A theoretically-based calibration and evaluation procedure for vibrating-tube densimeters

A calibration procedure for vibrating-tube densimeters is developed which properly accounts for the effects of pressure and temperature on the Youngʹs modulus and internal volume of the vibrating-tube. The calibration equation is based on the theoretical dependence of the Youngʹs modulus, the compressibility, and the thermal expansion coefficient of the tube material on temperature and pressure. Experience shows that the vibration period of the evacuated tube can shift a small amount over time as the stresses in the tube and welds age. Therefore, the calibration equation is formulated relative to a vacuum reference period to adjust for these shifts. A first-order approximation of our theoretically-based equation is also derived. The calibration procedure is accomplished in two parts. First, the evacuated tube is calibrated to characterize the elastic modulus and linear thermal expansion coefficient of the tube as a function of temperature. Second, the change of the internal volume of the tube with temperature and pressure is characterized using two or more well-characterized calibration fluids. A procedure for choosing calibration fluids, temperatures, and pressures for the calibration points is developed. The densimeters are thoroughly tested with a variety of gases and liquids to show the validity of the equation over the calibration range. Finally, the magnitude of the temperature and pressure corrections are shown using propane+i–butane as a test system.