01 January 2005
The two phases of Coriolis flow
Exploring problems and solutions in flowtube design.
By Manus Henry, Hoi Yeung, and Wade Mattar
Historical documentation proves Coriolis mass flowmeters are unable to perform well when presented with two-phase (gas/liquid) flow. The first problem is maintaining flowtube oscillation at higher levels of two-phase flow (typically 2-20% of gas by volume) can be difficult, even at low levels of gas. The second is how to get accurate mass flow and density readings from a Coriolis mass flowmeter when dealing with two-phase fluids, whether continuous, in bursts, or when the flowtube starts or finishes a batch in an empty condition. Dynamic response is relevant here. The Coriolis transmitter requires a highly responsive drive control system in order to maintain flowtube operation during two-phase flow.
The key problem in using Coriolis mass flowmeters to measure process fluids containing bursts or continuous two-phase flow is simple. Conventional Coriolis meters are not able to reliably maintain flowtube operation and generate accurate measurements; tens of seconds may elapse after resuming single phase flow before you restore nominal performance. One user suggests manufacturers should provide some Coriolis priorities in their meters—the ability to batch from empty and to accurately measure aerated liquids and two-phase flow. They should also provide faster response time and less latency (or the ability to do very short batches of a one-half second or less, even with pumps with pulsating flows, such as lobe, diaphragm, and piston pumps).
Flowtube design issues
The most common arrangement is to have a single driver at the midpoint of the measurement section of the flowtube. However, a few Coriolis designs use two drivers, including the B-shaped meter most often used in the Oxford research. This offers a simple but significant advantage in two-phase flow situations. Intrinsic safety considerations place a limit on the maximum drive energy (current and voltage) that you can supply to a single driver under high damping conditions. A second driver doubles the energy you can use to maintain flowtube operation without violating intrinsic safety limits. This in turn leads to better flowtube control, a higher amplitude of oscillation, and hence, a better signal-to-noise ratio than would be possible with a single driver operating on an otherwise identical flowtube.
Another design option is whether to have a single, continuous path through the flowtube, or to split the flow. Splits, or sudden changes in flowtube size, are potential trigger points for cavitation. More importantly is the issue of repeatability. A split may result in asymmetry in the distribution of gas between the two flowtube paths. This has two potential consequences. First, any imbalance may render flowtube control more difficult. Second, if plant-specific factors (such as the length of straight pipe before the meter, orientation of process piping bends, pressure and pressure drop) have an impact on the symmetry of two-phase flow within the flowmeter, it may be more difficult to develop a general measurement correction strategy that you can use in several applications.
Straight flowtube designs have become popular because they reduce pressure drop and have a compact design. However, compared with a typical bent flowtube, you could say the sensor signals arising from a straight tube have a high-frequency, low-amplitude, and low-phase difference range. In other words, they have a poorer signal-to-noise ratio. If you maintain flowtube oscillation during two-phase flow, it's at the expense of reducing the amplitude of oscillation by up to an order of magnitude. Two-phase flow also induces a higher degree of noise on the sensor signals. With a bent tube design, you might reduce the nominal sensor amplitude of 300mV for single phase to as low as 30mV with two-phase flow. A straight tube design may start with normal sensor amplitude of 30mV, so you can reduce it to only 3mV. Of course reduced signal levels will make it more difficult to extract good quality measurement signals and ensure continued flowtube oscillation.
Generating the drive signal
The operation of a Coriolis mass flowmeter depends on the proper oscillation of the flowtube. The drive signal(s) that the transmitter generates control this. The flowtube's oscillation (as the sensor signals indicate) is typically sinusoidal and thus characterized in terms of frequency, phase, and amplitude.
What constitutes optimal flowtube operation? One criterion is the flowtube should oscillate at its natural frequency of vibration at constant amplitude. This vibration will vary with the overall mass of the flowtube and hence the density of the process fluid. Usually measurement algorithms assume constant amplitude of oscillation over the calculation interval, so amplitude stability is relevant for measurement quality.
For oscillation at the natural frequency, the driving force needs to be 90º out of phase with the motion of vibration. The most commonly used form of sensor, based on a simple electromagnetic coil, actually measures velocity. Therefore, the sensor signal is already 90º out of phase with the motion of the flowtube.
An optimal drive signal would have the same frequency of oscillation and phase as the sensor signal, with drive amplitude selected to maintain constant sensor amplitude. Matching the drive output to the exact phase of the sensor signal is challenging. Of course, you can do it if you also match the oscillation. If you can't, the consequences depend on the degree of phase mismatch. With small levels of phase offset, and with benign process conditions, the effect is relatively minor—the drive signal draws more power than if it were entirely in phase. With more significant phase drift between driver and sensor, the oscillation becomes forced as opposed to natural. The drive energy requirement becomes significantly higher, and the drive frequency can drift away from its natural value. Finally, with large phase offset, the meter may cease vibrating entirely (stalling), or begin to oscillate in another mode of vibration at a frequency where the phase offset is closer to an integral multiple of 360º.
The most common technique for generating a drive signal has been positive feedback, whereby you multiply the sensor signal (containing the desired frequency and phase characteristics) by a drive gain factor (either by analog or digital means). The drive gain required to maintain the desired amplitude of oscillation is closely related to the damping on the flowtube. Assuming negligible delay in the analog feedback circuit, this ensures phase matching between sensor input and drive output. Positive feedback is easy to implement, but it provides only partial control of the drive waveform and cannot readily prevent unwanted components in the sensor signal. The alternative approach is drive waveform synthesis. Here the transmitter calculates a drive waveform digitally—a pure sine wave or square wave. Advantages over positive feedback include full control over the drive waveform, but the challenge is to match the phase of the sensor signal in real time.
Batching from empty
There are quite a few processes where the high accuracy and direct mass-flow measurement Coriolis technology provides would benefit metering batches. In many cases, however, it's not practical to ensure the flowmeter remains constantly full of fluid. Yet large errors may occur in partially filled Coriolis meters, or empty meters with wet flowtube walls. Hydraulic shock from the onset of flow, or a surge of air, may result in large measurement errors and stalling. Most Coriolis manufacturers are thus unable to recommend the use of their products in batch applications unless they can keep the flowtube full. For trials with the flowtubes kept full, we use a diverter system. With steady flow established, the diverter under transmitter control switches flow from a recirculation loop to a weigh scale. When we reach the target totalized flow, we switch the diverter back by the transmitter to the recirculation loop, and we note the finalized weigh-scale total. This procedure has the advantage of a more or less steady flow rate, but it introduces additional system non-repeatability by any variation between batches in the residual liquid in the pipe work leading to the weigh-scale. For the batching from empty trials, we permanently switch the diverter to feeding the weigh-scale, and the transmitter controls the flow simply by switching the pump on and off. As the outlet pipe opens to the air, when the pump is switched off, gravity drains the Coriolis meter, and so starts the next batch empty. This is the simplest possible arrangement.
For batching from full, the absolute repeatability is approximately constant at 3-4g down to batches as short as 62ms; at 31ms this rises to 7g. As a percentage of batch total, this varies from 0.1% for a 10s batch up to 10% for a 62ms batch. For batching from empty with trials 2s or longer, the absolute repeatability remains below 10g; for shorter batches, there is poorer performance. From a relative repeatability perspective, these results suggest you can obtain 1% repeatability batching from empty for batch totals corresponding to 2s or more at the nominal flow rate.
Continuous two-phase flow
Even if you maintain flowtube operation during bursts of two-phase flow, you could induce errors in the mass flow and density measurement by the physics of bubbles moving through a vibrating tube. However, simple theoretical models give only an approximation of the errors we observe in practice. Although the magnitude of the errors can be high, they are repeatable.
Drive control is critical to maintaining flowtube operation; but you still need to correct for induced measurement errors. Results from batching from empty trials have demonstrated good repeatability is possible even for short batches, while we're improving correction techniques for mass flow and density measurements with continuous two-phase flow.
Behind the byline
Manus Henry is with the Engineering Science Dept. at Oxford University in Oxford, United Kingdom. Hoi Yeung is with the Department of Process and Systems Engineering at Cranfield University, Cranfield, United Kingdom. Wade Mattar is Flow Specialist at Invensys Foxboro, Foxboro, Mass. Oxford University's Mihaela Duta and Michael Tombs contributed.
Why does two-phase flow make flowtube control difficult?
The main effect is a dramatic rise in the flowtube damping, perhaps by two orders of magnitude. Mechanical energy gets lost in the interactions between compressible bubbles, fluid, and flowtube walls, and the drive energy required to maintain oscillation rises sharply. Not only does the damping rise, but it varies rapidly, due to the chaotic nature of the interactions. Similarly, the frequency and amplitude of oscillation vary more than for single phase.
Consequences for drive output
Drive energy saturation. For any intrinsically safe flowtube, there is an absolute limit on the energy supplied to the drivers. The default amplitude of oscillation may not be sustainable. While many in the industry appreciate this limitation, some wrongly assume this is the main reason flowtubes stall. It is perfectly possible to maintain flowtube oscillation through two-phase flow even with an artificially low limit on, say, drive current. By far the most common cause of flowtube stalling is drive gain saturation.
Drive gain saturation. Some positive feedback drives cannot exceed a maximum drive gain limit due to amplifier saturation. This means there is a maximum multiplier between the sensor amplitude in and the drive signal out. Suppose you reach this limit, and the flowtube damping rises again due to yet more gas in the two-phase flow mix. A further rise in drive current to compensate for the increased damping is not possible, due to drive saturation. As a consequence, the sensor amplitude starts to reduce, but this in turn leads, again because of drive saturation, to a drop in the drive signal output; the end result is a catastrophic collapse in oscillation amplitude.
Poor tracking. The rapid changes in damping, amplitude, frequency, and phase on the sensor signal require fast and accurate tracking by the transmitter in order to generate an appropriate drive signal. If the drive control update rate is simply too slow, or there is too much dead time, the flowtube may stall due to inattention. A second, possibly worse, alternative is where you maintain oscillation, but inaccurate tracking leads to phase shift between input and output—leading to forced oscillation, and hence wayward frequency of oscillation and poor repeatability. In the high damping conditions of two-phase flow, this may be difficult to detect and correct.
Two-phase flow provides different challenges to both of the main drive techniques. With positive feedback, the quality of control is limited, as the drive gain is selected based on previous amplitude information while the drive signal itself is proportional to the sensor signal which is varying rapidly. Conversely, with synthesis techniques, the problem of tracking phase to ensure natural vibration becomes more difficult.
Versatile Coriolis technology booming
Because Coriolis technology is so versatile, the flowmeter market should grow at a compounded annual growth rate of 8.9% over the next five years, according to a December ARC Advisory Group report. The market was $404 million in 2003, and experts forecast it to be over $617 million by 2008. Coriolis flowmeters measure liquids, slurries, and gases.
One of the more significant growth opportunities for the technology lies in measuring natural gas. In fact, the American Gas Association recognized Coriolis meters for their natural gas applications, which will open new markets for the technology. Applications include production, processing, transmission, storage, distribution, and end-use fuel measurement.
Because it can measure mass flow directly, Coriolis meters have the upper hand on flowmetering technologies for compressed natural gas, which is a low pollutant and thus an increasing alternative fuel in transportation. Other advantages of Coriolis flow include no moving parts, minimal maintenance requirements, and direct mass measurement, which translates into low total cost of ownership for users. And users won't have to worry about changes in pressure, temperature, viscosity, and density when using Coriolis flowmeters, which leads to faster development for niche applications.
Asian markets for Coriolis flowmeters are the fastest growing because of the concentration of chemical, petrochemical, and oil and gas refining industries. North America is next, followed by India.