Thermodynamic Modeling with Equations of State: Present Challenges with Established Methods

Wilhelmsen, Øivind; Aasen, Ailo; Skaugen, Geir; Aursand, Peder; Austegard, Anders; Aursand, Eskil; Gjennestad, Magnus Aa.; Lund, Halvor; Linga, Gaute; Hammer, Morten

doi:10.1021/acs.iecr.7b00317

Cited by 121 publications

(70 citation statements)

References 100 publications

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“…By using binary interaction parameters, the Peng-Robinson EOS accurately represents vapor-liquid equilibrium compositions for mixtures of hydrocarbons. 59,60 The phase diagram of hexane-heptane at T = 298.15 K as calculated by the Peng-Robinson EOS is displayed in Fig. 3, where the binary interaction parameter is provided in Table II.…”

Section: Resultsmentioning

confidence: 99%

Tolman lengths and rigidity constants of multicomponent fluids: Fundamental theory and numerical examples

Aasen

Blokhuis

Wilhelmsen

2018

The Journal of Chemical Physics

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The curvature dependence of the surface tension can be described by the Tolman length (first-order correction) and the rigidity constants (second-order corrections) through the Helfrich expansion. We present and explain the general theory for this dependence for multicomponent fluids and calculate the Tolman length and rigidity constants for a hexane-heptane mixture by use of square gradient theory. We show that the Tolman length of multicomponent fluids is independent of the choice of dividing surface and present simple formulae that capture the change in the rigidity constants for different choices of dividing surface. For multicomponent fluids, the Tolman length, the rigidity constants, and the accuracy of the Helfrich expansion depend on the choice of path in composition and pressure space along which droplets and bubbles are considered. For the hexane-heptane mixture, we find that the most accurate choice of path is the direction of constant liquid-phase composition. For this path, the Tolman length and rigidity constants are nearly linear in the mole fraction of the liquid phase, and the Helfrich expansion represents the surface tension of hexane-heptane droplets and bubbles within 0.1% down to radii of 3 nm. The presented framework is applicable to a wide range of fluid mixtures and can be used to accurately represent the surface tension of nanoscopic bubbles and droplets.

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Section: Resultsmentioning

confidence: 99%

Tolman lengths and rigidity constants of multicomponent fluids: Fundamental theory and numerical examples

Aasen

Blokhuis

Wilhelmsen

2018

The Journal of Chemical Physics

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“…III C. The EoS was implemented in the in-house thermodynamic library presented in Ref. 16, and we refer to previous work for details on routines for solving phase equilibria. [43][44][45][46] A.…”

Section: Methodsmentioning

confidence: 99%

“…15 For some fluids, multiparameter EoSs are capable of representing the available experimental data within their accuracy. However, these EoSs have challenges 16 that restrict their widespread application. A shortcoming of the multiparameter EoS framework is the lack of binary mixing models for helium, neon, hydrogen, and deuterium.…”

Section: Introductionmentioning

confidence: 99%

Equation of state and force fields for Feynman–Hibbs-corrected Mie fluids. I. Application to pure helium, neon, hydrogen, and deuterium

Aasen

Hammer

Ervik

et al. 2019

The Journal of Chemical Physics

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We present a perturbation theory that combines the use of a third-order Barker–Henderson expansion of the Helmholtz energy with Mie-potentials that include first- (Mie-FH1) and second-order (Mie-FH2) Feynman–Hibbs quantum corrections. The resulting equation of state, the statistical associating fluid theory for Mie potentials of variable range corrected for quantum effects (SAFT-VRQ-Mie), is compared to molecular simulations and is seen to reproduce the thermodynamic properties of generic Mie-FH1 and Mie-FH2 fluids accurately. SAFT-VRQ Mie is exploited to obtain optimal parameters for the intermolecular potentials of neon, helium, deuterium, ortho-, para-, and normal-hydrogen for the Mie-FH1 and Mie-FH2 formulations. For helium, hydrogen, and deuterium, the use of either the first- or second-order corrections yields significantly higher accuracy in the representation of supercritical densities, heat capacities, and speed of sounds when compared to classical Mie fluids, although the Mie-FH2 is slightly more accurate than Mie-FH1 for supercritical properties. The Mie-FH1 potential is recommended for most of the fluids since it yields a more accurate representation of the pure-component phase equilibria and extrapolates better to low temperatures. Notwithstanding, for helium, where the quantum effects are largest, we find that none of the potentials give an accurate representation of the entire phase envelope, and its thermodynamic properties are represented accurately only at temperatures above 20 K. Overall, supercritical heat capacities are well represented, with some deviations from experiments seen in the liquid phase region for helium and hydrogen.

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“…The analytic representation of the first and second order perturbation theories as well as the analytic derivatives up to second order were next implemented in the thermodynamic framework described in Ref. [20], which allows thermodynamic properties to be computed with a high accuracy, and phase-equilibrium calculations to be performed with state-of-the-art algorithms [14].…”

Section: Perturbation Theorymentioning

confidence: 99%

“…With the parameterization of the perturbation theory detailed in Section 4, we used the thermodynamic framework presented in Ref. [20] to compute the JT inversion curve as analytical derivatives of the parameterization. The resulting JT inversion curve computed from the Barker-Henderson second-order perturbation theory is shown in Figure 11.…”

Section: Perturbation Theorymentioning

confidence: 99%

Thermodynamic properties of the 3D Lennard-Jones/spline model

et al. 2019

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In the Lennard-Jones spline (LJ/s) model, the Lennard-Jones (LJ) potential is truncated and splined so that both the pair potential and the force continuously approach zero at rc ≈ 1.74σ. It exhibits the same structural features as the LJ model, but the thermodynamic properties are different due to the shorter range of the potential. One advantage of the model is that simulation times are much shorter. In this work, we present a systematic map of the thermodynamic properties of the LJ/s model from molecular dynamics and Gibbs ensemble Monte Carlo simulations. Accurate results are presented for gas/liquid, liquid/solid and gas/solid coexistence curves, supercritical isotherms up to a reduced temperature of 2 (in LJ units), surface tensions, speed of sound, the Joule-Thomson inversion curve, and the second to fourth virial coefficients. The critical point for the LJ/s model is estimated to be T * c = 0.885 ± 0.002 and P * c = 0.075 ± 0.001, respectively. The triple point is estimated to T * tp = 0.547 ± 0.005 and P * tp = 0.0016 ± 0.0002. Despite the simplicity of the model, the acentric factor was found to be as large as 0.07±0.02. The coexistence densities, saturation pressure, and supercritical isotherms of the LJ/s model were fairly well represented by the Peng-Robison equation of state. We find that Barker-Henderson perturbation theory works much more poorly for the LJ/s model than for the LJ model. The first-order perturbation theory overestimates the critical temperature and pressure by about 10% and 90%, respectively. A second-order perturbation theory that uses the mean compressibility approximation shifts the critical point closer to simulation data, but makes the prediction of the saturation densities worse. It is hypothesized that the reason for this is that the mean compressibility approximation gives a poor representation of the second-order perturbation term for the LJ/s model and that a correction factor is needed at high densities.Our main conclusion is that we at the moment do not have a theory or model that adequately represents the thermodynamic properties of the LJ/s system.

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Thermodynamic Modeling with Equations of State: Present Challenges with Established Methods

Cited by 121 publications

References 100 publications

Tolman lengths and rigidity constants of multicomponent fluids: Fundamental theory and numerical examples

Tolman lengths and rigidity constants of multicomponent fluids: Fundamental theory and numerical examples

Equation of state and force fields for Feynman–Hibbs-corrected Mie fluids. I. Application to pure helium, neon, hydrogen, and deuterium

Thermodynamic properties of the 3D Lennard-Jones/spline model

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