Semi‐analytical nanoscale‐extended surface tension correlation

Zhang, Kaiqiang; Jia, Na; Liu, Lirong

doi:10.1002/aic.16622

Cited by 5 publications

(5 citation statements)

References 64 publications

(94 reference statements)

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“…Measured and calculated surface tensions of the pure hydrocarbons of C 2 H 6 , C 3 H 8 , C 4 H 10 , and C 8 H 18 in the bulk phase (BP) and nanopores (NP) at different temperatures.…”

Section: Resultsmentioning

confidence: 99%

“…It is worthwhile to mention that for the liquid–liquid and/or liquid–gas system, the surface tension and surface energy are equivalent since the molecules in the liquid/gas phase can be displaced without performing additional work . Thus, the surface energy can be determined from the semianalytical correlation below where ε LJ is the Lennard-Jones energy parameter, σ LJ is the Lennard-Jones size parameter, ρ L and ρ G are the liquid and gas phase densities, , r p is the pore radius, and ∫ 5 and ∫ 11 are mathematical functions proposed in the literature . The detailed information with respect to the semianalytical correlation can be found in section 4 in the Supporting Information.…”

Section: Methodsmentioning

confidence: 99%

“…It is worthwhile to mention that for the liquid−liquid and/or liquid−gas system, the surface tension and surface energy are equivalent since the molecules in the liquid/gas phase can be displaced without performing additional work. 44 Thus, the surface energy can be determined from the semianalytical correlation below 45 A A 4 ( )…”

Section: Methodsmentioning

confidence: 99%

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Thermodynamic Parameters for Quantitative Miscibility Interpretations from the Bulk to Nanometer Scale

Zhang

Liu

et al. 2020

Ind. Eng. Chem. Res.

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In this paper, quantitative thermodynamic parameters are quantified and applied to evaluate the oil–gas miscibility developments and to determine the minimum miscibility pressures (MMPs) from the bulk to nanometer scale. First, mathematical formulations of the Gibbs and interfacial energies and the solubility parameter in the bulk phase and nanopores are derived coupled with a modified equation of state and semianalytical correlation. Second, the calculated Gibbs and interfacial energies and solubility parameters are utilized to analyze the miscibility development, based on which specific thermodynamic MMP criteria are developed. The calculated MMPs from the new thermodynamic MMP criteria are compared with and validated by the measured MMPs of a total of 55 dead and live oil-pure and impure gas systems in the bulk phase and nanopores at different conditions. Moreover, the effects of temperature, oil and gas compositions, and pore radius on the MMP are evaluated. It is found that the miscibility interpretation may be in variation based on different thermodynamic properties even though the miscible state performs similarly in the macroscopic perspective. Three new thermodynamic MMP criteria are developed based on the first derivatives of the Gibbs energy and solubility parameter and the second derivative of the interfacial energy with respect to pressure, which are linearly regressed and extrapolated to determine the MMP with a critical linear correlation coefficient. The three thermodynamic criteria are found to be accurate and physically correct for the MMP determinations of various oil–gas systems in the bulk phase and nanopores at different conditions, wherein the solubility parameter and interfacial energy criteria are slightly better than the Gibbs energy criterion. Overall, the miscibility is strongly dependent on the temperature, oil and gas compositions, and pore radius.

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“…Measured and calculated surface tensions of the pure hydrocarbons of C 2 H 6 , C 3 H 8 , C 4 H 10 , and C 8 H 18 in the bulk phase (BP) and nanopores (NP) at different temperatures.…”

Section: Resultsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

See 1 more Smart Citation

Thermodynamic Parameters for Quantitative Miscibility Interpretations from the Bulk to Nanometer Scale

Zhang

Liu

et al. 2020

Ind. Eng. Chem. Res.

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“…Even when the authors' approach (Equation 12) with its wrong assumptions was regenerated, the predictions were remarkably far from the reported values either with the L-J parameters from Cuadros 15 or those presented by authors themselves. 1…”

Section: The Authors Have Applied the Approximation Ementioning

confidence: 99%

Comments on “Semi‐analytical nanoscale‐extended surface tension correlation”

2021

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“…During the phase equilibrium process, the liquid/vapor density has been widely explored with experimental methods, theoretical models, and empirical correlations, among which empirical correlations are simple and efficient to determine the liquid/vapor density profile . In our work, the critical temperature-dependent empirical correlation obtained with minimizing the sum of the quadratic average deviation is adopted, that is where T c is the critical temperature; ρ c is the critical density; ρ r is the reduced density, ρ r,l and ρ r,v are the reduced liquid and vapor densities, respectively.…”

Section: Mathematical Modelmentioning

confidence: 99%

Nanoconfinement Effect on Surface Tension: Perspectives from Molecular Potential Theory

Feng

Bakhshian

et al. 2020

Langmuir

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Liquid–vapor surface tension (ST) in nanopores attracts great attention in many industries because of the prosperity of nanoscience and nanotechnology. Here, considering the important emerging new physical phenomena induced by nanoconfinement effects, including curvature-dependent and shift-critical temperature (T c)-dependent effects, the anomalous variation of ST in nanopores is captured from the molecular potential perspective. Furthermore, a simple analytical model is proposed to determine the ST in nanopores by correlating these two effects with an easily accessible parameter, that is, normalized pore dimension, which is the ratio of the pore radius to Lennard-Jones size parameter. The model is validated to be reliable for determining the STs of different substances both in the bulk phase as well as nanopores through comparison with the experimental results and molecular simulations. Our results show that the reduction of ST induced by the nanoconfinement effects is visible when the pore diameter is within tens of nanometers, and the reduction is more sensitive as the pore size decreases. In detail, the curvature-dependent effect is remarkable in the pores with diameters ranging from a few nanometers to tens of nanometers. Moreover, a simply generalized formula is obtained to determine the curvature-dependent effect and the Tolman length for different substances. The shift-T c-dependent effect is not only related to the pore dimension but also depends on the temperature. As the pore size decreases, the critical temperature of confined fluids diverges significantly from the bulk values. While at high temperatures, the range of pore size impacted by the shift-Tc-dependent effect is enlarged. Additionally, the nanoconfined STs of different substances are calculated and compared. Overall, the new model captures the underlying physics behind the variation of STs in nanopores and can determine the nanoconfined STs reasonably. Moreover, the simple formulation of the model is beneficial to the practical applications in many chemical engineering processes, such as chemical separation, nucleation phenomenon, and capillary condensation.

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Semi‐analytical nanoscale‐extended surface tension correlation

Cited by 5 publications

References 64 publications

Thermodynamic Parameters for Quantitative Miscibility Interpretations from the Bulk to Nanometer Scale

Thermodynamic Parameters for Quantitative Miscibility Interpretations from the Bulk to Nanometer Scale

Comments on “Semi‐analytical nanoscale‐extended surface tension correlation”

Nanoconfinement Effect on Surface Tension: Perspectives from Molecular Potential Theory

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