Species Fugacity Calculation for a Hydrocarbon Mixture

Compute the fugacities of n-pentane and benzene in their equimolar mixture at 373.15 K and 50 bar.

Question

Species Fugacity Calculation for a Hydrocarbon Mixture

Compute the fugacities of n-pentane and benzene in their equimolar mixture at 373.15 K and 50 bar.

Accepted Answer

The simplest estimate is obtained using the Lewis-Randall rule and the results of Illustration 7.4-6. In this case we obtain

[latex]\begin{aligned}\bar{f}_{ PE }\left(373.15 K , 50 bar , x_{ PE }=0.5 ight) &=0.5 imes f_{ PE }(373.15 K , 50 bar ) \&=0.5 imes 6.22 bar =3.11 bar\end{aligned}[/latex]

and

[latex]\bar{f}_{ BZ }\left(373.15 K , 50 bar , x_{ BZ }=0.5 ight)=0.5 imes 1.98 bar =0.99 bar[/latex]

A better estimate is obtained using the Peng-Robinson equation of state with a value [latex]k_{ PE - BZ }=0.018[/latex] from Table 9.4-1. The results are

[latex]\begin{array}{l}\bar{f}_{ PE }\left(373.15 K , 50 bar , x_{ PE }=0.5 ight)=3.447 bar \\bar{f}_{ BZ }\left(373.15 K , 50 bar , x_{ BZ }=0.5 ight)=1.129 bar\end{array}[/latex]

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.

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