Diffusion of hydrocarbons diluted in supercritical carbon dioxide

Abstract

Mutual diffusion of six hydrocarbons (methane, ethane, isobutane, benzene, toluene or naphthalene) diluted in supercritical carbon dioxide ($${\hbox {CO}}_{2}$$ CO 2 ) 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 $${\hbox {CO}}_{2}$$ CO 2 + 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 $${\hbox {CO}}_{2}$$ CO 2 with benzene, toluene, n-dodecane and 1,2,3,4-tetrahydronaphthalene are conducted along the $$p =$$ 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 $${\hbox {CO}}_{2}$$ CO 2 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 $${\hbox {CO}}_{2}$$ CO 2 mixtures are assessed. An alternative two-step approach for the prediction of the infinite dilution Fick diffusion coefficient of supercritical $${\hbox {CO}}_{2}$$ CO 2 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 $${\hbox {CO}}_{2}$$ CO 2 . 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.

Mutual Diffusivities of Mixtures of Carbon Dioxide and Hydrogen and Their Solubilities in Brine: Insight from Molecular Simulations

“…To explain why the self-diffusivities of H 2 exceed those of CO 2 , the Stokes–Einstein (SE) relation , is used. The SE equation links the self-diffusivity of a microscopic entity in liquid, viscosity, temperature, and effective radius (or a hydrodynamic radius, R eff ) as , D normals normale normall normalf = k B T / 6 π η R normale normalf normalf Here, stick boundary conditions are assumed, , resulting in a factor of 6π in the SE equation, in contrast to the 4π factor used with slip boundary conditions. , It is also implicitly assumed that R eff in eq is unaffected by T . , Treating CO 2 and H 2 as spherical entities with an R eff equal to the bond length between carbon and oxygen (1.16 Å), and half the bond length between the two hydrogen atoms in H 2 (0.37 Å), the ratio of their self-diffusivities as per eq amounts to ca. 3.14, a value larger than unity.…”

“…11 , 127 It is also implicitly assumed that R eff in eq 7 is unaffected by T . 11 , 45 Treating CO 2 and H 2 as spherical entities with an R eff equal to the bond length between carbon and oxygen (1.16 Å), and half the bond length between the two hydrogen atoms in H 2 (0.37 Å), the ratio of their self-diffusivities as per eq 7 amounts to ca. 3.14, a value larger than unity.…”

“…Here, stick boundary conditions are assumed, 11,127 resulting in a factor of 6π in the SE equation, in contrast to the 4π factor used with slip boundary conditions. 11,127 It is also implicitly assumed that R eff in eq 7 is unaffected by T. 11,45 Treating CO 2 and H 2 as spherical entities with an R eff equal to the bond length between carbon and oxygen (1.16 Å), and half the bond length between the two hydrogen atoms in H 2 (0.37 Å), the the incorrect assumption that R eff remains constant with temperature, as also noted by Saric and colleagues, 44 and/or, (2) the oversimplified treatment of linear molecules like CO 2 and H 2 as spherical entities.…”

“…Saric et al 44 proposed a simple equation to predict the Widom line of dilute supercritical CO 2 mixtures as a function of pressure, solute mole fraction, and critical properties of the mixture components. In a separate study, Saric et al 45 examined the mutual diffusion of various hydrocarbons dispersed in supercritical carbon dioxide via MD simulations near the Widom line, between 290 and 345 K at 9 MPa. Fick diffusivities were strongly affected close to the critical region of the mixture due to the pronounced clustering of solute molecules.…”

“…Fick diffusivities were strongly affected close to the critical region of the mixture due to the pronounced clustering of solute molecules. Saric et al 45 pointed out that the validity of the Stokes–Einstein relation near the Widom line was questionable. A correlation function was proposed to facilitate quick calculations of Fick diffusivities for various binary mixtures.…”