Vibrating conduit sensors, such as Coriolis mass flowmeters and vibrating densitometers, typically operate by detecting motion of a vibrating conduit that contains a flowing material. Properties associated with the material in the conduit, such as mass flow, density and the like, can be determined by processing the measurement signals received from the motion transducers associated with the conduit. The vibration modes of the vibrating material-filled system generally are affected by the combined mass, stiffness and damping characteristics of the conduit and the material contained therein.
A typical dual-driver, or multiple input, multiple output (MIMO) Coriolis mass flowmeter includes one or more conduits, or flow tubes, that are connected inline in a pipeline or other transport system and convey material, e.g., fluids, slurries, emulsions, and the like, in the system. Each conduit may be viewed as having a set of natural vibration modes, including for example, simple bending, torsional, radial, and coupled modes. In a typical dual-driver Coriolis mass flow measurement application, a conduit is excited in one or more vibration modes as a material flows through the conduit, and motion of the conduit is measured at points spaced along the conduit. Excitation is typically provided by two actuators, e.g., electromechanical devices, such as voice coil-type drivers, that perturb the conduit in a periodic fashion. Mass flow rate may be determined by measuring time delay or phase differences between motions at the transducer locations. Two such transducers (or pickoff sensors) are typically employed in order to measure a vibrational response of the flow conduit or conduits, and are typically located at positions upstream and downstream of the actuator. The two pickoff sensors are connected to electronic instrumentation. The instrumentation receives signals from the two pickoff sensors and processes the signals in order to derive a mass flow rate measurement or a density measurement, among other things.
It is a problem that the one or more conduits may change with time, wherein an initial factory calibration may change over time as the conduits are corroded, eroded, or otherwise changed. As a consequence, the conduit stiffness may change from an initial representative stiffness value (or original measured stiffness value) over the life of the vibratory flowmeter.
Mass flow rate ({dot over (m)}) may be generated according to the equation:{dot over (m)}=FCF*[Δt−Δto]  (1)
The Flow Calibration Factor (FCF) is required to determine a mass flow rate measurement ({dot over (m)}) or a density measurement (ρ) of a fluid. The (FCF) term comprises a Flow Calibration Factor and typically comprises a geometric constant (G), Young's Modulus (E), and a moment of inertia (I), wherein:FCF=G*E*I  (2)The geometric constant (G) for the vibratory flowmeter is fixed and does not change. The Young's Modulus constant (E) likewise does not change. By contrast, the moment of inertia (I) may change. One way to track the changes in moment of inertia and FCF of a vibratory flowmeter is by monitoring the stiffness and residual flexibility of the flowmeter conduits. There are increasing demands for ever better ways to track changes in the FCF, which affect the fundamental performance of a vibratory flowmeter.
What is needed is a technique to track the FCF in a dual-driver flowmeter to verify the performance of the flowmeter with improved precision.