be confirmed from the temperature-concentration plots in Figures 5.30- 5.31, where the deviation increases as the mass fraction of water decreases, or in other words, as the mass fraction of glycerol and the temperature increases.
360 365 370 375 380 385 390 395 400 405 410 415 420
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Temperature, K
Mass Fraction of Water
w = 0 w = 15.93 w = 27.96
From the study of Coelho et al. (2011) regarding water and glycerol system but without the presence of salt, it has also been observed at high temperatures and high percentage of glycerol that the bubble points calculated by the UNIFAC Dortmund model are also lower than those of the experimental data. For this system as well as the systems with salt considered in this study, this is because the UNIFAC Dortmund model predicts the 𝜏𝑚𝑘 values for OH-OH interaction to be higher than the OH-H2O interaction by hydrogen bonding. This means that the OH groups of glycerol are predicted to have strong interactions with each other and weak interactions with water molecules, where as a result, water and glycerol are predicted to have weak interactions. This may have something to do with the proximity effects of the OH groups of glycerol with each other that have been neglected by the model. The interactions involved for each OH group of glycerol might have been affected by the other OH groups within the glycerol molecule, which should result to the changes in the binary interaction parameters for each OH group. Since this have been neglected by the UNIFAC Dortmund model, which assumes that all the OH groups have the same and constant binary interaction parameters regardless of their location in any molecule, this could be the reason why it provides poor prediction of bubble points for water and glycerol system with and without salt.
Finally, when water and glycerol system with KCl is compared to the same system with NaCl, certain differences can be observed. The addition of NaCl to a given water and glycerol mixture causes a greater increase in the bubble point and a more significant salting- out effect than the addition of KCl to the same solvent mixture. From the experimental data, this is because Na+ is smaller than K+ ion, thus Na+ has a greater charge density than K+. As a result, Na+ is surrounded by more molecules than K+, resulting to its greater capability to cause bubble point elevation and salting-in/salting-out effects. Using the UNIFAC Dortmund model as the basis, the 𝜏𝑚𝑘 values of the interactions with Na+ are higher than those of the interactions with K+. This implies that Na+ forms stronger interactions with other species than K+, hence it is predicted that it has greater capability to cause bubble point elevation and salting-in/salting-out effects. It can be observed that the molecular interactions