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Vibrating element viscometers

How vibrating element viscometers work, applications and considerations of coriolis sensors as viscometers by jmw
Posted: 21 Jun 04 (Edited 15 Jun 11)

Since this FAQ was written A further FAQ has been written which can be found in the "Petroleum Engineers Other Topics" FAQs or click here:
FAQ 698 1004; "How do we measure visccosity onliine?"

Process engineers should note carefully:
  • process viscosity measurement is not laboratory measurement and the objectives are often very different.
  • While Newtonian or non-Newtonian behaviour may be of concern to the laboratory, it is far less of a concern in many process measurements.
  • the key to good process viscosity measurement is the right instrument installed and operated in the recommended manner
  • Caution: many manufacturers supply niche market products with special application solutions that may not be applicable in other applications.
There are two types of viscosity measurement:

 Types of viscosity measurement
We can classify any process viscosity measurement into one of two types by applying the "temperature rule":

  • behavioural
  • analytical
The temperature rule
If we want the viscosity at the process temperature, it is a behavioural measurement.
If we want the viscosity at one or more reference temperatures, it is an analytical measurement.

Behavioural measurements are where all that we need to know is the viscosity at the process temperature.

The viscosity of the fluid affects the way it behaves in a process.

Typical applications: spraying, coating, dipping and atomizing, applications where the viscosity is an important indicator of how a fluid will behave in these processes.

Measuring the viscosity of a lubricant in a gearbox, at that temperature, tells us how able the oil is as a lubricant at that temperature.

 Analytical measurements  are where we need to know the viscosity at one or more reference temperatures.

This is important when measuring or controlling the quality of a fluid.

When blending lubricants the viscosity of the oil at both 40°C and at 100°C. is required

The viscosity can also be a also key indicator of another parameter. Molecular weight is an important factor in the control of polymerization or in quench oil heater control (e.g. ethylene cracker)
One of the ASTM standards defines the correlation between molecular weight and the viscosity at 40°C and at 100°C.

Note that some applications require both types of measurement.
Viscosity at gearbox temperature may indicate if the oil is performing as expected but measuring the viscosity at either of the reference temperatures indicate the degree to which the oil is deteriorated and if it needs changing. It isn't necessary to know the viscosity at both reference temperatures as the original oil quality is known. Viscosity is, incidentally, an indicator of some other oil quality parameters such as acid number.

Viscosity may be the quality factor of interest or an indicator parameter. It could be used to determine concentration or molecular weight., ignition index, viscosity gravity constant, %volume or mass, and so forth.
Unfortunately, no other parameter is sufficiently sensitive as to allow us to indicate viscosity. This is why, in hydrocarbon processes, if we cannot measure viscosity in the process, we must measure it in the laboratory. We cannot measure density or conductivity and infer the viscosity from that.

The sensitivity of viscosity to change is both its advantage and its Achilles heel.
While viscosity is very sensitive to quality change it is also equally sensitive to other factors.

In any application, we must discriminate a change in viscosity due to a temperature change from a change in viscosity due to a quality change.

In quench oil applications, ( a portion of the residuum is temperature controlled and sprayed back into the process to influence the condensation of lighter molecules into the residuum) as the temperature increases, so does the viscosity: increasing the quench-oil temperature results in fewer light hydrocarbons condensing into the residuum.

How does a vibrating element viscometer work?
In any spring-mass system the system is damped by the medium.

Consider a wine glass, bell or chime which is struck. It rings at a characteristic frequency. As time passes, the note will die away due to the damping on the system. The note can be sustained by monitoring the resonant frequency and applying a drive signal at this frequency. The amplitude and decay time are related to the viscous damping force.

Vibrating element sensors can be categorised as follows:
  • analogue measurements
  • digital measurements
They can also be categorized according to whether the sensor displace the fluid or not.

Analogue Devices
The signal amplitude at the resonant frequency is a function of the fluid viscosity.
Those devices that measure or use this amplitude relationship, and which are referred to here as "analogue" devices. adopt one of three approaches:
  • amplitude maintaining
  • amplitude measuring
  • Decay time measuring
Amplitude maintaining devices determine the viscosity from the energy required to maintain the amplitude at the resonant frequency at a constant value.
Amplitude measuring devices simply determine the viscosity from the amplitude at the resonant frequency.
Decay time devices excite the sensor at the resonant frequency and then monitor the time taken for the signal to decay e.g. by 50%.

Analogue devices are very common, and for a while, the only way to measure viscosity with a vibrating element device.
They are often very basic and simply calibrated.

Digital Devices
Examine the amplitude as a function of frequency. At low viscosities the energy is concentrated into a very narrow band of frequencies about a resonant frequency.
As the viscosity increases the energy is distributed over a wider range of frequencies with a corresponding lowering of the amplitude at resonance.

In the "digital" viscometer the device does not drive at the resonant frequency but alternates between the upper and lower 3dB frequencies, or half-power points, which are 90° phase shifted from each other.

The measurement of the frequencies at the 3dB points gives the bandwidth from which the dynamic viscosity can be determined.

Because it is frequencies, and not amplitude, that are measured, these can conveniently be described as "digital viscometers" in the same way that API defines "digital density meters".

Not all vibrating element viscometers are digital.

All vibrating element sensors (and most other process viscometers) measure the dynamic viscosity.
It is important, in some applications, and especially in hydrocarbon applications, to determine the kinematic viscosity.

In sensors that displace the fluid, the resonant frequency is a function of the effective mass of the sensor plus the effective mass of the fluid, which varies with fluid density. This allows us to determine the density from the same device we are using for viscosity.

For sensors that do not displace the fluid, resonant frequency is a function of the effective mass of the sensor only.

Kinematic viscosity is determined from the dynamic viscosity and the density:

where ν is the kinematic viscosity in cSt; η is the dynamic viscosity in cP and ρ is the density in kg/m3

Sensor features
Factors affecting viscosity measurement

Surface effects
Viscosity is very much a "surface centred" effect.
That is, the measurement is very sensitive to what happens on the effectivesurface of the sensor and far less influenced by what is happening in the fluid further away from the sensor.

Density is a function of the resonant frequency and can be considered "Mass centred". That is, the measurement is very much less sensitive to what happens on the surface of the sensor but more significantly affected by what happens in the effective mass of the fluid as a whole.
It is not unusual that such a sensor will give perfectly good density signals but very unstable viscosity signals if, for example, the sensor is coated or contaminated.

Pressure can affect the viscosity of a fluid. However, the magnitude of this effect is usually insignificant in any application.

Flow effects
Sensors that displace the fluid may be subject to flow effects. The viscosity may appear higher than it really is.
These effects are sensor dependent, but are only significant at low viscosities. They may be easily compensated for by using a slip stream installation, with a constant flowrate, and applying an offset to the calibration.
Some manufacturers opt for non-displacing designs for this reason, but in doing so they lose the ability to measure the density. In many behavioural applications this is not a concern. It is important in most analytical measurements.

There are two things to consider, the effect of temperature on the sensor and the effect of temperature on the fluid.
It is necessary to enquire closely about temperature effects on the device, especially analogue devices. For digital instruments, there are no significant temperature effects on the sensor. For analogue devices the effects are also usually negligible especially given the broad accuracy tolerance behavioural measurements accommodate.
However, the temperature effects on the fluid may give rise to any of the many possible secondary effects on the sensor. This makes good installation and operation essential and require very close attention to the manufacturer's installation recommendations. These effects can be sensor dependent.

The temperature effects in the fluid are most relevant in an analytical measurement.

The temperature viscosity relationship is complex. It requires an understanding of the effects of temperature to make a good behavioural measurement but it requires real ingenuity to use the relationship in an analytical measurement.

Analytical measurements in hydrocarbon applications:

For hydrocarbons Viscosity Vs Temperature is given by the relationship in ASTM D341 (many refiners have equivalent proprietary expressions):

Log10.log10( Ν+0.7)=A-B.log10(T+273)
where Ν is the kinematic viscosity at temperature T°C.

Small errors at the process temperature can become very significant at the reference temperature(s).

Unlike density, where the API equation is easily solved, the ASTM D341 equation requires some ingenuity to resolve for a practical process viscosity measurement.

In API the density equation, API provides values for K0 and K1 that may be assumed constant for all crudes, or another set of values for gasolenes that are assumed true for all gasolenes and so on. This means that from a single observation of density at one temperature the density at 15°C can be found.

Sadly, the ASTM D341 equation allows no such simple solutions. The constants A & B both vary significantly, even with a small quality change in a specific hydrocarbon. This means that to find the viscosity at a reference temperature we need the viscosity of the hydrocarbon at two other temperatures to find the values of A & B unique to that oil.

Note whereas the density variation in any fluid is comparatively small, viscosity variation can be very, very significant.

Consider an extreme example tar residue:
  • viscosity of 700,000cSt at 100°C and just 15cSt at 320°C.
  • density approx 950 kg/m3at 100[°}C and 800kg/m3 at 320°C
  • the viscosity has changed by a factor of 4700:1
  • the density has changed by a factor of 1.2:1.
There are two types of analytical measurement methods:
  • Direct Measurement Method; the sample stream temperature is controlled to the reference temperature such that the measured viscosity is the reference temperature viscosity. This method is suitable for all fluids
  • Indirect Measurement methods: the viscosity at the reference temperature(s) is found by calculation from the measurement at one or two process temperatures.

    There are three principal indirect methods:
  • Equation Method (hydrocarbons)
  • Multicurve (hydrocarbons) or Matrix (non-hydrocarbons; see following) ratio methods
  • Dual Viscometer method (hydrocarbons)
The dual viscometer method is suitable for almost all applications where there is a quantifiable relationship between viscosity and temperature. The other indirect methods are very much application dependent.

All are very sensor dependent.

Analytical measurement of viscosity in non-hydrocarbon applications:
When dealing with fluids other than hydrocarbons, where there are no suitable equations, a different method is required. The treatment may be similar to that used for the density of non-hydrocarbons e.g. a ratio method using a matrix of reference values but it requires far more care as the curve fitting equations can lead to errors where the reference data is not well organized.
In some simple applications, and where the process conditions do not vary significantly, much reduced solutions can be applied with good approximation. These are usually in niche applications with particular technologies, but are often not more widely applicable.

Applications Summary:

Analytical applications are complex and require considerable instrument accuracy and they require ingenuity in developing appropriate solutions. Many of the solutions are only applicable within niche market applications. Price is often  very secondary to performance.

Performance is the key and price is often a secondary consideration.
Behvioural applications are relatively simple and do not require any great instrument sophistication or accuracy though price is often a very significant factor.
Most successful viscometers are those used in behavioural applications.

Not all behavioural applications are simple.
There are many manufacturers, of several different technologies, who have enjoyed success in heavy fuel oil heater control applications for engines but have no success in heavy fuel oil heater applications for burners.

For a behavioural measurement it really doesn't matter if the sensor is only 1-5% accurate. Even 10% accurate is good enough in some cases.

Example: An RH35 Heavy fuel oil has a viscosity of 380cSt at 50°C but for optimum combustion the viscosity must be reduced to around 11cSt by heating to approximately 142°C. It is not critical if the viscosity varies between 10 and 12cSt. i.e. +/-10% of reading is often acceptable.

This generous tolerance allows a great many simplifications in how the sensor is driven, calibrated and the signal processed. Some sensors are very basic. Most are analogue devices.
Price is a primary consideration in these applications and sensors can be found for as little as $200-$300 (though for heavy fuel oils the price is more typically $2000-$3000 for engine applications and $12,000 to $13,000 for burner applications).

A fluids rheological properties hardly enter into the choice of a good process viscometer at all. It is often not important if the fluid is Newtonion or pseudoplastic. Successful measurement often depends on understanding and controlling the effects of process conditions and choosing the right sensor. The main problem is the temperature viscosity relationship.

Vibrating element sensors measure dynamic viscosity.
In viscosity measurement, multi-functionality is not always important. Many sensors measure only the dynamic viscosity and, in some applications, are only able to provide a repeatable value.
By itself, dynamic viscosity tells us very little, if anything, about quality, but a lot about behaviour.

Analytical measurements require more functionality. This means density and temperature measurement.
Density and dynamic viscosity give us kinematic viscosity. With temperature, these measurements make all sorts of other quality measurements possible; e.g. viscosity gravity constant, acid number, ignition index, molecular weight and so on.

Coriolis mass meters provide multi-functionality but be aware that mass meter manufacturers are divided about the extent to which they should follow this path. Because the mass meter operates at the resonant frequency these sensors can be used to measure viscosity exactly as dedicated viscosity meters. However, viscosity minimum range is very much related to the sensor the sheering surface. Most vibrating element viscosity sensors have a relatively small effective surface area  and can measure to very low viscosities e.g. 0.5cp and above. Mass meters are usually substantially bigger and with even greater sheering surfaces. Consequently the resolution is very poor at low viscosities. The majority of process viscosity measurements are in the viscosity range 0.5 to 2000cP.

In a mass meter, density measurement is a useful added feature which can contribute to the flow calculations; for example, the derivation of  volumetric flow. Some mass meter manufacturers utilize the sensor as a dedicated density meter, within the limits imposed by the sensors design as a mass flow meter, and obtain some excellent results.

However, when we consider viscosity as an added function, there is no relevance of viscosity to flow measurement in a mass flow meter. If we were talking about a positive displacement meter or a turbine meter, or even a single chord ultrasonic meter, viscosity is very relevant to the meter performance and, if viscosity were a capability of the primary flow sensor, would be a valuable added function. But it isn't so these meters often use separate process viscometers for viscosity correction of the meter factor.

This leaves us to consider the mass meters as dedicated viscometers.
Ignore the original Micromotion approach. This used a differential pressure transmitter across the inlet and outlet. The mass meter had the advantage (in this case) of a high pressure drop, and the advantage that the inlet and outlet ports were very close together making dP errors manageable. However, apart from those factors, the fact that a mass meter was used is of little relevance. In any event, unless for select applications or clients, this option is believed no longer to be available.

Our interest in mass meters is as vibrating element sensors.

Arguably the best way to measure viscosity with a vibrating element sensor is to go "digital" i.e. to use bandwidth, at least, in the currently available technologies.
As a dedicated viscosity sensor there would be some advantage to doing this with a mass meter sensor structure, but in a multi-functional mass meter, alternating between the upper and lower half power points would interfere with the phase difference measurements and hence compromise its performance as a mass meter.
Hence in a multi-functional mass meter amplitude methods are most probable but of questionable value.

If the mass meter sensor were to be offered for dedicated viscosity measurements, in the same way as it is offered for dedicated density measurements, bandwidth measurement methods could be used. However, whether these sensors have the potential to deleiver the necessary accuracy for analytical measurements is unknown and they would be very uncompetitive as behavioural measurement instruments where the price is rapidly dropping for vibrating element sensors.

The best that can be said is that mass meters, as vibrating element sensor structures, can measure viscosity but the question of performance is as yet unknown and the cost to benefit advantage far from established.

Note: the new Endress & Hauser Promass  is a multi-functional instrument. Viscosity is presumed to be an amplitude sustaining based analogue measurement and the accuracy is claimed as +/-5.0% of reading +/-0.5cP. The types of application in which this has been evaluated or in which it will be successful have yet to be determined.
It should be noted that some mass meters are available with very small bore tubes and may provide very good and low range viscosity potential but with small bore tubes we probably should not expect them to be used with dirty fluids. The current vibrating element sensors are used with all sorts of dirty fluids and slurries.
Most vibrating element sensors are available for insertion into large bore pipes or for tank applications. Flow through sensors would require a pumped by-pass but this is not a handicap though it may limit the range of applications.

The development of coriolis sensors as viscometers will interesting as some sensor configurations and sizes have real potential if they can deliver the right cost/benefit ratio in a market where the competition is fierce and where there are plenty of low cost solutions and some very accurate systems.


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