A collocation method for surface tension calculations with the density gradient theory

A combined density gradient theory with equation of state model for the study of surface tension of refrigerant fluids

An equation-of-state-based viscosity model for non-ideal liquid mixtures

Modeling interfacial tension in N2/n-alkane systems using corresponding state theory: Application to gas injection processes

Modeling interfacial tension and minimum miscibility pressure in paraffin-nitrogen systems: Application to gas injection processes

Thermodynamic modeling based on a generalized cubic equation of state for kerosene/LOx rocket combustion

Equations of state are widely used in compositional simulation to predict phase distribution and composition, which in turn facilitates prediction of compositionally dependent properties such as density, viscosity, interfacial tension, and enthalpy. A well-known problem confronted with naturally occuring hydrocarbon systems is characterization of the high molecular weight fraction (usually C7 +). The high molecular weight fraction must be split into an optimum number of pseudo-components each having a prescribed set of critical properties and interaction coefficients. Since procedures for doing this are largely empirical, typical equation of state packages must be tuned to available experimental data. Often available experimental data are limited in scope, or the ultimate simulation involves significant changes in temperature, pressure or composition. In each situation, tuned pseudo-component critical properties and/ or interaction parameters will manifest important temperature, pressure, and composition dependencies. Thus, a versatile phase description can effectively be ensured if tuning is automated internally within the equation of state package. In this paper, a methodology for achieving this task is described. First, the heavy fraction is split into a defined number of pseudo-components and starting values of binary interaction parameters and critical properties are obtained by using readily available correlations in the literature and/or mixing rules. Then, a linear optimization technique (two-phase method) is adopted for non-linear applications by using iterative techniques (iterative variables being pseudo-component binary interaction coefficients with CH4 and pseudo-component critical properties). Tuned sets of binary interaction parameters and critical properties of pseudo-components for a cubic equation of state are generated by using experimental depletion curves. As the computation progresses the tuned set replaces the default set to achieve further improvements. The success of this linear optimization routine is demonstrated for different reservoir oils.

A local composition extension of the van der Waals mixing rule for PR cubic equation of state

Representation of solid-supercritical fluid phase equilibria using cubic equations of state

Modification of the Kumar-Starling five-parameter cubic equation of state and extension to mixtures

Saturation densities of new refrigerant mixtures: Densité de saturation de nouveaux mélanges frigorigènes

The leading order terms in a curvature expansion of surface tension, the Tolman length (first order), and rigidities (second order) have been shown to play an important role in the description of nucleation processes. This work presents general and rigorous expressions to compute these quantities for any nonlocal density functional theory (DFT). The expressions hold for pure fluids and mixtures and reduce to the known expressions from density gradient theory (DGT). The framework is applied to a Helmholtz energy functional based on the perturbed chain polar statistical associating fluid theory (PCP-SAFT) and is used in an extensive investigation of curvature corrections for pure fluids and mixtures. Predictions from the full DFT are compared to two simpler theories: predictive DGT, which has a density and temperature dependent influence matrix derived from DFT, and DGT, where the influence parameter reproduces the surface tension predicted from DFT. All models are based on the same equation of state and predict similar Tolman lengths and spherical rigidities for small molecules, but the deviations between DFT and DGT increase with chain length for alkanes. For all components except water, we find that DGT underpredicts the value of the Tolman length but overpredicts the value of the spherical rigidity. An important basis for the calculation is an accurate prediction of the planar surface tension. Therefore, further work is required to accurately extract Tolman lengths and rigidities of alkanols because DFT with PCP-SAFT does not accurately predict surface tensions of these fluids.

An improved generalized three-parameter cubic equation of state for pure fluids

A universal cubic equation of state (UC EOS) is proposed based on a modification of the virial Percus-Yevick (PY) integral equation EOS for hard-sphere fluid. The UC EOS is extended to multi-component hard-sphere mixtures based on a modification of Lebowitz solution of PY equation for hard-sphere mixtures. And expressions of the radial distribution functions at contact (RDFC) are improved with the form as simple as the original one. The numerical results for the compressibility factor and RDFC are in good agreement with the simulation results. The average errors of the compressibility factor relative to MC data are 3.40%, 1.84% and 0.92% for CP3P, BMCSL equations and UC EOS, respectively. The UC EOS is a unique cubic one with satisfactory precision among many EOSs in the literature both for pure and mixture fluids of hard spheres.

We explore the properties of a simple analytic equation of state, proposed by Heyes and Woodcock [D. M. Heyes and L. V. Woodcock, Mol. Phys. 59, 1369 (1986)] which is a development of the van der Waals equation of state, improved with an analytically simple yet accurate hard-core component for the compressibility factor. We call this the hard-sphere van der Waals (HSvdW) equation of state. We show, for the first time, that the HSvdW equation of state gives analytic values for the critical parameters and that it gives significantly more realistic values for the critical density than the van der Waals and other cubic equations of state. For single-component square wells of arbitrary well width, the HSvdW equation of state also produces a critical temperature and pressure in agreement with those from a recent Gibbs Monte Carlo simulation study. The chief advantage over a similar equation of state with an alternative form for the hard-core compressibility factor, such as Carnahan–Starling, is that it leads to more tractable analytic expressions for thermodynamic properties without loss of accuracy. Extensive Monte Carlo computer simulations of square-well (SW) and square-shoulder (SS) fluids with variable well width have been performed. We have calculated the compressibility factor, internal energy, pair distribution functions, and coordination number (average number of particles within the soft-shell interaction range). We have also determined the gas–liquid coexistence curve using the particle insertion chemical potential method for the square-well case, λ=1.5σ, where λ is the diameter of the soft interaction shell. This agrees well with the Gibbs ensemble simulation coexistence curve. For the purpose of improving the attractive component of the HSvdW equation of state, we have made use of the SW and SS simulation data and that of other workers to develop another new simple equation of state based on the quasichemical local coordination number approximation (QCA) which is a lattice model of a fluid. The QCA is improved to include the local coordination of the hard-sphere fluid. Present adaptations extend the range of earlier QCA models to arbitrary well width and sign of the well (either attractive well or repulsive shoulder). The simulation coordination numbers are reproduced well by the present model, although there is little improvement in the overall equation of state over the simpler HSvdW.

The purpose of this paper is to compare three thermodynamic models to correlate the phase behavior of the highly polar system: carbon dioxide +1-heptanol. These three models rely either on the Peng–Robinson (PR) or on the Soave–Redlich–Kwong (SRK) equations of state and are all coupled with classical van der Waals one-fluid mixing rules. For the two first models, noted SRK/2PCMR and PR/2PCMR, where 2PCMR means two-parameter conventional mixing rule, a single set of temperature-independent binary parameters (kij and lij) was considered. The third model is the well-established PPR78 model also based on the PR equation of state (1978 version). In such a model, lij = 0 but the second binary interaction parameter (kij) is temperature-dependent and predicted by a group-contribution method. All available literature data in a wide range of pressures and temperatures and the global phase equilibrium diagram of the system were calculated with the three aforementioned models. Although the models used are simple, they are able to represent reasonably well the complex phase behavior of the system studied in this work.