Common Equations Of State Research Articles

Comparative analysis and computational optimization of potential-based multiphase lattice Boltzmann models

The potential-based multiphase lattice Boltzmann models are widely used because they root in thermodynamics and evade the interface tracking or integrating. This paper investigates several potential-based models with the common equations of state (EOS) by the theoretical analyses and numerical computations of the thermodynamic consistency and spurious currents. Surprisingly, the Shan–Chen model presents a superior accuracy compared to the Zhang–Chen models, although they are mathematically equivalent. We find that the great improvement is attributed to the square root form of the pseudopotential model, which significantly lessens the error of numerical gradient calculation. Inspired by the improvement, a general formula φ′=n−1φ1−n∂x(φn) is introduced for calculating the gradient, and the coefficient n=0.1 yields better results than n=0.5, which is equal to the pseudopotential model. This scheme is further applied to optimize the evaluation of the chemical potential model. The improved chemical potential model displays lower numerical errors in the liquid–gas transition region and smaller spurious currents near the curved phase interface than the pseudopotential model. Additionally, the improved model is confirmed to meet the Young–Laplace law and Galilean invariance.

New insight into prediction of phase behavior of natural gas hydrate by different cubic equations of state coupled with various mixing rules

Progress in hydrate thermodynamic study necessitates robust and fast models to be incorporated in reservoir simulation softwares. However, numerous models presented in the literature makes selection of the best, proper predictive model a cumbersome task. It is of industrial interest to make use of cubic equations of state (EOS) for modeling hydrate equilibria. In this regard, this study focuses on evaluation of three common EOSs including Peng–Robinson, Soave–Redlich–Kwong and Valderrama–Patel–Teja coupled with van der Waals and Platteeuw theory to predict hydrate P–T equilibrium of a real natural gas sample. Each EOS was accompanied with three mixing rules, including van der Waals (vdW), Avlonitis non-density dependent (ANDD) and general non-quadratic (GNQ). The prediction of cubic EOSs was in sufficient agreement with experimental data and with overall AARD% of less than unity. In addition, PR plus ANDD proved to be the most accurate model in this study for prediction of hydrate equilibria with AARD% of 0.166. It was observed that the accuracy of cubic EOSs studied in this paper depends on mixing rule coupled with them, especially at high-pressure conditions. Lastly, the present study does not include any adjustable parameter to be correlated with hydrate phase equilibrium data.

Systematic Misprediction of n-Alkane + Aromatic and Naphthenic Hydrocarbon Phase Behavior Using Common Equations of State

Phase equilibrium calculations based on 150 n-alkane + aromatic and n-alkane + naphthenic hydrocarbon binary mixtures were performed. These calculations were compared with experimental measurements whenever possible, and additional measurements were made as part of this work. The widely used Peng–Robinson (PR) and Soave–Redlich–Kwong (SRK) equations of state are shown to predict nonphysical liquid–liquid phase behavior for long-chain n-alkane + aromatic and long-chain n-alkane + naphthenic hydrocarbon binary mixtures with standard pure-component parameters (Tc, Pc, ω). Incorrect phase behavior prediction is shown to be insensitive to the selection of correlations for estimating pure-component properties for n-alkanes that are not available from experimental data. For cubic equations of state, correct phase behaviors are obtained only when negative values of the binary interaction parameters (kij) are used. For PC-SAFT, a noncubic equation of state (with standard parameter values defining molecules and wit...

Structural properties of hexagonal boron nitride

The electronic and structural properties of hexagonal boron nitride (BN) were studied using density functional theory calculations. Three different approximations for the exchange—correlation energy (the local density and two forms of the generalized gradient)—were used to calculate properties such as the bulk modulus, cohesive energy and lattice constants to determine their relative predictive abilities for this system. In general, calculations using the local density approximation produced properties slightly closer to experimental values than calculations with either generalized gradient approximations. Different stackings, or arrangements of one basal plane with respect to another, were examined to determine the equilibrium stacking(s) and it was found that the different stackings have similar cohesive energies and bulk moduli. Energy versus volume curves were calculated for each stacking using two different methods to determine their relative efficacy. Bulk moduli values obtained assuming no pressure dependence were closer to experimental values than those obtained from three common equations of state. Comparisons between the cohesive energies of hexagonal BN and cubic BN show that the cubic phase is more stable. The pressure/volume dependence of the band structure was studied for several different stackings and all showed similar behaviour, specifically a 3–4.5 eV band gap that was nearly independent of pressure in the −500 to +500 kb regime. These calculated results of the pressure/volume dependence of the band structure are the first reports for this system.

Interfacial Behavior in Type IV Systems

Type IV mixtures exhibit two heteroazeotropic lines, one at low temperature and the other meeting the supercritical range, characterized by the proximity of their critical end points (CEPs). Between these CEPs, the liquid phase is homogeneous inside a narrow range of temperature. The aim of this work is to analyze interface properties and wetting transitions for Type IV mixtures. Interfacial tensions have been calculated by means of the gradient theory, applied to binary van der Waals fluids. This approach is able to predict interfacial tension and phase equilibrium using a common equation of state (EOS). Results show that interfacial properties and wetting conditions are governed by the densities and the number of phases involved in equilibrium, a scenario that changes as temperature evolves from the low- to the high-temperature heteroazeotropic line.

Radial oscillations of relativistic stars

We present a new survey of the radial oscillation modes of neutron stars. This study complements and corrects earlier studies of radial oscillations. We present an extensive list of frequencies for the most common equations of state and some more recent ones. In order to check the accuracy, we use two different numerical schemes which yield the same results. The stimulation for this work comes from the need of the groups that evolve the full nonlinear Einstein equations to have reliable results from perturbation theory for comparison.

A simple non-local spallation failure model

A new, simple theoretical model to characterise the average continuum behaviour of the spall process is presented. Unlike all previous models, it is based on a non-local view of spallation and is applicable to both ductile and brittle materials. The model was incorporated into one and two dimensional hydrodynamic code to predict the free surface velocity of ductile and brittle targets in planar plate impact experiments, and can be extended to three dimensional problems. The results compared well with experimental data. The model can be used with common equations of state and constitutive equations.

C60 under pressure-bulk modulus and equation of state

C60 has been investigated under pressure up to 13 GPa using angular dispersive X-ray scattering and a diamond anvil cell. The resolution of the experimental setup allows to examine the volume decrease dV/dp under pressure even for pressures of a tenth of a GPa. The obtained data of numerous experimental runs result in a bulk modulus of 13.4 GPa, which is much smaller than the value reported by Duclos et al. [1]. At 170 K and 70 K a bulk modulus of 14.2 GPa and 14.7 GPa was obtained, respectively. The pressure induced fcc-sc transition at 300 K was clearly visible at approx. 0.3 GPa with a jump in the lattice parameter of 0.05 A. With increasing pressure we found an extreme change in dV/dp, which disables the usage of common equations of state (EOS), like the Murnaghan [2] or Birch [3] equation. Considering the small compressibility of the fullerence molecules we suggest a modified EOS to describe the experimental data.

Correlation of high-pressure phase equilibria in the retrograde region with three common equations of state

Phase equilibria in the retrograde regions were calculated for the methane — n-decane binary system and for a realistic natural-gas system (methane - Kensol-16). Calculations were performed using three equations of state (EOS): Peng-Robinson, Redlich-Kwong-Soave and Perturbed-Hard-Chain; calculations were compared to experiment. Liquid-drop-out curves and pressure-temperature diagrams were calculated between 301 and 369 K and pressures to 90 MPa. The binary system was represented best by the Peng-Robinson EOS. For the natural-gas system, the Perturbed-Hard Chain equation yielded the best results, although all equations of state showed appreciable deviations. Good results could only be obtained when binary coefficients were fitted to the experimental retrograde data. On a calcule l'equilibre de phase dans des regions retrogrades pour le systeme binaire methane — n-decane et pour un systeme au gaz naturel realiste (methane - Kensol-16). Les calculs ont ete effectues au moyen de trois equations d'etat, soit l'equation de Peng-Robinson, de Redlich-Kwong-Soave et de la chaine rigide perturbee; les calculs ont ete compares aux resultats experimentaux. Les courbes de la perte du liquide et les diagrammes des pressions et des temperatures ont ete calcules entre 301 et 369 K et les pressions jusqu'a 90 MPa. Le systeme binaire est mieux represente par l'equation d'etat de Peng-Robinson. Pour le systeme au gaz naturel, l'equation de la chaǐne rigide perturbee donne les meilleurs resultats, bien que toutes les equations d'etat montrent des ecarts appreciables. On a pu obtenir de bons resultats seulement lorsque les coefficients binaires ont ete adaptes aux donnees retrogrades experimentales.

An analysis of the industrial use of a phase equilibria prediction model based on thermodynamic perturbation theory

An extended Gubbins-Gray perturbation theory is analysed and compared with the results from a common equation of state. Industrially important phase equilibria are studied for systems relevant to natural gas and ‘syngas’ processing. Systematic test systems are developed. At present the success of the theory is limited and unsystematic, indicating that its predictive power is very small.

Computational aspects of equations of state: Fact and fiction

AbstractA detailed study has been made of the computing times for several common equations of state used by industry. The cubic equations are approximately equivalent to more complicated equations (e.g., perturbed hard chain and BWRS) for systems with eight or more components. Thus, it is not justified to choose cubic equations over other forms purely on the basis of computational advantage. Further, the study identifies mixing‐rule summations as the dominant consumer of computing time.

A common equation of state?—LiF, NaF, NaCl, NaI

Summary It has been exhibited that four alkali halides with the NaCl structure have a common reduced equation of state. We remark that it would be most useful indeed to extend the primary shock data to those other Li and Na halides which do not show a phase transformation under pressure to see if this observation holds up. If such a program were to be undertaken it probably would be better to express the primary data directly in terms of a reduced Hugoniot if possible, so that assumptions which must be made in translating the shock data to an isothermal equation of state could be omitted. We also should like to remark that this paper emphasized the fact that it would be most useful if equation of state data were expressed and plotted in reduced form and, when the circumstances allow, in composite form by the original investigators as Bernardes and Swenson [9] have done previously for the rare gases and the alkali metals.