Parachor Method Research Articles

Molecular simulation and experimental validation for surface tension of new Low-GWP refrigerant mixtures R32/CF3I and R1123/CF3I

This study demonstrated a new procedure for measuring surface tension using molecular dynamics (MD) simulations. The surface tension was measured by the differential capillary rise method for refrigerant mixtures R1123/CF3I and R32/CF3I, which have a low global warming potential. The information of the saturated density in the low-temperature region, which was necessary for data reduction, was supplemented by an MD simulation, which was validated using accurate measurement data near the critical point. The surface tension calculated from the pressure tensor obtained by the MD simulation deviated considerably. However, the surface tension obtained from the simulated density and composition in the vapor and liquid phases by the parachor method was in agreement with the measured values within the measurement uncertainty ranges from 0.15 mNm−1 to 0.35 mNm−1. The simulated density distribution showed positive surface activity at the vapor–liquid interface, indicating that R32 and R1123, with smaller polarities, tended to aggregate on the liquid surface. This helps interpret the empirically postulated decrease in the surface tension of the mixtures due to the concentration of substances with lower surface tension at the vapor–liquid interface.

Interfacial tension of water near to critical conditions by using the pendant drop method: New experimental data and a correlation based on the parachor method

The interfacial tension (IFT) at vapor/liquid equilibrium was measured for the pure water system following the saturation line (further named as water (l)/water (v) or pure water) as well as for the binary water/nitrogen system (further named water/nitrogen). In order to obtain vapor/liquid IFT data, the pendant drop method was applied in a high-pressure-high temperature view cell. The vapor/liquid IFT of the binary water/nitrogen system was investigated at 10, 15 and 18 MPa and for temperatures in the range of 323–598 K. For the water (l)/water (v) system, the temperature ranges from 423 K to 623 K at the respective saturation pressure. The IFT of the binary water/nitrogen system is in a similar range compared to the IFT of the pure water system up to temperatures of 500 K although showing an influence of the nitrogen pressure due to solubility and adsorption effects. At temperatures above 500 K, the IFT starts to considerably differ as a function of temperature, reflecting the respective phase behaviour of both systems. The parachor method following Macleod-Sugden was used to correlate the IFT of the binary water/nitrogen system, as well as the pure water system. The equation is in good agreement with the experimental results, showing an AAD of 4.97% for the water/nitrogen system and 3.02% for the pure water system. The obtained experimental results are further in good agreement with comparable literature data.

Surface tension and parachor for a new low-GWP refrigerant R1123/R32/R1234yf and its constituent binary pairs

Trifluoroethene R1123 is expected to be a low GWP refrigerant; however, it needs to be mixed with other stable refrigerants to avoid a disproportional reaction. This paper delivers one of the essential thermophysical properties surface tension for a low-GWP refrigerant mixture R1123/R32/1234yf measured by the differential capillary rise method in the temperature range from 225 to 345 K. The propagated uncertainty in surface tension with a 95% confidence level was typically 0.15 mNm−1. From the measured surface tension and calculated saturation densities, the parachor of R32 and R1123 were determined to be 91.6 and 123.3, respectively. The parachor of R1234yf was slightly dependent on a temperature, T, as 181.44−0.0319T. The variation in the surface tension of binary pairs against the composition was predicted by the correlation proposed by Di Nicola et al. (2018) and the parachor method with sufficient accuracy. Furthermore, the surface tension of ternary mixture R1123/R32/1234yf at compositions of 60/22/18 mass% and 22/70/08 mass% was also predicted by the parachor method with sufficient accuracy. Nevertheless, a slight deviation was confirmed at temperatures below 260 K. The prediction would be improved with subsequent studies in phase equilibrium. (191 words).

Surface thermodynamics of 2-chloroethanol with 2-dimethylaminoethanol and 2-diethylaminoethanol at different temperatures

ABSTRACT The surface tension of binary mixtures of 2-chloroethanol with 2-dimethylaminoethanol (DMAE) and 2-diethylaminoethanol (DEAE) was measured over the entire composition range at the temperatures 293.15 K to 313.15 K and atmospheric pressure. The excess values of surface tension were correlated with the Redlich-Kister polynomial equation. The experimental surface tension was correlated with five different theoretical models. The Hilderbrand and Scott theories for ideal solutions (HSIS) and their extensions of Guggenheim’s equation (HSEG), Volume Fraction Statistics, Sudgen method and modified New Parachor method were applied to determine the values of surface tension in the binary solvent systems. The surface tension data were further used to determine the surface thermodynamic properties such as surface entropy (SS) and surface enthalpy (HS) per unit surface area. The results have brought about some useful information on the extent of molecular interactions between the unlike molecules occurring at the surface and bulk.

Co-continuous phase prediction in poly(lactic acid) /poly(caprolactone) blends from melt viscosity measurements

ABSTRACT This paper investigates the effectiveness of a viscosity ratio model to predict phase inversion in poly(lactic acid)/poly(caprolactone) (PLA/PCL) blends. From capillary rheometry measurements, the melt viscosities of PLA and PCL were found to be 1298 and 1758 Pas respectively, at the temperature and shear strain rate of the melt blending process. Using these values, phase inversion was predicted to occur at 54 wt% of PCL. This prediction was validated both by optical microscopy and also by scanning electron microscopy (SEM) in which one of the phases had been removed by etching. For mechanical properties, the co-continuous phase morphology gave good ductility with balanced modulus and yield stress. Contact angle measurements were used to evaluate the surface energies of PLA and PCL. Experimental results of 35.5 and 44.0 mNm−1, respectively, agreed well with the values of 37.6 and 46.0 mNm−1 calculated from the Parachor method. Biodegradation tests in compost and degradation tests in phosphate buffer solution revealed that PLA and PCL hydrolyze by different mechanisms. PLA undergoes bulk degradation and brittle failure occurs after an incubation time, whereas PCL undergoes surface degradation. Prediction of phase inversion allows control of the morphology and hence the biodegradation and hydrolytic degradation behavior.

Modeling of Phase Equilibria and Surface Tension for N,N-Dimethylcyclohexylamine + Alcohol Mixtures at Different Temperatures

Surface tension and phase equilibria of N,N-dimethylcyclohexylamine (DMCA) mixtures with alcohol (propanol, iso-propanol, butanol, and iso-butanol) were modeled over the whole range of composition and different temperature ranging from (288.15 to 308.15) K. The predictive results of the Peng–Robinson equation of state with quadratic mixing rule indicated that the DMCA + alcohol mixtures are not azeotropic and that the bubble curve is linear, except for the DMCA + ethanol mixture. The surface tension of the binary mixtures was modeled with linear gradient theory, parachor method, Shereshefsky method, and Lamperski method. The linear gradient theory used as adjustment approach improved the results of surface tension prediction and correctly modeled this thermodynamic property for all mixtures, the flexibility of parachor method as an adjustment approach improved the predictive results for some mixtures, Shereshefsky method was able to successfully model the surface tension of the DMCA + ethanol, DMCA + propanol, and DMCA + butanol mixtures, and Lamperski method was able to successfully model the surface tension of the DMCA + propanol and DMCA + butanol mixtures, while the DMCA + ethanol and DMCA + isobutanol mixtures had an acceptable statistical deviation. Furthermore, Lamperski method was the best predicted model to model surface tension of the binary mixtures. Based on Shereshefsky model, the standard Gibbs energy of adsorption and the free energy change in the surface region were calculated. The free energy change was used to obtain the number of molecular layers in the surface region. Also, with Shereshefsky method it was obtained that alcohol is not absorbed at the surface which was also confirmed with Lamperski method. Finally, it is important to note that phase equilibria and surface tension of the DMCA + alcohol mixtures is modeled with theoretical approaches for the first time. On the other hand, for future experimental measurements of phase equilibria, our results could serve as an initial approximation of equilibrium, and the correlations obtained for the binary parameters of the linear gradient theory and parachor method can be used to predict surface tension at other temperatures outside the range 288.15 to 308.15 K.

Modeling Vapor–Liquid Equilibria and Surface Tension of Carboxylic Acids + Water Mixtures Using Peng–Robinson Equation of State and Gradient Theory

This work has been dedicated to modeling the vapor–liquid equilibria and surface tension of carboxylic acids + water mixtures at different temperatures. The Peng–Robinson equation of state with modified Huron–Vidal + Wilson mixing rule correctly models the vapor pressure and vapor mole fraction of these mixtures. The modified Huron–Vidal mixing rule was better than quadratic mixing rule to model the phase equilibria properties for the mixtures studied in this work. The parachor method and linear gradient theory were used to model the surface tension of these mixtures. Finally, a new symmetric parameter dependent on the liquid molar fraction and temperature was necessary to correctly adjust the surface tension of the carboxylic acids + water mixtures using linear gradient theory. The surface tension results obtained in this work are better than those published so far.

Surface tension and critical point measurements of methane + propane mixtures

Surface tension predictions of hydrocarbon mixtures at vapour-liquid equilibrium are crucially important and used in the design of many unit operations in the production of liquefied natural gas (LNG). Predictive models for surface tension are not well tested for hydrocarbon mixtures at high pressures due to the limited data available at relevant conditions. A differential capillary rise apparatus consisting of a high-pressure sapphire equilibrium cell was constructed and used to measure the surface tension of methane+propane mixtures along three isotherms T=(272.23, 285.51 and 303.34)K at pressures up to 9MPa. The capillary diameters were calibrated using pure saturated propane at 271K, and the technique was validated by measurements of pure ethane. The measured surface tensions were compared with the available data and the predictions of various models, including the Parachor method and Linear Gradient Theory: both were able to describe the data within their uncertainty. However, the default surface tension model for hydrocarbon mixtures implemented in the widely-used software package REFPROP 9.1 gave poor predictions; this was rectified through the implementation of the Parachor method in a beta-version of REFPROP 9.2. Critical points were also measured from observations of critical opalescence and the disappearance of the bulk interface. The measured mixture critical points were consistent with, and extended, literature values for this binary system. The measured critical points differed by between 0.5 and +27K from predictions made with the GERG-2008 equation of state (EOS) and between −5 and +10K for the Peng-Robinson EOS.

Determination of Gas-oil Interfacial Tension

Reliable knowledge of minimum miscibility pressure plays a vital parameter in the design and implementation of any miscible gas injection process and gas-oil interfacial tension extremely impacts on minimum miscibility pressure values. In this article two Iranian oil fields were investigated. Gas-oil interfacial tension technique relies on the measurements of gas/oil interfacial tension by pendant drop at several pressures and reservoir temperature for the first field and results were compared with generated values by the Parachor method. Then at different pressures and constant temperature (115°F) condition in the second field interfacial tension values have been evaluated for different oil-gas molar ratios.

Prediction of surface tension of binary mixtures with the parachor method

The parachor method for the estimation of the surface tension of binary mixtures is modified by considering temperature-dependent values of the parachor parameters. The temperature dependence is calculated by a least-squares fit of pure-solvent surface tension data to the binary parachor equation utilizing the Peng-Robinson equation of state for the calculation of equilibrium densities. A very good agreement between experimental binary surface tension data and the predictions of the modified parachor method are found for the case of the mixtures of carbon dioxide and butane, benzene, and cyclohexane, respectively. The surface tension is also predicted for three refrigerant mixtures, i.e. propane, isobutane, and chlorodifluoromethane, with carbon dioxide.

A Combined Experimental and Computational Study on Selected Physical Properties of Aminosilicones

A number of physical properties of aminosilicones have been determined experimentally and predicted computationally. It was found that COSMO-RS predicted the densities of the materials under study to within about 4% of the experimentally determined values. Vapor pressure measurements were performed, and all of the aminosilicones of interest were found to be significantly less volatile than the benchmark MEA material. COSMO-RS was reasonably accurate for predicting the vapor pressures for aminosilicones that were thermally stable. The heat capacities of all aminosilicones tested were between 2.0 and 2.3 J/(g·°C); again substantially lower than a benchmark 30% aqueous MEA solution. Surface energies for the aminosilicones were found to be 23.3–28.3 dyne/cm and were accurately predicted using the parachor method.

Applying parachor method to the prediction of ionic liquids surface tension based on modified group contribution

In this paper parachor method is applied to estimate surface tension of pure imidazolium based ionic liquids at the different temperatures. For this prediction a Modified Group Contribution Method is proposed to estimate the surface tension of ionic liquids covering wide ranges of temperature and chain length based on experimental data collected from literatures. The average relative error obtained from the comparison of experimental and calculated surface tension values for studied ionic liquids (less than 8.5%) shows the model has good accuracy in comparison with other predictive equations.

Density and Surface Tension of Ionic Liquids [H2N–C2mim][PF6] and [H2N–C3mim][PF6

Two amino functionalized ionic liquids 1-(2-aminoethyl)-3-methylimidazolium hexafluorophosphate, [H2N–C2mim][PF6], and 1-(3-aminopropyl)-3-methylimidazolium hexafluorophosphate, [H2N–C3mim][PF6], were synthesized and characterized. The density and surface tension of these ionic liquids were measured from (293.15 to 343.15) K. Their values decreased with increasing temperature. The physical properties such as coefficient of thermal expansion, molecular volume, standard molar entropy, lattice energy, and molar enthalpy of vaporization were estimated using experimental data. The critical temperature of the ionic liquids was estimated using Eötvos equations. The values were then used to estimate the boiling temperature of the ionic liquids according to methods of Rebelo. The interstice model was used to predict the thermal expansion coefficient of the ionic liquids, α, and the result was in very good agreement with the experimental value. In addition, the parachor method was used to predict the physical properties of the ionic liquids [H2N–Cnmim][PF6] (n = 4, 5, 6).

Effect of temperature on the physical properties of 1-butyl-3-methylimidazolium based ionic liquids with thiocyanate and tetrafluoroborate anions, and 1-hexyl-3-methylimidazolium with tetrafluoroborate and hexafluorophosphate anions

The effect of temperature on the physical properties of some ionic liquids was investigated. Density, refractive index, surface tension, dynamic and kinematic viscosities of 1-butyl-3-methylimidazolium based ionic liquids with thiocyanate and tetrafluoroborate, and 1-hexyl-3-methylimidazolium with tetrafluoroborate and hexafluorophosphate anions were measured at various temperatures (density from T=(278.15 to 363.15)K, refractive index from (293.15 to 343.15)K, surface tension from (283.15 to 333.15)K, dynamic viscosity from (283.15 to 368.15)K, and kinematic viscosity from (298.15 to 363.15)K). The volumetric properties for the ionic liquids were also calculated from the experimental values of the density at T=298.15K. The Vogel–Fulcher–Tammann (VFT) equation was applied to correlate experimental values of dynamic and kinematic viscosities as a function of temperature. As well, the relation between density and refractive index was correlated satisfactorily with several empirical equations such as Lorentz–Lorenz, Dale–Gladstone, Eykman, Oster, Arago–Biot, Newton and Modified–Eykman. Finally, the relation between surface tension and viscosity was investigated and the parachor method was used to predict density, refractive index and surface tension of the ionic liquids.

Modeling the thermal and physical properties of liquid and gas mixtures of Fischer–Tropsch synthesis products

The method of pseudocritical thermodynamic parameters and the Lee-Kesler equation of state are used for calculating the thermal and physical properties of a solution and a mixture of gaseous paraffins that are major constituents of Fischer-Tropsch synthesis products. The dynamic viscosities of a solution and a vapor are modeled using an original procedure proposed by the authors. A surface tension is calculated by the parachor method. The composition of liquid and gaseous products is found using a stable iteration scheme proposed by the authors. The model is tested by a comparison with experimental data from the literature for model mixtures of hydrocarbons. The results of calculating the composition and thermophysical properties of a mixture of paraffins that model the composition of synthesis products at different values of the chain propagation parameter, temperatures, and pressures are presented.

Petroleum mixtures: An efficient predictive method for surface tension estimations at reservoir conditions

The gradient theory of inhomogeneous fluid is for the first time used to study the fluid–fluid interfaces of real petroleum mixtures (gas condensate and oils) at reservoir conditions. The theory is combined with the volume-corrected Peng–Robinson equation of state which allows a good description of the vapour–liquid equilibria of these mixtures. First, it is demonstrated that a correlation that was derived previously to compute the influence parameters of pure hydrocarbons can be also used to obtain the influence parameters of cuts and pseudocompounds present in the petroleum fluids. It turns out that the gradient theory allows estimates of the surface tension in excellent agreement with the experimental data. In any case, it is found to be much more superior to the traditional parachor method that systematically underestimates the surface tension of these mixtures. Furthermore, unlike the parachor method, the gradient theory proves to be nearly insensitive to the compositional description of the fluid provided that the number of pseudocompounds is not too small (N > 5).

Physical properties of ionic liquids based on 1-alkyl-3-methylimidazolium cation and hexafluorophosphate as anion and temperature dependence

Densities ρ, speeds of sound u, and refractive indices n D were measured from T = (278.15 to 343.15) K. Dynamic viscosities η were measured from T = (293.15 to 323.15) K. Surface tensions σ were determined from T = (288.15 to 313.15) K. The physical properties data were measured at atmospheric pressure. The coefficients of thermal expansion α p of the ionic liquids were calculated from the experimental values of the density at several temperatures. The Parachor method was used to predict the densities, the refractive indices, and the surface tensions of the ionic liquids, and a comparison between experimental and predictive values was made at T = 298.15 K.

Modeling of the Surface Tension of Multicomponent Mixtures with the Gradient Theory of Fluid Interfaces

The gradient theory of fluid interfaces is for the first time applied, without any lumping, to complex mixtures of more than three components, here made up of hydrocarbons and of a high proportion of carbon dioxide, nitrogen, or methane. It is combined with the volume-corrected Peng-Robinson equation of state. No adjustable parameters are used in the influence parameters mixing rule, which allows use of the gradient theory in a predictive manner. It gives very good estimates of the surface tension of the complex mixtures studied. In any case, it is found to be much superior to the traditional parachor method. The gradient theory is also used to compute the density profiles of the mixture components in the interface; it confirms that the low interfacial tensions of the systems studied are principally induced by a local accumulation of carbon dioxide, nitrogen, or methane in the interface.

Simultaneous prediction of interfacial tension and phase equilibria in binary mixtures: An approach based on cubic equations of state with improved mixing rules

Vapor–liquid interfacial tensions of miscible mixtures have been predicted by applying the gradient theory to an improved Peng–Robinson equation of state. The modified Huron–Vidal mixing rule model has been considered for fitting vapor–liquid equilibrium data of miscible polar and non-polar mixtures and, then, for predicting the interfacial tension of these mixtures. According to results, an accurate and globally stable fitting of the vapor–liquid equilibrium data results on a physically coherent prediction of interfacial tensions in the full concentration range. In addition, we present a criteria based on the geometry of the grand potential function along the interface for assessing the predictive value of the GT. Calculations for subcritical binary mixtures are presented and compared to experimental data and the Parachor method for demonstrating the potential of the unified approach suggested in this work.

Sensitivity Analysis of Interfacial Tension Predictions for Hydrocarbon Fluids

The interfacial tension (IFT) of hydrocarbon fluids is commonly predicted by either the parachor method or the scaling law. The methods require equilibrium liquid and vapor phase composition and density. An equation of state would normally be required if experimental values are not available. However, the computation of density for simple hydrocarbons and reservoir fluids, despite the important advances achieved by cubic equations of state, still remains a weak link in these types of calculations. Thus, there exists a need to investigate the qualitative and quantitative effects, of such inaccuracies in the density, on IFT predictions. Moreover, the study presented in this work would be useful in reservoir engineering and enhanced oil recovery calculations. The results presented in this work indicate that the methods are highly sensitive to the inaccuracies in the density of both the liquid and the vapor phases. An error of around 10% in the liquid or the vapor density can result in an error of up to 200% in the estimated IFT. Two binary and one ternary mixture for which measured data on IFT, composition and density is reported in the literature form the basis of this study.