Equilibria Of Binary Mixtures Research Articles

Efficient Approximation with Space Filling Quadtrees: Application to Phase Equilibria in Binary Mixtures.

A relatively succinct set of property calculations can be used to construct efficient (in memory and speed) numerical approximations of that function in a rectangular domain. Through the use of adaptive subdivision with quadtrees and bi-Chebyshev expansions in each leaf, the function can be practically represented to the order of the noise in the function to be approximated. A further benefit is that evaluation of the approximation is noniterative and thus cannot fail to converge (a relatively common problem in thermophysical property libraries, especially for mixtures). Evaluation of the approximation function requires only a few bisection steps to identify the leaf of interest such that evaluation of the approximation data structure takes less than a microsecond. The technique is demonstrated by application to the vapor-liquid-equilibria evaluated with two different models (COSMO-SAC activity coefficient model and multifluid model). For the more expensive COSMO-SAC case, the approximation function is more than 2000 times faster to evaluate, and deviations in pressure are less than a part in 108 which is practically equal to the iteration convergence criterion.

Isobaric Vapor–Liquid Equilibrium for Binary Mixtures Composed of Pentamethylene Diisocyanate, 5-Chloropentyl Isocyanate, and Chlorobenzene at 10 kPa

Isobaric Vapor–Liquid Equilibrium for Binary Mixtures Composed of Pentamethylene Diisocyanate, 5-Chloropentyl Isocyanate, and Chlorobenzene at 10 kPa

Isobaric Vapor–Liquid Equilibrium of Binary Mixtures of 2-Methylpentanedioic Acid Dimethyl Ester and Dimethyl Adipate at 101.3, 50.0, 30.0, and 10.0 kPa

Isobaric Vapor–Liquid Equilibrium of Binary Mixtures of 2-Methylpentanedioic Acid Dimethyl Ester and Dimethyl Adipate at 101.3, 50.0, 30.0, and 10.0 kPa

Investigation on solid-liquid equilibrium for binary mixtures of carbon dioxide (R744) and alkanes: Propane (R290) and isobutane (R600a)

The solid-liquid equilibrium (SLE) of binary systems containing carbon dioxide (R744) and alkanes propane (R290) and isobutane (R600a) was experimentally investigated. A novel experimental setup using the cooling curve method was designed, built and verified, enabling SLE measurements at temperatures down to 173 K. The temperature and pressure of the triple point of carbon dioxide (CO2) were measured. The results for R744 and the binary mixture of carbon dioxide and propane were in agreement with the available literature data, demonstrating the accuracy of the experimental setup. Activity coefficients were determined for the binary mixtures studied. The Schröder and Wilson equations were used to calculate solubility over various temperatures and compositions. The Wilson model produced a very accurate correlation for the studied non-ideal binary mixtures, while the Schröder equation did not provide satisfactory results. Determined activity coefficients and SLE curves should be useful for the design of low-temperature refrigeration systems operating on carbon dioxide mixtures with low global warming potential.

Vapor-liquid equilibria of binary mixtures containing Stockmayer-type model fluids from Monte-Carlo simulations

In this contribution, the vapor-liquid equilibria (VLE) of binary mixtures containing Lennard-Jones (LJ), Stockmayer (LJ + point dipole, ST), and shifted Stockmayer (sST) fluids are investigated with molecular simulations. The LJ and ST fluids are commonly used nonpolar and polar model fluids, respectively. The sST fluid differs from the ST fluid in that the dipole is shifted away from the dispersive center, which results in the sST fluid exhibiting H-bonding-like behavior. By varying the dispersion energy of the LJ fluid and the dipole moments of the ST and sST fluids, and the dipole shift of the sST fluids, different mixtures are generated, which are investigated at several temperatures and concentrations. Differences in the phase behavior between mixtures containing ST and sST fluids are quantified and linked to differences in fluid structure. The reported data include the VLE envelopes, coexisting densities, activity coefficients, and enthalpies for liquid and vapor phases, as well as structural information on the fluids’ intermolecular orientations.

Measurement and Correlation of Vapor–Liquid Equilibrium for Binary Mixtures Composed of m-Xylene, Ethylbenzene, and 1, 2, 4-Trichlorobenzene at 101.3 kPa

Measurement and Correlation of Vapor–Liquid Equilibrium for Binary Mixtures Composed of m-Xylene, Ethylbenzene, and 1, 2, 4-Trichlorobenzene at 101.3 kPa

Systematic study of vapour–liquid equilibria in binary mixtures of fluids with different polarity from molecular simulations

ABSTRACT For engineering applications, one of the most important characteristics of fluid mixtures is the vapour–liquid equilibrium (VLE). Knowledge of the VLE of mixtures containing simple model components like Lennard-Jones (LJ) and Stockmayer (ST) fluids can offer insight into how different modes of molecular interaction shape the phase behaviour of mixtures. However, studies investigating such mixtures are still scarce in the literature, especially for mixtures with an LJ fluid as the high boiling substance. In this work, the VLE of mixtures consisting of LJ and ST fluids are studied with molecular simulation using the Grand Equilibrium method. The energy parameter and length parameter of the LJ fluids and the dipole moments of the ST fluids are varied systematically to generate different types of mixtures. These mixtures are investigated within a broad temperature range. VLE envelopes and molarities are reported as well as additional data on the bubble and dew line including enthalpies, chemical potentials, and activity coefficients. These data fill a gap in the literature by furthering the understanding of how polarity affects phase behaviour in mixtures and are therefore of critical importance, e.g. for the development of theoretical approaches for the description and prediction of phase behaviour for polar mixtures.

Vapor–Liquid Equilibrium in Binary and Ternary Azeotropic Solutions Acetonitrile-Ethanol-Water with the Addition of Amino Esters of Boric Acid

The effect of amino esters of boric acid (AEBA) on the conditions of vapor–liquid equilibrium in binary mixtures of acetonitrile–water, ethanol–acetonitrile and a three-component mixture of ethanol-acetonitrile-water was investigated. Residual curves and vapor–liquid phase equilibrium conditions (TPXY data) were experimentally measured at atmospheric pressure for a binary mixture of acetonitrile-AEBA and a triple mixture of acetonitrile-water-AEBA. Previously unknown energy binary parameters of groups B, CH2N with group CH3CN were determined for the UNIFAC model. The correction of the value of the binary parameter water—acetonitrile was carried out. On the basis of thermodynamic modeling, the degree of influence of AEBA on the relative volatility of acetonitrile in binary and ternary mixtures was analyzed. It is shown that the use of AEBA removes all azeotropic points in the studied mixtures. In this case, acetonitrile turns out to be a volatile component, and water is a non-volatile component in the entire concentration range.

Non-isoplethic measurement on the solid-liquid-vapor equilibrium of binary mixtures at cryogenic temperatures.

We measured the solid-liquid-vapor (SLV) equilibrium of binary mixtures during experiments that alternated between cooling the mixture and injecting the more-volatile component into the sample chamber; thus, the composition of the mixture changed (non-isoplethic) throughout the experiment. Four binary mixtures were used in the experiments to represent mixtures with miscible solid phases (N2/CO) and barely miscible solid solutions (N2/C2H6), as well as mixtures with intermediate solid miscibility (N2/CH4 and CO/CH4). We measured new SLV pressure data for the binary mixtures, except for N2/CH4, which are also available in the literature for verification in this work. While these mixtures are of great interest in planetary science and cryogenics, the resulting pressure data are also needed for modeling purposes. We found the results for N2/CH4 to be consistent with the literature. The resulting new SLV curve for CO/CH4 shows similarities to N2/CH4. Both have two density inversion points (bracketing the temperature range where the solid floats). This result is important for places such as Pluto, Triton, and Titan, where these mixtures exist in vapor, liquid, and solid phases. Based on our experiments, the presence of a eutectic is unlikely for the N2/CH4 and CO/CH4 systems. An azeotrope with or without a peritectic is likely, but further investigations are needed to confirm. The N2/CO system does not have a density inversion point, as the ice always sinks in its liquid. For N2/C2H6, new SLV pressure data were measured near each triple point of the pure components.

Modeling the solid-liquid equilibrium of binary mixtures of triacylglycerols using UNIFAC and predictive UNIQUAC models

The modeling of solid-liquid equilibrium is often performed assuming a series of theoretical simplifications, such as the compounds’ immiscibility in the solid phase. Unfortunately, this is not true for several systems, including food compounds. For example, triacylglycerol (TAG) molecules are the main components of fats and oils. Because of their characteristic solid transition phenomena such as polymorphism and solid solution formation, the quality of oil- and fat-based products is essentially dependent on TAG mixtures’ phase behavior. This work aimed to evaluate the use of a predictive approach based on UNIFAC and a predictive version of UNIQUAC to describe the solid-liquid equilibrium (SLE) behavior of binary mixtures containing TAG species. We put forth a validation test for the modeling approach, using experimental data of TAG mixtures solid-liquid phase diagrams taken from literature. Compared to the adjustable Margules equation and traditional UNIFAC structural parameters approaches, results showed that the predictive modeling approach is quite helpful in representing the experimental data despite limitations in calculating the nonideal behavior of the systems. It is noticeable that using models for calculating the activity coefficients in both phases was essential to the systems’ best description. The SLE theory-based predictive modeling approach used here can be further evaluated for designing mixtures with desired phase behavior, being an interesting tool for describing phase diagrams of TAG mixtures when no experimental data is available.

Understanding liquid-liquid equilibria in binary mixtures of hydrocarbons with a thermally robust perarylphosphonium-based ionic liquid.

Binary mixtures of hydrocarbons and a thermally robust ionic liquid (IL) incorporating a perarylphosphonium-based cation are investigated experimentally and computationally. Experimentally, it is seen that excess toluene added to the IL forms two distinct liquid phases, an “ion-rich” phase of fixed composition and a phase that is nearly pure toluene. Conversely, n-heptane is observed to be essentially immiscible in the neat IL. Molecular dynamics simulations capture both of these behaviours. Furthermore, the simulated composition of the toluene-rich IL phase is within 10% of the experimentally determined composition. Additional simulations are performed on the binary mixtures of the IL and ten other small hydrocarbons having mixed aromatic/aliphatic character. It is found that hydrocarbons with a predominant aliphatic character are largely immiscible with the IL, while those with a predominant aromatic character readily mix with the IL. A detailed analysis of the structure and energetic changes that occur on mixing reveals the nature of the ion-rich phase. The simulations show a bicontinuous phase with hydrocarbon uptake akin to absorption and swelling by a porous absorbent. Aromatic hydrocarbons are driven into the neat IL via dispersion forces with the IL cations and, to a lesser extent, the IL anions. The ion–ion network expands to accommodate the hydrocarbons, yet maintains a core connective structure. At a certain loading, this network becomes stretched to its limit. The energetic penalty associated with breaking the core connective network outweighs the gain from new hydrocarbon–IL interactions, leaving additional hydrocarbons in the neat phase. The spatially alternating charge of the expanded IL network is shown to interact favourably with the stacked aromatic subphase, something not possible for aliphatic hydrocarbons.

Phase Equilibria in Binary Mixtures of Water with Triglyme and Tetraglyme: Experimental Determination and Thermodynamic Modeling

Because of their many favorable properties and specifically balanced amphiphilic nature, glymes (oligomeric ethylene glycol diethers) are of great technological and theoretical interest. This study...

Accurate quantum-corrected cubic equations of state for helium, neon, hydrogen, deuterium and their mixtures

Cubic equations of state have thus far yielded poor predictions of the thermodynamic properties of quantum fluids such as hydrogen, helium and deuterium at low temperatures. Furthermore, the shape of the optimal α functions of helium and hydrogen have been shown to not decay monotonically as for other fluids. In this work, we derive temperature-dependent quantum corrections for the covolume parameter of cubic equations of state by mapping them onto the excluded volumes predicted by quantum-corrected Mie potentials. Subsequent regression of the Twu α function recovers a near classical behavior with a monotonic decay for most of the temperature range. The quantum corrections result in a significantly better accuracy, especially for caloric properties. While the average deviation of the isochoric heat capacity of liquid hydrogen at saturation exceeds 80% with the present state-of-the-art, the average deviation is 4% with quantum corrections. Average deviations for the saturation pressure are well below 1% for all four fluids. Using Péneloux volume shifts gives average errors in saturation densities that are below 2% for helium and about 1% for hydrogen, deuterium and neon. Parameters are presented for two cubic equations of state: Peng–Robinson and Soave–Redlich–Kwong. The quantum-corrected cubic equations of state are also able to reproduce the vapor-liquid equilibrium of binary mixtures of quantum fluids, and they are the first cubic equations of state that are able to accurately model the vapor-liquid equilibrium of the helium–neon mixture. Similar to the quantum-corrected Mie potentials that were used to develop the covolume corrections, an interaction parameter for the covolume is needed to represent the helium–hydrogen mixture to a high accuracy. The quantum-corrected cubic equation of state paves the way for technological applications of quantum fluids that require models with both high accuracy and computational speed.

Thermodynamic properties and fluid phase equilibrium of natural gas containing CO2 and H2O at extreme pressures typically found in pre-salt reservoirs

This paper presents an assessment on the use of Monte Carlo simulations and equations of state to calculate fluid phase equilibrium of natural gas containing CO2 and H2O at extreme pressures. Standard Gibbs ensemble Monte Carlo simulations in the canonical ensemble were used to study the coexistence properties of carbon dioxide and methane at temperatures ranging from the triple point up to the surroundings of the critical point. Vapor-liquid equilibrium of binary mixtures was investigated at temperatures of 230 K and 270 K, over a broad range of pressures. Simulation results obtained for binary mixtures showed that the different force fields and combining rules yield equivalent results, providing good accuracy at 230 K, whereas larger deviations were found at 270 K. Due to the highly non-ideal behavior and the individual characteristics of each components, vapor-liquid equilibrium of ternary mixtures was calculated using an equation of state based on the associating fluid theory (viz., PC-SAFT). The PC-SAFT equation with adjusted binary interaction parameters resulted in consistently low absolute average relative deviation of the water content, mostly within experimental uncertainty.

Equations for calculation of liquid-vapor equilibrium in binary mixtures containing methane

Equations describing the experimental data on liquid-vapor equilibrium in binary mixtures of methane with argon, carbon dioxide and helium have been compiled. The equations describe the dependence of pressure of liquid or vapor on temperature and composition. When compiling them, the program selected most significant coefficients of the equations. The standard deviations of experimental values of pressure from the calculated values range from 1.8 to 5.0%. The equations make it possible to determine the composition or temperature of the phases at known values of other parameters of phase equilibrium.

Thermodynamic equilibrium of binary mixtures on curved surfaces.

We study the global influence of curvature on the free energy landscape of two-dimensional binary mixtures confined on closed surfaces. Starting from a generic effective free energy, constructed on the basis of symmetry considerations and conservation laws, we identify several model-independent phenomena, such as a curvature-dependent line tension and local shifts in the binodal concentrations. To shed light on the origin of the phenomenological parameters appearing in the effective free energy, we further construct a lattice-gas model of binary mixtures on nontrivial substrates, based on the curved-space generalization of the two-dimensional Ising model. This allows us to decompose the interaction between the local concentration of the mixture and the substrate curvature into four distinct contributions, as a result of which the phase diagram splits into critical subdiagrams. The resulting free energy landscape can admit, as stable equilibria, strongly inhomogeneous mixed phases, which we refer to as "antimixed" states below the critical temperature. We corroborate our semianalytical findings with phase-field numerical simulations on realistic curved lattices. Despite this work being primarily motivated by recent experimental observations of multicomponent lipid vesicles supported by colloidal scaffolds, our results are applicable to any binary mixture confined on closed surfaces of arbitrary geometry.

Comparison between a soft computing model and thermodynamic models for prediction of phase equilibria in binary mixtures containing 1-alkanol, n-alkane, and CO2

In the present work, vapor-liquid equilibrium (VLE) for binary systems containing 1-alkanols, n-alkanes and CO2 were examined to compare the predictions of a soft computing model namely least square support vector machine optimized by coupled simulated annealing (CSA-LSSVM) with the predictions of two thermodynamic models namely perturbed chain statistical fluid association (PC-SAFT) and the Peng Robinson model coupled with Wong-Sandler mixing rule and non-random two liquid model (PR-WS-NRTL). Results revealed that all of the three models provide acceptable predictions for calculation of the vapor-liquid equilibrium data. However, it was found that the CSA-LSSVM model provides better predictions in comparison with the PC-SAFT and PR-WS-NRTL models in the studied systems.

Liquid–Liquid Equilibria in Binary Mixtures of Dihydroxy Alcohols and Imidazolium-Based Ionic Liquids

Binary liquid–liquid equilibria (LLE) for mixtures of dihydroxy alcohols and three imidazolium-based ionic liquids (ILs) were measured. The dihydroxy alcohols were 1,3-propanediol, 1,4-butanediol, ...

Improvement to PR+COSMOSAC EOS for Predicting the Vapor Pressure of Nonelectrolyte Organic Solids and Liquids

The PR+COSMOSAC EOS has been shown to be able to utilize quantum mechanical calculation results to predict the thermodynamic properties and fluid phase equilibrium with the only input of molecular structure. In this study, two modifications are introduced to further improve its accuracy in predicting vapor pressures of pure fluids. The average logarithmic deviation in vapor pressure (ALD-P) from the triple-point temperature to the normal boiling temperature for 1124 substances is reduced from 0.321 to 0.256 (or from 109.4% to 80.2%) (a reduction of 20% in ALD-P), while ALD-P from the normal boiling temperature to the critical temperature remains similar. The average absolute deviation (AAD) in the normal boiling temperature for 1405 substances is reduced from 16.32 to 14.25 K. Furthermore, its accuracy in predicting the critical properties and sublimation pressures (1140 substances) of pure fluids and vapor–liquid equilibrium of binary mixtures (1118 systems) is investigated and compared with the previous versions of PR+COSMOSAC. The accuracy of the revised PR+COSMOSAC EOS is generally improved, and the effect of each modification on the accuracy is discussed. This model is particularly useful when no experimental data are available.

(Solid + liquid) equilibrium of binary mixtures containing ethyl esters and p-xylene by differential scanning calorimetry

Current concerns regarding the environmental and economic sustainability of petroleum-based transportation fuels, including jet fuel, are driving interest into alternative fuels. To study the feasibility of using biodiesel in aviation engines, a deeper knowledge on solid–liquid equilibrium (SLE) of biodiesel/jet fuel blends is required. This work presents SLE data of binary mixtures containing p-xylene, a representative compound of aviation fuel, and fatty esters present in ethylic biodiesel. Experimental data were obtained through differential scanning calorimetry. A simple eutectic behavior was observed for all binary systems, although small regions of partial miscibility are also present. Observed eutectic temperature and composition (ethyl ester mole fraction) are 259.0 K and 0.45, 269.0 K and 0.32, 275.5 K and 0.22, 280.0 K and 0.15, and 247.7 K and 0.58 for systems containing ethyl laurate, ethyl myristate, ethyl palmitate, ethyl stearate and ethyl oleate, respectively. Good agreement was obtained between experimental and calculated data when using UNIFAC (Dortmund) model or Flory–Huggins equation, with root-mean-square deviations ranging from 0.47 to 1.90 K. The systems exhibit significant deviations from ideality, which cannot be neglected in model calculations.