A multi-fluid nonrandom lattice fluid model: Mixtures

A multi-fluid nonrandom lattice fluid model with no temperature dependence of close packed volumes of a mer, segment numbers and energy parameters of pure systems and its consistent method for phase equilibrium calculation were presented in the previous paper. In this work, the model was extended to mixtures by using consistent method for phase equilibrium calculation with fugacity coefficients derived from the present equation of state and it was applied to vapor-liquid equilibrium. We consistently tested the present model on 17 phase equilibrium data sets of vapor-liquid equilibria and compared it with the MF-NLF model and the SAFT model. The present model (3 pure parameters for pure component and one binary interaction parameter) showed better results for most systems than the MF-NLF model (6 adjustable pure parameters and one binary interaction parameter) and the SAFT model (3 pure parameters and one binary interaction parameter).     

A multi-fluid nonrandom lattice fluid model for mixtures containing nonionic surfactants

Surfactant systems show highly non-ideal phase behavior because of the inter-association and intra-association hydrogen bond. We present a lattice fluid equation of state that combines the multi-fluid nonrandom lattice fluid model with modified Veytsman statistics for intra+inter molecular association to calculate phase behavior for mixture containing surfactant systems. The literatureresults fitted to this model show good accordance for mixtures containing nonionic surfactant systems. This article is dedicated to Professor Chul Soo Lee in commemoration of his retirement from Department of Chemical and Biological Engineering of Korea University.     

Nonrandom lattice fluid group contribution parameter for vapor-liquid equilibrium of esters and their mixtures

A group contribution version of the nonrandom lattice fluid equation of state (NLF-GC EOS) has been used to predict the vapor-liquid phase equilibria (VLE) of esters and their mixtures. The investigated esters were divided into groups according to the contribution scheme. Two different types of parameters were regressed from experimental datasets. Size parameters were fitted to pure component properties, and the group-group energy interaction parameters were simultaneously fitted to several binary mixture data sets. For systems containing propylene oxide, missing binary VLE data was predicted by using the COSMO-RS method. Parameters obtained by using the COSMO-RS method were later used to successfully predict experimentally measured binary propylene oxide+esters systems. The overall good prediction capability of the NLF-GC EOS could be proven for the investigated systems. This article is dedicated to Professor Chul Soo Lee in commemoration of his retirement from Department of Chemical and Biological Engineering of Korea University.     

Unified equation of state based on the lattice fluid theory for phase equilibria of complex mixtures part II. Application to complex mixtures

In part I of the present article [Yoo et al., 1995], new rigorous and simplified lattice-fluid equations of state (EOS) were derived and their characteristic features of the molecular thermodynamic foundation were discussed by applying to pure fluids. In this part II, both EOSs were extended to various phase equilibrium properties of mixtures. Comparison of the models with experimental mixture data ranges from density, to equilibria of vaporliquid, vapor-solid and liquid-liquid phases for nonpolar/nonpolar, nonpolar/polar, polar/polar mixtures. Both models were also applied to supercritical fluid phase equilibria and activities of solvents in polymer solutions. With two temperature dependent parameters for pure compounds and one temperature-independent binary interaction energy parameter for a binary mixtures, results obtained to date illustrated that both EOSs are quantitatively applicable to versatile phase equilibria of mixtures over a wide range of temperatures, pressures and compositions.     

Modified Guggenheim-Huggins-Miller combinatorial factor and its application to lattice fluid equation of state

The Guggenheim-Huggins-Miller (GHM) combinatorial factor is modified by introducing a factor in the pair probability of a hole-hole pair. The proposed contribution is combined with the expanded quasi-chemical contribution and tested against saturated vapor pressure and liquid density. The proposed model correlates experimental saturated liquid density better than a quasi-chemical nonrandom lattice fluid (QLF) model based on original GHM combinatorial factor. The optimized parameters show a quite different behavior compared with that of the QLF model and the relationships between the parameters of two models are discussed. This article is dedicated to Professor Chul Soo Lee in commemoration of his retirement from Department of Chemical and Biological Engineering of Korea University.     

Unified equation of state based on the lattice fluid theory for phase equilibria of complex mixtures part I. Molecular thermodynamic framework

Consistent calculation of fugacities of fluid mixtures remains as one of the most important subjects in contemporary molecular thermodynamics. In practice, equations of state (EOSs) and g^E-models have been used. However, most EOSs are erroneous for condensed phases at high densities and g^E-models are inapplicable for pressuresensitive systems. Recently to remedy the shortcomings in both approaches, there has been a surge of new g^E-EOS mixing rules. By equating any set of EOS and g^E-models, the limitations in both approaches could be resolved significantly. However, the self-consistency in the underlying concept of those mixing rules remains controversial. During the last several years, the present authors proposed a new lattice-fluid EOS and its simplification relevant to phase equilibrium calculations. Without employing any g^E-EOS mixing rule and with only two parameters for a pure component and one adjustable interaction energy parameter for a binary mixture, results obtained to date demonstrated that the EOSs are quantitatively applicable to a great variety of phase equilibrium properties of mixtures, especially, for complex and/or macromolecular systems. In the present article we summarize the EOSs and extended the applications to liquid-liquid Equilibria. In part I, we discussed briefly the molecular thermodynamic aspects of general derivation of the EOS and a brief discussion of applying the EOSs to pure fluids while the illustrative application to various real mixture systems is discussed in part II.     

Calculation of complex phase equilibria in the critical region of fluid mixture based on multi-fluid lattice equation of state

Quantitative correlation of critical loci and multiphase behaviors has received considerable attention because the increased industrial importance of processes operating within the high-pressure region such as supercritical fluid extraction. However, in the critical region, classical thermodynamic models such as equations of state (EOS) frequently fail to correlate phase equilibrium properties. Recently, the present authors proposed a new lattice-hole EOS based on the multi-fluid approximation of the nonrandom lattice theory. The model requires only two molecular parameters reflecting size and interaction energy for a pure fluid and one additional interaction parameters for a binary mixture. In this work, the reliable applicability of the EOS was demonstrated to various phase equilibria of complex mixtures in the critical region. Demonstration of the EOS was made to calculate multiphase behaviors such as solid-liquidvapor (SLV) equilibria and critical loci of binary complex mixtures at high pressure. For P-T, P-x, and T-ρ phase diagrams tested, the model agrees well with experimental data. This paper was presented at the 8th APCChE (Asia Pacific Conferation of Chemical Engineering) Congress held at Seoul between August 16 and 19, 1999.     

A crossover multi-fluid nonrandom lattice fluid model for pure hydrocarbons and carbon dioxide near to and far from the critical region

The multi-fluid nonrandom lattice fluid model with the local composition concept is capable of describing thermodynamic properties for complex systems, but this model cannot represent the singular behavior of fluids near the critical region. In this research, the multi-fluid nonrandom lattice fluid model for pure fluids is combined with a crossover theory to obtain a crossover multi-fluid nonrandom lattice fluid model which incorporates the critical scaling laws valid asymptotically close to the critical point and reduces to the original classical multi-fluid nonrandom model far from the critical point. The crossover multi-fluid nonrandom lattice fluid model shows a great improvement in prediction of the thermodynamic properties of pure compounds near the critical region.     

A crossover quasi-chemical nonrandom lattice fluid model for pure carbon dioxide and hydrocarbons

Thequasi-chemical nonrandom lattice fluid model is capable of describing thermodynamic properties for complex systems containing associating fluids, polymer, biomolecules and surfactants, but this model fails to reproduce the singular behavior of fluids in the critical region. In this research, we used the quasi-chemical nonrandom lattice fluid model and combined this model with a crossover theory to obtain a crossover quasi-chemical nonrandom lattice fluid model which incorporated the critical scaling laws valid asymptotically close to the critical point and reduced to the original quasi-chemical nonrandom model far from the critical point. The crossover quasi-chemical nonrandom lattice fluid model showed a great improvement in prediction of the volumetric properties and second-order derivative properties near the critical region.     

Vapor-liquid equilibrium correlations for systems containing amines using a lattice fluid equation of state with hydrogen bonding

The nonrandom lattice equation of state with hydrogen bonding (NLF-HB EOS) was examined for the correlation of vapor-liquid equilibria (VLE) for binary amine and hydrocarbon mixture at various temperatures. For these mixtures, the consideration of hydrogen bondings in the lattice equation of state clearly improves the prediction for VLE. The amines were divided into four groups due to the different strength of the hydrogen bonding. For all groups, different hydrogen bonding parameters were obtained and evaluated. The effects of varying hydrogen bonding energies for NLF-HB EOS are discussed. For systems containing lower amines, the NLF-HB EOS showed excellent agreement with the experimental data. For the correlation of systems containing tertiary amine molecules, binary interaction parameter had to be involved instead of hydrogen bonding parameters.     

Liquid–liquid equilibrium correlations using lattice fluid equation of state with hydrogen bonding

The nonrandom lattice equation of state with hydrogen bonding (NLF-HB EOS) was examined for the correlation of liquid–liquid equilibria (LLE) for binary alcohol and hydrocarbon mixture in a wide pressure range. For hydrocarbon + alcohol mixtures the consideration of a hydrogen-bonding term in the lattice equation of state clearly improves the prediction for vapor–liquid equilibrium (VLE) as shown in previous works, but the prediction of LLE is still in question. In this paper, LLE data for alcohols (methanol and ethanol) + hydrocarbons (n-hexane to n-hexadecane) were correlated by NLF-HB EOS and results were compared with a cubic equation of state (Peng–Robinson EOS with the T–K Wilson based G^E model). Both equations of state showed similar degree of accuracies but with different number of adjustable parameters. The Peng–Robinson EOS based approach requires six temperature dependent coefficients for accurate calculation whereas NLF-HB EOS requires only two temperature dependent coefficients. The effects of varying hydrogen-bonding energies for NLF-HB EOS are discussed.     

Molecular dynamic simulation and equation of state of Lennard-Jones chain fluids

In order to study the thermodynamic properties of chain and polymeric fluids at the molecular level, we perform constant temperature molecular dynamics simulations of ‘repulsive’ and ‘full’ Lennard-Jones (LJ) chain fluids of lengths up to 16. In the simulation, the RATTLE algorithm to determine constraint forces and the Nose-Hoover thermostat to sample the canonical ensemble are used. For repulsive LJ chains, the compressibility factor of the chain fluids is predicted from first-order thermodynamic perturbation theory combined with the Week-Chandler-Andersen (TPT1-WCA) perturbation theory, and is compared to the simulation results. A good agreement between the theory and the simulation results is found particularly at liquid-like densities. For full LJ chains, two different versions of TPT1 are used to calculate the compressibility factor: one is TPT1-WCA, and the other is TPT1 with the Percus-Yevick approximation for the radial distribution function of the LJ spheres (TPT1-PY). At low and intermediate densities, TPT1-PY gives better predictions for the compressibility of the LJ chain fluids, whereas at high densities TPT1-WCA is more reliable.     

Development of a multi-fluid model for poly-disperse dense gas-solid fluidised beds, Part I: Model derivation and numerical implementation

We have derived a new set of closure equations for the rheologic properties of a dense gas-solid fluidised bed consisting of a multi-component mixture of slightly inelastic spheres, using the Chapman-Enskog solution procedure of successive approximations, where the particle velocity distribution of all particle species is assumed to be nearly Maxwellian around the particle mixture velocity with the particle mixture granular temperature. In this theory, differences in the mean velocities (i.e. particle segregation) and granular temperatures of the particle species result from higher order perturbation functions. Special attention is paid to assure thermodynamic consistency between the radial distribution function and the chemical potential of a hard-sphere particle specie appearing in the diffusion driving force when applying the revised Enskog theory, which is often overlooked. In the resulting closure equations, the rheologic properties of the particle mixture are explicitly described in terms of the particle mixture velocity and granular temperature, and the diffusion velocity and granular temperature of the individual particle phases can be computed from the mixture properties, which is a major advantage with respect to the numerical implementation. A new numerical solution strategy has been devised, which is an extension of the well-known SIMPLE algorithm and takes the compressibility of the solids phase directly into account, which allows for much larger time steps (about a factor of 10 larger). In Part 2 the simulation results obtained with the new model are compared with experimental data and discrete particle model (DPM) simulations.     

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

A 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.     

Continuous-velocity lattice gas cellular automata for miscible binary fluid and its application to simulation of interface instability

Continuous-velocity lattice gas cellular automata (CVLGA) is extended to miscible binary fluid systems. A new parameter is introduced in order to control the diffusivity of the fluids. The correlation between the diffusivity and the new parameter proves that there exists the maximum value of the diffusivity. Quantitative verifications of the model are carried out with numerical simulations of the diffusion phenomena across a falling fluid film. The model is then applied to the simulations of Rayleigh-Taylor instability during the gravitational mixing phenomena. The qualitative tendency of the growth of the interface instability is the same as that obtained in conventional numerical methods.     

Measurement of vapor sorption equilibria of polymer solutions and comparative correlation by g E -models and lattice equations of state

Solvent sorption equilibrium data of binary solvent-polymer systems were measured with a vacuum electro-microbalance equilibrium cell. Tested solvents were benzene,n-pentane, cyclohexane,n-hexane, water and methanol. Polymers tested were poly(dimethylsiloxane), poly(iso-butylene), polypropylene oxide) and poly(vinyl alcohol). Data obtained in the present study, together with existing literature data, were correlated by twog ^E- models, such as UNIQUAC and the Flory-Huggins model, and four equations of state which stem from the lattice fluid theory, such as models proposed by Flory, Sanchez and Lacombe, Panayiotou and Vera, and the NLF model proposed recently by the present authors. For each solvent-polymer system, the provided models give a quantitative correlation. The advantages and drawbacks of the g^E-model and equation of state approaches are also discussed.     

A new state model of liquid-vapor interfaces—to yield analytical expression for surface tension

Based on the van der Waals fluid model, a simple equation of state, unique for non-uniform fluids, is developed. It is applied to the liquid-vapor interface, to derive the density profile in the interfacial region. The density profile is used in conjunction with the gradient theory, to yield an expression for the surface tension of a saturated fluid as a function of temperature and fluid properties. The non-dimensionalized influence parameter of the gradient theory is assigned best-fit values, which are of a unity order of magnitude, as expected. The predicted surface tension values are in good agreement with experimental data, for a variety of fluids.     

A thixotropy model for fresh fluid concretes: Theory, validation and applications

In this paper, the methods used to measure and model thixotropy of fresh concrete in the civil engineering field are described and a simple thixotropy model is presented. It is shown that this model is in agreement with the experimental observations that can be found in the literature and a classification of SCC according to their flocculation rate A_thix is proposed. The predictions of the model are compared with experimental measurements obtained with a concrete rheometer. In the last part, two applications of the model are briefly presented as examples (pressure formwork prediction and multi-layer casting of fluid concretes). It is shown that according to the element to be cast (slab or wall), a non-thixotropic SCC (low flocculation rate) or a highly thixotropic SCC (high flocculation rate) is respectively more adapted.