A methodology is described to improve the accuracy of vibrating-tube-based density measurements of aerated liquids. In many applications, density measurements are employed to determine compositional information of process liquids. For most density measuring devices, the presence of a small, but unknown, quantity of entrained gaseous phase within the process mixture can introduce significant errors in both the measured mixture density as well as the interpreted density of the liquid phase. This paper describes an approach to measuring fluid density which couples a sonar-based speed-of-sound measurement with vibrating-tube-based density measurement, commonly used in coriolis mass and density meters, to determine the density of aerated liquids. It is well known that the accuracy of coriolis meters can be significantly degraded with the aeration of the process fluid. Augmenting the output of the coriolis meter with a speed of sound measurement provides a novel approach to improved density measurement for aerated fluids in two ways. Firstly, sound speed based gas volume fraction measurement provides a first-principles-based, real time measurement of the gas volume fraction and compressibility of the aerated process fluid. Secondly, the sound speed of the process fluid is used to compensate for the effect of the increased compressibility and inhomogeniety of aerated mixtures on the output of the coriolis density measurement. To illustrate the fundamental ways in which aeration impacts vibrating-tube density measurements, a simplified, lumped parameter model for the effects of aeration in vibrating tubes is developed. The model illustrates that the effects of aeration can be attributed to at least two independent mechanisms; 1) the density inhomogeniety of discrete gas bubbles and 2) increased mixture compressibility due to aeration. Analytical results are supported by experimental data which suggest that augmenting the density measurements from the coriolis meter with a sound speed measurement significantly enhances the ability determine the density of aerated liquids with an accuracy that approaches that for non-aerated mixtures.
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