A Vibrating Edge Supported Plate, Fabricated by the Methods of Micro Electro Mechanical System for the Simultaneous Measurement of Density and Viscosity:  Results for Methylbenzene and Octane at Temperatures between (323 and 423) K and Pressures in the Range (0.1 to 68) MPa

Abstract

In the petroleum industry, measurements of the density and viscosity of petroleum reservoir fluids are required to determine the value of the produced fluid and production strategy. These thermophysical properties are also useful for the design of separators and process equipment and to control production processes. To measure the density and viscosity of petroleum fluids requires a transducer that can operate up to reservoir conditions and, to guide value and exploitation calculations with sufficient rigor, provide results with an accuracy of about ± 1 % in density and ± 10 % in viscosity. Necessarily, these specifications place robustness as a superior priority to accuracy for the design. In this paper, we describe a Micro Electrical Mechanical System (MEMS) that is capable of providing both density and viscosity of fluids in which it is immersed at the desired operating conditions. This transducer is based on a vibrating plate, with dimensions of about 1 mm and mass of about 0.12 mg, clamped along one edge. The measured resonance frequency of the first bending mode in a vacuum at a temperature of 298 K is about 12 kHz with a quality factor about 2600. Measurements of the resonance frequency and quality factor of the first-order bending mode were combined with semiempirical working equations and the mechanical properties of the plate to determine the density and viscosity when immersed in methylbenzene at temperatures of (323 and 373) K and octane at temperatures between (323 and 423) K both at pressures below 68 MPa where the density varies between (619 and 890) kg·m-3 and the viscosity varies from (0.205 to 0.711) mPa·s. The measurements in methylbenzene at pressures between (0.1 and 68) MPa and a temperature of 323 K were used to determine the adjustable parameters in the semiempirical working equations. The expanded (k = 2) (twice the standard deviation) uncertainty, including the calibration, in density is about ± 0.2 % and in viscosity is about ± 2.5 %; at a temperature of 423 K, the expanded uncertainty in viscosity is about 6 %. The results obtained at temperatures below 423 K differed by less than ± 0.3 % for density and less than ± 5 % for viscosity from either accepted correlations of literature values or results documented by others with experimental techniques that utilize different principles and have quite different sources of systematic error. These differences are within a reasonable multiple of the relative combined expanded uncertainty of our measurements. For octane at a temperature of 423 K, the measured viscosity differed by less than 13 % from literature values while the density differed by less than ± 0.5 %.

A Vibrating Plate Fabricated by the Methods of Microelectromechanical Systems (MEMS) for the Simultaneous Measurement of Density and Viscosity: Results for Argon at Temperatures Between 323 and 423K at Pressures up to 68 MPa

“…For this work and that described in Ref. [34], the fluids are Newtonian so that their viscosity is independent of the rate of shear. However, non-Newtonian fluids are also encountered in the production of petroleum, as for example in the case of a drilling lubricant that contains sodium bentonite which has been added to increase the density.…”

“…The model, presented in detail elsewhere [34], describes the plate oscillating in an inviscid fluid decoupling the effect of viscosity and density so that the density is determined solely from the resonance frequency, and an independent equation is used to determine the viscosity. The plate is modeled as a beam supported at one end, z = 0 and y = 0, as illustrated schematically in Fig.…”

“…[34], from the temperature dependence of the adiabatic stiffness elastic constants obtained from McSkimin [36] and Nikanorov et al [37]. For the analyses presented here, we have taken the density of silicon to be ρ (Si, 293.15 K, 0.1 MPa) = 2, 329.081 kg·m −3 based on the values reported by Bettin and Toth [38], Fujii [39], and Waseda and Fujii [40,41].…”

“…[34]) at a temperature of 323 K, Eq. (2) predicts f (p = 0) = 57, 886 Hz which is about 4.7 times the measured value of 12,235 Hz.…”

“…In this article, we are concerned solely with argon at densities between 79 and 767 kg·m −3 and viscosities in the range of 26-57 µPa·s. In another article [34] we reported measurements when a similar MEMS densimeter/viscometer was exposed to liquid methylbenzene and octane with densities between 619 and 890 kg·m −3 and viscosities in the range of 0.205-0.711 mPa·s. For this work and that described in Ref.…”