Measurement of fluid properties
11035772 · 2021-06-15
Assignee
Inventors
Cpc classification
International classification
Abstract
Apparatuses and methods are disclosed for the analysing of non-Newtonian fluids and determining parameters to characterise the relationship between shear stresses and shear rates, i.e. the parameters of one or more rheological models of viscosity. A plurality of viscosity measurements are made in a fluid using one or more vibratory transducers operating at a plurality of frequencies. Parameters for the fluid are determined based on the measured viscosity values and the frequencies of vibration at which the viscosity measurements were obtained.
Claims
1. A method for analysing a non-Newtonian fluid, the method comprising: obtaining a plurality of viscosity measurements of a non-Newtonian fluid at plural frequencies of vibration, the viscosity measurements being made using at least one vibratory transducer; and, based on the obtained plurality of viscosity measurements and the plural frequencies of vibration, determining the value of one or more parameters of a model for the non-Newtonian fluid by approximating a shear rate quantity in the model by a frequency of vibration.
2. The method of claim 1, wherein the one or more parameters of the model are determined by approximating a shear stress quantity in the model by the product of a viscosity and a frequency of vibration.
3. The method of claim 1, wherein the or each of the at least one vibratory transducer is a resonant transducer and the plurality of viscosity measurements are obtained by determining Q factors based on resonance bandwidths at the respective frequencies of vibration.
4. The method of claim 1, wherein the one or more parameters for which values are determined comprise a yield stress of the fluid.
5. The method of claim 1, wherein the one or more parameters for which values are determined comprise one or more of: a consistency of the fluid, a power law index of the fluid, and a plastic viscosity of the fluid.
6. The method of claim 1, wherein the viscosity measurements are made while the fluid is in contact with and flowing around the at least one vibratory transducers.
7. An apparatus for analysing a non-Newtonian fluid, the apparatus comprising: one or more vibratory transducers for making a plurality of viscosity measurements of a non-Newtonian fluid, each of the plurality of viscosity measurements being made at a different frequency of vibration; and an electronic parameter estimator for, based on the plurality of viscosity measurements and the plural frequencies of vibration, determining the value of one or more parameters of a model for the non-Newtonian fluid by approximating a shear rate quantity in the model by a frequency of vibration.
8. The apparatus of claim 7, wherein the one or more parameters of the model are determined by approximating a shear stress quantity in the model by the product of a viscosity and a frequency of vibration.
9. The apparatus of claim 7, wherein the or each of the at least one vibratory transducer is a resonant transducer and the plurality of viscosity measurements are obtained by determining Q factors based on resonance bandwidths at the respective frequencies of vibration.
10. The apparatus of claim 7, wherein the one or more parameters for which values are determined comprise a yield stress of the fluid.
11. The apparatus of claim 7, wherein the one or more parameters for which values are determined comprise one or more of: a consistency of the fluid, a power law index of the fluid, and a plastic viscosity of the fluid.
12. The apparatus of claim 7, further comprising a temperature sensor for obtaining one or more temperature measurements of the fluid.
13. The apparatus of claim 7, wherein the model is a rheological model of viscosity for the fluid.
14. The apparatus of claim 13, wherein the model is one of the Casson model, the Bingham model, the power law model, and the Herschel-Bulkley model.
15. The apparatus of claim 7, wherein the or each of the at least one vibratory transducers is configured to vibrate at more than one frequency or in more than one mode.
16. The apparatus of claim 7, comprising a plurality of vibratory transducers each configured to vibrate at different frequencies, the plurality of viscosity measurements being made by the plurality of vibratory transducers.
17. The apparatus of claim 7, wherein the or each vibratory transducer is configured to vibrate in a torsional mode.
18. The apparatus of claim 7, wherein the viscosity measurements are made while the fluid is in contact with and flowing around the at least one vibratory transducers.
19. The apparatus of claim 18, wherein the viscosity measurements are made on-line in a fluid process.
20. A non-transitory computer-readable medium having stored thereon instructions for causing a processor of an apparatus to: obtain a plurality of viscosity measurements of a non-Newtonian fluid at plural frequencies of vibration, the viscosity measurements being made using at least one vibratory transducer; and, based on the obtained plurality of viscosity measurements and the plural frequencies of vibration, determine the value of one or more parameters of a model for the non-Newtonian fluid by approximating a shear rate quantity in the model by a frequency of vibration.
Description
BRIEF DESCRIPTION OF THE DRAWINGS
(1) Aspects of the invention will be described in more detail by way of example only with reference to the accompanying drawings. The components within the drawings are not necessarily to scale, emphasis instead being placed upon clearly illustrating principles.
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DETAILED DESCRIPTION OF SOME EMBODIMENTS
(8)
(9) While the chamber 6 is drawn in
(10) The resonant viscosity transducers are of a type described in U.S. Pat. No. 6,450,013, in which the transducers include a vibrating element configured to oscillate in a torsional mode. The vibrating element is immersed in the fluid and the viscosity is determined by correlation with the damping experienced by the element, i.e. the Q factor. In particular, each transducer comprises a sensor mounting 10, a semi-rigid connection member 12, a shaft 14 and a sense element 16. The shaft 14 and the sense element 16 are driven to vibrate torsionally with an angular frequency co. The sense element 16 is of relatively large mass and the shaft 14 and sense element 16 are formed, at least substantially and possibly entirely, of a metal material such as a stainless steel. The sense element 16 and shaft 14 both have a circular cross-section, i.e. they are circularly symmetrical about the axis of oscillatory rotation. An example transducer that may be suitable for determining the viscosity via vibration at a frequency is the XL7 model viscometer manufactured by Hydramotion Ltd of Malton, UK.
(11) The contents of the chamber 6 are pressurized to 10 Bar relative to atmospheric pressure. The sensing element is exposed to the viscous effect of the fluid in the sample 5. Increasing viscosity of the fluid causes an increased damping of the vibration in the sensor, resulting in a measurable reduced vibrational efficiency of the system.
(12) In this apparatus, the first viscosity transducer 100 is specially designed, via choice of stiffness and mass or moment of inertia of the resonant system, to have a low resonant frequency at 300 Hz, i.e. an angular frequency of approximately 1885 rad/s. The second viscosity transducer 120 is specially designed to have a higher resonant frequency at 1500 Hz, i.e. an angular frequency of approximately 9425 rad/s.
(13) To determine the viscosity at the resonant frequencies of the first and second viscosity transducers, the ‘Q factor’ of the vibration can be determined. The Q factor is a dimensionless parameter that indicates the level of damping of a resonator, wherein the level of damping is a function of the viscosity. In particular, it indicates the degree to which a resonator is underdamped. On a plot of frequency response, a high Q factor provides a high and narrow peak at the resonant frequency whereas a low Q factor provides a low and wide peak. Due to the change in width of the peak with damping, the Q factor can be defined as the ratio of the resonant frequency to the resonant bandwidth:
(14)
wherein ω.sub.R is the resonant frequency in radians per second and Δω is the Full Width at Half Maximum (FWHM), the bandwidth over which the power of the vibration is greater than half of the maximum (or equivalently the amplitude of vibration is greater than the maximum amplitude at resonance divided by √2), i.e. the bandwidth between the 3 dB points. The fluid viscosity is inversely proportional to the square of the Q factor and any constant of proportionality needed to compute the value of the viscosity measurement can be obtained by calibration with reference fluids of known viscosity. It should be noted that the measurement of viscosity at or corresponding to a frequency of vibration may comprise making amplitude measurements at more than one frequency, such as at the two FWHM points in order to obtain Δω, but a single viscosity measurement is obtained.
(15) The first and second viscosity transducers 100, 120 both provide viscosity measurements corresponding to their resonant frequencies. The first and second viscosity measurements η.sub.1, η.sub.2, and first and second angular frequencies ω.sub.1, ω.sub.2 are provided to a processing module (not shown) which processes these measurements to provide estimates of one or more fluid properties.
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(17) The process begins at start block 510 and transitions to block 510 where the first and second viscosity transducers 100, 120 each provide viscosity measurements η.sub.1, η.sub.2, corresponding to their resonant angular frequencies ω.sub.1, ω.sub.2. These are obtained at the processing module.
(18) At the following block 520, the processing module evaluates the yield stress σ.sub.0 and consistency parameter K from the measured η.sub.1, η.sub.2, ω.sub.1, and ω.sub.2 by substitution into the following equations derived from the Herschel-Bulkley model:
σ.sub.0=η.sub.1ω.sub.1−Kω.sub.1.sup.n
σ.sub.0=η.sub.2ω.sub.2−Kω.sub.2.sup.n.
(19) For operation in a fluid for which the power law index n is known, the processing module evaluates K and σ.sub.0 according to the following expressions derived from the simultaneous equations in η and ω above:
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(21) To determine values for K and σ.sub.0, the processing module may comprise a computer comprising a processor and a memory, the memory storing software that, when run by the processor, evaluates these expressions continuously and updates its estimates of K and σ.sub.0 based on the latest values of η.sub.1, η.sub.2, ω.sub.1, and ω.sub.2 received from the viscosity transducers 100, 120. As an alternative to a processor and memory, the processing module may include a field programmable gate array (FPGA) device configured to perform the operations of evaluating these expressions.
(22) The estimated values of K and σ.sub.0 are provided to an output device (not shown in
(23)
(24) The first and second viscosity measurements η.sub.1, η.sub.2, and first and second frequencies ω.sub.1, ω.sub.2 are provided to a processing module 18 which processes these measurements to provide estimates of one or more fluid properties.
(25) To provide estimates of parameters for the power law model, the processing module 18 evaluates the power law index n and consistency parameter K′ from the measured η.sub.1, η.sub.2, ω.sub.1, and ω.sub.2 by substitution into the following equations model
η.sub.1=K′ω.sub.1.sup.n-1
η.sub.2=K′ω.sub.2.sup.n-1.
(26) The processing module evaluates n and K′ according to the following expressions derived from the simultaneous equations in η and ω above:
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(29) The first, second and third viscosity measurements η.sub.1, η.sub.2, η.sub.3 and first and second frequencies ω.sub.1, ω.sub.2, ω.sub.3 are provided to a processing module (not shown) which processes these measurements to provide estimates of one or more fluid properties.
(30) The processing module evaluates the yield stress σ.sub.0 and consistency parameter K and power law index n from the measured η.sub.1, η.sub.2, η.sub.3, ω.sub.1, ω.sub.2, and ω.sub.3 by substitution into the following equations derived from the Herschel-Bulkley model:
σ.sub.0=η.sub.1ω.sub.1−Kω.sub.1.sup.n
σ.sub.0=η.sub.2ω.sub.2−Kω.sub.2.sup.n
σ.sub.0=η.sub.3ω.sub.3−Kω.sub.3.sup.n.
(31) The processing module finds values of the yield stress σ.sub.0 and consistency parameter K and power law index n that best fit the measured viscosities and frequencies via numerical optimization methods such as those found in MATLAB™ of The MathWorks, Inc.; see, for example, the MATLAB Optimization Toolbox.
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(33) The first, second and third viscosity measurements η.sub.1, η.sub.2, η.sub.3 and first and second frequencies ω.sub.1, ω.sub.2, ω.sub.3 are provided to a processing module (not shown) which processes these measurements to provide estimates of one or more fluid properties.
(34) As with the embodiment shown in
σ.sub.0=η.sub.1ω.sub.1−Kω.sub.1.sup.n
σ.sub.0=η.sub.2ω.sub.2−Kω.sub.2.sup.n
σ.sub.0=η.sub.3ω.sub.3−Kω.sub.3.sup.n.
(35) The processing module finds values of the yield stress σ.sub.0 and consistency parameter K and power law index n that best fit the measured viscosities and frequencies via numerical optimization methods such as those found in MATLAB™ of The MathWorks, Inc.; see, for example, the MATLAB Optimization Toolbox.
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(37) The viscosity transducer 600 comprises a sense element 16 on a shaft 14 extending from a threaded sensor mount 10. A processing module 18 is shown on the other side of the threaded sensor mount 10. The threaded portion of the sensor mount 10 engages with corresponding threads of a conduit 8. The sense element 16 and shaft extend along the axis of the conduit 8 facing upstream. The fluid-contacting portions of the viscosity transducer are formed of stainless steel (type 316) to resist corrosion and avoid contamination of the fluid. The conduit 8 includes a corner such that the fluid is diverted by the conduit walls to one side after it has passed the sense element 16 of the transducer 600, i.e. the viscosity transducer 600 is installed in an elbow section of the conduit 8.
(38) The processing module 18 outputs the plastic viscosity η.sub.p, the yield stress σ.sub.0, and the fluid temperature. The fluid temperature is obtained from a temperature sensor included in the sense element 16 of the viscosity transducer 600. The plastic viscosity η.sub.p and the yield stress σ.sub.0 are obtained from the measured η.sub.1, η.sub.2, ω.sub.1, and ω.sub.2 by substitution into the following equations derived from the Casson model and solving the equations for the plastic viscosity lip and the yield stress σ.sub.0:
σ.sub.0.sup.1/2=(η.sub.1ω.sub.1).sup.1/2−(η.sub.pω.sub.1).sup.1/2
σ.sub.0.sup.1/2=(η.sub.2ω.sub.2).sup.1/2−(η.sub.pω.sub.2).sup.1/2.
(39) In the examples shown in
(40) The variant apparatus of
(41) The examples shown in
(42) The techniques of the present disclosure may perform robustly regardless of the flow rate of the fluid relative to the one or more viscosity transducers. Further, they may perform robustly over a wide range of process conditions without operator intervention. Similarly, the particular fluid model parameter values estimated by the processing module may vary from those of the particular examples disclosed in
(43) In interpreting the disclosure, all terms should be interpreted in the broadest possible manner consistent with the context. In particular, the terms “comprises” and “comprising” should be interpreted as referring to elements, components, or steps in a non-exclusive manner, indicating that the referenced elements, components, or steps may be present, or utilized, or combined with other elements, components, or steps that are not expressly referenced. In the context of this disclosure, the term “based on” does not mean “based only on,” unless expressly specified otherwise. In other words, the term “based on” describes both “based only on” and “based at least on.” The term “determining” encompasses a wide variety of actions and, therefore, “determining” can include calculating, computing, processing, deriving, investigating, looking up (e.g., looking up in a table, a database or another data structure), ascertaining and the like. Also, “determining” can include receiving (e.g., receiving information), accessing (e.g., accessing data in a memory) and the like. Also, “determining” can include resolving, selecting, choosing, establishing and the like.
(44) The methods, process and algorithms that have been described may be stored as one or more instructions on a processor-readable or computer-readable medium. The term “computer-readable medium” refers to any available medium that can be accessed by a computer or processor. By way of example, and not limitation, such a medium may comprise RAM, ROM, EEPROM, flash memory, CD-ROM or other optical disk storage, magnetic disk storage or other magnetic storage devices, or any other medium that can be used to store desired program code in the form of instructions or data structures and that can be accessed by a computer. Disk and disc, as used herein, includes compact disc (CD), laser disc, optical disc, digital versatile disc (DVD), floppy disk and Blu-ray® disc where disks usually reproduce data magnetically, while discs reproduce data optically with lasers. It should be noted that a computer-readable medium may be tangible and non-transitory. In the context of this disclosure, the term “code” may refer to software, instructions, code or data that is/are executable by a computing device or processor.
(45) Software or instructions or data may also be transmitted over a transmission medium. For example, if the software is transmitted from a website, server, or other remote source using a coaxial cable, fibre optic cable, twisted pair, digital subscriber line (DSL), or wireless technologies such as infrared, radio, and microwave, then the coaxial cable, fibre optic cable, twisted pair, DSL, or wireless technologies such as infrared, radio, and microwave are included in the definition of transmission medium.
(46) The above detailed description of embodiments of the invention is not intended to be exhaustive or to limit the invention to the precise form disclosed above. While specific embodiments of, and examples for, the invention are described above for illustrative purposes, various equivalent modifications are possible within the scope of the invention, as those skilled in the relevant art will recognize. For example, while processes or blocks are presented in a given order, alternative embodiments may perform routines having steps, or employ systems having blocks, in a different order, and some processes or blocks may be deleted, moved, added, subdivided, combined, and/or modified. Each of these processes or blocks may be implemented in a variety of different ways. Also, while processes or blocks are at times shown as being performed in series, these processes or blocks may instead be performed in parallel, or may be performed at different times.
(47) The teachings of the invention provided herein can be applied to other systems, not necessarily the system described above. The elements and acts of the various embodiments described above can be combined to provide further embodiments.
(48) The headings provided herein are for convenience only and do not necessarily affect the scope or meaning of the aspects of this the disclosure defined by the claims.
(49) Some embodiments have been described. These embodiments are presented by way of example only and are not intended to limit the scope of the disclosure. Indeed, the novel methods, apparatus and systems described herein may be embodied in a variety of other forms. It should be apparent to those skilled in the art that many more modifications besides those already described are possible without departing from the inventive concepts herein.
(50) While endeavouring in the foregoing specification to draw attention to those features of the invention believed to be of particular importance, it should be understood that the applicant claims protection in respect of any patentable feature or combination of features referred to herein, and/or shown in the drawings, whether or not particular emphasis has been placed thereon.