Van Der Waals One-fluid Research Articles

Vapor-liquid equilibrium phase behavior of binary systems of carbon dioxide with dimethyl succinate or dimethyl glutarate

BackgroundTo develop process for separating dimethyl succinate (DMS) and dimethyl glutarate (DMG) with the aid of supercritical carbon dioxide, the vapor-liquid equilibrium (VLE) data of the related mixtures are fundamentally important. The VLE data were determined experimentally and correlated with various thermodynamic models in this study. MethodsThe isothermal VLE data were measured for carbon dioxide + DMS and carbon dioxide + DMG by using a semi-flow and a static types of apparatuses at temperatures from 313.15 K to 413.15 K and pressures up to 20 MPa. These VLE data were correlated with the Krichevsky-Ilinskaya (KI) equation, the Soave-Redlich-Kwong (SRK), the Peng-Robinson (PR) and the Patel-Teja (PT) equations of state incorporating with two-parameter one-fluid van der Waals mixing rules (vdW-2). Significant findingsThe results of this study provide the VLE data of carbon dioxide + DMS and + DMG and reveal the VLE phase transition behavior, especially crossing near critical region. The Henry's constant and critical loci were also estimated. The Peng-Robinson equation of state with the vdW-2 mixing rule yielded the best data correlation results. The optimal values of the binary interaction parameters were also obtained, which can be used in the separation process simulation and design.

Activity coefficients in nearly athermal mixtures predicted from equations of state: Don't blame the cubic when it is the lack of a third parameter!

The idea that cubic EoS's are very primitive and limited models, quite extended at present among researchers working on fluid properties and phase equilibria, has different roots, including some limitations observed specifically for classic and popular equations like Peng-Robinson (PR) or Soave-Redlich-Kwong (SRK). These are two-parameter models, i.e. they have only an attractive and a repulsive parameter to characterize each molecule, while other models like SAFT but also cubic –and still for non-associating molecules-introduce also a third parameter related somehow to the molecular structure or shape. One of the alluded limitations, actually a very clear one, is the complete failure in describing the non-ideality in nearly athermal mixtures, like those composed of n-alkanes with different chain lengths: SRK and PR predict positive deviations from ideality, which increase with the system asymmetry, while experimental measurements show exactly the opposite, i.e. increasing negative deviations from ideality. This provides an excellent opportunity to try to clarify whether such failure is due to the cubic nature of these classic models or to their two-parameter character and/or to the classic van der Waals one-fluid (vdW1f) mixing rules typically used. With that motivation, in this work we used models representing three different categories, in a completely predictive way: a two-parameter cubic EoS (PR), a three-parameter cubic EoS (RKPR) and a three-parameter SAFT EoS (PC-SAFT). Their predictions of infinite dilution activity coefficients were analyzed and compared, in contrast to available data for different mixtures of n-butane to n-octane as the lighter compound and paraffins ranging from C16 to C36 as the heavier, in both extremes of dilution. The obtained results, and their analysis, allowed us to extract very clear conclusions which were not present in the literature so far, regarding the importance of a third parameter in any type of EoS.

Viscosity of Lennard-Jones mixtures: A systematic study and empirical law.

A systematic study of the viscosity of the binary Lennard-Jones (LJ) mixtures is carried out by equilibrium molecular dynamics simulations via the Green-Kubo relation. The effects of mass, size, and energy-parameter asymmetries on the viscosity and the self-diffusion coefficients are examined separately, both in equimolar mixtures and by varying the molar fractions. The systems are mapped into an effective one-component model according to the van der Waals one-fluid (vdW1) model. Furthermore, using an empirical law for pure LJ liquids, similar to the one proposed recently for liquid sodium, it is shown that the viscosity of the mixtures studied here are well-predicted by the combination of vdW1 fluid and empirical law. The Stokes-Einstein relation in the mixtures has also been investigated. A possible simple extension of this relation, from pure liquids to mixtures, has been proposed and tested.

Coarse-grain modelling using an equation-of-state many-body potential: application to fluid mixtures at high temperature and high pressure

ABSTRACTA many-body, coarse-grain model, termed the product gas mixture model, is presented that accurately describes the thermodynamic behaviour of molecular mixtures. The coarse-grain model is developed by first approximating the mixture as a van der Waals one-fluid, and subsequently applying an exponential-6 equation-of-state to describe the forces and energies between particles in the spirit of the many-body model pioneered by Pagonabarraga and Frenkel. Isothermal dissipative particle dynamics simulations are carried out at thermochemical states that occur during decomposition of a prototypical energetic material, RDX (1,3,5-trinitro-1,3,5-triazinane). The product gas mixture model performance is assessed by comparing to an explicit-molecule model and a hard-core coarse-grain model based on the exponential-6 pair potential. Overall, the many-body, coarse-grain model is shown to accurately capture the structural and thermodynamic properties for the wide variety of thermochemical states considered, while the hard-core coarse-grain model cannot. The many-body, coarse-grain model overcomes the issues of transferability, scaling consistency and unphysical ordered phase behaviour that often afflict coarse-grain models. While specific thermochemical conditions related to RDX decomposition are considered, the results are generally applicable to the thermodynamic behaviour of other fluid mixtures at both moderate and extreme conditions.

Efficient ceria-zirconium oxide catalyst for carbon dioxide conversions: Characterization, catalytic activity and thermodynamic study

In this study, ceria-zirconia based catalysts (CeO2, ZrO2 and Ce0.5Zr0.5O2) were synthesized by hydrothermal method and characterized by N2-sorption, X-ray diffraction (XRD), scanning electron microscopy (SEM) and transmission electron microscopy (TEM). Acidity and basicity of synthesized catalysts were investigated by NH3 and CO2 temperature-programmed desorption (TPD). Brunauer-Emmett-Teller (BET) surface area of CeO2, Ce0.5Zr0.5O2 and ZrO2 were found to be 88, 117 and 70 m2 g−1 and average crystallite sizes was 9.48, 7.09 and 9.45 nm, respectively. These catalysts were further used for direct conversion of CO2 with methanol for the synthesis of dimethyl carbonate (DMC). DMC yield was found to be highly dependent upon the both basicity and acidity of catalysts. Ce0.5Zr0.5O2 catalysts showed better activity as compared to CeO2 and ZrO2 catalysts. Effect of reaction conditions (such as catalyst dose, reaction temperature and reaction time) and catalyst reusability was studied with Ce0.5Zr0.5O2 catalyst. The optimum operating condition for direct conversion of CO2 into DMC at constant pressure of 150 bar were found to be reaction time = 24 h, catalyst dose = 1.25 g and temperature = 120 °C. Moreover, chemical equilibrium modeling was performed using Peng–Robinson–Stryjek–Vera equation of state (PRSV-EoS) along with the van der Waals one-fluid (1PVDW) mixing rule to calculate the heat of reaction and Gibbs free energy change.

Semi-empirical models and a cubic equation of state for correlation of solids solubility in scCO2: Dyes and calix[4]arenes as illustrative examples

Knowledge of a compound's solubility in the supercritical solvent is crucial to the definition of the optimal operating conditions and consequently to the development of supercritical applications.The present paper examines the performance of two of the most widely used groups of models for correlating the solubility of solid solutes in supercritical carbon dioxide – equations of state (EoSs) and semi-empirical density based models. The Soave-Kwong-Redlich (SRK) EoS with the one-fluid van der Waals mixing rule represents cubic EoSs, while the group of the density-based models includes Chrastil, Kumar and Johnston, Bartle et al., Méndez-Santiago and Teja, Garlapati and Madras, Nejad et al. and Khansary et al. models.The seven solutes chosen as illustrative examples are compounds of interest to the dry dyeing processing techniques and biotechnological processes and have diverse structural complexity.The results obtained reveal that the more recently advocated density-based models (Garlapati and Madras, Nejad et al. and Khansary et al. models) perform better with overall average absolute deviations, AARD, of 6.5, 9.0 and 9.3%, respectively. The 6.7% overall AARD for the SRK CEoS is acceptable and it can be used as a reliable thermodynamic model to predict the solubility of any compound for which there is no sufficient experimental data available.

Erratum to: Thermodynamic modeling of vapor–liquid equilibrium for binary polyethylene glycol/solvent solutions using cubic equations of state: optimization and comparison of CEoS models

The cubic equation of state (CEoS) is a powerful method for calculation of (vapor + liquid) equilibrium in polymer solutions. Using CEoS for both the vapor and liquid phases allows one to calculate the non-ideality of polymer solutions based on a single EoS approach. In this research, vapor–liquid equilibrium calculations of Polyethylene glycol(Polyethylene oxide)/solvent solutions were carried out. In this approach eight models containing PRSV and SRK CEoS separately combined with four mixing rules namely one-parameter van der Waals one-fluid, two-parameter van der Waals one-fluid (vdW2), Wong–Sandler, and Zhong–Masuoka were applied to calculations of bubble point pressure. For the better prediction, the adjustable binary interaction parameters existing in any mixing rule were optimized. The results were very acceptable and satisfactory. The results of absolute average deviations between predicted results and experimental bubble point pressure data were calculated and presented. Although the capability of two cubic equations of state had a good agreement with experimental data and predict the correct type of phase behavior in all cases, the performance of the PRSV+vdW2 was more reliable than the other models.

Equation of State of Detonation Products Based on Chemical Equilibrium

An equation of state (EOS) model of detonation products based on chemical equilibrium is developed. The EOS of gaseous detonation products is described by Rosss modification of hard-sphere variation theory and the improved one-fluid van der Waals mixture model. The condensed phases of carbon are taken as a mixture of graphite, diamond, graphite-like liquid and diamond-like liquid. For a mixed system of detonation products, the free energy minimization principle is used to determine the equilibrium compositions of detonation products by solving chemical equilibrium equations. The potential function parameters have been renewed and the non-ideal fixing effects of the major detonation products have been taken into account. The calculated detonation parameters in our work for a variety of explosives are well in agreement with the experimental data.

Modeling of high-pressure vapor–liquid equilibrium in ionic liquids + gas systems using the PRSV equation of state

Ionic liquids are environmentally friendly solvents composed of large organic cations and relatively small inorganic anions, whose melting point is below T = 373.15 K. This is an arbitrary limit defined in order to organize the dramatically increasing number of possible applications in chemical processes. These compounds are regarded as potentially environmentally benign solvents due to their almost negligible vapor pressure, which essentially eliminates emission to the atmosphere; besides, they present a wide range of liquid existence. Ionic liquids are applicable in separation processes, such as recovery of valuable products and remotion of polluting agents in effluents [1–4] and are a new and exciting class of compounds that have the potential to overcome many of the problems associated with current CO 2-capture techniques. In this work, high-pressure vapor–liquid equilibrium (VLE) of 17 binary mixtures ionic liquid + gas has been modeled with the Peng–Robinson/Stryjek–Vera (PRSV) [5,6] equation of state (EoS) applying the Wong–Sandler (WS) [7] mixing rules, including the van Laar (VL) model for the excess Gibbs free energy [8] for the gamma–phi approach and the one-fluid van der Waals (VDW) mixing rules for the phi–phi approach. Critical properties and acentric factor of ionic liquids [pmim][Tf 2N] and [hmmim][Tf 2N] were determined using the extended group contribution method by Lydersen–Joback–Reid [9], while, for the other ionic liquids, these properties are available in the literature [10,11]. Experimental data were obtained from literature [12–18] and the adjustable parameters were fitted by minimizing the errors between predicted and experimental bubble pressure. van Laar and binary interaction parameters were regarded as temperature-dependent. The results, in terms of main deviations between experimental and calculated pressures for the 17 binary systems, are reasonably satisfactory (3.62% and 2.59% for the gamma–phi and phi–phi approaches, respectively).

Solubility of Ethanamide and 2-Propenamide in Supercritical Carbon Dioxide. Measurements and Correlation

Solubilities of ethanamide (acetamide) and 2-propenamide (acrylamide) in supercritical carbon dioxide were measured at T = (308.2, 318.2, and 333.2) K over the pressure range (9.0 to 40.0) MPa by a flow-type apparatus. The solubility of acetamide (2.3·10−4 to 31.3·10−4) in the overall region of measurements is approximately twice that of acrylamide (1.2·10−4 to 16.3·10−4). The solubility of both components increases with pressure, and the relative location of the crossover region is observed at about 12.0 MPa. The experimental data were correlated by using the Soave−Redlich−Kwong equation of state (EoS) with the one-fluid van der Waals mixing rule. In addition, the pure compound properties required for the modeling were also estimated.

Prediction of Double Retrograde Vaporization by Hybrid Global-Local Optimization Using Fuzzy Clustering Means

Retrograde vaporization calculation is a hard problem, which possesses several solutions and demands a robust algorithm. In the present work, we solved the double retrograde vaporization problem by hybrid global-local optimization. In fact, we propose a new methodology that involves fuzzy clustering means together with Luus-Jaakola and Nelder-Mead algorithms. We applied the proposed methodology to solve the double retrograde vaporization problem for binary systems of methane + n-butane. For this mixture, the dew point curve exhibits an S-shape at temperatures slightly below the critical temperature of the more volatile component. This binary mixture was modeled using the original Peng-Robinson equation of state and the classical one-fluid van der Waals mixing rule.

Solubility of ethylene in 2,2,4-trimethylpentane and 1-octene mixture

With a static type equilibrium cell and the pressure decaying method, the solubility of ethylene in a mixture of 2,2,4-trimethylpentane and 1-octene was measured in the temperature range of 323.15–423.15 K, pressure range of 5–25 bar, and 1-octene concentration from 0 to 85 wt%. The experimental results show that the solubility of ethylene in a 2,2,4-trimethylpentane and 1-octane mixture increases with system pressure but decreases with system temperature. The experimental solubility data were also expressed in the vapor–liquid equilibrium relationship and correlated by the bubble pressure calculation using the Peng–Robinson equation of state (PR EOS) incorporated with the van der Waals one-fluid and the Zhong–Masuoka mixing rules. Among the deviations between the experimental and correlated results, the largest value of average absolute relative deviation is 1.73% for pressure at 423.15 K and that of average absolute deviation is 0.0024 mol fraction for vapor composition at 373.15 K by the Zhong–Masuoka mixing rule.

Solubility of Ethylene in 2,2,4-Trimethylpentane at Various Temperatures and Pressures

In this study, the solubilities of ethylene in 2,2,4-trimethylpentane solvent at various temperatures between (323.15 and 423.15) K and pressures between (0.5 and 2.5) MPa were measured by the pressure decay method with vapor composition being analyzed on-line with a gas chromatography. The experimental results show that the solubility of ethylene in 2,2,4-trimethylpentane increases with increasing pressure and decreases with increasing temperature. The experimental data were also expressed in terms of vapor−liquid equilibrium and correlated by the bubble−pressure calculation with the Peng−Robinson equation of state incorporated with the van der Waals one-fluid (vdW-1) and the Zhong−Masuoka (Z-M) mixing rules with the consideration of binary interaction parameters. The results showed the vdW-1 mixing rule is slightly better than the Z-M mixing rule for pressure correlation, but the Z-M mixing rule is slightly better for vapor composition correlation. A semiempirical four-parameter solubility equation in t...

Modelling of the phase behaviour for the direct synthesis of dimethyl carbonate from CO 2 and methanol at supercritical or near critical conditions

This study is focused on modelling the phase equilibrium behaviour of the reaction mixture (CO 2 + methanol + DMC + H 2O) at high pressure–temperature conditions using the Patel–Teja (PT) and Peng–Robinson–Stryjek–Vera (PRSV) equations of state along with the van der Waals One-Fluid (1PVDW) mixing rule. The optimum values of the binary interaction parameters ( k ij ) were calculated from VLE data found in the literature, and then adjusted to a lineal temperature equation. As a result, the temperature-dependent model was applied to predict the fluid phase equilibria of the corresponding binary a ternary sub-systems and, later, successfully contrasted with experimental data. In addition, phase equilibrium data were experimentally measured at high pressure (8 MPa to 15 MPa) for the ternary system (CO 2 + methanol + DMC), in order to confirm the ability of the model to predict the phase behaviour of the ternary system at high pressure–temperature. The agreement between the experimental data and the proposed model enables to predict the phase equilibrium behaviour of the mixture (CO 2 + methanol + DMC + H 2O), and thus, optimise the operation conditions in several reaction and separation processes.

Modification of Sako-Wu-Prausnitz equation of state for fluid phase equilibria in polyethylene-ethylene systems at high pressures

In order to model phase equilibria at all pressures, it is necessary to have an equation of state. We have chosen the Sako-Wu-Prausnitz cubic equation of state, which had shown some promising results. However, in order to satisfy our demands, we had to modify it slightly and fit new pure component parameters. New pure component parameters have been determined for ethylene and the n-alkane series, using vapor pressure data, saturated liquid volume and one-phase PVT-data. For higher n-alkanes, where vapor pressure data are poor or not available, determination of the pure component parameters was made in part by extrapolation and in part by fitting to one-phase PVT-data. Using one-fluid van der Waals mixing rules, with one adjustable interaction parameter, good correlation of binary hydrocarbon system was obtained, except for the critical region. The extension of the equation of state to polyethylene systems is covered in this work. Using the determined parameters, flash and cloud point calculations were performed, and treating the polymer as polydisperse. The results fit data well.

The van der Waals one-fluid model for viscosity in Lennard–Jones fluids: Influence of size and energy parameters

This work aims to estimate the limitations of the van der Waals one-fluid (vdW1) approximation in the prediction of the viscosity of Lennard–Jones (LJ) mixtures. To do so, non-equilibrium molecular dynamics simulations have been performed. Results on mixtures have been compared to those of their equivalent pure fluids (in the sense of the vdW1 model). Several systems (146 configurations) are studied, which are composed of binary and ternary mixtures in various thermodynamic states and for different combining rules. In a first step, deviations induced separately by LJ molecular parameters (size or energy) have been analyzed. It is shown that the vdW1 model is well designed for the energy parameter in every configuration. On the contrary, for the size parameter, deviations induced by this one-fluid approach are shown to be large in dense state and low temperature systems. In a second step, the coupling effects of the LJ size and energy parameters with the mass are studied. It appears that an accurate one-fluid approximation for viscosity should involve a coupling between the mass and the size parameters in its formulation (which is not the case with the vdW1 model) but not between the mass and the energy.

The experiments and correlations of the solubility of ethylene in toluene solvent

Polymer cyclic olefin copolymer (COC) is produced from the reaction of attaching ethyl groups to the norbornene monomer in liquid phase. The first step of process is dissolving ethylene in a liquid phase where toluene is present as a cosolvent. Thus, the solubility of ethylene in liquid toluene is the most important factor affecting the production of COC. In this study, the solubility of ethylene in toluene was measured in the temperature range from 323.15 to 423.15 K and pressure range from 5 to 25 bar. The experiments were conducted by the method of pressure decaying with a newly designed apparatus. The experimental results show that the solubility of ethylene in toluene increases with increasing pressure but decreases with increasing temperature. The experimental solubility data were expressed in the vapor–liquid equilibrium relationship and correlated fairly well by the bubble–pressure calculation with the Peng–Robinson equation of state (PR EOS) incorporated with the van der Waals one-fluid and the Zhong–Masuoka mixing rules with the consideration of binary interaction parameters. The results showed the van der Waals (vdW-1) mixing rule is slightly better than the Z–M mixing rule for pressure correlation but the Z–M mixing rule is slightly better for vapor composition correlation. A semi-empirical solubility equation with four parameters for the present binary system was proposed in this study. This proposed model estimates the solubility easier and as accurate as the PR EOS does for the present system.

Modeling the high-pressure behavior of binary mixtures of carbon dioxide+alkanols using an excess free energy mixing rule

The behavior of binary mixtures of carbon dioxide+alkanol (1-butanol, 2-butanol, 1-pentanol, or 2-pentanol) at high pressures was modeled using the Stryjek-Vera version of the Peng-Robinson equation of state. Two mixing rules were compared for this purpose: the classical one-fluid van der Waals and the Wong-Sandler mixing rules. In the case of the latter mixing rule, the NRTL model for the excess Gibbs free energy was used. We observed that both mixing rules can reproduce the qualitative aspects of the critical diagrams of these binary mixtures. A comparison of the results shows that there is no clear superiority of one mixing rule over the other in terms of the ability to predict the critical behavior of these mixtures.

Helmholtz energy, extended corresponding states and local composition model for fluid mixtures

We present a model for the calculation of mixture properties. This model is based on the mixture residual Helmholtz energy given by the sum of two terms: one is the residual Helmholtz energy calculated by an extended corresponding states (ECS) model while the other is a correction term. The ECS model is based on methane as the reference fluid and shape factors that carry out the scaling of properties between the fluid of interest and the reference fluid. These shape factors are given by correlations in terms of reduced temperature and density. The application to mixtures is carried out with the one-fluid van der Waals mixture model. The correction term is temperature- and density-dependent as is given by a local composition mixing rule. Local compositions were calculated from a coordination number model based on lattice gas theory. With respect to binary-mixture properties, densities were calculated with an average absolute deviation (AAD) of 0.12%; speeds of sound were calculated with an AAD of 0.16% and bubble pressures were calculated with an AAD of 1.77%. Also, natural gas densities were calculated with AAD of 0.03% and natural gas speeds of sound were calculated with AAD of 0.049%. All these results are very satisfactory when compared with those obtained by modern mixture models.

Solubility of Ethylene in Mixtures of Toluene, Norbornene, and Cyclic Olefin Copolymer at Various Temperatures and Pressures

In this study, the solubilities of ethylene in mixtures of toluene, norbornene, and cyclic olefin copolymer (COC) were measured at various temperatures (between 323.15 and 423.15 K), pressures (between 5 and 25 bar), concentrations of norbornene (between 0 and 85 wt %), and concentrations of COC (between 0 and 40 wt %). The experiments were conducted by the pressure decaying method using a newly designed apparatus. The experimental results show that the solubility of ethylene increases with increasing system pressure but decreases with increasing system temperature in the above mixture. Another interesting observation is that the solubility decreases when the concentration of reaction product, COC, is increased. Thus, in addition to temperature and pressure, the COC concentration affects the reaction extent, and beyond a certain COC concentration, further reaction favoring COC generation is impossible because of the opposite effect on ethylene solubility. Also, in this study, the experimental solubility data were expressed in vapor−liquid equilibrium relationship and correlated by bubble-pressure calculations with the Peng−Robinson equation of state (PR EOS; Peng, D. Y.; Robinson, D. B. Ind. Eng. Chem. Fundam. 1976, 15, 59) incorporating the modified van der Waals one-fluid (vdW-1) mixing rules and the Zhong−Masuoka (Z−M; Zhong C.; Masuoka, H. Fluid Phase Equilib. 1996, 123, 59) mixing rules, including the consideration of binary interaction parameters. The average absolute deviation percentages (AAD) of the correlation are less than 3.0%, except that of pressure with the Z−M mixing rules.