Solubility of a Solid in Supercritical Fluid (SCF) Using an EOS McHugh and Paulaitis [J. Chem. Eng. Data, 25, 326 (1980)] report the following data for the solubility of naphthalene in carbon dioxide at temperatures slightly above the CO2 critical temperature and pressures considerably higher than

Question

Solubility of a Solid in Supercritical Fluid (SCF) Using an EOS

McHugh and Paulaitis [J. Chem. Eng. Data, 25, 326 (1980)] report the following data for the solubility of naphthalene in carbon dioxide at temperatures slightly above the [latex]CO _{2}[/latex] critical temperature and pressures considerably higher than its critical pressure.

T = 35.0°C		T = 60.4°C
P (bar)	[latex]y_{ N }[/latex]	P (bar)	[latex]y_{ N }[/latex]
86.8	0.0075	108.4	0.00524
98.2	0.00975	133.8	0.01516
133.0	0.01410	152.5	0.02589
199.5	0.01709	164.2	0.04296
255.3	0.01922	192.6	0.05386
		206.0	0.06259

Assuming that the [latex]CO _{2}[/latex]-naphthalene mixture obeys the Peng-Robinson equation of state with [latex]k_{ CO _{2}- N }=0.103[/latex], estimate the solubility of naphthalene in the [latex]CO _{2}[/latex] supercritical fluid (SCF). Also compute the predicted enhancement factors and the contribution of the Poynting factor to the enhancement factor.

Accepted Answer

Using the data in Illustration 12.1-1 and Table 6.6-1, and one of the Peng-Robinson mixture programs discussed in Appendix B and on the website to calculate the vapor-phase fugacities, the following results are obtained.

P (bar)	[latex]y_{ N }[/latex]	[latex]y_{ N }^{ ID }[/latex] (Eq. 12.1-19)	E	Poynting Factor
T = 35°C:
86.8	[latex]1.99 imes 10^{-3}[/latex]	[latex]3.21 imes 10^{-6}[/latex]	619	1.527
98.2	[latex]2.87 imes 10^{-3}[/latex]	[latex]2.84 imes 10^{-6}[/latex]	1 010	1.615
199.5	[latex]1.654 imes 10^{-2}[/latex]	[latex]1.40 imes 10^{-6}[/latex]	11 830	2.647
255.3	[latex]1.940 imes 10^{-2}[/latex]	[latex]1.09 imes 10^{-6}[/latex]	17 759	3.475
T = 60.4°C:
108.4	[latex]2.80 imes 10^{-3}[/latex]	[latex]2.21 imes 10^{-5}[/latex]	126	1.63
133.8	[latex]1.05 imes 10^{-2}[/latex]	[latex]1.79 imes 10^{-5}[/latex]	584	1.828
152.5	[latex]1.96 imes 10^{-2}[/latex]	[latex]1.57 imes 10^{-5}[/latex]	1246	1.989
164	[latex]2.64 imes 10^{-2}[/latex]	[latex]1.46 imes 10^{-5}[/latex]	1806	2.096
192.6	[latex]5.25 imes 10^{-2}[/latex]	[latex]1.25 imes 10^{-5}[/latex]	4211	2.383
206	[latex]6.61 imes 10^{-2}[/latex]	[latex]1.17 imes 10^{-5}[/latex]	5671	2.531

[latex]\ln \left[\frac{x_{1}\left(T_{1} ight) \gamma_{1}\left(\underline{x}, T_{1} ight)}{x_{1}\left(T_{2} ight) \gamma_{1}\left(\underline{x}, T_{2} ight)} ight]=-\frac{\Delta_{ fus } \underline{H}_{1}}{R}\left[\frac{1}{T_{1}}-\frac{1}{T_{2}} ight]=-\frac{ riangle_{ fus } \underline{H}_{1}}{R}\left[\frac{T_{2}-T_{1}}{T_{1} T_{2}} ight][/latex] (12.1-19a)

[latex]\ln \left[\frac{x_{1}\left(T_{1} ight)}{x_{1}\left(T_{2} ight)} ight]=-\frac{\Delta_{ ext {fus }} \underline{H}_{1}}{R}\left[\frac{1}{T_{1}}-\frac{1}{T_{2}} ight]=-\frac{ riangle_{ ext {fus }} \underline{H}_{1}}{R}\left[\frac{T_{2}-T_{1}}{T_{1} T_{2}} ight][/latex] (12.1-19b)

The predicted and measured naphthalene mole fractions in supercritical carbon dioxide are plotted in Fig. 12.1-1.

Comments

1. Note that the predictions for these extreme conditions are good. Indeed, with only one adjustable parameter [latex]\left(k_{ CO _{2}- N }=0.103 ight)[/latex], reasonable predictions are obtained for the solubility of naphthalene in supercritical carbon dioxide for a range of temperatures in the near critical region, and to moderately high pressures.

2. The enhancement factors here are very large, in fact, among the larger nonideal corrections encountered in chemical engineering thermodynamics. (Enhancement factors for other mixtures at cryogenic conditions of [latex]10^{9}[/latex] and larger have been reported.) Note that at T = 35°C and P = 255.3 bar, the solubility of naphthalene is enhanced by a factor of more than 17 700 above its ideal value; however, its total solubility is still small at less than 2 mol%.

3. The solubility of naphthalene in supercritical carbon dioxide at 60.4◦C increases from a mole fraction of 0.00240 at 1 bar (Illustration 12.1-4) to 0.098 at 291.3 bar. This illustrates the large increase in the solubility of a solute that may occur with increasing pressure, which is the basis of supercritical extraction to, for example, remove caffeine from coffee beans or fragrances and oils from plant material.

4. The Poynting corrections in this illustration are large, reaching values greater than 3. Consequently, the Poynting factor could not be ignored in this example. However, the main contribution to the enhancement factor arises from gas-phase nonidealities (the species fugacity coefficient, [latex]\bar{\phi}_{ i }[/latex]).

Table 6.6-1 The Critical and Other Constants for Selected Fluids
Substance	Symbol	Molecular Weight [latex]\left( g mol ^{-1} ight)[/latex]	[latex]T_{c}( K )[/latex]	[latex]P_{c}( MPa )[/latex]	[latex]V_{c}\left( m ^{3} / kmol ight)[/latex]	[latex]Z_{c}[/latex]	ω	[latex]T_{ ext {boil }}( K )[/latex]
Acetylene	[latex]C _{2} H _{2}[/latex]	26.038	308.3	6.14	0.113	0.271	0.184	189.2
Ammonia	[latex]NH _{3}[/latex]	17.031	405.6	11.28	0.0724	0.242	0.25	239.7
Argon	Ar	39.948	150.8	4.874	0.0749	0.291	-0.004	87.3
Benzene	[latex]C _{6} H _{6}[/latex]	78.114	562.1	4.894	0.259	0.271	0.212	353.3
n-Butane	[latex]C _{4} H _{10}[/latex]	58.124	425.2	3.8	0.255	0.274	0.193	272.7
Isobutane	[latex]C _{4} H _{10}[/latex]	58.124	408.1	3.648	0.263	0.283	0.176	261.3
1-Butene	[latex]C _{4} H _{8}[/latex]	56.108	419.6	4.023	0.24	0.277	0.187	266.9
Carbon dioxide	[latex]CO _{2}[/latex]	44.01	304.2	7.376	0.094	0.274	0.225	194.7
Carbon monoxide	CO	28.01	132.9	3.496	0.0931	0.295	0.049	81.7
Carbon tetrachloride	[latex]CCl _{4}[/latex]	153.823	556.4	4.56	0.276	0.272	0.194	349.7
n-Decane	[latex]C _{10} H _{22}[/latex]	142.286	617.6	2.108	0.603	0.247	0.49	447.3
n-Dodecane	[latex]C _{12} H _{26}[/latex]	170.34	658.3	1.824	0.713	0.24	0.562	489.5
Ethane	[latex]C _{2} H _{6}[/latex]	30.07	305.4	4.884	0.148	0.285	0.098	184.5
Ethyl ether	[latex]C _{4} H _{10} O[/latex]	74.123	466.7	3.638	0.28	0.262	0.281	307.7
Ethylene	[latex]C _{2} H _{4}[/latex]	28.054	282.4	5.036	0.129	0.276	0.085	169.4
Helium	He	4.003	5.19	0.227	0.0573	0.301	-0.387	4.21
n-Heptane	[latex]C _{7} H _{16}[/latex]	100.205	540.2	2.736	0.304	0.263	0.351	371.6
n-Hexane	[latex]C _{6} H _{14}[/latex]	86.178	507.4	2.969	0.37	0.26	0.296	341.9
Hydrogen	[latex]H _{2}[/latex]	2.016	33.2	1.297	0.065	0.305	-0.22	20.4
Hydrogen fluoride	HF	20.006	461	6.488	0.069	0.12	0.372	292.7
Hydrogen sulfide	[latex]H _{2} S[/latex]	34.08	373.2	8.942	0.0985	0.284	0.1	212.8
Methane	[latex]CH _{4}[/latex]	16.043	190.6	4.6	0.099	0.288	0.008	111.7
Naphthalene	[latex]C _{10} H _{8}[/latex]	128.174	748.4	4.05	0.41	0.267	0.302	491.1
Neon	Ne	20.183	44.4	2.756	0.0417	0.311	0	27
Nitric oxide	NO	30.006	180	6.485	0.058	0.25	0.607	121.4
Nitrogen	[latex]N _{2}[/latex]	28.013	126.2	3.394	0.0895	0.29	0.04	77.4
n-Octane	[latex]C _{8} H _{18}[/latex]	114.232	568.8	2.482	0.492	0.259	0.394	398.8
Oxygen	[latex]O _{2}[/latex]	31.999	154.6	5.046	0.0732	0.288	0.021	90.2
n-Pentane	[latex]C _{5} H _{12}[/latex]	72.151	469.6	3.374	0.304	0.262	0.251	309.2
Isopentane	[latex]C _{5} H _{12}[/latex]	72.151	460.4	3.384	0.306	0.271	0.227	301
Propane	[latex]C _{3} H _{8}[/latex]	44.097	369.8	4.246	0.203	0.281	0.152	231.1
Propylene	[latex]C _{3} H _{6}[/latex]	42.081	365	4.62	0.181	0.275	0.148	225.4
Refrigerant R12	[latex]CCl _{2} F _{2}[/latex]	120.914	385	4.124	0.217	0.28	0.176	243.4
Refrigerant HFC-134a	[latex]CH _{2} FCF _{3}[/latex]	102.03	374.23	4.06	0.198	0.258	0.332	247.1
Sulfur dioxide	[latex]SO _{2}[/latex]	64.063	430.8	7.883	0.122	0.268	0.251	263
Toluene	[latex]C _{7} H _{8}[/latex]	92.141	591.7	4.113	0.316	0.264	0.257	383.8
Water	[latex]H _{2} O[/latex]	18.015	647.3	22.048	0.056	0.229	0.344	373.2
Xenon	Xe	131.3	289.7	5.836	0.118	0.286	0.002	165
Source: Adapted from R. C. Reid, J. M. Prausnitz, and B. E. Poling, The Properties of Gases and Liquids, 4th ed.,McGraw-Hill, New York, 1986, Appendix A and other sources.

Question 12.1.6: Solubility of a Solid in Supercritical Fluid (SCF) Using an ...

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