A New General Correlation for the Influence Parameter in Density Gradient Theory and Peng–Robinson Equation of State for n-Alkanes
Abstract
1. Introduction
2. Density Gradient Theory and Peng–Robinson Equation of State
- (i)
- (ii)
- The fluid properties of the saturated single phases (vapor and liquid) are obtained from an EoS, so no other data sources or analytical expressions are necessary.
- (iii)
- The theory allows the calculation of the surface or interfacial tension, density profiles and their thickness, the surface enthalpy and entropy, and some other properties for the adsorption processes [80].
3. Sources of Data
4. New Correlation for the Reduced Influence Parameter
- decreases almost linearly in the range [], so it could be fitted to a linear expression:
- Near the critical point (), tends to infinity. To reproduce this behavior, an analytical expression such as the one proposed by Zuo and Stenby [70] has to be used:
5. Results and Discussion
5.1. Adjustable Coefficients for the Specific Correlation
5.2. Accuracy of the Proposed Specific Model
5.3. General Correlation
- The DIPPR data predicted using Sugden’s correlation will not be considered in the new global correlation, and only data in the range will be considered in the coefficient determination of the global correlation. The number of available data and fitting data for each fluid are compiled in Table 2.
- There are some fluids (see Figure 1) for which a considerable number of fitting data are available (i.e., n-heptane and n-hexane with 357 and 269 data, respectively), whereas in other cases the number of data is one (n-hexatriacontane and others). To have a suitable general correlation not biased by the data availability, the adjustable coefficients will be obtained by minimizing the overall mean absolute percentage deviation (OMAPDfit), defined as:
6. Conclusions
Supplementary Materials
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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CN | Fluid | MAPD | MD | PDm | |||||
---|---|---|---|---|---|---|---|---|---|
mol2/3) | mol2/3) | mol2/3) | (%) | (%) | (%) | ||||
1 | methane | 7.5(12+) | 5.086(88+) | −3.35(34+) | 127/126 | 0.97 | −0.28 | 8.5 | 0.11 |
2 | ethane | 5.1(10+) | 3.68(13+) | −3.63(31+) | 163/160 | 2.06 | −0.77 | 19.2 | 0.01 |
3 | propane | 4.92(48−) | 3.63(16−) | −3.08(24−) | 193/191 | 1.80 | 0.04 | 27.2 | 0.01 |
4 | n-butane | 3.70(51+) | 3.44(12+) | −3.75(23−) | 126/118 | 3.14 | 1.17 | 48.9 | 0.01 |
5 | n-pentane | 3.84(76−) | 3.488(80−) | −3.25(21−) | 149/143 | 1.72 | 1.03 | 36.5 | 0.01 |
6 | n-hexane | 3.8(14−) | 3.574(64+) | −3.18(17+) | 270/269 | 0.97 | 0.18 | 12.8 | 0.07 |
7 | n-heptane | 4.32(74+) | 3.560(68+) | −2.78(20+) | 363/357 | 0.89 | 0.09 | 9.7 | 0.22 |
8 | n-octane | 5.5(20−) | 3.702(65+) | −2.55(23+) | 196/194 | 1.04 | 0.43 | 41.1 | 0.01 |
9 | n-nonane | 0.0(81+) | 3.573(44+) | −2.86(21+) | 78 | 0.41 | 0.07 | 3.0 | 0.80 |
10 | n-decane | 3.8(26−) | 3.686(62−) | −2.16(27+) | 149 | 0.95 | −0.08 | 5.8 | 0.68 |
11 | n-undecane | 0.0(34+) | 3.663(53+) | −2.25(27+) | 60 | 0.55 | 0.05 | 2.6 | 0.49 |
12 | n-dodecane | 5.2(38+) | 3.633(65−) | −2.09(33−) | 100 | 0.91 | 0.30 | 6.7 | 0.91 |
13 | n-tridecane | 4(12+) | 3.655(45+) | −2.22(28+) | 48 | 0.33 | −0.02 | 1.3 | 0.69 |
14 | n-tetradecane | 15(14−) | 3.767(53−) | −1.85(44+) | 49 | 0.49 | 0.07 | 1.9 | 0.97 |
15 | n-pentadecane | 12(44+) | 3.705(44+) | −1.97(47+) | 40 | 0.40 | −0.01 | 2.0 | 0.67 |
16 | n-hexadecane | 7.7(37−) | 3.876(64+) | −2.19(67−) | 127 | 1.33 | 0.12 | 6.8 | 0.40 |
17 | n-heptadecane | 7.3(11−) | 3.914(54+) | −2.46(27−) | 44 | 0.44 | 0.08 | 2.1 | 0.78 |
18 | n-octadecane | 8.0(13+) | 3.990(59−) | −2.36(30−) | 39 | 0.48 | 0.05 | 1.9 | 0.79 |
19 | n-nonadecane | 8.13(79−) | 3.981(67−) | −2.48(24−) | 23 | 0.70 | 0.02 | 5.4 | 0.34 |
20 | n-eicosane | 7.7(11+) | 4.079(75−) | −2.78(26−) | 38 | 1.04 | −0.10 | 11.7 | 0.33 |
21 | n-heneicosane | 8.0(10+) | 4.225(76+) | −2.83(22+) | 28 | 0.47 | −0.18 | 2.8 | 0.07 |
22 | n-docosane | 7.8(12+) | 4.223(78+) | −2.75(31+) | 32 | 0.58 | −0.28 | 2.9 | 0.07 |
23 | n-tricosane | 7.8(12+) | 4.219(84−) | −2.84(27+) | 36 | 0.98 | 0.12 | 3.4 | 0.06 |
24 | n-tetracosane | 7.9(13+) | 4.286(96+) | −2.79(31+) | 36 | 0.93 | −0.11 | 3.8 | 0.98 |
25 | n-pentacosane | 8.17(67+) | 4.330(40−) | −2.54(10−) | 15 | 0.29 | −0.21 | 3.4 | 0.06 |
26 | n-hexacosane | 8.2(11+) | 4.352(49−) | −2.43(19−) | 31 | 0.30 | −0.04 | 3.7 | 0.06 |
27 | n-heptacosane | 8.07(60+) | 4.331(41−) | −2.42(12−) | 16 | 0.31 | −0.19 | 3.8 | 0.06 |
28 | n-octacosane | 7.80(97+) | 4.24(15−) | −2.35(25−) | 24 | 1.67 | 1.26 | 7.7 | 0.78 |
29 | n-nonacosane | 7.70(58+) | 4.278(42−) | −2.33(12−) | 16 | 0.31 | −0.18 | 3.9 | 0.06 |
30 | n-triacontane | 7.72(83+) | 4.276(95−) | −2.32(19−) | 22 | 1.29 | 0.86 | 6.0 | 0.84 |
32 | n-dotriacontane | 7.58(90+) | 4.356(45−) | −2.24(17−) | 25 | 0.32 | −0.09 | 4.0 | 0.06 |
36 | n-hexatriacontane | 7.65(58+) | 4.399(58−) | −2.15(15−) | 18 | 0.43 | −0.13 | 4.6 | 0.06 |
Overall mean absolute percentage deviation (defined in Equation (30)) | 0.79 |
CN | MAPD/MAPDfit | MD/MDfit | PDm/PDmfit | ||
---|---|---|---|---|---|
(%) | (%) | (%) | |||
1 | 127/126 | 12.99/13.05 | −12.99/−13.05 | 20.95/20.95 | 0.11/0.11 |
2 | 163/160 | 3.48/3.28 | −2.33/−2.29 | 15.80/14.41 | 0.01/0.02 |
3 | 193/191 | 2.14/2.00 | −0.49/−0.34 | 22.59/22.10 | 0.01/0.06 |
4 | 126/118 | 5.42/2.59 | 2.35/−0.70 | 75.48/15.04 | 0.01/0.03 |
5 | 149/143 | 3.53/2.06 | 3.00/1.51 | 62.01/17.12 | 0.01/0.02 |
6 | 270/269 | 1.82/1.76 | 1.20/1.14 | 17.35/16.20 | 0.01/0.04 |
7 | 363/357 | 2.94/2.71 | 2.90/2.68 | 20.39/17.97 | 0.01/0.05 |
8 | 196/194 | 2.41/2.00 | 2.17/1.76 | 45.07/5.72 | 0.01/1.00 |
9 | 78 | 3.52 | 3.52 | 6.93 | 0.99 |
10 | 149 | 3.80 | 3.74 | 9.71 | 0.12 |
11 | 60 | 4.36 | 4.36 | 10.43 | 0.30 |
12 | 100 | 4.98 | 4.98 | 12.18 | 0.91 |
13 | 48 | 4.30 | 4.30 | 5.86 | 0.99 |
14 | 49 | 3.60 | 3.39 | 5.72 | 0.97 |
15 | 40 | 4.19 | 4.19 | 5.37 | 0.95 |
16 | 127/117 | 2.40/2.31 | 1.52/1.90 | 7.31/7.17 | 0.08/1.00 |
17 | 44/34 | 1.56/1.06 | −0.13/0.80 | 7.16/2.15 | 0.07/0.78 |
18 | 39/29 | 1.57/0.55 | −0.92/0.34 | 9.37/1.40 | 0.07/1.00 |
19 | 23/12 | 2.85/1.20 | −2.49/−0.51 | 10.41/10.20 | 0.07/0.34 |
20 | 38/25 | 2.89/1.43 | −2.78/−1.26 | 17.69/17.69 | 0.33/0.33 |
21 | 28/14 | 5.86/4.78 | −5.86/−4.78 | 14.00/7.35 | 0.07/0.49 |
22 | 32/19 | 5.16/4.05 | −5.16/−4.05 | 13.18/6.99 | 0.07/0.54 |
23 | 36/22 | 5.05/3.74 | −5.05/−3.74 | 13.93/6.97 | 0.06/0.52 |
24 | 36/22 | 5.60/4.43 | −5.56/−4.36 | 14.37/7.22 | 0.06/0.61 |
25 | 15/ 1 | 6.92/3.48 | −6.92/−3.48 | 14.70/3.48 | 0.06/0.95 |
26 | 31/19 | 5.40/3.96 | −5.40/−3.96 | 14.97/4.45 | 0.06/0.81 |
27 | 16/ 1 | 6.45/3.32 | −6.45/−3.32 | 14.52/3.32 | 0.06/0.96 |
28 | 24/ 9 | 4.42/2.57 | −3.35/0.29 | 13.13/4.23 | 0.06/0.78 |
29 | 16/ 1 | 5.41/2.60 | −5.41/−2.60 | 12.95/2.60 | 0.06/0.97 |
30 | 22/ 7 | 4.64/2.57 | −3.91/−0.30 | 13.07/4.01 | 0.06/0.55 |
32 | 25/12 | 4.92/3.64 | −4.92/−3.64 | 12.61/4.23 | 0.06/0.85 |
36 | 18/ 1 | 5.67/3.48 | −5.67/−3.48 | 13.36/3.48 | 0.06/1.00 |
- | 2681/2427 | 75.48/22.10 | |||
OMAPD/ | OMD/ | ||||
OMAPDfit | OMDfit | ||||
32 | 4.38/3.35 | −1.38/−0.53 |
Name | Symbol | Units | |
---|---|---|---|
0 | No dependency (constant) | - | - |
1 | Critical pressure | Pa | |
2 | Critical temperature | K | |
3 | Acentric factor | - | |
4 | Critical compressibility factor | - | |
5 | Critical volume | L mol−1 | |
6 | Melting temperature | K | |
7 | Triple point temperature | K | |
8 | Normal boiling point temperature | K | |
9 | Logarithmic ratio between and | - | |
10 | Liquid molar volume at 298.15 K and 101,325 Pa | L mol−1 | |
11 | Radius of gyration | RG | m |
12 | Dipole moment | Cm | |
13 | Molar weight | kg kmol−1 | |
14 | Reduced triple point temperature | - | |
15 | Reduced normal boiling temperature | - | |
16 | Pseudo compressibility factor | ) | - |
17 | Reduced boiling temperature | - |
Adjustable Coefficients | RG | |||||
---|---|---|---|---|---|---|
() | 5.01227 | 4.91156 | 5.37325 | 6.48294 | 4.99955 | |
() | 4.40431 | 1.09159 | 0.662073 | 3.03929 | 0.625431 | |
0.885059 | 0.53364 | 0.595946 | 0.254804 | 0.452929 | ||
() | 1.08825 | 2.68771 | 4.84453 | 5.0875 | 3.52179 | |
0.519495 | 0.401163 | 0.542305 | 4.98139 | 0.405698 | ||
() | −2.92951 | −2.6442 | −2.05972 | −2.20715 | −3.45186 | |
Statistical figures for the fitting set | ||||||
OMAPDfit (%) | 1.78 | 1.94 | 1.99 | 2.16 | 2.18 | |
MDfit (%) | 0.04 | −0.02 | −0.13 | 0.16 | 0.24 | |
PDmfit (%) | 23.93 | 24.37 | 23.76 | 21.44 | 24.35 | |
Statistical figures for the whole set | ||||||
OMAPD (%) | 2.26 | 2.52 | 2.78 | 2.68 | 2.57 | |
MD (%) | −0.45 | −0.79 | −1.20 | −0.37 | 0.11 | |
PDm (%) | 65.02 | 63.50 | 68.36 | 81.76 | 64.95 |
CN | MAPD/MAPDfit | MD/MDfit | PDm/PDmfit | ||
---|---|---|---|---|---|
(%) | (%) | (%) | |||
1 | 127/126 | 2.49/2.45 | −2.20/−2.16 | 16.28/16.28 | 0.11/0.11 |
2 | 163/160 | 2.58/2.35 | 0.09/0.25 | 20.01/10.71 | 0.01/0.04 |
3 | 193/191 | 1.84/1.65 | 0.27/0.48 | 26.76/23.93 | 0.01/0.06 |
4 | 126/118 | 4.54/2.19 | 1.53/−1.02 | 65.02/10.03 | 0.01/0.03 |
5 | 149/143 | 2.42/1.25 | 1.75/0.54 | 51.44/11.26 | 0.01/0.02 |
6 | 270/269 | 1.72/1.69 | −0.37/−0.41 | 12.64/12.64 | 0.07/0.07 |
7 | 363/357 | 1.36/1.22 | 0.96/0.81 | 13.96/13.96 | 0.05/0.05 |
8 | 196/194 | 1.40/1.08 | −0.34/−0.68 | 35.68/4.47 | 0.01/0.19 |
9 | 78 | 0.54 | 0.38 | 3.76 | 0.54 |
10 | 149 | 1.55 | 0.97 | 8.52 | 0.12 |
11 | 60 | 1.77 | 1.77 | 11.63 | 0.30 |
12 | 100 | 2.37 | 2.34 | 7.96 | 0.91 |
13 | 48 | 1.66 | 1.66 | 4.26 | 0.69 |
14 | 49 | 0.96 | 0.61 | 3.76 | 0.72 |
15 | 40 | 1.67 | 1.67 | 4.58 | 0.74 |
16 | 127/117 | 1.77/1.73 | −0.24/−0.09 | 8.64/7.67 | 0.08/0.46 |
17 | 44/34 | 1.15/0.84 | −0.68/−0.39 | 8.56/2.20 | 0.07/0.78 |
18 | 39/29 | 1.50/1.08 | −1.24/−0.74 | 10.54/2.65 | 0.07/0.99 |
19 | 23/12 | 2.06/1.44 | −1.54/−0.64 | 11.62/7.08 | 0.07/0.34 |
20 | 38/25 | 2.48/1.97 | −2.18/−1.52 | 14.55/14.55 | 0.33/0.33 |
21 | 28/14 | 3.80/2.81 | −3.80/−2.81 | 14.97/3.63 | 0.07/0.49 |
22 | 32/19 | 3.15/2.48 | −3.15/−2.48 | 13.98/3.32 | 0.07/0.63 |
23 | 36/22 | 2.79/1.90 | −2.53/−1.47 | 14.82/3.23 | 0.06/0.64 |
24 | 36/22 | 3.02/2.20 | −2.92/−2.04 | 15.08/3.94 | 0.06/0.80 |
25 | 15/ 1 | 3.64/2.25 | −3.64/−2.25 | 15.32/2.25 | 0.06/0.95 |
26 | 31/19 | 2.32/1.39 | −2.31/−1.36 | 15.59/2.09 | 0.06/0.93 |
27 | 16/ 1 | 2.53/1.31 | −2.53/−1.31 | 15.04/1.31 | 0.06/0.96 |
28 | 24/ 9 | 3.33/4.91 | 1.05/4.91 | 13.58/8.81 | 0.06/0.78 |
29 | 16/ 1 | 2.22/0.07 | −0.92/0.07 | 13.24/0.07 | 0.06/0.97 |
30 | 22/ 7 | 3.07/4.39 | 0.83/4.39 | 13.29/7.22 | 0.06/0.84 |
32 | 25/12 | 1.64/0.55 | −0.11/0.55 | 12.66/0.97 | 0.06/0.87 |
36 | 18/ 1 | 2.88/1.30 | 0.45/1.30 | 13.31/1.30 | 0.06/1.00 |
Overall | 2681/2427 | 65.02/23.93 | |||
OMAPD/ | OMD/ | ||||
OMAPDfit | OMDfit | ||||
32 | 2.26/1.78 | −0.45/0.04 |
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Cachadiña, I.; Hernández, A.; Mulero, Á. A New General Correlation for the Influence Parameter in Density Gradient Theory and Peng–Robinson Equation of State for n-Alkanes. Molecules 2024, 29, 5643. https://doi.org/10.3390/molecules29235643
Cachadiña I, Hernández A, Mulero Á. A New General Correlation for the Influence Parameter in Density Gradient Theory and Peng–Robinson Equation of State for n-Alkanes. Molecules. 2024; 29(23):5643. https://doi.org/10.3390/molecules29235643
Chicago/Turabian StyleCachadiña, Isidro, Ariel Hernández, and Ángel Mulero. 2024. "A New General Correlation for the Influence Parameter in Density Gradient Theory and Peng–Robinson Equation of State for n-Alkanes" Molecules 29, no. 23: 5643. https://doi.org/10.3390/molecules29235643
APA StyleCachadiña, I., Hernández, A., & Mulero, Á. (2024). A New General Correlation for the Influence Parameter in Density Gradient Theory and Peng–Robinson Equation of State for n-Alkanes. Molecules, 29(23), 5643. https://doi.org/10.3390/molecules29235643