Viscosity Arrhenius parameters correlation: extension from pure to binary fluid mixtures

Knowledge of fluids’ physicochemical properties is mandatory for the design and optimisation of industrial processes and products. A data quantity of most importance, in this regard, turns out to be the value of fluid viscosity. Many empirical and semi-empirical formulas have been proposed in the literature to describe the viscosity of pure liquids and binary liquid mixtures. Recently, an interesting equation is proposed for pure solvents correlating the two parameters in the viscosity Arrhenius-type equation, namely the activation energy (E_a) and the pre-exponential factor (A_s). This paper aims to extend the said correlation to binary liquid mixtures. To achieve this purpose, statistical methods are applied using data sets from the literature of some solvent binary mixtures at different compositions and temperatures. The validation of the extended proposed equation for binary liquid mixtures is important since it simplifies the estimation of viscous behaviour and the ensuing calculations.     

One parameter friction theory models for viscosity

In this work the friction theory (f-theory) for viscosity modeling is used in conjunction with the SRK, PR and PRSV cubic equations of state in order to develop three one parameter general models for viscosity prediction. The models are considered one parameter models because they only require a characteristic critical velocity, which is a parameter normally not tabulated. The models use these rather simple cubic equations of state as a basis to obtain accurate modeling of the viscosity of fluids for wide ranges of temperature and pressure. The general models presented in this work are based on the viscosity behavior of n-alkanes from methane to n-octadecane. Although best performance is obtained for the considered n-alkanes, a good model performance is also obtained for other systems. Thus, recommended characteristic critical viscosity values for several systems are also reported in this work. However, in the case of n-alkanes, an empirical equation for the characteristic critical viscosity is provided so that no additional parameters are required. In addition, with the use of simple mixing rules, the viscosity of several binary to quaternary n-alkane mixtures can also be predicted with a satisfactory accuracy.     

An accurate empirical correlation for predicting natural gas viscosity

Natural gas viscosity is an important parameter in many gas and petroleum engineering calculations.This study presents a new empirical model for quickly calculating the natural gas viscosity.The model was derived from 4089 experimental viscosity data with varieties ranging from 0.01 to 21,and 1 to 3 of pseudo reduced pressure and temperature,respectively.The accuracy of this new empirical correlation has been compared with commonly used empirical models,including Lee et al.,Heidaryan et al.,Carr et al.,and Adel Elsharkawy correlations.The comparison indicates that this new empirical model can predict viscosity of natural gas with average absolute relative deviation percentage AARD (%) of 2.173.     

Density,Viscosity and Volatility of Binary Mixtures of Isopropyl Ether and <Emphasis Type="Italic">exo</Emphasis>-Tetrahydrodicyclopentadiene

Measurements of density, viscosity and vapor pressure for binary mixtures of exo-tetrahydrodicyclopentadiene (JP-10) with isopropyl ether are reported at temperatures of (293.15, 298.15, 303.15, 308.15, and 313.15) K over the entire composition range. The excess molar volumes, viscosity deviation and excess Gibbs energies of activation for the binary systems were calculated from the experimental values and fitted with the Redlich–Kister equation. Isopropyl ether was added to enhance the vapor pressure of JP-10. Experimental vapor pressure data were correlated by the Antoine equation. Several semi-empirical equations were used to correlate the viscosity data. The McAllister equation gives relatively satisfactory results for the correlation. The experimental and correlated data could be used in the development of models for mixtures of hydrocarbons with oxygenates.     

Surface tension and density of binary mixtures of monoalcohols,water and acetonitrile: equation of correlation of the surface tension

Measurements of the surface tension (σ) and density (ρ) of binary mixtures of monoalcohols, water and acetonitrile at 298.15 K and at atmospheric pressure, as a function of mole fraction (x) have been made. The experimental values of the deviation of surface tension and the excess of molar volume (Δσ, V ^E) have been correlated by the Redlich–Kister equation. An empirical correlation equation is presented for the study of the surface tension of these mixtures, and comparisons are made of the experimental values of surface tension versus those obtained with the correlation equation and with other models of correlation. Finally, with the purpose of corroborating the validity of the correlation equation, the latter is applied to other reference binary mixtures.     

The estimation of kinematic viscosity of petroleum crude oils and fractions with a neural net

This paper illustrates how a neural net, a three-layered perceptron, can be trained to estimate viscosities for undefined crude oils and fractions. Three Saudi-Arabian crude oils were employed to illustrate the use of the neural net to approximate the relation in a very simple manner with no need for a priori knowledge of the system. This empirical correlation was accurate to 98.74% if tested on experimental data not used during training, which is a fivefold improvement on average results obtained by two recently-proposed equations to estimate the viscosity of hydrocarbons. Although the neural net equation seems to be less transparent than former correlations, a method called backward analysis is proposed to analyze the weight matrix of the neural net in order to gain valuable insight into the viscosity system.     

Estimation of viscosities of 1-alkyl-3-methylimidazolium ionic liquids over a range of temperatures using a simple correlation

In this study, a new correlation is proposed for estimating 1-alkyl-3-methylimidazolium ionic liquid (IL) viscosities at different temperatures and atmospheric pressure. Since ILs are rather novel, many of their physical properties are still unavailable. Because of this limitation, the aim of this work was to propose a correlation with a new insight and approach, which requires a minimum number of physical properties as input parameters. In addition to minimal dependency on physical properties, further goals in the development of the model were generality, ease-of-use, simplicity and high accuracy. A total of 2073 literature viscosity datapoints at different temperatures for 38 different ILs were used and a correlation was developed which satisfied the above-mentioned goals. The IL viscosity models of Lazzús and Pulgar-Villarroel, and Gardas and Coutinho were compared to the proposed correlation. More reliable results were obtained by the proposed relation in comparison to literature models.     

Local composition in binary mixtures of Lennard-Jones fluids with differing sizes of components

Three Lennard-Jones binary liquid mixture systems obeying Lorentz-Berthelot rules, but having differing component sizes and energy parameters, have been used to calculate the local fractions of the two components around each type of central particle over the entire composition range from molecular-dynamics data. It is found that well-defined local fractions can be determined even in the case where the size difference between the particles is large. The results obtained are compared with values predicted by the Wilson and NRTL equations. It is confirmed that the NRTL equation gives satisfactory agreement only in the case of mixtures of components having the same size parameters. A new correlation is proposed by a modification of the NRTL equation. This correlation can predict reasonably well local-fraction data for all the Lennard-Jones liquid mixtures studied so far.     

A simple modification of the Flory—Huggins theory for polymers in non-polar or slightly polar solvents

Starting from the concept of free volume dissimilarity, a simple modification of the non-combinatorial part of the Flory—Huggins equation is proposed. According to this modification, a new relation is derived to calculate the activity of a solvent in mixture with a polymer. It contains two empirical parameters, whose values can be determined by regressing binary vapour—liquid experimental data. The proposed equation has been applied to several binary systems which can be grouped in three classes of mixtures: non-polar/non-polar, non-polar/polar and polar/polar. Satisfactory results have been obtained in the case of non-polar or slightly polar mixtures, however, for strongly polar systems, the new equation is inadequate. The proposed modification of the Flory—Huggins theory is particularly suitable for engineering calculations.     

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

A viscosity model based on the Eyring’s theory and a cubic equation of state (Peng–Robinson–Stryjek–Vera) has been applied to the correlation and prediction of experimental liquid viscosities of binary mixtures containing polar fluids within a wide range of temperature, pressure and composition (encompassing low-pressure and compressed liquid conditions). Highly non-idealities of the binary mixtures considered in this study were conveniently handled via the application of the Wong–Sandler approach for the mixing rules used in the cubic equation of state. The results obtained were highly satisfactory for various non-ideal binary mixtures over the whole composition range at a low pressure. The predictive capabilities of the present approach were also verified in the representation of liquid viscosities at elevated pressures preserving the same model parameters previously obtained at low pressure.     

New mixing rules in simple equations of state for representing vapour-liquid equilibria of strongly non-ideal mixtures

Huron, M.-J. and Vidal, J., 1979. New mixing rules in simple equations of state for representing vapour-liquid equilibria of strongly non-ideal mixtures. Fluid Phase Equilibria, 3: 255-271.Good correlations of vapour-liquid equilibria can be achieved by applying the same two-parameter cubic equation of state to both phases. The results primarily depend on the method used for calculating parameters and, for mixtures, on the mixing rule. True parameters are the covolume b and the energy parameter a/b. For this latter one, deviations from a linear weighting rule are closely connected to the excess free energy at infinite pressure. Thus any mixing rule gives a model for the excess free energy, or any accepted models for this property can be used as mixing rules.From the above, an empirical polynomial mixing rule is used for data smoothing and evaluation, while for practical work a local composition model is used. The mixing rule thus obtained can be reduced to the classical quadratic rule for some easily predicted values of the interaction energies. For highly polar systems, it includes three adjustable parameters. Using literature data, the new mixing rule is applied, in the low and high pressure range, to binary mixtures with one or two polar compounds, giving good data correlation and sometimes avoiding false liquid-liquid immiscibility.     

Homogeneous nucleation temperatures in aqueous mixed salt solutions

This is the first report on the measurement of homogeneous nucleation temperature, TH, in the presence of aqueous mixed salt systems of varying compositions and ionic strengths. The TH,m (TH value in aqueous mixed salt system) data for these systems have been analyzed in terms of a simple empirical equation. The TH,m values in simple aqueous mixed salts like NaCl-KCl can be approximated by linear summation of the products of ionic strength fraction and the TH values of pure salt solutions at the same ionic strength as that of the mixture. The empirical parameter, q0, indicating ionic interaction is related to the viscosity B-coefficients. The TH,m data, though correlated on the basis of the B-coefficients also depends upon the mixing of two ions of like charges. Further, a linear correlation exists between the q0 parameter and self-diffusion coefficient, D0, of the ionic solute. The q0 parameter is also well correlated with the rotational correlation time, tauch/tauc0 of the ionic species involved in the mixtures. It is possible to compute TH,m for the salt mixtures with no common ions from the knowledge of the TH,m values of the salt mixtures with common ions.     

The Relative Reduced Redlich–Kister and Herráez Equations for Correlating Excess Properties of N,N-Dimethylacetamide + Formamide Binary Mixtures at Temperatures from 298.15 K to 318.15 K

Excess molar volumes and viscosity deviations in binary mixtures of N,N-dimethylacetamide with formamide at (298.15, 308.15 and 318.15) K were calculated from experimental density and viscosity data presented in previous work. The density and viscosity data as well as their corresponding derived functions were used to test the applicability of two correlative equations: the reduced Redlich?CKister equation and the recently proposed Herráez equation. Their correlation abilities at different temperatures, and the use of different numbers of parameters, are discussed for the case of limiting experimental data. These relative functions are important to reduce the effect of temperature and, consequently, to reveal the effects of different types of interactions. Correlation between the two Arrhenius parameters of viscosity over the composition domains shows the existence of two distinct behaviors.     

聚电解质溶液性质的研究 Ⅱ.在有外加盐存在下聚电解质溶液的粘性行为

采用恒定外加盐浓度稀释法,测定了磺化聚砜钠盐在含不同浓度硝酸钠的二甲基甲酰胺中的粘度。根据实验数据处理,导出了如下的经验公式:式中第一项表示无外加盐时比浓粘度和浓度的关系,第二项表示有外加盐时对于比浓粘度的改正项。按照这个经验公式,可以很好地预期外加盐浓度不同时对比浓粘度曲线的影响。经验式还明显地表示了试样的特性粘数与外加盐浓度的关系。     

The relative reduced Redlich–Kister equations for correlating excess properties of N,N-dimethylacetamide + 2-methoxyethanol binary mixtures at temperatures from 298.15 K to 318.15 K

Knowledge and prediction of physicochemical properties of binary mixtures is of great importance for understanding intermolecular interactions. The literature shows that most such systems exhibit non-linear behaviour. Excess molar volumes, viscosity deviations and isentropic compressibility changes in N,N-dimethylacetamide?+?2-methoxyethanol binary mixtures at 298.15, 308.15 and 318.15?K were calculated from experimental density, viscosity and sound velocity data presented in previous work. Here these experimental values were used to test the applicability of the correlative reduced Redlich–Kister equation and the recently proposed Herráez equation as well as their corresponding relative functions. Their correlation ability at different temperatures, and the use of different numbers of parameters, is discussed for the case of limited experimental data. These relative functions are important to reduce the effect of temperature and, consequently, to reveal the effects of different types of interactions. Limiting excess partial molar volume at infinite dilution were deduced from different methods, activation parameters and partial molar Gibbs energy of activation of viscous flow against compositions were investigated. The results of these observations have been interpreted in terms of structural effects of the solvents. In this frame, a correlating equation is recently proposed by Belda and in order to assess the validity of the proposed equation, it has also been applied to the present system for molar volume properties.     

A semi-empirical equation of state applied to vapor-liquid equilibria calculations

A five-parameter equation of state is proposed to calculate the vapor-liquid equilibria of compounds in binary and multicomponent mixtures. This equation is closely related to a previous equation of state proposed by the author, the main modification being in the entropic term where the parameter m assumes a constant value for all compounds. It is shown that the van der Waals conditions at the critical point and the Morbidelli-Carra' algorithm enable the calculation of three other constants. Rules are given to calculate the remaining constant K which pertains to the enthalpic term. The proposed method only requires knowledge of the critical constants and of the normal boiling temperature as input parameters. A wide application of the new equation to both polar and non-polar binary systems indicates the following: the proposed method is predictive for ideal or nearly ideal mixtures; the correlation of mixtures of hydrocarbons having very different molar volumes can be obtained by optimizing only the binary interaction parameter linked to the enthalpic term; the new equation also correlates well with strongly non-ideal systems which exhibit a miscibility gap; the prediction of multicomponent vapor-liquid equilibria from the binary data alone is also reliable for both polar and non-polar mixtures.     

氨基酸季铵离子液体水溶液的密度和黏度

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Effect of Temperature and Composition on the Density and Viscosity of Binary Mixtures of Ionic Liquid with Alcohols

Density and viscosity were determined for the binary mixtures containing the ionic liquid 1-butyl-3-methylimidazolium thiocyanate ([BMIM][SCN]) and 1-alcohols (1-butanol, 1-pentanol and 1-hexanol) at six temperatures (298.15, 308.15, 318.15, 328.15, 338.15 and 348.15) K and ambient pressure. The density and viscosity correlation for these systems was tested by an empirical second-order polynomial and by the Vogel-Fucher-Tammann equation in wide ranges of temperatures. Excess molar volumes were described by the Redlich-Kister polynomial expansions. The density and viscosity variations with composition were described by polynomials. A qualitative analysis of the trend of the properties with solvent and temperature was performed. The obtained results indicate that ionic liquid interactions with 1-alcohols are strongly dependent on the special trend of packing of this ionic liquid into hydroxylic solvents. As previously observed, an increase of the 1-alcohol carbon-chain length leads to lower interactions on mixing. Electronic Supplementary Material  The online version of this article () contains supplementary material, which is available to authorized users.     

The Relative Reduced Redlich-Kister and Herráez Equations for Correlating Viscosities of 1,4-Dioxane + Water Mixtures at Temperatures from 293.15 K to 323.15 K

Viscosity deviations from ideal mixing for 1,4-dioxane + water mixtures over the entire range of composition at temperatures of (293.15, 303.15 and 313.15) K and atmospheric pressure were calculated from experimental viscosity data presented in a previous work. The temperature range was extended to 323.15 K with data from the literature. This system exhibits very large positive deviations due to strong heteromolecular interactions and also due to size differences of the unlike molecules. The viscosity data as well as their corresponding relative functions were used to test the applicability of two correlative equations: the reduced Redlich-Kister equation and the recently proposed Herráez equation. These relative functions are important to reduce the effect of temperature and, consequently, to reveal the effects of different types of interactions. Their correlation abilities at different temperatures, and using different numbers of parameters, are discussed for the case of limited experimental data. Generally, good agreement between experimental and calculated data was obtained with both equations provided more than three parameters were employed.