- Email: [email protected]
On-line viscosity measurement using Coriolis mass flowmeters
On-line viscosity measurement using Coriolis mass flowmeters P. Kalotay MicroMotion Inc., 7070 Winchester Circle, Boulder, CO 80301, USA Received 5 April 1994, Revised 11 July 1994
Industrial viscometers are available in large variety to measure for both Newtonian and non-Newtonian fluids. A simple system which uses the Coriolis mass flowmeter as a capillary tube has a growing range of applications. Employing the capillary principle, the rheological properties of time-independent Newtonian fluids and some non-Newtonian fluids can be successfuly measured. The method applies readily available and proven components, namely mass flowmeters and differential pressure transducers. Basic viscosity calibration can be achieved with suitable software. To add viscosity measurement capability to an existing flowmeter site in most cases requires only the installation and connection of a suitable differential pressure transducer.
Keywords: Coriolis flowmeters; viscosity; capillary tube
Introduction All practical viscosity measurements, either laboratory or process, are based on measurement of fundamental quantities, such as force or time, under certain welldefined conditions. The equipment generally satisfies the user's requirements, and provides some measure of the rheological properties. But just as with any other measurement method or transducer, none is universally applicable. Laboratory measurements - by definition - are not achieved 'on-line' and do not represent real-time measurements. Their use is limited to those processes where sample taking and laboratory evaluation delays are acceptable. Most modern processes require instantaneous measurements, preferably on-line. In certain industries (e.g. food, chemical, pharmaceutical) some operational requirements exist that practically eliminate everything but the simplest hardware. In these cases, both on-line and in-line measurements are preferred. No currently available process viscometer can fully satisfy the requirements if an obstructionless flow path with no dead spaces is mandatory or cleanin-place (CIP) equipment is required (i.e. in sanitary processes). In the last 10-12 years Coriolis mass flowmeters (CMFs) have become popular, and their market share is steadily growing. Though they are not the least expensive of all flowmeters, their inherent advantages - direct mass flow and density measurement, and process fluid temperature indication, all provided by 0955-5986/94/04/0303-06 © 1994 Butterworth-Heinemann Ltd
one single transducer- combined with high accuracy and wide turn-down range, make them a desirable choice. They are non-intrusive, have no moving parts and can be built to satisfy sanitary regulation requirements. Long, maintenance-free lifetime is an additional benefit. Several years ago the use of capillary viscometry was suggested as an extension of the measurement capabilities of the Coriolis mass flowmeter, based on the Hagen-Poiseuille law. 1 Considering that the Coriolis flowmeter tube inner diameter is constant by design, it was a natural choice to measure the pressure drop produced by the flow tubes and to calculate the viscosity of Newtonian fluids in the laminar flow zone. While the technique produces accurate pressure drop, and therefore accurate viscosity numbers, it also turned the perceived disadvantage of the relatively high pressure drop into a useful property. The idea rapidly attracted numerous applications. Users obtained another process variable measurement with minimum expense and complexity, by adding only a differential pressure transmitter. The result is a non-intrusive viscosity measurement, on-line, in-line and without any moving parts. The layout of a typical installation is shown in Figure 1.
Theory For Newtonian fluids in the laminar flow regime (where the Reynolds number Re is below the value typical of Flow Meas. Instrum., 1994 Volume 5 Number 4
303
P. Kalotay - On-line viscosity measurement using Coriolis mass flowmeters
viscosity, is constant. This fact allows viscosity calibration at a single, preferably high, flow-rate point only. In these applications, fluid temperature is not considered, since the validity of the Hagen-Poiseuille law is not affected by temperature. Therefore the use of equation (2) for laminar Newtonian flows is justified. The CMF-based measurement produces viscosity values at line conditions.
C)
Practical considerations In practice every flowmeter installation is different. Flowmeters and differential pressure transducers are separate components; therefore the installation of these components and their positions relative to each other and to other components of the system are not strictly defined. Their location and proper installation are critical and has strong influence on the system performance. The considerations listed below are not in any specific order of importance, and depending on the application some or possibly all of them may be critical.
"-"-V I S C O S I T Y "-,-- D E N S I T Y -'-MASS FLOW Figure 1 CMF viscosity measurement for Newtonian fluids. 1: CMF (Coriolis mass flowmeter); 2: differential pressure transmitter; 3: CMF flow transmitter
the critical zone onset*) the Hagen-Poiseuille law establishes in a vertical capillary tube the relationship between pressure drop, mass flow rate and viscosity: Q =
"n"R4 gc A P
8/~L
(1)
where Q = volumetric flow rate, R = pipe inside radius, /~ -- dynamic viscosity, gc = gravitational constant, Ap = pressure drop and L = length of the capillary tube between pressure taps. Rearranging the equation: "rr R4 gc Ap P.. = Kv Ap -/~8L m Q
(2)
where rh = mass flow rate and p = density have been substituted for volumetric flow, we obtain viscosity, which is directly proportional to the pressure drop and inversely proportional to the flow rate. The effect of gravity is not to be considered in a regular installation. All mechanical parameters of the system (tube physical characteristics, installation-dependent variables) are condensed into the Kv viscosity scaling factor. For a given Newtonian fluid at a given temperature the shear-force to shear-rate ratio, or the measure of * Re numbersas high as 4000 are generallyrecommended (Moody) asthe limit for laminarflow conditions. It is MicroMotion'sexperience that the practical and safe limit is between 1150 and 2000. In most practical applications the fluid viscosity and pressure drop considerationsproduce critical Re numberswell below these somewhat undefinedvalues. 304
Flow Meas. Instrum., 1994 Volume 5 Number 4
1. The flowmeter selection must satisfy all the requirements of the measurement (Newtonian fluid, Re number, tolerable pressure drop, adequate accuracy, material compatibility, compliance with regulatory agencies and codes, etc.). 2. Transducer errors generally increase when approaching the low end of the measurement range. Differential pressure transducers are known to have limited usable measurement ranges; more so than mass flowmeters. Since the viscosity value is the ratio of the differential pressure and the flow rate, keeping these variables in a suitable narrow range ultimately results in better viscosity accuracy. 3. Location of the Ap measurement is important. The Hagen-Poiseuille equation applies to constant diameter long (capillary) tubes and fully developed flow. Constant diameter assures uniform fluid velocity and consequently constant Re number between the Ap measuring ports. The Re number is implicitly included in the K factor, and therefore it must be the same throughout the entire length of the measurement section. Any change in fluid velocity caused by tube diameter variations produces pressure changes and directly affects the viscosity measurement. 4. The elevation of the pressure ports must be controlled. Theoretically, the ports could be in different elevations and the resulting pressure difference offset could be accounted for at calibration. However, this is only true when density is constant. If the process fluid density changes, the Ap measurement accuracy will be affected. Therefore the pressure ports should be at the same elevation. 5. Finally, the design and fabrication of the pressure ports. Generally standard industrial practices and guidelines that define orifice plate differential pressure sensor installation and measurement (i.e. as in volumetric flow) must be followed to every detail. Design considerations shall also include provisions for draining, cleaning and removal of accumulated debris, deposits, air-pockets etc.
P. Kalotay - On-line viscosity measurement using Coriolis mass flowmeters
The effects of temperature The viscosity of fluids is strongly temperature-dependent. For on-line process viscosity measurement, the only temperature-related consideration is to ensure that the mass flowmeter, which is the ~P generating element, shall be in its entirety at process temperature. If the process temperature is different from the ambient temperature, heat tracing or insulation can be installed to prevent the occurrence of temperature gradients at the flow tubes. Fuel oil measurements at boilers and pumping efficiency considerations in pipeline transport are typical cases where the fluid temperature is raised above ambient. When viscosity measurement has to produce reference values, for example in quality control or process performance measurements, further temperature considerations are necessary: 1. If the temperature to viscosity relationship of the process fluid is defined, a correction can be made by solving the characteristic equation in real time. In the majority of the applications (at mostly constant flow rates) the available CMF tube temperature measurement can be used. For more precise measurements or under rapidly fluctuating temperature conditions additional in-line fluid temperature measurement is recommended. 2. If several different fluids must be measured in the same process, the compensation may require use of more than a single characteristic fluid equation, or one equation with multiple sets of constants. Suitable software (see next section) offers a solution. 3. If the temperature-viscosity relationship is not known or mathematically not defined, a series of measurements must be collected with a reference data set. The resulting temperature and viscosity values can then be stored in a look-up table. During the process measurement, the computed viscosity value is interpolated (or extrapolated) as required.
veniently stored using suitable software. This can take advantage of digital communication to transmit and receive measured process variables (i.e. mass flow, density, differential pressure, temperature) to and from a personal computer or process controller. Suitable software can perform the required calculations using predetermined calibration constants, as defined by the equation(s) and then display the computed process parameters, including viscosity, on the monitor screen. The computed final values can be transmitted digitally to any desired location and also directly converted to electrical signals (4/20 mA, etc) for process use.
Reynolds number limitations All these measurements should be performed in the laminar flow zone. As the flow rate increases, at some point flow ceases to be laminar. But there is no reliable guide to predict at what Re number the turbulence will start. It depends strongly on the rheological characteristics of the fluid. Various approximations and calculations are available to obtain the Reynolds numbers of such fluids, such as the Bingham and power laws, in this critical zone. These Reynolds numbers may be as low as NRe=1150. At NRe=4000 almost all fluid flows are turbulent in the process environment. This is the upper limit of the transition zone. In this critical zone, between the end of laminar flow and the onset of the turbulent flow, no reliable viscosity measurement can be accomplished using the capillary method. Once the flow becomes fully developed turbulent flow, the viscosity measurement can be reliable, but the tube/pipe physical parameters will have a strong influence. Virtually every case is unique. Non-Newtonian fluids are generally, but not always, of relatively higher viscosity, so that Reynolds numbers remain low even at relatively high flow rates. During the design of the viscometer system the critical Re number must be determined with the applicable formulae.
Use of software Current commercial flowmeter transmitters solve a linear equation. More complex calculations require added computing power. Temperature characterizations (at constant shear rate) generally require solving an exponential (Arrhenius) equation. Interpolation between measured and stored values is also needed. For shear-sensitive (non-Newtonian) fluids the situation is more complex. Not only does temperature affect viscosity, but viscosity varies with flow rate as well. The measured viscosity is a function of both varying parameters. Approximate theories exist for some fluids, but there is no universally accepted approach useful in every case. It is relatively simple to create a temperature to viscosity or shear rate to viscosity matrix for those fluids that can be handled in open systems. Laboratory rotary viscometers are best suited to produce the required readings. In all other cases, depending on available options, other methods must be designed to collect the data. Temperature and shear rate models can be con-
Sanitary measurements There is another area where the CMF-based viscosity measurement is unique: sanitary installations. Based on available information, no existing process viscometer can fully satisfy agency requirements for CIP (clean-inplace) installations while being obstructionless and with no moving parts. Most CMFs are available with sanitary approvals. By using regular coaxial process isolators (Figure 2), a sanitary differential pressure measurement can be made while complying with agency approval requirements. The process isolators (two per system) separate the sanitary process from the differential pressure transmitter diaphragms and transmit the process line pressures sensed by the fluid that is contained between the solid body and the thin steel liner - via the oil-fill, shown by the heavy line. In addition most differential pressure transducers can be combined with diaphragm-type remote seals and used in certain sanitary systems. The concentric process isolators are available and are recommended for pipe sizes up to 75 mm (3 in) diameter. With larger Flow Meas. Instrum., 1994 Volume 5 Number 4
305
P. Kalotay - On-line viscosity measurement using Coriolis mass flowmeters
TO DP ANSMI TTER
f CUTAWAY
,~
I/I.,'I I[/1
O,L FiLL~Lz'I~I. ~z#
"~
/-STAINLESS ! STEEL
PRESSURE
may not be available, or it may not be suitable for calibration in open systems due to safety considerations. Gravimetric calibrations are done in open systems. [] System accuracy is strongly influenced by minor installation and construction details. Most obvious of all are the location and installation of the pressure taps or mounting of the flowmeter etc. It is not practical to construct or duplicate an entire flow section, including upstream and downstream piping with pressure taps, at any place but at the final installation. Even if the installation could be duplicated, process fluid limitations could prohibit most calibrations at the flowmeter manufacturer's laboratory. Therefore the only practical choice is field calibration. This approach is based on the assumption that the user knows the process fluid and its viscosity at well-defined line conditions. When the reference viscosity is measured, with temperature and shear effects compensated for, it is the precision of the characteristic equations that determines the system accuracy.
Calibration with Newtonian fluids
Figure 2 Process isolator cross-section (two per system)
diameters, diaphragm-type remote seals can be used successfully. The location of the seal and its design requires some special considerations to satisfy the requirements for identical upstream and downstream fluid velocities.
The calibration process Since the CMF measures mass flow and fluid density directly with very high accuracy, volumetric flow rate can also be calculated. Having volumetric and mass flow rate values available, it is the user's choice whether to measure dynamic viscosity (/~) or kinematic viscosity (v). The dynamic viscosity measurement is based on volumetric flow while kinematic viscosity is computed from mass flow. The choice can be made during the characterization or calibration of the system and can be changed any time. The main components of the system, the mass flowmeter and the differential pressure transducer, are factory-calibrated over their entire specified range. If required, they can be calibrated specifically for the projected operating range. The viscosity measurement, however, cannot be factory-calibrated for the following reasons: [] Most mass flowmeter calibrations are gravimetric, performed with water at ambient temperature. The low viscosity of water results in high Reynolds numbers and turbulent flow at most of the customerspecified flow rates, making viscosity calibration impossible. Calibration equipment using higher viscosity fluids is not readily available. [] Due to its proprietary composition, the process fluid 306
Flow Meas. Instrum., 1994 Volume 5 Number 4
The field-calibration process for Newtonian fluids is rather simple. 'SMART' transducers can be used that communicate digitally, simplifying interconnections. New models of CMF transmitters can also accept 4/ 20 mA process signals from ordinary (i.e. not SMART) differential pressure sensors and digitize the readings to compute viscosity sharing the microprocessor. There are no potentiometers or controls requiring manual adjustments; all system parameters and constants are entered and handled digitally. The user can have access to the setup functions either by using the hand-held data terminals common to all SMART transmitters or through the process control computer that runs the software. This software can contain also all the functions of a hand-held calibrator/communicator. The choice between absolute and kinematic viscosity measurement is made at this point. Once flow has started, the mass flow transmitter produces a viscosity reading based on a factory-supplied default value, using the initial Kv value of unity. The indicated viscosity will probably be well below the actual online viscosity value. At this point the user can enter the actual, known line viscosity in the selected units. The transmitter then can calculate the new Kv value and update the viscosity measurement, based on this last entry. No additional adjustment or trim is required. The newly entered Kv value can be maintained in nonvolatile memory. Entered values can be changed any time should the need arise, using the procedure just described. The computed viscosity can appear as a 4/20 or 0/20 mA output signal that can be independently set up and trimmed digitally as required. In addition, the digital viscosity value, along with all the other measured or computed process parameters, can be made available in several different communication protocols. The flow transmitter can output Bell 202 physical layer signals at 1200 baud, superimposed on the mA
P. Kalotay - On-line viscosity measurement using Coriolis mass flowmeters
signal or the RS-485 physical layer from 1.2 to 38.4 kbaud. The transmitter can also produce HART compatible signals over the Bell 202 or RS-485 connection, the MODBUS protocol over the RS-485 connection or even HART signals over the Bell 202 and MODBUS signals over the RS-485 simultaneously.
Non-Newtonian fluids The system can be used to measure the viscosity of non-Newtonian fluids as well, if the characteristic equation is available, using suitable software. The selected equation modifies the measured viscosity value to account for shear stress effects. The calibration for on-line viscosity measurement of non-Newtonian fluids is minimally more complicated than Newtonian fluid calibration. [] If a characteristic equation is available, the calibration process can consist of a single-point calibration under known conditions and the entering of the required coefficients into the selected formula. To determine the coefficients some preliminary testing or investigation of the fluid must be made. If the process fluid can be characterized with a laboratory process, scaled measurements can derive the shear rate to viscosity relationship. Similar tests can also be made to obtain temperature to viscosity characteristics. Once the data is available and the calibration has been performed, the system performance should be verified. [] The flow rate-dependent non-linearity of the viscosity can be approximated by employing a two-point calibration. This allows the positioning of a best-fit straight line over the shear force to shear rate curve. The calibration process can be similar to the singlepoint process, with the exception that the calibration must be performed at two different flow rates, using the same fluid, at the same temperature. The slope and the offset of the best-fit straight line can be automatically determined. This two-point calibration process can also be used to correct any other irregularity or deviation of a system that can be modelled by an offset linear function. This second approach cannot provide the accuracy that can be obtained by solving the proper equation. Numerous handbooks discuss various fluids and their rheologies to great detail. Some of the best practical help can be found in the works of Patton 2 and Steffe~ and in their literature references, even though most of these texts were written for certain specific industries.
over a 10:1 flow rate and a 10:1 viscosity range, at controlled constant temperature. Installations without process temperature controls and Newtonian fluids were generally within 2% of reading, even when the temperature characterization included extrapolation outside of the actual measurement range. Figure 3 shows viscosity and temperature data collected in a non-Newtonian fluid measurement. The viscosity (25-27 cPs) varies as a function of temperature (102-104 °F). The fluid flow rates varies between 200 and 1100 g s-~ during the test. The full-scale calibrated range in this application was 100 cPs. Another example is the implementation of the ASTM 341 D method for lube material characterization. This standard method allows the viscosity measurement of any lubrication blend product and projects the final product viscosity for two reference temperatures. Results obtained in an installation are shown in Figures 4 and 5. Figure 4 graphically depicts data collected by another user over a 4 month period in a high-volume blending operation. The products had an average viscosity around 10.3 cSt, somewhat varying as the blend recipe dictated. Every production batch was dripsampled and laboratory tested with a Cannon viscometer at a constant temperature. The viscosity measurement was taken on-line, and the reference viscosity computed using suitable software. Both measurement results and the error between the laboratory and the on-line measurement are shown for every product batch. The data shown in Figure 5 was taken at the same location, with additional products included. The measured viscosities varied between 10 and 430 cSt. The evaluation method was identical, using the Cannon reference. Due to the close agreement of the two measurements, the graph lines are practically on top of each other, except for the second high-viscosity batch, where the difference is visible and responsible for the nearly 2% of reading error. It is our experience that reduced precision is primarily caused by temperature measurement errors, 30.0
110
1{@ 27.0
lO6
107 24.0
100
lO5 21.0
lO4
Performance At the time of writing (December 1993) well over 100 CMF viscometer installations are operational, with many more in the construction or testing phase. In some installations the viscosity measurement is part of a closed process control loop. Operational and performance data are available for some installations from the users. With reliable and accurate final calibrations a precision better than 1% of reading is achievable for Newtonian fluids in laminar flow conditions, generally
f
100
18.0
lOI 15.0 1000 1100 1200 1300 1400 TIME (S)
Figure 3 Continuous on-line viscosity measurement. Volumetric flow varies between 200 and 11 cm 3 rain- 1: m , viscosity; - - , temperature Flow Meas. Instrum., 1994 Volume 5 Number 4
31)7
P. Kalotay - On-line viscosity measurement using Coriolis mass flowmeters
10.75
- 1.4
550 -
-I.2
500-
-1
480
- 0.8
400 -
3
[email protected] I0,r~10.5 -
- O.IS 360-
I0.46
+
o,
-
AN
5
10.4 -
-02 •-1.1~16 ~.
i0.':~ 10,3 10~";
--0.2
-
10.2 -
i
,~,
•-0.4
10.15 ~.0 10.1 10.06 I0
1'o
t ,~ ~ ~ ~ ,~ ";' i ~ l~+'11'21'31~l'51'e'l~'¢el'9~l"l BATCHES
1'5
~
~
a~
~
,ib
~.0
BATCHES
Figure 4 Laboratory vs. on-line viscosity measurements on a single product. Data collected over a four-month period: C), laboratory viscometer, II, MicroMotion; *, percentage error
Figure 5 Laboratory vs. on-line viscosity measurements of various products, between 10 and 450 cSt viscosity over a four-month period. Symbols as in Figure 4
time lag in the measurement and inadequate modelling or characterization of the process fluid. A significant percentage of all users do not calibrate the system to read in a given viscosity unit, but simply 'tune' their process to a certain indicated value, which in their experience is optimal to obtain the final product quality. Non-Newtonian fluids are most often measured in this manner.
of the drawbacks of sampling or other in-line system approaches. Low or no maintenance operation along with high-accuracy flow, density and viscosity measurement offers new solutions to old problems and numerous new applications as well, where previously other viscometers have failed.
Conclusion
The old capillary principle applied to direct mass flow metering provides low-cost and reliable on-line viscosity measurement for industrial processes, eliminating most
308
Flow Meas. Instrum., 1994 Volume 5 Number 4
References
1 Good Vibrations, MicroMotion Inc. Application Note No.IO, 1989 2 Patton, T. C. 'Paint flow and pigment dispersion', WileyInterscience, New York, 1979 3 Steffe, F. J. 'Rheological methods in food process engineering', Freeman Press, East Lansing, Michigan, 1992
Industrial viscometers are available in large variety to measure for both Newtonian and non-Newtonian fluids. A simple system which uses the Coriolis mass flowmeter as a capillary tube has a growing range of applications. Employing the capillary principle, the rheological properties of time-independent Newtonian fluids and some non-Newtonian fluids can be successfuly measured. The method applies readily available and proven components, namely mass flowmeters and differential pressure transducers. Basic viscosity calibration can be achieved with suitable software. To add viscosity measurement capability to an existing flowmeter site in most cases requires only the installation and connection of a suitable differential pressure transducer.
Keywords: Coriolis flowmeters; viscosity; capillary tube
Introduction All practical viscosity measurements, either laboratory or process, are based on measurement of fundamental quantities, such as force or time, under certain welldefined conditions. The equipment generally satisfies the user's requirements, and provides some measure of the rheological properties. But just as with any other measurement method or transducer, none is universally applicable. Laboratory measurements - by definition - are not achieved 'on-line' and do not represent real-time measurements. Their use is limited to those processes where sample taking and laboratory evaluation delays are acceptable. Most modern processes require instantaneous measurements, preferably on-line. In certain industries (e.g. food, chemical, pharmaceutical) some operational requirements exist that practically eliminate everything but the simplest hardware. In these cases, both on-line and in-line measurements are preferred. No currently available process viscometer can fully satisfy the requirements if an obstructionless flow path with no dead spaces is mandatory or cleanin-place (CIP) equipment is required (i.e. in sanitary processes). In the last 10-12 years Coriolis mass flowmeters (CMFs) have become popular, and their market share is steadily growing. Though they are not the least expensive of all flowmeters, their inherent advantages - direct mass flow and density measurement, and process fluid temperature indication, all provided by 0955-5986/94/04/0303-06 © 1994 Butterworth-Heinemann Ltd
one single transducer- combined with high accuracy and wide turn-down range, make them a desirable choice. They are non-intrusive, have no moving parts and can be built to satisfy sanitary regulation requirements. Long, maintenance-free lifetime is an additional benefit. Several years ago the use of capillary viscometry was suggested as an extension of the measurement capabilities of the Coriolis mass flowmeter, based on the Hagen-Poiseuille law. 1 Considering that the Coriolis flowmeter tube inner diameter is constant by design, it was a natural choice to measure the pressure drop produced by the flow tubes and to calculate the viscosity of Newtonian fluids in the laminar flow zone. While the technique produces accurate pressure drop, and therefore accurate viscosity numbers, it also turned the perceived disadvantage of the relatively high pressure drop into a useful property. The idea rapidly attracted numerous applications. Users obtained another process variable measurement with minimum expense and complexity, by adding only a differential pressure transmitter. The result is a non-intrusive viscosity measurement, on-line, in-line and without any moving parts. The layout of a typical installation is shown in Figure 1.
Theory For Newtonian fluids in the laminar flow regime (where the Reynolds number Re is below the value typical of Flow Meas. Instrum., 1994 Volume 5 Number 4
303
P. Kalotay - On-line viscosity measurement using Coriolis mass flowmeters
viscosity, is constant. This fact allows viscosity calibration at a single, preferably high, flow-rate point only. In these applications, fluid temperature is not considered, since the validity of the Hagen-Poiseuille law is not affected by temperature. Therefore the use of equation (2) for laminar Newtonian flows is justified. The CMF-based measurement produces viscosity values at line conditions.
C)
Practical considerations In practice every flowmeter installation is different. Flowmeters and differential pressure transducers are separate components; therefore the installation of these components and their positions relative to each other and to other components of the system are not strictly defined. Their location and proper installation are critical and has strong influence on the system performance. The considerations listed below are not in any specific order of importance, and depending on the application some or possibly all of them may be critical.
"-"-V I S C O S I T Y "-,-- D E N S I T Y -'-MASS FLOW Figure 1 CMF viscosity measurement for Newtonian fluids. 1: CMF (Coriolis mass flowmeter); 2: differential pressure transmitter; 3: CMF flow transmitter
the critical zone onset*) the Hagen-Poiseuille law establishes in a vertical capillary tube the relationship between pressure drop, mass flow rate and viscosity: Q =
"n"R4 gc A P
8/~L
(1)
where Q = volumetric flow rate, R = pipe inside radius, /~ -- dynamic viscosity, gc = gravitational constant, Ap = pressure drop and L = length of the capillary tube between pressure taps. Rearranging the equation: "rr R4 gc Ap P.. = Kv Ap -/~8L m Q
(2)
where rh = mass flow rate and p = density have been substituted for volumetric flow, we obtain viscosity, which is directly proportional to the pressure drop and inversely proportional to the flow rate. The effect of gravity is not to be considered in a regular installation. All mechanical parameters of the system (tube physical characteristics, installation-dependent variables) are condensed into the Kv viscosity scaling factor. For a given Newtonian fluid at a given temperature the shear-force to shear-rate ratio, or the measure of * Re numbersas high as 4000 are generallyrecommended (Moody) asthe limit for laminarflow conditions. It is MicroMotion'sexperience that the practical and safe limit is between 1150 and 2000. In most practical applications the fluid viscosity and pressure drop considerationsproduce critical Re numberswell below these somewhat undefinedvalues. 304
Flow Meas. Instrum., 1994 Volume 5 Number 4
1. The flowmeter selection must satisfy all the requirements of the measurement (Newtonian fluid, Re number, tolerable pressure drop, adequate accuracy, material compatibility, compliance with regulatory agencies and codes, etc.). 2. Transducer errors generally increase when approaching the low end of the measurement range. Differential pressure transducers are known to have limited usable measurement ranges; more so than mass flowmeters. Since the viscosity value is the ratio of the differential pressure and the flow rate, keeping these variables in a suitable narrow range ultimately results in better viscosity accuracy. 3. Location of the Ap measurement is important. The Hagen-Poiseuille equation applies to constant diameter long (capillary) tubes and fully developed flow. Constant diameter assures uniform fluid velocity and consequently constant Re number between the Ap measuring ports. The Re number is implicitly included in the K factor, and therefore it must be the same throughout the entire length of the measurement section. Any change in fluid velocity caused by tube diameter variations produces pressure changes and directly affects the viscosity measurement. 4. The elevation of the pressure ports must be controlled. Theoretically, the ports could be in different elevations and the resulting pressure difference offset could be accounted for at calibration. However, this is only true when density is constant. If the process fluid density changes, the Ap measurement accuracy will be affected. Therefore the pressure ports should be at the same elevation. 5. Finally, the design and fabrication of the pressure ports. Generally standard industrial practices and guidelines that define orifice plate differential pressure sensor installation and measurement (i.e. as in volumetric flow) must be followed to every detail. Design considerations shall also include provisions for draining, cleaning and removal of accumulated debris, deposits, air-pockets etc.
P. Kalotay - On-line viscosity measurement using Coriolis mass flowmeters
The effects of temperature The viscosity of fluids is strongly temperature-dependent. For on-line process viscosity measurement, the only temperature-related consideration is to ensure that the mass flowmeter, which is the ~P generating element, shall be in its entirety at process temperature. If the process temperature is different from the ambient temperature, heat tracing or insulation can be installed to prevent the occurrence of temperature gradients at the flow tubes. Fuel oil measurements at boilers and pumping efficiency considerations in pipeline transport are typical cases where the fluid temperature is raised above ambient. When viscosity measurement has to produce reference values, for example in quality control or process performance measurements, further temperature considerations are necessary: 1. If the temperature to viscosity relationship of the process fluid is defined, a correction can be made by solving the characteristic equation in real time. In the majority of the applications (at mostly constant flow rates) the available CMF tube temperature measurement can be used. For more precise measurements or under rapidly fluctuating temperature conditions additional in-line fluid temperature measurement is recommended. 2. If several different fluids must be measured in the same process, the compensation may require use of more than a single characteristic fluid equation, or one equation with multiple sets of constants. Suitable software (see next section) offers a solution. 3. If the temperature-viscosity relationship is not known or mathematically not defined, a series of measurements must be collected with a reference data set. The resulting temperature and viscosity values can then be stored in a look-up table. During the process measurement, the computed viscosity value is interpolated (or extrapolated) as required.
veniently stored using suitable software. This can take advantage of digital communication to transmit and receive measured process variables (i.e. mass flow, density, differential pressure, temperature) to and from a personal computer or process controller. Suitable software can perform the required calculations using predetermined calibration constants, as defined by the equation(s) and then display the computed process parameters, including viscosity, on the monitor screen. The computed final values can be transmitted digitally to any desired location and also directly converted to electrical signals (4/20 mA, etc) for process use.
Reynolds number limitations All these measurements should be performed in the laminar flow zone. As the flow rate increases, at some point flow ceases to be laminar. But there is no reliable guide to predict at what Re number the turbulence will start. It depends strongly on the rheological characteristics of the fluid. Various approximations and calculations are available to obtain the Reynolds numbers of such fluids, such as the Bingham and power laws, in this critical zone. These Reynolds numbers may be as low as NRe=1150. At NRe=4000 almost all fluid flows are turbulent in the process environment. This is the upper limit of the transition zone. In this critical zone, between the end of laminar flow and the onset of the turbulent flow, no reliable viscosity measurement can be accomplished using the capillary method. Once the flow becomes fully developed turbulent flow, the viscosity measurement can be reliable, but the tube/pipe physical parameters will have a strong influence. Virtually every case is unique. Non-Newtonian fluids are generally, but not always, of relatively higher viscosity, so that Reynolds numbers remain low even at relatively high flow rates. During the design of the viscometer system the critical Re number must be determined with the applicable formulae.
Use of software Current commercial flowmeter transmitters solve a linear equation. More complex calculations require added computing power. Temperature characterizations (at constant shear rate) generally require solving an exponential (Arrhenius) equation. Interpolation between measured and stored values is also needed. For shear-sensitive (non-Newtonian) fluids the situation is more complex. Not only does temperature affect viscosity, but viscosity varies with flow rate as well. The measured viscosity is a function of both varying parameters. Approximate theories exist for some fluids, but there is no universally accepted approach useful in every case. It is relatively simple to create a temperature to viscosity or shear rate to viscosity matrix for those fluids that can be handled in open systems. Laboratory rotary viscometers are best suited to produce the required readings. In all other cases, depending on available options, other methods must be designed to collect the data. Temperature and shear rate models can be con-
Sanitary measurements There is another area where the CMF-based viscosity measurement is unique: sanitary installations. Based on available information, no existing process viscometer can fully satisfy agency requirements for CIP (clean-inplace) installations while being obstructionless and with no moving parts. Most CMFs are available with sanitary approvals. By using regular coaxial process isolators (Figure 2), a sanitary differential pressure measurement can be made while complying with agency approval requirements. The process isolators (two per system) separate the sanitary process from the differential pressure transmitter diaphragms and transmit the process line pressures sensed by the fluid that is contained between the solid body and the thin steel liner - via the oil-fill, shown by the heavy line. In addition most differential pressure transducers can be combined with diaphragm-type remote seals and used in certain sanitary systems. The concentric process isolators are available and are recommended for pipe sizes up to 75 mm (3 in) diameter. With larger Flow Meas. Instrum., 1994 Volume 5 Number 4
305
P. Kalotay - On-line viscosity measurement using Coriolis mass flowmeters
TO DP ANSMI TTER
f CUTAWAY
,~
I/I.,'I I[/1
O,L FiLL~Lz'I~I. ~z#
"~
/-STAINLESS ! STEEL
PRESSURE
may not be available, or it may not be suitable for calibration in open systems due to safety considerations. Gravimetric calibrations are done in open systems. [] System accuracy is strongly influenced by minor installation and construction details. Most obvious of all are the location and installation of the pressure taps or mounting of the flowmeter etc. It is not practical to construct or duplicate an entire flow section, including upstream and downstream piping with pressure taps, at any place but at the final installation. Even if the installation could be duplicated, process fluid limitations could prohibit most calibrations at the flowmeter manufacturer's laboratory. Therefore the only practical choice is field calibration. This approach is based on the assumption that the user knows the process fluid and its viscosity at well-defined line conditions. When the reference viscosity is measured, with temperature and shear effects compensated for, it is the precision of the characteristic equations that determines the system accuracy.
Calibration with Newtonian fluids
Figure 2 Process isolator cross-section (two per system)
diameters, diaphragm-type remote seals can be used successfully. The location of the seal and its design requires some special considerations to satisfy the requirements for identical upstream and downstream fluid velocities.
The calibration process Since the CMF measures mass flow and fluid density directly with very high accuracy, volumetric flow rate can also be calculated. Having volumetric and mass flow rate values available, it is the user's choice whether to measure dynamic viscosity (/~) or kinematic viscosity (v). The dynamic viscosity measurement is based on volumetric flow while kinematic viscosity is computed from mass flow. The choice can be made during the characterization or calibration of the system and can be changed any time. The main components of the system, the mass flowmeter and the differential pressure transducer, are factory-calibrated over their entire specified range. If required, they can be calibrated specifically for the projected operating range. The viscosity measurement, however, cannot be factory-calibrated for the following reasons: [] Most mass flowmeter calibrations are gravimetric, performed with water at ambient temperature. The low viscosity of water results in high Reynolds numbers and turbulent flow at most of the customerspecified flow rates, making viscosity calibration impossible. Calibration equipment using higher viscosity fluids is not readily available. [] Due to its proprietary composition, the process fluid 306
Flow Meas. Instrum., 1994 Volume 5 Number 4
The field-calibration process for Newtonian fluids is rather simple. 'SMART' transducers can be used that communicate digitally, simplifying interconnections. New models of CMF transmitters can also accept 4/ 20 mA process signals from ordinary (i.e. not SMART) differential pressure sensors and digitize the readings to compute viscosity sharing the microprocessor. There are no potentiometers or controls requiring manual adjustments; all system parameters and constants are entered and handled digitally. The user can have access to the setup functions either by using the hand-held data terminals common to all SMART transmitters or through the process control computer that runs the software. This software can contain also all the functions of a hand-held calibrator/communicator. The choice between absolute and kinematic viscosity measurement is made at this point. Once flow has started, the mass flow transmitter produces a viscosity reading based on a factory-supplied default value, using the initial Kv value of unity. The indicated viscosity will probably be well below the actual online viscosity value. At this point the user can enter the actual, known line viscosity in the selected units. The transmitter then can calculate the new Kv value and update the viscosity measurement, based on this last entry. No additional adjustment or trim is required. The newly entered Kv value can be maintained in nonvolatile memory. Entered values can be changed any time should the need arise, using the procedure just described. The computed viscosity can appear as a 4/20 or 0/20 mA output signal that can be independently set up and trimmed digitally as required. In addition, the digital viscosity value, along with all the other measured or computed process parameters, can be made available in several different communication protocols. The flow transmitter can output Bell 202 physical layer signals at 1200 baud, superimposed on the mA
P. Kalotay - On-line viscosity measurement using Coriolis mass flowmeters
signal or the RS-485 physical layer from 1.2 to 38.4 kbaud. The transmitter can also produce HART compatible signals over the Bell 202 or RS-485 connection, the MODBUS protocol over the RS-485 connection or even HART signals over the Bell 202 and MODBUS signals over the RS-485 simultaneously.
Non-Newtonian fluids The system can be used to measure the viscosity of non-Newtonian fluids as well, if the characteristic equation is available, using suitable software. The selected equation modifies the measured viscosity value to account for shear stress effects. The calibration for on-line viscosity measurement of non-Newtonian fluids is minimally more complicated than Newtonian fluid calibration. [] If a characteristic equation is available, the calibration process can consist of a single-point calibration under known conditions and the entering of the required coefficients into the selected formula. To determine the coefficients some preliminary testing or investigation of the fluid must be made. If the process fluid can be characterized with a laboratory process, scaled measurements can derive the shear rate to viscosity relationship. Similar tests can also be made to obtain temperature to viscosity characteristics. Once the data is available and the calibration has been performed, the system performance should be verified. [] The flow rate-dependent non-linearity of the viscosity can be approximated by employing a two-point calibration. This allows the positioning of a best-fit straight line over the shear force to shear rate curve. The calibration process can be similar to the singlepoint process, with the exception that the calibration must be performed at two different flow rates, using the same fluid, at the same temperature. The slope and the offset of the best-fit straight line can be automatically determined. This two-point calibration process can also be used to correct any other irregularity or deviation of a system that can be modelled by an offset linear function. This second approach cannot provide the accuracy that can be obtained by solving the proper equation. Numerous handbooks discuss various fluids and their rheologies to great detail. Some of the best practical help can be found in the works of Patton 2 and Steffe~ and in their literature references, even though most of these texts were written for certain specific industries.
over a 10:1 flow rate and a 10:1 viscosity range, at controlled constant temperature. Installations without process temperature controls and Newtonian fluids were generally within 2% of reading, even when the temperature characterization included extrapolation outside of the actual measurement range. Figure 3 shows viscosity and temperature data collected in a non-Newtonian fluid measurement. The viscosity (25-27 cPs) varies as a function of temperature (102-104 °F). The fluid flow rates varies between 200 and 1100 g s-~ during the test. The full-scale calibrated range in this application was 100 cPs. Another example is the implementation of the ASTM 341 D method for lube material characterization. This standard method allows the viscosity measurement of any lubrication blend product and projects the final product viscosity for two reference temperatures. Results obtained in an installation are shown in Figures 4 and 5. Figure 4 graphically depicts data collected by another user over a 4 month period in a high-volume blending operation. The products had an average viscosity around 10.3 cSt, somewhat varying as the blend recipe dictated. Every production batch was dripsampled and laboratory tested with a Cannon viscometer at a constant temperature. The viscosity measurement was taken on-line, and the reference viscosity computed using suitable software. Both measurement results and the error between the laboratory and the on-line measurement are shown for every product batch. The data shown in Figure 5 was taken at the same location, with additional products included. The measured viscosities varied between 10 and 430 cSt. The evaluation method was identical, using the Cannon reference. Due to the close agreement of the two measurements, the graph lines are practically on top of each other, except for the second high-viscosity batch, where the difference is visible and responsible for the nearly 2% of reading error. It is our experience that reduced precision is primarily caused by temperature measurement errors, 30.0
110
1{@ 27.0
lO6
107 24.0
100
lO5 21.0
lO4
Performance At the time of writing (December 1993) well over 100 CMF viscometer installations are operational, with many more in the construction or testing phase. In some installations the viscosity measurement is part of a closed process control loop. Operational and performance data are available for some installations from the users. With reliable and accurate final calibrations a precision better than 1% of reading is achievable for Newtonian fluids in laminar flow conditions, generally
f
100
18.0
lOI 15.0 1000 1100 1200 1300 1400 TIME (S)
Figure 3 Continuous on-line viscosity measurement. Volumetric flow varies between 200 and 11 cm 3 rain- 1: m , viscosity; - - , temperature Flow Meas. Instrum., 1994 Volume 5 Number 4
31)7
P. Kalotay - On-line viscosity measurement using Coriolis mass flowmeters
10.75
- 1.4
550 -
-I.2
500-
-1
480
- 0.8
400 -
3
[email protected] I0,r~10.5 -
- O.IS 360-
I0.46
+
o,
-
AN
5
10.4 -
-02 •-1.1~16 ~.
i0.':~ 10,3 10~";
--0.2
-
10.2 -
i
,~,
•-0.4
10.15 ~.0 10.1 10.06 I0
1'o
t ,~ ~ ~ ~ ,~ ";' i ~ l~+'11'21'31~l'51'e'l~'¢el'9~l"l BATCHES
1'5
~
~
a~
~
,ib
~.0
BATCHES
Figure 4 Laboratory vs. on-line viscosity measurements on a single product. Data collected over a four-month period: C), laboratory viscometer, II, MicroMotion; *, percentage error
Figure 5 Laboratory vs. on-line viscosity measurements of various products, between 10 and 450 cSt viscosity over a four-month period. Symbols as in Figure 4
time lag in the measurement and inadequate modelling or characterization of the process fluid. A significant percentage of all users do not calibrate the system to read in a given viscosity unit, but simply 'tune' their process to a certain indicated value, which in their experience is optimal to obtain the final product quality. Non-Newtonian fluids are most often measured in this manner.
of the drawbacks of sampling or other in-line system approaches. Low or no maintenance operation along with high-accuracy flow, density and viscosity measurement offers new solutions to old problems and numerous new applications as well, where previously other viscometers have failed.
Conclusion
The old capillary principle applied to direct mass flow metering provides low-cost and reliable on-line viscosity measurement for industrial processes, eliminating most
308
Flow Meas. Instrum., 1994 Volume 5 Number 4
References
1 Good Vibrations, MicroMotion Inc. Application Note No.IO, 1989 2 Patton, T. C. 'Paint flow and pigment dispersion', WileyInterscience, New York, 1979 3 Steffe, F. J. 'Rheological methods in food process engineering', Freeman Press, East Lansing, Michigan, 1992