GB2543587B

GB2543587B - Method and means for monitoring fluid flow

Info

Publication number: GB2543587B
Application number: GB1518876.6A
Authority: GB
Inventors: Peter Lucas Gary
Original assignee: Iphase Ltd
Current assignee: Iphase Ltd
Priority date: 2015-10-25
Filing date: 2015-10-25
Publication date: 2019-08-14
Anticipated expiration: 2035-10-25
Also published as: GB201518876D0; GB2543587A

Description

Method and means for monitoring fluid flow

The present invention relates to a method and means for monitoring the flow of a fluid. Morespecifically, the invention relates to a method and means of calculating a flow velocity profileof a fluid using the simultaneous application of multiple magnetic fields.

Background

Electromagnetic flow meters are used in a variety of industries to monitor the flow ofconducting fluids. Electromagnetic flow meters utilise Faraday’s law of electromagneticinduction to induce a voltage in a conducting fluid as it moves through a magnetic field. Theflow rate of the conducting fluid is then derived from the measured induced voltage.

In US2013/0036817 Al, the teaching of which is incorporated herein by reference, it hasbeen shown that, by using a multi-electrode electromagnetic flow meter (EMFM) and bymeasuring the boundary potential distribution in either a uniform or a non-uniform magneticfield, it is possible, with the application of appropriate mathematical techniques, to‘reconstruct’ the axial velocity profile (the variation in axial velocity across the flow crosssection) of an electrically conducting fluid in a single phase pipe flow or an electricallyconducting continuous phase in a multiphase pipe flow. Having derived the axial velocityprofile, the flow meter and method may be suitable for determining the volumetric flow rateof the conducting fluid or of each phase of the multiphase fluid. Further informationregarding the techniques for reconstruction of axial velocity profiles may be found in"Proposed method for reconstructing velocity profiles using a multi-electrodeelectromagnetic flow meter” [Kollar L E, Lucas G P and Zhang Z. Meas. Sci. Technol. 25(2014) 075301 (14pp)], and "Reconstruction of velocity profiles in axisymmetric andasymmetric flows using an electromagnetic flow meter” [Kollar L E, Lucas G P and Meng Y.Meas. Sci. Technol. 26 (2015) 055301 (12pp)], the contents of which are also incorporatedherein by reference.

In WO 2015/1140574 Al, the contents of which are also incorporated herein by reference, animprovement to the device and method of US2013/0036817 Al is taught. Specifically, inWO 2015/1140574 Al, a multi-electrode EMFM device is disclosed in which axial velocityprofiles are reconstructed using uniform and non-uniform magnetic fields that are appliedconsecutively. Typically, in the device of WO 2015/140574 Al, a uniform magnetic field isapplied to the flow cross section of a conducting fluid for approximately one second,followed by a non-uniform magnetic field which is also applied for a period of approximatelyone second. This limits the rate at which the local axial velocity profile of the fluid flow canbe sampled (measured) to about once every two seconds.

However, after extensive research into the different types of fluid flow velocity profiles thatcan be reconstructed with the device of WO 2015/140574 Al, the inventor spotted a problem.Specifically, when reconstructing the velocity profiles of highly time-dependent flows, suchas transient fluid flow or specific types of multiphase flow, the rate at which the device ofWO 2015/140574 Al can sample (measure) the velocity profile of these types of flow is too slow, leading to inaccurate velocity profilereconstruction.

Summary

In order to solve this problem, the inventor first attempted to decrease the time periodsat which each of the steady uniform and non-uniform magnetic fields are applied,thereby increasing the rate at which the consecutive uniform and non-uniform magneticfields are applied and therefore increase the rate of sampling of the fluid flow.

However, the inventor discovered a problem with this method. Specifically, whenswitching between the uniform and non-uniform magnetic fields, there is a transient inthe relevant magnetic field that is caused by the electrical inductance and resistance ofthe coils. It is therefore necessary to wait for this transient to die away before therelevant magnetic field stabilises and the required flow induced potentials can bemeasured. There is therefore a limit to which the period of application of each of theuniform and non-uniform magnetic fields can be reduced, after which the magneticfields are always in transient and are never stable.

The inventor therefore performed further research into how the sampling rate of thedevice could be increased in order to be able to reconstruct the velocity flow profiles oftransient and multiphase flows.

According to a first aspect of the invention, there is provided an electromagnetic flowmeter for monitoring the flow of a conducting fluid, the electromagnetic flow metercomprising: a flow tube, through which flow tube said conducting fluid may flow;means for simultaneously generating both a predetermined, substantially uniformmagnetic field with a first frequency/; and a predetermined non-uniform magnetic fieldwith a second frequency /2, the second frequency f2 being different from the firstfrequency/; within the flow tube such that electrical potentials with frequencies/; and/2are induced in said conducting fluid as said fluid flows through the flow tube; a pluralityof voltage detectors configured to measure the induced electrical potentials withfrequencies /; and /2; and processing means for determining a flow velocity profile ofsaid conducting fluid on the basis of the measured induced electrical potentials withfrequencies /; and /2. The substantially uniform and non-uniform magnetic fields arenon-zero.

Simultaneous application of the uniform and non-uniform magnetic fields with differentfrequencies allows for the local axial velocity profile of the flow to be sampledsignificantly faster than in the prior art, for example tens or even hundreds of timesevery second. This is of major benefit in measuring the velocity profile of highly timedependent flows, such as multiphase flows or transient flows, allowing for the velocityprofiles of these types of flow to be measured more accurately.

In applying the uniform and non-uniform magnetic fields consecutively, it is necessaryto wait for transients in each of the applied magnetic fields to die away before the flowinduced potentials can be measured. This severely limits the rate at which thesepotentials can be measured, and consequently limits the rate at which velocity profilescan be reconstructed. This problem is avoided with the simultaneous application ofuniform and non-uniform magnetic fields with different frequencies.

In an embodiment, the means for simultaneously generating both the substantiallyuniform magnetic field and the non-uniform magnetic field comprises means for generating a single magnetic field comprising a substantially uniform magnetic fieldcomponent with a first frequency/; and a non-uniform magnetic field component with asecond frequency/2, the second frequency/2 being different from the first frequency/;.

Generating a single magnetic field comprising a substantially uniform, non-zeromagnetic field component with a first frequency /; and a non-uniform non-zeromagnetic field component with a second frequency /2, the second frequency /2 beingdifferent from the first frequency/; allows for the means for generating the simultaneousuniform and non-uniform magnetic fields to be kept simple and relatively inexpensive.

In an embodiment, the means for simultaneously generating both the substantiallyuniform magnetic field with a first frequency/; and the non-uniform magnetic field witha second frequency/2, the second frequency/2 being different from the first frequency/;comprises at least two coils, and a voltage generator, wherein the voltage generator isconfigured to apply a voltage to a first coil of the at least two coils of the form

and is configured to apply a voltage to a second coil of the at least two coils of the form

Applying voltages of this form to first and second coils allows for a reduction in theamount of computations needed to determine velocity flow profiles of sampled fluid.

In an embodiment, the voltage generator comprises means for producing the abovevoltages for application to the coils by direct digital synthesis; a power amplifier; and aD/A converter. Direct digital synthesis allows for very accurate generation of the abovevoltages, thereby increasing the accuracy of the reconstructed velocity flow profiles.

In an embodiment, / is substantially equal to 2/2. This ratio of frequenciesunexpectedly improves the accuracy of the reconstructed velocity profiles.

In an embodiment, /2 is between about 10 Hz and about 1000 Hz. This range offrequencies allows for improved accuracy of the calculated velocity profiles. A higherfrequency of /2 than about 1000 Hz causes the induction current of the means forgenerating the magnetic fields to be smaller, thereby reducing the accuracy of thereconstructed velocity profiles. Below 10 Hz, the EMFM isn’t as responsive.

In an embodiment, the induced electrical potential is measured as a boundary potentialdistribution at a boundary defined by the flow tube.

According to a second aspect, there is provided a method for determining a flowvelocity profile of a conducting fluid flowing in a flow tube, the method comprising:simultaneously generating a predetermined, substantially uniform magnetic field with afirst frequency /; and a predetermined non-uniform magnetic field with a secondfrequency /2, the second frequency /2 being different from the first frequency /; withinthe flow tube; measuring an electrical potential induced by said conducting fluid

flowing in the flow tube; determining the flow velocity profile of the conducting fluidflowing in the flow tube on the basis of the measured induced electrical potential.

Simultaneous application of the uniform and non-uniform magnetic fields allows for thelocal axial velocity profile of the flow to be sampled significantly faster than in the prior art, for example tens or even hundreds of times every second. This is of major benefit inmeasuring the velocity profile of highly time dependent flows, such as multiphase flowsor transient flows, allowing for the velocity profiles of these types of flow to bemeasured more accurately.

Furthermore, in applying the uniform and non-uniform magnetic fields consecutively, itis necessary to wait for transients in each of the applied magnetic fields to die awaybefore the flow induced potentials can be measured. This severely limits the rate atwhich these potentials can be measured, and consequently limits the rate at whichvelocity profiles can be reconstructed.

In an embodiment, simultaneously generating the predetermined, substantially uniformmagnetic field and the predetermined non-uniform magnetic field comprises generatinga single magnetic field comprising a substantially uniform magnetic field componentwith a first frequency fi and a non-uniform magnetic field component with a secondfrequency/2, the second frequency /2 being different from the first frequency/;.

Generating a single magnetic field comprising a substantially uniform, non-zeromagnetic field component with a first frequency // and a non-uniform non-zeromagnetic field component with a second frequency /2, the second frequency /2 beingdifferent from the first frequency // allows for the means for generating thesimultaneous uniform and non-uniform magnetic fields to be kept simple and relativelyinexpensive.

In an embodiment, determining the flow velocity profile comprises calculating adiscrete Fourier transform (DFT) of the measured induced electrical potential. Using aDFT is a particularly fast and efficient method of determining flow velocity profiles,since, unlike other algorithms (such as the Fast Fourier Transform), a DFT can becalculated at only the frequencies of interest. This is of particular use in the aboveapplication, since, due to the well-defined frequencies of the voltages applied to thecoils, only a few select frequencies are required to be transformed, thereby increasingthe efficiency and speed of the overall method.

In an embodiment, the substantially uniform magnetic field and the non-uniformmagnetic field are generated by simultaneously applying a voltage to a first coil of theform

and applying a voltage to a second coil of the form

In an embodiment, determining the flow velocity profile comprises calculating adiscrete Fourier transform (DFT) of the measured induced electrical potential atfrequencies f1 and /2.

Using a DFT is a particularly fast and efficient method of determining flow velocityprofiles, since, unlike other algorithms (like the Fast Fourier Transform), DFT can becalculated at only the frequencies of interest. This is of particular use in the aboveapplication, since, due to the defined frequencies of the voltages applied to the coils,only a few select frequencies are required to be transformed, thereby increasing theefficiency and speed of the overall method.

In an embodiment, f is substantially equal to 2/2. This ratio of frequenciesunexpectedly improves the accuracy of the reconstructed velocity profiles.

In an embodiment, /2 is between about 10 Hz and about 1000 Hz. This range offrequencies allows for improved accuracy of the calculated velocity profiles. A higherfrequency of f2 than about 1000 Hz causes the induction current of the means forgenerating the magnetic fields to be smaller, thereby reducing the accuracy of thereconstructed velocity profiles.

In an embodiment, the method further comprises calculating a phase shift between themeasured induced electrical potential and a flow induced electrical potential and thencorrecting for this phase shift. Correcting for this phase shift further improves theaccuracy of the reconstructed velocity profiles.

In an embodiment, the induced electrical potential is measured over a sampling periodof time T, wherein T is substantially equal to (/'2) 1. This sampling period unexpectedlyimproves the accuracy of the reconstructed velocity profiles.

Brief description of the drawings

In order to better understand the present invention, and to show how the same may becarried into effect, reference will now be made, by way of example only, to thefollowing drawings, in which:

Fig 1 shows a side view of an embodiment of the EMFM;

Fig 2 shows a top view of an embodiment of the EMFM;

Fig 3 shows an embodiment of the EMFM showing the position and number of theelectrodes around a boundary defined by the circumference of a flow tube; and

Fig 4 shows a reconstructed axial velocity profile of a fluid flowing through the flowtube.

Detailed Description

Throughout the following description and claims, the words “comprise” and“comprising” mean “including but not limited to”. “Uniform” will be used to mean ‘spatially uniform at any instant in time”. Of course, at anygiven spatial location the magnitude of the magnetic field varies (sinusoidally) with time. “Non-uniform” will be used to mean ‘spatially non-uniform at any instant in time”. Ofcourse, at any given spatial location the magnitude of the magnetic field varies (sinusoidally)with time. “Substantially” will be used to mean “good enough to perform its intended function”. Forexample, a “substantially uniform magnetic field” is intended to describe a uniform magneticfield that, on the whole and at any instant in time, does not have a varying magnitude in theregion in which the magnetic field is used to induce an electrical potential that will bemeasured, but which magnetic field may have some small spatial variations due to non-idealequipment, for example.

Fig 1 shows a side view of an electromagnetic flow meter (EMFM) 100 that is also describedin WO 2015/140574 Al. The EMFM comprises a flow tube 1 that is mounted within first andsecond coils of a Helmholtz coil 2. A conducting fluid may flow through the hollow interior 4of the flow tube 1. The flow tube is non-electrically conducting.

Fig 2 shows a top view of the EMFM, which gives further detail as to how the flow tube 1may be mounted within the Helmholtz coil 2.

Fig 3 shows a plurality of electrodes 3 arranged around the circumference of the flow tube 1.The electrodes 3 are able to measure the potential distribution created by a conducting fluidflowing through the flow tube 1, as disclosed in WO 2015/140574 Al. The electrodes arecircumferentially mounted on an internal surface of the flow tube so as to detect the inducedvoltage at various points on the internal circumference of the flow tube. The electrodes areequally spaced around the circumference of the flow tube so as to measure the local inducedvoltage throughout sections of the flow tube. The electrodes are made from a low magneticpermeability material (eg, stainless steel) and the flow tube is made from a non-electricallyconducting material. Alternatively, the flow tube comprises an outer conducting wall and aninner non-conducting liner, and the electrodes are electrically insulated from the outerconducting wall.

The technique of simultaneously applying uniform and non-uniform magnetic fields to theEMFM, instead of consecutively applying these fields, as detailed in WO 2015/140574 Al, ispossible because the EMFM is a linear system. In other words, for a given flow velocityprofile of conducting fluid, if the application of magnetic field B, gives rise to a flowinduced potential distribution Φ1, and the application of magnetic field B 2 gives rise to aflow induced potential distribution Φ2 then the application of magnetic field B, +B2 willgive rise to the flow induced potential distribution Φ, + Φ2.

For the EMFM shown in Figs 1 to 3, which comprises a flow tube 1; an array of, for example,sixteen electrodes 3 equally spaced around the boundary of the flow tube 1 and in contactwith the flowing conducting fluid; and a Helmholtz coil 4 comprising two coils denoted ‘Top coil’ and ‘Bottom coil’, voltages VT and VB may applied to thetop and bottom coils, respectively, where:

(1) and

(2)

As a result of these applied voltages, electrical currents IT and IB will flow in the topand bottom coils, respectively, where:

(3) and

(4) where Ψχ and Ψ2 are phase angles that arise because each of the top and bottom coilshave inductive and resistive impedances. The electrical currents IT and IB give rise toa time varying total magnetic field consisting of (i) a time varying magnetic field Bu (/)which at any instant in time is substantially uniform across a cross section of fluid flowand (ii) a time varying magnetic field Bnu (?) which at any instant in time is non-uniformin the flow cross section.

Because Bnu(/j arises from equal and opposite electrical currents in the top and bottomcoils then, at any instant in time, it may be referred to as an ‘anti-Helmholtz’ magneticfield. The frequency of Bu (/) is and the frequency of Bnu (0 is /2 ·

Let us make the definition that when the current in the top coil is in the clockwisedirection, when viewed from above in Fig 2, it is positive. Let us further define theuniform part of the magnetic field as being positive when it points in the - y direction(see Fig 2).

From equations 3 and 4 we may now write that at time t the magnetic flux densityBu (/) of the uniform part of the total magnetic field is given by

(5) where Bu max is the maximum value of the magnetic flux density associated with theuniform part of the total magnetic field. We may now make the further definition thatthe non-uniform part of the magnetic field, at position el3 in Fig 3, is positive when itpoints in the + y direction.

From equations 3 and 4 we may write that, at time t, the value B (P) of the non-uniform part of the magnetic field at position el3 is given by

(6) where Bop max is the maximum value of the non-uniform part of the magnetic field atthe position of electrode el3.

At the pth electrode in Fig 3, the total electrical potential Up tot, measured with respectto electrode e5, comprises (i) flow induced terms and (ii) inductively coupled (orquadrature) terms. As a result of the quadrature terms the measured potentials atfrequencies and f2 will not be in phase with Bu (t) and Bop (t), respectively, and soUp tat may be expressed as

(7) where U max and U max are the maximum values of the measured potentials at and/2 respectively.

As will be seen below, the values of U ax, U ax, yp l and y 2 (p = 1 to 16), alongwith the values of Ψ, and Ψ2, are required to calculate the inputs to a velocity profilereconstruction algorithm.

Then, a Discrete Fourier Transform (DFT) of Uptot at frequencies f and f2 iscalculated, which will enable Up max, Up max, γp j and γp 2 to be determined. Supposefor the pth electrode, the potential Uptot (measured with respect to electrode e5) issampled N times over a period T to give the sampled sequence x r (where to avoidN N aliasing — > 2j\ and — > 2/2, i.e., the Nyquist frequency is not exceeded). (8) (9)

The following relationships can then be derived: (10) (11) (12) (13)

In equations 12 and 13, calculation of the arguments of Xpl and Xp 2 must take intoconsideration the quadrants of the complex plane in which Xp x and Xp 2 lie.

In a similar manner to the example given above, the electrical current IT supplied to thetop coil (see equation 3) is also sampled N times over a period T , thereby enabling theDFT of the sampled signal to be obtained at frequencies and f2 , and thereby enabling the determination of I2, T/ and Ψ2 (equation 3). By calibration orcalculation Bu max and Bop max may be obtained from the calculated values of f andI2 , respectively.

At the pth electrode the maximum value Up y of the flow induced potential associatedwith the uniform component of the magnetic field can be calculated by eliminating theeffect of the quadrature potential at frequency , as follows:

(14)

Similarly, at the pth electrode the maximum value Up f of the flow induced potentialassociated with the non-uniform component of the magnetic field can be calculated byeliminating the effect of quadrature potential at frequency f2 . as follows:

(15)

The flow induced potential distribution U f (p = Ito 16) is identical to the potentialdistribution which would be obtained if a constant uniform magnetic field of fluxdensity Bu max were applied in the pipe cross section. The flow induced potentialdistribution U ? (p = Ito 16) is identical to the potential distribution which would beobtained if a constant non-uniform (anti-Helmholtz) magnetic field, with flux densityBopmax at electrode el3, were applied in the pipe cross section. Consequently, themeasured values of U ? and U p f (p = Ito 16), along with the values of SMmax and

Bop max may be used as inputs for the velocity profile reconstruction algorithms described inWO 2015/140574 Al and US2013/0036817 Al.

With the above technique, because the uniform and non-uniform magnetic fields are appliedsimultaneously, all of the required flow induced potential measurements needed toreconstruct a flow velocity profile can be obtained during a sampling interval T. allowing anew velocity profile to be reconstructed after each time interval T.

The DFT technique described by equations 8 and 9 performs optimally for j\ = 2/2 and forT = ( Consequently, new velocity profile images can be obtained at a rate equal to /2 images per second. For velocity profile imaging applications the value of f2 should be in therange of about 10 Hz to about 1000 Hz.

An example of a reconstructed flow velocity profile is shown in Fig 4.

The above method and apparatus may be used to increase the accuracy of measurement offlow profiles of fluids in the oil, gas, nuclear, chemical, food processing and miningindustries, for example.

The foregoing description has been presented for purposes of illustration and description. It isnot intended to be exhaustive or to limit the technology to the precise form disclosed. Manymodifications and variations are possible in the light of the above teaching. For example,another means (other than a Helmholtz coil) may be used to generate the uniform and/or non-uniform magnetic fields. The described embodiments were chosen in order to best explain theprinciples of the technology, and its practical application, to thereby enable others skilled inthe art to utilise the technology, including modifications as suited to a particular use. Thedescription and appended claims are intended to cover such alternatives and modifications asmay be included within the scope of the invention as defined by the appended claims.

Claims

Claims

1. An electromagnetic flow meter for monitoring the flow of a conducting fluid, theelectromagnetic flow meter comprising: a flow tube, through which flow tube said conducting fluid may flow; means for simultaneously generating both a predetermined, substantiallyuniform magnetic field with a first frequency ft and a predetermined non-uniform magnetic field with a second frequency /2, the second frequency /2being different from the first frequency ft. within the flow tube such thatelectrical potentials with frequencies ft and ft are induced in said conductingfluid as said fluid flows through the flow tube, wherein the means forsimultaneously generating both the substantially uniform magnetic field andthe non-uniform magnetic field comprises at least two coils; a plurality of voltage detectors configured to measure the induced electricalpotentials with frequencies/; and/2; and processing means for determining a flow velocity profile of said conductingfluid on the basis of the measured induced electrical potentials withfrequencies/; and/2.
2. The electromagnetic flow meter of claim 1, wherein the means for simultaneouslygenerating both the substantially uniform magnetic field and the non-uniformmagnetic field comprises means for generating a single magnetic field comprising asubstantially uniform magnetic field component and a non-uniform magnetic fieldcomponent. 3. The electromagnetic flow meter of claim 1 or claim 2, wherein the means forsimultaneously generating both the substantially uniform magnetic field and the non-uniform magnetic field comprises a voltage generator, wherein the voltage generatoris configured to apply a voltage to a first coil of the at least two coils of the form

and is configured to apply a voltage to a second coil of the at least two coils of theform
4. The electromagnetic flow meter of claim 3, wherein the voltage generator comprisesmeans for producing the voltages for application to the coils by direct digitalsynthesis; a power amplifier; and a D/A converter. 5. The electromagnetic flow meter of claim 3 or claim 4, wherein / is substantiallyequal to 2/2.

6. The electromagnetic flow meter of any of claims 3 to 5, wherein f2 is between 10 Hzand 1000 Hz. 7. The electromagnetic flow meter of any preceding claim, wherein the inducedelectrical potential is measured as a boundary potential distribution at a boundarydefined by the flow tube. 8. A method for determining a flow velocity profile of a conducting fluid flowing in aflow tube, the method comprising: simultaneously generating a predetermined, substantially uniform magneticfield with a first frequency f/ and a predetermined non-uniform magnetic fieldwith a second frequency /2, the second frequency /2 being different from thefirst frequency/; within the flow tube; measuring electrical potentials with frequencies fj and /2 induced by saidconducting fluid flowing in the flow tube; determining the flow velocity profile of the conducting fluid flowing in theflow tube on the basis of the measured induced electrical potentials withfrequencies/; and/2.
9. The method of claim 8, wherein simultaneously generating the predetermined,substantially uniform magnetic field and the predetermined non-uniform magneticfield comprises generating a single magnetic field comprising a substantially uniformmagnetic field component and a non-uniform magnetic field component. 10. The method of claim 8 or 9, wherein the induced electrical potential is measured as aboundary potential distribution at a boundary defined by the flow tube. 11. The method of claim 9 or claim 10, wherein the determining the flow velocity profilecomprises calculating a discrete Fourier transform (DFT) of the measured inducedelectrical potential. 12. The method of claim 9 or claim 10, wherein the substantially uniform magnetic fieldand the non-uniform magnetic field are generated by simultaneously applying avoltage to a first coil of the form

and applying a voltage to a second coil of the form
13. The method of claim 12, wherein the determining the flow velocity profile comprisescalculating a discrete Fourier transform (DFT) of the measured induced electricalpotential at frequencies f1 and f2.

14. The method of claim 12 or claim 13, wherein j\ is substantially equal to 2/2. 15. The method of any of claims 12 to 14, wherein /2 is between 10 Hz and 1000 Hz. 16. The method of any of claims 8 to 15, further comprising calculating a phase shiftbetween the measured induced electrical potential and a flow induced electricalpotential and then correcting for this phase shift. 17. The method of any of claims 12 to 16, wherein the induced electrical potential ismeasured over a sampling period of time T, wherein T is substantially equal to (/2)~1 . 18. A data storage medium storing computer-readable instructions which, if executed by aprocessor, cause the processor to perform a method as set out in any of claims 8 to 17. 19. A signal carrying computer-readable instructions which, if executed by a processor,causes the processor to perform a method as set out in any of claims 8 to 17. 20. Use of the apparatus of any of claims 1 to 7 to determine a flow velocity profile.