Calculation of LLE Using an Equation of State The experimental data for liquid-liquid equilibrium in the CO2–n-decane system appear in the following table.

Question

Calculation of LLE Using an Equation of State

The experimental data for liquid-liquid equilibrium in the [latex]CO _{2}[/latex]–n-decane system appear in the following table.

T (K)	P (bar)	[latex]x_{ CO _{2}}^{ I }[/latex]	[latex]x_{ CO _{2}}^{ II }[/latex]
235.65	10.58	0.577	0.974
236.15	10.75	0.582	0.973
238.15	11.52	0.602	0.970
240.15	12.38	0.627	0.965
242.15	13.19	0.659	0.960
244.15	14.14	0.695	0.954
246.15	15.10	0.734	0.942
248.15	16.11	0.783	0.916
248.74	16.38	0.850	0.850
Source: A. A. Kulkarni, B. Y. Zarah, K. D. Luks, and J. P. Kohn, J. Chem. Eng. Data, 19, 92 (1974).

Make predictions for the liquid-liquid equilibrium in this system using the Peng-Robinson equation of state with the binary interaction parameter equal to 0.114, as given in Table 9.4-1, as well as several other values of this parameter.

Accepted Answer

Using one of the Peng-Robinson equation-of-state flash programs on the website with the van der Waals one-fluid mixing rules, modified as just described for the liquid-liquid equilibrium calculation, gives the results shown in Fig. 11.2-6. There we see that no choice for the binary interaction parameter [latex]k_{12}[/latex] will result in predictions that are in complete agreement with the experimental data. In particular, the value of the binary interaction parameter determined from higher-temperature vapor-liquid equilibrium data [latex]\left(k_{12}=0.114\right)[/latex] results in a much higher liquidliquid critical solution temperature than is observed in the laboratory. Clearly, the Peng-Robinson equation-of-state prediction for liquid-liquid coexistence curve using the van derWaals one-fluid mixing rules is not of the correct shape for this system.

What should be stressed is not the poor accuracy of the equation-of-state predictions for the [latex]CO _{2}[/latex]–n-decane system, but rather the fact that the same, simple equation of state can lead to good vapor-liquid equilibrium predictions over a wide range of temperatures and pressures, as well as a qualitative description of liquid-liquid equilibrium at lower temperatures.

It should be noted, however, that the equation-of-state predictions for this system could be greatly improved using the Wong-Sandler mixing rule rather than the van der Waals one-fluid mixing rules. Using the mixing rule of Sec. 9.9 with the UNIQUAC activity coefficient model and temperature-independent parameters that have been fit only to the data at 235.65 K, the very good predictions at all other temperatures shown in Fig. 11.2-6 are obtained. Note that if the UNIQUAC modelwere used directly (that is, not in theWong-Sandler mixing rule), temperaturedependent parameters would be needed to obtain a fit of comparable quality. The success of this more complicated mixing rule with temperature-independent parameters results from the fact that there is a temperature dependence built into the equation of state.

[The folder Aspen Illustrations>Chapter 11>11.2-5 on theWiley website for this book provides the Aspen Plus[latex]^R[/latex] file to predict the liquid-liquid equilibrium for this system. In the folder is an Excel file Illustration 11.2-5.docx with the results of using the Peng-Robinson equation of state, and also with the NRTL and UNIQUAC activity coefficient models. The results are not very accurate.]

Table 9.4-1 Binary Interaction Parameters [latex]k_{12}[/latex] for the Peng-Robinson Equation of State*
	[latex]C _{2} H _{4}[/latex]	[latex]C _{2} H _{6}[/latex]	[latex]C _{3} H _{6}[/latex]	[latex]C _{3} H _{8}[/latex]	[latex]i- C _{4} H _{10}[/latex]	[latex]n- C _{4} H _{10}[/latex]	[latex]i- C _{5} H _{12}[/latex]	[latex]n- C _{6} H _{14}[/latex]	[latex]C _{6} H _{6}[/latex]	[latex]c- C _{6} H _{12}[/latex]	[latex]n- C _{7} H _{16}[/latex]	[latex]n- C _{8} H _{18}[/latex]	[latex]n- C _{10} H _{22}[/latex]	[latex]N _{2}[/latex]	[latex]CO[/latex]	[latex]CO _{2}[/latex]	[latex]SO _{2}[/latex]	[latex]H _{2} S[/latex]
[latex]CH _{4}[/latex]	0.022	-0.003	0.033	0.016	0.026	0.019	0.026	0.04	0.055	0.039	0.035	0.05	0.049	0.03	0.03	0.09	0.136	0.08
[latex]C _{2} H _{4}[/latex]		0.01				0.092			0.031		0.014		0.025	0.086	-0.022	0.056
[latex]C _{2} H _{6}[/latex]			0.089	0.001	-0.007	0.01	0.008	-0.04	0.042	0.018	0.007	0.019	0.014	0.044	0.026	0.13		0.086
[latex]C _{3} H _{6}[/latex]				0.007	-0.014									0.09	0.026	0.093		0.08
[latex]C _{3} H _{8}[/latex]					-0.007	0.003	0.027	0.001	0.023		0.006	0	0	0.078	0.03	0.12		0.08
[latex]i- C _{4} H _{10}[/latex]						0								0.1	0.04	0.13		0.047
[latex]n- C _{4} H _{10}[/latex]							0.017	-0.006			0.003	0.007	0.008	0.087	0.04	0.135		0.07
[latex]i- C _{5} H _{12}[/latex]							0.06		0.018	0.004				0.092	0.04	0.121		0.06
[latex]n- C _{5} H _{12}[/latex]									0.01	-0.004	0.007	0		0.1	0.04	0.125		0.063
[latex]n- C _{6} H _{14}[/latex]										0.013	-0.008			0.15	0.04	0.11		0.06
[latex]C _{6} H _{6}[/latex]											0.001	0.003	0.1	0.164	0.11	0.077	0.015
[latex]c- C _{6} H _{12}[/latex]														0.14	0.1	0.105
[latex]n- C _{7} H _{16}[/latex]												0		0.1	0.04	0.1		0.06
[latex]n- C _{8} H _{18}[/latex]														0.1	0.04	0.12		0.06
[latex]n- C _{10} H _{22}[/latex]														0.11	0.04	0.114		0.033
[latex]N _{2}[/latex]															0.012	-0.02	0.08	0.17
CO																0.03		0.054
[latex]CO _{2}[/latex]																	0.136	0.097
[latex]SO _{2}[/latex]
[latex]H _{2} S[/latex]
*Obtained from data in “Vapor-Liquid Equilibria for Mixtures of Low-Boiling Substances,” by H. Knapp, R. D¨oring, L. Oellrich, U. Pl¨ocker, and J. M. Prausnitz, DECHEMA Chemistry Data Series, Vol. VI, Frankfurt/Main, 1982, and other sources. Blanks indicate no data are available from which the k12 could be evaluated. In such case use estimates from mixtures of similar compounds.

Question 11.2.5: Calculation of LLE Using an Equation of State The experiment...

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