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 b s t r a c tA mathematical model is developed for a micro-electro-mechanical system (MEMS) instrument that has been designed primarily to measure the viscosity of fluids that are encountered during oil well exploration. It is shown that, in one mode of operation, the displacement of the device satisfies a fractional differential equation (FDE). The theory of FDEs is used to solve the governing equation in closed form and numerical solutions are also determined using a simple but efficient central difference scheme. It is shown how knowledge of the exact and numerical solutions enables the design of the device to be optimised. It is also shown that the numerical scheme may be extended to encompass the case of a nonlinear spring, where the resulting FDE is nonlinear.

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 the production strategy. Measurements of the density and viscosity of petroleum fluids require a transducer that can operate at reservoir conditions, and results with an uncertainty of about ±1% in density and ±10% in viscosity are needed to guide value and exploitation calculations with sufficient rigor. Necessarily, these specifications place robustness as a superior priority to accuracy for the design. A vibrating plate, with dimensions of the order of 1 mm and a mass of about 0.12 mg, clamped along one edge, has been fabricated, with the methods of Microelectromechanical (MEMS) technology, to provide measurements of both density and viscosity of fluids in which it is immersed. The resonance frequency (at pressure p = 0 is about 12 kHz) and quality factor (at p = 0 is about 2 800) of the first order bending (flexural) mode of the plate are combined with semi-empirical working equations, coefficients obtained by calibration, and the mechanical properties of the plate to provide the density and viscosity of the fluid into which it is immersed. When the device was surrounded by argon at temperatures between 348 and 423 K and at pressures between 20 and 68 MPa, the density and viscosity were determined with an expanded (k = 2) uncertainty, including the calibration, of about ±0.35% and ±3%, respectively. These results, when compared with accepted correlations for argon reported in the literature, were found to lie within ±0.8% for density and less than ±5% for viscosity of literature values, which are within a reasonable multiple of the relative combined expanded (k = 2) uncertainty.

The analysis of a new viscometer that takes the form of an oscillating plate, fabricated from silicon using the methods of micro-electro-mechanical-systems (MEMS) is considered. The instrument is designed principally for experimental use in the oil industry. The plate is 1.6 mm wide, 2.4 mm long, and 20µm thick. It is suspended from a 0.4 mm thick support by 48 square cross-section legs, each of length 0.5 mm width and depth of 20µm. The process of lithography is used to deposit layers atop the silicon. These layers can then be formed into resistors and metallic tracks. The tracks traverse the supporting legs to provide connections between the plate and external electronics. The oscillating plate is a mechanical element that can be set in motion by the force produced by the interaction between an electric current flowing in the plate and an externally applied magnetic field. The viscometer can be operated either in forced or transient mode and is intended for use in both Newtonian and non-Newtonian fluids. The motion of the viscometer is analyzed for incompressible fluids, using the Navier-Stokes equations to model the flow for both a Newtonian viscous fluid and a viscoelastic fluid where the stress is modeled by a reduced form of Maxwell's equations.