Vibrating-tube Densimeter Research Articles

Thermodynamics of ternary mixtures with gasoline additive: Volumetric, acoustic and optical properties

Abstract Excess molar volume (VmE), deviation in ultrasonic speed (Δu) and deviation in refractive index (Δn) of ternary mixtures with gasoline additives diisopropyl ether (DIPE) + benzene + n-heptane were derived from the measured density, ultrasonic speed and refractive index with Anton Paar vibrating tube densimeter, sound analyzer and Abbemat 200 refractometer, respectively at different temperature of 298.15 K, 308.15 K and 318.15 K and atmospheric pressure. The VmE values for the ternary mixtures were predicted using pragmatic equations and geometrical solution models employing constituent binary data. The VmE have also been interpreted using Prigogine-Flory-Patterson theory. The ultrasonic speed data was analyzed using like Nomato, van Dael, impedance dependence correlations and CFT theory at 298.15 K. Jacobson free length theory was employed to compute LfE and VaE at 298.15 K. The refractive indices of the ternary mixtures were also predicted using various mixing rules. The VmE,Δu, KSE and Δn derived values were also fitted to the Singh equation.

Density, compressibility and phase equilibrium of high pressure-high temperature reservoir fluids up to 473 K and 140 MPa

Experimental measurement of volumetric and phase equilibrium properties of two high pressure - high temperature reservoir fluids was performed in this work. One fluid is volatile oil and the other is gas condensate. The density, isothermal compressibility, saturation pressure, and liquid fraction below the saturation pressure were determined in the temperature range up to 473.15 K by using a high pressure vibrating tube densitometer and a PVT cell. The obtained data were modelled by using equations of state including Soave-Redlich-Kwong (SRK), Peng-Robinson (PR), volume translated SRK (SRK-VT), volume translated PR (PR-VT) and Perturbed-Chain Statistical Association Fluid Theory (PC-SAFT). Among these models, the performance in saturation pressure prediction is system-dependent and it is hard to generalize the observation. PC-SAFT models volumetric properties satisfactorily. Regarding density calculation, it performs similarly to SRK-VT and PR-VT for the two fluids investigated here. Concerning isothermal compressibility, PC-SAFT is slightly better.

Apparent molar volumes of sodium arsenate aqueous solution from 283.15 K to 363.15 K at ambient pressure: an experimental and thermodynamic modeling study

Abstract Densities of the sodium arsenate aqueous solution with the molality varied from (0.04165 to 0.37306) mol · kg−1 were determined experimentally at temperature intervals of 5 K from 283.15 K to 363.15 K and ambient pressure using a precise Anton Paar Digital vibrating-tube densimeter. The apparent molar volumes (V ϕ ), thermal expansion coefficient (α) and partial molar volume ( V ¯ B ) $({\bar V_{\rm{B}}})$ were obtained based on the results of density measurement. The 3D diagram of apparent molar volume against temperature and molality as well as the diagram of thermal expansion coefficient and partial molar volume against molality were plotted, respectively. On the basis of the Pitzer ion-interaction equation of apparent molar volume model, the Pitzer single-salt parameters ( ( β M,X ( 0 ) v , β M,X ( 1 ) v , β M,X ( 2 ) v and C M,X v , M X = N a 3 A s O 4 ) $(\beta _{{\rm{M,X}}}^{(0)v},\beta _{{\rm{M,X}}}^{(1)v},{\rm{ }}\beta _{{\rm{M,X}}}^{(2)v}{\rm{ and }}C_{{\rm{M,X}}}^v,MX = N{a_3}As{O_4})$ and their temperature-dependent correlation F(i, p, T) = a 1 + a 2ln(T/298.15) + a 3(T – 298.15) + a 4/(620 – T) + a 5/(T – 227) (where T is temperature in Kelvin, a i is the correlation coefficient) for Na3AsO4 were obtained on account of the least-squares method. Predictive apparent molar volumes agree well with the experimental values, and those results indicate that the single-salt parameters and their relational coefficients of temperature-dependence for Na3AsO4 obtained are reliable.

Measurement and correlation of the (p, ρ, T) behaviour of liquid ethylene glycol at temperatures from (283.3 to 393.1) K and pressures up to 100.1 MPa

The (p, ρ, T) behaviour of ethylene glycol was investigated over the temperature range from T = (283.3 to 393.1) K at pressures from p = (4.8 to 100.1) MPa utilizing a high-pressure vibrating-tube densimeter. This work extends the current data situation for the density of ethylene glycol with respect to temperature and pressure ranges. Four mathematical models for the vibrating-tube densimeter were used to calculate density from the measured oscillation period, and the influence of the model on the resulting density was investigated. The combined expanded uncertainty (k = 2) of the experimental densities was estimated to be 1.57 kg·m−3. The new experimental data were regressed to a Schilling-type correlation equation with its exponent parameters being the same as those for propylene glycol that we studied previously; in a second step, the correlation equation was optimized using an “artificial intelligence powered” modeling tool. With this optimization, the number of the parameters was reduced, while the goodness of the fitting was slightly improved. The combined expanded uncertainties (k = 2) of the correlation equations were estimated to be 1.59 kg·m−3 in the investigated (p, T) range. Carefully selected experimental data from literature generally agree with the correlation equations within the uncertainty of the equation.

Volumetric Properties in the NaAsO2 + H2O System at Temperature from 283.15 to 363.15 K and Atmospheric Pressure

Densities of sodium arsenite (NaAsO2) aqueous solution with the molality varied from 0.19570 to 1.94236 mol·kg−1 at temperature intervals of 5 K from 283.15 to 363.15 K and 101 ± 5 kPa were measured by a precise Anton Paar Digital vibrating-tube densimeter. Apparent molar volumes (VΦ) and thermal expansion coefficient (α) were obtained on the basis of experimental data. The 3D diagram of apparent molar volume against temperature and molality and the diagram of thermal expansion coefficient against molality were generated. According to the Pitzer ion-interaction equation of the apparent molar volume model, the Pitzer single-salt parameters (βM,X0υ, βM,X1υ, βM,X2υ, and CM,Xυ, MX = NaAsO2) and their temperature-dependent correlation F(i, p, T) = a1 + a2ln (T/298.15) + a3(T − 298.15) + a4/(620 − T) + a5/(T − 227) (where T is temperature in Kelvin and ai are the correlation coefficients) for NaAsO2 were obtained for the first time. The predictive apparent molar volumes agree well with the experimental values, and those results indicated that the single-salt parameters and the temperature-dependent formula are reliable.

Excess molar volumes of cyclohexanone with n-, sec-, or tert-butylbenzene: Application of the PFP theory and graph-theoretical approach

Excess molar volumes, VE, for the binary mixtures of cyclohexanone with n-, sec-, or tert-butylbenzene were measured over the entire composition range at (298.15, 303.15, 308.15 and 313.15) K and 0.1 MPa, by means of a vibrating-tube densimeter. VE data are sigmoid shape for the studied mixtures of cyclohexanone + n-butylbenzene (with negative VE values at lower mole fractions of cyclohexanone) and negative for the mixtures of cyclohexanone + sec-butylbenzene, and cyclohexanone + tert-butylbenzene over the whole composition range. The absolute values of excess equimolar volumes vary in the order: tert-butylbenzene > sec-butylbenzene > n-butylbenzene. The VE in the studied systems increase as the rising temperature. The Redlich-Kister equation was applied to fit the experimental data. Using the coefficients of the Redlich–Kister equation, excess partial molar volumes at infinite dilution, V¯iE,∞ were calculated for the three binary systems. Molecular non-bond energy, E for binary mixtures at the mole fraction of 0.5 and temperature of 298.15 K also were calculated by the MD simulations. The Prigogine–Flory–Patterson theory and Graph-theoretical approach were examined for the suitability by correlating experimental VE data with compositions.

High - temperature and high-pressure (p, ρ, T) measurements and derived thermodynamic properties of 1-octyl-3-methylimidazolium hexafluorophosphate

Densities of ionic liquid (IL) 1-octyl-3-methylimidazolium hexafluorophosphate [OMIM][PF6] at high temperatures and high pressures were measured. The measurements were made along 10 isotherms over a temperature range T = 278.15 to 413.15 K, at pressures up to 140 MPa by means of an Anton Paar DMA HPM vibration tube densimeter (VTD). The combined expanded relative uncertainties of the density, pressure and temperature measurements at the 95 % confidence level with a coverage factor of k = 2 are estimated to be 0.03 to 0.08 % (depending on temperature and pressure ranges), 0.1 %, and 0.015 K, respectively. We have critically assessed all of the reported high-pressure densities for [OMIM][PF6], together with the presented results, in order to carefully select primary data for development of a reference wide-ranging equation of state. Values of ??T isobars curvatures, (?2?/?T2)?, were estimated using the present high-pressure ?-T measurements and they were pretty low (0.78?10-7 to 1.50??10-7 m3 kg-1 K-1), indicating that the heat capacity of [OMIM][PF6] very weakly depends on pressure, since (?Cp/?P)T ?(?2?/?T2)?. Density data were fitted to the modified Tammann?Tait equation and the multiparametric polynomial-type equation of state (EOS) for the IL was developed using the measured high-pressure and high-temperature (p, ?, T) data. This EOS, together with our previous measured heat capacity data at atmospheric pressure, was used to calculate high-pressure and high-temperature derived thermodynamic properties, such as isothermal compressibility,isentropic compressibility, isobaric thermal expansion coefficient, heat capacities,etc.

P–ρ–T Data and Derivative Properties of 3-Methylpentane, 2,4-Dimethylpentane, and 2,3,4-Trimethylpentane from 283.15 to 363.15 K at Pressures up to 65 MPa

In this work, we present densities at high pressures of three branched hydrocarbons: 3-methylpentane, 2,4-dimethylpentane, and 2,3,4-trimethylpentane from 283.15 to 363.15 K and at pressures up to 65 MPa. We have used a vibrating tube densimeter along with the forced path calibration method. This method considers mechanical properties of the cell and allows us to reach standard uncertainties less than 0.0004 g·cm3. For 3-methylpentane, the new density data agree within 0.2% with densities from the literature. For the case of 2,4-dimethylpentane and 2,3,4-trimethylpentane, densities at high pressures have not been reported in the literature. Isobaric expansibility and isothermal compressibility are calculated using an equation of state correlated to the experimental density data.

Density of standard seawater by vibrating tube densimeter: Analysis of the method and results

Seawater density has a great importance in oceanography, since it drives the ocean currents that drift oxygen, heat, plankton and pollutants. If the density is measured with high accuracy, it can be also used for salinity determination. In this work, the density of standard seawater was measured at different absolute salinities from (10.044–38.178) g kg−1, in the temperature range of (278.15–313.15) K at atmospheric pressure. The measurements were carried out by means of a commercial vibrating tube densimeter, following the substitution method (alternating samples of seawater and water) and under conditions typical of the most oceanographic laboratories capabilities. Besides, an accurate analysis of the uncertainty of density was performed, obtaining a relative expanded uncertainty of 0.003% (k=2). Measurements were compared with the density values provided by the international reference equation of state: the Thermodynamic Equation of SeaWater-2010, TEOS-10.

Thermodynamic study of mixtures containing dibromomethane. II: volumes and enthalpies at 298.15 K

Excess molar volumes, VE, of binary mixtures of dibromomethane (DBM) with n-hexane, n-heptane, n-octane, cyclohexane, tetrachloromethane, dipropyl and dibutyl ether, tetrahydrofuran, and 3-pentanone are determined at 298.15 K in the whole composition range by means of a vibrating tube densimeter. For the same DBM mixtures plus with n-pentane and except with dipropyl ether and 3-pentanone, partial molar enthalpies, Hi, and excess molar enthalpies, HE, are obtained through a heat flow calorimeter and a titration method purposely devised. Both excess properties are positive for cyclohexane, tetrachloromethane, and n-alkanes, the latter exhibiting an increase with increasing number of carbon atoms. Dipropyl and dibutyl ether mixtures exhibit negative VE values, while n-hexane, tetrahydrofuran, and 3-pentanone mixtures show an S-shaped VE curve. Negative HEs are observed only for tetrahydrofuran, whereas dibutyl ether exhibits an S-shaped HE curve. HE results are compared with the predictions of the DISQUAC model. The partial molar volumes at infinite dilution, V°, as well as the enthalpies of solvation, ΔsolvH°, of the examined substances in DBM are evaluated and discussed also considering data on other compounds found in the literature. For V° and ΔsolvH°, a group additivity scheme is proposed to enable the estimation of these properties for other molecules and how much structural peculiarities such as chain length, polarity of groups, and cyclic structures influence their values.

Volumetric properties and the ion-interaction parameters of the binary system (CsB5O8 + H2O) at temperatures from (283.15 to 363.15) K and 101 kPa

This paper reports the densities of CsB5O8 (aq) in the range of salt concentrations from 0.02526 to 0.08148 mol·kg−1, which were determined by an accurate Anton Paar Digital vibrating-tube densimeter at 5 K intervals from 283.15 to 363.15 K and 101 kPa. The apparent molar volume (Vϕ), the coefficient of thermal expansion (α), apparent molar expansibility of the solute (ϕE) were calculated and variations of these properties against temperature and concentration were revealed minutely. According to Pitzer ion-interaction apparent molar volume model of aqueous electrolyte system, the Pitzer single salt parameters i.e. FMX (βMX0v, βMX1v and CMXv, M = Cs+, X = [B5O6(OH)4]-), the temperature-dependence equation [FMX (i, p, T) = a1 + a2ln(T/298.15) + a3(T-298.15) + a4/(620-T) + a5(T-227), i = βMX0v, βMX1v and CMXv] as well as their coefficients ai (i = 1 to 5) in the binary system were obtained, which is not reported in the literature. The fitted results of single salt parameters βMX0v, βMX1v and CMXv were in good agreement with the experiment values, indicating that the single salt parameters and temperature relational coefficients for Cs[B5O6(OH)4] obtained in this work are reliable.

Density and viscosity measurements of (piperazine + water) and (piperazine + 2-dimethylaminoethanol + water) at high pressures

The purpose of this paper is broadening the understanding of amine solution behaviour through the experimental measurements of density (up to 140 MPa) and viscosity (up to 100 MPa) in a temperature range from (293.15 to 393.15) K. The two selected blends are Piperazine (PZ) + Water (10% amine weight concentration) and Piperazine (PZ) + 2-Dimethylaminoethanol (DMAE) + Water (10% and 30% amine weight concentration, respectively). Densities were measured using a vibrating tube densimeter (Anton Paar DMA HPM) with an expanded uncertainty (k = 2) less than 0.7 kg·m−3. Viscosities were obtained using a falling body viscometer which was calibrated with water and dodecane. The viscosity expanded uncertainty (k = 2) ranges from 2.5% for the highest viscosity to 3.2% for the lowest one. Experimental data were fitted to modified Tammann-Tait equation for densities and modified VFT model for viscosities, obtaining good results for both equations.

(p,ρ,T) data of 1-butyl-3-methylimidazolium hexafluorophosphate

Herein, experimental pressure-density-temperature (p,ρ,T) data of 1-butyl-3-methylimidazolium hexafluorophosphate, [BMIM][PF6], are reported over a wide range of temperatures T = (278.15 to 413.15) K and pressures p = (0.101 to 140) MPa. These measurements were carried out using an Anton Paar DMA HPM vibrating tube densimeter. (p,ρ,T) data of [BMIM][PF6] were correlated with a designed equation of state (EoS). After a thorough analysis of the validity of the constructed EoS, various thermophysical properties such as: isothermal compressibility, isobaric thermal expansivity, differences in isobaric and isochoric heat capacities, thermal pressure coefficient, internal pressure, heat capacities at constant pressure and volume, speed of sound and isentropic exponent were then calculated. Finally, the predictive capability of various models available in the literature was then tested by using the collected (p,ρ,T) data to highlight the best approach to be used to evaluate the volumetric properties of the selected ionic liquid.

Compressed liquid densities of binary mixtures of difluoromethane (R32) and 2,3,3,3-tetrafluoroprop-1-Ene (R1234yf) at temperatures from (283 to 363) K and pressures up to 100 MPa

The compressed liquid densities of binary mixtures difluoromethane (R32) and 2,3,3,3-tetrafluoroprop-1-ene (R1234yf) were measured using a high pressure vibrating-tube densimeter over the temperatures from (283 to 363) K and pressures up to 100 MPa at five different compositions, xR32 = (0.189, 0.268, 0.500, 0.723, 0.904) in the present work. The combined expanded uncertainties of the temperature, pressure, mole fraction and the density with a level of confidence of 0.95 (k = 2) is estimated to be 16 mK, 0.062 MPa (p ≤ 60 MPa), 0.192 MPa (60 MPa < p < 100 MPa), 0.01 and up to 0.6 kg·m−3 depending on the temperature and pressure ranges, respectively. The experimental data were correlated using the modified Tait equation. The isothermal compressibility, κT, and the isobaric thermal expansivity, αp, were determined using liquid densities of mixtures and modified-Tait equation. Furthermore, the relative deviations of the experimental data with the equation of state (EOS) from Akasaka were lower than 1% from (283 to 363) K with the pressure up to 40 MPa.

Density and viscosity for binary mixtures of methyl decanoate with 1-propanol, 1-butanol, and 1-pentanol

In this work, the volumetric and viscometric properties of the mixtures of methyl decanoate with 1-propanol, 1-butanol, and 1-pentanol were investigated from 298.15 K to 333.15 K. The density data of the mixtures were obtained based on the vibrating-tube densimeter, and the kinematic viscosities of the mixtures were measured using the Ubbelohde capillary viscometer. Based on the experimental data, the excess molar volumes and viscosity deviations were calculated and correlated with the Redlich–Kister equation. In addition, the McAllister four-body model, Frenkel model, Grunberg-Nissan model, and Heric's model were used to correlate the viscosities of the mixtures.

Apparent molar volumes for Cs2B4O7 aqueous solution at temperatures from (283.15 to 363.15) K and 101 kPa

Densities for aqueous solutions of Cs2B4O7 at the molalities of (0.16635–0.69694) mol·kg−1 were measured with an Anton Paar Digital vibrating-tube densimeter at temperatures from 283.15 K to 363.15 K and 101 kPa. According to experimental data, apparent molar volume (Vϕ), partial molar volume (V¯ϕ), and the coefficient of thermal expansion (α) of the Cs2B4O7 aqueous solution were calculated, and their distributive behaviors against temperature and molality have been discussed in details. Considering the structure of Cs2B4O7 in aqueous solution system is in the form of Cs2[B4O5(OH)4], the Pitzer single-salt parameters (βM,X0v, βM,X1v, βM,X2v and CM,Xv) for Cs2[B4O5(OH)4] as well as temperature-dependence correlations were obtained for the first time on the basis of Pitzer ion-interaction apparent molar volume model of electrolytes. The deviations between the Pitzer single-salt parameters of Cs2[B4O5(OH)4] fitted at each temperatures based on the experimental data and those of the calculated values corresponding to the temperature-dependence equations on Pitzer single-salt parameters are all within ±0.1, indicating that the single-salt parameters and their temperature-dependence equations obtained in this work are reliable.

Speed of Sound and Derived Properties of Ethyl Nonanoate

Ethyl nonanoate is a promising component of biodiesel with a satisfactory cetane number and reactivity. The speeds of sound in ethyl nonanoate were measured by the Brillouin light scattering (BLS) method within the temperatures from 295.24 to 593.15 K and at pressures up to 10 MPa. The relative expanded uncertainty (k = 2) of our BLS experimental system is estimated to be less than 0.7%. The densities of ethyl nonanoate were measured using a vibrating tube densimeter at atmospheric pressure in the temperature range of 293.15–353.15 K, and the absolute average relative deviation between the experimental densities and the literature data is 0.12%. For temperatures between 303.15 and 353.15 K and at pressures up to 10 MPa, these measurements were used to calculate densities, isobaric heat capacities, and indirect derivative properties including the isobaric thermal expansion, the isothermal compressibility, the isentropic compressibility, and the internal pressure. The comparison between the calculated isoba...

Partial molar volumes of organic solutes in water. XXX. Two poly(ethylene glycol) monoalkyl ethers, C4E2 and C1E3, at temperatures T = 298 K to 573 K and pressures up to 30 MPa

Densities of dilute aqueous solutions of two aliphatic poly(ethylene glycol) monoalkyl ethers, H-(CH2)4-(O-CH2-CH2)2-OH (diethylene glycol monobutyl ether, C4E2) and H-CH2-(O-CH2-CH2)3-OH (triethylene glycol monomethyl ether, C1E3) measured in the temperature range from (298 to 573) K and at pressures up to 30 MPa using an automated flow vibrating-tube densimeter are reported. Standard molar volumes were evaluated from the measured data. A comparison with data previously measured for selected members of the homologous series of similar solutes (poly(ethylene glycols), glymes, 2-alkoxyethanols) is presented.

Liquid Densities and Speed of Sound for Ionic Liquid (2-HEAA and 2-HDEAA) + Alcohol (1-Propanol and 2-Propanol) Mixtures at T = (293.15–323.15 K) and Atmospheric Pressure

Liquid–liquid equilibrium data are widely used in many industrial sectors. For this reason, it is important to know thermodynamics binary mixture data to better understand molecular interactions between components. This work reports experimental density (ρ) and speed of sound (υ) data for 2-hydroxyethanolamine acetate + 1-propanol, 2-hydroxyethanolamine acetate + 2-propanol, 2-hydroxydiethanolamine acetate + 1-propanol, and 2-hydroxydiethanolamine acetate + 2-propanol binary mixtures, over a wide composition range, between 293.15 and 323.15 K, and at atmospheric pressure (101.3 kPa). For this purpose, a vibrating tube densitometer was used to perform density and speed of sound experimental measurements. From these data, important derivative properties have been calculated, such as isentropic compressibility (κs), apparent molar isentropic compressibility (κø), excess molar volumes (VmE), and apparent molar volume (VØ).

High-pressure densities of n-decane+o-xylene mixtures: Measurement and modelling

In this work, the liquid densities of n-decane/o-xylene mixtures were measured at four different component proportions, the mole fractions of n-decane are 0.2001, 0.4065, 0.5835, and 0.8041, respectively. The measurements were performed based on the high-pressure vibrating-tube densimeter, and the measured temperatures were from 283.15 K to 363.15 K and the pressures were from 0.1 MPa to 60 MPa. The Tammann-Tait equation was used to correlate the experimental densities, and the simplified Perturbed Associating Fluid Theory (sPC-SAFT) and Cubic Plus Associating (CPA) equation were used to predict the high-pressure densities of the mixtures with the binary interaction parameters. Derived properties, including isothermal compressibilities and isobaric thermal expansivities, were calculated from Tait equation, sPC-SAFT equation, and CPA equation, respectively. In addition, excess molar volumes of the considered mixtures were obtained and the effects of pressure and temperature on the excess molar volume were discussed.