Computation of Liquid Isothermal Compressibility from Density Measurements: An Application to Toluene

Abstract

A computation method was developed for estimating the compressibility and its uncertainty from density measurements carried out from atmospheric pressure to 100 MPa. For that purpose, first the ability of 19 equations for fitting density data and for calculating the isothermal compressibility was investigated. Among the equations of state tested, only 6 equations were selected for their suitability for deriving density data in the pressure range investigated. Then, a procedure for evaluating the combined standard uncertainty associated with the determination of the isothermal compressibility from the derivation of density data was tested. Finally, a numerical method was proposed for estimating the isothermal compressibility and its uncertainty from a limited number of experimental density data by considering a Monte Carlo procedure. As an example, the proposed numerical procedure was applied to liquid toluene. With this aim in mind, the density of liquid toluene was measured up to 100 MPa in the temperature range of 293.15–343.15 K by using a U-shape oscillating tube density meter.

Density, Speed of Sound, Compressibility, and Excess Properties of the Carbon Dioxide + n-Heptadecane Binary Mixture from 10 to 70 MPa

“…The isentropic compressibility κ S was directly obtained from measurements of the speed of sound and density carried out in the same conditions of pressure, temperature, and composition, using the so-called Newton Laplace relation The isothermal compressibility κ T , for its part, was determined from its simple definition 1/ρ­(∂ρ/∂ p ) T by considering a numerical Monte Carlo method for the differentiation of density with respect to pressure . Briefly, this three-step method consists, first, in perturbing density measurements according to their standard uncertainty, then, in fitting perturbed data with several equations of state and, finally, in differentiating the fitted equations analytically.…”

“…The isothermal compressibility κ T , for its part, was determined from its simple definition 1/ρ(∂ρ/∂p) T by considering a numerical Monte Carlo method for the differentiation of density with respect to pressure. 26 Briefly, this three-step method consists, first, in perturbing density measurements according to their standard uncertainty, then, in fitting perturbed data with several equations of state and, finally, in differentiating the fitted equations analytically. Hudleston, 27 Murnaghan, 28 and Tammann 29 equations of state were used for fitting density data of mixtures with low compressibility, whereas a Benedict−Webb−Rubin 30 type equation of state was considered for representing the high compressibility of mixtures with 85% and more of carbon dioxide.…”

Computation of Isobaric Thermal Expansivity from Liquid Density Measurements. Application to Toluene

“…In this differentiation via the curve-fitting method, the nonlinear regression makes it difficult to assess the standard uncertainty in the reported isobaric expansivity data by conventional uncertainty propagation methods. To solve this issue, a Monte Carlo method was used here to estimate the combined standard uncertainty in the density derivative as proposed for differentiation of density data with respect to pressure 29 and extended to the estimation of the expanded uncertainty in isobaric expansivity obtained using the curvefitting method U(α p,CF ). 30 According to the guide to the expression of uncertainty in measurement 31 this statistical method consists first in perturbing each original density data point so as to generate a pseudorandom distribution of N trials = 5000 for each data point.…”

Density, Viscosity, and Derivative Properties of Diethylene Glycol Monoethyl Ether Under High Pressure and Temperature

“…According to the smooth shape of isobaric curves and the narrow pressure range investigated, only three-parameter ( A , B , and C ) correlating functions were considered. They are the Tait equation, the Hudleston’s equation with l = ρ –1/3 , and the Murnaghan’s equation These three equations were randomly used for fitting and deriving the perturbed density data points in a Monte Carlo procedure that involves 5000 trials. The mean and the standard deviation of the resulting compressibilities were evaluated to determine both the compressibility and its uncertainty.…”

“…However, the values obtained by such derivations as well as their uncertainties are strongly influenced by choice of the fitting function. For this reason, it is recommended 16 to randomly use several correlating functions to fit and derivative density as a function of pressure. Thus, in the present work, we used three different equations for fitting density data at each temperature, T, before deriving it.…”