Species Fugacity Calculation Using the Peng-Robinson Equation of State

Compute the fugacities of ethane and n-butane in an equimolar mixture at 373.15 K and 1, 10, and 15 bar using the Peng-Robinson equation of state.

Question

Species Fugacity Calculation Using the Peng-Robinson Equation of State

Compute the fugacities of ethane and n-butane in an equimolar mixture at 373.15 K and 1, 10, and 15 bar using the Peng-Robinson equation of state.

Accepted Answer

Using the computer programs in Appendix B on the website for this book or Aspen Plus R[ltaex]^R[/latex] and from Table 9.4-1, with [latex]k_{ ET - BU }=0.010[/latex], the results below are obtained.

P	Z	[latex]\bar{f}_{ ET }\left(373.15, P, y_{ ET }=0.5\right)[/latex]	[latex]\bar{f}_{ BU }\left(373.15, P, y_{ BU }=0.5\right)[/latex]
1 bar	0.991	0.498 bar	0.493 bar
10 bar	0.910	4.836 bar	4.333 bar
15 bar	0.861	7.143 bar	6.024 bar

Comment

These results are similar to those obtained using either the Lewis-Randall rule or the virial equation of state. However, greater differences between the methods occur for gases as the pressure is increased. At higher pressures the results from the Peng-Robinson equation of state are expected to be the most 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 9.4.3: Species Fugacity Calculation Using the Peng-Robinson Equatio...

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