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Digital Density Measurement

How do we compare coriolis meters and density meters as density measurement devices? by jmw
Posted: 19 Jun 04 (Edited 24 Jun 04)

Digital Density Meters: how they work
This is a companion piece to the FAQ on Coriolis meters. You are recommended to read that FAQ first, but if you don't, please note the following:

There is no such thing as a ôCoriolis densityö meter.
This term is poor science and engineering despite it being found in an ISA instruments handbook as a collective term for all vibrating element  density transducers, whether they measure mass flow or not.
A more correct description for vibrating element density meters can be taken from the prior API standard where they are described as ôDigital Density Metersö, a term this author prefers and extends to some vibrating element viscosity meters. The term "digital density meters" does not discriminate between dedicated density meters and "coriolis" density meters. Discrimination must be based on performance and preference.

The intention is to discuss the density measurement capability of coriolis meters and density meters together. There are consequences of any design choices on performance and hence some features of sensors designed primarily as mass meter do affect their performance as digital density meters.

There are many coriolis meters, used for density measurement, so the discussion commences with a consideration of coriolis meters.

The fact that Coriolis mass flow meters operate at the resonant frequency is incidental to the measurement of mass flow but it has some useful benefits. This is what provides some of the ômulti-functionalityö of these instruments.

Interestingly, the first single straight tube full bore coriolis mass flow meter was produced by Solartron - they started with their tube digital density meter and added another pick off coil for the phase angle measurement. It didn't measure mass flow as well as a bent tube mass meter, but it will never be known how well it would have compared to the later straight tube mass meters (introduced as dedicated mass meters) since they stopped production in July 1994 and evolved no further.

Density is a function of the resonant frequency

Mass meter manufacturers recognise that the resonant frequency is a function of the effective mass of the system.
The effective mass is the sum of the effective mass of the sensor and the effective mass of the fluid.
The effective mass of the fluid varies with the volume of fluid contained and the density of the fluid contained.
In this, coriolis mass meters are equivalent to any vibrating element density meter, whether it measures the mass flow or not, and many do not.

History of mass meter density measurement development
The first mass flow meters were designed exclusively for mass flow rate and total measurements. Sensor design seeks to optimize the performance of the sensors as mass meters.

As the mass meter markets matured, mass meter manufacturers began to provide basic density measurements for added functionality. These first density measurements are very rudimentary.
When they began to offer these mass meter sensors for pure density applications, where the mass flow was often irrelevant to the application, it was necessary to improve the density performance without compromising the integrity of the sensor as a mass flow meter.
This is a vital design constraint.

When we consider dedicated digital density meters, they are designed solely for the measurement of density and the design is optimized for this function only.

Density measurement is a secondary consideration for mass meters. That doesnÆt mean mass meters are inferior to all dedicated density meter designs, many are significantly better. Most mass meters are targeted at the top end of flow meter applications and the sensors are very good for density measurement.
Density meter designs are more broadly targeted, so there are some very rudimentary low cost instruments available.
Different mass meter designs show unique properties compared to other designs. Some mass meters are better than others are at mass flow measurement and some are better than others are at density measurement.
MicromotionÆs Elite coriolis mass flow meter is claimed, by them, to be as good at measuring density as the Solartron digital density meter.

Not all density meters perform the same any more than all mass meters perform the same. Even when designing a dedicated density meter there are many other design considerations, and marketing objectives, taken into consideration. Many density meters are rudimentary devices. It is not about performance but about cost/benefit ratio in the target market.

Design features; what makes a good density meter
Density measurement performance for any vibrating element sensor is firstly a function of the sensor design.
It is also a function of two other main factors:
  • how the sensor is calibrated
  • how the signal is processed
These factors explain how mass flow meter density measurement has been improved, within the limits of the sensor designcompared to the early offerings; by improving the calibration and software to better exploit the fundamental capability of the sensor design.
 The same is also true of many dedicated density meters, now improved, but without any apparent sensor design changes.

Density measurement is not simply a function of the resonant frequency.

  • Density is not a simple function of the resonant frequency.
  • In early mass meters, and simple density meters, the relationship between density and frequency is treated as a simple straight line relationship. This is acceptable if the density does not vary significantly and great accuracy is not sought.
  • The frequency response will be a function of the sensor design.
The first step is to characterize the frequency response: this will require that the sensor is calibrated on more than one fluid, a minimum of three is necessary.

Before leaving frequency there are two more things to consider:

  • resolution and response time
  • noise
The majority of mass meters operate at quite low frequencies.
The lower the frequency, the lower the resolution or the longer the response time.

How is density measured? In the many density meters, frequency is determined from the time taken to count a large number of cycles.
Sensors, operating at around 1000Hz give both high resolution and fast response. This compares well to operating at around 80-150Hz, as many mass meters do, where it is immediately apparent that they cannot have both a fast response and a high resolution. Individual manufacturers will find the appropriate balance between these two affects for their design.

Pipe borne noise is typically at 80-100Hz.
At these frequencies noise propagates very well.
The effect of noise is that if the sensor operates at a frequency close to the noise frequency spectrum, then it must have a good signal to noise ratio for it not to be affected by pipe borne noise.
This in turn depends on the flexibility of the tube(s). More flexibility means more amplitude.
Also, the signal to noise ratio can be improved by putting more power into the signal. The result of more power is that early mass meters tended to be explosion proof rather than intrinsically safe.
However, when two ôidenticalö mass meters are operated in close proximity in connected pipe work, we have a phenomena known as ôcrosstalkö.
This is where the transmitted vibration created by one meter allows it to couple with the second meter. The two meters then tend to run at the same drive frequency irrespective of the density of the fluid within the meters.

This problem can be more prevalent when the drive signal power is higher to obtain better signal to noise ratios. The drive signals tend to propagate through the pipeline very well and persist at a higher amplitude than the background noise.
Some manufacturers overcame this problem by deliberately loading (adding mass) to one of the sensors so that they tend to run at different resonant frequencies.
With density meters or mass meters operating at higher frequencies, the signal from the sensor is far more rapidly attenuated in the pipe work connecting them, and cross talk is not a problem even when they are in very close proximity.
  • If the temperature changes there is a change in the Youngs modulus (stiffness) of the sensor materials. In fiscal measurement, at least one manufacturer uses NiSpan C as this has a very low temperature constant (about ten times better than stainless steel). Choice of materials can affect the performance.
  • temperature also causes a change in geometry; as temperature increases the tube expands to contain more volume of fluid.
  • The tube expands lengthways as well. This increases the compression forces along the axis, which also affects the density. In bent tube mass meters this is possibly not as bad as we might otherwise expect since the tube geometry is quite flexible. In straight tube sensors it can be very significant. In the Solartron tube density meter the vibrating tube has isolation bellows at either end which serve two functions, the first of which is to minimize the effect of temperature on the tube.
  • As pressure increases the tube tends to stiffen
  • the tube also tends to balloon slightly and contain more volume.
  • In bent tube meters {e.g. most mass meters) pressure tends to try and make the tubes straighten out.
So temperature and pressure effects are manifold. We have changes to the enclosed volume and changes in tube stiffness.
Velocity of sound effects
Velocity of sound effects are important for two reasons, but will not be discussed in detail here.
  • effect on the measured density; this is mostly neglected except for fiscal measurements and where the fluids are of low density, such as light hydrocarbons. The velocity of sound effect is unique to each fluid. It is also an important measurement in distilling and brewing and in some other liquid applications where some density meter manufacturers incorporate ultrasonic sensors to measure the velocity of sound in the fluid. In hydrocarbon service the velocity of sound is characterized for the principal fluid types.
  • Velocity of sound is also important when dealing with very low volumes of entrained gas
In low concentrations it can lead to instability. Air also tends to migrate to the tube walls, effectively isolating the liquid from the tubes. More on bubbles later, as this is not something accounted for in the calibration or software of standard digital density meters.
Viscosity effects:
The resonant frequency is a function of the density. However, the resonant frequency is less as viscosity increases. For many sensors the sensitivity to viscosity effects is quite low. In tube systems it is often not significant but in fork or rod types the effect can be pronounced. Some vibrating element density meters have a severely curtailed density range.
This effect is very sensor dependent. In one type of fork sensor the maximum viscosity is 500cP. In another, 20,000 cp or higher. Viscosity affects the working range and can introduce a density offset.

Fluid effects
We have considered the effects of temperature and pressure on the sensor.
Now we must consider the effects on the fluid.

  • as temperature increases, the density of the fluid decreases. This is not a linear relationship and the relationship varies from one fluid to another. In hydrocarbon service the relationship between temperature and density is well characterized and defined in API standards. For hydrocarbon service the software must incorporate this relationship. The density at 15degC (or 60degF) is found using an iterative equation. The number of iterative steps involved and the rounding of the calculation is defined in the standard. The software must conform to the requirements of the standard.
  • Where the fluids are not hydrocarbons and where the relationship is not characterized by an equation, alternative methods are required. Most typically these involve a variety of techniques which incorporate data from temperature density tables for the fluid or which depend on in-situ calibration of the algorithm employed. A typical approach is to establish a family of reference curves and to use a method of ratios to find the density at 15degC (60degF).
  • Fluids are often sufficiently compressible under pressure for this to become significant. The API density relationship therefore incorporates a pressure correction into the temperature density relationship.
  • For many other fluids the effect is not documented, even if it is significant enough to require correction. Often the operating pressure does not vary significantly and this effect may be noticed only as an offset and is simply corrected by applying an offset correction.
  • For most applications the fluid pressure effects are negligible and may be ignored.
From all the preceding we can see that density measurement is not a simple exercise if we are interested in accuracy. The reason many of the effects are considered significant is that the density of a liquid does not vary significantly anyway. This means that good resolution is vital and that the errors must be accounted for.

Note this early expression of density accuracy for a mass meter: +/-0.001gm/cc.
That seems pretty accurate?
But not usually accurate enough to worry about many of the effects discussed as they are often an order or two less significant.
Good dedicated density meters may quote a typical accuracy as: +/-1.0kg/m3.
Actually, that is pretty good; it is +/-0.0001gm/cc and easily achieved by many good density meters. In fiscal applications we can even see +/-0.15kg/m3 and now we are in among the same order of magnitude as many of the effects we have noted.

There is an important point to note when comparing sensors. Many sensors when comparing their published specifications, (whether mass meters or dedicated Density sensors) can appear to perform as well as each other. This is because they show only the performance at the calibration conditions.
It is vital, in critical density applications, to establish how they compare when fluid density varies with fluid quality and under the process conditions, taking account of the effects of temperature, pressure, etc.

When we consider the improvements in performance of mass meters as density measurement systems what we see is rarely the result of any change to the sensor design or manufacturing procedure.
Almost always, what we see is the result of improved calibration, taking greater account of the factors affecting the density performance, and more sophisticated software. The only exception would be the early change to phase lock loop drive.
This is also true of many density meters.

From this we should recognise that when we seek to compare mass meters with density meters as density measurement devices, we will see a wide range of capabilities in all of them. It is only when we compare the best performing of either that we find these devices can be fairly close in performance.

The majority of applications will not require the full capability of the best devices. But this is a problem the user must resolve, how to find and evaluate the cost/benefit of each product on offer. This requires an informed questioning of the suppliers.

Before we leave this area, we should consider the one major process problem that affects digital density meters and mass meters alike.

Problems with density measurement:
Entrained Gas


applications involving negligible amounts of entrained gas ù even as little as 2 percent volume ù have been poor candidates for Coriolis measurement.
and again


Our own analysis shows that up to 92 percent of all Coriolis measurement problems are due to entrained air or gas, yet in the vast majority of cases two-phase flow is not even recognized as the problem.
Wade Mattar; Invensys/Foxboro(http://www.automationtechies.com/sitepages/pid1353.php)
Even small amounts of bubbles, little enough to make an effect on the actual density, can disturb the operation of a vibrating element sensor (an many other types of density sensors). As the concentration increases the frequency becomes increasingly unstable and, in some sensors, the effect can be such that the sensor loses lock on the resonant frequency.
Velocity of sound effects are thought to have some effect here and in some designs, though the phenomena is not well enough investigated for a full understanding. Bubbles can also migrate to the tube walls where they insulate the sensor motion from the liquid.
There are many applications where bubbles are an important part of the process, such as coffee extract to spray dryers, and not just a contaminant. There are some solutions available to dedicated density meters such as operating at a different harmonic of the resonant frequency. The effects are often dramatic. Operating at a different harmonic may lose some accuracy but provides stability from 0% gas to 100% gas, invaluable in many applications here entrained gas is important.
In coffee extract where CO2 etc may be present in very significant amounts (the gas is what helps produce the ôgranularö form of instant coffee) density is a very important measurement.

This isnÆt the end of our consideration of mass meters as density meters, or indeed, of density meters since all must be judged as digital density meters irrespective of if they are also mass meters.
We can now measure the density at the process temperature and we can find the density at a reference temperature.
There are many applications where the density isnÆt what we are interested in.
Density is an indicator parameter that has a defined relationship with some other parameter. It could be we want to know the % solids in a slurry, the %mass or %volume of a mixture or solution.
The relationship between density at the reference temperature and the parameter is not linear either. To be sure, if the value varies vary little or we are using closed loop control to maintain a constant quality, then we could use the density as it stands or apply a linear relationship for the small range of variability. If we are interested in the varying quality over a range of conditions then we may need some algorithms in the software that we can use to model the density relationship to our parameter.
Many sensors do include such algorithms either as dedicated functions (° Brix, ° Twaddle, % Mass etc) or they may include a general equation which can be configured by the user.

A typical application: Caustic dilution
Many process plant operators use caustic cleaning solutions around the plant.
It is usual to buy in a concentrated caustic (e.g. 47%) and store it, and then dilute it to the strength required (e.g. 23%) when it is required.

There are two ways to do this.
  • Predictive
  • Feedback
Predictive; using mass meters:
  • Determine the necessary volume or mass ratio of the concentrated caustic to water, necessary to produce a solution of the required strength.
  • The caustic is then blended by batching the correct mass proportions into a tank using mass meters, and mixing them there, or pipeline blending by using the mass meters to control the flow rate ratios in the required proportions.
  • The predictive method depends on the assumption that the quality of the concentrated caustic does not vary from one delivered batch to another. To help ensure the validity of this assumption, the quality control of the concentrated caustic is much higher and hence, costs more money.
  • The assumption too, is that the product does not stratify in the tank i.e. there are no density or concentration gradients.
Most often, these assumptions are hard to justify. These systems therefore include another mass meter, this time used for density measurement. It is installed in a recirculation loop on the 23% storage tank. Additional small mounts of caustic or water are metered in as required (with minimal temperature change due to the exothermic reaction).

Feedback using density meters (now including mass meter density measurement):
  • In the feedback method, the caustic and water are blended in the pipeline and the density measured in the pipeline after a static mixer.
  • As the density tends to vary, the signal is used to modulate the caustic or water flow control valves to maintain the correct quality.
Because the system responds to changes in caustic quality, it is no longer necessary to enforce the very strict and expensive control on the quality of the concentrated caustic. Nor is a dilute caustic storage tank required.
Caustic can be on-demand blended to the required strength.
We need not refer to the measuring device as a mass meter. It is a density measurement. It doesnÆt matter if the sensor is a primarily amass meter with a density function or a dedicated density transducer provided it is capable of the necessary performance to meet the application requirements.

Mass flow is irrelevant unless it is used to account for the 23% caustic usage, in which case it needs to be in the main line and not in a slipstream.
Caustic blending is an exothermic reaction.
This means that when we measure density, we do so at a variable process temperature. We need to separate out the density variation due to temperature from the density variation due to change in concentration.
This is vital in a pipeline blending application but in a bulk tank, we can wait till the temperature has stabilized and where the small addition made do not cause a major temperature change. Under these circumstances, in the tank, and the application performance specification permitting, even a simple density measurement could be considered.

Otherwise, whether in tank or pipeline, we need to have a method of converting the density at the variable process temperature to the density at a reference temperature. This would have required better density measurement than most early mass meters were capable of, hence the predictive method and tank correction when using mass meters.
Many modern mass meters with improved calibration and software algorithms are now capable of feedback methods.

In some cases, we also need an algorithm to convert the density at the reference temperature to concentration.

The advantages of the feedback method are that on-demand blending is possible and that the intermediate storage tank is not required. This approach is possible using density measurement only where the density meter (dedicated density or mass flow sensor derived) has sufficient performance and appropriate software.

The issue of multi-functionality is by no means clear cut.
The fact that mass meters use resonant frequency as a key to how they operate as practical process instruments is something that can readily be exploited.
The degree to which this is possible depends on the inherent capability of the sensor and the calibration and software available. The software is not a problem but the necessary calibrations add cost. This cost is rarely justified where the density is simply an extra feature of the sensor as a mass meter but is necessary where the sensor is used as a density meter. To be worth while the sensor, any sensor, must be capable of the performance required.

Density isnÆt the only extra property that can be derived from a vibrating element sensor. Other properties can also be measured but the question then is whether it is a useful measurement. When freed of the constraint to be able to measure mass flow, vibrating element sensors may all be capable of even more powerful measurements. We have already seen that operating at different harmonics results in different factors becoming more or less dominant and this, in turn, can lead to deriving more useful fluid properties .

Some density meters are also used in conjunction with other sensors such as with velocity of sound sensors in the food and beverage industry, in brewing and distilling.

Suggested reading: the FAQ on Vibrating Element Digital Viscometers.

There exists a degree of confusion regarding density measurement that is partly due to the increase in the range of types of sensor used.
It is hoped that a new ISA standard will resolve these issues and provide clear guidance on choosing density meters.
It is hoped that this new standard is now nearing completion (if it isn't already complete).
It may be useful to consider a classification system so that sensors may be more easily selected by their classification. It is to be hoped that calibration methods, and their extent and the methods used will also be codified for the clarity of interpretation.
The author hopes too, to see an end of the term "coriolis density". Whatever the value of this term was, many mass meters today compete with dedicated density meters at a very high level of performance.

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