6.4 VLE data regression
6.4.1 Modelling results for the 1-propanol (1) + 4-methyl-2-pentanone (2) system
regression was done with the combined method (γ-Φ approach). Table 6-4 presents the regressed temperature dependent model binary interaction parameters, the ∆yavg, ∆Pavg (the deviation between measured values and modelled values) and the RMSD δln(γ1/γ2) values obtained from the regression of each isotherm. All the regression procedures used for this system were explained earlier in Section 6-4. The models and their combinations were carefully chosen in order to obtain the best fit to the experimental VLE data set. The data measured for the three isotherms of this system were regressed with four different types of thermodynamic model combinations namely: the NRTL-HOC, the WILSON-HOC, the UNIQUAC-HOC and the NRTL-NTH model combinations. This system exhibits an azeotrope at isotherm 353.15 K at x1 = y1 = 0.11. For the regression of each isotherm, two correlations for determining the fugacity coefficients (the HOC and the NTH) were each combined with an activity coefficient model (the NRTL) in order to determine the combination that best describes the experimental VLE data sets (i.e. the NRTL-HOC and the NRTL-NTH model combinations). The three activity coefficient models (the NRTL, WILSON and the UNIQUAC models) were varied with an equation of state model (HOC) for this same reason.
When the HOC equation of state model was combined with each of the three activity coefficient models, the three model combinations gave the same values for the ∆y1avg and
∆Pavg at 338.15K, but based on the RMSD δln(γ1/γ2) the NRTL-HOC model combination gave the best fit though not with much significant difference. When the NRTL activity coefficient model was combined with the HOC and NTH correlations for this isotherm
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(338.15 K) both model combinations gave the same values for the ∆y1avg and ∆Pavg but based on the RMSD δln(γ1/γ2) the NRTL-HOC combination fit the data well.
Following the same process explained above for the second isotherm (353.15 K), the same values of ∆y1avg and RMSD δln(γ1/γ2) were obtained when the HOC equation of state model was combined with each of the three activity coefficient models but based on the ∆Pavg the NRTL-HOC gave the best fit. When the NRTL activity coefficient model was combined with the HOC and the NTH correlations, the NRTL-HOC model combination gave the best fit based on the ∆y1avg. The RMSD δln(γ1/γ2) and ∆Pavg are the same.
For the third isotherm (368.15 K), the NRTL-HOC gave the best fit when equation of state model (HOC) was combined with each of the three activity coefficient models and when the activity coefficient model was combined with the two equations of state models. In order to verify the quality and consistency of the measured data, thermodynamic consistency testing was performed for the data set employing the point test (Van Ness, 1973) and direct test (Van Ness, 1975). The ∆yavg obtained for each VLE data set were compared with the value provided by Danner and Gess (1990) that for a data to be thermodynamically consistent the
∆yavg must be less than 0.01 (point test of Van Ness, 1973). All the data set measured for this system passed this quantitative criterion and as shown on the ∆y and ∆P plots for each isotherm, there is random scattering about the x-axis. The only exception is the data set of the third isotherm (368.15 K) that has the highest value of 0.012 for the NRTL-NTH model combination. Plots for the point test (y and P residuals) for each isotherm with the different model combinations are shown in Appendix A. The RMSD δln(γ1/γ2) values calculated for each data set were compared with the consistency index table of Van Ness (1995) in Chapter 3. All the data sets measured in this work (with no exception) passed this test with the highest value being 0.082 for the NRTL-NTH model combination at 368.15 K. the P-x-y plots showing the comparison of the three activity coefficient models for each isotherm are presented in Appendix A while the plots for the consistency tests performed for each isotherm are presented in Appendix A. The graphical representation of the comparison of the model fits to experimental VLE data for the three isotherms are presented below. All other P- x-y plots are presented in Appendix A. These plots show that the model combinations chosen for this work are able to describe the 1-propanol (1) + 4-methyl-2-pentanone well at the three isotherms.
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In conclusion, the NRTL-HOC model combination was found to fit all the data set measured for this system at the three isotherms well more than the other model combinations and the newly isothermal VLE data measured in this work are thermodynamically consistent.
Table 6-4: modelling results obtained for the 1-propanol (1) + 4-methyl-2-pentanone (2) system
model T/ K aij aji bij bji AAD
∆P/kPa
AAD
∆y
RMSD δln(γ1/γ2) NRTL-HOC 338.15 15.44 -10.7 -5055 3716 0.008 0.003 0.023
353.15 5.13 7.79 -1691 -2644 0.011 0.004 0.034 368.15 1.49 13.3 -519 -4706 0.031 0.010 0.074 NRTL-NTH 338.15 6.05 -5.82 -1876 2049 0.008 0.003 0.024 353.15 5.32 7.93 -1754 -2692 0.011 0.005 0.034 368.15 1.28 13.55 -438 -4798 0.030 0.012 0.082 WILSON-HOC 338.15 0.00 0.00 -97.9 -162 0.008 0.003 0.025 353.15 0.00 0.00 -120 -116 0.013 0.004 0.034 368.15 0.00 0.00 -179 -42.19 0.032 0.011 0.075 UNIQUAC-HOC 338.15 -0.63 0.266 0.00 0.00 0.008 0.003 0.024 353.15 0.00 0.00 -187 79.39 0.013 0.004 0.034 368.15 0.00 0.00 -137 47.68 0.033 0.011 0.075
u(T) = 0.06 K
bij and aij are the binary interaction parameters for the activity coefficient models in ASPEN, (τij = aij + bij/T), αij (non-randomness parameter) set to 0.3 for the NRTL-HOC and NRTL-NTH model combinations, RMSD δln(γ1/γ2) (the Root Mean Square deviation for the direct test)
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Figure 6-7: Fit of the NRTL-HOC and NRTL-NTH model combinations to the p-x-y plot of the 1-propanol (1) + 4-methyl-2-pentanone (2) system at 338.15 K for the combined method: (•) this work, (— ) NRTL-HOC, (- - - -) NRTL-NTH
Figure 6-8: Fit of the NRTL-HOC and NRTL-NTH model combinations to the x-y plot of the 1-propanol (1) + 4-methyl-2-pentanone (2) system at 338.15 K for the combined method: (•) this work, (— ) NRTL-HOC, (- - - -) NRTL-NTH
15 17 19 21 23 25 27 29
0,0 0,2 0,4 0,6 0,8 1,0
Pressure / kPa
x1,y1
0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0
0,0 0,2 0,4 0,6 0,8 1,0
y1
x1
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Figure 6-9: Point test (varying EOS) ∆y1 for the 1-propanol (1) + 4-methyl-2-pentanone (2) system at 338.15 K: (◦) NRTL-HOC, (∆) NRTL-NTH
Figure 6-10: Direct test (varying EOS): δln(γ1/γ2) for the 1-propanol (1) + 4-methyl-2- pentanone (2) system at 338.15 K : (◦) NRTL-HOC, (∆) NRTL-NTH
-0,012 -0,009 -0,006 -0,003 0,000 0,003 0,006 0,009
0,0 0,2 0,4 0,6 0,8 1,0
y1exp-y1calc
x1
-0,04 -0,02 0,00 0,02 0,04 0,06
0,0 0,2 0,4 0,6 0,8 1,0
δln(γ1/γ2)
x1
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Figure 6-11: Fit of the NRTL-HOC and NRTL-NTH model combinations to the P-x-y plot of the 1-propanol (1) + 4-methyl-2-pentanone (2) system at 353.15 K for the combined method: (•) this work, (— ) NRTL-HOC, (- - - -) NRTL-NTH
Figure 6-12: Fit of the NRTL-HOC and NRTL-NTH model combinations to the x-y plot of the 1-propanol (1) + 4-methyl-2-pentanone (2) system at 353.15 K for the combined method: (•) this work, (— ) NRTL-HOC, (- - - -) NRTL-NTH
30 35 40 45 50 55
0,0 0,2 0,4 0,6 0,8 1,0
P/ kPa
x1,y1
0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0
0,0 0,2 0,4 0,6 0,8 1,0
y1
x1
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Figure 6-13: Fit of the NRTL-HOC and NRTL-NTH model combinations to the P-x-y plot of the 1-propanol (1) + 4-methyl-2-pentanone (2) system at 368.15 K for the combined method: (•) this work, (— ) NRTL-HOC, (- - - -) NRTL-NTH
Figure 6-14: Fit of the NRTL-HOC and NRTL-NTH model combinations to the x-y plot of the 1-propanol (1) + 4-methyl-2-pentanone (2) system at 368.15 K for the combined method: (•) this work, (— ) NRTL-HOC, (- - - -) NRTL-NTH
50 55 60 65 70 75 80 85 90 95 100
0,0 0,2 0,4 0,6 0,8 1,0
P/ kPa
x1,y1
0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0
0,0 0,2 0,4 0,6 0,8 1,0
y1
x1
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Figure 6-15: Comparison between the experimentally determined liquid-phase activity coefficients and those calculated from the NRTL model for 1-propanol (1) + 4-methyl-2- pentanone (2) system at 338.15 K, 353.15 K and 368.15 K. 338.15 K (―), 353.15 K (…) and 368.15 K (- - -) for NRTL-HOC model combination; 338.15 K (○), 353.15 K (□) and 368.15 K (Δ), for experimental γ1; 338.15 K (●), 353.15 K (■) and 368.15 K (▲), for experimental γ2
Figure 6-15 is the illustrative plot of the liquid phase activity coefficient for the 1-propanol (1) + 4-methyl-2-pentanone system at 338.15 K, 353.15 K and 368.15 K. As shown on the plot, the NRTL-HOC model combination provided a good fit to the isothermal VLE data set.
-0,1 0,1 0,3 0,5 0,7 0,9
0 0,2 0,4 0,6 0,8 1
ln(γ1,γ2)
x1
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Figure 6-16: Temperature dependence of the NRTL-HOC model combination parameters for 1-propanol (1) + 4-methyl-2-pentanone (2) system. (■), g21-g12; (♦) g12-g21
6.4.2 Modelling results for the 2-propanol (1) + 4-methyl-2-pentanone (2) system