Diffusion of hydrocarbons diluted in supercritical carbon dioxide

Mutual diffusion of six hydrocarbons (methane, ethane, isobutane, benzene, toluene or naphthalene) diluted in supercritical carbon dioxide (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\hbox {CO}}_{2}$$\end{document}CO2) is studied by molecular dynamics simulation near the Widom line, i.e., in the temperature range from 290 to 345 K along the isobar 9 MPa. The \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\hbox {CO}}_{2}$$\end{document}CO2 + aromatics mixtures are additionally sampled at 10 and 12 MPa and an experimental database with Fick diffusion coefficient data for those systems is provided. Taylor dispersion experiments of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\hbox {CO}}_{2}$$\end{document}CO2 with benzene, toluene, n-dodecane and 1,2,3,4-tetrahydronaphthalene are conducted along the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p =$$\end{document}p= 10 MPa isobar. Maxwell–Stefan and Fick diffusion coefficients are analyzed, together with the thermodynamic factor that relates them. It is found that the peculiar behavior of the Fick diffusion coefficient of some \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\hbox {CO}}_{2}$$\end{document}CO2 mixtures in the extended critical region is a consequence of the thermodynamic factor minimum due to pronounced clustering on the molecular scale. Further, the strong dependence of the Fick diffusion coefficient on the molecular mass of the solute as well as the breakdown of the Stokes–Einstein relation near the Widom line are confirmed. Eleven correlations for the prediction of the Fick diffusion coefficient of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\hbox {CO}}_{2}$$\end{document}CO2 mixtures are assessed. An alternative two-step approach for the prediction of the infinite dilution Fick diffusion coefficient of supercritical \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\hbox {CO}}_{2}$$\end{document}CO2 mixtures is proposed. It requires only the state point in terms of temperature and pressure (or density) as well as the molecular solute mass as input parameters. First, entropy scaling is applied to estimate the self-diffusion coefficient of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\hbox {CO}}_{2}$$\end{document}CO2. Subsequently, this coefficient is used to determine the infinite dilution Fick diffusion coefficient of the mixture, based on the finding that these two diffusion coefficients exhibit a linear relationship, where the slope depends only on the molecular solute mass.


Predictive equations
Table S1.Average absolute relative deviation of the eleven correlations to the present simulation data along the isobars p = 9, 10 and 12 MPa, as well as to the present experimental data for CO 2 mixtures with benzene or toluene along the isobar p = 10 MPa.The abbreviations for the correlations are WC: Wilke-Chang, LT: Lai-Tan, FW: Funazukuri-Wakao, TC: Tyn-Calus, CK: Catchpole-King, HM: Hayduk-Minhas, mRG: modified Rice-Gray, mSE: modified SE.

Figure S1 . 13 Figure S2 .
Figure S1.Temperature dependence of the thermodynamic factor of CO 2 mixtures with 0.5 mol% (bottom), 1.0 mol% (center) and 1.5 mol% (top) of ethane (dark green), benzene (red) or naphthalene (green) along the isobar p = 9 MPa.Circles represent molecular simulation data.Solid lines depict the thermodynamic factor calculated with TREND 5.0 4 on the basis of the GERG-2008 EoS 5 for CO 2 + ethane, or on the basis of the Peng-Robinson EoS for CO 2 + benzene (k 12 = 0.0967) 6 or CO 2 + naphthalene (k 12 = 0.016, l 12 = −0.173) 7.Dotted lines indicate the thermodynamic factor minimum as inferred from molecular simulation data.

Figure S3 ./ 13 Figure S4 . 6 / 13 Figure S5 .
Figure S3.Temperature dependence of the thermodynamic factor of CO 2 mixtures with 1.0 mol% (bottom) and 1.5 mol% (top) of benzene along the isobars p = 10 MPa (triangles) and 12 MPa (squares).Symbols represent molecular simulation data at p = 9 MPa.Solid and dashed lines depict the thermodynamic factor calculated with TREND 5.0 4 on the basis of the Peng-Robinson EoS for CO 2 + benzene at 10 and 12 MPa, respectively.

Figure S6 .
Figure S6.Temperature dependence of the infinite dilution Fick diffusion coefficient of CO 2 + methane along the isobar p = 9 MPa.Circles represent molecular simulation data obtained from the extrapolation of the intra-diffusion coefficient of methane to the infinite dilution limit.Solid lines depict semi-empirical correlations8-17 and the dashed line shows the present predictive approach (Eqs.(2) to (4)) in the paper.

Figure S7 ./ 13 Figure S8 ./ 13 Figure S9 .
Figure S7.Temperature dependence of the infinite dilution Fick diffusion coefficient of CO 2 + isobutane along the isobar p = 9 MPa.Circles represent molecular simulation data obtained from the extrapolation of the intra-diffusion coefficient of isobutane to the infinite dilution limit.Solid lines depict semi-empirical correlations8-17 and the dashed line shows the present predictive approach (Eqs.(2) to (4)) in the paper.

Figure S10 .
Figure S10.Temperature dependence of the Fick diffusion coefficient at infinite dilution of CO 2 + naphthalene along the isobars p = 9 MPa (top), 10 MPa (center) and 12 MPa (bottom).Circles represent molecular simulation data obtained from the extrapolation of the intra-diffusion coefficient of naphthalene to the infinite dilution limit.Solid lines depict semi-empirical correlations8-17 and the dashed line shows the present predictive approach (Eqs.(2) to (4)) in the paper.

Figure S11 .
Figure S11.Rosenfeld's entropy scaling applied to the self-diffusion coefficient of CO 2 as a function of the reduced residual entropy (left) or the entropy scaling coordinate −(s r /s r T c,vc ) − ln(s r /s r T c,vc ) 18, 19 (right).Circles represent simulation data.Experimental data for the self-diffusion coefficient of CO 2 in combination with the reduced residual entropy obtained from the Span-Wagner EOS 20 are depicted by crosses.