Equation Of State For Fluid Research Articles

An equation of state for fluids by applying the tower—Well potential model

A simple theoretical equation of state is derived by applying the Tower-Well potential model about the molecular distribution based on the generalized van der Waals partition function. It needs only three molecular parameters which have distinct physical meanings. The resulting equation of state predicts rather well the vapor pressures, saturated liquid volumes, saturated vapor volumes and PVT thermodynamic properties of polar and structurally complex molecules over a wide temperature and pressure range.

An accurate equation of state for fluids of linear homonuclear fused hard spheres

A model relating the equation of state of linear homonuclear fused hard sphere fluids to the equation of state of the hard sphere fluid is derived from the pressure equation. The equation of state reproduces simulation data practically within their accuracy for diatomic and linear triatomic hard molecular fluids.

Equation of state for hard convex body fluids from the equation of state of the hard sphere fluid

A simple and accurate equation of state for fluids of hard convex molecules is derived from the pressure equation and the equation of state of the hard sphere fluid. The equation of state provides theoretical support to some equations of state used in perturbation theories for real molecular liquids. The equation of state reproduces the simulation data with an accuracy comparable to that derived from density functional theory.

Square-well dimers of different bond lengths

The equation of state for fluids made of square-well dimers of different bond lengths is studied. The pair correlation function for the hard dimer reference fluid was obtained from Monte Carlo simulations of hard dimers of two bond lengths, and these results were used with a local composition model and with perturbation theory to calculate the thermodynamic properties. Separate Monte Carlo simulations were performed for the compressibility factor of square-well dimer fluids of the same bond lengths. Bond lengths of 0·608 and 0·3826 were chosen since they are similar to the chlorine (Cl2) bond length and the C-C bond length in ethane. These simulation results and the simulation results of Yethiraj and Hall for tangent square-well dimers were used to test the theories. Good agreement is obtained between the theories and the simulation data.

Cosmological solution in wesson's 5D theory of gravity

Cosmological solutions that obey the perfect fluid equation of state in Wesson's gravitational theory are presented assuming that the fifth dimension subspace is also homogeneous and isotropic like the usual homogeneous isotropic cosmological model. It is shown that the scale factor scales as\(\sqrt t \) for the vanishing fifth component of the energy momentum tensor. The role of the fifth component as a cosmological constant is remarked, and an inflationary model is thus obtained.

A cubic simplified perturbed hard‐chain equation of state for fluids with chainlike molecules

AbstractThe simplified version of the perturbed hard‐chain theory (SPHCT) developed by Kim et al. (1986) is modified by reformulating the attractive portion of the canonical partition function for mixtures, and replacing the repulsive portion by a simple simulated expression. The final equation of state developed is cubic in volume. The test results on pure fluids, binary/multi‐component mixtures and reservoir fluids indicate that the CSPHC EOS retains the advantages of the original PHCT, and significant improvements over the SPHCT in predicting the VLE of heavy hydrocarbon‐containing/CO2‐containing mixtures, and liquid phase density are observed.

Thermodynamic properties of the methane-ethane systen

Abstract Our recently completed wide-ranging correlations for the thermophysical properties of methane and ethane fluids have enabled us to improve the extended corresponding states calculations for the properties of the binary mixtures. The pure fluid equations are based on the analytic Schmidt-Wagner equation of state and give improved results in the general region of the critical point. We use these pure fluid equations (and a reference fluid for which an equivalent equation is known) to calculate properties and compare with experimental PVT data, isochoric heat capacities, and sound speeds of binary mixtures of methane and ethane. We also examine the properties at the vapor-liquid boundary and compare the representation from the classical extended corresponding states calculations with quantities derived from a scaling theory model. The shape of the binary mixture phase boundary is improved with this model, however our new representation of the single phase properties provides only a slight improvement over models based on modified Benedict-Webb-Rubin pure fluid equations of state.

A unified equation of state for fluids of C-H-O-N-S-Ar composition and their mixtures up to very high temperatures and pressures

A unified 3-parameter equation of state (EOS) for fluids of C-H-O-N-S-Ar composition based on molecular dynamical simulated data and on an approximation of intermolecular interaction with α-exponential-6 potential is shown to be valid at high pressure and temperature. The equation is parameterized for H 2O, CO 2, CH 4, CO, O 2, H 2, Ar, N 2, NH 3, H 2S, SO 2, COS, and S 2 in the ranges of temperature ( T) from 400 K (700 K for H 2O) to 4000 K and pressure from 5 kbar to 1000 kbar. The equation allows one to calculate any mixture of the fluid species in the system applying one-fluid approximation (i.e., using the α-exponential-6 parameters obtained by using mixing rules for the potentials of the pure species). The equation reproduces most of the available experimental data in the limits of experimental accuracy of volume ( V) measurements.

Statistical-mechanical basis for accurate analytical equations of state for fluids

Abstract Theories of liquids have been developed over the past twenty years based on the recognition that the structure of a liquid is determined primarily by repulsive forces, so that fluids of hard bodies (spherical or nonspherical) can serve as useful reference states for perturbation theories. We show how these results can be extended to obtain simple analytical equations of state for real fluids, which include the low-density vapor and the supercritical fluid as well as the true liquid. These equations are quintic in the density (the van der Waals equation is cubic), and are very accurate (parts per thousand to a few percent in the density for nonpolar fluids). They are first-principles equations in the sense that the entire fluid p-v-T surface can be calculated if the intermolecular potential is known, but they can be used with much less input information. Because the parameters of the equations of state that depend only on the repulsion are insensitive to the detailed shape of the potential, knowledege of just the second virial coefficient as a function of temperature is sufficient to construct the p-v-T surface. Examples are given for a selection of fluids, including Ne, CH4 CO2, and H2O.

A new four‐parameter cubic equation of state for fluids

AbstractA simple cubic equation of state of the van der Waals type has been developed and successfully applied to both nonpolar and polar fluids. It contains four parameters and only one parameter is temperature‐dependent. The parameters have been determined by using reliable data of vapour pressure and saturated liquid volume, and correlated in terms of critical properties and acentric factor. The P‐V‐T relationships, vapour pressures, volumes, and enthalpies of vapourization were calculated for a variety of substances. Comparison of the calculated results with experimental data and with results obtained from other equations shows that the proposed equation is a superior one in overall performance.

The BACKPF equation of state for fluids of polar and moderately flexible molecules—application to mixtures

A new equation of state (BACKPF) recently proposed for pure fluids has been applied to the vapor—liquid equilibrium of a number of rather different binary mixtures. It is demonstrated that BACKPF is able to predict the phase diagram in qualitative agreement with the data from the pure fluid parameters alone, i.e. without requiring a binary interaction parameter.

Equation of state for fluids of spherical particles in d dimensions

An analytical equation of state for a d-dimensional fluid is presented, obtained as a generalization of a successful result for d=3. Agreement with available computer simulations and virial coefficients for d=1,2,4, and 5 indicates that the generalization is accurate.

Conformational equation of state for fluids of chain molecules

This paper discusses the mathematical formulation of the modelling of fluids of chain molecules as fluid mixtures of molecular conformations with the concentration of these conformations obtained through a constrained freeenergy minimization. Thermodynamic relationships can then be applied to obtain other properties, and an approximation is derived for the virial coefficients of chain molecules. Problems regarding the implementation of this approach through the virial equation at low densities and the generalized van der Waals equation of state at higher densities, and possible solutions to these, are also discussed. Feasibility studies for the case of n-octane show agreement with the experimental observations regarding the molecular shape in gas and liquid phases.

A three‐parameter cubic equation of state for fluids and fluid mixtures

AbstractA new cubic equation of state with three parameters is developed. The substance‐dependent critical compressibility factor, ζ, and the temperature‐dependent parameter, α, were correlated in terms of the acentric factor and reduced temperature. The P‐V‐T relationships, vapor pressures, volumes, and enthalpy departures of pure substances, and the compressibility factors, enthalpy departures, and vapor‐liquid equilibria of mixtures were calculated with the proposed equation. Comparison of the calculated results with experimental data shows that the proposed equation is accurate enough to be applied for design purposes.

Generalized flory theories for predicting properties of fluids containing long chain molecules

Two theories have been developed which predict the equation of state for fluids containing chain-like molecules. The Generalized Flory and Generalized Flory-Dimer theories are derived as generalizations of the well-known Flory lattice theory to continuous space. The theories are applied to fluids and fluid mixtures containing molecules which are modelled as chains of tangent hard spheres. The predicted pressures are in very good agreement with Monte Carlo simulations of pure fluids containing chains of 4, 8 and 16 spheres and with Monte Carlo and molecular dynamics simulations of a mixture of hard chains of length n=8 and n=1.

An equation of state for fluids of polar and moderately flexible molecules

A new equation of state is proposed, in which the useful features of the Perturbed Hard-Chain Theory (PHCT) and the BACK equation of state are combined. The effect of the density dependent degrees of freedom is considered in the spirit of PHCT and the nonsphericity of molecules in terms of the hard convex-body equation of state. Multipolar terms for the general nonlinear case are introduced in the spirit of a perturbation expansion around a spherical reference. The comparison of saturated fluid properties for some substances along the entire saturation curve indicates some improvement over the PHCT and BACK equation of state.

A new equation of state for athermal chains

A new equation of state for fluids containing athermal chain molecules is developed and compared to simulation results and existing theories in three, two, and one dimensions. The new expression, which builds upon the generalized Flory theory, contains no adjustable parameters and relates the compressibility factor of an n-mer fluid to the compressibility factors of monomer and dimer fluids at the same volume fraction. Comparisons with Monte Carlo results for three- and two-dimensional freely jointed chains show very good agreement, and the overall accuracy of the new expression appears comparable to Wertheim’s thermodynamic perturbation theory of polymerization. In one dimension the new expression reduces to the exact result. Application of the equation to chain models with internal constraints and overlapping hard sites is discussed and illustrated through comparisons with Monte Carlo results for rigid trimers. An extension of our approach to arbitrary reference fluids shows that the generalized Flory and new equations are the first two members of a family of increasingly accurate equations of state for chains.

Mechanical re-equilibration of fluid inclusions in San Carlos olivine by power-law creep

Fluid inclusions in San Carlos olivine stretch via plastic mechanisms when heat-treated at 1400° C and 0.1 MPa in controlled\(f_{O_2 } \) atmospheres for several days. Measurable changes in both inclusion dimensions and fluid densities occur; densities decrease from ≈1.0 to ≈0.7 g/cc. Stretching is fastest along 〈100〉, and slower along 〈001〉 and 〈010〉. The dislocation microstructure around the inclusions suggests that creep mechanisms operate. Uncertainties in the experimental determinations of stretching rates result from optical resolution limits, errors inherent in measuring homogenization temperatures, uncertainties in the fluid equation of state, and changes in fluid chemistry during the heat-treatment. Inclusion stretching by dislocation creep can be treated using a model developed for hot isostatic pressing. In this model, we assume spherical symmetry of plastic flow, that the material yields by steady-state power-law creep, and that the parameters for the constitutive law and fluid equation of state are known. Stretching rates are predicted to depend on the difference between the fluid pressure and the external pressure, the temperature, the constitutive law governing power-law creep, and geometry. Predicted stretching rates show fair, but not exact, agreement with experimentally measured rates. The amount of stretching predicted by the model is in rough agreement with estimates based on dislocation microstructures around natural inclusions, if xenolith ascent rates are of the order of 1 cm/s or faster.

Equation of state for square-well fluids

An equation of state for fluids of square-well molecules is obtained from the coordination number expressing the number of molecules in the square-well of a central molecule as a function of temperature and density. The critical state of a square-well fluid is determined from the equation.

Perturbed hard-core equations of state for fluids

The abilities of several equations of state in fitting p-V-T data of pure fluids have been compared. Also the temperature dependence of the characteristic parameters of each substance has been studied. All the equations of state discussed are of the form: p = p (ref) + p (att) where p(ref) accounts for the repulsive contributions to the pressure, while p(att) contains the contributions from the attractive forces. The best results correspond to an equation derived by Miyano and Masuoka from a perturbation theory, though Deiters equation gives results which are almost comparable to Miyano's one and it seems that Deiters equation is more suitable for further improvements and extension to more complex fluids.