In this method, a tuning fork resonator can be seen as a series connection of resistor, capacitor and inductor. The Butterworth–Van Dyke equivalent circuit is an important method to study the measurement of liquid density and viscosity. On the whole, fluid density and viscosity (D–V) sensors are becoming more widely used. The density and viscosity of reservoir fluids are the main parameters for fluid identification, determining fluid composition and dividing the oil–water interface, which can help oilfield companies determine reservoir recovery rates, predict productivity and guide reservoir development strategies. For more than a decade, tuning fork sensors have been used to detect the density and viscosity of fluids in complex downhole environments. In the wine industry, on-line density monitoring during fermentation is also crucial. In automotive industry, on-site monitoring viscosity of lubricants is a key indicator for tracking their performance. The measurement of fluid density and viscosity is essential in petrochemical, food, automotive and textile industries.

This model provides an idea for improving the accuracy of fluid component recognition in real time, and lays a foundation for the application of miniaturized and cost-effective downhole fluid density and viscosity sensors. When the measured resonance frequency and quality factor of the QTFs vary from 25,800–26,100 Hz and 28–41, the sensitivities of the quality factor affected by the fluid density increase. The results show that the relative mean square error in viscosity of the eight solutions evaluated by the hydrodynamic model is reduced by an order of magnitude comparing with Butterworth–Van Dyke equivalent circuit method. Then, the Sobol index method is chosen for explaining quantitatively how the resonance frequency and quality factor of the QTFs are affected by the fluid density and viscosity, respectively. Two examples are presented to verify the usability of this model. A hydrodynamic model of using quartz tuning forks (QTFs) for density and viscosity sensing, by measuring the resonance frequency and quality factor, has been established based on the cantilever beam theory applied to the atomic force microscope (AFM).

Fork oil actual viscosity chart