Force Transmission Errors in Magnetic Suspension Densimeters

Abstract

Techniques to determine and compensate for the force transmission error (FTE), including the magnetic effects of the fluid being measured, in magnetic suspension densimeters are presented. For a two-sinker densimeter, the forces on the balance are expressed for each of the weighings comprising a density determination (i.e., the two sinkers plus balance calibration and tare weights). This yields a system of four equations, which are solved for the fluid density, a balance calibration factor, a coupling factor (related to the FTE), and a quantity related to the balance tare. For a single-sinker densimeter, an in situ weighing of the sinker in vacuum compensates for the FTE of the apparatus itself. A determination of the fluid-specific effect requires measurements with two different sinkers-analogous to the two-sinker analysis, but with the measurements spread out over time. The apparatus part of the FTE is generally less than ±20 ppm. Measurements on propane, helium, neon, nitrogen, argon, toluene, and air are analyzed for the fluid-specific effect; this effect is correlated with the magnetic susceptibility of the fluid together with an apparatus constant. With this analysis, the force transmission "error" becomes an effect that can be accounted for rather than a significant source of uncertainty in density measurements carried out with magnetic suspension densimeters.

Certification Report for SRM 2214: Density of Iso-octane for Extended Ranges of Temperature and Pressure

“…The main advantage of the two-sinker method is that adsorption onto the surface of the sinkers, systematic errors in the weighing, and other effects that reduce the accuracy of most buoyancy techniques cancel. Equation (1) must be corrected for magnetic effects; this is considered in Section 4 and described in detail by McLinden et al [4].…”

Apparatus for accurate density measurements of fluids based on a magnetic suspension balance

“…By this method, densities over wide range of temperature and pressure can be measured. According to literature [3] and depending on the specifics of our apparatus, the fluid density is determined by relation…”

Force Transmission Error Analysis for a High-Pressure Single-Sinker Magnetic Suspension Densimeter

“…The FTE is the error caused by the magnetic behavior of the cell, the suspension coupling, and the measured fluid that leads to inaccuracies in the transmitted force measured at the high-precision balance. Different approaches exist to estimate and compensate for the FTE [7,8]. Kano et al [7] have proposed an analysis based upon a magnetostatic study of the MSD suspension.…”

“…Unfortunately, this approach requires a detailed knowledge of both the magnetic and geometric properties of the MSD and the fluid, which are not always available. McLinden et al [8] have developed an empirical analysis applicable to both two-and single-sinker MSDs. In their analysis, they attribute the FTE to two different sources.…”

“…McLinden et al [8] present a detailed explanation of each of the different sources of error and a mathematical model for its determination. The mathematical model results from force balances during the different measurements steps in the MSD.…”