Predicting Vapor-Phase Compositions from P-T-x Data

Using only the liquid-phase mole fraction and pressure data for the n-pentane–propionaldehyde system at 40°C given in Table 10.2-1, estimate the vapor compositions.

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Predicting Vapor-Phase Compositions from P-T-x Data

Using only the liquid-phase mole fraction and pressure data for the n-pentane–propionaldehyde system at 40°C given in Table 10.2-1, estimate the vapor compositions.

Accepted Answer

Using the method just described, the van Laar equation, and a parameter estimation computer program with the objective function of Eq. 10.2-16, we find

[latex]\min \sum_{\substack{\exp \ pts\j }}\left[P_{j}^{ exp }-P_{j}^{ calc } ight]^{2}=\min \sum_{\substack{\exp \ pts \ j}}\left[P_{j}^{\exp }-x_{1}^{j} \gamma_{1}^{j} P_{1}^{ vap }-\left(1-x_{1}^{j} ight) \gamma_{2}^{j} P_{2}^{ vap } ight]^{2}[/latex] (10.2-16)

[latex]\alpha=1.4106 \quad ext { and } \quad \beta=1.3438[/latex]

With these parameter values,we obtain the calculated pressures and vapor mole fractions given in Table 10.2-2. It is clear from this table that the predictions are reasonably accurate. The azeotrope is predicted to occur at approximately the correct composition and pressure, the calculated vapor mole fractions usually agree to within ±0.015 of the measured composition, and the maximum difference between the calculated and measured pressures is only 0.0174 bar. Indeed, the calculated results for this system are so close to the experimental data as to be almost indistinguishable from them on x -y or P-x -y plots.

[The folder the folder Aspen Illustrations>Chapter 10.2>10.2-5 on the Wiley website for this book contains the Aspen Plus[latex]^R[/latex] files for correlating the experimental data using the NRTL, UNIQUAC, Wilson and NRTL models. The results are given in separate Excel (.xlsx) files in that folder, and summarized in the Word file Illustration 10.2-5 w three models.docx]

Table 10.2-1 Vapor-Liquid Equilibrium Data for the n-Pentane (1)–Propionaldehyde (2) System at 40°C
[latex]x_{1}[/latex]	[latex]y_{1}[/latex]	P (bar)	[latex]x_{1}[/latex]	[latex]y_{1}[/latex]	P (bar)
0	0	0.7609	0.4463	0.5877	1.3354
0.0503	0.2121	0.9398	0.5031	0.6146	1.3494
0.1014	0.3452	1.0643	0.5610	0.6311	1.3568
0.1647	0.4288	1.1622	0.6812	0.6827	1.3636
0.2212	0.4685	1.2173	0.7597	0.7293	1.3567
0.3019	0.5281	1.2756	0.8333	0.7669	1.3353
0.3476	0.5539	1.2949	0.9180	0.8452	1.2814
0.4082	0.5686	1.3197	1.0	1.0	1.1541

Table 10.2-2 Comparison of Measured Vapor-Phase Mole Fractions for the n-Pentane–Propionaldehyde System at 40°C with Values Predicted from P-T-x Data
[latex]x_{1}[/latex]	[latex]y_{1}^{\exp }[/latex]	[latex]y_{1}^{calc }[/latex]	[latex]y_{1}^{\exp }[/latex]	[latex]y_{1}^{calc }[/latex]
0	0	0	0.7609	0.7609
0.0503	0.2121	0.2211	0.9398	0.9312
0.1014	0.3452	0.3424	1.0643	1.0555
0.1647	0.4288	0.4309	1.1622	1.1618
0.2212	0.4685	0.481	1.2173	1.2257
0.3019	0.5281	0.5286	1.2756	1.2846
0.3476	0.5539	0.5484	1.2949	1.3067
0.4082	0.5686	0.5702	1.3197	1.3208
0.4463	0.5877	0.5824	1.3354	1.3379
0.5031	0.6416	0.5996	1.3494	1.349
0.561	0.6311	0.6173	1.3568	1.3566
0.6812	0.6827	0.6609	1.3636	1.3604
0.7597	0.7293	0.7005	1.3567	1.35
0.8333	0.7669	0.7529	1.3353	1.3244
0.918	0.8452	0.8455	1.2814	1.264
1.0	1.0	1.0	1.1541	1.1541

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