GB2390683A

GB2390683A - Flow measurement

Info

Publication number: GB2390683A
Application number: GB0207979A
Authority: GB
Inventors: Andrew Hunt; John Desmond Pendleton; Malcolm David Byars
Original assignee: Process Tomography Ltd; PROCESS TOMOGRAPHY Ltd
Current assignee: Process Tomography Ltd; PROCESS TOMOGRAPHY Ltd
Priority date: 2002-04-06
Filing date: 2002-04-06
Publication date: 2004-01-14
Anticipated expiration: 2022-04-06
Also published as: GB2390683A9; GB2390683B; GB0207979D0

Abstract

Apparatus and method for monitoring the rate of flow through a conduit of at least one phase of a multi-phase flow. A first data set representing a first image of the flow is generated at a relatively high frame rate, the first image representing phase concentration at a first location along the length of the conduit. A second data set representing a second image of the flow is generated at a relatively high frame rate, the second image representing phase concentration at a second location spaced from the first location along the length of the conduit. A third data set representing a third image of the flow is generated at a relatively low frame rate, the third image representing phase concentration within the conduit. The first and second data sets are cross correlated with respect to time to derive a fourth data set representing the speed of flow along the conduit between the first and second locations, and the rate of flow is calculated from the phase concentration of the said at least one phase represented by the third data set, and the flow speed represented by the fourth data set. Electrodes of a capacitance tomography imaging system are used to generate images by capacitive or conductance measurements.

Description

i 23go683 FLOW MEASUREMENT

The present invention relates to a method and apparatus for measuring flow through a conduit. Flowing mixtures of fluids and solids occur in many industries. Such mixtures are known as multiphase flows, and may comprise, for example, any one of gas and liquid, gas and solid, liquid and solid or gas and liquid and solid. Multi-component flows are also commonplace in many applications and may be liquid and liquid, gas and liquid and liquid or any other combination of gas and liquid components. There are many applications which require flow metering of one or more of the phases present. Often only a subset of the phases present (e.g. solid particles) need to be metered, while another subset are present but do not need to be metered (e.g. it is not necessary to measure air flow in pneumatic conveying).

One known system derives volumetric flow rate from velocity and concentration measurements. In the known system both velocity and concentration distributions across the conduit are derived using tomographic imaging methods, wherein electrodes are positioned about the circumference of the conduit in which flow is occurring and an electrical property (impedance) of the matenal, such as permittivity, conductance or complex admittance is measured and an impedance image, which can be related to the concentration distribution across the conduit, is generated from the measured impedances. Generating first and second impedance images from separate sets of electrodes which are spaced apart along the length of the conduit, and performing a correlation between these first and second images allows the velocity distributions of one of the individual phases within the flowing mixture to be determined. Many tomographic imaging techniques are known. In the description that follows, an

Electrical Capacitance Tomography (ECT) technique (which can measure permittivity and conductance) is described, although those skilled in the art will realise that the

present invention is applicable to other forms of tomographic imaging. ECT can be used with non-conducting materials such as plastics, hydrocarbons, sand or glass and is often used with mixtures of two different dielectric materials, as the permittivity distribution of the dielectric materials corresponds to the concentration distribution.

The image resolution that may be achieved depends on the number of independent capacitance measurements, and images can be generated at frame rates of the order of hundreds of frames per second.

In a typical ECT system, each set of electrodes consists of twelve circumferentially spaced electrodes. If a high resolution image is to be generated, so as to enable an accurate measurement of a concentration distribution within the conduit, many sequential capacitance measurements must be made over a period of for example, 5ms. In turbulent flow conditions, an image which represents information accumulated over a period as long as Sms cannot provide the temporal resolution necessary to measure velocity accurately using correlation techniques. On the other hand, if the number of measurements contributing to an image is reduced to improve temporal resolution, the resolution of the concentration distribution is degraded. As a result, typically capacitancetomography is used to measure concentration whereas a different technique is used to measure flow velocity.

Currently, a disadvantage of the approach described is that a balance must be achieved so as to attain sufficiently accurate concentration measurements, while computing images quickly enough to calculate velocity.

It is an object of the present invention to obviate or mitigate the disadvantage described above.

According to the present invention, there is provided a method for monitoring the rate of flow through a conduit of at least one phase of a multi-phase flow, wherein a first data set representing a first image of the flow is generated at a relatively high frame rate, the first image representing phase concentration at a first location along the length of the conduit, a second data set representing a second image of the flow is

generated at a relatively high frame rate, the second image representing phase concentration at a second location spaced from the first location along the length of the conduit, a third data set representing a third image of the flow is generated at a relatively low frame rate, the third image representing phase concentration within the conduit, the first and second data sets are cross-correlated with respect to time to derive a fourth data set representing the speed of flow along the conduit between the first and second locations, and the rate of flow is calculated from the phase concentration of the said at least one phase represented by the third data set, and the flow speed represented by the fourth data set.

It can thus be appreciated that the first and second data sets may be generated using a relatively small number of measurements to create images representing a relatively low-resolution phase concentration at the first and second locations along the length of the conduit. The third data set may be generated using a larger number of measurements so as to generate a higher resolution image.

Preferably, a series of first data sets are generated, a series of second data sets are generated, a series of third data sets are generated, a series of fourth data sets are derived by correlating the series of first data sets and the series of second data sets, and the flow rate is calculated from the series of third data sets and the series of fourth data sets.

The first, second and third data sets may be obtained by applying excitation signals to electrodes located adjacent the conduit to generate measurement signals, and using tomographic imaging techniques to convert the measurement signals into the data sets. The first and second data sets may be generated using a tomographic imaging technique using a first number of electrode excitations, the third data set may be generated using a tomographic imaging technique using a second number of electrode excitations and the first number may be less than the second number. The tomographic imaging technique used to generate the first and second data sets may, for example, use a single electrode excitation. The or each electrode to be excited in

the tomographic imaging technique used to generate the first and second data sets may be chosen on the basis of the third data set.

The first and second data sets may be generated from measurement signals derived from first and second sets of electrodes spaced apart along the length of the conduit, and the third data set may be generated from measurement signals derived from a third set of electrodes, spaced apart from the first and second sets. Alternatively, the first, second and third data sets may be generated from measurement signals derived from only two sets of electrodes spaced apart along the length of the conduit, some of me measurement signals contributing to the third data set also contributing to the first or second data set.

The present invention further provides an apparatus for monitoring the rate of flow through a conduit of at least one phase of a multi-phase flow, comprising means for generating a first data set at a relatively high frame rate, the first data set representing a first (approximate, or lower resolution) image of the flow, the first image representing phase concentration at a first location along the length of the conduit, means for generating a second data set at a relatively high frame rate, the second data set representing a second (approximate or lower resolution) image of the flow, the second image representing phase concentration at a second location spaced from the first location along the length of the conduit, means for generating a third data set at a relatively low frame rate representing a third (more accurate or higher resolution) image of the flow, the third image representing phase concentration within the conduit, means for correlating the first and second data sets with respect to time to derive a fourth data set representing the speed of flow along the conduit between the first and second locations, and means for calculating the rate of flow from the phase concentration of the said at least one phase represented by the third data set, and the flow speed represented by the fourth data set.

An embodiment of the present invention will now be described, by way of example, with reference to the accompanying drawings, in which:

s Figure 1 is a schematic illustration of two-phase gas-liquid flows in vertical pipes; Figure 2 is a schematic illustration of gas-solid flows in horizontal pipes; Figure 3 is a schematic illustration of a known tomographic imaging system; Figure 4 is a sectional view through three conduits about which different sets of measurement electrodes suitable for use with the tomographic imaging system of Figure 3 have been positioned; Figure 5 is a schematic illustration of a guard electrode arrangement for use with a set of measurement electrodes such as those illustrated in figure 4; Figure 6 is a schematic illustration of gas- liquid slug flow; Figure 7 is a schematic illustration of a flow meter assembly which may be used to put the present invention into effect; Figure 8 is an illustration of sixteen different images obtained from a tomographic imaging system using different groups of electrode pairs as measurement electrodes; Figure 9 is a graph showing how concentration varies with time in a single pixel of two images generated by two sets of measurement electrodes spaced apart along the length of the conduit in which a gas-liquid slug flow has been established; Figure 10 shows pairs of images representing concentration distributions obtained for the same conditions as applied in the case of figure 9; Figures lla to 11c are graphs showing data generated by applying a correlation method to data represented in the graph of figure 9.

Referring to Figure 1, four conduits labelled A, B. C and D are shown. Each conduit 1 has a gas liquid mixture flowing through it in an upwards direction, with the gas flow being greater in B than A, greater in C than B. and greater in D than C. The differences in gas flow cause considerable differences in flow conditions within the four conduits. Conduit A shows a bubbly flow where small bubbles of gas 2 are carried through a liquid 3. Conduit B shows what is commonly known as a plug or slug flow where slugs of gas 2 are carried through a liquid 3. Conduit C shows a churn flow where liquid and gas particles intermingle in no discernible order, and conduit D shows annular flow when a channel of gas 2 is surrounded by the liquid 3 and the channel of gas 2 also contains bubbles of the liquid 3.

Referring to Figure 2, five horizontal conduits labelled E to I are shown each having a gas-solid mixture flowing therethrough. Uppermost conduit E shows a dispersed flow where small solid particles flow through the gas. Conduit F contains two clusters of solid particles 4 which are moving through the gas, together with a plurality of smaller particles. Conduit G shows a stationary flow where a single mass of solid particles 5 remains stationary within the conduit and gas and particles flow around the mass 5. Conduit H shows a flow wherein particles gather towards the bottom of the conduit, illustrating when is known as a stratified flow. Conduit I shows a slug flow which is similar to that illustrated in conduit B of figure 1.

The present invention provides a method of measuring volumetric flow rate of one phase of a multiphase flow such as those represented in the conduits of figures 1 and 2. It will be appreciated that measuring volumetric flow rate of individual phases will require different considerations in each flow type in order to obtain an accurate measurement, and a generally applicable measurement technique is highly desirable.

Referring now to figure 3, a Icuown ECT imaging system is illustrated. The system comprises a control computer 6 which communicates with in the illustrated example twelve electrodes 7 which are placed circumferentially about a conduit 8. The computer 6, which may conveniently be a standard personal computer, communicates

bidirectionally with the electrodes 7 through an interface 9, which contains electronic circuitry to measure capacitance from data returned from the electrodes 7.

Capacitance data obtained by the computer 6 from the interface 9 allows a coloured image of the conduit contents to be created, providing different substances within the conduit have different dielectric characteristics.

Referring to figure 4, three different ways of positioning eight electrodes 7 about conduit 8 are illustrated. In each of the three cases, an earthed screen 10 surrounds the electrode assembly so as to reduce interference. In a first configuration, illustrated in the left hand portion of figure 4, the electrodes 7 are positioned internally within the conduit 8. In a second configuration, illustrated in the central portion of figure 4, the electrodes 7 are embedded within the wall of the conduit 8, and in a third arrangement shown in the right hand portion of figure 4 the electrodes are positioned between the conduit 8 and the earth screen 10, that is, external to the conduit. 8.

In a system in which the conduit 8 is manufactured from an electrically conducting material, electrodes must be placed internally, as in the first configuration described above. However, if the conduit 8 is manufactured from electrically non-conducting material, the electrodes may be arranged in any of the configurations of figure 4. In figure 4, and in the description that follows, electrodes are allocated numbers which

increase in an anti-clockwise direction, with the electrode extending anti-clockwise from the three o'clock position being numbered one.

A number of different ECT measurement protocols are known, as capacitances can be measured between many combinations of groups of electrodes (which effectively become new "virtual electrodes"). Generally, with conduits of circular cross section, the simplest arrangement (hereinafter referred to as protocol 1) has been used where capacitance measurements are made between single pairs of electrodes. The measurement sequence for protocol 1 involves applying an alternating voltage from a low-impedance supply to one source electrode. The remaining detector electrodes are all held at zero (virtual ground) potential and the currents which flow into these detector electrodes, which are proportional to the inter-electrode capacitances are

measured. A second electrode is then selected as the source electrode and the sequence is repeated until all possible electrode pair capacitances have been measured. This generates M independent inter-electrode capacitance measurements, where Mis determined by equation (1): M= i 2 (1) and E is the number of electrodes located about the circumference of the conduit.

For example, if 12 electrodes are positioned about the circumference of a conduit, E = 12, and equation (1) determines that M = 66.

As the M measurements for a single frame of data are made sequentially, the capacitance data within the frame will be collected at different times and there will be some skewing of the data. Interpolation techniques can be used to de-skew this data if this effect is likely to produce significant errors.

Other possible protocols involve grouping electrodes and exciting them in pairs (protocol 2) and triplets (protocol 3). It will be appreciated that other protocols wherein larger groups of electrodes are excited together are also possible.

Equation (l) can be generalized to give a formula for the number of independent measurements for grouped electrodes: M = E(E (2P-1)) (2)

where

P (the protocol number) is the number of electrodes which are grouped together. Using more complex protocols allows the generation of a larger number of independent measurements for a given electrode size and capacitance measurement sensitivity than the simple single-pair arrangement of protocol 1. Improved image resolution is therefore achievable, although at the expense of the maximum image frame rater which falls as the protocol number (or number of electrodes) increases.

Thus, a balance must be achieved so as to obtain satisfactory resolution within an acceptable time.

When internal electrodes are used, as in the first configuration illustrated in figure 4, components of capacitance due to the electric field inside the electrodes will always

increase in proportion to material permittivity when a higher permittivity material is introduced between the electrodes. However when external electrodes are used, permittivity of the conduit wall causes non- linear changes in capacitance, which may increase or decrease depending on the conduit wall thickness and the permittivities of the conduit wall and contents. In general, ECT systems employing external electrodes are easier to design and fabricate than internal electrode sensors and they are also non-invasive.

Axial resolution and overall measurement sensitivity can be improved by the use of driven axial guard electrodes, located on either radial side of the measurement electrodes, as shown in figure 5. Measurement electrodes 11 occupy the central portion of figure 5. A first series of driven axial guard electrodes 12 are positioned adjacent one axial end of the measurement electrodes, the first series 12 containing one electrode for each measurement electrode 11. A second series of driven axial guard electrodes 13 are positioned adjacent the other axial end of the measurement electrodes, again, one electrode 13 being provided for each measurement electrode 1 1.

Earthed screening tracks 14 run axially between each measurement electrode 11 and the corresponding electrodes in the first and second series of guard electrodes 12, 13.

Earthed regions 15 are also provided at the axial extremes of the configuration

The driven axial guard electrodes 12, 13 are excited at the same electrical potentials as the associated measurement electrodes 11 and prevent the electric field from being

diverted to earth at the ends of the measurement electrodes. For large diameter vessels, axial guard electrodes are normally an essential requirement to ensure that the capacitances between opposing electrodes are measurable.

Methods of measuring flowrate of each individual phase in a multi-phase flow will now be described. It will be appreciated that if it is only desired to measure the flowrate of some phases, this may be done using similar methods. In the description

that follows, it is assumed that the phases are flowing in closed conduits, although it will be appreciated that this is not a fundamental restriction of the technique described. In general, at any point in the conduit cross-section and any point in time a particle of any phase may be present and may be moving in any direction at any speed. The concentration, c,, of each phase i (i = 1 to n where n is the total number of different phases) will at any instant be 1 or 0, but over time may be defined as the Faction of time that the phase is present at that point in the conduit. The density of each phase at any point, pi, (where i is as previously defined) may in general also be a function of time and space (particularly for vertical gas-liquid flows), but for flowmetering is usually considered to be locally constant. The velocity of the fluid particle is a vector v,(x,y,z,t), but usually flowmetering applications are interested only in the axial velocity along the conduit which is denoted v,, although this remains a function of time and space. Thus we may express the mass flowrate, m, of any of the phases at any particular cross-section of the pipe as: m,=T i p,civ,.dt.dA <' A T where: T is the time over which the measurement is made;

corresponding to a nominal flow rate of plastic pellets of approximately 630 Kg per hour. Referring to figure 9, there is illustrated a graph showing for one pixel of an image how concentration of pellets varies with time at two regions spaced apart along the length of the conduit. Time is shown on the horizontal axis, and concentration values, normalised between O and 1 are shown on the left hand vertical axis. Each of these concentration values was generated using the fast and relatively inaccurate measurement process described above, using a relatively small number of electrode excitations. The data was captured at a frame rate of 180 lips using an ECT sensor having two sets of eight electrodes (X and Y in figure 7) of axial length 3 cm, separated by driven guard electrodes. The data plotted is for a single pixel close to the centre of the conduit cross section.

The variation of concentration at the first set of electrodes (X in figure 7) is shown by a trace 19 and the variation of concentration at the second set of electrodes (Y in figure 7), down stream of the first, is shown by a trace 20. The axial offset (upstream electrode edge to upstream electrode edge) between the first and second sets of electrodes is 13cm. The data shows a short slug of pellets at around 6 seconds, with a longer slug of pellets between 7.4 and 8.3 seconds. In both cases it can be seen that the slug arrives at the first set of electrodes (illustrated by the trace 19) before it reaches the second set of electrodes (illustrated by the trace 20). Hence the slugs are moving in the direction of the air flow (upwards) with positive velocities.

It can be seen that the second trace 20 is in fact very similar to the first trace 19 shifted to the right by a particular time interval. This is the expected result, showing the mixture is flowing along the length of the conduit. The main differences between the two traces 19, 20 can be attributed to noise in the measurement process, and can therefore be discarded for the purposes of the measurements described below. As the axial offset between the two electrode sets (X and Y in figure 7) is known (13cm), calculation of the time taken to travel between the two sets, will allow velocity to be calculated.

Averaging over the period T. it can be seen that c/<v> = V during the passage of the liquid slug for a period of tS and <camp> = 0 during the passage of the air. The correct mass flowrate of liquid is thus: m,= Tp,A tsV whereas using the 'space average' approximation of equation (5), <c/> = 1, <v> = V during the passage of the liquid slug for a period of ts and <c> = 0, TV'> = 0 during the passage of the air we obtain: m, = T p'A tsV T an answer which is wrong by a factor ts/T.

Most multiphase flowmeters in use today use equation (5) with various means of measuring time and space averages of concentration and velocity. Because the fundamental basis of this approach is flawed, these techniques must be used either with mixing or correction based on flow regime information. Mixing is very expensive of energy and capital equipment, while it can be seen from the discussion above that corrections based on flow regime will be complex and difficult to prove in practice. Any mixing process which is sufficient to allow the use of equation (5) will often lead to a flow which cannot be easily separated at the other end of the pipeline for processing which results in additional cost.

The primary advantage of imaging in flowrate measurement is that the averaging may be carried out correctly. Every other technique averages either in time or space first, thus effectively removing any ability to achieve accuracy.

The present invention obtains a velocity distribution from two tomographic images taken at spatially different locations, and cross- correlates between the time-series values of concentration in each pixel with the equivalent pixel in the adjacent image plane. When correlation has been carried out the time taken for a particle to travel a predetermined distance is known, and thus, in simple terms, its velocity can be calculated. However, conflicting demands face the use of correlation with flow

imaging to generate flowrate information as in typical industrial flows image reconstruction may limit the frame rate to perhaps a few hundred frames per second, whereas several kilohertz is required to achieve any meaningful correlation velocity resolution. A flow meter arrangement which may be used to put the present invention into effect is illustrated in figure 7. Flow indicated by an arrow 16 occurs along a conduit 17.

Two sets of electrodes X and Y are positioned about the conduit 17, and are separated by a distance L. Measurements taken from each set of electrodes X, Y are input to a cross correlation calculator 18 so as to obtain velocity distribution information.

An ECT technique as described above generates a cross sectional image of concentration from each set of electrodes X, Y. and the images are projected onto an array of pixels. The time variation of concentration in each pixel is then cross-

correlated using the cross-correlation calculator 18 with the time variation of concentration of the same relative pixel in each image and the cross-correlation of the two values being used to evaluate a transit velocity between the two sets of measurement electrodes. The mass flowrate of the phases in the pipe is be derived using a method as is now described.

Correlation between images obtained using electrodes X and electrodes Y of figure 7, can only give an average velocity of interfaces within the averaging region chosen.

Thus if the cross section is divided up into rectangular pixels, in each pixel the integral of the cross product can be undertaken, and in some of the pixels a local gas velocity will be measured from the entrained solid particles (assuming sufficient resolution), while in others the measurement will represent the solids velocity from the speed of the gas pockets within the dense solid region. In theory, the smaller the pixel the greater the accuracy, since]:Av,.c,.a, approaches closer to the true cross-

product integral. However, as the pixel size decreases there is less coherence of the flow structure along the pipe (due to non-axial velocities and dispersion of the flow structures) and the ability to achieve a satisfactory correlation coefficient and identify

a time lag will decrease. In practice there will be an optimum pixel size to achieve good correlation. In addition as the pixel size decreases the number of correlations increases and the greater the processing time to reconstruct the image, perform the correlation, and calculate the crossproduct. If the number of pixels is greater than the number of distinct flow regions by a reasonable number, so say six pixels or more, there is clearly a good chance that the summation will give a reasonable sample of all the different velocity and concentration regions and the total flowrate calculation may be reasonable.

If a,/ are the areas representative of the velocity of phase i (i = 1 to m) and am are the areas representative of the velocity of phase 2 (k = 1 to n), c,/ are the average concentrations of phase 1 in those areas representative of phase 1 and ck2 are the average concentrations of phase 2 in the areas representative of the velocity of phase 2, and v/ and vk2 are the cross-correlation velocities in those areas, then the flowrates of phases 1 and 2 are approximated by equations 6 and 7.

m ml = Plot ailcilvil (6) i=l n m2=p2Z ak2ck2vk2 () Equations (6) and (7) assume that the sum of all the areas is the pipe cross-sectional area, an assumption which is true if the section is broken up into contiguous pixels.

In equations (6) and (7) the regions of the flow cross-section a are defined from fully reconstructed images, the concentrations c are time averages within those areas, and the velocities v are cross-correlation velocities from sensor segments representative of those areas. This approach might give the advantage of using full image information to break the cross-section down into suitable regions, while giving the opportunity for cross-correlation at high speed on a limited number of capacitanceelectrode pairs. It is envisaged in this approach that the Fill image might be reconstructed at a relatively slow rate, depending on the nature of the flow, while the correlation process would be

virtually continuous, with the choice of segments to correlate being modified as the average flow structure changes.

If it is assumed that the ECT measurement system has a separate capacitance measurement channel for each electrode (a current system is a good approximation to this and future ECT systems will fully meet this condition), then the data capture rate depends critically on the number of different "views" required to reconstruct an image. The term view is used to mean an electrode excitation pattern where at least one electrode is excited at a potential above ground as a source electrode and the other electrodes are held at virtual ground potential as guard or detector electrodes. For each view, the signals in the measurement channels connected to the detector electrodes are measured to obtain the capacitance values between the source and detector electrodes.

Each analogue measurement charnel in the ECT system contains a filter which has a finite bandwidth to limit the electrical noise in the system. In a current system, this bandwidth is around 2 kHz, which results in a filter settling time around 500 uS. Each time the view is changed, it is necessary to wait for a period equal to the settling time of the filter, to allow the signal from the filter output to stabilise, before it can be measured using an Analogue to Digital Converter (ADC).

The image and concentration distribution resolution and accuracy increases as the number of views increases. However, as explained above, this occurs at the expense of the maximum frame rate. While the priority for the concentration measurement is to produce as detailed an image as possible, the priority for the velocity measurement is to capture concentration distributions at the highest possible frame rate.

To capture a full set of measurement data for a twelve electrode sensor, eleven views are required, needing ten view changes, i.e. a minimum of 5000uS or 5mS to capture a full set of data for one frame. Hence the fastest possible frame rate will be 200 fps.

If, on the other hand, a single view is used (that is a single electrode excitation), a full set of detector channel outputs can be captured every 500uS, resulting in a maximum frame capture rate of 2000fps, although at a lower image resolution.

Therefore, while the use of multiple views is desirable to determine a concentration distribution, use of a single view is desirable for velocity calculation, given the increase in frame rate by an order of magnitude. The present invention provides a system in which both techniques are combined so as to effectively measure both concentration and velocity.

The present invention obtains a full view set captured at a modest frame rate to obtain capacitance data from which to reconstruct a concentration distribution image, while using a limited view set captured at a higher frame rate to obtain data from which to deduce the velocity distribution. It is necessary to consider the accuracy of an image created using a single view, or a small number of views, and test data showing the effect of such image recreation is shown in figure 8. These tests determine the number of views needed to construct an acceptable image for velocity distribution measurement purposes.

Figure 8 shows a number of different reconstructions of the same set of capacitance data for a test object (a dielectric rod located close to and between electrodes S and 6) in an eight electrode sensor. The last image (bottom right) shows the full reconstruction, using seven views (twenty eight capacitance measurements) of the test object. Reading vertically down from the top left, the first eight images show the results of reconstructing a single view (seven capacitance measurements) with one electrode acting as the source electrode only. It can be seen that the results are reasonably accurate except for the case where the source electrode is close to the test object, for example, when electrodes 5 or 6 are used as source electrodes, as in the fifth and sixth images, reading vertically down from the top left.

Reading vertically down from the top of the third column, the next four images show the result of constructing with two views (thirteen capacitance measurements) with diametrically opposed source electrodes (i. e. 1 and 5, 2 and 8, 3 and 7, 4 and 8, 4), for the full set of possible pairs. These two views provide a reasonable image in each case, regardless of the pair of source electrodes. The images shown in the fourth column show a few more partial views followed by the full view image (seven views, twenty eight capacitance measurements), which represents the best image that may be obtained using the ECT system configured in this way.

From the test data illustrated in figure 8, it is clear that a single view may be adequate to provide data for the velocity measurement. The situation is improved if the optimum source electrode is chosen. In practice, the concentration image obtained from the full measurement set may be used to determine which source electrode to choose for the single view measurement. Altematively, a pair of views provide a more reliable image if two views can be computed in the necessary time.

There are two practical ways in a measurement scheme in which relatively high speed relatively low resolution images may be used for velocity calculations, while relatively low speed, relatively high resolution images are used for concentration calculations: (a) Use three sets of measurement electrodes, one for the slower concentration measurement and the remaining two for the faster velocity correlation measurement.

(b) Use two sets of measurement electrodes and interleave or alternate the fast and slow capacitance measurements on a first set of electrodes, while using a second set of electrodes solely for high speed low resolution measurements to calculate velocity.

Calculation of a flow rate of a phase in a two phase flow, using a system in accordance with the present invention, will now be described with reference to figures 9 to 11. A few seconds of flow of plastic pellets flowing upwards in a vertical conduit were measured to generate the illustrated data. The nominal air velocity was 1.6 m/s,

corresponding to a nominal flow rate of plastic pellets of approximately 630 Kg per hour. Referring to figure 9, there is illustrated a graph showing for one pixel of an image how concentration of pellets varies with time at two regions spaced apart along the length of the conduit. Time is shown on the horizontal axis, and concentration values, norrnalised between O and 1 are shown on the left hand vertical axis. Each of these concentration values was generated using the fast and relatively inaccurate measurement process described above, using a relatively small number of electrode excitations. The data was captured at a frame rate of 180 lips using an ECT sensor having two sets of eight electrodes (X and Y in figure 7) of axial length 3 cm, separated by driven guard electrodes. The data plOHed is for a single pixel close to the centre of the conduit cross section.

Figure 10 shows tomographic images reconstructed from data obtained at the first and second electrode sets along the length of the conduit. The six upper images show data obtained from the higher electrode set, and the six lower images show data obtained front the lower electrode set. The images form pairs, such that the two images in a given column are each taken at the same time. The times at which the image pairs were generated are represented by dotted lines at times 5.5566, 6.1011, 6.5123 7.3681, 7.9959 and 8.3016. It can be seen that differences exist between the two images of each pair, indicating that slugs of pellets are flowing through the conduit, and being detected by the tomographic method.

The time taken for the pellets to move between the first and second electrode sets can be calculated from the concentration data plotted in Figure 9 using an cross-

correlation technique. The crosscorrelation method samples a time window of given width from each of the two traces. The sampled region of one trace is kept stationary, whilst the sampled region of the other trace is shifted along the horizontal axis relative to the stationary trace. At a given shift, the traces will substantially match. That is, if trace 19 is shifted forward by a distance representing a given time period, it will lie approximately coincident with the trace 20. The shift required to achieve this effect indicates the time delay between the pellets passing the two electrode sets.

The cross-correlation technique multiplies the values of the first and second trace together at all sampling points within the predetermined time window. These products are then added to give a value for the crosscorrelation function at that shift. If the shift is such that the traces are effectively coincident, the cross-correlation function will have a high peak.

Correlograms generated from the data of figure 9 are illustrated in figures I la to I lc.

The series of correlograms of figure 1 la were generated using a time window of 0.36s, the series of correlograms of figure 1 lb were generated using a time window of 1 second and the series of correlograms of figure tic were generated using time window of 5 seconds.

The peak of the correlograms shows the shift necessary to obtain coincidence of the traces 19, 20 of figure 9. The dotted vertical line in each correlogram indicates the point of zero shift. Thus, measuring the distance from the dotted line to the peak of a correlograrn provides a calculation of the time delay between the slug passing the first and second measurement points.

In order to obtain meaningful time delay data from the correlograms, a clear peak is required, offset from the line of zero shift. Thus it can be seen that while the correlograms of figure l Ic all have a clear peak, allowing time delay to be measured unambiguously, the correlograms of figures 1 la and 1 lb are less clear.

Velocity plots are also shown in figure 9. The plotted velocities are shown on the right hand vertical axis. Traces 2] are derived from the correlation of figure 1 la, traces 22 are derived from the correlation of figure 1 lb and traces 23 are derived from the correlation of figure 1 lo. It will be seen that the quality of the correlation (defined by the quality of the peak of the correlogram) determines the continuity of the velocity calculation, as where there is no clear peak, velocity cannot be effectively measured for the reasons described above.

The velocity plot for the shortest time window is denoted by the trace 21. The trace 21 is very discontinuous as the velocity has only been plotted when correlation is achievable with a window of this width. This situation only occurs around the leading and trailing edges of the slugs, where the peak velocity is around 3.5 m/S.

If the correlation window is widened to 1 second as in the correlograms of figure 1 lb, the results are shown in the trace 22 of figure 9. Correlation is now possible over most of the period, with maximum values around 3m/S. One notable feature is that short periods of negative (downwards) velocity can now be seen at times around 5.6 and 7 seconds. This corresponds with visual observations obtained during the data capture process, with some pellets falling vertically downwards under the action of gravity.

If the correlation window is opened up further to 5 seconds (as in the correlograms of figure tic), the velocity trace 22 is now continuous, although the maximum calculated velocity value is now lower.

As described above, the velocity values obtained vary in dependence upon the width of window chosen. In practice, it will be necessary to configure the window length upon commissioning of the system. This configuration will be based upon secondary measurements of velocity, and user experience.

When the trace is discontinuous, as in the case of the trace 21, one possible way of obtaining meaningful data is to apply an assumption, such that velocity is assumed to remain constant until a further velocity measurement is obtained. This is shown in figure 9, where a portion of the discontinuous trace 22 is made continuous by broken lines 24 applying the aforesaid assumption.

The calculations described above yield a time delay of 75 mS between the first and second electrode sets, with an electrode set spacing of 13 cm. This corresponds to a velocity of 1.7 m/S which is close to the known air velocity (1.6 m/S). This figure corresponds approximately to the velocities obtained by correlation at times which correspond to the slugs passing through the two sets of electrodes.

The process described above is applied to correlate values at each pixel in the conduit cross section, and thus achieve a velocity value for each pixel.

Having derived velocity values using the method described above, concentration measurements may be obtained using a relatively slower ECT technique in a conventional way.

Recalling equation (6): m ml=P ailcilvi1 (6) /=1

it can be seen that C'' and V, will be obtained as described above, and the area a, of the pixel being measured will be known. This data will be known for all pixels, and thus the summation can be evaluated. The density of the phase being measured is also known, and thus the flow rate can be determined.

The process described above can be directly applied to a two phase flow where it is known that a concentration c of between 0 and 1 of the first phase means that the concentration of the second phase is 1-c. If a flow having a larger number of phases is to be monitored, this can be achieved using a supplementary measurement method so as to determine which phase is present at a given point of the conduit cross section.

For example gamma rays may be used to determine the permittivity of the phase present at a given point. Other methods of applying the method of the present invention to flows having more than two phases include the application of heuristic methods to determine which phase is likely to be present at a given point of the conduit cross section.

Claims

1. A method for monitoring the rate of flow through a conduit of at least one phase of a multi-phase flow, wherein a first data set representing a first image of the flow is generated at a relatively high frame rate, the first image representing phase concentration at a first location along the length of the conduit, a second data set representing a second image of the flow is generated at a relatively high frame rate, the second image representing phase concentration at a second location spaced from the first location along the length of the conduit, a third data set representing a third image of the flow is generated at a relatively low frame rate, the third image representing phase concentration within the conduit, the first and second data sets are cross-correlated with respect to time to derive a fourth data set representing thee speed of flow along the conduit between the first and second locations, and the rate of flow is calculated from the phase concentration of the said at least one phase represented by the third data set, and the flow speed represented by the fourth data set.

2. A method according to claim 1, wherein a series of first data sets are generated, a series of second data sets are generated, a series of third data sets are generated, a series of fourth data sets are derived by correlating the series of first data sets and the series of second data sets, and the flow rate is calculated from the series of third data sets and the series of fourth data sets.

3. A method according to claim 1 or 2, wherein the first, second and third data sets are obtained by applying excitation signals to electrodes located adjacent the conduit to generate measurement signals, and using tomographic imaging techniques to convert the measurement signals into the data sets.

4. A method according to claim 3, wherein the first and second data sets are generated using a tomographic imaging technique using a first number of electrode excitations, the third data set is generated using a tomographic imaging technique using a second number of electrode excitations and the first number is less than the second number.

5. A method according to claim 4, wherein the tomographic imaging technique used to generate the first and second data sets uses a single electrode excitation.

6. A method according to claim 4 or 5, wherein the or each electrode to be excited in the tomographic imaging technique used to generate the first and second data sets is chosen on the basis of the third data set.

7. A method according to any one of claims 3 to 6, wherein the tomographic measurements measure an electrical property of the material.

8. A method according to claim 7, wherein the electrical property is capacitance.

9. A method according to claim 7, wherein the electrical property is conductance.

10. A method according to claim 7, wherein the electrical property is complex admittance.

11. A method according to any one of claims 3 to 10, wherein the first data set is generated from measurement signals derived from first and second sets of electrodes spaced apart along the length of the conduit, and the third data set is generated from measurement signals derived from a third set of electrodes, spaced apart from the first and second sets

12. A method according to any one of claims 3 to 10, wherein the first, second and third data sets are generated from measurement signals derived from two sets of electrodes spaced apart along the length of the conduit, some of the measurement signals contributing to the third data set also contributing to the first or second data set.

13. An apparatus for monitoring the rate of flow through a conduit of at least one phase of a multi-phase flow, comprising means for generating a first data set at a

l (# relatively high frame rate, the first data set representing a first image of the flow, the first image representing phase concentration at a first location along the length of the conduit, means for generating a second data set at a relatively high frame rate, the second data set representing a second image of the flow, the second image representing phase concentration at a second location spaced from the first location along the length of the conduit, means for generating a third data set at a relatively low frame rate representing a third image of the flow, the third image representing phase concentration within the conduit, means for correlating the first and second data sets with respect to time to derive a fourth data set representing the speed of flow along the conduit between the first and second locations, and means for calculating the rate of flow from the phase concentration of the said at least one phase represented by the third data set, and the flow speed represented by the fourth data set.

14. An apparatus according to claim 13 for carrying out a method according to any one of claims 1 to 12.

15. A method substantially as hereinbefore described, with reference to the accompanying drawings.

16. An apparatus substantially as hereinbefore described, with reference to the accompanying drawings.