Kenneth E. Starling

Equation of State for Nonattracting Rigid Spheres

A new equation of state for rigid spheres has been developed from an analysis of the reduced virial series. Comparisons with existing equations show that the new formula possesses superior ability to describe rigid‐sphere behavior.

Thermodynamic Properties of a Rigid‐Sphere Fluid

The excess thermodynamic properties for a rigid‐sphere fluid have been calculated with an accurate equation of state. Values of (PV / NkT), and (H − H°) / RT, (S − S°) / R, (G − G°) / RT, and (f / P) are reported for a wide range of fluid density.

A molecular theory for the thermodynamic behavior of polar mixtures. I. The statistical-mechanical local-composition model

Abstract The statistical-mechanical basis for the local-composition model is presented. In the statistical-mechanical framework, local compositions are expressed in terms of the potential of mean force, so that the approximations required to obtain the expressions commonly utilized can be analyzed and new and improved expressions can be developed. The consistency relations required for the use of the excess free energy for the configurational energy in the local-composition model are investigated in general. As a test, the local-composition model is applied to the case of Lennard—Jones mixtures. It is also demonstrated that the statistical-mechanical expressions for the internal energy in the local-composition model can be related to experimentally measurable quantities. This will allow direct comparison of nonstatistical and statistical-mechanical formulations of the local-composition model using experimental data for actual fluid mixtures of interest.

Improved analytical representation of argon thermodynamic behavior

Abstract The equation of state of Gosman and coworkers has been used extensively to calculate the thermodynamic properties of simple fluids. Gosmans equation of state, however, is inadequate when calculations are made (a) for liquids at low temperatures, (b) for fluids at very high temperatures and pressures, (c) for the derived thermodynamic properties such as enthalpy, entropy, etc., at low temperatures. One of the objectives of this work was to improve the equation of state and extend its use to lower temperatures and higher pressures. Based on perturbation theory using Poples expansion for moderately anisotropic fluids, the equation of state accurately represents vapor pressures, densities and enthalpy departures of vapor, liquid, and fluid states as functions of three parameters (reduced temperature, reduced density and acentric factor) over the range Tr = 0.3 to 3.3 and Pr = 0 to 132 for simple fluids. The result is an improved analytical representation of these properties at low temperatures and high pressures for simple fluids. This equation of state should be useful for calculating reference system properties in perturbation equation of state studies.

The statistical mechanical local composition theory: The balance equations and concentration effects in nonideal mixtures

Abstract The statistical mechanical local composition theory proposed in a previous paper (Lee et al.) is here applied to the study of the ‘number conservation’ conditions on the local compositions. It is demonstrated that detailed balances in molecule numbers using the rigorous statistical mechanical definitions for local compositions yield relations consistent with the Flemr and McDermott—Ashton conditions when well-defined assumptions are utilized. With the assumption that the nearest neighbor coordination numbers z a and z b for each component in a binary mixture are equal, the Flemr conditions are obtained. This assumption is implicit in Wilsons formulation. Allowing z a and z b to differ corresponds to a two-fluid theory. Calculations demonstrate that the detailed balance is satisfied by statistical mechanical calculations using the Percus—Yevick equation for argon—nitrogen mixtures in both the gas and liquid states. It is shown that formulations of two-fluid local composition methods, such as that of Renon and Prausnitz, which assume that the ratio z a / z b is constant, are consistent with the statistical mechanical local composition theory only in the limit of dilute solutions. The Percus—Yevick calculations show that there are wide variations in nearest neighbor numbers and the ratio z a / z b varies with composition even for simple mixtures such as the argon and nitrogen fluids studied here.

Correlation of the transport properties of simple fluids at low temperatures and high pressures based on the generalized Eucken relation and the molecular dynamics of hard sphere fluid

A generalized correlation is developed for the viscosity and thermal conductivity of isotropic fluids under high pressures (up to 200 MPa) and low temperatures (down to 85 K). Two known observations have been taken into consideration in the development of the correlation. First, the Alder correction factors for the Enskog theory values of transport coefficients obtained from molecular dynamics simulations for hard sphere fluids are incorporated. The inclusion of these corrections in the theory makes it possible to describe correctly the density dependence of the hard sphere viscosity and thermal conductivity at high pressures. The hydrodynamic “cage” effect, which is manifested in the molecular motions of dense fluid systems, is thus correctly accounted for. Second, the generalized Eucken relation, which relates the thermal conductivity to the viscosity, is incorporated. As a consequence, an internally consistent correlation is obtained, which can adequately predict the behavior of the thermal conductivity from given values of viscosity. Tests on simple fluids, such as argon, krypton, etc., show that the correlation is valid within a few percent for the entire fluid range where experimental data are available for comparison, and also along the vapor-liquid saturation line, with the exclusion of the critical region. Furthermore, since the variables appearing in the theory are in reduced form, a corresponding states correlation is established for isotropic fluids.

Exponential Virial Equation of State

An equation of state is derived which has promise for the prediction of high‐density fluid behavior. An approximate form of this new equation yields expressions for approximate virial coefficients of all orders as functions of lower‐order exact virial coefficients. Use of only the exact second and third virial coefficients in the second‐order approximate equation leads to accurate prediction of rigid‐sphere fluid behavior at high densities where even the fourth‐order virial equation fails. For real fluids, the second‐order approximate equation is accurate to high densities for temperatures above the Boyle temperature. At moderately lower temperatures, the third‐order approximate equation yields accurate predictions at high densities where the third‐order virial equation is in error.

Inconsistencies in dew points from different algorithm types possible causes and solutions

Calculations of natural gas dew points are quite important in the gas processing industry. A number of software packages used by the industry have multiple options for calculations of dew points. One option is to fix the pressure and the software will calculate the dew point temperature. Another option is to have the software generate the phase envelope for the natural gas mixture. A third option is for the user to perform flash calculations at a fixed pressure and varying temperatures until the amount of condensed liquid is arbitrarily small. Sometimes, these three different options yield three different calculated dew points. Because the three different dew point options involve nested iterative loops which solve for liquid and vapor densities and component fugacities as well as the temperature or vapor fraction, the three options should agree within some measure of the different convergence criteria used by the three options, provided the methodology used in a given option does not fail. Examples of dew point calculation differences by the three options are presented and some analysis of which option best represents the equation of state used is given. In addition, possible methods for reducing the inconsistencies are discussed.

A group contribution and equation of state approach for coal fluid calorimetric properties

Abstract This work examines the relationship between the calorimetric properties of coal fluids and their molecular functional group composition. A set of functional groups appropriate for the characterization of the coal fluids is proposed. Coal fluid samples that have had their calorimetric properties measured have been characterized using proton n.m.r., i.r. and elemental analysis. These characterizations are then used in a chemical structural model to determine the composition of the coal liquid in terms of the proposed functional groups. These functional group concentrations are used to estimate the ideal gas calorimetric properties of the fluid using Bensons method. The residual calorimetric properties are then determined using an existing equation of state methodology. The result of the combination of characterization and correlation demonstrates a significant improvement over the existing equation of state based, properties estimation system.

Perturbation theory for anisotropic fluid transport coefficients

A first order perturbation theory for the transport coefficients of anisotropic fluids is derived in the spirit of the Pople expansion for thermodynamic properties. For a specified transport coefficient, the corresponding unaveraged time correlation function is expanded in the anisotropic perturbation potential about the isotropic reference system correlation function. Expansion of all terms in the correlation function, including the propagator and, therefore, the Liouville operator, the flux for the specified transport coefficient, and the distribution function leads to the appropriate perturbation expression for each transport coefficient. The pertinent relations are presented for the coefficients of self‐diffusion, viscosity, and thermal conductivity. The applicability of the perturbation theory is demonstrated for viscosity.